When evaluating the effect of carbon dioxide (CO2) changes on Earth’s climate, it is widely assumed that instantaneous radiative forcing from a doubling of a given CO2 concentration (IRF2×CO2) is constant and that variances in climate sensitivity arise from differences in radiative feedbacks or dependence of these feedbacks on the climatological base state. Here, we show that the IRF2×CO2 is not constant, but rather depends on the climatological base state, increasing by about 25% for every doubling of CO2, and has increased by about 10% since the preindustrial era primarily due to the cooling within the upper stratosphere, implying a proportionate increase in climate sensitivity. This base-state dependence also explains about half of the intermodel spread in IRF2×CO2, a problem that has persisted among climate models for nearly three decades.
Williams, Andrew I., Nadir Jeevanjee, and Jonah Bloch-Johnson, March 2023: Circus tents, convective thresholds, and the non-linear climate response to tropical SSTs. Geophysical Research Letters, 50(6), DOI:10.1029/2022GL101499. Abstract
Using model simulations, we demonstrate that the climate response to localized tropical sea surface temperature (SST) perturbations exhibits numerous non-linearities. Most pronounced is an asymmetry in the response to positive and negative SST perturbations. Additionally, we identify a “magnitude-dependence” of the response on the size of the SST perturbation. We then explain how these non-linearities arise as a robust consequence of convective quasi-equilibrium and weak (but non-zero) temperature gradients in the tropical free-troposphere, which we encapsulate in a “circus tent” model of the tropical atmosphere. These results demonstrate that the climate response to SST perturbations is fundamentally non-linear, and highlight potential deficiencies in work which has assumed linearity in the response.
Jeevanjee, Nadir, and Linjiong Zhou, March 2022: On the resolution-dependence of anvil cloud fraction and precipitation efficiency in radiative-convective equilibrium. Journal of Advances in Modeling Earth Systems, 14(3), DOI:10.1029/2021MS002759. Abstract
Tropical anvil clouds are an important player in Earth's climate and climate sensitivity, but simulations of anvil clouds are uncertain. Here we identify and investigate one source of uncertainty by demonstrating a marked increase of anvil cloud fraction with resolution in cloud-resolving simulations of radiative-convective equilibrium. This increase in cloud fraction can be traced back to the resolution dependence of horizontal mixing between clear and cloudy air. A mixing timescale is diagnosed for each simulation using the cloud fraction theory of Seeley, Jeevanjee, Langhans, and Romps (2019) (https://doi.org/10.1029/2018GL080747) and is found to scale linearly with grid spacing, as expected from a simple scaling law. Thus mixing becomes more efficient with increasing resolution, generating more evaporation in middle and lower tropospheric updrafts. This decreases their precipitation efficiency (PE), thereby increasing their overall mass flux, leading to greater detrainment at the anvil level and hence higher anvil cloud fraction. The decrease in PE also yields a marked increase in relative humidity with resolution.
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.
Jeevanjee, Nadir, November 2022: Three rules for the decrease of tropical convection with global warming. Journal of Advances in Modeling Earth Systems, 14(11), DOI:10.1029/2022MS003285. Abstract
Tropical convection is expected to decrease with warming, in a variety of ways. Specific incarnations of this idea include the “stability-iris” hypothesis of decreasing anvil cloud coverage, as well as the decrease of both tropospheric and cloud-base mass fluxes with warming. This paper seeks to encapsulate these phenomena into three “rules,” and to explore their interrelationships and robustness, using both analytical reasoning as well as cloud-resolving and global climate simulations. We find that each of these rules can be derived analytically from the usual expression for clear-sky subsidence, so they all embody the same essential physics. But, these rules do not all provide the same degree of constraint: the stability-iris effect is not entirely robust due to unconstrained microphysical degrees of freedom, and the decrease in cloud-base mass flux is not entirely robust due to unconstrained effects of entrainment and detrainment. Tropospheric mass fluxes on the other hand are shown to be well-constrained theoretically, and when evaluated in temperature coordinates they exhibit a monotonic decrease with warming at all vertical levels and across a hierarchy of models.
Morrison, Hugh, Nadir Jeevanjee, and Jun-Ichi Yano, November 2022: Dynamic pressure drag on rising buoyant thermals in a neutrally stable environment. Journal of the Atmospheric Sciences, 79(11), DOI:10.1175/JAS-D-21-0274.13045-3063. Abstract
This study examines dynamic pressure drag on rising dry buoyant thermals. A theoretical expression for drag coefficient Cd as a function of several other nondimensional parameters governing thermal dynamics is derived based on combining the thermal momentum budget with the similarity theory of Scorer. Using values for these nondimensional parameters from previous studies, the theory suggests drag on thermals is small relative to that on solid spheres in laminar or turbulent flow. Two sets of numerical simulations of thermals in an unstratified, neutrally stable environment using an LES configuration of the Cloud Model 1 (CM1) are analyzed. One set has a relatively low effective Reynolds number Re and the other has an order-of-magnitude-higher Re; these produce laminar and turbulent resolved-scale flows, respectively. Consistent with the theoretical Cd, the magnitude of drag is small in all simulations. However, whereas the laminar thermals have Cd ≈ 0.01, the turbulent thermals have weakly negative drag (Cd ≈ −0.1). This difference is explained by the laminar thermals having near vertical symmetry but the turbulent thermals exhibiting considerable vertical asymmetry of their azimuthally averaged flows. In the laminar thermals, buoyancy rapidly becomes concentrated around the main centers of rotation located along the horizontal central axis, leading to expansion of thermals via baroclinic vorticity generation but doing little to break vertical symmetry of the flow. Vertical asymmetry of the azimuthally averaged flow of turbulent thermals is attributed mainly to small-scale resolved eddies that are concentrated in the upper part of the thermals.
Tropical cyclone (TC) potential intensity (PI) theory has a well-known form, consistent with a Carnot cycle interpretation of TC energetics, which relates PI to mean environmental conditions: the difference between surface and TC outflow temperatures and the air–sea enthalpy disequilibrium. PI has also been defined as a difference in convective available potential energy (CAPE) between two parcels, and quantitative assessments of future changes make use of a numerical algorithm based on this definition. Here, an analysis shows the conditions under which these Carnot and CAPE-based PI definitions are equivalent. There are multiple conditions, not previously enumerated, which in particular reveal a role for irreversible entropy production from surface evaporation. This mathematical analysis is verified by numerical calculations of PI’s sensitivity to large changes in surface-air relative humidity. To gain physical insight into the connection between the CAPE and Carnot formulations of PI, we use a recently developed analytic theory for CAPE to derive, starting from the CAPE-based definition, a new approximate formula for PI that nearly recovers the previous Carnot PI formula. The derivation shows that the difference in undilute buoyancies of saturated and environmental parcels that determines CAPE PI can in fact be expressed as a difference in the parcels’ surface moist static energy, providing a physical link between the Carnot and CAPE formulations of PI. This combination of analysis and physical interpretation builds confidence in previous numerical CAPE-based PI calculations that use climate model projections of the future tropical environment.
Jeevanjee, Nadir, Daniel D B Koll, and Nicholas J Lutsko, July 2021: “Simpson's Law” and the spectral cancellation of climate feedbacks. Geophysical Research Letters, 48(14), DOI:10.1029/2021GL093699. Abstract
Feedback analyses aim to isolate processes in the climate system which may amplify or diminish its response to an external forcing. In calculating feedbacks due to the warming of the atmosphere, however, a choice must be made as to whether the absolute or relative humidity (RH) is to be held fixed as the impact of warming is assessed. Here we examine these impacts frequency-by-frequency in the infrared spectrum, and find that fixing the RH leads to a much simpler picture than fixing absolute humidity.
Clear-sky CO2 forcing is known to vary significantly over the globe, but the state dependence that controls this is not well understood. Here we extend the formalism of Wilson and Gea-Banacloche to obtain a quantitatively accurate analytical model for spatially varying instantaneous CO2 forcing, which depends only on surface temperature T s, stratospheric temperature, and column relative humidity (RH). This model shows that CO2 forcing can be considered a swap of surface emission for stratospheric emission, and thus depends primarily on surface–stratosphere temperature contrast. The strong meridional gradient in CO2 forcing is thus largely due to the strong meridional gradient in T s. In the tropics and midlatitudes, however, the presence of H2O modulates the forcing by replacing surface emission with RH-dependent atmospheric emission. This substantially reduces the forcing in the tropics, introduces forcing variations due to spatially varying RH, and sets an upper limit (with respect to T s variations) on CO2 forcing that is reached in the present-day tropics. In addition, we extend our analytical model to the instantaneous tropopause forcing, and find that this forcing depends on T s only, with no dependence on stratospheric temperature. We also analyze the τ = 1 approximation for the emission level and derive an exact formula for the emission level, which yields values closer to τ = 1/2 than to τ = 1.
Various studies have suggested that Earth's clear-sky outgoing longwave radiation (OLR) varies linearly with surface temperature, with a longwave clear-sky feedback that is, independent of surface temperature and relative humidity. However, this uniformity conflicts with the notion that humidity controls tropical stability (e.g., the “furnace” and “radiator fins” of Pierrehumbert (1995, https://doi.org/10.1175/1520-0469(1995)052%3C1784:TRFATL%3E2.0.CO;2)). Here, we use a column model to explore the dependence of longwave clear-sky feedback on both surface temperature and relative humidity. We find that a strong humidity dependence in the feedback emerges above 275 K, which stems from the closing of the H2O window, and that the furnace and radiator fins are consequences of this dependence. We then clarify that radiator fins are better characterized by tropical variations in clear-sky feedback than OLR. Finally, we construct a simple model for estimating the all-sky feedback and find that although clouds lower the magnitude of longwave feedback, the humidity-dependence persists.
Schneider, Tapio, Nadir Jeevanjee, and Robert H Socolow, June 2021: Accelerating progress in climate science. Physics Today, 74(6), DOI:10.1063/PT.3.4772.
Seeley, Jacob T., and Nadir Jeevanjee, February 2021: H2O windows and CO2 radiator fins: A clear‐sky explanation for the peak in equilibrium climate sensitivity. Geophysical Research Letters, 48(4), DOI:10.1029/2020GL089609. Abstract
Recent explorations of the state‐dependence of Earth’s equilibrium climate sensitivity (ECS) have revealed a pronounced peak in ECS at a surface temperature of ∼310 K. This ECS peak has been observed in models spanning the model hierarchy, suggesting a robust physical source. Here, we propose an explanation for this ECS peak using a novel spectrally resolved decomposition of clear‐sky longwave feedbacks. We show that the interplay between spectral feedbacks in H2O‐dominated and CO2‐dominated portions of the longwave spectrum, along with moist‐adiabatic amplification of upper‐tropospheric warming, conspire to produce a minimum in the feedback parameter, and a corresponding peak in ECS, at a surface temperature of 310 K. Mechanism‐denial tests highlight three key ingredients for the ECS peak: (1) H2O continuum absorption to quickly close spectral windows at high surface temperature; (2) moist‐adiabatic tropospheric temperatures to enhance upper‐tropospheric warming; and (3) energetically consistent increases of CO2 with surface temperature.
The cooling-to-space (CTS) approximation says that the radiative cooling of an atmospheric layer is dominated by that layer’s emission to space, while radiative exchange with layers above and below largely cancel. Though the CTS approximation has been demonstrated empirically and is thus fairly well-accepted, a theoretical justification is lacking. Furthermore, the intuition behind the CTS approximation cannot be universally valid, as the CTS approximation fails in the case of pure radiative equilibrium.
Motivated by this, we investigate the CTS approximation in detail. We frame the CTS approximation in terms of a novel decomposition of radiative flux divergence, which better captures the cancellation of exchange terms. We also derive validity criteria for the CTS approximation, using simple analytical theory. We apply these criteria in the context of both gray gas pure radiative equilibrium (PRE) as well as radiative-convective equilibrium (RCE), to understand how the CTS approximation arises and why it fails in PRE. When applied to realistic gases in RCE, these criteria predict that the CTS approximation should hold well for H2O but less so for CO2, a conclusion we verify with line-by-line radiative transfer calculations. Along the way we also discuss the well-known ‘τ = 1 law’, and its dependence on the choice of vertical coordinate.
Atmospheric radiative cooling is a fundamental aspect of the Earth’s greenhouse effect, and is intrinsically connected to atmospheric motions. At the same time, basic aspects of longwave radiative cooling, such as its characteristic value of 2 K/day, its sharp decline (or ‘kink’) in the upper troposphere, and the large values of CO2 cooling in the stratosphere, are difficult to understand intuitively or estimate with pencil-and-paper. Here we pursue such understanding by building simple spectral (rather than gray) models for clear-sky radiative cooling. We construct these models by combining the cooling-to-space approximation with simplified greenhouse gas spectroscopy and analytical expressions for optical depth, and we validate these simple models with line-by-line calculations.
We find that cooling rates can be expressed as a product of the Planck function, a vertical emissivity gradient, and a characteristic spectral width derived from our simplified spectroscopy. This expression allows for a pencil-and-paper estimate of the 2 K/day tropospheric cooling rate, as well as an explanation of enhanced CO2 cooling rates in the stratosphere. We also link the upper tropospheric kink in radiative cooling to the distribution of H2O absorption coefficients, and from this derive an analytical expression for the kink temperature Tkink ≈ 220 K. A further, ancillary result is that gray models fail to reproduce basic features of atmospheric radiative cooling.
McKim, Brett A., Nadir Jeevanjee, and D Lecoanet, January 2020: Buoyancy‐Driven Entrainment in Dry Thermals. Quarterly Journal of the Royal Meteorological Society, 146(726), DOI:10.1002/qj.3683. Abstract
Turner (1957) proposed that dry thermals entrain because of buoyancy (via a constraint which requires an increase in the radius a). This however, runs counter to the scaling arguments commonly used to derive the entrainment rate, which rely on either the self‐similarity of Scorer (1957) or the turbulent entrainment hypothesis of Morton et al. (1956). The assumption of turbulence‐driven entrainment was investigated by Lecoanet and Jeevanjee (2018), who found that the entrainment efficiency e varies by less than 20% between laminar (Re = 630) and turbulent (Re = 6300) thermals. This motivated us to utilize Turner's argument of buoyancy‐controlled entrainment in addition to the thermal's vertical momentum equation to build a model for thermal dynamics which does not invoke turbulence or self‐similarity. We derive simple expressions for the thermals' kinematic properties and their fractional entrainment rate ε and find close quantitative agreement with the values in direct numerical simulations. In particular, our expression for entrainment rate is consistent with the parameterization ε ~ B/w2, for Archimedean buoyancy B and vertical velocity w. We also directly validate the role of buoyancy‐driven entrainment by running simulations where gravity is turned off midway through a thermal's rise. The entrainment efficiency e is observed to drop to less than 1/3 of its original value in both the laminar and turbulent cases when g = 0, affirming the central role of buoyancy in entrainment in dry thermals.
The linearity of global‐mean outgoing longwave radiation (OLR) with surface temperature is a basic assumption in climate dynamics. This linearity manifests in global climate models, which robustly produce a global‐mean longwave clear‐sky (LWCS) feedback of 1.9 W/m2/K, consistent with idealized single‐column models (Koll & Cronin, 2018, https//:doi.org/10.1073/pnas.1809868115). However, there is considerable spatial variability in the LWCS feedback, including negative values over tropical oceans (known as the “super‐greenhouse effect”) which are compensated for by larger values in the subtropics/extratropics. Therefore, it is unclear how the idealized single‐column results are relevant for the global‐mean LWCS feedback in comprehensive climate models. Here we show with a simple analytical theory and model output that the compensation of this spatial variability to produce a robust global‐mean feedback can be explained by two facts: (1) When conditioned upon free‐tropospheric column relative humidity (RH), the LWCS feedback is independent of RH, and (2) the global histogram of free‐tropospheric column RH is largely invariant under warming.
Chua, Xin Rong, Yi Ming, and Nadir Jeevanjee, August 2019: Investigating the Fast Response of Precipitation Intensity and Boundary Layer Temperature to Atmospheric Heating Using a Cloud‐Resolving Model. Geophysical Research Letters, 46(15), DOI:10.1029/2019GL082408. Abstract
Coarse‐resolution global climate models cannot explicitly resolve the intensity distribution of tropical precipitation and how it responds to a forcing. We use a cloud‐resolving model to study how imposed atmospheric radiative heating (such as that caused by greenhouse gases or absorbing aerosols) may alter precipitation intensity in the setting of radiative‐convective equilibrium. It is found that the decrease in total precipitation is realized through reducing weak events. The intensity of strong precipitation events is maintained by a cancellation between the moistening of air parcels and weakening of updrafts. A boundary layer energy budget analysis suggests that free‐tropospheric heating raises boundary layer temperatures mainly through a reduction in rain re‐evaporation. This insight leads to a predictive scaling for the surface sensible and latent flux changes. The results imply that cloud microphysical processes play a key role in shaping the temperature and precipitation responses to atmospheric heating.
Entrainment in cumulus convection remains ill-understood and difficult to quantify. For instance, entrainment is widely believed to be a fundamentally turbulent process, even though Turner (1957) pointed out that dry thermals entrain primarily because of buoyancy (via a dynamical constraint requiring an increase in radius r). Furthermore, entrainment has been postulated to obey a 1/r scaling, but this scaling has not been firmly established.
Here, we study the classic case of dry thermals in a neutrally stratified environment using fully resolved direct numerical simulation. We combine this with a thermal tracking algorithm which defines a control volume for the thermal at each time, allowing us to directly measure entrainment. We vary the Reynolds number Re of our thermals between laminar (Re ≈ 600) and turbulent (Re ≈ 6000) regimes, finding only a 20% variation in entrainment rate ɛ, supporting the claim that turbulence is not necessary for entrainment. We also directly verify the postulated ε ~ 1/r scaling law.
Po-Chedley, S, M D Zelinka, and Nadir Jeevanjee, et al., November 2019: Climatology explains intermodel spread in tropical upper tropospheric cloud and relative humidity response to greenhouse warming. Geophysical Research Letters, 46(22), DOI:10.1029/2019GL084786. Abstract
The response of upper tropospheric clouds and relative humidity (RH) to warming is important to the overall sensitivity of the Earth to increasing greenhouse gas concentrations. Previous research has shown that changes in hydrologic fields should closely track rising isotherms in a warming climate. Here we show that the distribution of tropical clouds and RH in general circulation models (GCMs) is approximately constant under greenhouse warming when using temperature as a vertical coordinate. By assuming that these fields are an invariant function of atmospheric temperature and that temperature change follows a dilute moist adiabat, we are able to accurately predict cloud fraction and RH changes in the tropical upper troposphere (150‐400 hPa) in 27 GCMs. Our results indicate that intermodel spread in changes of tropical upper tropospheric clouds and RH is closely related to differences in model climatology and could be substantially reduced if model ensembles reliably reproduced observed climatologies.
Seeley, Jacob T., and Nadir Jeevanjee, et al., January 2019: Formation of Tropical Anvil Clouds by Slow Evaporation. Geophysical Research Letters, 46(1), DOI:10.1029/2018GL080747. Abstract
Tropical anvil clouds play a large role in the Earth's radiation balance, but their effect on global warming is uncertain. The conventional paradigm for these clouds attributes their existence to the rapidly declining convective mass flux below the tropopause, which implies a large source of detraining cloudy air there. Here we test this paradigm by manipulating the sources and sinks of cloudy air in cloud‐resolving simulations. We find that anvils form in our simulations because of the long lifetime of upper‐tropospheric cloud condensates, not because of an enhanced source of cloudy air below the tropopause. We further show that cloud lifetimes are long in the cold upper troposphere because the saturation specific humidity is much smaller there than the condensed water loading of cloudy updrafts, which causes evaporative cloud decay to act very slowly. Our results highlight the need for novel cloud‐fraction schemes that align with this decay‐centric framework for anvil clouds.
Seeley, Jacob T., Nadir Jeevanjee, and David M Romps, February 2019: FAT or FiTT: Are Anvil Clouds or the Tropopause Temperature Invariant?Geophysical Research Letters, 46(3), DOI:10.1029/2018GL080096. Abstract
The Fixed Anvil Temperature (FAT) hypothesis proposes that upper tropospheric cloud fraction peaks at a special isotherm that is independent of surface temperature. It has been argued that a FAT should result from simple ingredients: Clausius‐Clapeyron, longwave emission from water vapor, and tropospheric energy and mass balance. Here the first cloud‐resolving simulations of radiative‐convective equilibrium designed to contain only these basic ingredients are presented. This setup does not produce a FAT: the anvil temperature varies by about 40% of the surface temperature range. However, the tropopause temperature varies by only 4% of the surface temperature range, which supports the existence of a Fixed Tropopause Temperature (FiTT). In full‐complexity radiative‐convective equilibrium simulations, the spread in anvil temperature is smaller by about a factor of 2, but the tropopause temperature remains more invariant than the anvil temperature by an order of magnitude. In other words, our simulations have a FiTT, not a FAT.
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.
Jeevanjee, Nadir, and David M Romps, November 2018: Mean precipitation change from a deepening troposphere. Proceedings of the National Academy of Sciences, 115(45), DOI:10.1073/pnas.1720683115. Abstract
Global climate models robustly predict that global mean precipitation should increase at roughly 2–3% K−1, but the origin of these values is not well understood. Here we develop a simple theory to help explain these values. This theory combines the well-known radiative constraint on precipitation, which says that condensation heating from precipitation is balanced by the net radiative cooling of the free troposphere, with an invariance of radiative cooling profiles when expressed in temperature coordinates. These two constraints yield a picture in which mean precipitation is controlled primarily by the depth of the troposphere, when measured in temperature coordinates. We develop this theory in idealized simulations of radiative–convective equilibrium and also demonstrate its applicability to global climate models.
By introducing an equivalence between magnetostatics and the equations governing buoyant motion, we derive analytical expressions for the acceleration of isolated density anomalies (thermals). In particular, we investigate buoyant acceleration, defined as the sum of the Archimedean buoyancy B and an associated perturbation pressure gradient. For the case of a uniform spherical thermal, the anomaly fluid accelerates at 2B/3, extending the textbook result for the induced mass of a solid sphere to the case of a fluid sphere. For a more general ellipsoidal thermal, we show that the buoyant acceleration is a simple analytical function of the ellipsoid’s aspect ratio. The relevance of these idealized uniform-density results to turbulent thermals is explored by analyzing direct numerical simulations of thermals at a Reynolds number (Re) of 6300. We find that our results fully characterize a thermal’s initial motion over a distance comparable to its length. Beyond this buoyancy-dominated regime, a thermal develops an ellipsoidal vortex circulation and begins to entrain environmental fluid. Our analytical expressions do not describe the total acceleration of this mature thermal, but they still accurately relate the buoyant acceleration to the thermal’s mean Archimedean buoyancy and aspect ratio. Thus, our analytical formulas provide a simple and direct means of estimating the buoyant acceleration of turbulent thermals.
To understand Earth's climate, climate modelers employ a hierarchy of climate models spanning a wide spectrum of complexity and comprehensiveness. This essay, inspired by the World Climate Research Programme's recent ‘Model Hierarchies Workshop’, attempts to survey and synthesize some of the current thinking on climate model hierarchies, especially as presented at the workshop. We give a few formal descriptions of the hierarchy, and survey the various ways it is used to generate, test, and confirm hypotheses. We also discuss some of the pitfalls of contemporary climate modeling, and how the ‘elegance’ advocated for by Held [2005] has (and has not) been used to address them. We conclude with a survey of current activity in hierarchical modeling, and offer suggestions for its continued fruitful development.
We describe how convective vertical velocities wc vary in the ‘gray zone’ of horizontal resolution, using both hydrostatic and non-hydrostatic versions of GFDL's FV3 dynamical core, as well as analytical solutions to the equations of motion. We derive a simple criterion (based on parcel geometries) for a model to resolve convection, and find that O(100m) resolution can be required for convergence of wc. We also find, both numerically and analytically, that hydrostatic systems over-estimate wc, by a factor of 2 - 3 in the convection-resolving regime. This over-estimation is simply understood in terms of the ‘effective buoyancy pressure’ of Jeevanjee and Romps (2015, 2016).
