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## Abstract

In zonally averaged chemical transport models of the stratosphere, quasi-isentropic mixing is represented by diffusion in latitude. However, it is fairly certain that the real mixing is to some extent nonlocal, so that the diffusive representation is not formally justifiable. This issue is explored from a point of view that combines theory and empiricism. Several models of mixing are described and compared. The most general, including as special cases all of the other models considered, is the integral or “transilient matrix” model. Some known properties of transilient matrices are discussed in a more formal way than has been done previously, and some new results concerning these matrices and associated equations are derived. Simpler models include the familiar diffusion model, a simple model of nonlocal mixing in which tracer concentrations are everywhere relaxed toward the global average, and a “leaky barrier” model in which two regions of nonlocal mixing are separated by a weakly diffusive transport barrier. Solutions to the latter two models, with linear chemistry included to allow nontrivial steady states, are used to derive their “effective diffusivities.” These are then used to test how well a diffusion model can mimic the behavior of the nonlocal mixing models over finite regions of parameter space. The diffusion model proves fairly robust, yielding fairly accurate results in situations where no formal argument indicates that it should. These results provide qualified support, from a purely empirical perspective, for the practice of using the diffusion model to represent stratospheric mixing in zonally averaged models. Several important caveats suggest nonetheless that exploration of more theoretically satisfactory representations is warranted.

## Abstract

In zonally averaged chemical transport models of the stratosphere, quasi-isentropic mixing is represented by diffusion in latitude. However, it is fairly certain that the real mixing is to some extent nonlocal, so that the diffusive representation is not formally justifiable. This issue is explored from a point of view that combines theory and empiricism. Several models of mixing are described and compared. The most general, including as special cases all of the other models considered, is the integral or “transilient matrix” model. Some known properties of transilient matrices are discussed in a more formal way than has been done previously, and some new results concerning these matrices and associated equations are derived. Simpler models include the familiar diffusion model, a simple model of nonlocal mixing in which tracer concentrations are everywhere relaxed toward the global average, and a “leaky barrier” model in which two regions of nonlocal mixing are separated by a weakly diffusive transport barrier. Solutions to the latter two models, with linear chemistry included to allow nontrivial steady states, are used to derive their “effective diffusivities.” These are then used to test how well a diffusion model can mimic the behavior of the nonlocal mixing models over finite regions of parameter space. The diffusion model proves fairly robust, yielding fairly accurate results in situations where no formal argument indicates that it should. These results provide qualified support, from a purely empirical perspective, for the practice of using the diffusion model to represent stratospheric mixing in zonally averaged models. Several important caveats suggest nonetheless that exploration of more theoretically satisfactory representations is warranted.

## Abstract

Climatologically, the equatorial western Pacific warm pool region is a local minimum in surface evaporation and a local maximum in precipitation. The moist static energy budget in this situation requires a collocated minimum in radiative cooling of the atmosphere, which is supplied by the greenhouse effect of high clouds associated with the precipitation. However, this diagnostic statement does not explain why the evaporation minimum should coexist with the precipitation maximum. A simple physical model of the Walker circulation is used as the basis for an argument that the surface heat budget and the radiative effects of high clouds are essential to the existence of this feature, while variations in surface wind speed are not, though the latter may play an important role in determining the sea surface temperature.

## Abstract

Climatologically, the equatorial western Pacific warm pool region is a local minimum in surface evaporation and a local maximum in precipitation. The moist static energy budget in this situation requires a collocated minimum in radiative cooling of the atmosphere, which is supplied by the greenhouse effect of high clouds associated with the precipitation. However, this diagnostic statement does not explain why the evaporation minimum should coexist with the precipitation maximum. A simple physical model of the Walker circulation is used as the basis for an argument that the surface heat budget and the radiative effects of high clouds are essential to the existence of this feature, while variations in surface wind speed are not, though the latter may play an important role in determining the sea surface temperature.

## Abstract

Observational studies suggest that the stratospheric quasi-biennial oscillation (QBO) can modulate tropical deep convection. The authors use a cloud-resolving model with a limited domain, representing a convective column in the tropics, to study the mechanisms of this modulation. The large-scale circulation is parameterized using the weak temperature gradient (WTG) approximation, under which the parameterized large-scale vertical motion acts to relax the horizontal-mean temperature toward a specified reference profile. Temperature variations typically seen in easterly and westerly phases are imposed in the upper troposphere and lower stratosphere of this reference profile. The responses of convection are studied over different sea surface temperatures, holding the reference temperature profile fixed. This can be thought of as studying the response of convection to the QBO over different “relative SSTs” and also corresponds to different equilibrium precipitation rates in the control simulation. The equilibrium precipitation rate shows slight increases in response to a QBO easterly phase temperature perturbation over small SST anomalies and strong decreases over large SST anomalies, and vice versa for the QBO westerly phase perturbation. A column moist static energy budget analysis reveals that the QBO modulates the convective precipitation through two pathways: it changes the high-cloud properties and thus the column radiative cooling, and it alters the shape of the large-scale vertical motion and thus the efficiency of energy transport by the large-scale flow. The nonmonotonicity of the precipitation response with respect to relative SST results from the competition of these two effects.

## Abstract

Observational studies suggest that the stratospheric quasi-biennial oscillation (QBO) can modulate tropical deep convection. The authors use a cloud-resolving model with a limited domain, representing a convective column in the tropics, to study the mechanisms of this modulation. The large-scale circulation is parameterized using the weak temperature gradient (WTG) approximation, under which the parameterized large-scale vertical motion acts to relax the horizontal-mean temperature toward a specified reference profile. Temperature variations typically seen in easterly and westerly phases are imposed in the upper troposphere and lower stratosphere of this reference profile. The responses of convection are studied over different sea surface temperatures, holding the reference temperature profile fixed. This can be thought of as studying the response of convection to the QBO over different “relative SSTs” and also corresponds to different equilibrium precipitation rates in the control simulation. The equilibrium precipitation rate shows slight increases in response to a QBO easterly phase temperature perturbation over small SST anomalies and strong decreases over large SST anomalies, and vice versa for the QBO westerly phase perturbation. A column moist static energy budget analysis reveals that the QBO modulates the convective precipitation through two pathways: it changes the high-cloud properties and thus the column radiative cooling, and it alters the shape of the large-scale vertical motion and thus the efficiency of energy transport by the large-scale flow. The nonmonotonicity of the precipitation response with respect to relative SST results from the competition of these two effects.

## Abstract

This paper examines the influence of imposed drying, intended to represent horizontal advection of dry air, on parameterized deep convection interacting with large-scale dynamics in a single-column model framework. Two single-column models, one based on the NASA Goddard Earth Observing System general circulation model version 5 (GEOS5) and the other developed by Bony and Emanuel, are run in weak temperature gradient mode. Drying is imposed by relaxation of the specific humidity field toward zero within a specified vertical layer. The strength of the drying is controlled by specifying either the relaxation time scale or the vertically integrated drying tendency; results are insensitive to which specification is used.

The two models reach very different solutions for the same boundary conditions and model configuration. Even when adjustments to the boundary conditions and model parameters are made to render the precipitation rates similar, large differences in the profiles of relative humidity and large-scale vertical velocity persist. In both models, however, drying in the middle troposphere is more effective, per kg m^{−2} s^{−1} (or W m^{−2}) of imposed drying, in suppressing precipitation than is drying in the lower troposphere. Even when compared at equal relaxation time (corresponding to weaker net drying in the middle than lower troposphere), middle-tropospheric drying is comparably effective to lower-tropospheric drying. Upper-tropospheric drying has a relatively small effect on precipitation, although large drying in the upper troposphere cannot be imposed as a steady state because of the lack of moisture there. Consistent with the other model differences, the gross moist stabilities of the two models are quite different and vary somewhat differently as a function of imposed drying, but in both models the gross moist stability increases as the drying is increased when it is less than around 30 W m^{−2} and located in the middle troposphere. For lower-tropospheric drying, the gross moist stability either decreases with increased drying or increases more slowly than for middle-tropospheric drying.

## Abstract

This paper examines the influence of imposed drying, intended to represent horizontal advection of dry air, on parameterized deep convection interacting with large-scale dynamics in a single-column model framework. Two single-column models, one based on the NASA Goddard Earth Observing System general circulation model version 5 (GEOS5) and the other developed by Bony and Emanuel, are run in weak temperature gradient mode. Drying is imposed by relaxation of the specific humidity field toward zero within a specified vertical layer. The strength of the drying is controlled by specifying either the relaxation time scale or the vertically integrated drying tendency; results are insensitive to which specification is used.

The two models reach very different solutions for the same boundary conditions and model configuration. Even when adjustments to the boundary conditions and model parameters are made to render the precipitation rates similar, large differences in the profiles of relative humidity and large-scale vertical velocity persist. In both models, however, drying in the middle troposphere is more effective, per kg m^{−2} s^{−1} (or W m^{−2}) of imposed drying, in suppressing precipitation than is drying in the lower troposphere. Even when compared at equal relaxation time (corresponding to weaker net drying in the middle than lower troposphere), middle-tropospheric drying is comparably effective to lower-tropospheric drying. Upper-tropospheric drying has a relatively small effect on precipitation, although large drying in the upper troposphere cannot be imposed as a steady state because of the lack of moisture there. Consistent with the other model differences, the gross moist stabilities of the two models are quite different and vary somewhat differently as a function of imposed drying, but in both models the gross moist stability increases as the drying is increased when it is less than around 30 W m^{−2} and located in the middle troposphere. For lower-tropospheric drying, the gross moist stability either decreases with increased drying or increases more slowly than for middle-tropospheric drying.

## Abstract

This study discusses the direct diagnosis of stratosphere–troposphere exchange. The method introduced by Wei is applied to the Goddard Earth Observation System assimilated dataset. In many respects, the results generally agree with those of other studies using the same method and different datasets. However, sensitivity tests and theoretical considerations indicate that the instantaneous two-way exchange may be significantly exaggerated by the Wei method, because the method is rather sensitive to input data errors such as those that are invariably present in assimilated datasets. The method becomes somewhat better conditioned as the results are more heavily averaged, but this also reduces the method’s ability to diagnose two-way exchange. Additionally, when the flux across various surfaces is averaged over the globe and the entire year, the result implies unrealistically large imbalances in the annually averaged mass budget of the stratosphere. This could be caused by modest biases in the model used to perform the data assimilation. Since pure model simulations have an internal dynamical consistency that is lacking in assimilated datasets, the analysis appears to explain the fairly large discrepancies between the two-way fluxes obtained in studies using models and those obtained in studies using assimilated datasets. It may also explain the discrepancies between the net fluxes obtained by the Wei method and those obtained by other methods.

## Abstract

This study discusses the direct diagnosis of stratosphere–troposphere exchange. The method introduced by Wei is applied to the Goddard Earth Observation System assimilated dataset. In many respects, the results generally agree with those of other studies using the same method and different datasets. However, sensitivity tests and theoretical considerations indicate that the instantaneous two-way exchange may be significantly exaggerated by the Wei method, because the method is rather sensitive to input data errors such as those that are invariably present in assimilated datasets. The method becomes somewhat better conditioned as the results are more heavily averaged, but this also reduces the method’s ability to diagnose two-way exchange. Additionally, when the flux across various surfaces is averaged over the globe and the entire year, the result implies unrealistically large imbalances in the annually averaged mass budget of the stratosphere. This could be caused by modest biases in the model used to perform the data assimilation. Since pure model simulations have an internal dynamical consistency that is lacking in assimilated datasets, the analysis appears to explain the fairly large discrepancies between the two-way fluxes obtained in studies using models and those obtained in studies using assimilated datasets. It may also explain the discrepancies between the net fluxes obtained by the Wei method and those obtained by other methods.

## Abstract

A model of intermediate complexity based on quasi-equilibrium theory—a version of the Quasi-Equilibrium Tropical Circulation Model with a prognostic atmospheric boundary layer, as well as two free-tropospheric modes in momentum, and one each in moisture and temperature—is used in a zonally symmetric aquaplanet configuration to study the sensitivity of the Hadley circulation to the sea surface temperature (SST) latitudinal distribution. For equatorially symmetric SST forcing with large SST gradients in the tropics, the model simulates the classical double Hadley cell with one equatorial intertropical convergence zone (ITCZ). For small SST gradients in the tropics, the model exhibits multiple equilibria, with one equatorially symmetric equilibrium and two asymmetric equilibria (mirror images of each other) with an off-equatorial ITCZ.

Further investigation of the feedbacks at play in the model shows that the assumed vertical structure of temperature variations is crucial to the existence and stability of the asymmetric equilibria. The free-tropospheric moisture–convection feedback must also be sufficiently strong to sustain asymmetric equilibria. Both results suggest that the specific physics of a given climate model condition determine the existence of multiple equilibria via the resulting sensitivity of the convection to free-tropospheric humidity and the vertical structure of adiabatic heating. The symmetry-breaking mechanism and resulting multiple equilibria have their origin in the local multiple equilibria that can be described by a single-column model using the weak temperature gradient approximation.

An additional experiment using an SST latitudinal distribution with a relative minimum at the equator shows that the feedbacks controlling these multiple equilibria might be relevant to the double-ITCZ problem.

## Abstract

A model of intermediate complexity based on quasi-equilibrium theory—a version of the Quasi-Equilibrium Tropical Circulation Model with a prognostic atmospheric boundary layer, as well as two free-tropospheric modes in momentum, and one each in moisture and temperature—is used in a zonally symmetric aquaplanet configuration to study the sensitivity of the Hadley circulation to the sea surface temperature (SST) latitudinal distribution. For equatorially symmetric SST forcing with large SST gradients in the tropics, the model simulates the classical double Hadley cell with one equatorial intertropical convergence zone (ITCZ). For small SST gradients in the tropics, the model exhibits multiple equilibria, with one equatorially symmetric equilibrium and two asymmetric equilibria (mirror images of each other) with an off-equatorial ITCZ.

Further investigation of the feedbacks at play in the model shows that the assumed vertical structure of temperature variations is crucial to the existence and stability of the asymmetric equilibria. The free-tropospheric moisture–convection feedback must also be sufficiently strong to sustain asymmetric equilibria. Both results suggest that the specific physics of a given climate model condition determine the existence of multiple equilibria via the resulting sensitivity of the convection to free-tropospheric humidity and the vertical structure of adiabatic heating. The symmetry-breaking mechanism and resulting multiple equilibria have their origin in the local multiple equilibria that can be described by a single-column model using the weak temperature gradient approximation.

An additional experiment using an SST latitudinal distribution with a relative minimum at the equator shows that the feedbacks controlling these multiple equilibria might be relevant to the double-ITCZ problem.

## Abstract

The Madden–Julian oscillation (MJO) and the boreal summer intraseasonal oscillation (BSISO) are fundamental modes of variability in the tropical atmosphere on the intraseasonal time scale. A linear model, using a moist shallow water equation set on an equatorial beta plane, is developed to provide a unified treatment of the two modes and to understand their growth and propagation over the Indian Ocean. Moisture is assumed to increase linearly with longitude and to decrease quadratically with latitude. Solutions are obtained through linear stability analysis, considering the gravest (*n* = 1) meridional mode with nonzero meridional velocity. Anomalies in zonal moisture advection and surface fluxes are both proportional to those in zonal wind, but of opposite sign. With observation-based estimates for both effects, the zonal advection dominates, and drives the planetary-scale instability. With a sufficiently small meridional moisture gradient, the horizontal structure exhibits oscillations with latitude and a northwest–southeast horizontal tilt in the Northern Hemisphere, qualitatively resembling the observed BSISO. As the meridional moisture gradient increases, the horizontal tilt decreases and the spatial pattern transforms toward the “swallowtail” structure associated with the MJO, with cyclonic gyres in both hemispheres straddling the equatorial precipitation maximum. These results suggest that the magnitude of the meridional moisture gradient shapes the horizontal structures, leading to the transformation from the BSISO-like tilted horizontal structure to the MJO-like neutral wave structure as the meridional moisture gradient changes with the seasons. The existence and behavior of these intraseasonal modes can be understood as a consequence of phase speed matching between the equatorial mode with zero meridional velocity (analogous to the dry Kelvin wave) and a local off-equatorial component that is characterized by considering an otherwise similar system on an *f* plane.

## Abstract

The Madden–Julian oscillation (MJO) and the boreal summer intraseasonal oscillation (BSISO) are fundamental modes of variability in the tropical atmosphere on the intraseasonal time scale. A linear model, using a moist shallow water equation set on an equatorial beta plane, is developed to provide a unified treatment of the two modes and to understand their growth and propagation over the Indian Ocean. Moisture is assumed to increase linearly with longitude and to decrease quadratically with latitude. Solutions are obtained through linear stability analysis, considering the gravest (*n* = 1) meridional mode with nonzero meridional velocity. Anomalies in zonal moisture advection and surface fluxes are both proportional to those in zonal wind, but of opposite sign. With observation-based estimates for both effects, the zonal advection dominates, and drives the planetary-scale instability. With a sufficiently small meridional moisture gradient, the horizontal structure exhibits oscillations with latitude and a northwest–southeast horizontal tilt in the Northern Hemisphere, qualitatively resembling the observed BSISO. As the meridional moisture gradient increases, the horizontal tilt decreases and the spatial pattern transforms toward the “swallowtail” structure associated with the MJO, with cyclonic gyres in both hemispheres straddling the equatorial precipitation maximum. These results suggest that the magnitude of the meridional moisture gradient shapes the horizontal structures, leading to the transformation from the BSISO-like tilted horizontal structure to the MJO-like neutral wave structure as the meridional moisture gradient changes with the seasons. The existence and behavior of these intraseasonal modes can be understood as a consequence of phase speed matching between the equatorial mode with zero meridional velocity (analogous to the dry Kelvin wave) and a local off-equatorial component that is characterized by considering an otherwise similar system on an *f* plane.

## Abstract

A set of idealized cloud-permitting simulations is performed to explore the influence of small islands on precipitating convection as a function of large-scale wind speed. The islands are situated in a long narrow ocean domain that is in radiative–convective equilibrium (RCE) as a whole, constraining the domain-average precipitation. The island occupies a small part of the domain, so that significant precipitation variations over the island can occur, compensated by smaller variations over the larger surrounding oceanic area.

While the prevailing wind speeds vary over flat islands, three distinct flow regimes occur. Rainfall is greatly enhanced, and a local symmetric circulation is formed in the time mean around the island, when the prevailing large-scale wind speed is small. The rainfall enhancement over the island is much reduced when the wind speed is increased to a moderate value. This difference is characterized by a change in the mechanisms by which convection is forced. A thermally forced sea breeze due to surface heating dominates when the large-scale wind is weak. Mechanically forced convection, on the other hand, is favored when the large-scale wind is moderately strong, and horizontal advection of temperature reduces the land–sea thermal contrast that drives the sea breeze. Further increases of the prevailing wind speed lead to strong asymmetry between the windward and leeward sides of the island, owing to gravity waves that result from the land–sea contrast in surface roughness as well as upward deflection of the horizontal flow by elevated diurnal heating. Small-amplitude topography (up to 800-m elevation is considered) has a quantitative impact but does not qualitatively alter the flow regimes or their dependence on wind speed.

## Abstract

A set of idealized cloud-permitting simulations is performed to explore the influence of small islands on precipitating convection as a function of large-scale wind speed. The islands are situated in a long narrow ocean domain that is in radiative–convective equilibrium (RCE) as a whole, constraining the domain-average precipitation. The island occupies a small part of the domain, so that significant precipitation variations over the island can occur, compensated by smaller variations over the larger surrounding oceanic area.

While the prevailing wind speeds vary over flat islands, three distinct flow regimes occur. Rainfall is greatly enhanced, and a local symmetric circulation is formed in the time mean around the island, when the prevailing large-scale wind speed is small. The rainfall enhancement over the island is much reduced when the wind speed is increased to a moderate value. This difference is characterized by a change in the mechanisms by which convection is forced. A thermally forced sea breeze due to surface heating dominates when the large-scale wind is weak. Mechanically forced convection, on the other hand, is favored when the large-scale wind is moderately strong, and horizontal advection of temperature reduces the land–sea thermal contrast that drives the sea breeze. Further increases of the prevailing wind speed lead to strong asymmetry between the windward and leeward sides of the island, owing to gravity waves that result from the land–sea contrast in surface roughness as well as upward deflection of the horizontal flow by elevated diurnal heating. Small-amplitude topography (up to 800-m elevation is considered) has a quantitative impact but does not qualitatively alter the flow regimes or their dependence on wind speed.

## Abstract

A single-column modeling approach is proposed to study the interaction between convection and large-scale dynamics using the quasigeostrophic (QG) framework. This approach extends the notion of “parameterization of large-scale dynamics,” previously applied in the tropics via the weak temperature gradient approximation and other comparable methods, to the extratropics, where balanced adiabatic dynamics plays a larger role in inducing large-scale vertical motion. The diabatic heating in an air column is resolved numerically by a single-column model or a cloud-resolving model. The large-scale vertical velocity, which controls vertical advection of temperature and moisture, is computed through the QG omega equation including the dry adiabatic terms and the diabatic heating term. The component due to diabatic heating can be thought of as geostrophic adjustment to that heating and couples the convection to the large-scale vertical motion. The approach is demonstrated using two representations of convection: a single-column model and linear response functions derived by Z. Kuang from a large set of cloud-resolving simulations. The results are qualitatively similar in both cases. The behavior of convection that is strongly coupled to large-scale dynamics is significantly different from that in the uncoupled case. The positive feedback of the diabatic heating on the large-scale vertical motion reduces the stability of the system, extends the decay time scale after initial perturbations, and increases the amplitude of convective responses to transient large-scale perturbations or imposed forcings. The diabatic feedback of convection on vertical motion is strongest for horizontal wavelengths on the order of the Rossby deformation radius.

## Abstract

A single-column modeling approach is proposed to study the interaction between convection and large-scale dynamics using the quasigeostrophic (QG) framework. This approach extends the notion of “parameterization of large-scale dynamics,” previously applied in the tropics via the weak temperature gradient approximation and other comparable methods, to the extratropics, where balanced adiabatic dynamics plays a larger role in inducing large-scale vertical motion. The diabatic heating in an air column is resolved numerically by a single-column model or a cloud-resolving model. The large-scale vertical velocity, which controls vertical advection of temperature and moisture, is computed through the QG omega equation including the dry adiabatic terms and the diabatic heating term. The component due to diabatic heating can be thought of as geostrophic adjustment to that heating and couples the convection to the large-scale vertical motion. The approach is demonstrated using two representations of convection: a single-column model and linear response functions derived by Z. Kuang from a large set of cloud-resolving simulations. The results are qualitatively similar in both cases. The behavior of convection that is strongly coupled to large-scale dynamics is significantly different from that in the uncoupled case. The positive feedback of the diabatic heating on the large-scale vertical motion reduces the stability of the system, extends the decay time scale after initial perturbations, and increases the amplitude of convective responses to transient large-scale perturbations or imposed forcings. The diabatic feedback of convection on vertical motion is strongest for horizontal wavelengths on the order of the Rossby deformation radius.

## Abstract

The authors introduce a simple model for the time-dependent evolution of tropical “hot spots,” or localized regions where the sea surface temperature (SST) becomes unusually high for a limited period of time. The model consists of a simple zero-dimensional atmospheric model coupled to an ocean mixed layer. For plausible parameter values, steady solutions of this model can become unstable to time-dependent oscillations, which are studied both by linear stability analysis and explicit time-dependent nonlinear simulation. For reasonable parameter values, the oscillations have periods ranging from intraseasonal to subannual. For parameter values only slightly beyond the threshold for instability, the oscillations become strongly nonlinear, and have a recharge–discharge character.

The basic mechanism for the instability and oscillations comes from cloud-radiative and wind-evaporation feedbacks, which play the same role in the dynamics and are lumped together into a single parameterization. This is possible because, under the assumption that the shortwave and longwave radiative effects of high clouds cancel at the top of the atmosphere, their net effect is only to transfer energy from the ocean to the atmosphere exactly as a surface flux does, and because the two processes are observed to be approximately in phase on intraseasonal timescales. Both feedbacks move energy from the ocean to the atmosphere in convective regions, intensifying the convection and thus destabilizing the system. The same energy transfer cools the ocean, which eventually (but not instantaneously, because of the mixed layer’s heat capacity) reduces the SST enough to render the model stable to deep convection, shutting off the convection. At that point the SST begins warming again under the resulting clear skies, starting the cycle over.

The authors also examine the forced linear response of the model, in a weakly stable regime, to an imposed atmospheric oscillation. This is meant to crudely represent forcing by an atmospheric intraseasonal oscillation. The model’s response as a function of mixed layer depth is not monotonic, but has a maximum around 10–20 m, which happens to be close to the observed value in the western Pacific warm pool.

## Abstract

The authors introduce a simple model for the time-dependent evolution of tropical “hot spots,” or localized regions where the sea surface temperature (SST) becomes unusually high for a limited period of time. The model consists of a simple zero-dimensional atmospheric model coupled to an ocean mixed layer. For plausible parameter values, steady solutions of this model can become unstable to time-dependent oscillations, which are studied both by linear stability analysis and explicit time-dependent nonlinear simulation. For reasonable parameter values, the oscillations have periods ranging from intraseasonal to subannual. For parameter values only slightly beyond the threshold for instability, the oscillations become strongly nonlinear, and have a recharge–discharge character.

The basic mechanism for the instability and oscillations comes from cloud-radiative and wind-evaporation feedbacks, which play the same role in the dynamics and are lumped together into a single parameterization. This is possible because, under the assumption that the shortwave and longwave radiative effects of high clouds cancel at the top of the atmosphere, their net effect is only to transfer energy from the ocean to the atmosphere exactly as a surface flux does, and because the two processes are observed to be approximately in phase on intraseasonal timescales. Both feedbacks move energy from the ocean to the atmosphere in convective regions, intensifying the convection and thus destabilizing the system. The same energy transfer cools the ocean, which eventually (but not instantaneously, because of the mixed layer’s heat capacity) reduces the SST enough to render the model stable to deep convection, shutting off the convection. At that point the SST begins warming again under the resulting clear skies, starting the cycle over.

The authors also examine the forced linear response of the model, in a weakly stable regime, to an imposed atmospheric oscillation. This is meant to crudely represent forcing by an atmospheric intraseasonal oscillation. The model’s response as a function of mixed layer depth is not monotonic, but has a maximum around 10–20 m, which happens to be close to the observed value in the western Pacific warm pool.