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- Author or Editor: J. David Neelin x
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Abstract
A model is developed for tropical air–sea interaction studies, which is intermediate in complexity between the large coupled general circulation models (coupled GCMs) coming into use and the simple two-level models with which pioneering El Niño–Southern Oscillation studies were carried out. The model consists of a stripped-down tropical Pacific ocean GCM, coupled to an atmospheric model which is sufficiently simple that steady state solutions may be found for low level flow and surface stress, given oceanic boundary conditions. This hybrid coupling of an ocean GCM to a steady atmospheric model permits examination of the nature of interannual coupled oscillations in the absence of atmospheric noise. Tests of the atmospheric model against an atmospheric GCM simulation of El Niño anomalies are presented, and the ocean model climatology is examined under several different conditions. Experiments with the coupled model exhibit a variety of behaviors within a realistic parameter range. These indicate a partial bifurcation diagram in which the coupled system undergoes a Hopf bifurcation from a stable climatology, giving rise to sustained El Niño-period oscillations. The amplitude, period and eastward extent of these oscillations increase with the strength of coupling and the El Niño-period oscillation itself becomes unstable to a higher frequency coupled mode which coexists with it and may affect predictability. The difference between these flow regimes may be relevant to results found by other investigators in coupled GCM experiments.
Abstract
A model is developed for tropical air–sea interaction studies, which is intermediate in complexity between the large coupled general circulation models (coupled GCMs) coming into use and the simple two-level models with which pioneering El Niño–Southern Oscillation studies were carried out. The model consists of a stripped-down tropical Pacific ocean GCM, coupled to an atmospheric model which is sufficiently simple that steady state solutions may be found for low level flow and surface stress, given oceanic boundary conditions. This hybrid coupling of an ocean GCM to a steady atmospheric model permits examination of the nature of interannual coupled oscillations in the absence of atmospheric noise. Tests of the atmospheric model against an atmospheric GCM simulation of El Niño anomalies are presented, and the ocean model climatology is examined under several different conditions. Experiments with the coupled model exhibit a variety of behaviors within a realistic parameter range. These indicate a partial bifurcation diagram in which the coupled system undergoes a Hopf bifurcation from a stable climatology, giving rise to sustained El Niño-period oscillations. The amplitude, period and eastward extent of these oscillations increase with the strength of coupling and the El Niño-period oscillation itself becomes unstable to a higher frequency coupled mode which coexists with it and may affect predictability. The difference between these flow regimes may be relevant to results found by other investigators in coupled GCM experiments.
Abstract
A modified shallow water model with simplified mixed layer dynamics and a sea surface temperature (SST) equation is employed to gain a theoretical understanding of the modes and mechanisms of coupled air-sea interaction in the tropics. Approximations suggested by a scaling analysis are used to obtain analytic results for the eigenmodes of the system. A slow time scale, unstable eigenmode associated with the time derivative of the SST equation is suggested to be important in giving rise to interannual oscillations. This slow SST mode is not necessarily linked to conventional equatorial oceanic wave modes. A useful limit of this mode is explored in which the wave speed of uncoupled oceanic wave modes is fast compared to the time scales that arise from the coupling. This is referred to as the fast-wave limit. The dispersion relationship in this limit is used to present a number of coupled feedback mechanisms, which contribute simultaneously to the instability of the SST mode.
It is suggested that interannual oscillations observed in a hybrid coupled general circulation model (HGCM) are related to the slow SST mode. A method of testing applicability of the fast-wave limit in any coupled model through distorted physics experiments is presented. Such experiments with the HGCM are employed to demonstrate that the fast-wave limit is quite a good approximation for interannual oscillations at moderate coupling. It is shown that the time delay associated with oceanic wave propagation across the basin is not essential to the existence of interannual coupled oscillations.
Asymptotic expressions are also derived for the eigenvalues of coupled Rossby and Kelvin wave modes in the simple model. The manner in which various coupling mechanisms affect the stability of these modes is discussed and the results are used to explain the behavior of a secondary bifurcation found in the HGCM in terms of coupled Kelvin wave instability. For coupled Rossby and Kelvin modes, various coupling mechanisms oppose one another, suggesting that instability of these modes will be less robust to changes of model parameters and basic state than that of the SST mode, in which all coupling mechanisms tend to give growth.
Abstract
A modified shallow water model with simplified mixed layer dynamics and a sea surface temperature (SST) equation is employed to gain a theoretical understanding of the modes and mechanisms of coupled air-sea interaction in the tropics. Approximations suggested by a scaling analysis are used to obtain analytic results for the eigenmodes of the system. A slow time scale, unstable eigenmode associated with the time derivative of the SST equation is suggested to be important in giving rise to interannual oscillations. This slow SST mode is not necessarily linked to conventional equatorial oceanic wave modes. A useful limit of this mode is explored in which the wave speed of uncoupled oceanic wave modes is fast compared to the time scales that arise from the coupling. This is referred to as the fast-wave limit. The dispersion relationship in this limit is used to present a number of coupled feedback mechanisms, which contribute simultaneously to the instability of the SST mode.
It is suggested that interannual oscillations observed in a hybrid coupled general circulation model (HGCM) are related to the slow SST mode. A method of testing applicability of the fast-wave limit in any coupled model through distorted physics experiments is presented. Such experiments with the HGCM are employed to demonstrate that the fast-wave limit is quite a good approximation for interannual oscillations at moderate coupling. It is shown that the time delay associated with oceanic wave propagation across the basin is not essential to the existence of interannual coupled oscillations.
Asymptotic expressions are also derived for the eigenvalues of coupled Rossby and Kelvin wave modes in the simple model. The manner in which various coupling mechanisms affect the stability of these modes is discussed and the results are used to explain the behavior of a secondary bifurcation found in the HGCM in terms of coupled Kelvin wave instability. For coupled Rossby and Kelvin modes, various coupling mechanisms oppose one another, suggesting that instability of these modes will be less robust to changes of model parameters and basic state than that of the SST mode, in which all coupling mechanisms tend to give growth.
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Abstract
The vertically integrated moist static energy equation provides a convenient starting point for the construction of simple models of the time-mean low level convergence in the tropics. A vertically integrated measure of the moist static stability, the “gross moist stability,” proves to be of central importance. Minima in this quantity mark the positions of the tropical convergence zones. We argue that the positions of these minima are determined by the time-mean moisture field, which is, in turn, closely tied to the time-mean surface temperature.
Abstract
The vertically integrated moist static energy equation provides a convenient starting point for the construction of simple models of the time-mean low level convergence in the tropics. A vertically integrated measure of the moist static stability, the “gross moist stability,” proves to be of central importance. Minima in this quantity mark the positions of the tropical convergence zones. We argue that the positions of these minima are determined by the time-mean moisture field, which is, in turn, closely tied to the time-mean surface temperature.
Abstract
The interaction between the collective effects of cumulus convection and large-scale dynamics is examined using the Betts–Miller moist convective adjustment (MCA) parameterization in a linearized primitive equation model on an equatorial β plane. In Part I of this paper, an analytical approach to the eigenvalue problem is taken using perturbation expansions in the cumulus adjustment time, which is short compared to planetary dynamical time scales. The modes of tropical variability that arise under MCA are dominated by the presence of moist processes; some modes act to adjust the system rapidly toward a convectively adjusted state, while others evolve on time scales set by the large-scale dynamics subject to near-adjusted (quasi equilibrium) thermodynamical constraints. Of the latter, a single vertical mode stands out, which obeys special balances implied by the quasi-equilibrium constraints and is the only propagating deep convective mode. The propagation speed is determined by an internally defined gross moist stability. For the Kelvin meridional mode, the phase speed and vertical structure are highly suggestive of those of the Madden–Julian (MJ) oscillation.
For the simple case considered here, which assumes a homogeneous, separable basic state and sufficiently large zonal scales, the modes of variability found under MCA are all stable under reasonable conditions, although a large subclass of modes (including the MJ mode) is only slowly decaying. This contrasts with many studies using Kuo-like convective parameterizations, which have conjectured that convective instability of the second kind (CISK) plays a role in maintaining planetary-scale tropical variability. The authors suggest that a terminology is needed by which to refer to convective interaction with dynamics (CID), without necessarily assuming that large-scale instability arises from this interaction. Under MCA, there is strong CID but not generally CISK. Instability of the MJ mode can occur through evaporation–wind feedback. This behavior under MCA provides a suggestive prototype for tropical motions evolving under quasi-equilibrium convective constraints.
Abstract
The interaction between the collective effects of cumulus convection and large-scale dynamics is examined using the Betts–Miller moist convective adjustment (MCA) parameterization in a linearized primitive equation model on an equatorial β plane. In Part I of this paper, an analytical approach to the eigenvalue problem is taken using perturbation expansions in the cumulus adjustment time, which is short compared to planetary dynamical time scales. The modes of tropical variability that arise under MCA are dominated by the presence of moist processes; some modes act to adjust the system rapidly toward a convectively adjusted state, while others evolve on time scales set by the large-scale dynamics subject to near-adjusted (quasi equilibrium) thermodynamical constraints. Of the latter, a single vertical mode stands out, which obeys special balances implied by the quasi-equilibrium constraints and is the only propagating deep convective mode. The propagation speed is determined by an internally defined gross moist stability. For the Kelvin meridional mode, the phase speed and vertical structure are highly suggestive of those of the Madden–Julian (MJ) oscillation.
For the simple case considered here, which assumes a homogeneous, separable basic state and sufficiently large zonal scales, the modes of variability found under MCA are all stable under reasonable conditions, although a large subclass of modes (including the MJ mode) is only slowly decaying. This contrasts with many studies using Kuo-like convective parameterizations, which have conjectured that convective instability of the second kind (CISK) plays a role in maintaining planetary-scale tropical variability. The authors suggest that a terminology is needed by which to refer to convective interaction with dynamics (CID), without necessarily assuming that large-scale instability arises from this interaction. Under MCA, there is strong CID but not generally CISK. Instability of the MJ mode can occur through evaporation–wind feedback. This behavior under MCA provides a suggestive prototype for tropical motions evolving under quasi-equilibrium convective constraints.
Abstract
Convective interaction with dynamics (CID) dictates the structure and behavior of the eigenmodes of the tropical atmosphere under moist convective adjustment (MCA) when the convective adjustment time scale, τ c, is much smaller than dynamical time scales, as examined analytically in Part I. Here, the modes are reexamined numerically to include the effects of finite τ c, again for a primitive equation model with the Betts-Miller MCA parameterization. The numerical results at planetary scales are consistent with the analytical approach, with two well-separated classes of vertical modes: one subset evolves at the cumulus time scale, while the other subset evolves at a time scale set by the large-scale dynamics. All modes are stable for homogeneous basic states in the presence of simple mechanical damping effects. Thus, there is no CISK at any scale under MCA. However, the finite τ c effect has the property of selectively damping the smallest scales while certain vertical modes at planetary scales decay only slowly. This planetary scale selection contrasts to many linear CISK studies, which tend to select the smallest scale.
The Madden–Julian mode, which resembles the observed tropical intraseasonal oscillation, is found as a single vertical mode arising through Kelvin wave-CID. When the evaporation-wind feedback is included, this slowly decaying MJ mode is selectively destabilized at wavenumber one or two, consistent with the observations in the tropics. Stochastic forcing by nonresolved mesoscale processes can also potentially account for the existence of large-scale tropical variance. When the stochastic forcing occurs in the thermodynamic equation, the propagating deep-convective mode at planetary scales is the most strongly excited. Kinematic forcing excites slowly decaying kinematically dominated modes but cannot account for the characteristics of observed Madden-Julian variance.
Abstract
Convective interaction with dynamics (CID) dictates the structure and behavior of the eigenmodes of the tropical atmosphere under moist convective adjustment (MCA) when the convective adjustment time scale, τ c, is much smaller than dynamical time scales, as examined analytically in Part I. Here, the modes are reexamined numerically to include the effects of finite τ c, again for a primitive equation model with the Betts-Miller MCA parameterization. The numerical results at planetary scales are consistent with the analytical approach, with two well-separated classes of vertical modes: one subset evolves at the cumulus time scale, while the other subset evolves at a time scale set by the large-scale dynamics. All modes are stable for homogeneous basic states in the presence of simple mechanical damping effects. Thus, there is no CISK at any scale under MCA. However, the finite τ c effect has the property of selectively damping the smallest scales while certain vertical modes at planetary scales decay only slowly. This planetary scale selection contrasts to many linear CISK studies, which tend to select the smallest scale.
The Madden–Julian mode, which resembles the observed tropical intraseasonal oscillation, is found as a single vertical mode arising through Kelvin wave-CID. When the evaporation-wind feedback is included, this slowly decaying MJ mode is selectively destabilized at wavenumber one or two, consistent with the observations in the tropics. Stochastic forcing by nonresolved mesoscale processes can also potentially account for the existence of large-scale tropical variance. When the stochastic forcing occurs in the thermodynamic equation, the propagating deep-convective mode at planetary scales is the most strongly excited. Kinematic forcing excites slowly decaying kinematically dominated modes but cannot account for the characteristics of observed Madden-Julian variance.
Abstract
Coupled ocean-atmosphere models exhibit a variety of forms of tropical interannual variability that may be understood as different flow regimes of the coupled system. The parameter dependence of the primary bifurcation is examined in a “stripped-down” version of the Zebiak and Cane model using the equatorial band approximation for the sea surface temperature (SST) equation as by Neelin. In Part I of this three-part series, numerical results are obtained for a conventional semispectral version; Parts II and III use an integral formulation to generate analytical results in simplifying limits. In the uncoupled case and in the fast-wave limit (where oceanic adjustment occurs fast compared to SST time scales), distinct sets of modes occur that are primarily related to the time scales of SST change (SST modes) and of oceanic adjustment (ocean-dynamics modes). Elsewhere in the parameter space, the leading modes are best characterized as mixed SST/ocean-dynamics modes; in particular, the continuous surfaces in parameter space formed by the eigenvalues of each type of mode can join.
A regime in the fast-wave limit in which the most unstable mode is purely growing, with SST anomalies in the eastern Pacific, proves to be a useful starting point for describing these mergers. This mode is linked to several oscillatory regimes by surfaces of degeneracy in the parameter space, at which two degrees of freedom merge. Within the fast-wave limit, changes in parameters controlling the strength of the surface layer or the atmospheric structure produce continuous transition of the stationary mode to propagating modes. Away from the fast-wave limit, the stationary mode persists at strong coupling even when time scales of ocean dynamics become important. On the weaker coupling side, the stationary mode joins to an oscillatory mode with mixed properties, with a standing oscillation in SST whose growth and spatial form may be understood from the SST mode at the fast-wave limit but whose period depends on subsurface oceanic dynamics. The oceanic dynamics, however, is only remotely related to that of the uncoupled problem. In fact, this standing-oscillatory mixed mode is insensitive to low-coupling complications involving connections to a sequence of uncoupled ocean modes at different parameter values, most of which are members of a discretized scattering spectrum. The implication that realistic coupled regimes are best understood from strong rather than weak coupling is pursued in Parts II and III. The interpretation of the standing-oscillatory regime as a stationary SST mode perturbed by wave dynamics gives a rigorous basis to the original physical interpretation of a simple model of Suarez and Schopf. However, viewing the connected modes as different regimes of a mixed SST/ocean-dynamics mode allows other simple models to be interpreted as alternate approximations to the same eigensurface; it also makes clear why varying degrees of propagating and standing oscillation can coexist in the same coupled mode.
Abstract
Coupled ocean-atmosphere models exhibit a variety of forms of tropical interannual variability that may be understood as different flow regimes of the coupled system. The parameter dependence of the primary bifurcation is examined in a “stripped-down” version of the Zebiak and Cane model using the equatorial band approximation for the sea surface temperature (SST) equation as by Neelin. In Part I of this three-part series, numerical results are obtained for a conventional semispectral version; Parts II and III use an integral formulation to generate analytical results in simplifying limits. In the uncoupled case and in the fast-wave limit (where oceanic adjustment occurs fast compared to SST time scales), distinct sets of modes occur that are primarily related to the time scales of SST change (SST modes) and of oceanic adjustment (ocean-dynamics modes). Elsewhere in the parameter space, the leading modes are best characterized as mixed SST/ocean-dynamics modes; in particular, the continuous surfaces in parameter space formed by the eigenvalues of each type of mode can join.
A regime in the fast-wave limit in which the most unstable mode is purely growing, with SST anomalies in the eastern Pacific, proves to be a useful starting point for describing these mergers. This mode is linked to several oscillatory regimes by surfaces of degeneracy in the parameter space, at which two degrees of freedom merge. Within the fast-wave limit, changes in parameters controlling the strength of the surface layer or the atmospheric structure produce continuous transition of the stationary mode to propagating modes. Away from the fast-wave limit, the stationary mode persists at strong coupling even when time scales of ocean dynamics become important. On the weaker coupling side, the stationary mode joins to an oscillatory mode with mixed properties, with a standing oscillation in SST whose growth and spatial form may be understood from the SST mode at the fast-wave limit but whose period depends on subsurface oceanic dynamics. The oceanic dynamics, however, is only remotely related to that of the uncoupled problem. In fact, this standing-oscillatory mixed mode is insensitive to low-coupling complications involving connections to a sequence of uncoupled ocean modes at different parameter values, most of which are members of a discretized scattering spectrum. The implication that realistic coupled regimes are best understood from strong rather than weak coupling is pursued in Parts II and III. The interpretation of the standing-oscillatory regime as a stationary SST mode perturbed by wave dynamics gives a rigorous basis to the original physical interpretation of a simple model of Suarez and Schopf. However, viewing the connected modes as different regimes of a mixed SST/ocean-dynamics mode allows other simple models to be interpreted as alternate approximations to the same eigensurface; it also makes clear why varying degrees of propagating and standing oscillation can coexist in the same coupled mode.
Abstract
The properties of the eigenmodes of the coupled tropical ocean-atmosphere system, linearized about a climatological basic state—and hence of the first bifurcation, which strongly determines the nature of the interannual variability, such as El Niño—show considerable dependence on the parameters of the coupled system. These eigenmodes are examined in a modified shallow-water model with simplified mixed-layer dynamics and a sea surface temperature (SST) equation, coupled to a simple atmospheric model. The model is designed so as to make analytical approximations feasible in various limits, as in a previous study by Neelin where the x-periodic case was analyzed. The realistic case of a finite ocean basin is treated here. An integral formulation of the eigenvalue problem is derived that provides a basis for making consistent approximations that include the effects of atmospheric and oceanic boundary conditions. We provide a scaling analysis to select parameters that give the most succinct insights into the behavior of the system, and outline the portions of this parameter space that are accessible to analytic results through the limits explored here and in Part III of this study. Important limits include the fast-wave limit, the limit where the time scale of ocean adjustment is fast compared to the time scale of SST change by coupled processes, and its converse, the fast-SST limit. The region of validity of the weak-coupling limit overlaps both of these, while that of the strong-coupling limit overlaps the fast-SST limit and approaches the region of validity of the fast-wave limit without a formal matching region.
In this part, we examine the weak-coupling limit, in which one expects the modes to be most closely related to those of the uncoupled problem. Here we treat two classes of mode from the uncoupled case: the SST modes (related to the time derivative of the SST equation) and the discrete modes from the ocean-dynamics spectrum, the ocean basin modes. From the numerical results of Part I, we know that away from the weak-coupling and fast-wave limits, the continuous surfaces in parameter space formed by the eigenvalues of each type of mode are joined, so that through most of parameter space the coupled modes are best characterized as mixed SST/ocean-dynamics modes. Series solutions for the weakly coupled modes are found to have radii of convergence that extend over modest but significant ranges of coupling values. The transition from the uncoupled modes to the fundamentally coupled mixed modes is examined. For the SST modes, coupling effects come to dominate the structure of basin-scale modes even at tiny coupling values. The structure of the ocean basin modes persists over a perceptible range of coupling, but structure changes involving the SST equation enter importantly as coupling is increased and the transition to mixed-mode structure occurs at small coupling, well within the range of the weak-coupling limit. This suggests that intuition and terminology borrowed from the uncoupled system is of limited value in analyzing coupled models and that it is more productive to consider prototype modes in fully coupled regimes.
Abstract
The properties of the eigenmodes of the coupled tropical ocean-atmosphere system, linearized about a climatological basic state—and hence of the first bifurcation, which strongly determines the nature of the interannual variability, such as El Niño—show considerable dependence on the parameters of the coupled system. These eigenmodes are examined in a modified shallow-water model with simplified mixed-layer dynamics and a sea surface temperature (SST) equation, coupled to a simple atmospheric model. The model is designed so as to make analytical approximations feasible in various limits, as in a previous study by Neelin where the x-periodic case was analyzed. The realistic case of a finite ocean basin is treated here. An integral formulation of the eigenvalue problem is derived that provides a basis for making consistent approximations that include the effects of atmospheric and oceanic boundary conditions. We provide a scaling analysis to select parameters that give the most succinct insights into the behavior of the system, and outline the portions of this parameter space that are accessible to analytic results through the limits explored here and in Part III of this study. Important limits include the fast-wave limit, the limit where the time scale of ocean adjustment is fast compared to the time scale of SST change by coupled processes, and its converse, the fast-SST limit. The region of validity of the weak-coupling limit overlaps both of these, while that of the strong-coupling limit overlaps the fast-SST limit and approaches the region of validity of the fast-wave limit without a formal matching region.
In this part, we examine the weak-coupling limit, in which one expects the modes to be most closely related to those of the uncoupled problem. Here we treat two classes of mode from the uncoupled case: the SST modes (related to the time derivative of the SST equation) and the discrete modes from the ocean-dynamics spectrum, the ocean basin modes. From the numerical results of Part I, we know that away from the weak-coupling and fast-wave limits, the continuous surfaces in parameter space formed by the eigenvalues of each type of mode are joined, so that through most of parameter space the coupled modes are best characterized as mixed SST/ocean-dynamics modes. Series solutions for the weakly coupled modes are found to have radii of convergence that extend over modest but significant ranges of coupling values. The transition from the uncoupled modes to the fundamentally coupled mixed modes is examined. For the SST modes, coupling effects come to dominate the structure of basin-scale modes even at tiny coupling values. The structure of the ocean basin modes persists over a perceptible range of coupling, but structure changes involving the SST equation enter importantly as coupling is increased and the transition to mixed-mode structure occurs at small coupling, well within the range of the weak-coupling limit. This suggests that intuition and terminology borrowed from the uncoupled system is of limited value in analyzing coupled models and that it is more productive to consider prototype modes in fully coupled regimes.
Abstract
A class of model for simulation and theory of the tropical atmospheric component of climate variations is introduced. These models are referred to as quasi-equilibrium tropical circulation models, or QTCMs, because they make use of approximations associated with quasi-equilibrium (QE) convective parameterizations. Quasi-equilibrium convective closures tend to constrain the vertical temperature profile in convecting regions. This can be used to generate analytical solutions for the large-scale flow under certain approximations. A tropical atmospheric model of intermediate complexity is constructed by using the analytical solutions as the first basis function in a Galerkin representation of vertical structure. This retains much of the simplicity of the analytical solutions, while retaining full nonlinearity, vertical momentum transport, departures from QE, and a transition between convective and nonconvective zones based on convective available potential energy. The atmospheric model is coupled to a one-layer land surface model with interactive soil moisture and simulates its own tropical climatology. In the QTCM version presented here, the vertical structure of temperature variations is truncated to a single profile associated with deep convection. Though designed to be accurate in and near regions dominated by deep convection, the model simulates the tropical and subtropical climatology reasonably well, and even has a qualitative representation of midlatitude storm tracks.
The model is computationally economical, since part of the solution has been carried out analytically, but the main advantage is relative simplicity of analysis under certain conditions. The formulation suggests a slightly different way of looking at the tropical atmosphere than has been traditional in tropical meteorology. While convective scales are unstable, the large-scale motions evolve with a positive effective stratification that takes into account the partial cancellation of adiabatic cooling by diabatic heating. A consistent treatment of the moist static energy budget aids the analysis of radiative and surface heat flux effects. This is particularly important over land regions where the zero net surface flux links land surface anomalies. The resulting simplification highlights the role of top-of-the-atmosphere fluxes including cloud feedbacks, and it illustrates the usefulness of this approach for analysis of convective regions. Reductions of the model for theoretical work or diagnostics are outlined.
Abstract
A class of model for simulation and theory of the tropical atmospheric component of climate variations is introduced. These models are referred to as quasi-equilibrium tropical circulation models, or QTCMs, because they make use of approximations associated with quasi-equilibrium (QE) convective parameterizations. Quasi-equilibrium convective closures tend to constrain the vertical temperature profile in convecting regions. This can be used to generate analytical solutions for the large-scale flow under certain approximations. A tropical atmospheric model of intermediate complexity is constructed by using the analytical solutions as the first basis function in a Galerkin representation of vertical structure. This retains much of the simplicity of the analytical solutions, while retaining full nonlinearity, vertical momentum transport, departures from QE, and a transition between convective and nonconvective zones based on convective available potential energy. The atmospheric model is coupled to a one-layer land surface model with interactive soil moisture and simulates its own tropical climatology. In the QTCM version presented here, the vertical structure of temperature variations is truncated to a single profile associated with deep convection. Though designed to be accurate in and near regions dominated by deep convection, the model simulates the tropical and subtropical climatology reasonably well, and even has a qualitative representation of midlatitude storm tracks.
The model is computationally economical, since part of the solution has been carried out analytically, but the main advantage is relative simplicity of analysis under certain conditions. The formulation suggests a slightly different way of looking at the tropical atmosphere than has been traditional in tropical meteorology. While convective scales are unstable, the large-scale motions evolve with a positive effective stratification that takes into account the partial cancellation of adiabatic cooling by diabatic heating. A consistent treatment of the moist static energy budget aids the analysis of radiative and surface heat flux effects. This is particularly important over land regions where the zero net surface flux links land surface anomalies. The resulting simplification highlights the role of top-of-the-atmosphere fluxes including cloud feedbacks, and it illustrates the usefulness of this approach for analysis of convective regions. Reductions of the model for theoretical work or diagnostics are outlined.
