An idealized aquaplanet moist global atmospheric model with realistic radiative transfer but no clouds and no convective parameterization is found to possess multiple climate equilibria. When forced symmetrically about the equator, in some cases the Inter Tropical Convergence Zone (ITCZ) migrates to an off-equatorial equilibrium position. Mechanism denial experiments prescribing relative humidity imply that radiation-circulation coupling is essential to this instability. The cross-equatorial asymmetry occurs only when the underlying slab ocean is sufficiently deep and the atmosphere's spectral dynamical core is sufficiently coarse (∼T170 or less with our control parameters). At higher resolutions, initializing with an asymmetric state indicates metastability with very slow (thousands of days) return to hemispheric symmetry. There is some sensitivity to the model timestep, which affects the time required to transition to the asymmetric state, with little effect on the equilibrium climate. The instability is enhanced when the planetary boundary layer scheme favors deeper layers or by a prescribed meridional heat transport away from the equator within the slab. The instability is not present when the model is run with a convective parameterization scheme commonly utilized in idealized moist models. We argue that the instability occurs when the asymmetric heating associated with a spontaneous ITCZ shift drives a circulation that rises poleward of the perturbed ITCZ. These results serve as a warning of the potential for instability and non-uniqueness of climate that may complicate studies with idealized models of the tropical response to perturbations in forcing.
Chang, Chiung-Yin, and Isaac M Held, June 2022: A scaling theory for the diffusivity of poleward eddy heat transport based on Rhines scaling and the global entropy budget. Journal of the Atmospheric Sciences, 79(6), DOI:10.1175/JAS-D-21-0242.11743-1758. Abstract
Diffusive theories for the meridional atmospheric energy transport can summarize our understanding of this central aspect of the general circulation. They can also be utilized in simple models of Earth’s energy balance to help interpret the response of the system to perturbations. A theory for this diffusivity of eddy heat transport is described based on Rhines scaling and the global entropy budget, each of which provides a constraint between the kinetic energy dissipation and the diffusivity. An expression for the diffusivity is then obtained by eliminating the dissipation from this set of two constraints. The theory can be thought of as a generalization of the theories of Held–Larichev and Barry–Craig–Thuburn. The theory is compared to simulations of the Held–Suarez idealized dry atmospheric model. Limitations of the theory are emphasized. The form of the theory allows it to be readily generalized to a moist atmosphere.
Syukoro (Suki) Manabe’s Nobel Prize in Physics was awarded largely for his early work on one-dimensional models of “radiative–convective equilibrium” (RCE), which produced the first credible estimates of Earth’s climate sensitivity. This article reviews that work and tries to identify those aspects that make it so distinctive. We argue that Manabe’s model of RCE contained three crucial ingredients. These are (i) a tight convective coupling of the surface to the troposphere, (ii) an assumption of fixed relative humidity rather than fixed absolute humidity, and (iii) a sufficiently realistic representation of greenhouse gas radiative transfer. Previous studies had separately identified these key ingredients, but none had properly combined them. We then discuss each of these ingredients in turn, highlighting how subsequent research in the intervening decades has only cemented their importance for understanding global climate change. We close by reflecting on the elegance of Manabe’s approach and its lasting value.
Although classical theories of midlatitude momentum fluxes focus on the wave–mean flow interaction, wave–wave interactions may be important for generating long waves. It is shown in this study that this nonlinear generation has implications for eddy momentum fluxes in some regimes. Using a two-layer quasigeostrophic model of a baroclinic jet on a β plane, statistically steady states are explored in which the vertically integrated eddy momentum flux is divergent at the center of the jet, rather than convergent as in Earthlike climates. One moves toward this less familiar climate from more Earthlike settings by reducing either β, frictional drag, or the width of the baroclinic zone, or by increasing the upper bound of resolvable wavelengths by lengthening the zonal channel. Even in Earthlike settings, long waves diverge momentum from the jet, but they are too weak to compete with short unstable waves that converge momentum. We argue that long waves are generated by breaking of short unstable waves near their critical latitudes, where long waves converge momentum while diverging momentum at the center of the jet. Quasi-linear models with no wave–wave interaction can qualitatively capture the Earthlike regime but not the regime with momentum flux divergence at the center of the jet, because the nonlinear wave breaking and long-wave generation processes are missing. Therefore, a more comprehensive theory of atmospheric eddy momentum fluxes should take into account the nonlinear dynamics of long waves.
Extreme heat under global warming is a concerning issue for the growing tropical population. However, model projections of extreme temperatures, a widely used metric for extreme heat, are uncertain on regional scales. In addition, humidity needs to be taken into account to estimate the health impact of extreme heat. Here we show that an integrated temperature–humidity metric for the health impact of heat, namely, the extreme wet-bulb temperature (TW), is controlled by established atmospheric dynamics and thus can be robustly projected on regional scales. For each 1 °C of tropical mean warming, global climate models project extreme TW (the annual maximum of daily mean or 3-hourly values) to increase roughly uniformly between 20° S and 20° N latitude by about 1 °C. This projection is consistent with theoretical expectation based on tropical atmospheric dynamics, and observations over the past 40 years, which gives confidence to the model projection. For a 1.5 °C warmer world, the probable (66% confidence interval) increase of regional extreme TW is projected to be 1.33–1.49 °C, whereas the uncertainty of projected extreme temperatures is 3.7 times as large. These results suggest that limiting global warming to 1.5 °C will prevent most of the tropics from reaching a TW of 35 °C, the limit of human adaptation.
We describe the baseline coupled model configuration and simulation characteristics of GFDL's Earth System Model Version 4.1 (ESM4.1), which builds on component and coupled model developments at GFDL over 2013–2018 for coupled carbon‐chemistry‐climate simulation contributing to the sixth phase of the Coupled Model Intercomparison Project. In contrast with GFDL's CM4.0 development effort that focuses on ocean resolution for physical climate, ESM4.1 focuses on comprehensiveness of Earth system interactions. ESM4.1 features doubled horizontal resolution of both atmosphere (2° to 1°) and ocean (1° to 0.5°) relative to GFDL's previous‐generation coupled ESM2‐carbon and CM3‐chemistry models. ESM4.1 brings together key representational advances in CM4.0 dynamics and physics along with those in aerosols and their precursor emissions, land ecosystem vegetation and canopy competition, and multiday fire; ocean ecological and biogeochemical interactions, comprehensive land‐atmosphere‐ocean cycling of CO2, dust and iron, and interactive ocean‐atmosphere nitrogen cycling are described in detail across this volume of JAMES and presented here in terms of the overall coupling and resulting fidelity. ESM4.1 provides much improved fidelity in CO2 and chemistry over ESM2 and CM3, captures most of CM4.0's baseline simulations characteristics, and notably improves on CM4.0 in (1) Southern Ocean mode and intermediate water ventilation, (2) Southern Ocean aerosols, and (3) reduced spurious ocean heat uptake. ESM4.1 has reduced transient and equilibrium climate sensitivity compared to CM4.0. Fidelity concerns include (1) moderate degradation in sea surface temperature biases, (2) degradation in aerosols in some regions, and (3) strong centennial scale climate modulation by Southern Ocean convection.
Gliatto, M T., and Isaac M Held, March 2020: Overtransmission of Rossby Waves at a Lower-Layer Critical Latitude in the Two-Layer Model. Journal of the Atmospheric Sciences, 77(3), DOI:10.1175/JAS-D-19-0055.1. Abstract
Rossby waves, propagating from the midlatitudes toward the tropics, are typically absorbed by critical latitudes (CLs) in the upper troposphere. However, these waves typically encounter CLs in the lower troposphere first. We study a two-layer linear scattering problem to examine the effects of lower CLs on these waves. We begin with a review of the simpler barotropic case to orient the reader. We then progress to the baroclinic case using a two-layer quasigeostrophic model in which there is vertical shear in the mean flow on which the waves propagate, and in which the incident wave is assumed to be an external-mode Rossby wave. We use linearized equations and add small damping to remove the critical-latitude singularities. We consider cases in which either there is only one CL, in the lower layer, or there are CLs in both layers, with the lower-layer CL encountered first. If there is only a CL in the lower layer, the wave’s response depends on the sign of the mean potential vorticity gradient at this lower-layer CL: if the PV gradient is positive, then the CL partially absorbs the wave, as in the barotropic case, while for a negative PV gradient, the CL is a wave emitter, and can potentially produce overreflection and/or overtransmission. Our numerical results indicate that overtransmission is by far the dominant response in these cases. When an upper-layer absorbing CL is encountered, following the lower-layer encounter, one can still see the signature of overtransmission at the lower-layer CL.
Simulations of baroclinic cyclones often cannot resolve moist convection but resort to convective parametrization. An exception is the hypohydrostatic rescaling, which in principle can be used to better represent convection with no increase in computational cost. The rescaling is studied in the context of a quasi-steady, convectively active, baroclinic cyclone. This is a novel framework with advantages due to the unambiguous time-mean structure. The rescaling is evaluated against high-resolution solutions up to a 5-km grid spacing. A theoretical scaling combining convective-scale dynamics and synoptic-scale energy balance is derived and verified by the simulations. It predicts the insensitivity of the large-scale flow to resolution and moderate rescaling, and a weak bias in the cyclone intensity under very large rescaling. The theory yields a threshold for the rescaling factor that avoids large-scale biases. Below the threshold, the rescaling can be used to control resolution errors at the convective scale, such as the distribution of extreme precipitation rates.
A diagnostic framework is developed to explain the response of tropical cyclones (TCs) to climate in high-resolution global atmospheric models having different complexity of boundary conditions. The framework uses vortex dynamics to identify the large-scale control on the evolution of TC precursors—first non-rotating convective clusters and then weakly rotating seeds. In experiments with perturbed sea surface temperature (SST) and CO2 concentration from the historical values, the response of TCs follows the response of seeds. The distribution of seeds is explained by the distribution of the non-rotating convective clusters multiplied by a probability that they transition to seeds. The distribution of convective clusters is constrained by the large-scale vertical velocity and is verified in aquaplanet experiments with shifting Inter tropical Convergence Zones. The probability of transition to seeds is constrained by the large-scale vorticity via an analytical function, representing the relative importance between vortex stretching and vorticity advection, and is verified in aquaplanet experiments with uniform SST. The consistency between seed and TC responses breaks down substantially when the realistic SST is perturbed such that the spatial gradient is significantly enhanced or reduced. In such cases, the difference between the responses is explained by a change in the ventilation index, which influences the fraction of seeds that develop into TCs. The proposed TC-climate relationship serves as a framework to explain the diversity of TC projection across models and forcing scenarios.
Anthropogenic aerosols have been postulated to have a cooling effect on climate, but its magnitude remains uncertain. Using atmospheric general circulation model simulations, we separate the land temperature response into a fast response to radiative forcings and a slow response to changing oceanic conditions and find that the former accounts for about one fifth of the observed warming of the Northern Hemisphere land during summer and autumn since the 1960s. While small, this fast response can be constrained by observations. Spatially varying aerosol effects can be detected on the regional scale, specifically warming over Europe and cooling over Asia. These results provide empirical evidence for the important role of aerosols in setting regional land temperature trends and point to an emergent constraint that suggests strong global aerosol forcing and high transient climate response.
GFDL's new CM4.0 climate model has high transient and equilibrium climate sensitivities near the middle of the upper half of CMIP5 models. The CMIP5 models have been criticized for excessive sensitivity based on observations of present‐day warming and heat uptake and estimates of radiative forcing. An ensemble of historical simulations with CM4.0 produces warming and heat uptake that are consistent with these observations under forcing that is at the middle of the assessed distribution. Energy budget‐based methods for estimating sensitivities based on these quantities underestimate CM4.0's sensitivities when applied to its historical simulations. However, we argue using a simple attribution procedure that CM4.0's warming evolution indicates excessive transient sensitivity to greenhouse gases. This excessive sensitivity is offset prior to recent decades by excessive response to aerosol and land use changes.
We document the configuration and emergent simulation features from the Geophysical Fluid Dynamics Laboratory (GFDL) OM4.0 ocean/sea‐ice model. OM4 serves as the ocean/sea‐ice component for the GFDL climate and Earth system models. It is also used for climate science research and is contributing to the Coupled Model Intercomparison Project version 6 Ocean Model Intercomparison Project (CMIP6/OMIP). The ocean component of OM4 uses version 6 of the Modular Ocean Model (MOM6) and the sea‐ice component uses version 2 of the Sea Ice Simulator (SIS2), which have identical horizontal grid layouts (Arakawa C‐grid). We follow the Coordinated Ocean‐sea ice Reference Experiments (CORE) protocol to assess simulation quality across a broad suite of climate relevant features. We present results from two versions differing by horizontal grid spacing and physical parameterizations: OM4p5 has nominal 0.5° spacing and includes mesoscale eddy parameterizations and OM4p25 has nominal 0.25° spacing with no mesoscale eddy parameterization.
MOM6 makes use of a vertical Lagrangian‐remap algorithm that enables general vertical coordinates. We show that use of a hybrid depth‐isopycnal coordinate reduces the mid‐depth ocean warming drift commonly found in pure z* vertical coordinate ocean models. To test the need for the mesoscale eddy parameterization used in OM4p5, we examine the results from a simulation that removes the eddy parameterization. The water mass structure and model drift are physically degraded relative to OM4p5, thus supporting the key role for a mesoscale closure at this resolution.
Chang, Chiung-Yin, and Isaac M Held, June 2019: The control of surface friction on the scales of baroclinic eddies in a homogeneous quasigeostrophic two-layer model. Journal of the Atmospheric Sciences, 76(6), DOI:10.1175/JAS-D-18-0333.1. Abstract
In idealized models of the extratropical troposphere, both β and surface friction can control the equilibrated scales of baroclinic eddies by stopping the inverse cascade. A scaling theory on how surface friction alone sets these scales is proposed by Held (1999) in the case of a quadratic drag law. However, the theory breaks down when friction is modeled by linear damping, and there are other reasons to suspect that it is oversimplified. An ideal system to test the theory is the homogeneous two-layer quasigeostrophic model in the β = 0 limit with quadratic damping. This study investigates some numerical simulations of the model to analyze two causes of the theory’s breakdown. They are 1) the asymmetry between two layers due to confinement of friction to the lower layer, and 2) deviation from a spectrally local inverse energy cascade due to the spread of wavenumbers over which energy is input into the barotropic mode. The former is studied by comparing the simulations with drag appearing asymmetrically or symmetrically between the two layers. The latter is addressed with a heuristic modification of the theory. A regime where eddies equilibrate without an inverse cascade is also examined. A comparison is then made between quadratic and linear drag simulations. The connection to a competing theory based on the dynamics of equivalent barotropic vortices with thermal signatures is further discussed. Finally, we present an example of an inhomogeneous statistically steady state to argue that the diffusivity obtained from the homogeneous model has relevance to more realistic configurations.
Held, Isaac M., April 2019: 100 Years of Progress in Understanding the General Circulation of the Atmosphere In A Century of Progress in Atmospheric and Related Sciences: Celebrating the American Meteorological Society Centennial, Boston, MA, Meteorological Monographs, American Meteorological Society, 59, DOI:10.1175/AMSMONOGRAPHS-D-18-0017.16.1-6.23. Abstract
Some of the advances of the past century in our understanding of the general circulation of the atmosphere are described, starting with a brief summary of some of the key developments from the first half of the twentieth century, but with a primary focus on the period beginning with the midcentury breakthrough in baroclinic instability and quasigeostrophic dynamics. In addition to baroclinic instability, topics touched upon include the following: stationary wave theory, the role played by the two-layer model, scaling arguments for the eddy heat flux, the subtlety of large-scale eddy momentum fluxes, the Eliassen–Palm flux and the transformed Eulerian mean formulation, the structure of storm tracks, and the controls on the Hadley cell.
We describe GFDL's CM4.0 physical climate model, with emphasis on those aspects that may be of particular importance to users of this model and its simulations. The model is built with the AM4.0/LM4.0 atmosphere/land model and OM4.0 ocean model. Topics include the rationale for key choices made in the model formulation, the stability as well as drift of the pre‐industrial control simulation, and comparison of key aspects of the historical simulations with observations from recent decades. Notable achievements include the relatively small biases in seasonal spatial patterns of top‐of‐atmosphere fluxes, surface temperature, and precipitation; reduced double Intertropical Convergence Zone bias; dramatically improved representation of ocean boundary currents; a high quality simulation of climatological Arctic sea ice extent and its recent decline; and excellent simulation of the El Niño‐Southern Oscillation spectrum and structure. Areas of concern include inadequate deep convection in the Nordic Seas; an inaccurate Antarctic sea ice simulation; precipitation and wind composites still affected by the equatorial cold tongue bias; muted variability in the Atlantic Meridional Overturning Circulation; strong 100 year quasi‐periodicity in Southern Ocean ventilation; and a lack of historical warming before 1990 and too rapid warming thereafter due to high climate sensitivity and strong aerosol forcing, in contrast to the observational record. Overall, CM4.0 scores very well in its fidelity against observations compared to the Coupled Model Intercomparison Project Phase 5 generation in terms of both mean state and modes of variability and should prove a valuable new addition for analysis across a broad array of applications.
An unprecedented disruption of the Quasi-Biennial Oscillation (QBO) started to develop from late 2015. The early development of this event is analyzed using the space-time spectra of eddies from reanalysis data. While the extratropical waves propagating horizontally into the tropics were assumed to be the main driver for the disruption, it was not clear why these waves dissipated near the jet core instead of jet edge as linear theory predicts. This study shows that the drastic deceleration of the equatorial jet was largely brought about by a single strong wave packet, and the local winds experienced by the wave packet served as a better indicator of the wave breaking latitude than the zonal mean winds.
Surprisingly, tropical mixed Rossby gravity waves also made an appreciable contribution to the deceleration of the equatorial westerly jet by the horizontal eddy momentum fluxes, especially before January 2016. The horizontal eddy momentum fluxes associated with the tropical waves arise from the deformation of the wave structure when background westerlies increase with height. These horizontal eddy momentum anomalies from the tropical waves are commonly observed in the reanalysis data, but are typically much weaker than those in the 2015/2016 winter. The possibility exists that exceptionally strong equatorially trapped waves precondition the flow to disruption by an extratropical disturbance.
Purpose of Review:
Tropical cyclones (TCs) are strongly influenced by the large-scale environment of the tropics and will, therefore, be modified by climate changes. Numerical simulations designed to understand the sensitivities of TCs to environmental changes have typically followed one of two approaches: single-storm domain sizes with convection-permitting resolution and uniform thermal boundary conditions or comprehensive global high-resolution (about 50 km in the horizontal) atmospheric general circulation model (GCM) simulations. The approaches reviewed here rest between these two and are an important component of hierarchical modelling of the atmosphere: aquaplanet TC simulations.
Recent Findings:
Idealized model configurations have revealed controls on equilibrium TC size in large-domain simulations of rotating radiative-convective equilibrium. Simulations that include differential rotation (spherical geometry) but retain uniform thermal forcing have revealed a new mechanism of TC propagation change via storm-scale dynamics and show a poleward shift in genesis in response to warming. Simulations with Earth-like meridional thermal forcing gradients have isolated competing influences on TC genesis via shifts in the atmospheric general circulation and the temperature dependence of TC genesis in the absence of mean circulation changes.
Summary:
Aquaplanet simulations of TCs with variants that include or inhibit certain processes have recently emerged as a research methodology that has advanced the understanding of the climatic controls on TC activity. Looking forward, idealized boundary condition model configurations can be used as a bridge between GCM resolution and convection-permitting resolution models and as a tool for identifying additional mechanisms through which climate changes influence TC activity.
Mooring, Todd A., Isaac M Held, and R John Wilson, August 2019: Effects of the Mean Flow on Martian Transient Eddy Activity: Studies with an Idealized General Circulation Model. Journal of the Atmospheric Sciences, 76(8), DOI:10.1175/JAS-D-18-0247.1. Abstract
The extent to which the eddy statistics of the Martian atmosphere can be inferred from the mean state and highly simplified assumptions about diabatic and frictional processes is investigated using an idealized general circulation model (GCM) with Newtonian relaxation thermal forcing. An iterative technique, adapted from previous terrestrial studies, is used to generate radiative equilibrium temperatures such that the three-dimensional time mean temperature fields of the idealized model match means computed from the Mars Analysis Correction Data Assimilation (MACDA) reanalysis. Focusing on a period of strong northern hemisphere eddy activity prior to winter solstice, it is found that the idealized model reproduces some key features of the spatial patterns of the MACDA eddy temperature variance and kinetic energy fields. The idealized model can also simulate aspects of MACDA’s seasonal cycle of spatial patterns of low-level eddy meridional wind and temperature variances. The most notable weakness of the model is its eddy amplitudes—both their absolute values and seasonal variations are quite unrealistic, for reasons unclear. The idealized model was also run with a mean flow based on output from the Geophysical Fluid Dynamics Laboratory (GFDL) full-physics Mars GCM. The idealized model captures the difference in mean flows between MACDA and the GFDL Mars GCM and reproduces a bias in the more complex model’s eddy zonal wavenumber distribution. This implies that the mean flow is an important influence on transient eddy wavenumbers and that improving the GFDL Mars GCM’s mean flow would make its eddy scales more realistic.
Anber, Usama, Nadir Jeevanjee, Lucas Harris, and Isaac M Held, July 2018: Sensitivity of Radiative‐Convection Equilibrium to Divergence Damping in GFDL‐FV3 Based Cloud‐Resolving Model Simulations. Journal of Advances in Modeling Earth Systems, 10(7), DOI:10.1029/2017MS001225. Abstract
Using a non‐hydrostatic model based on a version of GFDL's FV3 dynamical core at a cloud‐resolving resolution in radiative‐convective equilibrium (RCE) configuration, the sensitivity of the mean RCE climate to the magnitude and scale‐selectivity of the divergence damping is explored. Divergence damping is used to reduce small‐scale noise in more realistic configurations of this model. This sensitivity is tied to the strength (and width) of the convective updrafts, which decreases (increases) with increased damping and acts to organize the convection, dramatically drying out the troposphere and increasing the outgoing longwave radiation.
Increased damping also results in a much‐broadened precipitation probability distribution and larger extreme values, as well as reduction in cloud fraction, which correspondingly decreases the magnitude of shortwave and longwave cloud radiative effects. Solutions exhibit a monotonic dependence on the strength of the damping and asymptotically converge to the inviscid limit. While the potential dependence of RCE simulations on resolution and microphysical assumptions are generally appreciated, these results highlight the potential significance of the choice of sub‐grid numerical diffusion in the dynamical core.
In comprehensive and idealized general circulation models, hemispherically asymmetric forcings lead to shifts in the latitude of the Intertropical Convergence Zone (ITCZ). Prior studies using comprehensive GCMs (with complicated parameterizations of radiation, clouds, and convection) suggest that the water vapor feedback tends to amplify the movement of the ITCZ in response to a given hemispherically asymmetric forcing, but this effect has yet to be elucidated in isolation. This study uses an idealized moist model, coupled to a full radiative transfer code, but without clouds, to examine the role of the water vapor feedback in a targeted manner.
In experiments with interactive water vapor and radiation, the ITCZ latitude shifts roughly twice as much off the equator as in cases with the water vapor field seen by the radiation code prescribed to a static hemisperically-symmetric control distribution. Using energy flux equator theory for the latitude of the ITCZ, the amplification of the ITCZ shift is attributed primarily to the longwave water vapor absorption associated with the movement of the ITCZ into the warmer hemisphere, further increasing the net column heating asymmetry. Local amplification of the imposed forcing by the shortwave water vapor feedback plays a secondary role. Experiments varying the convective relaxation time, an important parameter in the convection scheme used in the idealized moist model, yield qualitatively similar results, suggesting some degree of robustness to the model physics; however, the sensitivity experiments do not preclude that more extreme modifications to the convection scheme could lead to qualitatively different behavior.
This paper introduces an idealized general circulation model (GCM) in which water vapor and clouds are tracked as tracers, but are not allowed to affect circulation either through latent heat release or cloud radiative effects. The cloud scheme includes an explicit treatment of cloud microphysics and diagnoses cloud fraction from a prescribed sub-grid distribution of total water. The model is capable of qualitatively capturing many large-scale features of water vapor and cloud distributions outside of the boundary layer and deep tropics. The subtropical dry zones, mid-latitude storm tracks and upper-tropospheric cirrus are simulated reasonably well. The inclusion of cloud microphysics (namely rain re-evaporation) has a modest but significant effect of moistening the lower troposphere in this model. When being subjected to a uniform fractional increase of saturated water vapor pressure, the model produces little change in cloud fraction. A more realistic perturbation, which considers the non-linearity of the Clausius-Clapeyron relation and spatial structure of CO2-induced warming, results in a substantial reduction in the free-tropospheric cloud fraction. This is reconciled with an increase of relative humidity by analyzing the probability distributions of both quantities, and may help explain partly similar decreases in cloud fraction in full GCMs. The model provides a means to isolate individual processes or model components for studying their influences on cloud simulation in the extratropical free troposphere.
In this two-part paper, a description is provided of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL). This version, with roughly 100km horizontal resolution and 33 levels in the vertical, contains an aerosol model that generates aerosol fields from emissions and a “light” chemistry mechanism designed to support the aerosol model but with prescribed ozone. In Part I, the quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode – with prescribed sea surface temperatures (SSTs) and sea ice distribution – is described and compared with previous GFDL models and with the CMIP5 archive of AMIP simulations. The model's Cess sensitivity (response in the top-of-atmosphere radiative flux to uniform warming of SSTs) and effective radiative forcing are also presented. In Part II, the model formulation is described more fully and key sensitivities to aspects of the model formulation are discussed, along with the approach to model tuning.
In Part II of this two-part paper, documentation is provided of key aspects of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL). The quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode has been provided in Part I. Part II provides documentation of key components and some sensitivities to choices of model formulation and values of parameters, highlighting the convection parameterization and orographic gravity wave drag. The approach taken to tune the model's clouds to observations is a particular focal point. Care is taken to describe the extent to which aerosol effective forcing and Cess sensitivity have been tuned through the model development process, both of which are relevant to the ability of the model to simulate the evolution of temperatures over the last century when coupled to an ocean model.
Zurita-Gotor, Pablo, and Isaac M Held, July 2018: The finite amplitude evolution of mixed Kelvin-Rossby wave instability and equatorial superrotation in a shallow water model and an idealized GCM. Journal of the Atmospheric Sciences, 75(7), DOI:10.1175/JAS-D-17-0386.1. Abstract
An instability involving the resonant interaction of a Rossby and a Kelvin wave has been proposed to drive Equatorial superrotation in planetary atmospheres with substantially smaller radius or smaller rotation rate than the Earth, that is, with large thermal Rossby number. To pursue this idea, this paper investigates the equilibration mechanism of Kelvin-Rossby instability by simulating the unforced initial value problem in a shallow-water and in a multi-level primitive-equation model. Although the instability produces equatorward momentum fluxes in both models, only the multi-level model is found to superrotate. It is argued that the shortcoming of the shallow-water model is due to its difficulty in representing Kelvin wave breaking and dissipation, which is crucial for accelerating the flow in the tropics. In the absence of dissipation, the zonal momentum fluxed into the tropics is contained in the eddy contribution to the mass-weighted zonal wind rather than the zonal-mean zonal flow itself. In the shallow-water model, the zonal-mean zonal flow is only changed by the eddy potential vorticity flux, which is very small in our flow in the tropics and can only decelerate the flow in the absence of external vorticity stirring.
Climate models generate a wide range of precipitation responses to global warming in the African Sahel, but all that use the NOAA Geophysical Fluid Dynamics Laboratory AM2.1 model as their atmospheric component dry the region sharply. This study compares the Sahel’s wet season response to uniform 2 K SST warming in AM2.1 using either its default convective parameterization, Relaxed Arakawa-Schubert (RAS), or an alternate, the University of Washington (UW) parameterization, using the moist static energy (MSE) budget to diagnose the relevant mechanisms.
UW generates a drier, cooler control Sahel climate than does RAS and a modest rainfall increase with SST warming rather than a sharp decrease. Horizontal advection of dry, low-MSE air from the Sahara Desert – a leading-order term in the control MSE budget with either parameterization – is enhanced with oceanic warming, driven by enhanced meridional MSE and moisture gradients spanning the Sahel. With RAS, this occurs throughout the free troposphere and is balanced by anomalous MSE import through anomalous subsidence, which must be especially large in the mid-troposphere where the moist static stability is small. With UW, the strengthening of the meridional MSE gradient is mostly confined to the lower troposphere, due in part to comparatively shallow prevailing convection. This necessitates less subsidence, enabling convective and total precipitation to increase with UW, although both large-scale precipitation and precipitation minus evaporation decrease. This broad set of hydrological and energetic responses persists in simulations with SSTs varied over a wide range.
Lutsko, Nicholas J., Isaac M Held, Pablo Zurita-Gotor, and Amanda K O'Rourke, November 2017: Lower Tropospheric Eddy Momentum Fluxes in Idealized Models and Reanalysis Data. Journal of the Atmospheric Sciences, 74(11), DOI:10.1175/JAS-D-17-0099.1. Abstract
In Earth’s atmosphere eddy momentum fluxes (EMFs) are largest in the upper troposphere, but EMFs in the lower troposphere, although modest in amplitude, have an intriguing structure. To document this structure the EMFs in the lower tropospheres of a two-layer quasi-geostrophic model, a primitive equation model and the southern hemisphere of a reanalysis dataset are investigated. The lower tropospheric EMFs are very similar in the cores of the jets in both models and in the reanalysis data, with EMF divergence (opposing the upper tropospheric convergence) due to relatively long waves with slow eastward phase speeds, and EMF divergence (as in the upper troposphere) due to shorter waves with faster eastward phase speeds.
We take advantage of the two-layer model’s ability to capture the EMF divergence by long waves to provide a qualitative picture of the underlying dynamics that relies on the negative potential vorticity gradient in the lower layer of the model. Eddies excited by baroclinic instability mix efficiently through a wide region in the lower layer, centered on the latitude of maximum westerlies and encompassing the lower layer critical latitudes. Near these critical latitudes the mixing is enhanced, resulting in increased EMF convergence, with compensating EMF divergence in the center of the jet. The EMF convergence at faster phase speeds is due to deep eddies which propagate on the upper tropospheric potential vorticity gradient.
The severity of the double Intertropical Convergence Zone (DI) problem in climate models can be measured by a tropical precipitation asymmetry index (PAI), indicating whether tropical precipitation favors the Northern Hemisphere or the Southern Hemisphere. Examination of 19 Coupled Model Intercomparison Project phase 5 models reveals that the PAI is tightly linked to the tropical sea surface temperature (SST) bias. As one of the factors determining the SST bias, the asymmetry of tropical net surface heat flux in Atmospheric Model Intercomparison Project (AMIP) simulations is identified as a skillful predictor of the PAI change from an AMIP to a coupled simulation, with an intermodel correlation of 0.90. Using tropical top-of-atmosphere (TOA) fluxes, the correlations are lower but still strong. However, the extratropical asymmetries of surface and TOA fluxes in AMIP simulations cannot serve as useful predictors of the PAI change. This study suggests that the largest source of the DI bias is from the tropics and from atmospheric models.
Tropical cyclones are studied under the idealized framework of rotating radiative-convective equilibrium, achieved in a large doubly-periodic f -plane by coupling the column physics of a global atmospheric model to rotating hydrostatic dynamics. Unlike previous studies which prescribe uniform sea surface temperature (SST) over the domain, SSTs are now predicted by coupling the atmosphere to a simple slab ocean model. With coupling, SSTs under the eyewall region of tropical cyclones (TCs) become cooler than the environment. However, the domain still fills up with multiple long-lived TCs in all cases examined, including at the limit of very small depth of the slab. The cooling of SSTs under the eyewall increases as the depth of the slab ocean layer decreases but levels off at roughly 6.5 K as the depth approaches zero. At the eyewall, the storm interior is decoupled from the cooler surface and moist entropy is no longer well-mixed along the angular momentum surface in the boundary layer. TC intensity is reduced from the potential intensity computed without the cooling, but the intensity reduction is smaller than that estimated by a potential intensity taking into account the cooling and assuming that moist entropy is well mixed along angular momentum surfaces within the atmospheric boundary layer.
Balaji, V, Rusty Benson, Bruce Wyman, and Isaac M Held, October 2016: Coarse-grained component concurrency in Earth system modeling: parallelizing atmospheric radiative transfer in the GFDL AM3 model using the Flexible Modeling System coupling framework. Geoscientific Model Development, 9(10), DOI:10.5194/gmd-9-3605-2016. Abstract
Climate models represent a large variety of processes on a variety of timescales and space scales, a canonical example of multi-physics multi-scale modeling. Current hardware trends, such as Graphical Processing Units (GPUs) and Many Integrated Core (MIC) chips, are based on, at best, marginal increases in clock speed, coupled with vast increases in concurrency, particularly at the fine grain. Multi-physics codes face particular challenges in achieving fine-grained concurrency, as different physics and dynamics components have different computational profiles, and universal solutions are hard to come by.
We propose here one approach for multi-physics codes. These codes are typically structured as components interacting via software frameworks. The component structure of a typical Earth system model consists of a hierarchical and recursive tree of components, each representing a different climate process or dynamical system. This recursive structure generally encompasses a modest level of concurrency at the highest level (e.g., atmosphere and ocean on different processor sets) with serial organization underneath.
We propose to extend concurrency much further by running more and more lower- and higher-level components in parallel with each other. Each component can further be parallelized on the fine grain, potentially offering a major increase in the scalability of Earth system models.
We present here first results from this approach, called coarse-grained component concurrency, or CCC. Within the Geophysical Fluid Dynamics Laboratory (GFDL) Flexible Modeling System (FMS), the atmospheric radiative transfer component has been configured to run in parallel with a composite component consisting of every other atmospheric component, including the atmospheric dynamics and all other atmospheric physics components. We will explore the algorithmic challenges involved in such an approach, and present results from such simulations. Plans to achieve even greater levels of coarse-grained concurrency by extending this approach within other components, such as the ocean, will be discussed.
Lutsko, Nicholas J., and Isaac M Held, September 2016: The Response of an Idealized Atmosphere to Orographic Forcing: Zonal vs Meridional Propagation. Journal of the Atmospheric Sciences, 73(9), DOI:10.1175/JAS-D-16-0021.1. Abstract
A dry atmospheric general circulation model is forced with large-scale, Gaussian orography in an attempt to isolate a regime in which the model responds linearly to orographic forcing, and then to study the departures from linearity as the orography is increased in amplitude. In contrast to previous results, which emphasized the meridional propagation of orographically-forced stationary waves, using the standard Held-Suarez (H-S) control climate it is found that the linear regime is characterized by a meridionally-trapped, zonally propagating wave. Meridionally-trapped waves of this kind have been seen in other contexts, where they have been termed “circumglobal waves”. As the height of the orography is increased the circumglobal wave co-exists with a meridionally propagating wave and for large enough heights the meridionally propagating wave dominates the response. A barotropic model on a sphere reproduces this trapped wave in the linear regime and also reproduces the transition to meridional propagation with increasing amplitude. However, mean flow modification by the stationary waves is very different in the two models, making it difficult to argue that the transitions have the same causes. When adding asymmetry across the equator to the H-S control climate and placing the orography in the cooler hemisphere, it becomes harder to generate trapped waves in the GCM and the trapping becomes sensitive to the shape of the orography. The barotropic model overestimates the trapping in this case. These results suggest that an improved understanding of the role of circumglobal waves will be needed to understand the stationary wave field and its sensitivity to the changes in the zonal mean climate.
Tropical cyclone (TC)-permitting general circulation model simulations are performed with spherical geometry and uniform thermal forcing, including uniform sea surface temperature (SST) and insolation. The dependence of the TC number and TC intensity on SST is examined in a series of simulations with varied SST. The results are compared to corresponding simulations with doubly periodic f-plane geometry, rotating radiative convective equilibrium. The turbulent equilibria in simulations with spherical geometry have an inhomogenous distribution of TCs with the density of TCs increasing from low-to-high latitudes. The preferred region of TC genesis is the subtropics, but genesis shifts poleward and becomes less frequent with increasing SST. Both rotating radiative convective equilibrium and spherical geometry simulations have decreasing TC number and increasing TC intensity as SST is increased.
Uncertainty in equilibrium climate sensitivity impedes accurate climate projections. While the inter-model spread is known to arise primarily from differences in cloud feedback, the exact processes responsible for the spread remain unclear. To help identify some key sources of uncertainty, we use a developmental version of the next generation Geophysical Fluid Dynamics Laboratory global climate model (GCM) to construct a tightly controlled set of GCMs where only the formulation of convective precipitation is changed. The different models provide simulation of present-day climatology of comparable quality compared to the CMIP5 model ensemble. We demonstrate that model estimates of climate sensitivity can be strongly affected by the manner through which cumulus cloud condensate is converted into precipitation in a model’s convection parameterization, processes that are only crudely accounted for in GCMs. In particular, two commonly used methods for converting cumulus condensate into precipitation can lead to drastically different climate sensitivity, as estimated here with an atmosphere/land model by increasing sea surface temperatures uniformly and examining the response in the top-of-atmosphere energy balance. The effect can be quantified through a bulk convective detrainment efficiency, which measures the ability of cumulus convection to generate condensate per unit precipitation. The model differences, dominated by shortwave feedbacks, come from broad regimes ranging from large-scale ascent to subsidence regions. Given current uncertainties in representing convective precipitation microphysics and our current inability to find a clear observational constraint that favors one version of our model over the others, the implications of this ability to engineer climate sensitivity needs to be considered when estimating the uncertainty in climate projections.
The sensitivity of global tropical cyclone (TC) activity to changes in a zonally-symmetric sea surface temperature (SST) distribution and the associated large-scale atmospheric circulation are investigated. High-resolution (~50-km horizontal grid spacing) atmospheric general circulation model simulations with maximum SST away from the equator are presented. Simulations with both fixed SST and slab ocean lower boundary conditions are compared.
The simulated TCs that form on the poleward flank of the Intertropical Convergence Zone (ITCZ) are tracked and changes in the frequency and intensity of those storms are analyzed between the different experiments. The total accumulated cyclone energy (ACE) increases as the location of the maximum SST shifts further away from the equator. The location of the ITCZ also shifts in conjunction with changes to the SST profile, and this plays an important role in mediating the frequency and intensity of the TCs that form within this modeling framework.
Fueglistaler, Stephan, Claire Radley, and Isaac M Held, July 2015: The distribution of precipitation and the spread in tropical upper tropospheric temperature trends in CMIP5/AMIP simulations. Geophysical Research Letters, 42(14), DOI:10.1002/2015GL064966. Abstract
Reconciling observations and simulations of tropical upper tropospheric temperature trends remains an important problem in climate science. Examining atmospheric models running over observed sea surface temperatures (SSTs), Flannaghan et al. (2014) show that this reconciliation is affected by the SST data set used, and that a precipitation-weighted SST (PSST) is valuable in explaining this result. Here, we show that even for CMIP5 AMIP simulations forced with identical SSTs, tropical upper tropospheric temperature trends across models (and between ensemble members) show a substantial spread (standard deviation ~10% of the average trend). About 60% of this spread between ensemble means, as well as deviations from the ensemble means, can be explained by PSST calculated from the time-evolving precipitation in each model run. Both PSST and atmospheric temperature trends show statistical evidence for systematic differences between models. We conclude that the response of precipitation patterns to changes in SST patterns is a significant source of uncertainty for tropical temperature trends.
Anthropogenically forced changes to the mean and spatial pattern of sea surface temperatures (SSTs) alter tropical atmospheric meridional energy transport throughout the seasonal cycle – in total, its partitioning between the Hadley cells and eddies, and, for the Hadley cells, the relative roles of the mass flux and the gross moist stability (GMS). We investigate this behavior using an atmospheric general circulation model forced with SST anomalies caused by either historical greenhouse gas or aerosol forcing, dividing the SST anomalies into two components: the tropical mean SST anomaly applied uniformly, and the full SST anomalies minus the tropical mean.
For greenhouse gases, the polar-amplified SST spatial pattern partially negates enhanced eddy poleward energy transport driven by mean warming. Both SST components weaken winter Hadley cell circulation and alter GMS. The Northern Hemisphere-focused aerosol cooling induces northward energy flux anomalies in the deep tropics, which manifest partially via strengthened northern and weakened southern Hadley cell overturning. Aerosol-induced GMS changes also contribute to the northward energy fluxes. A simple thermodynamic scaling qualitatively captures these changes, though it performs less well for the greenhouse gas simulations. The scaling provides an explanation for the tight correlation demonstrated in previous studies between shifts in the Intertropical Convergence Zone position and cross-equatorial energy fluxes.
It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held, I.M., Larichev, V.D., 1996. A scaling theory for horizontally homogeneous baroclinically unstable ow on a beta plane. J. Atmos. Sci. 53, 946–952., which ignores the effect of bottom friction.
It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held and Larichev (1996), which ignores the effect of bottom friction.
Lutsko, Nicholas J., Isaac M Held, and Pablo Zurita-Gotor, August 2015: Applying the Fluctuation-Dissipation Theorem to a Two-Layer Model of Quasi-Geostrophic Turbulence. Journal of the Atmospheric Sciences, 72(8), DOI:10.1175/JAS-D-14-0356.1. Abstract
The Fluctuation-Dissipation Theorem (FDT) provides a means of calculating the response of a dynamical system to a small force by constructing a linear operator which depends only on data from the internal variability of the unperturbed system. Here the FDT is used to estimate the response of a two-layer quasi-geostrophic model to two zonally symmetric torques, both barotropic, with the same sign of the forcing in the two layers, and baroclinic, with opposite sign forcing in the two layers. The supercriticality of the model is also varied to test how the FDT fares as this parameter is varied. To perform the FDT calculations the data is decomposed onto Empirical Orthogonal Functions (EOFs) and the criterion of North et al. (1982) is used as a guide for how many EOFs to retain in the FDT calculations. In the barotropic case good qualitative estimates are obtained for all values of the supercriticality, though the FDT consistently overestimates the response, perhaps due to significant non-Gaussian behavior present in the model. Nevertheless, this adds to the evidence that the annular mode time-scale plays an important role in determining response of the mid-latitudes to small perturbations. The baroclinic case is more challenging for the FDT. However by constructing different bases with which to calculate the EOFs it is shown that the issue in this case is that the baroclinic variability is poorly sampled, not that the FDT fails. The strategies developed in order to generate these estimates may be applicable in situations in which the FDT is applied to larger systems.
Zurita-Gotor, Pablo, Isaac M Held, and Malte Jansen, September 2015: Kinetic energy-conserving hyperdiffusion can improve low-resolution atmospheric models. Journal of Advances in Modeling Earth Systems, 7(3), DOI:10.1002/2015MS000480. Abstract
Motivated by findings that energetically-consistent subgrid dissipation schemes can improve eddy-permitting ocean simulations, this work investigates the impact of the subgrid dissipation scheme on low-resolution atmospheric dynamical cores. A kinetic energy-conserving dissipation scheme is implemented in the model adding a negative viscosity term that injects back into the eddy field the kinetic energy dissipated by horizontal hyperdiffusion. The kinetic energy-conserving scheme enhances numerical convergence when horizontal resolution is changed with fixed vertical resolution and gives superior low-resolution results. Improvements are most obvious for eddy kinetic energy but also found in other fields, particularly with strong or little scale-selective horizontal hyperdiffusion. One advantage of the kinetic energy-conserving scheme is that it reduces the sensitivity of the model to changes in the subgrid dissipation rate, providing more robust results.
Flannaghan, Thomas J., Stephan Fueglistaler, Isaac M Held, S Po-Chedley, Bruce Wyman, and Ming Zhao, December 2014: Tropical temperature trends in Atmospheric General Circulation Model simulations and the impact of uncertainties in observed SSTs. Journal of Geophysical Research: Atmospheres, 119(23), DOI:10.1002/2014JD022365. Abstract
The comparison of trends in various climate indices in observations and models is of fundamental importance for judging the credibility of climate projections. Tropical tropospheric temperature trends have attracted particular attention as this comparison may suggest a model deficiency [Santer et al., 2005; Christy et al., 2007, 2010; Fu et al., 2011; Thorne et al., 2011]. One can think of this problem as composed of two parts: one focused on tropical surface temperature trends and the associated issues related to forcing, feedbacks, and ocean heat uptake; and a second part focusing on connections between surface and tropospheric temperatures and the vertical profile of trends in temperature. Here, we focus on the atmospheric component of the problem. We show that two ensembles of GFDL HiRAM model runs (similar results are shown for NCAR's CAM4 model) with different commonly used prescribed sea surface temperatures (SSTs), namely the HadISST1 and ‘Hurrell’ data sets, have a difference in upper tropical tropospheric temperature trends (~0.1 K/decade at 300 hPa for the period 1984-2008) that is about a factor 3 larger than expected from moist adiabatic scaling of the tropical average SST trend difference. We show that this surprisingly large discrepancy in temperature trends is a consequence of SST trend differences being largest in regions of deep convection. Further, trends, and the degree of agreement with observations, not only depend on SST data set and the particular atmospheric temperature data set, but also on the period chosen for comparison. Due to the large impact on atmospheric temperatures, these systematic uncertainties in SSTs need to be resolved before the fidelity of climate models’ tropical temperature trend profiles can be assessed.
We live in interesting times as we watch diverse effects of human activities on Earth's climate emerge from natural variability. In predicting the outcome of this evolving inadvertent experiment, climate science faces many challenges, some of which have been outlined in this series of Science Perspectives (1–6): reducing the uncertainty in climate sensitivity; explaining the recent slowdown in the rate of warming and its implications for understanding internal variability; uncovering the factors that control how and where the land will become drier as it warms; quantifying the cooling due to anthropogenic aerosols; explaining the curious evolution of atmospheric methane; and predicting changes in extreme weather. In addition to these challenges, the turbulent and chaotic atmospheric and oceanic flows seemingly limit predictability on various time scales. Is the climate system just too complex for useful prediction?
In the near future we expect the resolution of many IPCC-class ocean models to enter the “eddy-permitting” regime. At this resolution models can produce reasonable eddy-like disturbances, but can still not properly resolve geostrophic eddies at all relevant scales. Adequate parameterizations representing sub-grid eddy effects are thus necessary. Most eddy-permitting models presently employ some kind of hyper-viscosity, which is shown to cause a significant amount of energy dissipation. However, comparison to higher resolution simulations shows that only enstrophy, but almost no energy, should be dissipated below the grid-scale. As a result of the artificial energy sink associated with viscous parameterizations, the eddy fields in eddy permitting models are generally not energetic enough.
To overcome this problem, we propose a class of sub-grid parameterizations which dissipate enstrophy but little or no energy. The idea is to combine a standard hyperviscous closure with some mechanism to return dissipated energy to the resolved flow. Enstrophy dissipation remains ensured because the energy is returned at larger scales. Two simple ways to return the energy are proposed: one using a stochastic excitation and one using a negative Laplacian viscosity. Both approaches are tested in an idealized two-layer quasi-geostrophic model. Either approach is shown to greatly improve the solutions in simulations with typical eddy-permitting resolutions. The adaptation of the proposed parameterization for use in realistic ocean models is discussed.
Kang, Sarah M., Isaac M Held, and F Xie, April 2014: Contrasting the tropical responses to zonally asymmetric extratropical and tropical thermal forcing. Climate Dynamics, 42(7-8), DOI:10.1007/s00382-013-1863-0. Abstract
The mechanism is investigated by which extratropical thermal forcing with a finite zonal extent produces global impact. The goal is to understand the near-global response to a weakened Atlantic meridional overturning circulation suggested by paleoclimate data and modeling studies. An atmospheric model coupled to an aquaplanet slab mixed layer ocean, in which the unperturbed climate is zonally symmetric, is perturbed by prescribing cooling of the mixed layer in the Northern Hemisphere and heating of equal magnitude in the Southern Hemisphere, over some finite range of longitudes. In the case of heating/cooling confined to the extratropics, the zonally asymmetric forcing is homogenized by midlatitude westerlies and extratropical eddies before passing on to the tropics, inducing a zonally symmetric tropical response. In addition, the zonal mean responses vary little as the zonal extent of the forced region is changed, holding the zonal mean heating fixed, implying little impact of stationary eddies on the zonal mean. In contrast, when the heating/cooling is confined to the tropics, the zonally asymmetric forcing produces a highly localized response with slight westward extension, due to advection by mean easterly trade winds. Regardless of the forcing location, neither the spatial structure nor the zonal mean responses are strongly affected by wind–evaporation–sea surface temperature feedback.
Coupled climate model simulations of volcanic eruptions and abrupt changes in CO2 concentration are compared in multiple realizations of Geophysical Fluid Dynamics Laboratory’s (GFDL) CM2.1. The change in global-mean surface temperature (GMST) is analyzed to determine whether a fast component of the climate sensitivity of relevance to the transient climate response (TCR, defined with the 1% yr−1 CO2-increase scenario) can be estimated from shorter-timescale climate changes. The fast component of the climate sensitivity estimated from the response of the climate model to volcanic forcing is similar to that of the simulations forced by abrupt CO2 changes, but is 5–15% smaller than the TCR. In addition, the partition between the top-of-atmosphere radiative restoring and ocean heat uptake is similar across radiative forcing agents. The possible asymmetry between warming and cooling climate perturbations, which may affect the utility of volcanic eruptions for estimating the TCR, is assessed by comparing simulations of abrupt CO2 doubling to abrupt CO2 halving. There is slightly less (~5%) GMST change in 0.5 × CO2 simulations than in 2 × CO2 simulations on the short (~10-yr) timescales relevant to the fast component of the volcanic signal. However, inferring the TCR from volcanic eruptions is more sensitive to uncertainties from internal climate variability and the estimation procedure.
The response of the GMST to volcanic eruptions is similar in GFDL’s CM2.1 and CM3, even though the latter has a higher TCR associated with a multidecadal timescale in its response. This is consistent with the expectation that the fast component of the climate sensitivity inferred from volcanic eruptions is a lower bound for the TCR.
Zhou, W, Isaac M Held, and Stephen T Garner, March 2014: Parameter study of tropical cyclones in rotating radiative-convective equilibrium with column physics and resolution of a 25 km GCM. Journal of the Atmospheric Sciences, 71(3), DOI:10.1175/JAS-D-13-0190.1. Abstract
Rotating radiative-convective equilibrium is studied by extracting the column physics of a meso-scale resolution global atmospheric model that simulates realistic hurricane frequency statistics and coupling it to rotating hydrostatic dynamics in doubly-periodic domains. The parameter study helps in understanding the tropical cyclones simulated in the global model and also provides a reference point for analogous studies with cloud resolving models.
The authors first examine the sensitivity of the equilibrium achieved in a large square domain (2×104 km on a side) to sea surface temperature, ambient rotation rate and surface drag coefficient. In such a large domain, multiple tropical cyclones exist simultaneously. The size and intensity of these tropical cyclones are investigated.
The variation of rotating radiative-convective equilibrium with domain size is also studied. As domain size increases, the equilibrium evolves through four regimes: a single tropical depression, an intermittent tropical cyclone with intensity widely varying, a single sustained storm, and finally multiple storms. As SST increases or ambient rotation rate f decreases, the sustained storm regime shifts towards larger domain size. The storm’s natural extent in large domains can be understood from this regime behavior.
The radius of maximum surface wind, although only marginally resolved, increases with SST and increases with f for small f when the domain is large enough. But these parameter dependencies can be modified or even reversed if the domain is smaller than the storm’s natural extent.
Blackburn, M, Ming Zhao, and Isaac M Held, et al., October 2013: The Aqua Planet Experiment (APE): CONTROL SST Simulation. Journal of the Meteorological Society of Japan, 91A, DOI:10.2151/jmsj.2013-A02. Abstract
Climate simulations by 16 atmospheric general circulation models (AGCMs) are compared on an aqua-planet, a water-covered Earth with prescribed sea surface temperature varying only in latitude. The idealised configuration is designed to expose differences in the circulation simulated by different models. Basic features of the aqua-planet climate are characterised by comparison with Earth.
The models display a wide range of behaviour. The balanced component of the tropospheric mean flow, and mid-latitude eddy covariances subject to budget constraints, vary relatively little among the models. In contrast, differences in damping in the dynamical core strongly influence transient eddy amplitudes. Historical uncertainty in modelled lower stratospheric temperatures persists in APE.
Aspects of the circulation generated more directly by interactions between the resolved fluid dynamics and parameterized moist processes vary greatly. The tropical Hadley circulation forms either a single or double inter-tropical convergence zone (ITCZ) at the equator, with large variations in mean precipitation. The equatorial wave spectrum shows a wide range of precipitation intensity and propagation characteristics. Kelvin mode-like eastward propagation with remarkably constant phase speed dominates in most models. Westward propagation, less dispersive than the equatorial Rossby modes, dominates in a few models or occurs within an eastward propagating envelope in others. The mean structure of the ITCZ is related to precipitation variability, consistent with previous studies.
The aqua-planet global energy balance is unknown but the models produce a surprisingly large range of top of atmosphere global net flux, dominated by differences in shortwave reflection by clouds. A number of newly developed models, not optimised for Earth climate, contribute to this. Possible reasons for differences in the optimised models are discussed.
The aqua-planet configuration is intended as one component of an experimental hierarchy used to evaluate AGCMs. This comparison does suggest that the range of model behaviour could be better understood and reduced in conjunction with Earth climate simulations. Controlled experimentation is required to explore individual model behaviour and investigate convergence of the aqua-planet climate with increasing resolution.
Bony, Sandrine, Isaac M Held, and Stephen M Griffies, et al., September 2013: Carbon Dioxide and Climate: Perspectives on a Scientific Assessment In Climate Science for Serving Society Research, Modeling and Prediction Priorities, DOI:10.1007/978-94-007-6692-1_14. Abstract
Many of the findings of the Charney Report on CO2-induced climate change published in 1979 are still valid, even after 30 additional years of climate research and observations. This paper considers the reasons why the report was so prescient, and assesses the progress achieved since its publication. We suggest that emphasis on the importance of physical understanding gained through the use of theory and simple models, both in isolation and as an aid in the interpretation of the results of General Circulation Models, provided much of the authors’ insight at the time. Increased emphasis on these aspects of research is likely to continue to be productive in the future, and even to constitute one of the most efficient routes towards improved climate change assessments.
Surface wind (U10) and significant wave height (Hs) response to global warming are investigated using a coupled atmosphere-wave model by perturbing the sea surface temperatures (SSTs) with anomalies generated by WGCM CMIP-3 coupled models that use the IPCC/AR4/A1B scenario late in the 21st century.
Several consistent changes were observed across all four realizations for the seasonal means: robust increase of U10 and Hs in the Southern Ocean for both the austral summer and winter due to the poleward shift of the jet stream; a dipole pattern of the U10 and Hs with increases in the northeast sector and decreases at the mid-latitude during the boreal winter in the North Atlantic due to the more frequent occurrence of the positive phases of NAO; and strong decrease of U10 and Hs at the tropical western Pacific Ocean during the austral summer, which might be caused by the joint effect of the weakening of the Walker circulation and the large hurricane frequency decrease in the South Pacific.
Changes of the 99th percentile U10 and Hs are twice as strong as changes in the seasonal means, and the maximum changes are mainly dominated by the changes in hurricanes. Robust strong decreases of U10 and Hs in the South Pacific are obtained due to the large hurricane frequency decrease, while the results in the Northern Hemisphere basins differ among the models. An additional sensitivity experiment suggests that the qualitative response of U10 and Hs is not affected by using SST anomalies only and maintaining the radiative forcing unchanged (using 1980 values) as in this study.
A global climate model that factors in the observed temperature of the surface ocean in the eastern equatorial Pacific offers an explanation for the recent hiatus in global warming
Twenty-first-century projections of Atlantic climate change are downscaled to explore the robustness of potential changes in hurricane activity. Multimodel ensembles using the phase 3 of the Coupled Model Intercomparison Project (CMIP3)/Special Report on Emissions Scenarios A1B (SRES A1B; late-twenty-first century) and phase 5 of the Coupled Model Intercomparison Project (CMIP5)/representative concentration pathway 4.5 (RCP4.5; early- and late-twenty-first century) scenarios are examined. Ten individual CMIP3 models are downscaled to assess the spread of results among the CMIP3 (but not the CMIP5) models. Downscaling simulations are compared for 18-km grid regional and 50-km grid global models. Storm cases from the regional model are further downscaled into the Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model (9-km inner grid spacing, with ocean coupling) to simulate intense hurricanes at a finer resolution.
A significant reduction in tropical storm frequency is projected for the CMIP3 (−27%), CMIP5-early (−20%) and CMIP5-late (−23%) ensembles and for 5 of the 10 individual CMIP3 models. Lifetime maximum hurricane intensity increases significantly in the high-resolution experiments—by 4%–6% for CMIP3 and CMIP5 ensembles. A significant increase (+87%) in the frequency of very intense (categories 4 and 5) hurricanes (winds ≥ 59 m s−1) is projected using CMIP3, but smaller, only marginally significant increases are projected (+45% and +39%) for the CMIP5-early and CMIP5-late scenarios. Hurricane rainfall rates increase robustly for the CMIP3 and CMIP5 scenarios. For the late-twenty-first century, this increase amounts to +20% to +30% in the model hurricane’s inner core, with a smaller increase (~10%) for averaging radii of 200 km or larger. The fractional increase in precipitation at large radii (200–400 km) approximates that expected from environmental water vapor content scaling, while increases for the inner core exceed this level.
The response of hurricane frequency to climate changes in an aquaplanet configuration of a 50-km resolution atmospheric general circulation model is examined. The lower boundary condition is an energetically consistent slab ocean with a prescribed cross-equatorial ocean heat flux, which breaks the hemispheric symmetry and moves the Intertropical Convergence Zone (ITCZ) off the equator. In this idealized configuration, hurricane frequency increases in response to radiatively forced warming. The ITCZ shifts poleward when the model is warmed with fixed cross-equatorial ocean heat flux, and it is argued that the increase in hurricane frequency results from this poleward shift. Varying the imposed cross-equatorial ocean heat flux amplitude with fixed radiative forcing can isolate the effect of ITCZ shifts. If an increase in radiative forcing is accompanied by a reduction in the ocean heat flux amplitude such that the position of the ITCZ is unchanged, the simulated hurricane frequency decreases under warmed conditions.
Potter, Samuel F., T Reichler, and Isaac M Held, July 2013: Reflection of barotropic Rossby Waves in sheared flow and validity of the WKB approximation. Journal of the Atmospheric Sciences, 70(7), DOI:10.1175/JAS-D-12-0315.1. Abstract
We discuss reflection of barotropic Rossby waves in an idealized framework with potential applications to tropical-extratropical and inter-hemispheric interactions. Meridional propagation of Rossby waves has often been studied using the WKB approximation. The WKB approximation neglects reflection. We investigate the amount of reflection in simple shear profiles and attempt to evaluate the validity of using the WKB approximation to understand the meridional propagation of Rossby waves. In addition to solving for the reflection coefficient numerically, we are able to derive exact and approximate forms of the reflection coefficient in certain parameter regimes. An application to the observed climatology is discussed in light of our findings.
Impacts of tropical temperature changes in the upper troposphere (UT) and the tropical tropopause layer (TTL) on tropical cyclone (TC) activity are explored. UT and lower TTL cooling both lead to an overall increase in potential intensity (PI), while temperatures 70hPa and higher have negligible effect. Idealized experiments with a high-resolution global model show that lower temperatures in the UT are associated with increases in global and North Atlantic TC frequency, but modeled TC frequency changes are not significantly affected by TTL temperature changes nor do they scale directly with PI.
Future projections of hurricane activity have been made with models that simulate the recent upward Atlantic TC trends while assuming or simulating very different tropical temperature trends. Recent Atlantic TC trends have been simulated by: i) high-resolution global models with nearly moist-adiabatic warming profiles, and ii) regional TC downscaling systems that impose the very strong UT and TTL trends of the NCEP Reanalysis, an outlier among observational estimates. Impact of these differences in temperature trends on TC activity is comparable to observed TC changes, affecting assessments of the connection between hurricanes and climate. Therefore, understanding the character of and mechanisms behind changes in UT and TTL temperature is important to understanding past and projecting future TC activity changes. We conclude that the UT and TTL temperature trends in NCEP are unlikely to be accurate, and likely drive spuriously positive TC and PI trends, and an inflated connection between absolute surface temperature warming and TC activity increases.
Williamson, D L., Ming Zhao, and Isaac M Held, et al., October 2013: The Aqua Planet Experiment (APE): Response to Changed Meridional SST Profile. Journal of the Meteorological Society of Japan, 91A, DOI:10.2151/jmsj.2013-A03. Abstract
This paper explores the sensitivity of Atmospheric General Circulation Model (AGCM) simulations to changes in the meridional distribution of sea surface temperature (SST). The simulations are for an aqua-planet, a water covered Earth with no land, orography or sea-ice and with specified zonally symmetric SST. Simulations from 14 AGCMs developed for Numerical Weather Prediction and climate applications are compared. Four experiments are performed to study the sensitivity to the meridional SST profile. These profiles range from one in which the SST gradient continues to the equator to one which is flat approaching the equator, all with the same maximum SST at the equator.
The zonal mean circulation of all models shows strong sensitivity to latitudinal distribution of SST. The Hadley circulation weakens and shifts poleward as the SST profile flattens in the tropics. One question of interest is the formation of a double versus a single ITCZ. There is a large variation between models of the strength of the ITCZ and where in the SST experiment sequence they transition from a single to double ITCZ. The SST profiles are defined such that as the equatorial SST gradient flattens, the maximum gradient increases and moves poleward. This leads to a weakening of the mid-latitude jet accompanied by a poleward shift of the jet core. Also considered are tropical wave activity and tropical precipitation frequency distributions. The details of each vary greatly between models, both with a given SST and in the response to the change in SST.
One additional experiment is included to examine the sensitivity to an off-equatorial SST maximum. The upward branch of the Hadley circulation follows the SST maximum off the equator. The models that form a single precipitation maximum when the maximum SST is on the equator shift the precipitation maximum off equator and keep it centered over the SST maximum. Those that form a double with minimum on the equatorial maximum SST shift the double structure off the equator, keeping the minimum over the maximum SST. In both situations only modest changes appear in the shifted profile of zonal average precipitation. When the upward branch of the Hadley circulation moves into the hemisphere with SST maximum, the zonal average zonal, meridional and vertical winds all indicate that the Hadley cell in the other hemisphere dominates.
Identifying the prime drivers of the twentieth-century multidecadal variability in the Atlantic Ocean is crucial for predicting how the Atlantic will evolve in the coming decades and the resulting broad impacts on weather and precipitation patterns around the globe. Recently Booth et al (2012) showed that the HadGEM2-ES climate model closely reproduces the observed multidecadal variations of area-averaged North Atlantic sea surface temperature in the 20th century. The multidecadal variations simulated in HadGEM2-ES are primarily driven by aerosol indirect effects that modify net surface shortwave radiation. On the basis of these results, Booth et al (2012) concluded that aerosols are a prime driver of twentieth-century North Atlantic climate variability. However, here it is shown that there are major discrepancies between the HadGEM2-ES simulations and observations in the North Atlantic upper ocean heat content, in the spatial pattern of multidecadal SST changes within and outside the North Atlantic, and in the subpolar North Atlantic sea surface salinity. These discrepancies may be strongly influenced by, and indeed in large part caused by, aerosol effects. It is also shown that the aerosol effects simulated in HadGEM2-ES cannot account for the observed anti-correlation between detrended multidecadal surface and subsurface temperature variations in the tropical North Atlantic. These discrepancies cast considerable doubt on the claim that aerosol forcing drives the bulk of this multidecadal variability.
Zhao, Ming, Isaac M Held, and Gabriel A Vecchi, et al., September 2013: Robust direct effect of increasing atmospheric CO2 concentration on global tropical cyclone frequency: a multi-model inter-comparison. U.S. CLIVAR Variations, 11(3), 17-23.
This study describes a 29-year (1981 to 2009) global ocean surface gravity wave simulation generated by a coupled atmosphere-wave model using NOAA/GFDL’s High Resolution Atmosphere Model (HIRAM) and the WAVEWATCH III surface wave model developed and used operationally at NOAA/NCEP. Extensive evaluation of monthly mean significant wave height (SWH) against in situ buoys, satellite altimeter measurements, and ERA-40 reanalysis show very good agreements in terms of magnitude, spatial distribution, and scatter. The comparisons with satellite altimeter measurements indicate that the SWH low bias in ERA-40 reanalysis has been improved in our model simulations. The model fields show strong response to the NAO in the North Atlantic and the SOI in the Pacific Ocean that are well connected with the atmospheric responses. For the NAO in winter, the strongest subpolar wave responses are found near the Northern Europe coast and the coast of Labrador rather than in the central Northern Atlantic where the wind response is strongest. Similarly, for the SOI in the Pacific Ocean, the wave responses are strongest in the northern Bering Sea and the Antarctic coast.
An approach to climate change feedback analysis is described in which tropospheric relative humidity replaces specific humidity as the state variable that, along with the temperature structure, surface albedos and clouds, controls the magnitude of the response of global mean surface temperature to a radiative forcing. Despite being simply a regrouping of terms in the feedback analysis, this alternative perspective has the benefit of removing most of the pervasive cancellation between water and lapse rate feedbacks seen in models. As a consequence, the individual feedbacks have less scatter than in the traditional formulation. The role of cloud feedbacks in controlling climate sensitivity is also reflected more clearly in the new formulation.
The plausibility of the high end of global warming projections in recent assessments is a subject of debate. A study of multi-model climate simulations argues that we need to take the possibility of strong warming seriously.
Kang, Sarah M., and Isaac M Held, April 2012: Tropical precipitation, SSTs and the surface energy budget: A zonally symmetric perspective. Climate Dynamics, 38(9-10), DOI:10.1007/s00382-011-1048-7. Abstract
The relative importance of sea surface temperatures
(SSTs) and the surface energy budget to tropical
precipitation is examined by comparing models with zonally
symmetric climates, both fixed SST and coupled to a
slab mixed layer ocean. Two models are considered with
differing surface flux formulations and in each case solutions
that are symmetric about the equator are perturbed to
create interhemispheric asymmetry. When SSTs are prescribed
in the two models with different flux formulations,
the magnitude of tropical precipitation response to identical
SST anomalies is significantly different, but the differences
can be understood in terms of the altered surface fluxes. In
contrast, when the net surface energy fluxes are constrained
to be identical in mixed layer simulations of the two different
models, the response of tropical precipitation to
perturbations in the surface energy balance is very similar.
Both perspectives predict qualitatively the same precipitation
response, but the energy budget better predicts the
magnitude of the precipitation response. Thus, we argue
that the atmospheric energy budget, controlled in these
experiments primarily by the surface energy budget, is
more fundamental to the control of tropical precipitation
than the SSTs, in these simulations with axisymmetric
climates. We touch briefly on a complication in the interpretation
of the model results due to the fact that fixed SST
and slab-ocean versions of the model can produce different
Hadley cell strengths for the same SSTs.
Muller, C J., and Isaac M Held, August 2012: Detailed investigation of the self-aggregation of convection in cloud-resolving simulations. Journal of the Atmospheric Sciences, 69(8), DOI:10.1175/JAS-D-11-0257.1. Abstract
In models of radiative-convective equilibrium it is known that convection can spontaneously aggregate into one single localized moist region if the domain is large enough. The large changes in the mean climate state and radiative fluxes accompanying this self-aggregation raise questions as to what simulations at lower resolutions with parametrized convection, in similar homogeneous geometries, should be expected to produce to be considered successful in mimicking a cloud-resolving model.
We investigate this self-aggregation in a non-rotating, three-dimensional cloud-resolving model on a square domain without large-scale forcing. We find that self-aggregation is not only sensitive to the domain size, but also to the horizontal resolution. With horizontally homogeneous initial conditions, convective aggregation only occurs on domains larger than about 200 km and with resolutions coarser than about 2 km in the model examined. The system exhibits hysteresis, so that with aggregated initial conditions, convection remains aggregated even at our finest resolution, 500 m, as long as the domain is greater than 200-300 km.
The sensitivity of self-aggregation to resolution and domain size in this model is due to the sensitivity of the distribution of low clouds to these two parameters. Indeed, the mechanism responsible for the aggregation of convection is the dynamical response to the longwave radiative cooling from low clouds. Strong longwave cooling near cloud top in dry regions forces downward motion, which by continuity generates inflow near cloud top and near-surface outflow from dry regions. This circulation results in the net export of moist static energy from regions with low moist static energy, yielding a positive feedback.
Voigt, A, Isaac M Held, and Jochem Marotzke, January 2012: Hadley cell dynamics in a virtually dry Snowball Earth atmosphere. Journal of the Atmospheric Sciences, 69(1), DOI:10.1175/JAS-D-11-083.1. Abstract
The Hadley cell of a virtually dry Snowball Earth atmosphere under equinox insolation is studied in a comprehensive atmospheric general circulation model. In contrast to the Hadley cell of modern Earth, momentum transport by dry convection, which is modelled as vertical diffusion of momentum, is important in the upper branch of the Snowball Earth Hadley cell. In the zonal momentum balance, mean meridional advection of mean absolute vorticity is not only balanced by eddies but also by vertical diffusion of zonal momentum. Vertical diffusion also contributes to the meridional momentum balance by decelerating the Hadley cell through downgradient mixing of meridional momentum between its upper and lower branches. When vertical diffusion of momentum is suppressed in the upper branch, the Hadley cell strengthens by a factor of about two. This is in line with the effect of vertical diffusion in the meridional momentum balance but in contrast with its effect in the zonal momentum balance. Neither axisymmetric Hadley cell theories based on angular momentum conservation nor eddy-permitting Hadley cell theories that neglect vertical diffusion of momentum are applicable to the Snowball Earth Hadley cell. Since the Snowball Earth Hadley cell is a particular realization of a dry Hadley cell, these results show that an appropriate description of dry Hadley cells should take into account vertical transport of momentum by dry convection.
Williamson, D L., M Blackburn, B J Hoskins, Ming Zhao, and Isaac M Held, et al., 2012: In The APE Atlas, NCAR Technical Note NCAR/TN-484+STR, Boulder, Colorado, National Center for Atmospheric Research, DOI:10.5065/D6FF3QBR.
Zhao, Ming, and Isaac M Held, April 2012: TC-permitting GCM simulations of hurricane frequency response to sea surface temperature anomalies projected for the late 21st century. Journal of Climate, 25(8), DOI:10.1175/JCLI-D-11-00313.1. Abstract
A tropical cyclone permitting global atmospheric model is used to explore hurricane frequency response to sea surface temperature (SST) anomalies generated by coupled models for the late 21st century. Results are presented for SST anomalies averaged over 18 models as well as from 8 individual models. For each basin, there exists large inter-model spread in the magnitude and even the sign of the frequency response among the different SST projections. These sizable variations in response are explored to understand features of SST distributions that are important for the basin-wide hurricane responses. In the N. Atlantic, the E. Pacific and the S. Indian basins, most (72-86%) of the inter-model variance in storm frequency response can be explained by a simple relative SST index defined as a basin's storm development region SST minus the tropical mean SST. The explained variance is significantly lower in the S. Pacific (48%) and much lower in the W. Pacific basin (27%).
Several atmospheric parameters are utilized to probe changes in tropical atmospheric circulation and thermodynamical properties relevant to storm genesis in the model. While all present strong correlation to storm response in some basins, a parameter measuring tropospheric convective mass-flux stands out as skillful in explaining the simulated differences for all basins. Globally, in addition to a modest reduction of total storm frequency, the simulations exhibit a small but robust eastward and poleward migration of genesis frequency in both the N. Pacific and the N. Atlantic oceans. This eastward migration of storms can also be explained by changes in convection.
High resolution global climate models (GCM) have been increasingly utilized for simulations of the global number and distribution of tropical cyclones (TCs), and how they might change with changing climate. In contrast, there is a lack of published studies on the sensitivity of TC genesis to parameterized processes in these GCMs.The uncertainties in these formulations might be an important source of uncertainty in the future projections of TC statistics.
In this study, we investigate the sensitivity of the global number of TCs in present-day simulations using the Geophysical Fluid Dynamics Laboratory HIgh Resolution Atmospheric Model (GFDL HIRAM) to alterations in physical parameterizations. Two parameters are identified to be important in TC genesis frequency in this model. They are the horizontal cumulus mixing rate which controls the entrainment into convective cores within the convection parameterization, and the strength of the damping of the divergent component of the horizontal flow. The simulated global number of TCs exhibits non-intuitive response to incremental changes of both parameters. As the cumulus mixing rate increases, the model produces non-monotonic response in global TC frequency with an initial sharp increase and then decrease. However, storm mean intensity rises montonically with the mixing rate. As the strength of the divergence damping increases, the model produces a continuous increase of global number of TCs and hurricanes with little change in storm mean intensity. Mechanisms for explaining these non-intuitive responses are discussed.
The Geophysical Fluid Dynamics Laboratory (GFDL) has developed a coupled general circulation model (CM3) for atmosphere, oceans, land, and sea ice. The goal of CM3 is to address emerging issues in climate change, including aerosol-cloud interactions, chemistry-climate interactions, and coupling between the troposphere and stratosphere. The model is also designed to serve as the physical-system component of earth-system models and models for decadal prediction in the near-term future, for example, through improved simulations in tropical land precipitation relative to earlier-generation GFDL models. This paper describes the dynamical core, physical parameterizations, and basic simulation characteristics of the atmospheric component (AM3) of this model.
Relative to GFDL AM2, AM3 includes new treatments of deep and shallow cumulus convection, cloud-droplet activation by aerosols, sub-grid variability of stratiform vertical velocities for droplet activation, and atmospheric chemistry driven by emissions with advective, convective, and turbulent transport. AM3 employs a cubed-sphere implementation of a finite-volume dynamical core and is coupled to LM3, a new land model with eco-system dynamics and hydrology.
Most basic circulation features in AM3 are simulated as realistically, or more so, than in AM2. In particular, dry biases have been reduced over South America. In coupled mode, the simulation of Arctic sea ice concentration has improved. AM3 aerosol optical depths, scattering properties, and surface clear-sky downward shortwave radiation are more realistic than in AM2. The simulation of marine stratocumulus decks and the intensity distributions of precipitation remain problematic, as in AM2.
The last two decades of the 20th century warm in CM3 by .32°C relative to 1881-1920. The Climate Research Unit (CRU) and Goddard Institute for Space Studies analyses of observations show warming of .56°C and .52°C, respectively, over this period. CM3 includes anthropogenic cooling by aerosol cloud interactions, and its warming by late 20th century is somewhat less realistic than in CM2.1, which warmed .66°C but did not include aerosol cloud interactions. The improved simulation of the direct aerosol effect (apparent in surface clear-sky downward radiation) in CM3 evidently acts in concert with its simulation of cloud-aerosol interactions to limit greenhouse gas warming in a way that is consistent with observed global temperature changes.
Air pollution (ozone and particulate matter in surface air) is strongly linked to synoptic weather and thus is likely sensitive to climate change. In order to isolate the responses of air pollutant transport and wet removal to a warming climate, we examine a simple carbon monoxide (CO)–like tracer (COt) and a soluble version (SAt), both with the 2001 CO emissions, in simulations with the GFDL chemistry-climate model (AM3) for present (1981-2000) and future (2081-2100) climates. In 2081-2100, projected reductions in lower tropospheric ventilation and wet deposition exacerbate surface air pollution as evidenced by higher surface COt and SAt concentrations. However, the average horizontal general circulation patterns in 2081-2100 are similar to 1981-2000, so the spatial distribution of COt changes little. Precipitation is an important factor controlling soluble pollutant wet removal, but the total global precipitation change alone does not necessarily indicate the sign of the soluble pollutant response to climate change. Over certain latitudinal bands, however, the annual wet deposition change can be explained mainly by the simulated changes in large-scale (LS) precipitation. In regions such as North America, differences in the seasonality of LS precipitation and tracer burdens contribute to an apparent inconsistency of changes in annual wet deposition versus annual precipitation. As a step towards an ultimate goal of developing a simple index that can be applied to infer changes in soluble pollutants directly from changes in precipitation fields as projected by physical climate models, we explore here a “Diagnosed Precipitation Impact” (DPI) index. This index captures the sign and magnitude (within 50%) of the relative annual mean changes in the global wet deposition of the soluble pollutant. DPI can only be usefully applied in climate models in which LS precipitation dominates wet deposition and horizontal transport patterns change little as climate warms. Our findings support the need for tighter emission regulations, for both soluble and insoluble pollutants, to obtain a desired level of air quality as climate warms.
The distribution of radiocarbon (14C) in the ocean and atmosphere has fluctuated on timescales ranging from seasons to millennia. It is thought that these fluctuations partly reflect variability in the climate system, offering a rich potential source of information to help understand mechanisms of past climate change. Here, a long simulation with a new, coupled model is used to explore the mechanisms that redistribute 14C within the Earth system on inter-annual to centennial timescales. The model, CM2Mc, is a lower-resolution version of the Geophysical Fluid Dynamics Laboratory's CM2M model, uses no flux adjustments, and incorporates a simple prognostic ocean biogeochemistry model including 14C. The atmospheric 14C and radiative boundary conditions are held constant, so that the oceanic distribution of 14C is only a function of internal climate variability. The simulation displays previously-described relationships between tropical sea surface 14C and the model-equivalents of the El Niño Southern Oscillation and Indonesian Throughflow. Sea surface 14C variability also arises from fluctuations in the circulations of the subarctic Pacific and Southern Ocean, including North Pacific decadal variability, and episodic ventilation events in the Weddell Sea that are reminiscent of the Weddell Polynya of 1974–1976. Interannual variability in the air-sea balance of 14C is dominated by exchange within the belt of intense Southern Westerly winds, rather than at the convective locations where the surface 14C is most variable. Despite significant interannual variability, the simulated impact on air-sea exchange is an order of magnitude smaller than the recorded atmospheric 14C variability of the past millennium. This result partly reflects the importance of variability in the production rate of 14C in determining atmospheric 14C, but may also reflect an underestimate of natural climate variability, particularly in the Southern Westerly winds.
The effects on tropical cyclone statistics of doubling CO2, with fixed sea surface
temperatures (SSTs), are compared to the effects of a 2K increase in SST, with fixed
CO2, using a 50km resolution global atmospheric model. Confirming earlier results of
Yoshimura and Sugi (2005), a significant fraction of the reduction in globally averaged
tropical storm frequency seen in simulations in which both SST and CO2 are increased can be
thought of as the effect of the CO2 increase with fixed SSTs. Globally, the model produces a
decrease in tropical cyclone frequency of about 10% due to doubling of CO2 and an additional
10% for a 2K increase in SST, resulting in roughly a 20% reduction when both effects are
present. The relative contribution of the CO2 effect to the total reduction is larger in the
Northern than in the Southern Hemisphere. The average intensity of storms increases in the
model with increasing SST, but intensity remains roughly unchanged, or decreases slightly,
with the increase in CO2 alone. As a result, when considering the frequency of more intense
cyclones, the intensity increase tends to compensate for the reduced total cyclone numbers for
the SST increase in isolation but not for the CO2 increase in isolation. Changes in genesis
in these experiments roughly follow changes in mean vertical motion, reflecting changes in
convective mass fluxes. Discussion is provided of one possible perspective on how changes in
the convective mass flux might alter genesis rates.
In "Open Source Climate Model Development Is Worth It," Isaac Held explains that a fully open source climate-modeling effort could be of great pedagogical value and maybe even of direct scientific importance by providing a toolbox for active researchers and people new to the field. In "Should Climate Models Be Open Source?" David Randall explains that community-based climate model development can be facilitated by coding the model in a modular fashion, but it can cause problems because the real climate system isn't modular.
Skillfully predicting North Atlantic hurricane activity months in advance is of potential
societal significance and a useful test of our understanding of the factors controlling
hurricane activity. We describe a statistical-dynamical hurricane forecasting system,
based on a statistical hurricane model, with explicit uncertainty estimates, built from a
suite of high-resolution global atmospheric dynamical model integrations spanning a
broad range of climate states. The statistical model uses two climate predictors: the sea
surface temperature (SST) in the tropical North Atlantic and SST averaged over the
global tropics. The choice of predictors is motivated by physical considerations, results of
high-resolution hurricane modeling and of statistical modeling of the observed record.
The statistical hurricane model is applied to a suite of initialized dynamical global
climate model forecasts of SST to predict North Atlantic hurricane frequency, which
peaks in the August-October season, from different starting dates. Retrospective forecasts
of the 1982-2009 period indicate that skillful predictions can be made from as early as
November of the previous year – that is, skillful forecasts for the coming North Atlantic
hurricane season could be made as the current one is closing. Based on forecasts
initialized between November 2009 and March 2010, the model system predicts that the
upcoming 2010 North Atlantic hurricane season will likely be more active than the 1982-
2009 climatology, with the forecasts initialized in March 2010 predicting an expected
hurricane count of eight and a 50% probability of counts between six (the 1966-2009
median) and nine.
Several recent models suggest that the frequency of Atlantic tropical cyclones could decrease as the climate warms. However, these models are unable to reproduce storms of category 3 or higher intensity. We explored the influence of future global warming on Atlantic hurricanes with a downscaling strategy by using an operational hurricane-prediction model that produces a realistic distribution of intense hurricane activity for present-day conditions. The model projects nearly a doubling of the frequency of category 4 and 5 storms by the end of the 21st century, despite a decrease in the overall frequency of tropical cyclones, when the downscaling is based on the ensemble mean of 18 global climate-change projections. The largest increase is projected to occur in the Western Atlantic, north of 20°N.
The fast and slow components of global warming in a comprehensive climate model are isolated by examining the response to an instantaneous return to pre-industrial forcing. The response is characterized by an initial fast exponential decay with an e-folding time smaller than 5 years, leaving behind a remnant that evolves more slowly. The slow component is estimated to be small at present, as measured by the global mean near-surface air temperature, and, in the model examined, grows to 0.4C by 2100 in the A1B SRES scenario and then to 1.4C by 2300 if one holds radiative forcing fixed after 2100. The dominance of the fast component at present is supported by examining the response to an instantaneous doubling of CO2 and by the excellent fit to the model's ensemble mean 20th century evolution with a simple one-box model with no long times scales.
Knutson, Thomas R., J McBride, Johnny C L Chan, Kerry A Emanuel, G Holland, Christopher Landsea, Isaac M Held, James Kossin, A K Srivastava, and M Sugi, March 2010: Tropical cyclones and climate change. Nature Geoscience, 3, DOI:doi:10.1038/ngeo779. Abstract
Whether the characteristics of tropical cyclones have changed or will change in a warming climate — and if so, how — has been the subject of considerable investigation, often with conflicting results. Large amplitude fluctuations in the frequency and intensity of tropical cyclones greatly complicate both the detection of long-term trends and their attribution to rising levels of atmospheric greenhouse gases. Trend detection is further impeded by substantial limitations in the availability and quality of global historical records of tropical cyclones. Therefore, it remains uncertain whether past changes in tropical cyclone activity have exceeded the variability expected from natural causes. However, future projections based on theory and high-resolution dynamical models consistently indicate that greenhouse warming will cause the globally averaged intensity of tropical cyclones to shift towards stronger storms, with intensity increases of 2–11% by 2100. Existing modelling studies also consistently project decreases in the globally averaged frequency of tropical cyclones, by 6–34%. Balanced against this, higher resolution modelling studies typically project substantial increases in the frequency of the most intense cyclones, and increases of the order of 20% in the precipitation rate within 100 km of the storm centre. For all cyclone parameters, projected changes for individual basins show large variations between different modelling studies.
We propose a modification to the standard forcing/feedback diagnostic energy balance model to account for 1) differences between effective and equilibrium climate sensitivities and 2) the variation of effective sensitivity over time in climate change experiments with coupled atmosphere-ocean climate models. In the spirit of Hansen et al (2005) we introduce an efficacy factor to the ocean heat uptake. Comparing the time-evolution of the surface warming in high and low efficacy models demonstrates the role of this efficacy in the transient response to CO2 forcing. Abrupt CO2 increase experiments show that the large efficacy of the Geophysical Fluid Dynamics Laboratory's CM2.1 model sets up in the first two decades following the increase in forcing. The use of an efficacy is necessary to fit this model's global mean temperature evolution in periods with both increasing and stable forcing. The inter-model correlation of transient climate response with ocean heat uptake efficacy is greater than its correlation with equilibrium climate sensitivity in an ensemble of climate models used for the 3rd and 4th IPCC assessments. When computed at the time of doubling in the standard experiment with 1%/yr increase in CO2, the efficacy is variable amongst the models but is generally greater than 1, averages between 1.3 and 1.4, and is as large as 1.75 in several models.
Zhang, Rong, Sarah M Kang, and Isaac M Held, January 2010: Sensitivity of climate change induced by the weakening of the Atlantic Meridional Overturning Circulation to cloud feedback. Journal of Climate, 23(2), DOI:10.1175/2009JCLI3118.1. Abstract
A variety of observational and modeling studies show that changes in the Atlantic Meridional Overturning Circulation (AMOC) can induce rapid global scale climate change. In particular, a substantially weakened AMOC leads to a southward shift of the Intertropical Convergence Zone (ITCZ) in both the Atlantic and the Pacific. However, the simulated amplitudes of the AMOC induced tropical climate change differ substantially among different models. In this paper, we study the sensitivity to cloud feedback of the climate response to a change in the AMOC using a coupled ocean-atmosphere model (GFDL CM2.1). Without cloud feedback, the simulated AMOC-induced climate change in this model is weakened substantially. Low cloud feedback has a strong amplifying impact on the tropical ITCZ shift in this model, while the effects of high cloud feedback are weaker. We conclude that cloud feedback is an important contributor to the uncertainty in the global response to AMOC changes.
Retrospective predictions of seasonal hurricane activity in the Atlantic and
East Pacific are generated using an atmospheric model with 50km horizontal resolution and
simply persisting sea surface temperature (SST) anomalies from June through the hurricane
season. Using an ensemble of 5 realizations for each year between 1982 and 2008, the
correlations of the model mean with observations of basin-wide hurricane frequency are 0.69
in the North Atlantic and 0.58 in the East Pacific. In the North Atlantic, a significant part of the
degradation in skill as compared to a model forced with observed SSTs during the hurricane
season (correlation 0.78) can be explained by the change from June through the hurricane
season in one parameter, the difference between the SST in the main development region and
the tropical mean SST. In fact, simple linear regression models with this one predictor perform
nearly as well as the full dynamical model for basin-wide hurricane frequency in both the
East Pacific and the North Atlantic. The implication is that the quality of seasonal forecasts
based on a coupled atmosphere-ocean model will depend in large part on the model’s ability
to predict the evolution of this difference between main development region SST and tropical
mean SST.
Zhao, Ming, and Isaac M Held, December 2010: An analysis of the effect of global warming on the intensity of Atlantic hurricanes using a GCM with statistical refinement. Journal of Climate, 23(23), DOI:10.1175/2010JCLI3837.1. Abstract
A statistical intensity adjustment is utilized to extract information from tropical cyclone
simulations in a 50km-resolution global model. A simple adjustment based on the modeled
and observed probability distribution of storm life-time maximum wind speed allows the
GCM to capture the differences between observed intensity distributions in active/inactive
year composites from the 1981-2008 period in the N. Atlantic. This intensity adjustment is
then used to examine the atmospheric model’s responses to different sea surface temperature
anomalies generated by coupled models for the late 21st century. In the North Atlantic all
simulations produce a reduction in the total number of cyclones, but with large inter-model
spread in the magnitude of the reduction. The intensity response is positively correlated with
changes in frequency across the ensemble. Yet there is, on average, an increase in intensity
in these simulations despite the mean reduction in frequency. We argue that it is useful to
decompose these intensity changes into two parts: an increase in intensity that is intrinsic to
the climate change experiments; and a change in intensity positively correlated with frequency,
just as in the active/inactive historical composites. Isolating the intrinsic component, which
is relatively independent of the details of the SST warming pattern, we find an increase in
storm-lifetime maximum winds of 5-10 ms−1 for storms with intensities of 30-60 ms−1, by
the end of the 21st century. The effects of change in frequency, which are dependent on the
details of the spatial structure of the warming, must then be superimposed on this intrinsic
change.
Atlantic tropical cyclone activity has trended upward in recent decades. The increase coincides with favorable changes in local sea surface temperature and other environmental indices, principally associated with vertical shear and the thermodynamic profile. The relative importance of these environmental factors has not been firmly established. A recent study using a high-resolution dynamical downscaling model has captured both the trend and interannual variations in Atlantic storm frequency with considerable fidelity. In the present work, this downscaling framework is used to assess the importance of the large-scale thermodynamic environment relative to other factors influencing Atlantic tropical storms.
Separate assessments are done for the recent multidecadal trend (1980–2006) and a model-projected global warming environment for the late 21st century. For the multidecadal trend, changes in the seasonal-mean thermodynamic environment (sea surface temperature and atmospheric temperature profile at fixed relative humidity) account for more than half of the observed increase in tropical cyclone frequency, with other seasonal-mean changes (including vertical shear) having a somewhat smaller combined effect. In contrast, the model’s projected reduction in Atlantic tropical cyclone activity in the warm climate scenario appears to be driven mostly by increased seasonal-mean vertical shear in the western Atlantic and Caribbean rather than by changes in the SST and thermodynamic profile.
Kang, Sarah M., D M W Frierson, and Isaac M Held, September 2009: The tropical response to extratropical thermal forcing in an idealized GCM: The importance of radiative feedbacks and convective parameterization. Journal of the Atmospheric Sciences, 66(9), DOI:10.1175/2009JAS2924.1. Abstract
The response of tropical precipitation to extratropical thermal forcing is reexamined using an idealized moist atmospheric GCM that has no water vapor or cloud feedbacks, simplifying the analysis while retaining the aquaplanet configuration coupled to a slab ocean from the authors’ previous study. As in earlier studies, tropical precipitation in response to high-latitude forcing is skewed toward the warmed hemisphere. Comparisons with a comprehensive GCM in an identical aquaplanet, mixed-layer framework reveal that the tropical responses tend to be much larger in the comprehensive GCM as a result of positive cloud and water vapor feedbacks that amplify the imposed extratropical thermal forcing.
The magnitude of the tropical precipitation response in the idealized model is sensitive to convection scheme parameters. This sensitivity as well as the tropical precipitation response can be understood from a simple theory with two ingredients: the changes in poleward energy fluxes are predicted using a one-dimensional energy balance model and a measure of the “total gross moist stability” [Δm, which is defined as the total (mean plus eddy) atmospheric energy transport per unit mass transport] of the model tropics converts the energy flux change into a mass flux and a moisture flux change. The idealized model produces a low level of compensation of about 25% between the imposed oceanic flux and the resulting response in the atmospheric energy transport in the tropics regardless of the convection scheme parameter. Because Geophysical Fluid Dynamics Laboratory Atmospheric Model 2 (AM2) with prescribed clouds and water vapor exhibits a similarly low level of compensation, it is argued that roughly 25% of the compensation is dynamically controlled through eddy energy fluxes. The sensitivity of the tropical response to the convection scheme in the idealized model results from different values of Δm: smaller Δm leads to larger tropical precipitation changes for the same response in the energy transport.
Solomon, S, R Dole, Richard A Feely, Isaac M Held, R W Higgins, J Payne, E Shea, U Varanasi, and Marian B Westley, December 2009: A vision for Climate Services in NOAA. Fisheries, 34(12), 607-609.
A global atmospheric model with roughly 50 km horizontal grid spacing is used to simulate the interannual variability of tropical cyclones using observed sea surface temperatures (SSTs) as the lower boundary condition. The model's convective parameterization is based on a closure for shallow convection, with much of the deep convection allowed to occur on resolved scales. Four realizations of the period 1981–2005 are generated. The correlation of yearly Atlantic hurricane counts with observations is greater than 0.8 when the model is averaged over the four realizations, supporting the view that the random part of this annual Atlantic hurricane frequency (the part not predictable given the SSTs) is relatively small (< 2 hurricanes/yr). Correlations with observations are lower in the East, West and South Pacific (roughly 0.6, 0.5 and 0.3) and insignificant in the Indian ocean. The model trends in Northern Hemisphere basin-wide frequency are consistent with the observed trends in the IBTrACS database. The model generates an upward trend of hurricane frequency in the Atlantic and downward trends in the East and West Pacific over this time frame. The model produces a negative trend in the Southern Hemisphere that is larger than that in the IBTrACS.
The same model is used to simulate the response to the SST anomalies generated by coupled models in the CMIP3 archive, using the late 21st century in the A1B scenario. Results are presented for SST anomalies computed by averaging over 18 CMIP3 models and from individual realizations from three models. A modest reduction of global and Southern Hemisphere hurricane frequency is obtained in each case, but the results in individual Northern Hemisphere basins differ among the models. The vertical shear in the Atlantic Main Development Region (MDR) and the difference between the MDR SST and the tropical mean SST are well correlated with the model's Atlantic storm frequency, both for interannual variability and for the intermodel spread in global warming projections.
Rotating radiative–convective equilibrium, using the column physics and resolution of GCMs, is proposed as a useful framework for studying the tropical storm–like vortices produced by global models. These equilibria are illustrated using the column physics and dynamics of a version of the GFDL Atmospheric Model 2 (AM2) at resolutions of 220, 110, and 55 km in a large 2 × 104 km square horizontally homogeneous domain with fixed sea surface temperature and uniform Coriolis parameter. The large domain allows a number of tropical storms to exist simultaneously. Once equilibrium is attained, storms often persist for hundreds of days. The number of storms decreases as sea surface temperatures increase, while the average intensity increases. As the background rotation is decreased, the number of storms also decreases. At these resolutions and with this parameterization of convection, a dense collection of tropical storms is always the end state of moist convection in the cases examined.
Kang, Sarah M., Isaac M Held, D M W Frierson, and Ming Zhao, 2008: The response of the ITCZ to extratropical thermal forcing: Idealized slab-ocean experiments with a GCM. Journal of Climate, 21(14), DOI:10.1175/2007JCLI2146.1. Abstract
Using a comprehensive atmospheric GCM coupled to a slab mixed layer ocean, experiments are performed to study the mechanism by which displacements of the intertropical convergence zone (ITCZ) are forced from the extratropics. The northern extratropics are cooled and the southern extratropics are warmed by an imposed cross-equatorial flux beneath the mixed layer, forcing a southward shift in the ITCZ. The ITCZ displacement can be understood in terms of the degree of compensation between the imposed oceanic flux and the resulting response in the atmospheric energy transport in the tropics. The magnitude of the ITCZ displacement is very sensitive to a parameter in the convection scheme that limits the entrainment into convective plumes. The change in the convection scheme affects the extratropical–tropical interactions in the model primarily by modifying the cloud response. The results raise the possibility that the response of tropical precipitation to extratropical thermal forcing, important for a variety of problems in climate dynamics (such as the response of the tropics to the Northern Hemisphere ice sheets during glacial maxima or to variations in the Atlantic meridional overturning circulation), may be strongly dependent on cloud feedback. The model configuration described here is suggested as a useful benchmark helping to quantify extratropical–tropical interactions in atmospheric models.
Increasing sea surface temperatures in the tropical Atlantic Ocean and measures of Atlantic hurricane activity have been reported to be strongly correlated since at least 1950 (refs 1, 2, 3, 4, 5), raising concerns that future greenhouse-gas-induced warming6 could lead to pronounced increases in hurricane activity. Models that explicitly simulate hurricanes are needed to study the influence of warming ocean temperatures on Atlantic hurricane activity, complementing empirical approaches. Our regional climate model of the Atlantic basin reproduces the observed rise in hurricane counts between 1980 and 2006, along with much of the interannual variability, when forced with observed sea surface temperatures and atmospheric conditions7. Here we assess, in our model system7, the changes in large-scale climate that are projected to occur by the end of the twenty-first century by an ensemble of global climate models8, and find that Atlantic hurricane and tropical storm frequencies are reduced. At the same time, near-storm rainfall rates increase substantially. Our results do not support the notion of large increasing trends in either tropical storm or hurricane frequency driven by increases in atmospheric greenhouse-gas concentrations.
Lee, M-I, M J Suarez, I-S Kang, Isaac M Held, and D Kim, October 2008: A moist benchmark calculation for atmospheric general circulation models. Journal of Climate, 21(19), DOI:10.1175/2008JCLI1891.1. Abstract
A benchmark calculation is designed to compare the climate and climate sensitivity of atmospheric general circulation models (AGCMs). The experimental setup basically follows that of the aquaplanet experiment (APE) proposed by Neale and Hoskins, but a simple mixed layer ocean is embedded to enable air–sea coupling and the prediction of surface temperature. In calculations with several AGCMs, this idealization produces very strong zonal-mean flow and exaggerated ITCZ strength, but the model simulations remain sufficiently realistic to justify the use of this framework in isolating key differences between models. Because surface temperatures are free to respond to model differences, the simulation of the cloud distribution, especially in the subtropics, affects many other aspects of the simulations. The analysis of the simulated tropical transients highlights the importance of convection inhibition and air–sea coupling as affected by the depth of the mixed layer. These preliminary comparisons demonstrate that this idealized benchmark provides a discriminating framework for understanding the implications of differing physics parameterization in AGCMs.
Medeiros, Brian, Bjorn Stevens, Isaac M Held, Ming Zhao, D L Williamson, J Olson, and Christopher S Bretherton, October 2008: Aquaplanets, climate sensitivity, and low clouds. Journal of Climate, 21(19), DOI:10.1175/2008JCLI1995.1. Abstract
Cloud effects have repeatedly been pointed out as the leading source of uncertainty in projections of future climate, yet clouds remain poorly understood and simulated in climate models. Aquaplanets provide a simplified framework for comparing and understanding cloud effects, and how they are partitioned as a function of regime, in large-scale models. This work uses two climate models to demonstrate that aquaplanets can successfully predict a climate model's sensitivity to an idealized climate change. For both models, aquaplanet climate sensitivity is similar to that of the realistic configuration. Tropical low clouds appear to play a leading role in determining the sensitivity. Regions of large-scale subsidence, which cover much of the tropics, are most directly responsible for the differences between the models. Although cloud effects and climate sensitivity are similar for aquaplanets and realistic configurations, the aquaplanets lack persistent stratocumulus in the tropical atmosphere. This, and an additional analysis of the cloud response in the realistically configured simulations, suggests the representation of shallow (trade wind) cumulus convection, which is ubiquitous in the tropics, is largely responsible for differences in the simulated climate sensitivity of these two models.
The extent to which the climate will change due to an external forcing depends largely on radiative feedbacks, which act to amplify or damp the surface temperature response. There are a variety of issues that complicate the analysis of radiative feedbacks in global climate models, resulting in some confusion regarding their strengths and distributions. In this paper, the authors present a method for quantifying climate feedbacks based on “radiative kernels” that describe the differential response of the top-of-atmosphere radiative fluxes to incremental changes in the feedback variables. The use of radiative kernels enables one to decompose the feedback into one factor that depends on the radiative transfer algorithm and the unperturbed climate state and a second factor that arises from the climate response of the feedback variables. Such decomposition facilitates an understanding of the spatial characteristics of the feedbacks and the causes of intermodel differences. This technique provides a simple and accurate way to compare feedbacks across different models using a consistent methodology. Cloud feedbacks cannot be evaluated directly from a cloud radiative kernel because of strong nonlinearities, but they can be estimated from the change in cloud forcing and the difference between the full-sky and clear-sky kernels. The authors construct maps to illustrate the regional structure of the feedbacks and compare results obtained using three different model kernels to demonstrate the robustness of the methodology. The results confirm that models typically generate globally averaged cloud feedbacks that are substantially positive or near neutral, unlike the change in cloud forcing itself, which is as often negative as positive
Chen, Gang, Isaac M Held, and W A Robinson, August 2007: Sensitivity of the Latitude of the Surface Westerlies to Surface Friction. Journal of the Atmospheric Sciences, 64(8), DOI:10.1175/JAS3995.1. Abstract
The sensitivity to surface friction of the latitude of the surface westerlies and the associated eddy-driven midlatitude jet is studied in an idealized dry GCM. The westerlies move poleward as the friction is reduced in strength. An increase in the eastward phase speed of midlatitude eddies is implicated as playing a central role in this shift.
This shift in latitude is mainly determined by changes in the friction on the zonal mean flow rather than the friction on the eddies. If the friction on the zonal mean is reduced instantaneously, the response reveals two distinctive adjustment time scales. In the fast adjustment over the first 10–20 days, there is an increase in the barotropic component of zonal winds and a substantial decrease in the eddy kinetic energy; the shift in the surface westerlies and jet latitude occurs in a slower adjustment. The space–time eddy momentum flux spectra suggest that the key to the shift is a poleward movement in the subtropical critical latitude associated with the faster eastward phase speeds in the dominant midlatitude eddies. The view is supported by simulating the upper-tropospheric dynamics in a stochastically stirred nonlinear shallow water model.
Chen, Gang, and Isaac M Held, November 2007: Phase speed spectra and the recent poleward shift of Southern Hemisphere surface westerlies. Geophysical Research Letters, 34, L21805, DOI:10.1029/2007GL031200. Abstract
The poleward shift of the Southern Hemisphere surface westerlies in recent decades is examined in reanalysis data and in the output of coupled atmosphere-ocean and uncoupled atmospheric models. The space-time spectra of the eddy momentum fluxes in the upper troposphere reveal a trend that marks an increase in the eastward phase speed of the tropospheric eddies accompanied by a poleward displacement of the region of wave breaking in the subtropics. A dynamical mechanism is suggested that may help explain the connections among the lower stratospheric wind anomalies, the increased eastward propagation of tropospheric eddies and the poleward shift of the tropospheric circulation.
Christensen, J H., and Isaac M Held, et al., 2007: Regional climate projections In Climate Change 2007: The Physical Science Basis, Cambridge University Press, Cambridge, UK, Cambridge University Press, 847-940.
Frierson, D M., Isaac M Held, and Pablo Zurita-Gotor, May 2007: A gray-radiation aquaplanet moist GCM. Part II: Energy transports in altered climates. Journal of the Atmospheric Sciences, 64(5), DOI:10.1175/JAS3913.1. Abstract
A simplified moist general circulation model is used to study changes in the meridional transport of moist static energy by the atmosphere as the water vapor content is increased. The key assumptions of the model are gray radiation, with water vapor and other constituents having no effect on radiative transfer, and mixed layer aquaplanet boundary conditions, implying that the atmospheric meridional energy transport balances the net radiation at the top of the atmosphere. These simplifications allow the authors to isolate the effect of moisture on energy transports by baroclinic eddies in a relatively simple setting.
The authors investigate the partition of moist static energy transport in the model into dry static energy and latent energy transports as water vapor concentrations are increased, by varying a constant in the Clausius–Clapeyron relation. The increase in the poleward moisture flux is rather precisely compensated by a reduction in the dry static energy flux. These results are interpreted with diffusive energy balance models (EBMs). The simplest of these is an analytic model that has the property of exact invariance of total energy flux as the moisture content is changed, but the assumptions underlying this model are not accurately satisfied by the GCM. A more complex EBM that includes expressions for the diffusivity, length scale, velocity scale, and latitude of maximum baroclinic eddy activity provides a better fit to the GCM’s behavior.
Convection cannot be explicitly resolved in general circulation models given their typical grid size of 50 km or larger. However, by multiplying the vertical acceleration in the equation of motion by a constant larger than unity, the horizontal scale of convection can be increased at will, without necessarily affecting the larger-scale flow. The resulting hypohydrostatic system has been recognized for some time as a way to improve numerical stability on grids that cannot well resolve nonhydrostatic gravity waves. More recent studies have explored its potential for better representing convection in relatively coarse models.
The recent studies have tested the rescaling idea in the context of regional models. Here the authors present global aquaplanet simulations with a low-resolution, nonhydrostatic model free of convective parameterization, and describe the effect on the global climate of very large rescaling of the vertical acceleration. As the convection expands to resolved scales, a deepening of the troposphere, a weakening of the Hadley cell, and a moistening of the lower troposphere is found, compared to solutions in which the moist convection is essentially hydrostatic. The growth rate of convective instability is reduced and the convective life cycle is lengthened relative to synoptic phenomena. This problematic side effect is noted in earlier studies and examined further here.
Held, Isaac M., Ming Zhao, and Bruce Wyman, January 2007: Dynamic radiative-convective equilibria using GCM column physics. Journal of the Atmospheric Sciences, 64(1), 228-238. Abstract PDF
The behavior of a GCM column physics package in a nonrotating, doubly periodic, homogeneous setting with prescribed SSTs is examined. This radiative–convective framework is proposed as a useful tool for studying some of the interactions between convection and larger-scale dynamics and the effects of differing modeling assumptions on convective organization and cloud feedbacks.
For the column physics utilized here, from the Geophysical Fluid Dynamics Laboratory (GFDL) AM2 model, many of the properties of the homogeneous, nonrotating model are closely tied to the fraction of precipitation that is large-scale, rather than convective. Significant large-scale precipitation appears above a critical temperature and then increases with further increases in temperature. The amount of large-scale precipitation is a function of horizontal resolution and can also be controlled by modifying the convection scheme, as is illustrated here by modifying assumptions concerning entrainment into convective plumes. Significant similarities are found between the behavior of the homogeneous model and that of the Tropics of the parent GCM when ocean temperatures are increased and when the convection scheme is modified.
Held, Isaac M., 2007: Progress and problems in large-scale atmospheric dynamics In The Global Circulation of the Atmosphere, T. Schneider and A. Sobel, eds., Princeton, NJ, Princeton University Press, 1-21.
A model diagnosis has been performed on the nocturnal Great Plains low-level jet (LLJ), which is one of the key elements of the warm season regional climate over North America. The horizontal–vertical structure, diurnal phase, and amplitude of the LLJ are well simulated by an atmospheric general circulation model (AGCM), thus justifying a reevaluation of the physical mechanisms for the formation of the LLJ based on output from this model. A diagnosis of the AGCM data confirms that two planetary boundary layer (PBL) processes, the diurnal oscillation of the pressure gradient force and of vertical diffusion, are of comparable importance in regulating the inertial oscillation of the winds, which leads to the occurrence of maximum LLJ strength during nighttime. These two processes are highlighted in the theories for the LLJ proposed by Holton (1967) and Blackadar (1957). A simple model is constructed in order to study the relative roles of these two mechanisms. This model incorporates the diurnal variation of the pressure gradient force and vertical diffusion coefficients as obtained from the AGCM simulation. The results reveal that the observed diurnal phase and amplitude of the LLJ can be attributed to the combination of these two mechanisms. The LLJ generated by either Holton’s or Blackadar’s mechanism alone is characterized by an unrealistic meridional phase shift and weaker amplitude.
It is also shown that the diurnal phase of the LLJ exhibits vertical variations in the PBL, more clearly at higher latitudes, with the upper PBL wind attaining a southerly peak several hours earlier than the lower PBL. The simple model demonstrates that this phase tilt is due mainly to sequential triggering of the inertial oscillation from upper to lower PBL when surface cooling commences after sunset. At lower latitudes, due to the change of orientation of prevailing mean wind vectors and the longer inertial period, the inertial oscillation in the lower PBL tends to be interrupted by strong vertical mixing in the following day, whereas in the upper PBL, the inertial oscillation can proceed in a low-friction environment for a relatively longer duration. Thus, the vertical phase tilt initiated at sunset is less evident at lower latitudes.
In
this study, a new modeling framework for simulating Atlantic hurricane
activity is introduced. The model is an 18-km-grid nonhydrostatic regional
model, run over observed specified SSTs and nudged toward observed
time-varying large-scale atmospheric conditions (Atlantic domain wavenumbers
0–2) derived from the National Centers for Environmental Prediction (NCEP)
reanalyses. Using this “perfect large-scale model” approach for 27 recent
August–October seasons (1980–2006), it is found that the model successfully
reproduces the observed multidecadal increase in numbers of Atlantic
hurricanes and several other tropical cyclone (TC) indices over this period.
The correlation of simulated versus observed hurricane activity by year
varies from 0.87 for basin-wide hurricane counts to 0.41 for U.S.
landfalling hurricanes. For tropical storm count, accumulated cyclone
energy, and TC power dissipation indices the correlation is 0.75, for major
hurricanes the correlation is 0.69, and for U.S. landfalling tropical
storms, the correlation is 0.57. The model occasionally simulates hurricanes
intensities of up to category 4 (942 mb) in terms of central pressure,
although the surface winds (< 47 m s-1 ) do not exceed category-2
intensity. On interannual time scales, the model reproduces the observed
ENSO-Atlantic hurricane covariation reasonably well. Some notable aspects of
the highly contrasting 2005 and 2006 seasons are well reproduced, although
the simulated activity during the 2006 core season was excessive. The
authors conclude that the model appears to be a useful tool for exploring
mechanisms of hurricane variability in the Atlantic (e.g., shear versus
potential intensity contributions). The model may be capable of making
useful simulations/projections of pre-1980 or twentieth-century Atlantic
hurricane activity. However, the reliability of these projections will
depend on obtaining reliable large-scale atmospheric and SST conditions from
sources external to the model.
Lee, M-I, S D Schubert, M J Suarez, Isaac M Held, Arun Kumar, T L Bell, J-K E Schemm, Ngar-Cheung Lau, Jeff J Ploshay, H-K Kim, and S-H Yoo, May 2007: Sensitivity to horizontal resolution in the AGCM simulations of warm season diurnal cycle of precipitation over the United States and Northern Mexico. Journal of Climate, 20(9), DOI:10.1175/JCLI4090.1. Abstract
This study examines the sensitivity of the North American warm season diurnal cycle of precipitation to changes in horizontal resolution in three atmospheric general circulation models, with a primary focus on how the parameterized moist processes respond to improved resolution of topography and associated local/regional circulations on the diurnal time scale. It is found that increasing resolution (from approximately 2° to ½° in latitude–longitude) has a mixed impact on the simulated diurnal cycle of precipitation. Higher resolution generally improves the initiation and downslope propagation of moist convection over the Rockies and the adjacent Great Plains. The propagating signals, however, do not extend beyond the slope region, thereby likely contributing to a dry bias in the Great Plains. Similar improvements in the propagating signals are also found in the diurnal cycle over the North American monsoon region as the models begin to resolve the Gulf of California and the surrounding steep terrain. In general, the phase of the diurnal cycle of precipitation improves with increasing resolution, though not always monotonically. Nevertheless, large errors in both the phase and amplitude of the diurnal cycle in precipitation remain even at the highest resolution considered here. These errors tend to be associated with unrealistically strong coupling of the convection to the surface heating and suggest that improved simulations of the diurnal cycle of precipitation require further improvements in the parameterizations of moist convection processes.
Lee, M-I, S D Schubert, M J Suarez, Isaac M Held, Ngar-Cheung Lau, Jeff J Ploshay, Arun Kumar, H-K Kim, and J-K E Schemm, June 2007: An analysis of the warm-season diurnal cycle over the continental United States and Northern Mexico in general circulation models. Journal of Hydrometeorology, 8(3), DOI:10.1175/JHM581.1. Abstract
The diurnal cycle of warm-season rainfall over the continental United States and northern Mexico is analyzed in three global atmospheric general circulation models (AGCMs) from NCEP, GFDL, and the NASA Global Modeling Assimilation Office (GMAO). The results for each model are based on an ensemble of five summer simulations forced with climatological sea surface temperatures.
Although the overall patterns of time-mean (summer) rainfall and low-level winds are reasonably well simulated, all three models exhibit substantial regional deficiencies that appear to be related to problems with the diurnal cycle. Especially prominent are the discrepancies in the diurnal cycle of precipitation over the eastern slopes of the Rocky Mountains and adjacent Great Plains, including the failure to adequately capture the observed nocturnal peak. Moreover, the observed late afternoon–early evening eastward propagation of convection from the mountains into the Great Plains is not adequately simulated, contributing to the deficiencies in the diurnal cycle in the Great Plains. In the southeast United States, the models show a general tendency to rain in the early afternoon—several hours earlier than observed. Over the North American monsoon region in the southwest United States and northern Mexico, the phase of the broad-scale diurnal convection appears to be reasonably well simulated, though the coarse resolution of the runs precludes the simulation of key regional phenomena.
All three models employ deep convection schemes that assume fundamentally the same buoyancy closure based on simplified versions of the Arakawa–Schubert scheme. Nevertheless, substantial differences between the models in the diurnal cycle of convection highlight the important differences in their implementations and interactions with the boundary layer scheme. An analysis of local diurnal variations of convective available potential energy (CAPE) shows an overall tendency for an afternoon peak—a feature well simulated by the models. The simulated diurnal cycle of rainfall is in phase with the local CAPE variation over the southeast United States and the Rocky Mountains where the local surface boundary forcing is important in regulating the diurnal cycle of convection. On the other hand, the simulated diurnal cycle of rainfall tends to be too strongly tied to CAPE over the Great Plains, where the observed precipitation and CAPE are out of phase, implying that free atmospheric large-scale forcing plays a more important role than surface heat fluxes in initiating or inhibiting convection.
How anthropogenic climate change will affect hydroclimate in the arid regions of southwestern North America has implications for the allocation of water resources and the course of regional development. Here we show that there is a broad consensus among climate models that this region will dry in the 21st century and that the transition to a more arid climate should already be under way. If these models are correct, the levels of aridity of the recent multiyear drought or the Dust Bowl and the 1950s droughts will become the new climatology of the American Southwest within a time frame of years to decades.
While the Northern Hemisphere mean surface temperature has clearly warmed over the 20th century due in large part to increasing greenhouse gases, this warming has not been monotonic. The departures from steady warming on multidecadal timescales might be associated in part with radiative forcing, especially solar irradiance, volcanoes, and anthropogenic aerosols. It is also possible that internal oceanic variability explains a part of this variation. We report here on simulations with a climate model in which the Atlantic Ocean is constrained to produce multidecadal fluctuations similar to observations by redistributing heat within the Atlantic, with other oceans left free to adjust to these Atlantic perturbations. The model generates multidecadal variability in Northern Hemisphere mean temperatures similar in phase and magnitude to detrended observations. The results suggest that variability in the Atlantic is a viable explanation for a portion of the multidecadal variability in the Northern Hemisphere mean temperature record.
We
present
a
mechanism
for
exchange
of
quantities
between
components
of
a
coupled
Earth
system
model,
where
each
component
is
independently
discretized.
The
exchange
grid
is
formed
by
overlaying
two
grids,
such
that
each
exchange
grid
cell
has
a
unique
parent
cell
on
each
of
its
antecedent
grids.
In
Earth
System
models
in
particular,
processes
occurring
near
component
surfaces
require
special
surface
boundary
layer
physical
processes
to
be
represented
on
the
exchange
grid.
The
exchange
grid
is
thus
more
than
just
a
stage
in
a
sequence
of
regrid-
ding
between
component
grids.
We
present
the
design
and
use
of
a
2-dimensional
exchange
grid
on
a
horizontal
planetary
surface
in
the
GFDL
Flexible
Modeling
System
(FMS),
highlighting
issues
of
parallelism
and
performance
The formulation and simulation characteristics of two new global coupled climate models developed at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL) are described. The models were designed to simulate atmospheric and oceanic climate and variability from the diurnal time scale through multicentury climate change, given our computational constraints. In particular, an important goal was to use the same model for both experimental seasonal to interannual forecasting and the study of multicentury global climate change, and this goal has been achieved.
Two versions of the coupled model are described, called CM2.0 and CM2.1. The versions differ primarily in the dynamical core used in the atmospheric component, along with the cloud tuning and some details of the land and ocean components. For both coupled models, the resolution of the land and atmospheric components is 2° latitude × 2.5° longitude; the atmospheric model has 24 vertical levels. The ocean resolution is 1° in latitude and longitude, with meridional resolution equatorward of 30° becoming progressively finer, such that the meridional resolution is 1/3° at the equator. There are 50 vertical levels in the ocean, with 22 evenly spaced levels within the top 220 m. The ocean component has poles over North America and Eurasia to avoid polar filtering. Neither coupled model employs flux adjustments.
The control simulations have stable, realistic climates when integrated over multiple centuries. Both models have simulations of ENSO that are substantially improved relative to previous GFDL coupled models. The CM2.0 model has been further evaluated as an ENSO forecast model and has good skill (CM2.1 has not been evaluated as an ENSO forecast model). Generally reduced temperature and salinity biases exist in CM2.1 relative to CM2.0. These reductions are associated with 1) improved simulations of surface wind stress in CM2.1 and associated changes in oceanic gyre circulations; 2) changes in cloud tuning and the land model, both of which act to increase the net surface shortwave radiation in CM2.1, thereby reducing an overall cold bias present in CM2.0; and 3) a reduction of ocean lateral viscosity in the extratropics in CM2.1, which reduces sea ice biases in the North Atlantic.
Both models have been used to conduct a suite of climate change simulations for the 2007 Intergovernmental Panel on Climate Change (IPCC) assessment report and are able to simulate the main features of the observed warming of the twentieth century. The climate sensitivities of the CM2.0 and CM2.1 models are 2.9 and 3.4 K, respectively. These sensitivities are defined by coupling the atmospheric components of CM2.0 and CM2.1 to a slab ocean model and allowing the model to come into equilibrium with a doubling of atmospheric CO2. The output from a suite of integrations conducted with these models is freely available online (see http://nomads.gfdl.noaa.gov/).
Manuscript received 8 December 2004, in final form 18 March 2005
Frierson, D M., Isaac M Held, and Pablo Zurita-Gotor, 2006: A Gray-Radiation Aquaplanet moist GCM. Part I: Static stability and eddy scale. Journal of the Atmospheric Sciences, 63(10), DOI:10.1175/JAS3753.1. Abstract
In this paper, a simplified moist general circulation model is developed and used to study changes in the atmospheric general circulation as the water vapor content of the atmosphere is altered. The key elements of the model physics are gray radiative transfer, in which water vapor and other constituents have no effect on radiative fluxes, a simple diffusive boundary layer with prognostic depth, and a mixed layer aquaplanet surface boundary condition. This GCM can be integrated stably without a convection parameterization, with large-scale condensation only, and this study focuses on this simplest version of the model. These simplifications provide a useful framework in which to focus on the interplay between latent heat release and large-scale dynamics. In this paper, the authors study the role of moisture in determining the tropospheric static stability and midlatitude eddy scale. In a companion paper, the effects of moisture on energy transports by baroclinic eddies are discussed.
The authors vary a parameter in the Clausius–Clapeyron relation to control the amount of water in the atmosphere, and consider circulations ranging from the dry limit to 10 times a control value. The typical length scale of midlatitude eddies is found to be remarkably insensitive to the amount of moisture in the atmosphere in this model. The Rhines scale evaluated at the latitude of the maximum eddy kinetic energy fits the model results for the eddy scale well. Moist convection is important in determining the extratropical lapse rate, and the dry stability is significantly increased with increased moisture content.
The current generation of coupled climate models run at the Geophysical Fluid Dynamics Laboratory (GFDL) as part of the Climate Change Science Program contains ocean components that differ in almost every respect from those contained in previous generations of GFDL climate models. This paper summarizes the new physical features of the models and examines the simulations that they produce. Of the two new coupled climate model versions 2.1 (CM2.1) and 2.0 (CM2.0), the CM2.1 model represents a major improvement over CM2.0 in most of the major oceanic features examined, with strikingly lower drifts in hydrographic fields such as temperature and salinity, more realistic ventilation of the deep ocean, and currents that are closer to their observed values. Regional analysis of the differences between the models highlights the importance of wind stress in determining the circulation, particularly in the Southern Ocean. At present, major errors in both models are associated with Northern Hemisphere Mode Waters and outflows from overflows, particularly the Mediterranean Sea and Red Sea.
Using the climate change experiments generated for the Fourth Assessment of the Intergovernmental Panel on Climate Change, this study examines some aspects of the changes in the hydrological cycle that are robust across the models. These responses include the decrease in convective mass fluxes, the increase in horizontal moisture transport, the associated enhancement of the pattern of evaporation minus precipitation and its temporal variance, and the decrease in the horizontal sensible heat transport in the extratropics. A surprising finding is that a robust decrease in extratropical sensible heat transport is found only in the equilibrium climate response, as estimated in slab ocean responses to the doubling of CO2 , and not in transient climate change scenarios. All of these robust responses are consequences of the increase in lower-tropospheric water vapor.
Historical climate simulations of the period 1861–2000 using two new Geophysical Fluid Dynamics Laboratory (GFDL) global climate models (CM2.0 and CM2.1) are compared with observed surface temperatures. All-forcing runs include the effects of changes in well-mixed greenhouse gases, ozone, sulfates, black and organic carbon, volcanic aerosols, solar flux, and land cover. Indirect effects of tropospheric aerosols on clouds and precipitation processes are not included. Ensembles of size 3 (CM2.0) and 5 (CM2.1) with all forcings are analyzed, along with smaller ensembles of natural-only and anthropogenic-only forcing, and multicentury control runs with no external forcing.
Observed warming trends on the global scale and in many regions are simulated more realistically in the all-forcing and anthropogenic-only forcing runs than in experiments using natural-only forcing or no external forcing. In the all-forcing and anthropogenic-only forcing runs, the model shows some tendency for too much twentieth-century warming in lower latitudes and too little warming in higher latitudes. Differences in Arctic Oscillation behavior between models and observations contribute substantially to an underprediction of the observed warming over northern Asia. In the all-forcing and natural-only forcing runs, a temporary global cooling in the models during the 1880s not evident in the observed temperature records is volcanically forced. El Niño interactions complicate comparisons of observed and simulated temperature records for the El Chichón and Mt. Pinatubo eruptions during the early 1980s and early 1990s.
The simulations support previous findings that twentieth-century global warming has resulted from a combination of natural and anthropogenic forcing, with anthropogenic forcing being the dominant cause of the pronounced late-twentieth-century warming. The regional results provide evidence for an emergent anthropogenic warming signal over many, if not most, regions of the globe. The warming signal has emerged rather monotonically in the Indian Ocean/western Pacific warm pool during the past half-century. The tropical and subtropical North Atlantic and the tropical eastern Pacific are examples of regions where the anthropogenic warming signal now appears to be emerging from a background of more substantial multidecadal variability.
The climate feedbacks in coupled ocean–atmosphere models are compared using a coordinated set of twenty-first-century climate change experiments. Water vapor is found to provide the largest positive feedback in all models and its strength is consistent with that expected from constant relative humidity changes in the water vapor mixing ratio. The feedbacks from clouds and surface albedo are also found to be positive in all models, while the only stabilizing (negative) feedback comes from the temperature response. Large intermodel differences in the lapse rate feedback are observed and shown to be associated with differing regional patterns of surface warming. Consistent with previous studies, it is found that the vertical changes in temperature and water vapor are tightly coupled in all models and, importantly, demonstrate that intermodel differences in the sum of lapse rate and water vapor feedbacks are small. In contrast, intermodel differences in cloud feedback are found to provide the largest source of uncertainty in current predictions of climate sensitivity.
The climate response to idealized changes in the atmospheric CO2 concentration by the new GFDL climate model (CM2) is documented. This new model is very different from earlier GFDL models in its parameterizations of subgrid-scale physical processes, numerical algorithms, and resolution. The model was constructed to be useful for both seasonal-to-interannual predictions and climate change research. Unlike previous versions of the global coupled GFDL climate models, CM2 does not use flux adjustments to maintain a stable control climate. Results from two model versions, Climate Model versions 2.0 (CM2.0) and 2.1 (CM2.1), are presented.
Two atmosphere–mixed layer ocean or slab models, Slab Model versions 2.0 (SM2.0) and 2.1 (SM2.1), are constructed corresponding to CM2.0 and CM2.1. Using the SM2 models to estimate the climate sensitivity, it is found that the equilibrium globally averaged surface air temperature increases 2.9 (SM2.0) and 3.4 K (SM2.1) for a doubling of the atmospheric CO2 concentration. When forced by a 1% per year CO2 increase, the surface air temperature difference around the time of CO2 doubling [transient climate response (TCR)] is about 1.6 K for both coupled model versions (CM2.0 and CM2.1). The simulated warming is near the median of the responses documented for the climate models used in the 2001 Intergovernmental Panel on Climate Change (IPCC) Working Group I Third Assessment Report (TAR).
The thermohaline circulation (THC) weakened in response to increasing atmospheric CO2. By the time of CO2 doubling, the weakening in CM2.1 is larger than that found in CM2.0: 7 and 4 Sv (1 Sv 106 m3 s−1), respectively. However, the THC in the control integration of CM2.1 is stronger than in CM2.0, so that the percentage change in the THC between the two versions is more similar. The average THC change for the models presented in the TAR is about 3 or 4 Sv; however, the range across the model results is very large, varying from a slight increase (+2 Sv) to a large decrease (−10 Sv).
Sun, D-Z, T Zhang, C Covey, Stephen A Klein, William D Collins, J J Hack, J T Kiehl, Gerald A Meehl, Isaac M Held, and M J Suarez, 2006: Radiative and Dynamical Feedbacks over the Equatorial Cold Tongue: Results from Nine Atmospheric GCMs. Journal of Climate, 19(16), DOI:10.1175/JCLI3835.1. Abstract
The equatorial Pacific is a region with strong negative feedbacks. Yet coupled general circulation models (GCMs) have exhibited a propensity to develop a significant SST bias in that region, suggesting an unrealistic sensitivity in the coupled models to small energy flux errors that inevitably occur in the individual model components. Could this “hypersensitivity” exhibited in a coupled model be due to an underestimate of the strength of the negative feedbacks in this region? With this suspicion, the feedbacks in the equatorial Pacific in nine atmospheric GCMs (AGCMs) have been quantified using the interannual variations in that region and compared with the corresponding calculations from the observations. The nine AGCMs are the NCAR Community Climate Model version 1 (CAM1), the NCAR Community Climate Model version 2 (CAM2), the NCAR Community Climate Model version 3 (CAM3), the NCAR CAM3 at T85 resolution, the NASA Seasonal-to-Interannual Prediction Project (NSIPP) Atmospheric Model, the Hadley Centre Atmospheric Model (HadAM3), the Institut Pierre Simon Laplace (IPSL) model (LMDZ4), the Geophysical Fluid Dynamics Laboratory (GFDL) AM2p10, and the GFDL AM2p12. All the corresponding coupled runs of these nine AGCMs have an excessive cold tongue in the equatorial Pacific.
The net atmospheric feedback over the equatorial Pacific in the two GFDL models is found to be comparable to the observed value. All other models are found to have a weaker negative net feedback from the atmosphere—a weaker regulating effect on the underlying SST than the real atmosphere. Except for the French (IPSL) model, a weaker negative feedback from the cloud albedo and a weaker negative feedback from the atmospheric transport are the two leading contributors to the weaker regulating effect from the atmosphere. The underestimate of the strength of the negative feedbacks by the models is apparently linked to an underestimate of the equatorial precipitation response. All models have a stronger water vapor feedback than that indicated in Earth Radiation Budget Experiment (ERBE) observations. These results confirm the suspicion that an underestimate of the regulatory effect from the atmosphere over the equatorial Pacific region is a prevalent problem. The results also suggest, however, that a weaker regulatory effect from the atmosphere is unlikely solely responsible for the hypersensitivity in all models. The need to validate the feedbacks from the ocean transport is therefore highlighted.
Since the mid-nineteenth century the Earth's surface has warmed1, 2, 3, and models indicate that human activities have caused part of the warming by altering the radiative balance of the atmosphere1, 3. Simple theories suggest that global warming will reduce the strength of the mean tropical atmospheric circulation4, 5. An important aspect of this tropical circulation is a large-scale zonal (east–west) overturning of air across the equatorial Pacific Ocean—driven by convection to the west and subsidence to the east—known as the Walker circulation6. Here we explore changes in tropical Pacific circulation since the mid-nineteenth century using observations and a suite of global climate model experiments. Observed Indo-Pacific sea level pressure reveals a weakening of the Walker circulation. The size of this trend is consistent with theoretical predictions, is accurately reproduced by climate model simulations and, within the climate models, is largely due to anthropogenic forcing. The climate model indicates that the weakened surface winds have altered the thermal structure and circulation of the tropical Pacific Ocean. These results support model projections of further weakening of tropical atmospheric circulation during the twenty-first century4, 5, 7.
Wyant, M C., Christopher S Bretherton, Julio T Bacmeister, J T Kiehl, Isaac M Held, Ming Zhao, Stephen A Klein, and Brian J Soden, 2006: A comparison of low-latitude cloud properties and their response to climate change in three AGCMs sorted into regimes using mid-tropospheric vertical velocity. Climate Dynamics, 27(2-3), DOI:10.1007/s00382-006-0138-4. Abstract
Low-latitude cloud distributions and cloud responses to climate perturbations are compared in near-current versions of three leading U.S. AGCMs, the NCAR CAM 3.0, the GFDL AM2.12b, and the NASA GMAO NSIPP-2 model. The analysis technique of Bony et al. (Clim Dyn 22:71–86, 2004) is used to sort cloud variables by dynamical regime using the monthly mean pressure velocity ω at 500 hPa from 30S to 30N. All models simulate the climatological monthly mean top-of-atmosphere longwave and shortwave cloud radiative forcing (CRF) adequately in all ω-regimes. However, they disagree with each other and with ISCCP satellite observations in regime-sorted cloud fraction, condensate amount, and cloud-top height. All models have too little cloud with tops in the middle troposphere and too much thin cirrus in ascent regimes. In subsidence regimes one model simulates cloud condensate to be too near the surface, while another generates condensate over an excessively deep layer of the lower troposphere. Standardized climate perturbation experiments of the three models are also compared, including uniform SST increase, patterned SST increase, and doubled CO2 over a mixed layer ocean. The regime-sorted cloud and CRF perturbations are very different between models, and show lesser, but still significant, differences between the same model simulating different types of imposed climate perturbation. There is a negative correlation across all general circulation models (GCMs) and climate perturbations between changes in tropical low cloud cover and changes in net CRF, suggesting a dominant role for boundary layer cloud in these changes. For some of the cases presented, upper-level clouds in deep convection regimes are also important, and changes in such regimes can either reinforce or partially cancel the net CRF response from the boundary layer cloud in subsidence regimes. This study highlights the continuing uncertainty in both low and high cloud feedbacks simulated by GCMs.
Galewsky, J, Adam H Sobel, and Isaac M Held, 2005: Diagnosis of subtropical humidity dynamics using tracers of last saturation. Journal of the Atmospheric Sciences, 62(9), DOI:10.1175/JAS3533.1. Abstract
A technique for diagnosing the mechanisms that control the humidity in a general circulation model (GCM) or observationally derived meteorological analysis dataset is presented. The technique involves defining a large number of tracers, each of which represents air that has last been saturated in a particular region of the atmosphere. The time-mean tracer fields show the typical pathways that air parcels take between one occurrence of saturation and the next. The tracers provide useful information about how different regions of the atmosphere influence the humidity elsewhere. Because saturation vapor pressure is a function only of temperature and assuming mixing ratio is conserved for unsaturated parcels, these tracer fields can also be used together with the temperature field to reconstruct the water vapor field. The technique is first applied to an idealized GCM in which the dynamics are dry and forced using the Held-Suarez thermal relaxation, but the model carries a passive waterlike tracer that is emitted at the surface and lost due to large-scale condensation with zero latent heat release and no condensate retained. The technique provides an accurate reconstruction of the simulated water vapor field. In this model, the dry air in the subtropical troposphere is produced primarily by isentropic transport and is moistened somewhat by mixing with air from lower levels, which has not been saturated since last contact with the surface. The technique is then applied to the NCEP-NCAR reanalysis data from December-February (DJF) 2001/02, using the offline tracer transport model MATCH. The results show that the dryness of the subtropical troposphere is primarily controlled by isentropic transport of very dry air by midlatitude eddies and that diabatic descent from the tropical upper troposphere plays a secondary role in controlling the dryness of the subtropics.
Held, Isaac M., 2005: The gap between simulation and understanding in climate modeling. Bulletin of the American Meteorological Society, 86(11), 1609-1614. Abstract PDF
The problem of creating truly convincing numerical simulations of our Earth's climate will remain a challenge for the next generation of climate scientists. Hopefully, the ever increasing power of computers will make this task somewhat less frustrating than it is at present. But, increasing computational power also raises issues as to how we would like to see climate modeling and the study of climate dynamics evolve in the twenty-first century. One of the key issues we will need to address is the widening gap between simulation and understanding.
The Sahel, the transition zone between the Saharan desert and the rainforests of Central Africa and the Guinean Coast, experienced a severe drying trend from the 1950s to the 1980s, from which there has been partial recovery. Continuation of either the drying trend or the more recent ameliorating trend would have far-ranging implications for the economy and ecology of the region. Coupled atmosphere/ocean climate models being used to simulate the future climate have had difficulty simulating Sahel rainfall variations comparable to those observed, thus calling into question their ability to predict future climate change in this region. We describe simulations using a new global climate model that capture several aspects of the 20th century rainfall record in the Sahel. An ensemble mean over eight realizations shows a drying trend in the second half of the century of nearly half of the observed amplitude. Individual realizations can be found that display striking similarity to the observed time series and drying pattern, consistent with the hypothesis that the observations are a superposition of an externally forced trend and internal variability. The drying trend in the ensemble mean of the model simulations is attributable to anthropogenic forcing, partly to an increase in aerosol loading and partly to an increase in greenhouse gases. The model projects a drier Sahel in the future, due primarily to increasing greenhouse gases.
High-resolution (0.1‹ ~ 0.1‹) geostationary satellite infrared radiances at 11 ƒÊm in combination with gridded (2.5‹ ~ 2.0‹) hourly surface precipitation observations are employed to document the spatial structure of the diurnal cycle of summertime deep convection and associated precipitation over North America. Comparison of the diurnal cycle pattern between the satellite retrieval and surface observations demonstrates the reliability of satellite radiances for inferring the diurnal cycle of precipitation, especially the diurnal phase. On the basis of the satellite radiances, we find that over most land regions, deep convection peaks in the late afternoon and early evening, a few hours later than the peak of land surface temperature. However, strong regional variations exist in both the diurnal phase and amplitude, implying that topography, land-sea contrast, and coastline curvature play an important role in modulating the diurnal cycle. Examples of such effects are highlighted over Florida, the Great Plains, and the North American monsoon region.
for climate research developed at the Geophysical Fluid Dynamics Laboratory (GFDL) are presented. The atmosphere model, known as AM2, includes a new gridpoint dynamical core, a prognostic cloud scheme, and a multispecies aerosol climatology, as well as components from previous models used at GFDL. The land model, known as LM2, includes soil sensible and latent heat storage, groundwater storage, and stomatal resistance. The performance of the coupled model AM2–LM2 is evaluated with a series of prescribed sea surface temperature (SST) simulations. Particular focus is given to the model's climatology and the characteristics of interannual variability related to E1 Niño– Southern Oscillation (ENSO).
One AM2–LM2 integration was performed according to the prescriptions of the second Atmospheric Model Intercomparison Project (AMIP II) and data were submitted to the Program for Climate Model Diagnosis and Intercomparison (PCMDI). Particular strengths of AM2–LM2, as judged by comparison to other models participating in AMIP II, include its circulation and distributions of precipitation. Prominent problems of AM2– LM2 include a cold bias to surface and tropospheric temperatures, weak tropical cyclone activity, and weak tropical intraseasonal activity associated with the Madden–Julian oscillation.
An ensemble of 10 AM2–LM2 integrations with observed SSTs for the second half of the twentieth century permits a statistically reliable assessment of the model's response to ENSO. In general, AM2–LM2 produces a realistic simulation of the anomalies in tropical precipitation and extratropical circulation that are associated with ENSO.
We explore the effects of a quadratic drag, similar to that used in bulk aerodynamic formulas, on the inverse cascade of homogeneous two-dimensional turbulence. If a two-dimensional fluid is forced at a relatively small scale, then an inverse cascade of energy will be generated that may then be arrested by such a drag at large scales. Both scaling arguments and numerical experiments support the idea that in a statistically steady state the length scale of energy-containing eddies will not then depend on the energy input to the system; rather, the only external parameter that defines this scale is the quadratic drag coefficient itself. A universal form of the spectrum is suggested, and numerical experiments are in good agreement. Further, the turbulent transfer of a passive tracer in the presence of a uniform gradient is well predicted by scaling arguments based solely on the energy cascade rate and the nonlinear drag coefficient.
Lapeyre, G, and Isaac M Held, July 2004: The role of moisture in the dynamics and energetics of turbulent baroclinic eddies. Journal of the Atmospheric Sciences, 61(14), 1693-1710. Abstract PDF
The effects of moisture on nonlinear baroclinic eddies are examined in the context of a horizontally homogeneous two-layer quasigeostrophic model. Using an explicit equation for moisture and a simple parameterization of latent heat release, the present study focuses on how moisture affects the statistically steady state of a baroclinically unstable flow. It is shown that, when latent heating is weak, the flow is dominated by jets and baroclinic waves, just as in the corresponding dry model. In this regime, the concept of an effective static stability can be used, which allows one to interpret some aspects of the moist simulations in terms of an equivalent dry model. It is found that a useful way of diagnosing the effective static stability is by relating it to the eddy fluxes of moisture and moist potential vorticity; no a priori theory for its value is presented here. As the strength of latent heating is increased, the flow rather suddenly becomes vortex dominated, with an asymmetry between strong low-level cyclones and weak anticyclones that has no analog in the dry model. It is argued that this asymmetry develops because of a correlation between low-level vorticity and moisture that results from the correlated horizontal transports of moisture and vorticity. The energetics of the simulations and the efficiency of energy production by latent heat release are discussed.
Shell, K M., and Isaac M Held, 2004: Abrupt transition to strong superrotation in an axisymmetric model of the upper troposphere. Journal of the Atmospheric Sciences, 61(23), 2928-2935. Abstract PDF
Abrupt transitions to strongly superrotating states have been found in some idealized models of the troposphere. These transitions are thought to be caused by feedbacks between the eddy momentum flux convergence in low latitudes and the strength of the equatorial flow. The behavior of an axisymmetric shallow-water model with an applied tropical torque is studied here to determine if an abrupt transition can be realized without eddy feedbacks. The upper-tropospheric layer is relaxed to a radiative equilibrium thickness, exchanging mass and thus momentum with the nonmoving lower layer. For low values of the applied torque, the circulation is earthlike; however, for larger values, an abrupt transition to a strongly superrotating state can occur. In some cases, the system remains superrotating as the torque is subsequently decreased. A simple analytical model is used to better understand the system. The bifurcation is caused by a feedback between the applied torque and the strength of the Hadley cell. As the torque increases, the strength of the cell decreases, reducing the damping caused by momentum transfer from the lower layer.
Diffusive eddy closure theory for estimating the poleward heat flux is reexamined and tested in the context of a two-layer homogeneous model. Consideration of the inverse energy cascade induced by baroclinic turbulence on the β plane leads to an expression for diffusivity in terms of the kinetic energy dissipation and the β effect. A key step in the closure is the identification of this diffusivity with that for potential vorticity in the lower of the two layers in the model. This assumption is then combined with an exact expression relating the diffusivity to the baroclinic energy generation and the mean vertical shear. The theory is closed by identifying the kinetic energy dissipation entering the inverse cascade argument with the baroclinic energy production. It is found that the first constraint in isolation based on inverse cascade arguments between the diffusivity of lower-layer potential vorticity and the kinetic energy dissipation is robust and accurate, whereas the final theory relating diffusivity to vertical shear remains useful but has somewhat degraded accuracy and is more sensitive to model parameters, such as numerical resolution and small-scale dissipation. In the limit of large supercriticality, this theory reduces to that of Held and Larichev. However, it is much more accurate in reproducing numerical results from a two-layer homogeneous model on a β plane for the moderate supercriticalities that are typical of model atmospheres. The problems involved in generalizing this result to models with more layers on the vertical or with a continuous stratification are discussed.
Many aspects of geophysical flows can be described compactly in terms of potential vorticity dynamics. Since potential temperature can fluctuate at boundaries, however, the boundary conditions for potential vorticity dynamics are inhomogeneous, which complicates considerations of potential vorticity dynamics when boundary effects are dynamically significant.
A formulation of potential vorticity dynamics is presented that encompasses boundary effects. It is shown that, for arbitrary flows, the generalization of the potential vorticity concept to a sum of the conventional interior potential vorticity and a singular surface potential vorticity allows one to replace the inhomogeneous boundary conditions for potential vorticity dynamics by simpler homogeneous boundary conditions (of constant potential temperature). Functional forms of the surface potential vorticity are derived from field equations in which the potential vorticity and a potential vorticity flux appear as sources of flow quantities in the same way in which an electric charge and an electric current appear as sources of fields in electrodynamics. For the generalized potential vorticity of flows that need be neither balanced nor hydrostatic and that can be influenced by diabatic processes and friction, a conservation law holds that is similar to the conservation law for the conventional interior potential vorticity. The conservation law for generalized potential vorticity contains, in the quasigeostrophic limit, the well-known dual relationship between fluctuations of potential temperature at boundaries and fluctuations of potential vorticity in the interior of quasigeostrophic flows. A nongeostrophic effect described by the conservation law is the induction of generalized potential vorticity by baroclinicity at boundaries, an effect that plays a role, for example, in mesoscale flows past topographic obstacles. Based on the generalized potential vorticity concept, a theory is outlined of how a wake with lee vortices can form in weakly dissipative flows past a mountain. Theoretical considerations and an analysis of a simulation show that a wake with lee vortices can form by separation of a generalized potential vorticity sheet from the mountain surface, similar to the separation of a friction-induced vorticity sheet from an obstacle, except that the generalized potential vorticity sheet can be induced by baroclinicity at the surface.
Held, Isaac M., Mingfang Ting, and H Wang, 2002: Northern winter stationary waves: theory and modeling. Journal of Climate, 15(16), 2125-2144. Abstract PDF
A review is provided of stationary wave theory, the theory for the deviations from zonal symmetry of the climate. To help focus the discussion the authors concentrate exclusively on northern winter. Several theoretical issues, including the external Rossby wave dispersion relation and vertical structure, critical latitude absorption, the nonlinear response to orography, and the interaction of forced wave trains with preexisting zonal asymmetries, are chosen for discussion while simultaneously presenting a decomposition of the wintertime stationary wave field using a nonlinear steady-state model.
Pauluis, O M., and Isaac M Held, 2002: Entropy budget of an atmosphere in radiative-convective equilibrium. Part I: Maximum work and frictional dissipation. Journal of the Atmospheric Sciences, 59(2), 125-139. Abstract PDF
The entropy budget of an atmosphere in radiative-convective equilibrium is analyzed here. The differential heating of the atmosphere, resulting from surface heat fluxes and tropospheric radiative cooling, corresponds to a net entropy sink. In statistical equilibrium, this entropy sink is balanced by the entropy production due to various irreversible processes such as frictional dissipation, diffusion of heat, diffusion of water vapor, and irreversible phase changes. Determining the relative contribution of each individual irreversible process to the entropy budget can provide important information on the behavior of convection.
The entropy budget of numerical simulations with a cloud ensemble model is discussed. In these simulations, it is found that the dominant irreversible entropy source is associated with irreversible phase changes and diffusion of water vapor. In addition, a large fraction of the frictional dissipation results from falling precipitation, and turbulent dissipation accounts for only a small fraction of the entropy production.
This behavior is directly related to the fact that the convective heat transport is mostly due to the latent heat transport. In such cases, moist convection acts more as an atmospheric dehumidifier than as a heat engine. The amount of work available to accelerate convective updrafts and downdrafts is much smaller than predicted by studies that assume that moist convection behaves mostly as a perfect heat engine.
Pauluis, O M., and Isaac M Held, 2002: Entropy budget of an atmosphere in radiative-convective equilibrium. Part II: Latent heat transport and moist processes. Journal of the Atmospheric Sciences, 59(2), 140-149. Abstract PDF
In moist convection, atmospheric motions transport water vapor from earth's surface to the regions where condensation occurs. This transport is associated with three other aspects of convection: the latent heat transport, the expansion work performed by water vapor, and the irreversible entropy production due to diffusion of water vapor and phase changes. An analysis of the thermodynamic transformations of atmospheric water yields what is referred to as the entropy budget of the water substance, providing a quantitative relationship between these three aspects of moist convection. The water vapor transport can be viewed as an imperfect heat engine that produces less mechanical work than the corresponding Carnot cycle because of diffusion of water vapor and irreversible phase changes.
The entropy budget of the water substance provides an alternative method of determining the irreversible entropy production due to phase changes and diffusion of water vapor. This method has the advantage that it does not require explicit knowledge of the relative humidity or of the molecular flux of water vapor for the estimation of the entropy production. Scaling arguments show that the expansion work of water vapor accounts for a small fraction of the work that would be produced in the absence of irreversible moist processes. It is also shown that diffusion of water vapor and irreversible phase changes can be interpreted as the irreversible counterpart to the continuous dehumidification resulting from condensation and precipitation. This leads to a description of moist convection where it acts more as an atmospheric dehumidifier than as a heat engine.
Smith, K S., G Boccaletti, C C Henning, I Marinov, Chi-Yung Tam, Isaac M Held, and Geoffrey K Vallis, 2002: Turbulent diffusion in the geostrophic inverse cascade. Journal of Fluid Mechanics, 469, 13-48. Abstract PDF
Motivated in part by the problem of large-scale lateral turbulent heat transport in the Earth's atmosphere and oceans, and in part by the problem of turbulent transport itself, we seek to better understand the transport of a passive tracer advected by various types of fully developed two-dimensional turbulence. The types of turbulence considered correspond to various relationships between the streamfunction and the advected field. Each type of turbulence considered possesses two quadratic invariants and each can develop an inverse cascade. These cascades can be modified or halted, for example, by friction, a background vorticity gradient or a mean temperature gradient. We focus on three physically realizable cases: classical two-dimensional turbulence, surface quasi-geostrophic turbulence, and shallow-water quasi-geostrophic turbulence at scales large compared to the radius of deformation. In each model we assume that tracer variance is maintained by a large-scale mean tracer gradient while turbulent energy is produced at small scales via random forcing, and dissipated by linear drag. We predict the spectral shapes, eddy scales and equilibrated energies resulting from the inverse cascades, and use the expected velocity and length scales to predict integrated tracer fluxes.
When linear drag halts the cascade, the resulting diffusivities are decreasing functions of the drag coefficient, but with different dependences for each case. When [beta] is significant, we find a clear distinction between the tracer mixing scale, which depends on [beta] but is nearly independent of drag, and the energy-containing (or jet) scale, set by a combination of the drag coefficient and [beta]. Our predictions are tested via high- resolution spectral simulations. We find in all cases that the passive scalar is diffused down-gradient with a diffusion coefficient that is well-predicted from estimates of mixing length and velocity scale obtained from turbulence phenomenology.
Sobel, Adam H., Isaac M Held, and Christopher S Bretherton, 2002: The ENSO signal in tropical tropospheric temperature. Journal of Climate, 15(18), 2702-2706. Abstract PDF
Interannual anomalies in tropical tropospheric temperature have been shown to be related to interannual anomalies in tropical mean sea surface temperature (SST) by a simple moist adiabatic relationship. On physical grounds, it is less obvious than it might at first seem that this should be the case. It is expected that the free-tropospheric temperature should be sensitive primarily to SST anomalies in regions in which the mean SST is high and deep convection is frequent, rather than to the tropical mean SST. The tropical mean also includes nonconvecting regions in which the SST has no direct way of influencing the free troposphere. However, interannual anomalies of SST averaged over regions of high monthly mean precipitation are very similar to interannual anomalies of tropical mean SST. Empirical orthogonal function analysis of the monthly SST histograms for the period of 1982–98 reveals a leading mode, well separated from the others, whose structure is very similar to a simple shift of the annual and climatological mean histogram, without change of shape. As a consequence, many different ways of sampling the histogram will yield similar anomaly time series, and the adequacy of the mean SST for predicting the tropospheric temperature appears coincidental from the point of view of the uncoupled atmospheric problem with given SST. There is a suggestion in the results that changes in the histogram shape may be significant for the tropospheric temperature anomalies associated with some large El Niño events and that in those events it is indeed the SST anomalies in the convective regions that are most important in controlling the tropospheric temperature.
Held, Isaac M., 2001: The partitioning of the poleward energy transport between the tropical ocean and atmosphere. Journal of the Atmospheric Sciences, 58(8), 943-948. Abstract PDF
The mass transport in the shallow, wind-driven, overturning cells in the tropical oceans is constrained to be close to the mass transport in the atmospheric Hadley cell, assuming that zonally integrated wind stresses on land are relatively small. Therefore, the ratio of the poleward energy transport in low latitudes in the two media is determined by the ratio of the atmospheric gross static stability to that of the ocean. A qualitative discussion of the gross stability of each medium suggests that the resulting ratio of oceanic to atmospheric energy transport, averaged over the Hadley cell, is roughly equal to the ratio of the heat capacity of water to that of air at constant pressure, multiplied by the ratio of the moist- to the dry-adiabatic lapse rates near the surface. The ratio of oceanic to atmospheric energy transport should be larger than this value near the equator and smaller than this value near the poleward boundary of the Hadley cell.
Kushner, P J., Isaac M Held, and Thomas L Delworth, 2001: Southern Hemisphere atmospheric circulation response to global warming. Journal of Climate, 14(10), 2238-2249. Abstract PDF
The response of the Southern Hemisphere (SH), extratropical, atmospheric general circulation to transient, anthropogenic, greenhouse warming is investigated in a coupled climate model. The extratropical circulation response consists of a SH summer half-year poleward shift of the westerly jet and a year-round positive wind anomaly in the stratosphere and the tropical upper troposphere. Along with the poleward shift of the jet, there is a poleward shift of several related fields, including the belt of eddy momentum-flux convergence and the mean meridional overturning in the atmosphere and in the ocean. The tropospheric wind response projects strongly onto the model's "Southern Annular Mode" (also known as the "Antarctic oscillation"), which is the leading pattern of variability of the extratropical zonal winds.
Pauluis, O M., V Balaji, and Isaac M Held, 2001: Reply. Journal of the Atmospheric Sciences, 58(9), 1178-1179.
Schneider, Tapio, and Isaac M Held, 2001: Discriminants of Twentieth-Century changes in earth surface temperatures. Journal of Climate, 14(3), 249-254. Abstract PDF
An approach to identifying climate changes is presented that does not hinge on simulations of natural climate variations or anthropogenic changes. Observed interdecadal climate variations are decomposed into several discriminants, mutually uncorrelated spatiotemporal components with a maximal ratio of interdecadal-to-intradecadal variance. The dominant discriminants of twentieth-century variations in surface temperature exhibit large-scale warming in which, particularly in the Northern Hemisphere summer months, localized cooling is embedded. The structure of the large-scale warming is consistent with expected effects of increases in greenhouse gas concentrations. The localized cooling, with maxims on scales of 1000-2000 km over East Asia, eastern Europe, and North America, is suggestive of radiative effects of anthropogenic sulfate aerosols.
Stocker, T F., Thomas L Delworth, Stephen M Griffies, Isaac M Held, V Ramaswamy, and Brian J Soden, et al., 2001: Physical climate processes and feedbacks In Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge, UK, Cambridge University Press, 418-470.
Water vapor is the dominant greenhouse gas, the most important gaseous source of infrared opacity in the atmosphere. As the concentrations of other greenhouse gases, particularly carbon dioxide, increase because of human activity, it is centrally important to predict how the water vapor distribution will be affected. To the extent that water vapor concentrations increase in a warmer world, the climatic effects of the other greenhouse gases will be amplified. Models of the Earth's climate indicate that this is an important positive feedback that increases the sensitivity of surface temperatures to carbon dioxide by a factor of two when considered in isolation from other feedbacks, and possibly by as much as a factor of three or more when interactions with other feedbacks are considered. Critics of this consensus have attempted to provide reasons why modeling results are overestimating the strength of this feedback.
Our uncertainty concerning climate sensitivity is disturbing. The range most often quoted for the equilibrium global mean surface temperature response to a doubling of CO2 concentrations in the atmosphere is 1.5°C to 4.5°C. If the Earth lies near the upper bound of this sensitivity range, climate changes in the twenty-first century will be profound. The range in sensitivity is primarily due to differing assumptions about how the Earth's cloud distribution is maintained; all the models on which these estimates are based possess strong water vapor feedback. If this feedback is, in fact, substantially weaker than predicted in current models, sensitivities in the upper half of this range would be much less likely, a conclusion that would clearly have important policy implications. In this review, we describe the background behind the prevailing view on water vapor feedback and some of the arguments raised by its critics, and attempt to explain why these arguments have not modified the consensus within the climate research community.
Pauluis, O M., V Balaji, and Isaac M Held, 2000: Frictional dissipation in a precipitating atmosphere. Journal of the Atmospheric Sciences, 57(7), 989-994. Abstract PDF
The frictional dissipation in the shear zone surrounding falling hydrometeors is estimated to be 2-4 W m-2 in the Tropics. A numerical model of radiative-convective equilibrium with resolved three-dimensional moist convection confirms this estimate and shows that the precipitation-related dissipation is much larger than the dissipation associated with the turbulent energy cascade from the convective scale. Equivalently, the work performed by moist convection is used primarily to lift water rather than generate kinetic energy of the convective airflow. This fact complicates attempts to use the entropy budget to derive convective velocity scales.
Eddy length scales, eddy velocity scales, and the amplitude of eddy fluxes in the mid-latitude troposphere are discussed, primarily from the qualitative perspective provided by studies of quasi-geostrophic turbulence. The utility of a diffusive picture for the near surface poleward flux of heat is emphasized, as is the extent to which a full closure theory for the troposphere, including the interior potential vorticity fluxes, must revolve around this theory for the heat flux. A central problem in general circulation theory is then to determine which factors control the horizontal diffusivity near the surface. The baroclinic eddy production problem has distinctive features that make it stand out from other inhomogeneous turbulence problems such as Benard convection and laboratory shear flows, the crucial point being that there can be scale separation between the eddies and the scale of the mean flow inhomogeneity in the direction of the relevant transport. This scale separation makes diffusive closures more compelling. In addition, it allows one to compute diffusivities from models of homogeneous turbulence.
Held, Isaac M., 1999: Planetary waves and their interaction with smaller scales In The Life Cycles of Extratropical Cyclones, Boston, MA, American Meteorological Society, 101-109.
Held, Isaac M., and Tapio Schneider, 1999: The surface branch of the zonally averaged mass transport circulation in the troposphere. Journal of the Atmospheric Sciences, 56(11), 1688-1697. Abstract PDF
The near-surface branch of the overturning mass transport circulation in the troposphere, containing the equatorward flow, is examined in isentropic and geometric coordinates. A discussion of the zonal momentum balance within isentropic layers shows that the equatorward flow at a given latitude is confined to isentropic layers that typically intersect the surface at that latitude. As a consequence of mass transport within the surface mixed layer, much of the equatorward flow occurs in layers with potential temperatures below the mean surface potential temperature.
In the conventional transformed Eulerian mean formulation for geometric coordinates, the surface branch of the overturning circulation is represented in an unrealistic manner: streamlines of the residual circulation do not close above the surface. A modified residual circulation is introduced that is free from this defect and has the additional advantage that its computation, unlike that of the conventional residual circulation, does not require division by the static stability, which may approach zero in the planetary boundary layer. It is then argued that cold air advection by the residual circulation is responsible for the formation of surface inversions at all latitudes in idealized GCMs with weak thermal damping. Also included is a discussion of how a general circulation theory for the troposphere must be built upon a theory for the near-surface meridional mass fluxes.
Kushner, P J., and Isaac M Held, 1999: Potential vorticity thickness fluxes and wave-mean flow interaction. Journal of the Atmospheric Sciences, 56(7), 948-958. Abstract PDF
The use of eddy flux of thickness between density surfaces has become a familiar starting point in oceanographic studies of adiabatic eddy effects on the mean density distribution. In this study, a dynamical analogy with the density thickness flux approach is explored to reexamine the theory of nonzonal wave-mean flow interaction in two-dimensional horizontal flows. By analogy with the density thickness flux, the flux of thickness between potential vorticity (PV) surfaces is used as a starting point for a residual circulation formulation for nonzonal mean flows. Mean equations for barotropic PV dynamics are derived in which a modified mean velocity with an eddy-induced component advects a modified mean PV that also has an eddy-induced component. For small-amplitude eddies, the results are analogous to recent results of McDougall and McIntosh derived for stratified flow.
The dynamical implications of this approach are then examined. The modified mean PV equation provides a decomposition of the eddy forcing of the mean flow into contributions from wave transience, wave dissipation, and wave-induced mass redistribution between PV contours. If the mean flow is along the mean PV contours, the contribution from wave-induced mass redistribution is "workless" in Plumb's sense that it is equivalent to an eddy-induced stress that is perpendicular to the mean flow. This contribution is also associated with the convergence along the mean streamlines of a modified PV flux that is equal to the difference between the PV flux and the rotational PV flux term identified by Illari and Marshall. The cross-stream component of the modified PV flux is related to wave transience and dissipation.
Zhang, Y, and Isaac M Held, 1999: A linear stochastic model of a GCM's midlatitude storm tracks. Journal of the Atmospheric Sciences, 56(19), 3416-3435. Abstract PDF
A linear stochastic model is used to simulate the midlatitude storm tracks produced by an atmospheric GCM. A series of six perpetual insolation/SST GCM experiments are first performed for each month. These experiments capture the "midwinter suppression" of the Pacific storm track in a particularly clean way. The stochastic model is constructed by linearizing the GCM about its January climatology and finding damping and stirring parameters that best reproduce that model's eddy statistics. The model is tested by examining its ability to simulate other GCM integrations when the basic state is changed to the mean flow of those models, while keeping the stirring and damping unchanged.
The stochastic model shows an impressive ability to simulate a variety of eddy statistics. It captures the midwinter suppression of the Pacific storm track qualitatively and is also capable of simulating storm track responses to El Niño. The model results are sensitive to the manner in which the model is stirred. Best results for eddy variances and fluxes are obtained by stirring the temperature and vorticity at low levels. However, a better simulation of the spatial structure of the dominant wave train as defined by covariance maps is obtained by stirring the temperature equation only, and at all levels.
Kushner, P J., and Isaac M Held, 1998: A test, using atmospheric data, of a method for estimating oceanic eddy diffusivity. Geophysical Research Letters, 25(22), 4213-4216. Abstract PDF
G. Holloway has proposed a simple method to estimate the effective horizontal eddy diffusivity for oceanic tracers using satellite measurements of sea-surface height variability. In this method, the diffusivity is assumed to scale as the r.m.s. eddy geostrophic streamfunction. This method should apply analogously in an atmospheric context, in which the energetic eddies are well resolved in data sets and models, and in which both the effective diffusivity and tracer fluxes can be directly calculated. We evaluate Holloway's method using lower-tropospheric daily atmospheric reanalysis data, and find that at a given height the method successfully yields estimates of the divergent part of the atmospheric sensible heat flux, to within a fairly uniform scaling factor
Swanson, K L., P J Kushner, and Isaac M Held, 1997: Dynamics of barotropic storm tracks. Journal of the Atmospheric Sciences, 54(7), 791-810. Abstract PDF
Longitudinal variations in the upper-troposphere time-mean flow strongly modulate the structure and amplitude of upper-tropospheric eddies. This barotropic modulation is studied using simple models of wave propagation through zonally varying basic states that consist of contours separating regions of uniform barotropic potential vorticity. Such basic states represent in a simple manner the potential vorticity distribution in the upper troposphere. Predictions of the effect of basic-state zonal variations on the amplitude and spatial structure of eddies and their associated particle displacements are made using conservation of wave action or, equivalently, the linearized "pseudoenergy" wave activity. The predictions are confirmed using WKB theory and linear numerical calculations. The interaction of finite-amplitude disturbances with the basic flow is also analyzed numerically using nonlinear contour-dynamical simulations. It is found that breaking nonlinear contour waves undergo irreversible amplitude attenuation, scale lengthening, and frequency lowering upon passing through a region of weak basic-state flow.
Treguier, A M., Isaac M Held, and V D Larichev, 1997: Parameterization of quasigeostrophic eddies in primitive equation ocean models. Journal of Physical Oceanography, 27(4), 567-580. Abstract PDF
A parameterization of mesoscale eddy fluxes in the ocean should be consistent with the fact that the ocean interior is nearly adiabatic. Gent and McWilliams have described a framework in which this can be approximated in z-coordinate primitive equation models by incorporating the effects of eddies on the buoyancy field through an eddy-induced velocity. It is also natural to base a parameterization on the simple picture of the mixing of potential vorticity in the interior and the mixing of buoyancy at the surface. The authors discuss the various constraints imposed by these two requirements and attempt to clarify the appropriate boundary conditions on the eddy-induced velocities at the surface. Quasigeostrophic theory is used as a guide to the simplest way of satisfying these constraints.
Held, Isaac M., and V D Larichev, 1996: A scaling theory for horizontally homogeneous, baroclinically unstable flow on a Beta plane. Journal of the Atmospheric Sciences, 53(7), 946-952. PDF
Kushnir, Y, and Isaac M Held, 1996: Equilibrium atmospheric response to North Atlantic SST anomalies. Journal of Climate, 9(6), 1208-1220. Abstract PDF
The equilibrium general circulation model (GCM) response to sea surface temperature (SST) anomalies in the western North Atlantic region is studied. A coarse resolution GCM, with realistic lower boundary conditions including topography and climatological SST distribution, is integrated in perpetual January and perpetual October modes, distinguished from one another by the strength of the midlatitude westerlies. An SST anomaly with a maximum of 4°C is added to the climatological SST distribution of the model with both positive and negative polarity. These anomaly runs are compared to one another, and to a control integration, to determine the atmospheric response. In all cases warming (cooling) of the midlatitude ocean surface yields a warming (cooling) of the atmosphere over and to the the east of the SST anomaly center. The atmospheric temperature change is largest near the surface and decreases upward. Consistent with this simple thermal response, the geopotential height field displays a baroclinic response with a shallow anomalous low somewhat downstream from the warm SST anomaly. The equivalent barotropic, downstream response is weak and not robust. To help interpret the results, the realistic GCM integrations are compared with parallel idealized model runs. The idealized model has full physics and a similar horizontal and vertical resolution, but an all-ocean surface with a single, permanent zonal asymmetry. The idealized and realistic versions of the GCM display compatible response patterns that are qualitatively consistent with stationary, linear, quasigeostrophic theory. However, the idealized model response is stronger and more coherent. The differences between the two model response patterns can be reconciled based on the size of the anomaly, the model treatment of cloud-radiation interaction, and the static stability of the model atmosphere in the vicinity of the SST anomaly. Model results are contrasted with other GCM studies and observations.
Pavan, V, and Isaac M Held, 1996: The diffusive approximation for eddy fluxes in baroclinically unstable jets. Journal of the Atmospheric Sciences, 53(9), 1262-1272. Abstract PDF
A series of statistically steady states for baroclinically unstable jets in a two-layer quasigeostrophic model is examined, in order to evaluate diffusive approximation to the eddy potential vorticity or heat fluxes. The flow is forced by thermal relaxation to an unstable "radiative equilibrium" temperature gradient. The statistically steady states are studied as a function of the width of the radiative equilibrium jet. A local diffusive "theory" for the eddy fluxes is obtained from integrations of a homogenous, doubly periodic model with prescribed environmental potential vorticity gradients. The flux-gradient relationship generated by the homogenous model predicts the magnitude and shape fo the eddy fluxes in the unstable jet flows remarkably well, as long as the jet is not too narrow. The results confirm the relevance of diffusive closures for eddy potential vorticity and heat fluxes in such flows. For narrow jets that produce eddy fluxes with a half-width of one to two radii of deformation, this local theory underpredicts the fluxes.
Sun, D-Z, and Isaac M Held, 1996: A comparison of modeled and observed relationships between interannual variations of water vapor and temperature. Journal of Climate, 9(4), 665-675. Abstract PDF
The correlations between interannual variations of tropical mean water vapor and temperature in the simulations by a low resolution (R15) GCM are stronger than those in the rawinsonde observations. The rate of fractional increase of tropical mean water vapor with temperature in the model simulations is also larger than that from the observations. The largest discrepancies are found in the region immediately above the tropical convective boundary layer (850-600 mb). The rate of fractional increase of tropical mean water vapor with temperature in the model simulations is close to that for a constant relative humidity. The correlations between variations of water vapor in the upper troposphere and those in the lower troposphere are also stronger in the model simulations than in the observations. In the horizontal, the characteristic spatial patterns of the normalized water vapor variations in the model simulations and observations are similar. The water vapor-temperature relationship in simulations by a GCM with a somewhat higher spatial resolution (R30) is almost identical to that in the simulations by the low resolution (R15) GCM. The implications of these findings for the radiative feedback of water vapor are discussed.
Brantstator, G, and Isaac M Held, 1995: Westward propagating normal modes in the presence of stationary background waves. Journal of the Atmospheric Sciences, 52(2), 247-262. Abstract PDF
Eigenvectors and eigenvalues of the nondivergent barotropic vorticity equation linearized about zonally asymmetric wintertime mean flows are calculated to determine which barotropic modes might contribute to westward propagating disturbances observed in nature. Of particular interest are modes that correspond to a recurring pattern concentrated in the Western Hemisphere with a period of about 25 days reported by Branstator and Kushnir.
The most unstable modes of November-March means from individual years tend to be westward propogating and have a structure that is similar to the observed 25-day pattern.
By following the evolution of each Rossby-Haurwitz mode as the basic state is gradually changed from a state of rest to an observed mean state, it is demonstrated that all but about eight of the Rossby-Haurwitz modes will be modified beyond recognition by the action of the time mean flow. One of these,the second gravest antisymmetric zonal wavenumber-one mode (denoted {1,3} and sometimes referred to as the 16-day wave), has a structure that bears some resemblance to the observed 25-day pattern, but it is typically neutral. The structural similarity between this mode and the 25-day pattern is not as pronounced as the similarity between the most unstable modes and the 25-day pattern. Furthermore, the mode for the observed basic state that {1,3} evolves to depends on the path by which the resting state is transformed into the observed state, suggesting that {1,3} cannot always be thought of as a distinct mode in the presence of a realistic background. The results indicate that even if {1,3} can be considered to exist in wintertime mean flows, it is distinct from the most unstable modes on those flows. By slowly changing the basic states that support the westward propogating unstable modes until they are equal to the climatological January state that earlier studies have shown produces quasi-stationary teleconnection-like modes, it is demonstrated that the unstable westward propagating and quasi-stationary modes are related to each other.
The dynamics of quasi-geostrophic flow with uniform potential vorticity reduces to the evolution of buoyancy, or potential temperature, on horizontal boundaries. There is a formal resemblance to two-dimensional flow, with surface temperature playing the role of vorticity, but a different relationship between the flow and the advected scalar creates several distinctive features. A series of examples are described which highlight some of these features: the evolution of an eliptical vortex; the start-up vortex shed by flow over a mountain; the instability of temperature filaments; the `edge wave' critical layer; and mixing in an overturning edge wave. Characteristics of the direct cascade of the tracer variance to small scales in homogeneous turbulence, as well as the inverse energy cascade, are also described. In addition to its geophysical relevance, the ubiquitous generation of secondary instabilities and the possibility of finite-time collapse make this system a potentially important, numerically tractable, testbed for turbulence theories.
Larichev, V D., and Isaac M Held, 1995: Eddy amplitudes and fluxes in a homogenous model of fully developed baroclinic instability. Journal of Physical Oceanography, 25(10), 2285-2297. Abstract PDF
A horizontally homogenous two-layer quasigeostrophic model with imposed environmental vertical shear is used to study eddy energies and fluxes in the regime in which an inverse barotropic energy cascade excites eddies of much larger scale than the deformation radius. It is shown that the eddy potential vorticity flux, "thickness" flux, and the extraction of energy from the background flow are dominated by the largest eddies excited by the cascade, and not by deformation-scale eddies. The role of the latter is a catalytic one of transferring the baroclinic energy cascading downscale into the barotropic mode, thereby energizing the inverse cascade.
Based on this picture, scaling arguments are developed for the eddy energy level and potential vorticity flux in statistical equilibrium. The potential vorticity flux can be thought of as generated by a diffusivity of magnitude Ukd/k20, where U is the difference between the mean currents in the two layers, kd is the inverse of the deformation radius, and k0 is the wavenumber of the energy-containing eddies. This result is closely related to that proposed by Green, although the underlying dynamical picture is different.
Held, Isaac M., and M J Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bulletin of the American Meteorological Society, 75(10), 1825-1830. Abstract PDF
A benchmark calculation is proposed for evaluating the dynamical cores of atmospheric general circulation models independently of the physical parameterizations. The test focuses on the long-term statistical properties of a fully developed general circulation; thus, it is particularly appropriate for intercomparing the dynamics used in climate models. To illustrate the use of this benchmark, two very different atmospheric dynamical cores-one spectral, one finite difference-are compared. It is found that the long-term statistics produced by the two models are very similar. Selected results from these calculations are presented to initiate the intercomparison.
Kushnir, Y, and Isaac M Held, 1994: The wintertime general circulation model response to North Atlantic SST anomalies In The Atlantic Climate Change Program, Proceedings from the principal investigators meeting, NOAA, University Corporation for Atmospheric Research, 121-124.
Phillipps, Peter, and Isaac M Held, 1994: The response to orbital pertubations in an atmospheric model coupled to a slab ocean. Journal of Climate, 7(5), 767-782. Abstract PDF
The sensitivity of an atmospheric GCM coupled to a mixed-layer ocean to changes in orbital parameters is investigated. Three experiments are compared. One has perihelion at summer solstice and a large obliquity; another has perihelion at winter solstice and low obliquity. The first of these is favorable for warm summers; the second for cool summers. A third experiment, with perihelion at summer solstice and the lower value of obliquity, is used to examine the relative importance of the changes in perihelion and obliquity. The eccentricity is set at 0.04 in all cases.
Surface temperature responses are as large as 15°C, with the largest response over North America in summer. Changes in monsoons and Arctic sea ice are consistent with previous GCM studies. A perpetual summer version of the atmospheric model is used to investigate the positive feedback due to soil moisture. Drying of the soil over North America is found to increase the temperature response by approximately 50% and is also essential to the decrease in summertime precipitation in that region. Soil moisture changes also enhance the precipitation response over central Africa, but have little effect on the model's Asian monsoon.
The orbital parameters most favorable for expansion of the Northern Hemisphere glaciers, that is, minimal seasonality, do not produce permanent snow cover. Several model deficiencies that act to accelerate the melting of snow in spring may be responsible.
Pierrehumbert, R T., Isaac M Held, and K L Swanson, 1994: Spectra of local and nonlocal two-dimensional turbulence. Chaos, Solitons, and Fractals, 4(6), 1111-1116. Abstract
We propose a family of two-dimensional incompressible fluid models indexed by a parameter a e [0, infinity], and discuss the spectral scaling properties for homogenous, isotropic turbulence in these models. The family includes two physically realizable members. It is shown that the enstrophy cascade is spectrally local for a < 2, but becomes dominated by nonlocal interactions for a > 2. Numerical simulations indicate that the spectral slopes are systematically steeper than those predicted by the local scaling argument.
Held, Isaac M., 1993: Large-scale dynamics and global warming. Bulletin of the American Meteorological Society, 74(2), 228-241. Abstract PDF
Predictions of future climate change raise a variety of issues in large-scale atmospheric and oceanic dynamics. Several of these are reviewed in this essay, including the sensitivity of the circulation of the Atlantic Ocean to increasing freshwater input at high latitudes; the possibility of greenhouse cooling in the southern oceans; the sensitivity of monsoonal circulations to differential warming of the two hemispheres; the response of midlatitude storms to changing temperature gradients and increasing water vapor in the atmosphere; and the possible importance of positive feedback between the mean winds and eddy-induced heating in the polar stratosphere.
Radiative-convective statistical equilibria are obtained using a two-dimensional model in which radiative transfer is interactive with the predicted moisture and cloud fields. The domain is periodic in x, with a width of 640 km, and extends from the ground to 26 km. The lower boundary is a fixed-temperature water-saturated surface. The model produces a temperature profile resembling the mean profile observed in the tropics. A number of integrations of several months' duration are described in this preliminary examination of the model's qualitative behavior.
The model generates a QBO-like oscillation in the x-averaged winds with an apparent period of ~60 days. This oscillation extends into the troposphere and influences the convective organization. In order to avoid the associated large vertical wind shears, calculations are also performed in which the x-averaged winds are constrained to vanish. The convection then evolves into a pattern in which rain falls only within a small part of the domain. The moisture field appears to provide the memory that localizes the convection. If the vertical shears are fixed in a modest nonzero value, this localization is avoided. Comparing calculations with surface temperatures of 25°C and 30°C, the planetary albedo is found to decrease with increasing temperature, primarily due to a reduction in low-level cloudiness.
Held, Isaac M., and Peter Phillipps, 1993: Sensitivity of the eddy momentum flux to meridional resolution in atmospheric GCMs. Journal of Climate, 6(3), 499-507. Abstract PDF
GCM experiments with zonally symmetric climates are used to demonstrate that the increase in the meridional eddy momentum fluxes and zonal surface winds that occurs when resolution is increased is primarily due to the increase in meridional rather than zonal resolution. It is argued that the sensitivity to meridional resolution reflects the need to resolve the small scales generated in the Rossby wave field as waves radiate from the midlatitude baroclinic eddy source region into regions with small mean winds. Some additional experiments highlight the sensitivity of surface winds and eddy momentum fluxes to the subgrid-scale horizontal mixing formulation in low-resolution models.
Lee, S, and Isaac M Held, 1993: Baroclinic wave packets in models and observations. Journal of the Atmospheric Sciences, 50(10), 1413-1428. Abstract PDF
Coherent baroclinic wave packets are present in the Southern Hemisphere, most clearly in the summer season. These coherent packets are also found in a hierarchy of models of nonlinear baroclinic instability - a two-layer quasigeostrophic (QG) model on a beta-plane, a two-level primitive equation (PE) model, and a general circulation model. The flows are chaotic, but the packet itself can remain remarkably coherent, despite the complex evolution of the flow within the packet. In both QG and PE models, the packets become more robust as the supercriticality of the flow is reduced. In both models and the observations, the packets move with a group velocity that is greater than the phase speed of the individual disturbances, so that these disturbances exhibit downstream development. The structure of the baroclinic waves in the packet as a function of longitude resembles the life cycles of sinusoidal baroclinic waves as a function of time. More than one packet can exist in the domain at the same time. In the QG model, the number of packets increases in a systematic way as the length of the channel increases.
Stephenson, D B., and Isaac M Held, 1993: GCM response of northern winter stationary waves and storm tracks to increasing amounts of carbon dioxide. Journal of Climate, 6(10), 1859-1870. Abstract PDF
The response of the Geophysical Fluid Dynamics Laboratory (GFDL) coupled ocean-atmosphere R15, 9-level GCM to gradually increasing CO2 amounts is analyzed with emphasis on the changes in the stationary waves and storm tracks in the Northern Hemisphere wintertime troposphere. A large part of the change is described by an equivalent-barotropic stationary wave with a high over eastern Canada and a low over southern Alaska. Consistent with this, the Atlantic jet weakens near the North American coast.
Perpetual winter runs of an R15, nine-level atmospheric GCM with sea surface temperature, sea ice thickness, and soil moisture values prescribed from the coupled GCM results are able to reproduce the coupled model's response qualitatively. Consistent with the weakened baroclinicity associated with the stationary wave change, the Atlantic storm track weakens with increasing CO2 concentrations while the Pacific storm track does not change in strength substantially.
An R15, nine-level atmospheric model linearized about the zonal time-mean state is used to analyze the contributions to the stationary wave response. With mountains, diabatic heating, and transient forcings the linear model gives a stationary wave change in qualitative agreement with the change seen in the coupled and perpetual models. Transients and diabatic heating appear to be the major forcing terms, while changes in zonal-mean basic state and topographic forcing play only a small role. A substantial part of the diabatic response is due to changes in tropical latent heating.
Cook, K H., and Isaac M Held, 1992: The stationary response to large-scale orography in a general circulation model and a linear model. Journal of the Atmospheric Sciences, 49(6), 525-539. Abstract PDF
Stationary waves generated over orography in a linear model and a general circulation model (GCM) are cmpared to examine how the atmosphere's response is established for small mountains and how linear theory breaks down over large orographic features. Both models have nine vertical levels and are low-resolution (R15) spectral models. The linear model solves the stationary linear primitive equations. The GCM's control integration uses zonally uniform and hemispherically symmetric boundary conditions, with a global swamp surface. Five experiments are performed by perturbing the GCM with Gaussian mountains of various heights introduced in midlatitudes. The stationary wave model is linearized about zonal mean fields from the GCM climatology.
The linear model's response to a Gaussian mountain at 45°N latitude is dominated by a single wave train radiating toward the southeast. For mountain heights between 0.7 and 2 km, the GCM's stationary waves are similar to the linear model response to orography, although amplitudes increase less rapidly than linearly with mountain height. For larger mountains, closed isentropes and distinctly nonlinear flow occur along the surface of the mountain and a large poleward-radiating wave train develops. The development of closed isentropes, and the breakdown of linear theory, can be predicted whenever the slope of the surface exceeds the slope of the isentropes in the unperturbed (no mountain) basic state.
Garner, Stephen T., N Nakamura, and Isaac M Held, 1992: Nonlinear equilibration of two-dimensional eady waves: a new perspective. Journal of the Atmospheric Sciences, 49(21), 1984-1996. Abstract PDF
The equilibration of two-dimensional baroclinic waves differs fundamentally from equilibration in three dimensions because two-dimensional eddies cannot develop meridional temperature or velocity structure. It was shown in an earlier paper that frontogenesis together with diffusive mixing in a two-dimensional Eady wave brings positive potential vorticity (PV) anomalies deep into the atmosphere from both boundaries and allows the disturbance to settle into a steady state without meridional gradients. Here we depart from the earlier explanation of this equilibration and associate the PVintrusions with essentially the same kind of vortex "roll-up" that characterizes the evolution of barotropic shear layers. To avoid subgrid turbulence parameterizations and computational diffusion, the analogy is developed using Eady's generalized baroclinic instability problem. Eady's generalized model has two semi-infinite regions of large PV surrounding a layer of relatively small PV. Without boundaries, frontal collapse, or strong diffusion the model still produces equilibrated states, with structure similar to the vortex streets that emerge from unstable barotropic shear layers. The similarity is greatest when the baroclinic development is viewed in isentropic coordinates. The contrast between the present equilibrated solutions, which exhibit no vertical tilt, and Blumen's diffusive frontogenesis model, which allows the wave to retain its phase tilt, is briefly discussed. The equilibration of two-dimensional baroclinic waves differs fundamentally from equilibration in three dimensions because two-dimensional eddies cannot develop meridional temperature or velocity structure. It was shown in an earlier paper that frontogenesis together with diffusive mixing in a two-dimensional Eady wave brings positive potential vorticity (PV) anomalies deep into the atmosphere from both boundaries and allows the disturbance to settle into a steady state without meridional gradients. Here we depart from the earlier explanation of this equilibration and associate the PVintrusions with essentially the same kind of vortex "roll-up" that characterizes the evolution of barotropic shear layers. To avoid subgrid turbulence parameterizations and computational diffusion, the analogy is developed using Eady's generalized baroclinic instability problem. Eady's generalized model has two semi-infinite regions of large PV surrounding a layer of relatively small PV. Without boundaries, frontal collapse, or strong diffusion the model still produces equilibrated states, with structure similar to the vortex streets that emerge from unstable barotropic shear layers. The similarity is greatest when the baroclinic development is viewed in isentropic coordinates. The contrast between the present equilibrated solutions, which exhibit no vertical tilt, and Blumen's diffusive frontogenesis model, which allows the wave to retain its phase tilt, is briefly discussed.
Held, Isaac M., and E O'Brien, 1992: Quasigeostrophic turbulence in a three-layer model: effects of vertical structure in the mean shear. Journal of the Atmospheric Sciences, 49(19), 1861-1870. Abstract PDF
A three-layer, horizontally homogeneous, quasigeostrophic model is selected as one of the simplest environments in which to study the sensitivity of baroclinic eddy fluxes in the atmosphere to the vertical structure of the basic-state temperature gradients or vertical wind shears. Eddy statistics obtained from the model are interpreted in terms of linear theory and a modified "baroclinic adjustment" hypothesis. Both linear theory and the baroclinic adjustment construction are found to provide useful predictions for the vertical structure of the eddy potential vorticity flux.
For equal values of the mean vertical shear, eddy fluxes and energies are greater when the shear is concentrated at lower levels (d2U / dz2 < 0)than when the shear is concentrated at higher levels (d2U / dz2 > 0). Eddy fluxes are more sensitive to lower-than to upper-level mean temperature gradients. This relative sensitivity is a function of g = f2 l / (b N2H), where l is the mean vertical shear and H is the depth of the fluid. It is enhanced as g is reduced, as the unstable modes become shallower, until the eddies become almost completely insensitive to the strength of the upper-layer wind for g < 0.5.
Held, Isaac M., and E O'Brien, 1991: Quasi-geostrophic turbulence in a three-layer model In Eighth Conference on Atmospheric and Oceanic Waves and Stability, Boston, MA, American Meteorological Society, 7-8.
Lee, S, and Isaac M Held, 1991: Baroclinic wave packets in models and observations In Eighth Conference on Atmospheric and Oceanic Waves and Stability, Boston, MA, American Meteorological Society, 71-72.
Lee, S, and Isaac M Held, 1991: Subcritical instability and hysteresis in a two-layer model. Journal of the Atmospheric Sciences, 48(8), 1071-1077. Abstract PDF
A two-layer quasi-geostrophic model forced by surface friction and radiative relaxation to a jetlike wind profile can exist in either a wave-free state or in a finite-amplitude wave state, over a substantial region of the model's parameter space. The friction on the lower layer must be much stronger than the thermal relaxation, and the upper layer must be nearly inviscid, for this behavior to be observed. Consistent with this behavior, weakly unstable waves are found that do not stabilize the flow; instead, their growth rate increases with wave amplitude. We attempt to provide a physical explanation for this behavior in terms of 1) the competition between the stabilizing effect of the lower-layer potential vorticity fluxes and the destabilizing effect of nonlinear critical layer formation associated with the upper-layer fluxes, and 2) the tendency of surface drag to restore the vertical shear at the center of the jet by damping the surface westerlies generated by the baroclinic instability.
Randel, W J., and Isaac M Held, 1991: Phase speed spectra of transient eddy fluxes and critical layer absorption. Journal of the Atmospheric Sciences, 48(5), 688-697. Abstract PDF
Tropospheric zonal mean eddy fluxes of heat and momentum, and the divergence of the Eliassen-palm flux, are decomposed into contributions from different zonal phase speeds. Data analyzed are ECMWF operational global analyses covering 1980-87. Eastward moving medium-scale waves (zonal waves 4-7) dominate the spectra of lower tropospheric heat fluxes in both hemispheres and all seasons. Upper tropospheric wave flux spectra are similar to the low level spectra in midlatitudes, but shift to slower zonal phase speeds as low latitudes are approached. The cause of this shift is the selective absorption of faster moving components in midlatitudes as the waves propagate meridionally. Latitude-phase speed distributions of eddy fluxes are constructed and compared to the zonal mean wind structure. These results demonstrate that upper tropospheric eddies break and decelerate the zonal mean flow approximately 10°-20° in latitude away from their critical line (where phase speed equals zonal wind speed). Comparisons are also made with results from the middle stratosphere.
Tao, X, and Isaac M Held, 1991: Interaction between the subtropic jet and Rossby waves in a multi-layer isentropic model In Eighth Conference on Atmospheric and Oceanic Waves and Stability, Boston, MA, American Meteorological Society, 47-50.
Fyfe, John C., and Isaac M Held, 1990: The two-fifths and one-fifth rules for Rossby wave breaking in the WKB limit. Journal of the Atmospheric Sciences, 40(6), 697-706. Abstract PDF
A stationary Rossby wave, sinusoidal in longitude, is slowly switched on, and the meridional propagation of the resulting wave front through a shear flow is examined. Initially the flow is westerly everywhere and therefore free of critical layers. The transition from reversible to irreversible behavior as the wave amplitude is increased is described. It is shown that under slowly varying conditions in an inviscid quasi-linear model, a steady state is obtained if, and only if, the mean flow is decelerated by less than two-fifths of its initial value as a result of the passage of the wave front. If this passage causes a larger mean flow reduction, a pile-up of wave activity in the shear layer culminates in the generation of a critical layer, qualitatively as in Dunkerton's model of gravity wave-mean flow interaction. This qualitative picture is shown to be preserved in the quasi-linear model when the slowly varying assumption breaks down.
Fully nonlinear calculations show that these quasi-linear results are only part of the story. Once the mean flow is decelerated by two-fifths of its initial value in the fully nonlinear model, rapid wave breaking and irreversible mixing occur in the shear layer. But more slowly developing wave breaking also occurs for wave amplitudes that are too small to produce the two-fifths deceleration. Overturning of contours can be shown to occur in the quasi-linear slowly varying model once the mean flow has been decelerated by one-fifth of its initial value, and this appears to be the critical value for wave breaking to occur in the nonlinear integrations.
Held, Isaac M., and Peter Phillipps, 1990: A barotropic model of the interaction between the Hadley cell and a Rossby wave. Journal of the Atmospheric Sciences, 47(7), 856-869. Abstract PDF
A barotropic model is described that is designed to study the interaction of the Hadley cell with a Rossby wave forced in midlatitudes by a stationary "topographic" source. The Hadley cell is driven by a mass source/sink that is partly fixed, representing solar heating, and partly dependent on the layer thickness, representing infrared cooling. The response of the mean zonal and meridional winds to infinitesimal wave forcing is analyzed in detail; then the forcing is gradually increased to examine the departures from linearity.
Held, Isaac M., and Mingfang Ting, 1990: Orographic versus thermal forcing of stationary waves: The importance of the mean low-level wind. Journal of the Atmospheric Sciences, 47(4), 495-500. Abstract PDF
The amplitude of the linear, stationary response to low-level extratropical heating decreases as the magnitude of the low-level mean flow increases, while the amplitude of the orographically forced waves increases. As a result, linear theory predicts that the relative importance of thermal and orographic forcing for the extratropical stationary wave field is very sensitive to the magnitude of the zonal low-level winds. In the process of illustrating this sensitivity, we also show how the dependence of the orographic response on the low level winds can be distorted by a numerical sigma-coordinate model.
Ting, Mingfang, and Isaac M Held, 1990: The stationary wave response to a tropical SST anomaly in an idealized GCM. Journal of the Atmospheric Sciences, 47(21), 2546-2566. Abstract PDF
The upper tropospheric stationary wave response to a tropical sea surface temperature (SST) anomaly is examined with an idealized general circulation model (GCM) as well as steady linear and nonlinear models. The control climate of the GCM is zonally symmetric; this symmetric climate is then perturbed by a dipolar SST anomaly centered at the equator. Two experiments, with anomaly amplitudes differing by a fact of two, have been conducted. The response is very linear in the amplitude of the SST anomaly.
A steady, baroclinic model linearized about a zonally symmetric basic state simulates the GCM's stationary wave reasonably well when it is forced by anomalous heating as well as anomalous transients. When decomposing the GCMs flow into parts forced separately by heating and transients, tropical transients are found to play a dissipative role to first approximation, reducing the amplitude of the response to heating by a factor of two. The effects of extratropical transients are relatively weak. A steady nonlinear model is also used to evaluate the importance of transients and confirms the diagnosis based on the linear model.
Part of the tropical transients seems to be forced by tropical convection and part by midlatitude disturbances propagating into the tropics. The anomalous extratropical transients include a part related to a shift in the model's storm track and a part related to barotropic instability of the stationary wave, but the effects of both of these changes are relatively weak due to the absence of strong extratropical climatic zonal asymmetries in the model.
The dissipative role of transients in this model is contrasted with the positive feedback found by Held, et al. (1989) in a GCM with realistic boundary conditions. The calculations in that paper are repeated, and the direct linear response to thermal forcing is found to be sensitive to the damping included in the model; but the positive feedback from the transients is robust to changes in the linear model. We speculate that a strong asymmetric storm track, with a well-defined barotropic decay region, is needed for the positive feedback to occur.
Feldstein, S B., and Isaac M Held, 1989: Barotropic decay of baroclinic waves in a two-layer beta-plane model. Journal of the Atmospheric Sciences, 46(22), 3416-3430. Abstract PDF
A two-layer quasi-geostrophic model is used to study the effects of a meridionally sheared zonal flow on the life cycle of a weakly unstable baroclinic wave. In most of the cases analyzed, the fluid is inviscid with the exception of scale-selective fourth-order horizontal diffusion. The initial zonal flow is identically zero in the lower layer. The character of the eddy life cycle in the limit of weak supercriticality is shown to depend on whether or not the meridional shear in the upper layer is strong enough to produce a critical latitude for the wave.
If the shear is sufficiently weak, the wave undergoes periodic amplitude vacillation characterized by symmetric baroclinic growth and baroclinic decay. However, when the meridional shear is strong enough to allow for the existence of a critical layer, the flow undergoes an asymmetric life cycle which resembles that found by Simmons and Hoskins in a primitive equation model on the sphere: the wave grows baroclinically but decays barotropically toward a wave-free state. Throughout the barotropic decay stage, the wave is breaking and being absorbed either at or before the critical layer. As the supercriticality is increased, strong reflection begins to occur at the location of the wave breaking, resulting in irregular amplitude vacillaton. Consistent with critical layer theory, when a reflecting state is created the solution is sensitive to the inclusion of higher zonal harmonics of the fundamental wave.
By relaxing the potential vorticity distribution back to an unstable state, periodic solutions are obtained in which each episode of growth and decay is similar to that found in these nearly inviscid solutions.
Held, Isaac M., S W Lyons, and S Nigam, 1989: Transients and the extratropical response to El Niño. Journal of the Atmospheric Sciences, 46(1), 163-174. Abstract PDF
A baroclinic stationary wave model linearized about a zonally symmetric flow is used to interpret the extratropical atmospheric response to El Niño produced by a general circulation model. When forced by the anomalous diabatic heating and tendency due to transients, the linear model provides a useful simulation of this response. The direct response to anomalous diabatic heating is found to be small in the extratropics; the dominant term is the response to the anomalous transients, particularly the anomalous upper tropospheric transients in the vorticity equation. These results are complementary to those obtained with a nonlinear barotropic model by Held and Kang, and indicate that the anomalous subtropical convergence which plays a key role in that study is itself primarily forced by the anomalous transients. One can distinguish between two distinct parts of the response of the transients to the tropical heating: the movement of the Pacific storm track associated with the anomalous extratropical wave train, and changes in the penetration of Rossby waves into the tropics resulting from the modified tropical winds.
Nakamura, N, and Isaac M Held, 1989: Nonlinear equilibration of two-dimensional eady waves. Journal of the Atmospheric Sciences, 46(19), 3055-3064. Abstract PDF
The initial-value problem for Eady's model is reexamined using a two-dimensional (x-z) primitive equation model. It is generally accepted that a finite amplitude instability of Eady's basic state will produce a frontal discontinuity in a finite time. When diffusion prevents the frontal discontinuity from forming, the wave amplitude eventually stops growing and begins to oscillate. We analyze this equilibration and suggest that it is a result of enhanced potential vorticity in the frontal region that is mixed into the interior from the boundaries. The dynamics of equilibration is crudely captured in a modified quasi-geostrophic model in which the zonal-mean static stability is allowed to vary. The magnitude of the meridional wind speed of the equlibrated wave is O(N0H), where N0 is the initial buoyancy frequency and H is the depth of the fluid. This is of the same order as the amplitude of the wave predicted by semigeostrophic theory at the point of frontal collapse. Scaling arguments are presented to determine the three-dimensional flows for which this equilibration mechanism should be important. It is argued that this mechanism is likely to be of some importance for shallow cyclones forming in regions of weak low-level static stability.
Cook, K H., and Isaac M Held, 1988: Stationary waves of the ice age climate. Journal of Climate, 1(8), 807-819. Abstract PDF
A linearized, steady state, primitive equation model is used to simulate the climatological zonal asymmetries (stationary eddies) in the wind and temperature fields of the 18000 YBP climate during winter. We compare these results with the eddies simulated in the ice age experiments of Broccoli and Manabe, who used CLIMAP boundary conditions and reduced atmospheric CO2 in an atmospheric general circulation model (GCM) coupled with a static mixed layer ocean model. The agreement between the models is good, indicating that the linear model can be used to evaluate the relative influences of orography, diabatic heating, and transient eddy heat and momentum transports in generating stationary waves. We find that the orographic forcing dominates in the ice age climate. The mechanical influence of the continental ice sheets on the atmosphere is responsible for most of the changes between the present day and ice age stationary eddies. This concept of the ice age climate is complicated by the sensitivity of the stationary eddies to the large increase in the magnitude of the zonal mean meridional temperature gradient simulated in the ice age GCM.
Lau, Ngar-Cheung, Isaac M Held, and J David Neelin, 1988: The Madden-Julian Oscillation in an idealized general circulation model. Journal of the Atmospheric Sciences, 45(24), 3810-3832. Abstract PDF
The structure of the intraseasonal oscillations in the tropics of an idealized general circulation model with a zonally symmetric climate is described. Space-time spectra show a peak in zonal winds and velocity potential at the equator in zonal wavenumbers 1 and 2, corresponding to eastward-propagating power at phase speeds of ~ 18 m s-1. This speed is significantly greater than that of the observed oscillation but comparable to that obtained in similar models by Hayashi and Sumi and Swinbank et al. The corresponding eastward-propagating power in the precipitation spectrum is concentrated in wavenumbers 2-5. A composite procedure is used to describe the three-dimensional structure of the model's oscillation. The oscillation is characterized by circulation cells oriented along the equatorial zonal plane, with enhanced precipitation in the region of rising motion. Zonal wind changes tend to be positively correlated with geopotential height changes at the same level. Positive perturbations in the water vapor mixing ratio, evaporation, and lower tropospheric horizontal moisture convergence all exhibit distinct eastward displacements from the center of convection.
Two different linear models are used to interpret the GCM results. The response to the GCM's composited diabatic heating field is first computed using a linear primitive equation model on the sphere. This linear model requires strong damping above the heated region, as well as near the surface, to produce a pattern in rough agreement with the GCM. A simple Kelvin wave-CISK model, in which the vertical structure of the heating is taken from the composite, is then shown to be capable of reproducing the phase speed simulated in the GCM.
Nigam, S, Isaac M Held, and S W Lyons, 1988: Linear simulation of the stationary eddies in a GCM. Part II: The. Journal of the Atmospheric Sciences, 45(9), 1433-1452. Abstract PDF
The validity of linear stationary wave theory in accounting for the zonal asymmetries of the winter-averaged tropospheric circulation obtained in a general circulation model (GCM) is ascertained. The steady linear primitive equation model used towards this end has the same vertical and zonal resolution as the spectral GCM, but is finite-differenced in the meridional direction. It is linearized about a zonally symmetric basic state and forced by topography and 3-dimensional diabatic heating and transient flux convergence fields, all of which are taken from the GCM. As in Part I (in which we studied a GCM with a flat lower boundary), we obtained the best correspondence between the GCM and the linear solutions when when strong Rayleigh friction is included in the linear model not only near the surface, but in the interior of the tropical troposphere as well.
There is sufficient quantitative correspondence between the GCM and the linear solution to justify decomposing the linear simulation into parts forced by different processes, although in some regions, such as over North America, the simulation is unsatisfactory. Different fields give different impressions as to the relative importance of orography, heating, and transients. The eddy zonal vorticity field in the upper troposphere shows the orographic and thermal plus transient contributions to be nearly equal in amplitude, whereas the eddy meridional velocity field, dominated by shorter zonal scales, shows the orographic contribution to be decisively dominant. Although there is no systematic phase relationship between these two contributions, they are roughly in phase over the east Asian coast, where each of them is largest. They also contribute roughly equal amounts to the low level Siberian high.
Other findings are that (i) the 300 mb extratropical response to tropical forcing reaches 50 gpm over Alaska (given our frictional parameterization), which is smaller than the response to local thermal forcing, (ii) the responses to sensible heating and lower tropospheric thermal transients are strongly anticorrelated, and (iii) the circulation in the vicinity of the Andes in the GCM is not attributable to direct mechanical forcing by the mountains.
Panetta, R L., and Isaac M Held, 1988: Baroclinic eddy fluxes in a one-dimensional model of quasi-geostrophic turbulence. Journal of the Atmospheric Sciences, 45(22), 3354-3365. Abstract PDF
Statistically steady states of a two-layer quasi-geostrophic model truncated to retain only the zonal mean flow and one nonzero zonal wavenumber, but with high meridional resolution, are described. The model is forced by imposing a time-mean unstable meridional temperature gradient, assuming that deviations from the time-mean are doubly periodic. A comparison is made with a more conventional channel model with the same zonal truncation, in which the flow is forced by radiative relaxation to an unstable temperature gradient. It is shown that the statistics of the channel model approach those of the doubly periodic model as the width of the unstable region in the former is increased. Implications for parameterization theories are discussed.
Held, Isaac M., 1987: New conservation laws for linear quasi-geostrophic waves in shear. Journal of the Atmospheric Sciences, 44(16), 2349-2351. Abstract PDF
There exists an infinite set of quadratic conserved quantities for linear quasi-geostrophic waves in horizontal and vertical shear, the first two members of the set corresponding to the pseudomomentum and pseudo-energy conservation laws that lead to the Rayleigh-Kuo (or Charney-Stern) and the Fjortoft stability criteria. This infinite hierarchy of conservation laws follows from the conservation of the pseudomomentum in each eigenmode of the shear flow.
Held, Isaac M., and I-S Kang, 1987: Barotropic models of the extratropical response to El Niño. Journal of the Atmospheric Sciences, 44(23), 3576-3586. Abstract PDF
A series of linear and nonlinear barotropic models are used to interpret the extratropical response to El Niño equatorial surface temperatures as simulated by an atmospheric general circulation model (GCM). The divergence, time-mean vorticity tendency due to transients, and the zonal mean flow are specified from the GCM, and the deviation of the streamfunction from its zonal mean flow are specified from the GCM, and the deviation of the streamfunction from its zonal mean at an upper-tropospheric level is predicted. Nonlinear steady-state model s suggest that the extratropical wave train is primarily forced from the central rather than the western Pacific and that subtropical divergence anomalies are of more importance than tropical anomalies. These nonlinear solutions can be reproduced with little loss in accuracy by linearizing about the zonally asymmetric climatological flow. If one linearizes about the zonally symmetric flow, the part of the solution forced from the western Pacific deteriorates significantly. The solution in the tropics and subtropics also deteriorates if advection of vorticity by the divergent flow is omitted.
Forcing by transients plays a secondary role in generating the extratropical wave train in these barotropic models, but it is pointed out that the subtropical convergence that forces the bulk of this wave train could itself be closely related to anomalies in the transient forcing.
An example of the barotropic decay of wavelike midlatitude disturbance in the presence of a shear flow on the sphere is examined. The linear theory for the evolution of the disturbance is first described, with emphasis on the importance of the pseudomomentum spectrum for the resulting drag on the mean flow. After a brief discussion of the ways in which this linear theory can break down, a high-resolution nonlinear numerical model is used to examine the dependence of the mean-flow modification and the qualitative character of the decay on the amplitude of the initial disturbance.
Neelin, J D., and Isaac M Held, 1987: Modeling tropical convergence based on the moist static energy budget. Monthly Weather Review, 115(1), 3-12. Abstract PDF
The vertically integrated moist static energy equation provides a convenient starting point for the construction of simple models of the time-mean low level convergence in the tropics. A vertically integrated measure of the moist static stability, the "gross moist stability," proves to be of central importance. Minima in this quantity mark the positions of the tropical convergence zones. We argue that the positions of these minima are determined by the time-mean moisture field, which is, in turn, closely tied to the time-mean surface temperature.
Neelin, J D., Isaac M Held, and K H Cook, 1987: Evaporation-wind feedback and low-frequency variability in the tropical atmosphere. Journal of the Atmospheric Sciences, 44(16), 2341-2348. Abstract PDF
A mechanism by which feedback between zonal wind perturbations and evaporation can create unstable, low-frequency modes in a simple two-layer model of the tropical troposphere is presented. The modes resemble the 30-50 day oscillation. A series of general circulation model experiments designed to test the effect of suppressing this feedback on low-frequency variability in the model tropics is described. The results suggest that the evaporation-wind feedback can be important to the amplitude of the spectral peak corresponding to the 30-50 day oscillation in the model, but that the existence of the oscillation does not depend on it. The feedback is found to have a much more dramatic effect on low-frequency variability when sea surface temperatures are fixed than when the lower boundary is a zero heat capacity "swamp."
Panetta, R L., Isaac M Held, and R T Pierrehumbert, 1987: External Rossby waves in the two-layer model. Journal of the Atmospheric Sciences, 44(20), 2924-2933. Abstract PDF
In order to clarify the extent to which the two-layer model can successfully simulate the remote tropospheric response to localized stationary forcing, the structure of stationary Rossby waves in the two-layer model is compared with that in continuous models. One finds a close correspondence when the two-layer flow is supercritical in the sense of the Phillips' criterion, except for the possibility of upstream propagation in the two-layer model when the lower-layer wind is small. When the two-layer flow is subcritical, the stationary waves can be very seriously distorted. The manner in which neutral modes are spatially or temporally destabilized by damping in the two-layer model is contrasted with similar results for Charney's model.
Held, Isaac M., R T Pierrehumbert, and R L Panetta, 1986: Dissipative destabilization of external Rossby waves. Journal of the Atmospheric Sciences, 43(4), 388-396. Abstract PDF
External Rossby waves in vertical shear can be destabilized by thermal damping. They can also be destabilized by damping of potential vorticity if this damping is larger in the lower than in the upper troposphere. Results are described in detail for Charney's model. Implications for the effects of diabatic heating and mixing due to smaller scale transients on equivalent barotropic stationary or quasi-stationary long waves are discussed. It is pointed out that energy or potential enstrophy budgets may indicate that transients are damping the long waves while, in fact, their presence is destabilizing these waves.
Kang, I-S, and Isaac M Held, 1986: Linear and nonlinear diagnostic models of stationary eddies in the upper troposphere during northern summer. Journal of the Atmospheric Sciences, 43(24), 3045-3057. Abstract PDF
The upper tropospheric circulation during northern summer produced by a general circulation model (GCM) is studied using linear and nonlinear barotropic models and by analyzing a streamfunction budget. The model experiments and the budget calculations both show a simple Sverdrup balance to be a useful first approximation for the largest scales during this season. In this Sverdrup balance, the advection of planetary vorticity by the divergent component of the flow is found to be significant, particularly in the Southern Hemisphere tropics.
Nonlinear barotropic models improve the simulation of regional structures. The correct position of the Tibetan high is explained by Sverdrup balance, but its amplitude and structure are reasonably well simulated only with the nonlinear models. With climatological forcing, the time-averaged solutions of the nonlinear model are insensitive to the strength of the damping included in the model. The difference between the GCM's climatology and the GCM's flow in a particular summer is more difficult to model because of the large contribution of anomalous transients to the maintenance of the flow. However, strongly damped models produce simulations that bear some resemblance to the anomalous flow, at least in the tropics.
To estimate the potential importance of vertical transport of momentum during moist convection, a damping proportional to the precipitation rate in the GCM is added in the nonlinear model. The estimated damping time scale for the eddy streamfunction is ~ 5 days in the northern tropics, but the changes in the predicted stationary eddy streamfunction are modest.
Nigam, S, Isaac M Held, and S W Lyons, 1986: Linear simulation of the stationary eddies in a general circulation model. Part I: The no-mountain model. Journal of the Atmospheric Sciences, 43(23), 2944-2961. Abstract PDF
The quantitative validity of linear stationary wave theory is examined by comparing the results from a linear primitive equation model on the sphere with the stationary eddies produced by a general circulation model (GCM). The GCM simulated has a flat lower boundary, so that the stationary eddies can be thought of as forced by heating (sensible, latent and radiative) and time-averaged transient eddy flux convergences. Orographic forcing is examined in the second part of this study. The distribution of the diabatic heating and transient eddy flux convergences and the zonally symmetric basic state are taken directly from the GCM's climatology for Northern winter (DJF). Strong Rayleigh friction is included in the linear model wherever the zonal mean wind is small, as well as near the surface.
The linear model is found to simulate the stationary eddy pattern of the GCM with considerable skill in both midlatitudes and the tropics. Some deficiencies include the inaccurate simulation of the upper tropospheric geopotential over North America and distortion of the wind field near the low-level zero-wind line in the subtropics. Decomposition of the linear solution shows that 1) the extratropical upper tropospheric eddy pattern generated by tropical forcing is significant but smaller than that due to extratropical forcing, 2) the upper-level extratropical pattern deteriorates somewhat when forcing by transients is removed, while the low-level pattern deteriorates dramatically and 3) there is considerable compensation between the effects of low-level thermal transients and extratropical sensible heating, to the point that we argue that this decomposition is not physically meaningful. The sensitivity of the results to the Rayleigh friction formulation is discussed, as is the effect of replacing the transients with thermal damping.
Held, Isaac M., 1985: Pseudomomentum and the orthogonality of modes in shear flows. Journal of the Atmospheric Sciences, 42(21), 2280-2288. Abstract PDF
Linear modes on shear flows are not orthogonal in the sense of energy; if two modes are present, the eddy energy is not equal to the sum of the eddy energy in the separate modes. However, linear modes are othogonal in the sense of pseudomomentum (or pseudoenergy). Two applications of this result to planetary waves in horizontal and vertical shear are discussed. 1) The qualitative character of the evolution of a disturbance to a stable meridional shear flow, as described by the barotropic vorticity equation, depends critically on whether the disturbance projects primarily onto discrete modes or onto continuum modes that cascade enstrophy to small meridional scales. It is demonstrated that the pseudomomentum and pseudoenergy orthogonality relations provide a natural framework for examining the relative excitation of discrete and continuum modes. 2) Using a quasi-geostrophic potential vorticity equation, it is shown that pseudomomentum orthogonality provides a simple explanation for how quasi-stationary neutral external modes of large amplitude can be excited by a small initial disturbance.
Held, Isaac M., and B J Hoskins, 1985: Large-scale eddies and the general circulation of the troposphere. Advances in Geophysics, 28A, 3-31. PDF
Held, Isaac M., R L Panetta, and R T Pierrehumbert, 1985: Stationary external Rossby waves in vertical shear. Journal of the Atmospheric Sciences, 42(9), 865-883. Abstract PDF
The structure of stationary Rossby waves in the presence of a mean westerly zonal flow with vertical shear is examined. There is typically only one stationary vertical mode, the external mode, trapped within the troposphere. For more that one tropospheric mode to exist, we find that vertical shears must be smaller than those usually observed in extratropical latitudes. The vertical structure, horizontal wavenumber and group velocity of the external mode, and the projection onto this mode of topographic and thermal forcing are studied with continuous models (a linear shear profile as well as more realistic basic states), and a finite-differenced model with resolution and upper boundary condition similar to that used in GCMs. We point out that the rigid-lid upper boundary condition need not create artificial stationary resonances, as the artificial stationary vertical modes that are created are often horizontally evanescent.
The results are presented in a form which allows one to design the equivalent barotropic model that captures the external mode's contribution to the stationary wave field. It is found, in particular, that the wind blowing over the topography in such a barotropic model should generally be larger than the surface wind but smaller than the wind at the equivalent barotropic level. Also, the group velocity of the stationary external mode in realistic vertical shear is found to be considerably greater than that of the stationary Rossby wave in the equivalent barotropic model.
Sardeshmukh, P D., and Isaac M Held, 1984: The vorticity balance in the tropical upper troposphere of a general circulation model. Journal of the Atmospheric Sciences, 41(5), 768-778. Abstract PDF
The time mean vorticity balance in the summertime tropical upper troposphere of an atmospheric general circulation model constructed at the Geophysical Fluid Dynamics Laboratory is examined, with particular emphasis on the detailed balance in the Tibetan anticyclone. The model produces a reasonable simulation of the large-scale features of the northern summer 200 mb flow in the tropics, without the inclusion of subgrid scale processes that strongly damp the upper tropospheric vorticity. the vorticity balance is essentially nonlinear and nearly inviscid. There is considerable cancellation between the stretching and horizontal advection of vorticity by the time mean flow in the vicinity of the Tibetan anticyclone, with much of the remainder balanced by vertical advection and twisting. Mixing by the resolved transients is not negligible in some regions, but considerably smaller than the horizontal advection overall and less well correlated with the stretching. Subgrid scale mixing (consisting only of a biharmonic horizontal diffusion) plays a negligible role in this vorticity budget.
To relate this study to linear models of the stationary flow in the tropics, the steady state barotropic vorticity equation on the sphere is linearized about the GCM's July mean zonal flow at 200 mb and forced with the GCM's July mean vortex stretching. It is found that the strength of the Tibetan anticyclone can be reproduced only by including a very strong damping of vorticity in this linear model. The strong damping needed by other authors (e.g., Holton and Colton) in their linear diagnoses of the tropical upper tropospheric vorticity balance is therefore interpreted as possibly accounting for neglected nonlinearities, and not necessarily cumulus friction. Our conclusions are, however, potentially suspect, since the terms in our vorticity budget have considerable structure on the smallest scales that can be resolved by the GCM.
Held, Isaac M., 1983: External Rossby waves and the barotropic response to stationary forcing In IAMAP-WMO Symposium on Maintenance of the Quasi-Stationary Components of the Flow in the Atmosphere and in Atmospheric Models, Geneva, Switzerland, World Meteorological Organization, 53-54.
Held, Isaac M., 1983: Stationary and quasi-stationary eddies in the extratropical troposphere: theory In Large-scale Dynamical Processes in the Atmosphere, New York, NY, Academic Press, 127-168. PDF
Held, Isaac M., and D G Andrews, 1983: On the direction of the eddy momentum flux in baroclinic instability. Journal of the Atmospheric Sciences, 40(9), 2220-2231. Abstract PDF
The direction of the vertically-integrated horizontal eddy flux momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eady's model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potential vorticity gradient is negligible. However, some exceptions to this general rule exist.
Nigam, S, and Isaac M Held, 1983: The influence of critical latitude on topographically forced stationary waves in a barotropic model. Journal of the Atmospheric Sciences, 40(11), 2610-2622. Abstract PDF
A nondivergent barotropic model on a sphere is used to study the effects of a critical latitude on stationary atmospheric waves forced by topography. Linear and "quasi-linear" calculations are performed with an idealized wavenumber 3 mountain and with realistic topography. Qusai-linear dynamics, where mean flow changes are due to momentum flux convergence, "form drag" and relaxation to a prescribed climatological mean flow, produces an S-shaped kink in the zonal mean absolute vorticity gradient near the critical latitude, resulting in enhanced reflection. The component of the quasi-linear solution resulting from enhanced reflection at the calculation with realistic topography and zonal flow, this reflected component is found to be dominated by a wave train emanating from the western tropical Pacific and propagating northward and then eastward across the Pacific Ocean and the North American continent. This wave train results from the reflection of the Himalayan wave train at the zero-wind latitude in the tropical winter troposphere.
The vorticity gradients in the monthly mean statistics of Oort (1983) show structure near the critical latitude similar to that produced in our quasi-linear model, suggesting that some reflection of incident Rossby waves is likely in the atmosphere, at least in the western Pacific, and that the wind structure responsible for this reflection may be created in part by the stationary Rossby waves themselves.
Nigam, S, and Isaac M Held, 1983: Linear and quasi-linear stationary waves: influence of a critical latitude In IAMAP-WMO Symposium on Maintenance of the Quasi-Stationary Components of the Flow in the Atmosphere and in Atmospheric Models, Geneva, Switzerland, World Meteorological Organization, 279-282.
Held, Isaac M., 1982: On the height of the tropospause and the static stability of the troposphere. Journal of the Atmospheric Sciences, 39(2), 412-417. Abstract PDF
Speculative arguments are presented that describe how radiative and dynamical constraints conspire to determine the height of the tropopause and the tropospheric static stability in midlatitudes and in the tropics. The arguments suggest an explanation for the observation that climatological isentropic slopes in midlatitudes are close to the critical slope required for baroclinic instability in a two-layer model.
Held, Isaac M., 1982: Climate models and the astronomical theory of the ice ages. Icarus, 50(2-3), 449-461. Abstract PDF
Attempts at determining the climatic response to perturbations in the Earth's orbital parameters are reviewed. The relationship between equilibrium and nonequilibrium responses and its implications for climatic sensitivity are discussed in the context of an empirical model due to Imbrie and Imbrie. Some counterintuitive features of the linear equilibrium response to the perihelion cycle in a simple energy balance model are then described in detail. The results of North and Coakley and of Pollard are examined as examples of results that are, respectively, discouraging and mildly encouraging for proponents of the astronomical theory of the ice ages. The attempt by Suarez and Held to address some of the deficiencies in the simplest energy balance models is reviewed, followed by a brief preview of some calculations of relevance to the ice age problem performed by Manabe and co-workers with an atmospheric general circulation model.
Held, Isaac M., D I Linder, and M J Suarez, 1981: Albedo feedback, the meridional structure of the effective heat diffusivity, and climatic sensitivity: Results from dynamic and diffusive models. Journal of the Atmospheric Sciences, 38(9), 1911-1927. Abstract PDF
The sensitivity of a two-level primitive equation atmospheric model to solar constant perturbations is examined in the presence of surface albedo feedback. The model is simplified to the point that a large number of numerical experiments can be performed and statistically steady states defined with relative ease. Exceptionally sensitive equilibrium states are found that are unrelated to the large and small ice-cap instabilities obtained in the simplest diffusive energy balance models. Similar results are produced in a two-level diffusive model closely patterned after the dynamic model, and in a more highly idealized one-level model, by choosing a diffusivity with pronounced meridional structure resembling that of the effective diffusivity of the dynamic model. Sensitive states occur in the diffusive models when the albedo gradient enters the region equatorward of 60 degrees in which the effective heat diffusivity of the atmosphere increases with increasing latitude.
Haidvogel, D B., and Isaac M Held, 1980: Homogeneous quasi-geostrophic turbulence driven by a uniform temperature gradient. Journal of the Atmospheric Sciences, 37(12), 2644-2660. Abstract PDF
Statistically steady states consistent with a horizontally uniform time-averaged temperature gradient in a two-layer quasi-geostrophic model on a beta-plane are found by numerically integrating the equations for deviations from this mean state in a doubly periodic domain. Based on the result that the flow statistics are not strongly dependent on the size of the domain, it is suggested that this homogeneous flow is physically realizable. Statistically steady states consistent with a horizontally uniform time-averaged temperature gradient in a two-layer quasi-geostrophic model on a beta-plane are found by numerically integrating the equations for deviations from this mean state in a doubly periodic domain. Based on the result that the flow statistics are not strongly dependent on the size of the domain, it is suggested that this homogeneous flow is physically realizable.
The dependence of the eddy heat and potential vorticity fluxes and eddy energy level on various model parameters (the beta effect, surface drag, small-scale horizontal mixing) is described. Implications for eddy flux paramterization theories are discussed.
Held, Isaac M., and A Y Hou, 1980: Nonlinear axially symmetric circulations in a nealy inviscid atmosphere. Journal of the Atmospheric Sciences, 37(3), 515-533. Abstract PDF
The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory [similar to that introduced by Schneider (1977)] is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distributions of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.
Suarez, M J., and Isaac M Held, 1979: The sensitivity of an energy balance climate model to variations in the orbital parameters. Journal of Geophysical Research, 84(C8), 4825-4836. Abstract PDF
The responses of a zonally symmetric model of the global energy balance to perturbations in incident solar radiation are analyzed. The model is forced with seasonally varying insolation and incorporates in a simple way the positive feedback due to the high albedo of snow and sea ice. Meridional energy transport due to atmospheric motions is simulated with lateral diffusion of heat. Meridional energy transport by oceanic currents is ignored, as are possible variations in cloudiness. Emphasis is placed on the model's sensitivity to the latitudinal and seasonal redistribution of insolation produced by variations in the obliquity, the eccentricity, and the longitude of perihelion of the earth's orbit. It is found that when albedos are allowed to vary, increased seasonal variation of insolation leads to increased temperature in the northern hemisphere. In all cases considered, the latitudinal extent of perennial snow cover in the northern hemisphere is particularly sensitive to the perturbations, a response suggestive of the large fluctuations of continental glaciers during the Pleistocene. When the model is forced with the orbital variations of the past 150,000 years, its response is qualitatively similar to the geologic record of that period.
Held, Isaac M., 1978: The tropospheric lapse rate and climatic sensitivity: Experiments with a two-level atmospheric model. Journal of the Atmospheric Sciences, 35(11), 2083-2098. Abstract PDF
The sensitivity of both moist and dry versions of a two-level primitive equation atmospheric model to variations in the solar constant is analyzed. The models have fixed surface albedos, fixed cloudiness and a zero heat flux lower boundary condition, and are forced with annual mean solar fluxes. An attempt is made to understand the response of the static stability in these model atmospheres and the importance of these changes in stability for the climatic responses of other parts of the system.
In the moist model, the static stability increases in low latitudes but decreases in high latitudes as the solar constant increases, resulting in considerable latitudinal structure in the sensitivity of surface temperatures and zonal winds. In the dry model the stability decreases at all latitudes as the solar constant increases. It is argues that this decrease in stability in the dry model, through its effect on ientropic slopes and the supercriticality of the flow, is responsible for the observed large increases in eddy energies and fluxes. Parameterization schemes for the eddy heat flux are critically examined in light ofthese results.
Held, Isaac M., and M J Suarez, 1978: A two-level primitive equation atmospheric model designed for climatic sensitivity experiments. Journal of the Atmospheric Sciences, 35, 206-299. Abstract PDF
A useful but as yet under-utilized tool for climatic studies is an atmospheric model in which the time evolution of large-scale eddies is resolved explicitly, but in a relatively simple dynamical framework. One such model is described in detail in this study- a two-level primitive equation model on a sphere with variable static stability, finite-differenced in the meridional direction but Fourier analyzed and then very severely truncated in the zonal direction. Two versions of the model -moist and dry- are developed, the maintenance of the model's static stability being markedly different in the two versions.
Statistically steady states are obtained for a variety of spectral truncations for both versions of the model in order to determine the fewest zonal wavenumbers one can retain and still obtain a reasonable zonally averaged circulation. Including only one wave, of wavelength typical of strongly unstable waves in midlatitudes, results in a circulation with a subpolar jet as well as a subtropical jet in the zonal wind. The addition of a longer wave (i.e., the addition of wavenumber 3 to wavenumber 6) results in the destruction of the subpolar jet. No further dramatic changes in the zonally averaged flow occur as more waves are added to the system.
Features of the model's dynamics which might limit its utility are emphasized, notably the dependence of the strength of the Hadley cell on the details of the convective adjustment scheme. We find, however, that the total energy transported by the Hadley cell is insensitive to such details.
Climatic senstivity experiments with these models will be described in forthcoming papers.
Held, Isaac M., 1975: Momentum transport by quasi-geostrophic eddies. Journal of the Atmospheric Sciences, 32(7), 1494-1497. Abstract PDF
Some results due to Kuo concerning momentum fluxes in barotropic flows are generalized so as to apply to quasi-geostrophic flows on a beta-plane. It is shown that linear, amplifying waves on an arbitrary zonal flow cause a net transport of westerly momentum out of that part of the fluid in which Raleigh's stability criterion (as generalized by Charney and Stern, and by Pedlosky) is satisfied locally. Also, it is shown that if quasi-geostrophic eddies are introduced by some "external" agent into a region in which the zonal flow satisfies the stability criterion, then westerly momentum will flow into this region.
Held, Isaac M., and M J Suarez, 1974: Simple albedo feedback models of the icecaps. Tellus, 26(6), 613-629. Abstract
A series of simple models of the albedo feedback mechanism and its effect on the global climate are solved analytically. All of the models are similar to one considered by Budyko. The seasonal variation in incident solar radiation is ignored. Emphasis is placed on the parameter dependence of the models' sensitivity to changes in the solar constant. It is found in all cases that increasing the efficiency of the poleward transport of energy increases this sensitivity. It is also suggested that knowledge of the partitioning of the transport between the atmosphere and the oceans is of considerable importance for estimating sensitivity. The stability of equilibrium states is determined from the properties of small perturbations away from equilibrium. It is observed that relaxation times of perturbations can be increased considerably by the albedo feedback mechanism. The effect of variations in the obliquity of the planet's orbit on sensitivity and stability is also analyzed. The results indicate that albedo feedback may increase the significance of obliquity variations on Mars, as well as on the Earth.
