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J. David Neelin

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J. David Neelin

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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.

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J. David Neelin

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J. David Neelin

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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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Ning Zeng and J. David Neelin

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Using a coupled atmosphere–land–vegetation model of intermediate complexity, the authors explore how vegetation–climate interaction and internal climate variability might influence the vegetation distribution in Africa. When the model is forced by observed climatological sea surface temperature (SST), positive feedbacks from vegetation changes tend to increase the spatial gradient between desert regions and forest regions at the expense of savanna regions. When interannual variation of SST is included, the climate variability tends to reduce rainfall and vegetation in the wetter regions and to increase them in the drier regions along this gradient, resulting in a smoother desert–forest transition. This effect is most dramatically demonstrated in a model parameter regime for which multiple equilibria (either a desertlike or a forestlike Sahel) can exist when strong vegetation–climate feedbacks are allowed. However, the presence of a variable SST drives the desertlike state and the forestlike state toward an intermediate grasslike state, because of nonlinearities in the coupled system. Both vegetation and interannual variability thus play active roles in shaping the subtropical savanna ecosystem.

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Fiaz Ahmed and J. David Neelin

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Precipitation clusters are contiguous raining regions characterized by a precipitation threshold, size, and the total rainfall contained within—termed the cluster power. Tropical observations suggest that the probability distributions of both cluster size and power contain a power-law range (with slope ~ −1.5) bounded by a large-event “cutoff.” Events with values beyond the cutoff signify large, powerful clusters and represent extreme events. A two-dimensional stochastic model is introduced to reproduce the observed cluster distributions, including the slope and the cutoff. The model is equipped with coupled moisture and weak temperature gradient (WTG) energy equations, empirically motivated precipitation parameterization, temporally persistent noise, and lateral mixing processes, all of which collectively shape the model cluster distributions. Moisture–radiative feedbacks aid clustering, but excessively strong feedbacks push the model into a self-aggregating regime. The power-law slope is stable in a realistic parameter range. The cutoff is sensitive to multiple model parameters including the stochastic forcing amplitude, the threshold moisture value that triggers precipitation, and the lateral mixing efficiency. Among the candidates for simple analogs of precipitation clustering, percolation models are ruled out as unsatisfactory, but the stochastic branching process proves useful in formulating a neighbor probability metric. This metric measures the average number of nearest neighbors that a precipitating entity can spawn per time interval and captures the cutoff parameter sensitivity for both cluster size and power. The results here suggest that the clustering tendency and the horizontal scale limiting large tropical precipitating systems arise from aggregate effects of multiple moist processes, which are encapsulated in the neighbor probability metric.

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J. David Neelin and Ning Zeng

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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.

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Chia Chou and J. David Neelin

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Mechanisms that determine the tropical precipitation anomalies under global warming are examined in an intermediate atmospheric model coupled with a simple land surface and a mixed layer ocean. To compensate for the warm tropospheric temperature, atmospheric boundary layer (ABL) moisture must increase to maintain positive convective available potential energy (CAPE) in convective regions. In nonconvective regions, ABL moisture is controlled by different balances and does not increase as much, creating a spatial gradient of ABL moisture anomalies. Associated with this spatial pattern of the ABL moisture anomalies are two main mechanisms responsible for the anomalous tropical precipitation. In the “upped-ante mechanism,” increases in ABL moisture are opposed by imported dry air wherever inflow from nonconvective regions over margins of convective regions occurs. The ABL moisture is not enough to meet the higher “convective ante” induced by the warmer tropospheric temperature, so precipitation is decreased. In the “anomalous gross moist stability mechanism,” gross moist stability is reduced due to increased ABL moisture. As a result, convection is enhanced and precipitation becomes heavier over convective regions. While the upped-ante mechanism induces negative precipitation anomalies over the margins of convective regions, the anomalous gross moist stability mechanism induces positive precipitation anomalies within convective regions. The importance of variation in gross moist stability, which is likely to differ among climate models, is suggested as a potential factor causing discrepancies in the predicted regional tropical precipitation changes.

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Jiayan Yang and J. David Neelin

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An interdecadal oscillation in a coupled ocean–ice system was identified in a previous study. This paper extends that study to further examine the stability of the oscillation and the sensitivity of its frequency to various parameters and forcing fields. Three models are used: (i) an analytical box model; (ii) a two-dimensional model for the ocean thermohaline circulation (THC) coupled to a thermodynamic ice model, as in the authors’ previous study; (iii) a three-dimensional ocean general circulation model (OGCM) coupled to a similar ice model. The box model is used to elucidate the essential feedbacks that give rise to this oscillation and to identify the most important parameters and processes that determine the period. Numerical experiments in the 2D THC–ice model show that the model stability is sensitive to the ocean–ice coupling coefficient, the eddy diffusivity, and the strength of the thermohaline-circulation feedback per unit surface-polar density perturbation. The coupled model becomes more stable toward low coupling, greater diffusion, and weaker THC feedback. The period of the oscillation is less sensitive to these parameters. Nonlinear effects in the sea-ice model become important in the higher ocean–ice coupling regime where the effective sea-ice damping associated with this nonlinearity stabilizes the model. Surface Newtonian damping is also tested. The 3D OGCM, which includes both wind stress and buoyancy forcings, is used to test this coupled ocean–ice mechanism in a more realistic model setting. This model generates an interdecadal oscillation whose characteristics and phase relations among the model variables are similar to the oscillation obtained in the 2D models. The major difference is that the oscillation frequency is considerably lower. This difference can be explained in terms of the analytical box model solution in which the period of the oscillation depends on the rate of anomalous density production by melting/cooling of sea ice per SST anomaly, times the rate of warming/cooling by anomalous THC heat advection per change in density anomaly. The 3D model has a smaller THC response to high-latitude density perturbations than in the 2D model, and anomalous velocities in the 3D case tend to follow the mean isotherms so the anomalous heat advection is reduced. This slows the ocean–ice feedback process, leading to the longer oscillation period.

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J. David Neelin and Wenjie Weng

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Effects of ocean–atmosphere feedback processes and large-scale atmospheric stochastic forcing on the interdecadal climate variability in the North Atlantic and North Pacific Oceans are examined in a simple midlatitude ocean–atmosphere model. In the ocean, the authors consider a linearized perturbation system with quasigeostrophic shallow-water ocean dynamics and a sea surface temperature (SST) equation for a surface mixed layer. The atmosphere is represented as stochastic wind stress and heat flux forcing. This includes a noise component that depends on SST, as well as an additive component that is independent of SST. Coupling is represented by the SST dependent stochastic process, in which SST influences the probability density function of the atmospheric noise both in shifting the mean and affecting the variance. It thus includes a multiplicative noise component. The model results in both oceans indicate that large-scale additive atmospheric stochastic forcing alone (the uncoupled case) can give coherent spatial patterns in the ocean and sometimes even a weak power spectral peak at interdecadal periods. Coupling due to the SST dependent stochastic process can produce a more distinct power-spectral peak relative to the uncoupled ocean. Moreover, the time and spatial scales of the interdecadal mode are insensitive to the standard deviation of the multiplicative noise. Thus a deterministic feedback limit can be used to simplify the coupled model for further investigation of the physical mechanisms of the interdecadal mode.

In both uncoupled and coupled cases, the period of the interdecadal oscillation is determined by the zonal length scale of atmospheric wind stress and oceanic Rossby wave dynamics. The atmospheric spatial pattern sets the length scale of large-scale wave motion in the ocean. This wave propagates to the west due to oceanic Rossby wave dynamics and is dissipated at the western boundary. However, in the coupled case, the SST anomalies generated by geostrophic current can feed back to the atmosphere, which in turn brings some information back to the east and reexcites oceanic waves there. Although the magnitude of the feedback of SST on the atmosphere is much smaller than atmospheric internal variability, its effects are significant.

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