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- Author or Editor: Isaac M. Held x

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## Abstract

The climate feedbacks in coupled oceanâ€“atmosphere models are compared using a coordinated set of twenty-first-century climate change experiments. Water vapor is found to provide the largest positive feedback in all models and its strength is consistent with that expected from constant relative humidity changes in the water vapor mixing ratio. The feedbacks from clouds and surface albedo are also found to be positive in all models, while the only stabilizing (negative) feedback comes from the temperature response. Large intermodel differences in the lapse rate feedback are observed and shown to be associated with differing regional patterns of surface warming. Consistent with previous studies, it is found that the vertical changes in temperature and water vapor are tightly coupled in all models and, importantly, demonstrate that intermodel differences in the sum of lapse rate and water vapor feedbacks are small. In contrast, intermodel differences in cloud feedback are found to provide the largest source of uncertainty in current predictions of climate sensitivity.

## Abstract

The climate feedbacks in coupled oceanâ€“atmosphere models are compared using a coordinated set of twenty-first-century climate change experiments. Water vapor is found to provide the largest positive feedback in all models and its strength is consistent with that expected from constant relative humidity changes in the water vapor mixing ratio. The feedbacks from clouds and surface albedo are also found to be positive in all models, while the only stabilizing (negative) feedback comes from the temperature response. Large intermodel differences in the lapse rate feedback are observed and shown to be associated with differing regional patterns of surface warming. Consistent with previous studies, it is found that the vertical changes in temperature and water vapor are tightly coupled in all models and, importantly, demonstrate that intermodel differences in the sum of lapse rate and water vapor feedbacks are small. In contrast, intermodel differences in cloud feedback are found to provide the largest source of uncertainty in current predictions of climate sensitivity.

## Abstract

A two-layer quasi-geostrophic model is used to study the effects of a meridionally sheared zonal flow on the life cycle of a weakly unstable baroclinic wave. In most of the cases analyzed, the fluid is inviscid with the exception of scale-selective fourth-order horizontal diffusion. The initial zonal flow is identically zero in the lower layer. The character of the eddy life cycle in the limit of weak supercritically is shown to depend on whether or not the meridional shell in the upper layer is strong enough to produce a critical latitude for the wave.

If the shear is sufficiently weak, the wave undergoes periodic amplitude vacillation characterized by symmetric growth and *baroclinic* decay. However, when the meridional shear is strong enough to allow for the existence of a critical layer, the flow undergoes an asymmetric life cycle which resembles that found by Simmons and Hoskins in a primitive equation model on the sphere: the wave grows baroclinically but decays *barotropically* toward a wave-free state. Throughout the barotropic decay stage, the wave is breaking and being absorbed either at or before the critical layer. As the supercriticality is increased, strong reflection begins to occur at the location of the wave breaking, resulting in irregular amplitude vacillation. Consistent with critical layer theory, when a reflecting state is created the solution is sensitive to the inclusion of higher zonal harmonies of the fundamental wave.

By relaxing the potential vorticity distribution back to an unstable state, periodic solutions are obtained in which each episode of growth and decay is similar to that found in these nearly inviscid solutions.

## Abstract

A two-layer quasi-geostrophic model is used to study the effects of a meridionally sheared zonal flow on the life cycle of a weakly unstable baroclinic wave. In most of the cases analyzed, the fluid is inviscid with the exception of scale-selective fourth-order horizontal diffusion. The initial zonal flow is identically zero in the lower layer. The character of the eddy life cycle in the limit of weak supercritically is shown to depend on whether or not the meridional shell in the upper layer is strong enough to produce a critical latitude for the wave.

If the shear is sufficiently weak, the wave undergoes periodic amplitude vacillation characterized by symmetric growth and *baroclinic* decay. However, when the meridional shear is strong enough to allow for the existence of a critical layer, the flow undergoes an asymmetric life cycle which resembles that found by Simmons and Hoskins in a primitive equation model on the sphere: the wave grows baroclinically but decays *barotropically* toward a wave-free state. Throughout the barotropic decay stage, the wave is breaking and being absorbed either at or before the critical layer. As the supercriticality is increased, strong reflection begins to occur at the location of the wave breaking, resulting in irregular amplitude vacillation. Consistent with critical layer theory, when a reflecting state is created the solution is sensitive to the inclusion of higher zonal harmonies of the fundamental wave.

By relaxing the potential vorticity distribution back to an unstable state, periodic solutions are obtained in which each episode of growth and decay is similar to that found in these nearly inviscid solutions.

## Abstract

*f*plane is extended to a Î² plane. In terms of the nondimensional number Î¾=

*U*/(Î²Î»

^{2}), where Î» is the deformation radius and

*U*is the mean thermal wind, the result for the rms eddy velocity

*V*, the characteristic wavenumber of the energy-containing eddies and of the eddy-driven jets

*k*

_{j}, and the magnitude of the eddy diffusivity for potential vorticity

*D*, in the limit Î¾ â‰« 1, are as follows:

*V*

*U*

*k*

_{j}^{âˆ’1}

*D*

*U*

^{2}

*V*

*T*

^{2}

^{âˆ’1}

*k*

_{j}*T*

*D*

^{2}

*T*

^{3}

^{âˆ’1}

*T*is a timescale determined by the environment; in particular, it equals Î»

*U*

^{âˆ’1}in the two-layer model and

*N*(

*f*âˆ‚

_{z}

*U*)

^{âˆ’1}in a continuous flow with uniform shear and stratification. This same scaling has also been suggested as relevant to a continuously stratified fluid in the opposite limit, Î¾ â‰ª 1. Therefore, the authors suggest that it may be of general relevance in planetary atmosphere and in the oceans.

## Abstract

*f*plane is extended to a Î² plane. In terms of the nondimensional number Î¾=

*U*/(Î²Î»

^{2}), where Î» is the deformation radius and

*U*is the mean thermal wind, the result for the rms eddy velocity

*V*, the characteristic wavenumber of the energy-containing eddies and of the eddy-driven jets

*k*

_{j}, and the magnitude of the eddy diffusivity for potential vorticity

*D*, in the limit Î¾ â‰« 1, are as follows:

*V*

*U*

*k*

_{j}^{âˆ’1}

*D*

*U*

^{2}

*V*

*T*

^{2}

^{âˆ’1}

*k*

_{j}*T*

*D*

^{2}

*T*

^{3}

^{âˆ’1}

*T*is a timescale determined by the environment; in particular, it equals Î»

*U*

^{âˆ’1}in the two-layer model and

*N*(

*f*âˆ‚

_{z}

*U*)

^{âˆ’1}in a continuous flow with uniform shear and stratification. This same scaling has also been suggested as relevant to a continuously stratified fluid in the opposite limit, Î¾ â‰ª 1. Therefore, the authors suggest that it may be of general relevance in planetary atmosphere and in the oceans.

## Abstract

The sensitivity of an atmospheric GCM coupled to a mixed-layer ocean to changes in orbital parameters is investigated. Three experiments are compared. One has perihelion at summer solstice and a large obliquity; another has perihelion at winter solstice and a low obliquity. The first of these is favorable for warm summers; the second for cool summers. A third experiment, with perihelion at summer solstice and the lower value of obliquity, is used to examine the relative importance of the changes in perihelion and obliquity. The eccentricity is set at 0.04 in all cases.

Surface temperature responses are as large as 15Â°C, with the largest response over North America in summer. Changes in monsoons and Arctic sea ice are consistent with previous GCM studies. A perpetual summer version of the atmospheric model is used to investigate the positive feedback due to soil moisture. Drying of the soil over North America is found to increase the temperature response by approximately 50% and is also essential to the decrease in summertime precipitation in that region. Soil moisture changes also enhance the precipitation response over central Africa, but have little effect on the model's Asian monsoon.

The orbital parameters most favorable for expansion of the Northern Hemisphere glaciers, that is, minimal seasonality, do not produce permanent snow cover. Several model deficiencies that act to accelerate the melting of snow in spring may be responsible.

## Abstract

The sensitivity of an atmospheric GCM coupled to a mixed-layer ocean to changes in orbital parameters is investigated. Three experiments are compared. One has perihelion at summer solstice and a large obliquity; another has perihelion at winter solstice and a low obliquity. The first of these is favorable for warm summers; the second for cool summers. A third experiment, with perihelion at summer solstice and the lower value of obliquity, is used to examine the relative importance of the changes in perihelion and obliquity. The eccentricity is set at 0.04 in all cases.

Surface temperature responses are as large as 15Â°C, with the largest response over North America in summer. Changes in monsoons and Arctic sea ice are consistent with previous GCM studies. A perpetual summer version of the atmospheric model is used to investigate the positive feedback due to soil moisture. Drying of the soil over North America is found to increase the temperature response by approximately 50% and is also essential to the decrease in summertime precipitation in that region. Soil moisture changes also enhance the precipitation response over central Africa, but have little effect on the model's Asian monsoon.

The orbital parameters most favorable for expansion of the Northern Hemisphere glaciers, that is, minimal seasonality, do not produce permanent snow cover. Several model deficiencies that act to accelerate the melting of snow in spring may be responsible.

## Abstract

In models of radiativeâ€“convective equilibrium it is known that convection can spontaneously aggregate into one single localized moist region if the domain is large enough. The large changes in the mean climate state and radiative fluxes accompanying this self-aggregation raise questions as to what simulations at lower resolutions with parameterized convection, in similar homogeneous geometries, should be expected to produce to be considered successful in mimicking a cloud-resolving model.

The authors investigate this self-aggregation in a nonrotating, three-dimensional cloud-resolving model on a square domain without large-scale forcing. It is found that self-aggregation is sensitive not only to the domain size, but also to the horizontal resolution. With horizontally homogeneous initial conditions, convective aggregation only occurs on domains larger than about 200km and with resolutions coarser than about 2km in the model examined. The system exhibits hysteresis, so that with aggregated initial conditions, convection remains aggregated even at our finest resolution, 500m, as long as the domain is greater than 200â€“300km.

The sensitivity of self-aggregation to resolution and domain size in this model is due to the sensitivity of the distribution of low clouds to these two parameters. Indeed, the mechanism responsible for the aggregation of convection is the dynamical response to the longwave radiative cooling from low clouds. Strong longwave cooling near cloud top in dry regions forces downward motion, which by continuity generates inflow near cloud top and near-surface outflow from dry regions. This circulation results in the net export of moist static energy from regions with low moist static energy, yielding a positive feedback.

## Abstract

In models of radiativeâ€“convective equilibrium it is known that convection can spontaneously aggregate into one single localized moist region if the domain is large enough. The large changes in the mean climate state and radiative fluxes accompanying this self-aggregation raise questions as to what simulations at lower resolutions with parameterized convection, in similar homogeneous geometries, should be expected to produce to be considered successful in mimicking a cloud-resolving model.

The authors investigate this self-aggregation in a nonrotating, three-dimensional cloud-resolving model on a square domain without large-scale forcing. It is found that self-aggregation is sensitive not only to the domain size, but also to the horizontal resolution. With horizontally homogeneous initial conditions, convective aggregation only occurs on domains larger than about 200km and with resolutions coarser than about 2km in the model examined. The system exhibits hysteresis, so that with aggregated initial conditions, convection remains aggregated even at our finest resolution, 500m, as long as the domain is greater than 200â€“300km.

The sensitivity of self-aggregation to resolution and domain size in this model is due to the sensitivity of the distribution of low clouds to these two parameters. Indeed, the mechanism responsible for the aggregation of convection is the dynamical response to the longwave radiative cooling from low clouds. Strong longwave cooling near cloud top in dry regions forces downward motion, which by continuity generates inflow near cloud top and near-surface outflow from dry regions. This circulation results in the net export of moist static energy from regions with low moist static energy, yielding a positive feedback.

## Abstract

This study investigates the parameter dependence of eddy heat flux in a homogeneous quasigeostrophic two-layer model on a *Î²* plane with imposed environmental vertical wind shear and quadratic frictional drag. We examine the extent to which the results can be explained by a recently proposed diffusivity theory for passive tracers in two-dimensional turbulence. To account for the differences between two-layer and two-dimensional models, we modify the two-dimensional theory according to our two-layer *f*-plane analyses reported in an earlier study. Specifically, we replace the classic Kolmogorovian spectral slope, âˆ’5/3, assumed to predict eddy kinetic energy spectrum in the former with a larger slope, âˆ’7/3, suggested by a heuristic argument and fit to the model results in the latter. It is found that the modified theory provides a reasonable estimate within the regime where both *c*
_{D} is the nondimensional drag coefficient divided by the depth of the layer, *k*
_{d} is the wavenumber of deformation radius, and *U* is the imposed background vertical wind shear). For values of

## Abstract

This study investigates the parameter dependence of eddy heat flux in a homogeneous quasigeostrophic two-layer model on a *Î²* plane with imposed environmental vertical wind shear and quadratic frictional drag. We examine the extent to which the results can be explained by a recently proposed diffusivity theory for passive tracers in two-dimensional turbulence. To account for the differences between two-layer and two-dimensional models, we modify the two-dimensional theory according to our two-layer *f*-plane analyses reported in an earlier study. Specifically, we replace the classic Kolmogorovian spectral slope, âˆ’5/3, assumed to predict eddy kinetic energy spectrum in the former with a larger slope, âˆ’7/3, suggested by a heuristic argument and fit to the model results in the latter. It is found that the modified theory provides a reasonable estimate within the regime where both *c*
_{D} is the nondimensional drag coefficient divided by the depth of the layer, *k*
_{d} is the wavenumber of deformation radius, and *U* is the imposed background vertical wind shear). For values of

A benchmark calculation is proposed for evaluating the dynamical cores of atmospheric general circulation models independently of the physical parameterizations. The test focuses on the long-term statistical properties of a fully developed general circulation; thus, it is particularly appropriate for intercomparing the dynamics used in climate models. To illustrate the use of this benchmark, two very different atmospheric dynamical coresâ€”one spectral, one finite differenceâ€”are compared. It is found that the long-term statistics produced by the two models are very similar. Selected results from these calculations are presented to initiate the intercomparison.

A benchmark calculation is proposed for evaluating the dynamical cores of atmospheric general circulation models independently of the physical parameterizations. The test focuses on the long-term statistical properties of a fully developed general circulation; thus, it is particularly appropriate for intercomparing the dynamics used in climate models. To illustrate the use of this benchmark, two very different atmospheric dynamical coresâ€”one spectral, one finite differenceâ€”are compared. It is found that the long-term statistics produced by the two models are very similar. Selected results from these calculations are presented to initiate the intercomparison.

## Abstract

The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory [similar to that introduced by Schneider (1977)] is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distribution of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

## Abstract

The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory [similar to that introduced by Schneider (1977)] is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distribution of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

## Abstract

A review is provided of stationary wave theory, the theory for the deviations from zonal symmetry of the climate. To help focus the discussion the authors concentrate exclusively on northern winter. Several theoretical issues, including the external Rossby wave dispersion relation and vertical structure, critical latitude absorption, the nonlinear response to orography, and the interaction of forced wave trains with preexisting zonal asymmetries, are chosen for discussion while simultaneously presenting a decomposition of the wintertime stationary wave field using a nonlinear steady-state model.

## Abstract

A review is provided of stationary wave theory, the theory for the deviations from zonal symmetry of the climate. To help focus the discussion the authors concentrate exclusively on northern winter. Several theoretical issues, including the external Rossby wave dispersion relation and vertical structure, critical latitude absorption, the nonlinear response to orography, and the interaction of forced wave trains with preexisting zonal asymmetries, are chosen for discussion while simultaneously presenting a decomposition of the wintertime stationary wave field using a nonlinear steady-state model.

## Abstract

The behavior of a GCM column physics package in a nonrotating, doubly periodic, homogeneous setting with prescribed SSTs is examined. This radiativeâ€“convective framework is proposed as a useful tool for studying some of the interactions between convection and larger-scale dynamics and the effects of differing modeling assumptions on convective organization and cloud feedbacks.

For the column physics utilized here, from the Geophysical Fluid Dynamics Laboratory (GFDL) AM2 model, many of the properties of the homogeneous, nonrotating model are closely tied to the fraction of precipitation that is large-scale, rather than convective. Significant large-scale precipitation appears above a critical temperature and then increases with further increases in temperature. The amount of large-scale precipitation is a function of horizontal resolution and can also be controlled by modifying the convection scheme, as is illustrated here by modifying assumptions concerning entrainment into convective plumes. Significant similarities are found between the behavior of the homogeneous model and that of the Tropics of the parent GCM when ocean temperatures are increased and when the convection scheme is modified.

## Abstract

The behavior of a GCM column physics package in a nonrotating, doubly periodic, homogeneous setting with prescribed SSTs is examined. This radiativeâ€“convective framework is proposed as a useful tool for studying some of the interactions between convection and larger-scale dynamics and the effects of differing modeling assumptions on convective organization and cloud feedbacks.

For the column physics utilized here, from the Geophysical Fluid Dynamics Laboratory (GFDL) AM2 model, many of the properties of the homogeneous, nonrotating model are closely tied to the fraction of precipitation that is large-scale, rather than convective. Significant large-scale precipitation appears above a critical temperature and then increases with further increases in temperature. The amount of large-scale precipitation is a function of horizontal resolution and can also be controlled by modifying the convection scheme, as is illustrated here by modifying assumptions concerning entrainment into convective plumes. Significant similarities are found between the behavior of the homogeneous model and that of the Tropics of the parent GCM when ocean temperatures are increased and when the convection scheme is modified.