# Bibliography - Geoffrey K Vallis

- McKim, Brett A., Nadir Jeevanjee, and Geoffrey K Vallis, September 2021:
**Joint dependence of longwave feedback on surface temperature and relative humidity**.*Geophysical Research Letters*,**48(18)**, DOI:10.1029/2021GL094074.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.

- Chai, Junyi, Malte Jansen, and Geoffrey K Vallis, August 2016:
**Equilibration of a baroclinic planetary atmosphere toward the limit of vanishing bottom friction**.*Journal of the Atmospheric Sciences*,**73(8)**, DOI:10.1175/JAS-D-15-0329.1.This paper discusses whether and how a baroclinic atmosphere can equilibrate with very small bottom friction in a dry, primitive equation, general circulation model. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and it is damped by a linear friction near the lower boundary. When friction is decreased by four orders of magnitude, kinetic energy dissipation by friction gradually becomes negligible, while “energy recycling” becomes dominant. In this limit kinetic energy is converted back into potential energy at the largest scales, thus closing the energy cycle without significant frictional dissipation. The momentum fluxes are of opposite sign in the upper and lower atmosphere: in the upper atmosphere, eddies converge momentum into the westerly jets, however, in the lower atmosphere, the eddies diverge momentum out of the westerly jets. The secondary circulation driven by the meridional eddy momentum fluxes thus acts to increase the baroclinicity of the westerly jet. This regime may be relevant for the Jovian atmosphere, where the frictional time scale may be much larger than the radiative damping time scale.

- Chai, Junyi, and Geoffrey K Vallis, July 2014:
**The role of criticality on the horizontal and vertical scales of extratropical eddies in a dry GCM**.*Journal of the Atmospheric Sciences*,**71(7)**, DOI:10.1175/JAS-D-13-0351.1.This paper discusses the sensitivity of the horizontal and vertical scales of extratropical eddies when criticality is varied in a dry, primitive equation, general circulation model. Criticality is a measure of extratropical isentropic slope and when defined appropriately its value is often close to one for Earth’s climate. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and criticality is increased by increasing the thermal relaxation rate on the mean flow. When criticality varies near one, it is shown that there exists a weakly nonlinear regime in which the eddy scale increases with criticality without involving an inverse cascade, while at the same time the Rossby radius may in fact decrease. The quasi-geostrophic instability of Charney problem is revisited. It is demonstrated that both the horizontal and vertical scales of the most unstable wave depend on criticality, and simple estimates for the two scales are obtained. We reconcile the opposite trends of the eddy scale and Rossby radius and obtain an estimate for the eddy scale in terms of the Rossby radius and criticality that is broadly consistent with simulations.

- Jucker, Martin, Stephan Fueglistaler, and Geoffrey K Vallis, October 2014:
**Stratospheric sudden warmings in an idealized GCM**.*Journal of Geophysical Research: Atmospheres*,**119(9)**, DOI:10.1002/2014JD022170.An idealized general circulation model with an analytically described Newtonian cooling term is employed to study the occurrence rate of sudden stratospheric warmings (SSWs) over a wide range of parameters. In particular, the sensitivity of the SSW occurrence rates to orographic forcing and both relaxation temperature and damping rate is evaluated. The stronger the orographic forcing and the weaker radiative forcing (in both temperature and damping rate), the higher the SSW frequency. The separate effects of the damping rates at low and high latitudes are somewhat more complex. Generally, lower damping rates result in higher SSW frequency. However, if the low and high latitude damping rates are not the same, SSW frequency tends to be most sensitive to a fractional change in the lower of the two damping rates. In addition, the effect of the damping rates on the stratospheric residual circulation is investigated. It is found that higher high-latitude damping rate results in deeper but narrower circulation, whereas higher low-latitude damping rates cause strengthening of the streamfunction in the tropical mid to upper stratosphere. Finally, the relation between easily measured and compared climatological fields and the SSW occurrence rate is determined. The average stratospheric polar zonal mean zonal wind shows a strong anti-correlation with the SSW frequency. In the troposphere, there is a high correlation between the meridional temperature gradient and SSW frequency, suggesting that the strength of synoptic activity in the troposphere may be an important influence on SSW occurrence.

- Potter, Samuel F., Geoffrey K Vallis, and J L Mitchell, February 2014:
**Spontaneous superrotation and the role of Kelvin waves in an idealized dry GCM**.*Journal of the Atmospheric Sciences*,**71(2)**, DOI:10.1175/JAS-D-13-0150.1.The nondimensional parameter space of an idealized dry primitive equations model is explored to find superrotating climate states. The model has no convective parameterization and is forced using a simple thermal relaxation to a prescribed radiative equilibrium temperature. It is demonstrated that of four nondimensional parameters that determine the model’s state only the thermal Rossby number has a significant effect on superrotation. The mode that drives the transition to superrotation in an intermediate thermal Rossby number atmosphere is shown to behave like a Kelvin wave in the tropics.

- Farneti, Riccardo, and Geoffrey K Vallis, September 2013:
**Meridional Energy Transport in the Coupled Atmosphere-Ocean system: Compensation and Partitioning**.*Journal of Climate*,**26(18)**, DOI:10.1175/JCLI-D-12-00133.1.The variability and compensation of the meridional energy transport in the atmosphere and ocean are examined with a state-of-the-art (GFDL CM2.1) and an Intermediate Complexity (GFDL ICCM) Coupled Model. On decadal time scales, a high degree of compensation between the energy transport in the atmosphere (AHT) and ocean (OHT) is found in the North Atlantic. The variability of the total or planetary heat transport (PHT) is much smaller than the variability in either AHT or OHT alone, a feature referred to as ‘Bjerknes’ compensation’. Natural decadal variability stems from the Atlantic meridional overturning circulation (AMOC), which leads OHT variability. The PHT is positively correlated with the OHT, implying that the atmosphere is compensating, but imperfectly, for variations in ocean transport. Because of the fundamental role of the AMOC in generating the decadal OHT anomalies, Bjerknes compensation is expected to be active only in coupled models with a low-frequency AMOC spectral peak. The AHT and the transport in the oceanic gyres are positively correlated, because the gyre transport responds to the atmospheric winds, so militating against long-term variability involving the wind-driven flow. Moisture and sensible heat transports in the atmosphere are also positively correlated at decadal time scales. We further explore the mechanisms and degree of compensation with a simple, diffusive, two-layer Energy Balance Model. Taken together, our results suggest that compensation can be interpreted as arising from the highly efficient nature of the meridional energy transport in the atmosphere responding to ocean variability rather than any a priori need for the top-of-atmosphere radiation budget to be fixed.

- Jucker, Martin, Stephan Fueglistaler, and Geoffrey K Vallis, November 2013:
**Maintenance of the stratospheric structure in an idealized general circulation model**.*Journal of the Atmospheric Sciences*,**70(11)**, DOI:10.1175/JAS-D-12-0305.1.We explore the maintenance of the stratospheric structure in a primitive equation model that is forced by a Newtonian cooling with a prescribed radiative equilibrium temperature field. Models such as this are well suited to analyze and address questions regarding the nature of wave propagation and troposphere-stratosphere interactions. We focus on the lower to mid-stratosphere, and take the mean annual cycle, with its large interhemispheric variations in radiative background state and forcing, as a benchmark that we would like to simulate with reasonable verisimilitude. A reasonably realistic basic stratospheric temperature structure is a necessary first step in understanding stratospheric dynamics. We first show that using a realistic radiative background temperature field based on radiative transfer calculations substantially improves the basic structure of the model stratosphere compared to previously used setups. We then explore what physical processes are needed to maintain the seasonal cycle of temperature in the lower stratosphere. We find that an improved stratosphere and a seasonally varying topographically-forced stationary waves are, in themselves, insufficient to produce a seasonal cycle of sufficient amplitude in the tropics, even if the topographic forcing is large. We show that upwelling associated with baroclinic wave activity is an important influence on the tropical lower stratosphere, and that the seasonal variation of tropospheric baroclinic activity contributes significantly to the seasonal cycle of the lower tropical stratosphere. Given a reasonably realistic basic stratospheric structure and a seasonal cycle in both stationary wave activity and tropospheric baroclinic instability we are able to obtain a seasonal cycle in the lower stratosphere of amplitude comparable to the observations.

- Nikurashin, M, Geoffrey K Vallis, and Alistair Adcroft, January 2013:
**Routes to energy dissipation for geostrophic flows in the Southern Ocean**.*Nature Geoscience*,**6(1)**, DOI:10.1038/ngeo1657.Wind power inputs at the surface ocean are dissipated through smaller-scale processes in the ocean interior and turbulent boundary layer. Simulations suggest that seafloor topography enhances turbulent mixing and energy dissipation in the ocean interior.

- O'Rourke, Amanda K., and Geoffrey K Vallis, August 2013:
**Jet Interaction and the Influence of a Minimum Phase Speed Bound on the Propagation of Eddies**.*Journal of the Atmospheric Sciences*,**70(8)**, DOI:10.1175/JAS-D-12-0303.1.The feedback between planetary-scale eddies and analogs of the mid-latitude eddy-driven jet and the subtropical jet is investigated in a barotropic β-plane model. In the model the subtropic jet is generated by a relaxation process and the eddy-driven jet by an imposed wavemaker. We propose a minimum zonal phase speed bound in addition to the established upper bound, where the zonal phase speed of waves must be less than that of the zonal mean zonal flow. Cospectral analysis of eddy momentum flux convergence shows that eddy activity is generally restricted by these phase speed bounds. The wavenumber dependent minimum phase speed represents a turning line for meridionally propagating waves. We vary the separation distance between the relaxation and stirring regions and find that a sustained, double jet state is achieved when either a critical or turning latitude forms in the interjet region. The interjet turning latitude filters eddies by zonal wavenumber such that shorter waves tend to be reflected off of the relaxed jet and are confined to the eddy-driven jet. The interjet region is transparent to long waves that act to blend the jets and may be associated with barotropic instability. The eddy-driven and relaxed jets tend to merge owing to the propagation of these long waves through the relaxed jet waveguide.

- Zhang, Yu, and Geoffrey K Vallis, October 2013:
**Ocean heat uptake in eddying and non-eddying ocean circulation models in a warming climate**.*Journal of Physical Oceanography*,**43(10)**, DOI:10.1175/JPO-D-12-078.1.Ocean heat uptake is explored with non-eddying (2°), eddy-permitting (0.25°) and eddy-resolving (0.125°) ocean circulation models in a domain representing the Atlantic basin connected to a southern circumpolar channel with flat bottom. The model is forced with a wind stress and a restoring condition for surface buoyancy that is linearly dependent on temperature, both being constant (in time) in the control climate. When the restore temperature is instantly enhanced regionally, two distinct processes are found relevant for the ensuing heat uptake: heat uptake into the ventilated thermocline forced by Ekman pumping and heat absorption in the deep ocean through meridional overturning circulation (MOC). Temperature increases in the thermocline occur on the decadal timescale whereas, over most of the abyss, it is the millennial time scale that is relevant, and the strength of MOC in the channel matters for the intensity of heat uptake. Under global, uniform warming, the rate of increase of total heat content increases with both diapycnal diffusivity and strengthening southern ocean westerlies. In models with different resolutions, ocean responses to uniform warming share similar patterns with important differences. The transfer by mesoscale eddies is insufficiently resolved in the eddy-permitting model, resulting in steep isopycnals in the channel and weak lower MOC, and this in turn leads to weaker heat uptake in the abyssal ocean. Also, the reduction of the northern-hemisphere meridional heat flux (that occurs in a warmer world because of a weakening of MOC) increases with resolution. Consequently, the cooling tendency near the polar edge of the subtropical gyre is most significant in the eddy-resolving model.

- Zurita-Gotor, Pablo, and Geoffrey K Vallis, July 2013:
**The determination of extratropical tropopause height in an idealized gray-radiation model**.*Journal of the Atmospheric Sciences*,**70(7)**, DOI:10.1175/JAS-D-12-0209.1.This paper investigates the mechanisms that determine the extratropical tropopause height, extending previous results with a Newtonian cooling model. A primitive equation model forced by a meridional gradient of incoming solar radiation, with the outgoing infra-red radiation calculated using a simple gray radiation scheme, is now used. The tropopause is defined as the top of the boundary layer over which dynamical heat transport moves the temperature away from radiative equilibrium, and its height estimated from the isentropic mass flux. Depending on parameters, this tropopause may or may not be associated with a sharp stratification change, and it may or may not be possible to define a thermal tropopause. The mass flux and thermal tropopause display similar sensitivity to external parameters when the latter can be defined, a sensitivity in good agreement with predictions by a radiative constraint. In some contrast to the Newtonian model, the radiative constraint is now quite effective in preventing adjustment to marginal criticality with realistic parameters. The meridional structure of the thermal tropopause displays a jump in height at the jet latitude, which appears to be due to the formation of a mixing barrier at the jet maximum when baroclinicity has a finite vertical scale. As meridional potential vorticity mixing is inhibited across the jet, a discontinuity is created between weakly stratified air on its warm side and strongly stratified air on its cool side. The meridional stratification contrast is created by adiabatic cooling and warming by the residual circulation, as this circulation must be deflected vertically to avoid the mixing barrier at the jet maximum.

- Ilicak, M, and Geoffrey K Vallis, May 2012:
**Simulations and scaling of horizontal convection**.*Tellus A*,**64**, 18377, DOI:10.3402/tellusa.v64i0.18377.In this paper we describe the results of various numerical simulations of sideways or horizontal convection. Specifically, a two-dimensional Boussinesq fluid is both heated and cooled from its upper surface, but the walls and the bottom of the tank are insulating and have no flux of heat through them. We perform experiments with a range of Rayleigh numbers up to 10

^{11}, obtained by systematically reducing the diffusivity. We also explore the effects of a nonlinear equation of state and of a mechanical force imposed on the top surface at a fixed Rayleigh number. We find that, when there is no mechanical forcing, both the energy dissipation and the strength of the circulation itself monotonically fall with decreasing diffusivity. At Rayleigh numbers greater than 10^{10}the flow is unsteady; however, the eddying flow is still much weaker than the steady flow at smaller Rayleigh numbers. At high Rayleigh numbers, the stratification and the mean circulation are increasingly confined to a thin layer at the upper surface, with the layer thickness decreasing according to Ra^{−1/5}. There is no evidence that the flow ever enters a regime that is independent of Rayleigh number. Using a nonlinear equation of state makes little difference to the flow phenomenology at a moderate Rayleigh number. The addition of an imposed stress at the upper surface makes a significant difference in the flow. A strong, energy-dissipating circulation can be maintained even at Ra =10^{9}, and the stratification extends more deeply into the fluid than in the unstressed case. Overall, our results are consistent with the notion that in the absence of mechanical forcing a fluid that is heated and cooled from above cannot maintain a deep stratification or a strong sustained flow at high Rayleigh numbers, even if the interior flow is unsteady. - Kidston, J, and Geoffrey K Vallis, November 2012:
**The relationship between the speed and the latitude of an eddy-driven jet in a stirred barotropic model**.*Journal of the Atmospheric Sciences*,**69(11)**, DOI:10.1175/JAS-D-11-0300.1.A stirred barotropic model on a sphere is used to investigate the relationship between the speed and the latitude of an eddy-driven jet. When the wind-speed is increased in the model, the jet shifts poleward, despite the fact that the stirring of vorticity remains statistically constant. The cause is found to be increasing meridional shear that results from increasing the wind-speed in a meridionally confined region, and reduces the absolute vorticity gradient on the flanks of the jet. This has two related consequences. The first is that wave propagation is discouraged, as a turning latitude is created where the absolute vorticity gradient tends to zero. On the sphere, this occurs first at high-latitude, thereby shifting wave dissipation towards the equator. The reduced high-latitude dissipation causes a poleward shift of the jet. The second consequence occurs when the vorticity gradient actually becomes negative, in which case the waves may over reflect, where an instability present, providing a high-latitude source of pseudomomentum. This may further encourage the jet to shift poleward. The relevance of the barotropic dynamics to more realistic atmospheres is unclear, but the inter-model variability of the poleward shift of the jet in response to increasing CO

_{2}across a suite of state of the art GCMs is consistent with the barotropic dynamics, suggesting further investigation is warranted. - Nikurashin, M, and Geoffrey K Vallis, October 2012:
**A Theory of the Interhemispheric Meridional Overturning Circulation and Associated Stratification**.*Journal of Physical Oceanography*,**42(10)**, DOI:10.1175/JPO-D-11-0189.1.A quantitative theoretical model of the meridional overturning circulation and associated deep stratification in an interhemispheric, single-basin ocean with a circumpolar channel is presented. The theory includes the effects of wind, eddies, and diapycnal mixing, and predicts the deep stratification and overturning streamfunction in terms of the surface forcing and other parameters of the problem. It relies on a matching among three regions: the circumpolar channel at high southern latitudes, a region of isopycnal outcrop at high northern latitudes and the ocean basin between. The theory describes both the middepth and abyssal cells of a circulation representing North Atlantic Deep Water and Antarctic Bottom Water. It suggests that whereas the strength of the middepth overturning cell is primarily set by the wind stress in the circumpolar channel, mid depth stratification results from a balance between the wind-driven upwelling in the channel and deep water formation at high northern latitudes. Diapycnal mixing in the ocean interior can lead to warming and upwelling warm of deep waters. However, for parameters most representative of the present ocean mixing seems to play a minor role for the middepth cell. In contrast, the abyssal cell is intrinsically diabatic and controlled by a balance between the deep mixing-driven upwelling and the residual of the wind-driven and eddy-induced circulations in the Southern Ocean. The theory makes explicit predictions about how the stratification and overturning circulation vary with the wind strength, diapycnal diffusivity and mesoscale eddy effects. The predictions compare well with numerical results from a coarse-resolution general circulation model.

- Xie, P, and Geoffrey K Vallis, January 2012:
**The passive and active nature of ocean heat uptake in idealized climate change experiments**.*Climate Dynamics*,**38(3-4)**, DOI:10.1007/s00382-011-1063-8.The influence of ocean circulation changes on heat uptake is explored using a simply-configured primitive equation ocean model resembling a very idealized Atlantic Ocean. We focus on the relative importance of the redistribution of the existing heat reservoir (due to changes in the circulation) and the contribution from anomalous surface heat flux, in experiments in which the surface boundary conditions are changed. We perform and analyze numerical experiments over a wide range of parameters, including experiments that simulate global warming and others that explore the robustness of our results to more general changes in surface boundary conditions. We find that over a wide range of values of diapycnal diffusivity and Southern Ocean winds, and with a variety of changes in surface boundary conditions, the spatial patterns of ocean temperature anomaly are nearly always determined as much or more by the existing heat reservoir redistribution than by the nearly passive uptake of temperature due to changes in the surface boundary conditions. Calculating heat uptake by neglecting the existing reservoir redistribution, which is similar to treating temperature as a passive tracer, leads to significant quantitative errors notably at high-latitudes and, secondarily, in parts of the main thermocline. Experiments with larger circulation changes tend to produce a relatively larger magnitude of existing reservoir redistribution, and a faster growing effective heat capacity of the system. The effective heat capacity is found to be sensitive to both vertical diffusivity and Southern Ocean wind.

- Farneti, Riccardo, and Geoffrey K Vallis, January 2011:
**Mechanisms of interdecadal climate variability and the role of ocean–atmosphere coupling**.*Climate Dynamics*,**36(1-2)**, DOI:10.1007/s00382-009-0674-9.Climate variability and mid-latitude mechanisms of ocean–atmosphere interactions are investigated with coupled and uncoupled integrations of a three-dimensional ocean–atmosphere–land–ice climate model of intermediate complexity. We focus on the decadal and interdecadal variability of the system and give a statistical and dynamical description of its oceanic and atmospheric signatures. In our coupled control integration, an oceanic oscillation of a period of around 20 years is found to be associated with variability of the meridional overturning circulation and is manifested by surface anomalies of temperature and salinity. On such timescales the oceanic oscillation is able to imprint itself on the atmosphere, which then covaries with the ocean at the oscillation period. The essentially slaved atmospheric pattern helps maintain the oceanic oscillation by providing large-scale anomalous heat fluxes, so catalyzing the oscillation. That is to say, because the atmosphere covaries with the ocean the damping felt by the ocean is less than what would be felt with a fixed atmosphere, so broadening the parameter regime over which such variability occurs. In addition to the presence of an atmosphere, the period and amplitude of the oscillation are found to be influenced both by the oceanic vertical diffusivity κ v , by geometrical factors, and by the presence of stochastic heat fluxes. In general, oscillations occur most readily for large values of κ v , when the mean state of the ocean is characterized by a strong meridional overturning circulation. If κ v is sufficiently strong, the ocean will oscillate even in the absence of a dynamical atmosphere. However, for more realistic values of κ v , the presence of an interacting atmosphere is required for significant oscillations. If the ocean is forced by imposed stochastic heat fluxes, instead of a fully interacting atmosphere, then decadal-scale oscillations can be produced suggestive of a damped oscillator. However, the parameter range over which oscillations occur is smaller than when the ocean is coupled to full atmosphere. More generically, the ability of comprehensive coupled ocean–atmosphere models to produce multi-decadal variability, realistic or otherwise, will depend on the oceanic mean state, and so on the diapycnal diffusivity of the modelled ocean, as well as on the ability of the atmosphere to reduce the damping felt by the ocean and so on the atmosphere’s ability to respond to persistent sea-surface temperature anomalies.

- Kidston, J, Geoffrey K Vallis, S M Dean, and J A Renwick, July 2011:
**Can the increase in the eddy length scale under global warming cause the poleward shift of the jet streams?***Journal of Climate*,**24(4)**, DOI:10.1175/2010JCLI3738.1.The question of whether an increase in the atmospheric eddy length scale may cause a poleward shift of the mid-latitude jet streams is addressed. An increase in the length scale of the eddy reduces its zonal phase-speed and so causes eddies to dissipate further from the jet core. If the eddy dissipation region on the poleward flank of the jet overlaps with the eddy source latitudes, shifting this dissipation to higher latitudes will alter which latitudes are a net source of baroclinic eddies, and hence the eddy-driven jet stream may shift polewards. This behavior does not affect the equatorward flank of the jet in the same way because the dissipation region on the equatorward flank is well separated from the source latitudes. An experiment with a barotropic model is presented in which an increase in the length scale of a mid-latitude perturbation results in a poleward shift in the acceleration of the zonal flow. Initial investigations indicate that this behavior is also important in both observational data and the output of comprehensive general circulation models (GCMs). A simplified GCM is used to show that the latitude of the eddy-driven jet is well correlated with the eddy length scale. It is argued that the increase in the eddy length scale causes the poleward shift of the jet in these experiments, rather than vice-versa.

- Nikurashin, M, and Geoffrey K Vallis, March 2011:
**A theory of deep stratification and overturning circulation in the ocean**.*Journal of Physical Oceanography*,**41(3)**, DOI:10.1175/2010JPO4529.1.A simple theoretical model of the deep stratification and meridional overturning circulation in an idealized single-basin ocean with a circumpolar channel is presented. The theory includes the effects of wind, eddies, and diapycnal mixing, predicts the deep stratification in terms of the surface forcing and other problem parameters, makes no assumption of zero residual circulation, and consistently accounts for the interaction between the circumpolar channel and the rest of the ocean. The theory shows that dynamics of the overturning circulation can be characterized by two limiting regimes, corresponding to weak and strong diapycnal mixing. The transition between the two regimes is described by a nondimensional number characterizing the strength of the diffusion-driven compared to the wind-driven overturning circulation. In the limit of weak diapycnal mixing deep stratification throughout the ocean is produced by the effects of wind and eddies in a circumpolar channel and maintained even in the limit of vanishing diapycnal diffusivity and in a flat-bottomed ocean. The overturning circulation across the deep stratification is driven by the diapycnal mixing in the basin away from the channel but is sensitive, through changes in stratification, to the wind and eddies in the channel. In the limit of strong diapycnal mixing deep stratification is primarily set by eddies in the channel and diapycnal mixing in the basin away from the channel, with the wind over the circumpolar channel playing a secondary role. Analytical solutions for the deep stratification and overturning circulation in the limit of weak diapycnal mixing and numerical solutions that span the regimes of weak to strong diapycnal mixing are presented. The theory is tested with a coarse-resolution ocean general circulation model configured in an idealized geometry. A series of experiments performed to examine the sensitivity of the deep stratification and the overturning circulation to variations in wind stress and diapycnal mixing compare well with predictions from the theory.

- Padilla, L E., Geoffrey K Vallis, and C W Rowley, November 2011:
**Probabilistic estimates of transient climate sensitivity subject to uncertainty in forcing and natural variability**.*Journal of Climate*,**24(21)**, DOI:10.1175/2011JCLI3989.1.In this paper we address the impact of uncertainty on estimates of transient climate sensitivity (TCS) of the globally averaged surface temperature, including both uncertainty in past forcing and internal variability in the climate record. We provide a range of probabilistic estimates of the TCS that combine these two sources of uncertainty for various underlying assumptions about the nature of the uncertainty. We also provide estimates of how quickly the uncertainty in the TCS may be expected to diminish in the future as additional observations become available. We make these estimates using a nonlinear Kalman filter coupled to a stochastic, global energy balance model, using the filter and observations to constrain the model parameters. We verify that model and filter are able to emulate the evolution of a comprehensive, state-of-the-art atmosphere-ocean general circulation model and to accurately predict the TCS of the model, and then apply the methodology to observed temperature and forcing records of the 20th century. For uncertainty assumptions best supported by global surface temperature data up to the present time, we find a most-likely present-day estimate of the transient climate sensitivity to be 1.6 K with 90% confidence the response will fall between 1.3–2.6 K, and we estimate that this interval may be 45% smaller by the year 2030. We calculate that emissions levels equivalent to forcing of less than 475 ppmv CO

_{2}concentration are needed to ensure that the transient temperature response will not exceed 2 K with 95% confidence. This is an assessment for the short-to-medium term and not a recommendation for long-term stabilization forcing; the equilibrium temperature response to this level of CO_{2}may be much greater. The flat temperature trend of the last decade has a detectable but small influence on TCS. We describe how the results vary if different uncertainty assumptions are made, and we show they are robust to variations in the initial prior probability assumptions. - Venaille, A, Geoffrey K Vallis, and K S Smith, September 2011:
**Baroclinic turbulence in the ocean: analysis with primitive equation and quasi-geostrophic simulations**.*Journal of Physical Oceanography*,**41(9)**, DOI:10.1175/JPO-D-10-05021.1.This paper examines the factors determining the distribution, length scale, magnitude and structure of mesoscale oceanic eddies in an eddy-resolving primitive equation simulation of the Southern Ocean (MESO). In particular, we investigate the hypothesis that the primary source of mesoscale eddies is baroclinic instability acting locally on the mean state. Using local mean vertical profiles of shear and stratification from an eddying primitive equation simulation, we integrate the forced-dissipated quasi-geostrophic equations in a doubly periodic domain at various locations. We also perform a linear stability analysis of the profiles. The scales, energy levels and structure of the eddies found in the MESO simulation are compared to those predicted by the linear analysis, as well as to the eddying structure of the quasi-geostrophic simulations. This allows us to quantitatively estimate the role of local non-linear effects and cascade phenomena in the generation of the eddy field. We find that typically there is a modest transfer of energy (an ‘inverse cascade’) to larger scales in the horizontal, with the length scale of the resulting eddies typically comparable to or somewhat larger than the wavelength of the most unstable mode. The eddies are, however, manifestly nonlinear and in many locations the turbulence is fairly well-developed. Coherent structures also ubiquitously emerge during the non-linear evolution of the eddy field. There is a near universal tendency toward the production of grave vertical scales, with the barotropic and first baroclinic modes dominating almost everywhere, but there is a degree of surface intensification that is not captured by these modes. Although the results from the local quasi-geostrophic model compare well with those of the primitive equation model in many locations, some profiles do not equilibrate in the quasi-geostrophic model. In many cases bottom friction plays an important quantitative role in determining the final scale and magnitude of eddies in the quasi-geostrophic simulations.

- Zurita-Gotor, Pablo, and Geoffrey K Vallis, April 2011:
**Dynamics of mid-latitude tropopause height in an idealized model**.*Journal of the Atmospheric Sciences*,**68(4)**, DOI:10.1175/2010JAS3631.1.This paper investigates the factors that determine the equilibrium state, and in particular the height and structure of the tropopause, in an idealized primitive-equation model forced by Newtonian cooling in which the eddies can determine their own depth. Previous work has suggested that the mid-latitude tropopause height may be understood as the intersection between a radiative and a dynamical constraint. The dynamical constraint relates to the lateral transfer of energy, which in mid-latitudes is largely effected by baroclinic eddies, and its representation in terms of mean-flow properties. Various theories have been proposed and investigated for the representation of the eddy transport in terms of the mean flow, including a number of diffusive closures and the notion that the flow evolves to a state marginally supercritical to baroclinic instability. The radiative constraint expresses conservation of energy and so must be satisfied, although it need not necessarily be useful in providing a tight constraint on tropopause height. In this paper we explore if and how the marginal criticality and radiative constraints do work together to produce an equilibrated flow and a tropopause that is internal to the fluid. We investigate whether these two constraints are consistent with simulated variations in the tropopause height and in the mean state when the external parameters of an idealized primitive equation model are changed. It is found that when the vertical redistribution of heat is important the radiative constraint tightly constrains the tropopause height and prevents an adjustment to marginal criticality. In contrast, when the stratification adjustment is small, the radiative constraint is only loosely satisfied and there is a tendency for the flow to adjust to marginal criticality. In those cases an alternative dynamical constraint would be needed in order to close the problem and determine the eddy transport and tropopause height in terms of forcing and mean flow.

- Ferrari, R, Stephen M Griffies, A J George Nurser, and Geoffrey K Vallis, April 2010:
**A boundary-value problem for the parameterized mesoscale eddy transport**.*Ocean Modelling*,**32(3-4)**, DOI:10.1016/j.ocemod.2010.01.004.We present a physically and numerically motivated boundary-value problem for each vertical ocean column, whose solution yields a parameterized mesoscale eddy-induced transport streamfunction. The new streamfunction is a nonlocal function of the properties of the fluid column. It is constructed to have a low baroclinic mode vertical structure and to smoothly transition through regions of weak stratification such as boundary layers or mode waters. It requires no matching conditions or regularization in unstratified regions; it satisfies boundary conditions of zero transport at the ocean surface and bottom; and it provides a sink of available potential energy for each vertical seawater column, but not necessarily at each location within the column. Numerical implementation of the methodology requires the solution of a one-dimensional tridiagonal problem for each vertical column. To illustrate the approach, we present an analytical example based on the nonlinear Eady problem and two numerical simulations.

- Griffies, Stephen M., Alistair Adcroft, Anand Gnanadesikan, Robert Hallberg, Matthew J Harrison, Sonya Legg, C M Little, M Nikurashin, Anna Pirani, Bonita L Samuels, J R Toggweiler, and Geoffrey K Vallis, et al., September 2010:
**Problems and prospects in large-scale ocean circulation models**In*Ocean Obs '09*, 21-25 September, Venice, Italy, ESA Special Publication, DOI:10.5270/OceanObs09.cwp.38.We overview problems and prospects in ocean circulation models, with emphasis on certain developments aiming to enhance the physical integrity and flexibility of large-scale models used to study global climate. We also consider elements of observational measures rendering information to help evaluate simulations and to guide development priorities. http://www.oceanobs09.net/blog/?p=88

- Held, Isaac M., Michael Winton, Ken Takahashi, Thomas L Delworth, Fanrong Zeng, and Geoffrey K Vallis, May 2010:
**Probing the fast and slow components of global warming by returning abruptly to pre-industrial forcing**.*Journal of Climate*,**23(9)**, DOI:10.1175/2009JCLI3466.1.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 CO

_{2}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. - Kidston, J, S M Dean, J A Renwick, and Geoffrey K Vallis, February 2010:
**A robust increase in the eddy length scale in the simulation of future climates**.*Geophysical Research Letters*,**37**, L03806, DOI:10.1029/2009GL041615.Output from the Coupled Model Intercomparison Phase 3 are analysed. It is shown that for the ‘A2’ business as usual scenario, every model exhibits an increase in the eddy length scale in the future compared with the simulation of 20th Century climate. The increase in length scale is on the order of 5% by the end of the 21st century, and the Southern Hemisphere exhibits a larger increase than the Northern Hemisphere. The inter-model variability in the increase in the eddy length scale is correlated with the variability in the increase in dry static stability at 700 hPa. Inspection of the NCEP/NCAR reanalysis data indicates that the eddy length scale in the Southern Hemisphere may have increased in recent decades.

- Kidston, J, D M W Frierson, J A Renwick, and Geoffrey K Vallis, December 2010:
**Observations, simulations, and dynamics of jet stream variability and annular modes**.*Journal of Climate*,**23(23)**, DOI:10.1175/2010JCLI3235.1.The characteristics of the dominant pattern of extra-tropical variability (the so-called annular modes) are examined in the context of the theory that eddy-driven jets are self-maintaining. It is shown that there is genuine hemispheric symmetry in the variation of the zonal wind in the Southern Hemisphere but not the Northern Hemisphere. The annular mode is shown to be baroclinic in nature; it is associated with changes in the baroclinic eddy source latitude, and the latitude of the eddy source region is organized by the mean flow. This behavior is expected if there is a baroclinic feedback that encourages the maximum baroclinic instability to be coincident with the maximum zonal wind-speed, and discourages the meridional vacillation of the eddy-driven jet stream. It is shown that the strength of the thermally indirect circulation that gives rise to the baroclinic feedback appears to influence the time scale of the annular mode. When the thermally indirect circulation is stronger the annular mode has a longer e-folding time in a simplified GCM. Preliminary results indicate that the same dynamics are important in the real atmosphere.

- Kidston, J, and Geoffrey K Vallis, November 2010:
**Relationship between eddy-driven jet latitude and width**.*Geophysical Research Letters*,**37**, L21809, DOI:10.1029/2010GL044849.The relationship between the latitude and the width of the eddy-driven jet is examined. We find that there is strong correlation between jet latitude and jet width, with jets located towards the pole being broader. The broadening of the jet with increased latitude appears to be a consequence of increased barotropic instability. When the jet is located towards the pole, the reduced planetary vorticity gradient is more easily overwhelmed by the negative relative vorticity gradient on the flanks of the jet, and this allows a horizontal shear instability to occur. Enstrophy diagnostics show that when the condition of a negative vorticity gradient is met, the effects of barotropic instability are indeed more prevalent.

- Mitchell, J L., and Geoffrey K Vallis, December 2010:
**The transition to superrotation in terrestrial atmospheres**.*Journal of Geophysical Research: Planets*,**115**, E12008, DOI:10.1029/2010JE003587.We show that by changing a single nondimensional number, the thermal Rossby number, global atmospheric simulations with only axisymmetric forcing pass from an Earth‐like atmosphere to a superrotating atmosphere that more resembles the atmospheres of Venus or Titan. The transition to superrotation occurs under conditions in which equatorward propagating Rossby waves generated by baroclinic instability at intermediate and high latitudes are suppressed, which will occur when the deformation radius exceeds the planetary radius. At large thermal Rossby numbers following an initial, nearly axisymmetric phase, a global baroclinic wave of zonal wave number one generated by mixed barotropic‐baroclinic instability dominates the eddy flux of zonal momentum. The global wave converges eastward zonal momentum to the equator and deposits westward momentum at intermediate latitudes during spin‐up and before superrotation emerges, and the baroclinic instability ceases once superrotation is established. A global barotropic mode of zonal wave number one generated by a mix of high‐ and low‐latitude barotropic instability is responsible for maintaining superrotation in the statistically steady state. At intermediate thermal Rossby numbers, momentum flux by the global baroclinic mode is subdominant relative to smaller baroclinic modes, and thus strong superrotation does not develop.

- Vallis, Geoffrey K., 2010:
**Mechanisms of climate variability from years to decades**In*Stochastic Physics and Climate Modelling*, Cambridge, UK, Cambridge University Press, 1-34. - Zurita-Gotor, Pablo, and Geoffrey K Vallis, May 2010:
**Circulation sensitivity to heating in a simple model of baroclinic turbulence**.*Journal of the Atmospheric Sciences*,**67(5)**, DOI:10.1175/2009JAS3314.1.This paper examines the sensitivity of the circulation of an idealized primitive equation two-level model on the form and strength of the heating, aiming to understand the qualitatively different sensitivity of the isentropic slope on differential heating reported by previous idealized studies when different model formulations are used. It is argued that this contrasting behavior might arise from differences in the internal determination of the heating. To test this contention, the two-level model is forced using two different heating formulations: a standard Newtonian cooling formulation and a highly simplified formulation in which the net lower-to-upper troposphere heat transport is prescribed by construction. The results are interpreted using quasigeostrophic turbulent closures, which have previously been shown to have predictive power for the model. It is found that the strength of the circulation, as measured by eddy length and velocity scales and by the strength of the energy cycle, scales with the vertical heating (the lower-to-upper troposphere heat transport), with a weak dependence. By contrast, the isentropic slope is only sensitive to the structure of the heating, as measured by the ratio between meridional versus vertical heating, and not to the actual strength of the heating. In general the heating is internally determined, and this ratio may either increase or decrease as the circulation strengthens. It is shown that the sign of the sensitivity depends on the steepness of the relation between vertical heating and stratification for the particular heating formulation used. The quasigeostrophic limit (fixed stratification) and the prescribed heating model constrain the possible range of behaviors and provide bounds of sensitivity for the model. These results may help explain the different sensitivity of the isentropic slope on differential heating for dry and moist models and for quasigeostrophic and primitive equation models.

- Farneti, Riccardo, and Geoffrey K Vallis, July 2009:
**An Intermediate Complexity Climate Model (ICCMp1) based on the GFDL flexible modelling system**.*Geoscientific Model Development*,**2(2)**, DOI:10.5194/gmd-2-73-2009.An intermediate complexity coupled ocean-atmosphere-land-ice model, based on the Geophysical Fluid Dynamics Laboratory (GFDL) Flexible Modelling System (FMS), has been developed to study mechanisms of ocean-atmosphere interactions and natural climate variability at interannual to interdecadal and longer time scales. The model uses the three-dimensional primitive equations for both ocean and atmosphere but is simplified from a "state of the art" coupled model by using simplified atmospheric physics and parameterisation schemes. These simplifications provide considerable savings in computational expense and, perhaps more importantly, allow mechanisms to be investigated more cleanly and thoroughly than with a more elaborate model. For example, the model allows integrations of several millennia as well as broad parameter studies. For the ocean, the model uses the free surface primitive equations Modular Ocean Model (MOM) and the GFDL/FMS sea-ice model (SIS) is coupled to the oceanic grid. The atmospheric component consists of the FMS B-grid moist primitive equations atmospheric dynamical core with highly simplified physical parameterisations. A simple bucket model is implemented for our idealised land following the GFDL/FMS Land model. The model is supported within the standard MOM releases as one of its many test cases and the source code is thus freely available. Here we describe the model components and present a climatology of coupled simulations achieved with two different geometrical configurations. Throughout the paper, we give a flavour of the potential for this model to be a powerful tool for the climate modelling community by mentioning a wide range of studies that are currently being explored.

- Gerber, Edwin P., and Geoffrey K Vallis, February 2009:
**On the zonal structure of the North Atlantic Oscillation and annular modes**.*Journal of the Atmospheric Sciences*,**66(2)**, DOI:10.1175/2008JAS2682.1.The zonal structure and dynamics of the dipolar patterns of intraseasonal variability in the extratropical atmosphere—namely, the North Atlantic Oscillation (NAO) and the so-called annular modes of variability—are investigated in an idealized general circulation model. Particular attention is focused on the relationships linking the zonal structure of the stationary waves, synoptic variability (i.e., the storm tracks), and the zonal structure of the patterns of intraseasonal variability. Large-scale topography and diabatic anomalies are introduced to modify and concentrate the synoptic variability, establishing a recipe for a localized storm track. Comparison of the large-scale forcing, synoptic variability, and patterns of intra-seasonal variability suggests a nonlinear relationship between the large-scale forcing and the variability. It is found that localized NAO-like patterns arise from the confluence of topographic and diabatic forcing and that the patterns are more localized than one would expect based on superposition of the responses to topography and thermal forcing alone. The connection between the eddy life cycle of growth and decay and the localization of the intraseasonal variability is investigated. Both the termination of the storm track and the localization of the intraseasonal variability in the GCM depend on a difluent region of weak upper-level flow, where eddies break and dissipate rather than propagate energy forward through downstream development. The authors' interpretation suggests that the North Atlantic storm track and the NAO are two manifestations of the same phenomenon. Conclusions from the GCM study are critiqued by comparison with observations.

- Vallis, Geoffrey K., and Riccardo Farneti, October 2009:
**Meridional energy transport in the coupled atmosphere-ocean system: scaling and numerical experiments**.*Quarterly Journal of the Royal Meteorological Society*,**135(644)**, DOI:10.1002/qj.498.We explore meridional energy transfer in the coupled atmosphere-ocean system, with a focus on the extratropics. We present various elementary scaling arguments for the partitioning of the energy transfer between atmosphere and ocean, and illustrate those arguments by numerical experimentation. The numerical experiments are designed to explore the effects of changing various properties of the ocean (its size, geometry and diapycnal diffusivity), the atmosphere (its water vapour content) and the forcing of the system (the distribution of incoming solar radiation and the rotation rate of the planet). We find that the energy transport associated with wind-driven ocean gyres is closely coupled to the energy transport of the midlatitude atmosphere so that, for example, the heat transport of both systems scales in approximately the same way with the meridional temperature gradient in midlatitudes. On the other hand, the deep circulation of the ocean is not tightly coupled with the atmosphere and its energy transport varies in a different fashion. Although for present-day conditions the atmosphere transports more energy polewards than does the ocean, we find that a wider or more diffusive ocean is able to transport more energy than the atmosphere. The polewards energy transport of the ocean is smaller in the Southern Hemisphere than in the Northern Hemisphere; this arises because of the effects of a circumpolar channel on the deep overturning circulation. The atmosphere is able to compensate for changes in oceanic heat transport due to changes in diapycnal diffusivity or geometry, but we find that the compensation is not perfect. We also find that the transports of both atmosphere and ocean decrease if the planetary rotation rate increases substantially, indicating that there is no a priori constraint on the total meridional heat transport in the coupled system.

- Zurita-Gotor, Pablo, and Geoffrey K Vallis, April 2009:
**Equilibration of baroclinic turbulence in primitive equations and quasigeostrophic models**.*Journal of the Atmospheric Sciences*,**66(4)**, DOI:10.1175/2008JAS2848.1.This paper investigates the equilibration of baroclinic turbulence in an idealized, primitive equation, two-level model, focusing on the relation with the phenomenology of quasigeostrophic turbulence theory. Simulations with a comparable two-layer quasigeostrophic model are presented for comparison, with the deformation radius in the quasigeostrophic model being set using the stratification from the primitive equation model. Over a fairly broad parameter range, the primitive equation and quasigeostrophic results are in qualitative and, to some degree, quantitative agreement and are consistent with the phenomenology of geostrophic turbulence. The scale, amplitude, and baroclinicity of the eddies and the degree of baroclinic instability of the mean flow all vary fairly smoothly with the imposed parameters; both models are able, in some parameter ranges, to produce supercritical flows. The criticality in the primitive equation model, which does not have any convective parameterization scheme, is fairly sensitive to the external parameters, most notably the planet size (i.e., the f/β ratio), the forcing time scale, and the factors influencing the stratification. In some parameter settings of the models, although not those that aremost realistic for the earth's atmosphere, it is possible to produce eddies that are considerably larger than the deformation scales and an inverse cascade in the barotropic flow with a −5/3 spectrum. The vertical flux of heat is found to be related to the isentropic slope.

- Vallis, Geoffrey K., and Edwin P Gerber, 2008:
**Local and hemispheric dynamics of the North Atlantic Oscillation, annular patterns and the zonal index**.*Dynamics of Atmospheres and Oceans*,**44(3-4)**, DOI:10.1016/j.dynatmoce.2007.04.003.In this paper we discuss the atmospheric dynamics of the North Atlantic Oscillation (NAO), the zonal index, and annular patterns of variability (also known as annular modes). Our goal is to give a unified treatment of these related phenomena, to make explicit how they are connected and how they differ, and to illustrate their dynamics with the aid of an idealized primitive equation model. Our focus is on tropospheric dynamics. We first show that the structure of the empirical orthogonal functions (EOFs) of the NAO and annular modes follows, at least in part, from the structure of the baroclinic zone. Given a single baroclinic zone, and concomitantly a single eddy-driven jet, the meridional structure of the EOFs follows from the nature of the jet variability, and if the jet variability is constrained to conserve zonal momentum then the observed structure of the EOF can be explained with a simple model. In the zonal direction, if the baroclinic zone is statistically uniform then so is the first EOF, even though there may be little correlation of any dynamical fields in that direction. If the baroclinic activity is zonally concentrated, then so is the first EOF. Thus, at the simplest order of description, the NAO is a consequence of the presence of an Atlantic storm track; the strong statement of this would be that the NAO is the variability of the Atlantic storm track. The positive phase of the NAO corresponds to eddy momentum fluxes (themselves a consequence of wave breaking) that push the eddy-driven jet polewards, separating it distinctly from the subtropical jet. The negative phase of the NAO is characterized by an equatorial shift and, sometimes, a weakening of the eddy fluxes and no separation between sub-tropical and eddy-driven jets. Variations in the zonal index (a measure of the zonally averaged zonal flow) also occur as a consequence of such activity, although the changes occurring are not necessarily synchronous at different longitudes, and the presence of annular modes (i.e., the associated patterns of variability) does not necessarily indicate zonally symmetric dynamics. The NAO, is not, however, a consequence of purely local dynamics, for the storm tracks depend for their existence on patterns of topographic and thermal forcing of near hemispheric extent. The Atlantic storm track in particular is a consequence of the presence of the Rocky mountains, the temperature contrast between the cold continent and warm ocean, and the lingering presence of the Pacific storm track. The precise relationship between the NAO and the storm tracks remains to be determined, as do a number of aspects of storm track dynamics, including their precise relation to the stationary eddies and to the regions of largest baroclinicity. Similarly, the influences of the stratosphere and of sea-surface temperature anomalies, and the causes and predictability of the inter-annual variability of the NAO remain open problems.

- Zhao, R, and Geoffrey K Vallis, 2008:
**Parameterizing mesoscale eddies with residual and Eulerian schemes, and a comparison with eddy-permitting models**.*Ocean Modelling*,**23(1-2)**, DOI:doi:10.1016/j.ocemod.2008.02.005.In this paper we explore and test certain parameterization schemes that aim to represent the effects of unresolved mesoscale eddies on the larger-scale flow. In particular, we examine a scheme based on the residual or transformed Eulerian mean formulation of the equations, in which the eddies are parameterized by a large vertical viscosity in the momentum equations, with no skew flux parameterization appearing in the tracer (e.g., temperature or salinity) evolution equations, although terms that parameterize diffusion along isopycnal surfaces remain. The residual scheme is compared both to a conventional parameterization that uses a skew diffusion (or equivalently advection by a skew velocity), and to eddy-permitting calculations. Although in principle almost equivalent to certain forms of skew flux schemes, the residual formulation is found to have certain practical advantages over the conventional scheme in some circumstances, and in particular near the upper boundary where conventional schemes are sensitive to the choice of tapering but the residual scheme is less so. The residual scheme also enables the horizontal viscosity – which is mainly applied to maintain model stability – to be reduced. Finally, the residual scheme is somewhat easier to implement, and the tracer transport is easier to interpret. On the other hand, the residual scheme gives, at least formally, a transformed velocity, not the Eulerian velocity and will not be appropriate in all circumstances

- Cash, B A., P J Kushner, and Geoffrey K Vallis, 2007:
**Comment on “On the presence of annular variability in an aquaplanet model” by Masahiro Watanabe**.*Geophysical Research Letters*,**34**, L03707, DOI:10.1029/2006GL027274. - Fučkar, N S., and Geoffrey K Vallis, 2007:
**Interhemispheric influence of surface buoyancy conditions on a circumpolar current**.*Geophysical Research Letters*,**34**, L14605, DOI:10.1029/2007GL030379.This study shows that the surface buoyancy conditions in the Northern Hemisphere may influence the stratification and transport of the Antarctic Circumpolar Current (ACC). We use a course-resolution ocean general circulation model (OGCM) in an idealized single-basin configuration with a circumpolar channel. A decrease in the magnitude of the surface temperature meridional gradient in the Northern Hemisphere reduces production of the deep water, affecting the interhemispheric Meridional Overturning Circulation (MOC) and deepening the thermocline in both hemispheres. The induced change of stratification in the Southern Hemisphere circumpolar region increases the zonal volume transport of circumpolar current because of an increase in the local meridional density gradient and the associated thermal wind shear, which is the dominant baroclinic component of the total volume transport. The result is robust to variations in the background vertical mixing and the parameterization scheme for mesoscale eddies.

- Garner, Stephen T., D M W Frierson, Isaac M Held, O M Pauluis, and Geoffrey K Vallis, June 2007:
**Resolving convection in a global hypohydrostatic model**.*Journal of the Atmospheric Sciences*,**64(6)**, DOI:10.1175/JAS3929.1.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.

- Gerber, Edwin P., and Geoffrey K Vallis, 2007:
**Eddy–Zonal Flow Interactions and the Persistence of the Zonal Index**.*Journal of the Atmospheric Sciences*,**64(9)**, DOI:10.1175/JAS4006.1.An idealized atmospheric general circulation model is used to investigate the factors controlling the time scale of intraseasonal (10–100 day) variability of the extratropical atmosphere. Persistence on these time scales is found in patterns of variability that characterize meridional vacillations of the extratropical jet. Depending on the degree of asymmetry in the model forcing, patterns take on similar properties to the zonal index, annular modes, and North Atlantic Oscillation. It is found that the time scale of jet meandering is distinct from the obvious internal model time scales, suggesting that interaction between synoptic eddies and the large-scale flow establish a separate, intraseasonal time scale. A mechanism is presented by which eddy heat and momentum transport couple to retard motion of the jet, slowing its meridional variation and thereby extending the persistence of zonal index and annular mode anomalies. The feedback is strong and quite sensitive to model parameters when the model forcing is zonally uniform. However, the time scale of jet variation drops and nearly all sensitivity to parameters is lost when zonal asymmetries, in the form of topography and thermal perturbations that approximate land–sea contrast, are introduced. A diagnostic on the zonal structure of the zonal index provides intuition on the physical nature of the index and annular modes and hints at why zonal asymmetries limit the eddy–mean flow interactions.

- Zhang, Rong, and Geoffrey K Vallis, August 2007:
**The role of bottom vortex stretching on the path of the North Atlantic Western Boundary Current and on the Northern Recirculation Gyre**.*Journal of Physical Oceanography*,**37(8)**, DOI:10.1175/JPO3102.1.The mechanisms affecting the path of the depth-integrated North Atlantic western boundary current and the formation of the northern recirculation gyre are investigated using a hierarchy of models, namely, a robust diagnostic model, a prognostic model using a global 1° ocean general circulation model coupled to a two-dimensional atmospheric energy balance model with a hydrological cycle, a simple numerical barotropic model, and an analytic model. The results herein suggest that the path of this boundary current and the formation of the northern recirculation gyre are sensitive to both the magnitude of lateral viscosity and the strength of the deep western boundary current (DWBC). In particular, it is shown that bottom vortex stretching induced by a downslope DWBC near the south of the Grand Banks leads to the formation of a cyclonic northern recirulation gyre and keeps the path of the depth-integrated western boundary current downstream of Cape Hatteras separated from the North American coast. Both south of the Grand Banks and at the crossover region of the DWBC and Gulf Stream, the downslope DWBC induces strong bottom downwelling over the steep continental slope, and the magnitude of the bottom downwelling is locally stronger than surface Ekman pumping velocity, providing strong positive vorticity through bottom vortex stretching effects. The bottom vortex-stretching effect is also present in an extensive area in the North Atlantic, and the contribution to the North Atlantic subpolar and subtropical gyres is on the same order as the local surface wind stress curl. Analytic solutions show that the bottom vortex stretching is important near the western boundary only when the continental slope is wider than the Munk frictional layer scale.

- Vallis, Geoffrey K., 2006:
*Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation*, Cambridge, UK: Cambridge University Press, 745 pp. - Zhang, Rong, and Geoffrey K Vallis, 2006:
**Impact of Great Salinity Anomalies on the Low-Frequency Variability of the North Atlantic Climate**.*Journal of Climate*,**19(3)**, DOI:10.1175/JCLI3623.1.In this paper, it is shown that coherent large-scale low-frequency variabilities in the North Atlantic Ocean—that is, the variations of thermohaline circulation, deep western boundary current, northern recirculation gyre, and Gulf Stream path—are associated with high-latitude oceanic Great Salinity Anomaly events. In particular, a dipolar sea surface temperature anomaly (warming off the U.S. east coast and cooling south of Greenland) can be triggered by the Great Salinity Anomaly events several years in advance, thus providing a degree of long-term predictability to the system. Diagnosed phase relationships among an observed proxy for Great Salinity Anomaly events, the Labrador Sea sea surface temperature anomaly, and the North Atlantic Oscillation are also discussed.

- Cash, B A., P J Kushner, and Geoffrey K Vallis, 2005:
**Zonal asymmetries, teleconnections, and annular patterns in a GCM**.*Journal of the Atmospheric Sciences*,**62(1)**, DOI:10.1175/JAS-3361.1.The influence of zonally asymmetric boundary conditions on the leading modes of variability in a suite of atmospheric general circulation models is investigated. The set of experiments consists of nine model configurations, with varying degrees and types of zonal asymmetry in their boundary conditions. The structure of the leading EOF varies with the zonal asymmetry of the base state for each model configuration . In particular, a close relationship is found between the structure of the EOF and the model storm tracks. An approximately linear relationship is found to hold between the magnitude of the zonal asymmetry of the leading EOF and of the storm tracks in the models. It is shown that this linear relationship extends to the observations. One-point correlation maps centered on the regions where the EOFs reach their maximum amplitude show similar structures for all configurations. These structures consist of a north-south dipole, resembling the observed structure of the North Atlantic Oscillation (NAO). They are significantly more zonally localized than the leading EOF, but do resemble one-point correlation maps and sector EOFs calculated for a simulation with zonally symmetric boundary conditions. Thus, the leading EOF for each simulation appears to represent the longitudinal distribution of zonally localized NAO -like patterns. This longitudinal distribution appears to be tied to the distribution of high-frequency eddies, as represented by the storm tracks. A detailed momentum budget for each case confirms that high-frequency eddies play a crucial role in producing the NAO-like patterns. Other dynamical processes also play an important role, but vary with the details of the simulation.

- Dewar, W K., R M Samelson, and Geoffrey K Vallis, 2005:
**The ventilated pool: A model of subtropical mode water**.*Journal of Physical Oceanography*,**35(2)**, DOI:10.1175/JPO-2681.1.An analytical model of subtropical mode water is presented, based on ventilated thermocline theory and on numerical solutions of a planetary geostrophic basin model. In ventilated thermocline theory, the western pool is a region bounded on the east by subsurface streamlines that outcrop at the western edge of the interior, and in which additional dynamical assumptions are necessary to complete the solution. Solutions for the western pool were originally obtained under the assumption that the potential vorticity of the subsurface layer was homogenized. In the present theory, it is instead assumed that all of the water in the pool region is ventilated and, therefore, that all the Sverdrup transport is carried in the uppermost, outcropping layer. The result is the formation of a deep, vertically homogeneous, fluid layer in the northwest corner of the subtropical gyre that extends from the surface to the base of the ventilated thermocline. This ventilated pool is an analog of the observed subtropical mode waters. The pool also has the interesting properties that it determines its own boundaries and affects the global potential vorticity–pressure relationship. When there are multiple outcropping layers, ventilated pool fluid is subducted to form a set of nested annuli in ventilated, subsurface layers, which are the deepest subducted layers in the ventilated thermocline.

- Gerber, Edwin P., and Geoffrey K Vallis, 2005:
**A stochastic model for the spatial structure of annular patterns of variability and the North Atlantic oscillation**.*Journal of Climate*,**18(12)**, DOI:10.1175/JCLI3337.1.Meridional dipoles of zonal wind and geopotential height are found extensively in empirical orthogonal function (EOF) analysis and single-point correlation maps of observations and models. Notable examples are the North Atlantic Oscillation and the so-called annular modes (or the Arctic Oscillation). Minimal stochastic models are developed to explain the origin of such structure. In particular, highly idealized, analytic, purely stochastic models of the barotropic, zonally averaged zonal wind and of the zonally averaged surface pressure are constructed, and it is found that the meridional dipole pattern is a natural consequence of the conservation of zonal momentum and mass by fluid motions. Extension of the one-dimensional zonal wind model to two-dimensional flow illustrates the manner in which a local meridional dipole structure may become zonally elongated in EOF analysis, producing a zonally uniform EOF even when the dynamics is not particularly zonally coherent on hemispheric length scales. The analytic system then provides a context for understanding the existence of zonally uniform patterns in models where there are no zonally coherent motions. It is also shown how zonally asymmetric dynamics can give rise to structures resembling the North Atlantic Oscillation. Both the one- and two-dimensional results are manifestations of the same principle: given a stochastic system with a simple red spectrum in which correlations between points in space (or time) decay as the separation between them increases, EOF analysis will typically produce the gravest mode allowed by the system’s constraints. Thus, grave dipole patterns can be robustly expected to arise in the statistical analysis of a model or observations, regardless of the presence or otherwise of a dynamical mode.

- Gnanadesikan, Anand, Richard D Slater, P S Swathi, and Geoffrey K Vallis, July 2005:
**The energetics of ocean heat transport**.*Journal of Climate*,**18(14)**, DOI:10.1175/JCLI3436.1.A number of recent papers have argued that the mechanical energy budget of the ocean places constraints on how the thermohaline circulation is driven. These papers have been used to argue that climate models, which do not specifically account for the energy of mixing, potentially miss a very important feedback on climate change. This paper reexamines the question of what energetic arguments can teach us about the climate system and concludes that the relationship between energetics and climate is not straightforward. By analyzing the buoyancy transport equation, it is demonstrated that the large-scale transport of heat within the ocean requires an energy source of around 0.2 TW to accomplish vertical transport and around 0.4 TW (resulting from cabbeling) to accomplish horizontal transport. Within two general circulation models, this energy is almost entirely supplied by surface winds. It is also shown that there is no necessary relationship between heat transport and mechanical energy supply.

- Henning, C C., and Geoffrey K Vallis, 2005:
**The effects of mesoscale eddies on the stratification and transport of an ocean with a circumpolar channel**.*Journal of Physical Oceanography*,**35(5)**, DOI:10.1175/JPO2727.1.The effects of eddies in a primitive equation ocean model configured in a single hemisphere domain with circumpolar channels at their poleward ends are investigated; in particular, two regimes for the mass balance in the channel are investigated. With small overlying winds, the channel stratification is largely set by diffusion operating in the gyre portion of the domain: the depth scale varies with a fractional power of the diffusivity but has little dependence on the wind stress. As the winds are increased, the depth becomes increasingly controlled by a tendency toward small residual circulation. In this limit, a scaling theory is derived for the stratification in the channel that predicts the overall depth of the thermocline as a power of the wind stress and that allows the eddy length scale to differ from the channel length scale. The predicted depth depends on the details of the closure chosen for the eddy buoyancy flux, but in general it varies as some fractional power of the wind stress, and a channel-only numerical simulation agrees well with this prediction. When a gyre region is added to the channel, vertical diffusion in the gyre exerts some control on the channel stratification even at higher winds, forcing the mass balance into a mixed regime in which both eddy and diffusive effects are important. The depth scale varies less with the wind stress than in a channel-only configuration, and the residual mean circulation in the channel is maintained by the convergence of cross-isopycnal eddy buoyancy fluxes.

- Loving, J L., and Geoffrey K Vallis, 2005:
**Mechanisms for climate variability during glacial and interglacial periods**.*Paleoceanography*,**20**, PA4024, DOI:10.1029/2004PA001113.This paper suggests and explores mechanisms relevant to millennial-scale climate variability during glacial periods. In particular, we present the results of model studies that are able to reproduce many aspects of observed glacial climate variability (e.g., Dansgaard-Oeschger oscillations) without external forcing and that provide a natural explanation for the prevalence of high-amplitude variability in glacial climates and the relative stability of the Holocene. We show that the role of sea ice is critical to cold climate variability because of the effective reduction in the high-latitude meridional sea surface temperature gradient resulting from sea ice expansion and the associated role of sea ice in inhibiting heat flux from the ocean to atmosphere. Thus as sea ice expands in a cooler climate, the high-latitude oceanic heat loss to the atmosphere is inhibited, the thermohaline circulation weakens, and the sinking regions move equatorward, leading to a shallower and weaker deep circulation. This weak circulation is unstable, and intermittent high-amplitude oscillations occur on a timescale and with a spatial structure very similar to Dansgaard-Oeschger cycles. Consistent results are found using both a three-dimensional ocean circulation model coupled to an energy balance atmospheric model and with a much simpler ocean box model. In general, freshening plays a secondary role in the weakening of the North Atlantic thermohaline circulation. Significant freshening is required to alter the stable northern deepwater formation that occurs in a warm climate such as today's Holocene, but once this freshening threshold is achieved, the thermohaline circulation shifts to reverse overturning with sinking in the tropics.

- Scaife, Adam A., J R Knight, Geoffrey K Vallis, and C K Folland, 2005:
**A stratospheric influence on the winter NAO and North Atlantic surface climate**.*Geophysical Research Letters*,**32**, L18715, DOI:10.1029/2005GL023226.The North Atlantic Oscillation (NAO) has a profound effect on winter climate variability around the Atlantic basin. Strengthening of the NAO in recent decades has altered surface climate in these regions at a rate far in excess of global mean warming. However, only weak NAO trends are reproduced in climate simulations of the 20th Century, even with prescribed climate forcings and historical sea-surface conditions. Here we show that the unexplained strengthening of the NAO can be fully simulated in a climate model by imposing observed trends in the lower stratosphere. This implies that stratospheric variability needs to be reproduced in models to fully simulate surface climate variations in the North Atlantic sector. Despite having little effect on global mean warming, we show that downward coupling of observed stratospheric circulation changes to the surface can account for the majority of change in regional surface climate over Europe and North America between 1965 and 1995.

- Cash, B A., P J Kushner, and Geoffrey K Vallis, 2004:
**Reply**.*Journal of the Atmospheric Sciences*,**61(8)**, 954-956. - Grianik, N, Isaac M Held, K S Smith, and Geoffrey K Vallis, January 2004:
**The effects of quadratic drag on the inverse cascade of two-dimensional turbulence**.*Physics of Fluids*,**16(1)**, DOI:10.1063/1.1630054.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.

- Henning, C C., and Geoffrey K Vallis, 2004:
**The effects of mesoscale eddies on the main subtropical thermocline**.*Journal of Physical Oceanography*,**34(11)**, 2428-2443.The effects of mesoscale eddies on the main subtropical thermocline are explored using a simply configured wind- and buoyancy-driven primitive equation numerical model in conjunction with transformed Eulerian mean diagnostics and simple scaling ideas and closure schemes. If eddies are suppressed by a modest but nonnegligible horizontal diffusion and vertical diffusion is kept realistically small, the model thermocline exhibits a familiar two-regime structure with an upper, advectively dominated ventilated thermocline and a lower, advective– diffusive internal thermocline, and together these compose the main thermocline. If the horizontal resolution is sufficiently high and the horizontal diffusivity is sufficiently low, then a vigorous mesoscale eddy field emerges. In the mixed layer and upper-mode-water regions, the divergent eddy fluxes are manifestly across isopycnals and so have a diabatic effect. Beneath the mixed layer, the mean structure of the upper (i.e., ventilated) thermocline is still found to be dominated by mean advective terms, except in the "mode water" region and close to the western boundary current. The eddies are particularly strong in the mode-water region, and the low-potential-vorticity pool of the noneddying case is partially eroded away as the eddies try to flatten the isopycnals and reduce available potential energy. The intensity of the eddies decays with depth more slowly than does the mean flow, leading to a three-way balance among eddy flux convergence, mean flow advection, and diffusion in the internal thermocline. Eddies subduct water along isopycnals from the surface into the internal thermocline, replenishing its water masses and maintaining its thickness. Just as in the noneddying case, the dynamics of the internal thermocline can be usefully expressed as an advective–diffusive balance, but where advection is now by the residual (eddy-induced plus Eulerian mean) circulation. The eddy-induced advection partially balances the mean upwelling through the base of the thermocline, and this leads to a slightly thicker thermocline than in the noneddying case. The results suggest that as the diffusivity goes to zero, the residual circulation will go to zero but the thickness of the internal thermocline may remain finite, provided eddy activity persists.

- Vallis, Geoffrey K., Edwin P Gerber, P J Kushner, and B A Cash, February 2004:
**A mechanism and simple dynamical model of the North Atlantic Oscillation and annular modes**.*Journal of the Atmospheric Sciences*,**61(3)**, 264-280.A simple dynamical model is presented for the basic spatial and temporal structure of the large-scale modes of intraseasonal variability and associated variations in the zonal index. Such variability in the extratropical atmosphere is known to be represented by fairly well-defined patterns, and among the most prominent are the North Atlantic Oscillation (NAO) and a more zonally symmetric pattern known as an annular mode, which is most pronounced in the Southern Hemisphere. These patterns may be produced by the momentum fluxes associated with large-scale midlatitude stirring, such as that provided by baroclinic eddies. It is shown how such stirring, as represented by a simple stochastic forcing in a barotropic model, leads to a variability in the zonal flow via a variability in the eddy momentum flux convergence and to patterns similar to those observed. Typically, the leading modes of variability may be characterized as a mixture of “wobbles” in the zonal jet position and “pulses” in the zonal jet strength. If the stochastic forcing is statistically zonally uniform, then the resulting patterns of variability as represented by empirical orthogonal functions are almost zonally uniform and the pressure pattern is dipolar in the meridional direction, resembling an annular mode. If the forcing is enhanced in a zonally localized region, thus mimicking the effects of a storm track over the ocean, then the resulting variability pattern is zonally localized, resembling the North Atlantic Oscillation. This suggests that the North Atlantic Oscillation and annular modes are produced by the same mechanism and are manifestations of the same phenomenon. The time scale of variability of the patterns is longer than the decorrelation time scale of the stochastic forcing, because of the temporal integration of the forcing by the equations of motion limited by the effects of nonlinear dynamics and friction. For reasonable parameters these produce a decorrelation time of the order of 5–10 days. The model also produces some long-term (100 days or longer) variability, without imposing such variability via the external parameters except insofar as it is contained in the nearly white stochastic forcing.

- Cash, B A., P J Kushner, and Geoffrey K Vallis, 2002:
**The structure and composition of the annular modes in an aquaplanet general circulation model**.*Journal of the Atmospheric Sciences*,**59(23)**, 3399-3414.The annular mode simulated by an atmospheric general circulation model with a zonally symmetric lower boundary is investigated. The annular mode, defined as the leading empirical orthogonal function (EOF) of the zonal-mean surface pressure, has a meridional structure consisting of a north–south dipole, similar to observations. The leading EOF of the zonally varying surface pressure has the same meridional structure and is also zonally symmetric. Because the lower boundary is zonally symmetric, composites of days with high projection onto the mode have, to within sampling error, no zonal structure. However, individual periods during which the zonal-mean surface pressure projects strongly onto the annular mode are dominated by zonally localized structures. Thus, the model annular mode represents a zonally homogeneous distribution of zonally localized events with a similar meridional structure, rather than a zonally symmetric mode of variability per se. Individual annular-mode events typically show a north–south teleconnection pattern whose meridional structure closely resembles the annular mode and whose zonal structure extends 60° to 90° in longitude, with a slight northwest–southeast offset between its centers of action. Similar structures are found for EOFs calculated over a subset of the domain corresponding to the width of the Atlantic basin. The spatial structure of both the teleconnection pattern and the regional EOFs resemble the observed North Atlantic Oscillation (NAO) pattern.

- 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.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.

- Smith, K S., and Geoffrey K Vallis, 2002:
**The scales and equilibration of midocean eddies: Forced-dissipative flow**.*Journal of Physical Oceanography*,**32(6)**, 1699-1720.The statistical dynamics of midocean eddies, generated by baroclinic instability of a zonal mean flow, are studied in the context of homogeneous stratified quasigeostrophic tubulence. Existing theory for eddy scales and energies in fully developed turbulence is generalized and applied to a system with surface-intensified stratification and arbitrary zonal shear. The theory gives a scaling for the magnitude of the eddy potential vorticity flux, and its (momentum conserving) vertical structure. The theory is tested numerically by varying the magnitude and mode of the mean shear, the Coriolis gradient, and scale thickness of the stratification and found to be partially successful. It is found that the dynamics of energy in high ( m > 1) baroclinic modes typically resembles the turbulent diffusion of a passive scalar, regardless of the stratification profile, although energy in the first mode does not. It is also found that surface-intensified stratification affects the baroclinicity of flow: as thermocline thickness is decreased, the (statistically equilibrated) baroclinic energy levels remain nearly constant but the statistically equilibrated level of barotropic eddy energy falls. Eddy statistics are found to be relatively insensitive to the magnitude of linear bottom drag in the small drag limit. The theory for the magnitude and structure of the eddy potential vorticity flux is tested against a 15-layer simulation using profiles of density and shear representative of those found in the mid North Atlantic; the theory shows good skill in representing the vertical structure of the flux, and so might serve as the basis for a parameterization of eddy fluxes in the midocean. Finally, baroclinic kinetic energy is found to concentrate near the deformation scale. To the degree that surface motions represent baroclinic eddy kinetic energy, the present results are consistent with the observed correlation between surface eddy scales and the first radius of deformation.

- Huck, T, Geoffrey K Vallis, and A C de Verdière, 2001:
**On the robustness of the interdecadal modes of the Thermohaline Circulation**.*Journal of Climate*,**14(5)**, 940-963.Ocean models in box geometry forced by constant surface fluxes of density have been found to spontaneously generate interdecadal oscillations of the thermohaline circulation. This paper analyzes the sensitivity of these oscillations to various physical effects, including the presence of mesoscale turbulence, various thermal surface boundary conditions, and the presence of wind forcing or bottom topography. The role of unstable long baroclinic waves is also reexamined in an attempt to understand the oscillation period. In idealized geometry, it is found that the low-frequency variability of the thermohaline circulation under quasi-constant surface fluxes is a robust feature of the large-scale circulation. It is not strongly affected by energetic mesoscale turbulence; the oscillation period is relatively invariant with respect to varying resolution and momentum and tracer horizontal mixing coefficients, although it loses some regularity as shorter and longer periods of variability emerge when the mesoscale activity increases in strength with smaller mixing coefficients. The oscillations are also retained as the ocean model is coupled to an interactive atmospheric energy balance model: the thermohaline modes are robust to a range of exchange coefficients that widens with the amplitude of the mean circulation. The presence of an additional wind-forced component generally weakens the oscillation, and depending on the relative strength of thermodynamic and dynamic forcings, the oscillation may be completely killed. A simple interpretation is given, highlighting the role of upward Ekman pumping in damping density anomalies. Finally, the interaction of these baroclinic modes with bottom topography depends strongly on the relative directions of the mean topographic features and the mean currents and baroclinic waves, but usually results in a damping influence.

- Smith, K S., and Geoffrey K Vallis, 2001:
**The scales and equilibration of midocean eddies: Freely evolving flow**.*Journal of Physical Oceanography*,**31(2)**, 554-571.Quasigeostrophic turbulence theory and numerical simulation are used to study the mechanisms determining the scale, structure, and equilibration of mesoscale ocean eddies. The present work concentrates on using freely decaying geostrophic turbulence to understand and explain the vertical and horizontal flow of energy through a stratified, horizontally homogenous geostrophic fluid. It is found that the stratification profile, in particular the presence of pycnocline, has significant, qualitative effects on the efficiency and spectral pathways of energy flow. Specifically, with uniform stratification, energy in high baroclinic modes transfers directly, quickly (within a few eddy turnaround times), and almost completely to the barotropic mode. By contrast, in the presence of oceanlike stratification, kinetic energy in high baroclinic modes transfers intermediately to the first baroclinic mode, whence it transfers inefficiently (and incompletely) to the barotropic mode. The efficiency of transfer to the barotropic mode is reduced as the pycnocline is made increasingly thin, The β effect, on the other hand, improves the efficiency of barotropization, but for oceanically realistic parameters this effect is relatively unimportant compared to the effects of nonuniform stratification. Finally, the nature of turbulent cascade dynamics is such as to lead to a concentration of first baroclinic mode kinetic energy near the first radius of deformation, which, in the case of a nonuniform and oceanically realistic stratification, has a significant projection at the surface. This may in part explain recent observations of surface eddy scales by TOPEX/Poseidon satellite altimetry, which indicate a correlation of surface-height variance with the scale of the first deformation radius.

- Vallis, Geoffrey K., 2000:
**Large-scale circulation and production of stratification: Effects of wind, geometry, and diffusion**.*Journal of Physical Oceanography*,**30(5)**, 933-954.The combined effects of wind, geometry, and diffusion on the stratification and circulation of the ocean are explored by numerical and analytical methods. In particular, the production of deep stratification in a simply configured numerical model with small diffusivity is explored. In the ventilated thermocline of the subtropical gyre, the meridional temperature gradient is mapped continuously to a corresponding vertical profile, essentially independently of (sufficiently small) diffusivity. Below this, as the vertical diffusivity tends to zero, the mapping becomes discontinuous and is concentrated in thin diffusive layers or internal thermoclines. It is shown that the way in which the thickness of the main internal thermocline (i.e, the diffusive lower part of the main thermocline) , and the meridional overturning circulation, scales with diffusivity differs according to the presence or absence of a wind stress. For realistic parameter values, the ocean is in a scaling regime in which wind effects are important factors in the scaling of the thermohaline circulation, even for the single hemisphere, flat-bottomed case. It is shown that deep stratification may readily be produced by the combined effects of surface thermodynamic forcing and geometry. The form of the stratification, but not its existence, depends on the diffusivity. Such deep stratification is efficiently produced , even in single-basin, single-hemisphere simulations, in the presence of a partially topographically blocked channel at high latitudes, provided there is also a surface meridional temperature gradient across the channel. For sufficiently simple geometry and topography, the abyssal stratification is a maximum at the height of the topography. In the limit of small diffusivity, the stratification becomes concentrated in a thin diffusive layer, or front, whose thickness appears to scale as the one-third power of the diffusivity. Above and below this diffusive abyssal thermocline are thick, largely adiabatic and homogeneous water masses. In two hemisphere integrations, the water above the abyssal thermocline may be either "intermediate' water from the same hemisphere as the channel, or "deep" water from the opposing hemisphere, depending on whether the densest water from the opposing hemisphere is denser than the surface water at the equatorward edge of the channel. The zonal velocity in the channel is in thermal wind balance, thus determined more by the meridional temperature gradient across the channel than by the wind forcing. If the periodic channel extends equatorward past the latitude of zero wind-stress curl, the poleward extent of the ventilated thermocline, and the surface source of the mode water, both then lie at the equatorial boundary of the periodic circumpolar channel, rather than where the wind stress curl changes sign.

- Smith, K S., and Geoffrey K Vallis, 1999:
**Linear baroclinic instability in extended regime geostrophic models**.*Journal of the Atmospheric Sciences*,**56(11)**, 1579-1593.The linear wave and baroclinic instability properties of various geostrophic models valid when the Rossby number is small are investigated. The models are the "L

_{1}" dynamics, the "geostrophic potential vorticity" equations, and the more familiar quasigeostrophic and planetary geostrophic equations. Multilayer shallow water equations are used as a control. The goal is to determine whether these models accurately portray linear baroclinic instability properties in various geophysically relevant parameter regimes, in a highly idealized and limited set of cases. The L_{1}and geostrophic potential vorticity models are properly balanced (devoid of inertio-gravity waves, except possibly at solid boundaries), valid on the B plane, and contain both quasigeostrophy and planetary geostrophy as limits in different parameter regimes; hence, they are appropriate models for phenomena that span the deformation and planetary scales of motion. The L_{1}model also includes the "frontal geostrophic" equations as a third limit. In fact, the choice to investigate such relatively unfamiliar models is motivated precisely by their applicability to multiple scales of motion. The models are cast in multilayer form, and the dispersion properties and eigenfunctions of wave modes and baroclinic instabilities produced are found numerically. It is found that both the L_{1}and geostrophic potential vorticity models have sensible linear stability properties with no artifactual instabilities or divergences. Their growth rates are very close to those of the shallow water equations in both quasigeostrophic and planetary geostrophic parameter regimes. The growth rate of baroclinic instability in the planetary geostrophic equations is shown to be generally less than the growth rate of the other models near the deformation radius. The growth rate of the planetary geostrophic equations diverges at high wavenumbers, but it is shown how this is ameliorated by the presence of the relative vorticity term in the geostrophic potential vorticity equations. - Wells, M L., Geoffrey K Vallis, and E A Silver, 1999:
**Tectonic processes in Papua New Guinea and past productivity in the eastern equatorial Pacific Ocean**.*Nature*,**398**, 601-604.Phytoplankton growth in the eastern equatorial Pacific Ocean today accounts for about half of the 'new' production—the fraction of primary production fuelled by externally supplied nutrients—in the global ocean. The recent demonstration that an inadequate supply of iron limits primary production in this region supports earlier speculation that, in the past, fluctuations in the atmospheric deposition of iron-bearing dust may have driven large changes in productivity. But we argue here that only small (2 nM) increases in the iron concentration in source waters of the upwelling Equatorial Undercurrent are needed to fuel intense diatom production across the entire eastern equatorial Pacific Ocean. Episodic increases in iron concentrations of this magnitude or larger were probably frequent in the past because a large component of the undercurrent originates in the convergent island-arc region of Papua New Guinea, which has experienced intensive volcanic, erosional and seismic activity over the past 16 million years. Cycles of plankton productivity recorded in eastern equatorial Pacific sediments may therefore reflect the influence of tectonic processes in the Papua New Guinea region superimposed on the effects of global climate forcing.

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