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Valerio Lucarini and Peter H. Stone

Abstract

A thorough analysis of the stability of the uncoupled Rooth interhemispheric three-box model of thermohaline circulation (THC) is presented. The model consists of a northern high-latitude box, a tropical box, and a southern high-latitude box, which correspond to the northern, tropical, and southern Atlantic Ocean, respectively. Restoring boundary conditions are adopted for the temperature variables, and flux boundary conditions are adopted for the salinity variables. This paper examines how the strength of THC changes when the system undergoes forcings that are analogous to those of global warming conditions by applying the equilibrium state perturbations to the moisture and heat fluxes into the three boxes. In each class of experiments, using suitably defined metrics, the authors determine the boundary dividing the set of forcing scenarios that lead the system to equilibria characterized by a THC pattern similar to the present one from those that drive the system to equilibria with a reversed THC. Fast increases in the moisture flux into the northern high-latitude box are more effective than slow increases in leading the THC to a breakdown, while the increases of moisture flux into the southern high-latitude box strongly inhibit the breakdown and can prevent it, as in the case of slow increases in the Northern Hemisphere. High rates of heat flux increase in the Northern Hemisphere destabilize the system more effectively than low ones; increases in the heat fluxes in the Southern Hemisphere tend to stabilize the system.

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Shuntai Zhou and Peter H. Stone

Abstract

Lorenz's two-level model on a sphere is used to investigate how the results of Part I are modified when the interaction of the vertical eddy heat flux and static stability is included. In general, the climate state does not depend very much on whether or not this interaction is included, because the poleward eddy heat transport dominates the eddy forcing of mean temperature and wind fields. However, the climatic sensitivity is significantly affected. Compared to two-level model results with fixed static stability, the poleward eddy heat flux is less sensitive to the meridional temperature gradient and the gradient is more sensitive to the forcing. For example, the logarithmic derivative of the eddy flux with respect to the gradient has a slope that is reduced from ∼15 on a β-plane with fixed static stability and ∼6 on a sphere with fixed static stability, to ∼3 to 4 in the present model. This last result is more in line with analyses from observations. The present model also has a stronger baroclinic adjustment than that in Part I, more like that in two-level β-plane models with fixed static stability, that is, the midlatitude isentropic slope is very insensitive to the forcing, the diabatic heating, and the friction, unless the forcing is very weak.

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Shuntai Zhou and Peter H. Stone

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An efficient two-level model on a sphere that is based on the balance equations with fixed static stability is developed and used to study how eddies arising from baroclinic instability interact with the temperature structure. The model gives a much better simulation of the eddy momentum flux and of the total eddy forcing of the zonal-mean temperature and zonal wind fields than do quasigeostrophic β-plane models. Nonetheless, the results are qualitatively similar. The midlatitude eddy regimes range between two extreme cases. In one, the eddies have no effect on the temperature and zonal wind fields, and in the other (similar to the observed atmosphere), the eddy forcing of the temperature and zonal wind fields is dominated by the eddy beat flux. Also, a kind of baroclinic adjustment occurs in the regimes where eddy effects are strong, with the meridional temperature gradient in midlatitudes being proportional to the static stability. Quantitatively some of the model's results differ significantly from those based on the quasigeostrophic β-plane. For example, the temperature structure is much more sensitive to the external forcing, and the eddy beat flux is less sensitive to the temperature structure.

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Valerio Lucarini and Peter H. Stone

Abstract

A thorough analysis of the stability of a coupled version of an interhemispheric three-box model of thermohaline circulation (THC) is presented. This study follows a similarly structured analysis of an uncoupled version of the same model presented in Part I of this paper. The model consists of a northern high-latitude box, a tropical box, and a southern high-latitude box, which can be thought of as corresponding to the northern, tropical, and southern Atlantic Ocean, respectively. This paper examines how the strength of THC changes when the system undergoes forcings representing global warming conditions.

Since a coupled model is used, a direct representation of the radiative forcing is possible because the main atmospheric physical processes responsible for freshwater and heat fluxes are formulated separately. Each perturbation to the initial equilibrium is characterized by the total radiative forcing realized, by the rate of increase, and by the north–south asymmetry. Although only weakly asymmetric or symmetric radiative forcings are representative of physically reasonable conditions, general asymmetric forcings are considered in order to get a more complete picture of the mathematical properties of the system. The choice of suitably defined metrics makes it possible to determine the boundary dividing the set of radiative forcing scenarios that lead the system to equilibria characterized by a THC pattern similar to the present one, from those that drive the system to equilibria where the THC is reversed. This paper also considers different choices for the atmospheric transport parameterizations and for the ratio between the high-latitude and tropical radiative forcing. It is generally found that fast forcings are more effective than slow forcings in disrupting the present THC pattern, forcings that are stronger in the northern box are also more effective in destabilizing the system, and very slow forcings do not destabilize the system whatever their asymmetry, unless the radiative forcings are very asymmetric and the atmospheric transport is a relatively weak function of the meridional temperature gradient. In this latter case some relevant hysteresis graphs of the system are presented. The changes in the strength of the THC are primarily forced by changes in the latent heat transport in the hemisphere because of its sensitivity to temperature, which arises from the Clausius–Clapeyron relation.

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Véronique Bugnion, Chris Hill, and Peter H. Stone

Abstract

Using the adjoint of a fully three-dimensional primitive equation ocean model in an idealized geometry, spatial variations in the sensitivity to surface boundary forcing of the meridional overturning circulation’s strength are studied. Steady-state sensitivities to diapycnal mixing, wind stress, freshwater, and heat forcing are examined. Three different, commonly used, boundary-forcing scenarios are studied, both with and without wind forcing. Almost identical circulation is achieved in each scenario, but the sensitivity patterns show major (quantitative and qualitative) differences. Sensitivities to surface forcing and diapycnal mixing are substantially larger under mixed boundary conditions, in which fluxes of freshwater and heat are supplemented by a temperature relaxation term or under flux boundary conditions, in which climatological fluxes alone drive the circulation, than under restoring boundary conditions. The sensitivity pattern to diapycnal mixing, which peaks in the Tropics is similar both with and without wind forcing. Wind does, however, increase the sensitivity to diapycnal mixing in the regions of Ekman upwelling and decreases it in the regions of Ekman downwelling. Wind stress in the Southern Oceans plays a crucial role in restoring boundary conditions, but the effect is largely absent under mixed or flux boundary conditions. The results highlight how critical a careful formulation of the surface forcing terms is to ensuring a proper response to changes in forcing in ocean models.

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Véronique Bugnion, Chris Hill, and Peter H. Stone

Abstract

Multicentury sensitivities in a realistic geometry global ocean general circulation model are analyzed using an adjoint technique. This paper takes advantage of the adjoint model’s ability to generate maps of the sensitivity of a diagnostic (i.e., the meridional overturning’s strength) to all model parameters. This property of adjoints is used to review several theories, which have been elaborated to explain the strength of the North Atlantic’s meridional overturning. This paper demonstrates the profound impact of boundary conditions in permitting or suppressing mechanisms within a realistic model of the contemporary ocean circulation. For example, the so-called Drake Passage Effect in which wind stress in the Southern Ocean acts as the main driver of the overturning’s strength, is shown to be an artifact of boundary conditions that restore the ocean’s surface temperature and salinity toward prescribed climatologies. Advective transports from the Indian and Pacific basins play an important role in setting the strength of the overturning circulation under “mixed” boundary conditions, in which a flux of freshwater is specified at the ocean’s surface.

The most “realistic” regime couples an atmospheric energy and moisture balance model to the ocean. In this configuration, inspection of the global maps of sensitivity to wind stress and diapycnal mixing suggests a significant role for near-surface Ekman processes in the Tropics. Buoyancy also plays an important role in setting the overturning’s strength, through direct thermal forcing near the sites of convection, or through the advection of salinity anomalies in the Atlantic basin.

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Peter H. Stone and Mao-Sung Yao

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A number of perpetual January simulations are carried out with a two-dimensional (2-D) zonally averaged model employing various parameterizations of the eddy fluxes of heat (potential temperature) and moisture. The parameterizations are evaluated by comparing these results with the eddy fluxes calculated in a parallel simulation using a three-dimensional (3-D) general circulation model with zonally symmetric forcing. The 3-D model's performance in turn is evaluated by comparing its results using realistic (nonsymmetric) boundary conditions with observations.

Branscome's parameterization of the meridional eddy flux of heat and Leovy's parameterization of the meridional eddy flux of moisture simulate the seasonal and latitudinal variations of these fluxes reasonably well, while somewhat underestimating their magnitudes. In particular, Branscome's parameterization underestimates the vertically integrated flux of heat by about 30%, mainly because it misses out the secondary peak in this flux near the tropopause; and Leovy's parameterization of the meridional eddy flux of moisture underestimates the magnitude of this flux by about 20%. The analogous parameterizations of the vertical eddy fluxes of heat and moisture are found to perform much more poorly, i.e., they give fluxes only one quarter to one half as strong as those calculated in the 3-D model. New parameterizations of the vertical eddy fluxes are developed that take into account the enhancement of the eddy mixing slope in a growing baroclinic wave due to condensation, and also the effect of eddy fluctuations in relative humidity. The new parameterizations, when tested in the 2-D model, simulate the seasonal, latitudinal, and vertical variations of the vertical eddy fluxes quite well, when compared with the 3-D model, and only underestimate the magnitude of the fluxes by 10% to 20%.

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Yuriy P. Krasovskiy and Peter H. Stone

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The four-box coupled atmosphere–ocean model of Marotzke is solved analytically, by introducing the approximation that the effect of oceanic heat advection on ocean temperatures is small (but not negligible) compared to the effect of surface heat fluxes. The solutions are written in a form that displays how the stability of the thermohaline circulation depends on the relationship between atmospheric meridional transports of heat and moisture and the meridional temperature gradient. In the model, these relationships are assumed to be power laws with different exponents allowed for the dependence of the transports of heat and moisture on the gradient. The approximate analytic solutions are in good agreement with Marotzke’s exact numerical solutions, but show more generally how the destabilization of the thermohaline circulation depends on the sensitivity of the atmospheric transports to the meridional temperature gradient. The solutions are also used to calculate how the stability of the thermohaline circulation is changed if model errors are “corrected” by using conventional flux adjustments. Errors like those common in GCMs destabilize the model’s thermohaline circulation, even if conventional flux adjustments are used. However, the resulting errors in the magnitude of the critical perturbations necessary to destabilize the thermohaline circulation can be corrected by modifying transport efficiencies instead.

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James S. Risbey and Peter H. Stone

Abstract

The Sacramento Basin is used as the focus for a case study testing whether general circulation models (GCMS) are capable of simulating the large-scale and synoptic-scale processes important in studies of regional water resources. Output from a variety of GCMs developed at GISS and NCAR were examined, but only results from Community Climate Model (CCM) simulations are presented since they are typical. The stationary waves, jet streams, and storm tracks in the North Pacific-North America region in the CCM simulators show major differences from the observations, both in the mean and in their interannual variations. In addition, although the stationary wave and jet stream patterns associated with individual storms in the basin exhibit robust differences from mean fields in the observations, these differences are not captured in the models. Consequently, the larger-scale fields necessary for driving nested models and impact models for the basin, or for western North America in general, are problematic in these models.

The model deficiencies persist at resolutions as high as T106. Also, the use of time series of observed ocean boundary conditions does little to improve model deficiencies. Consequently, the deficiencies in the model large-scale circulation features can be attributed to the model subgrid-scale parameterizations, underscoring the need to improve model parameterizations.

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Xiaoli Wang, Peter H. Stone, and Jochem Marotzke

Abstract

A hybrid coupled ocean–atmosphere model is used to investigate the stability of the thermohaline circulation (THC) to an increase in the surface freshwater forcing in the presence of interactive meridional transports in the atmosphere. The ocean component is the idealized global general circulation model used in Part I. The atmospheric model assumes fixed latitudinal structure of the heat and moisture transports, and the amplitudes are calculated separately for each hemisphere from the large-scale sea surface temperature (SST) and SST gradient, using parameterizations based on baroclinic stability theory. The ocean–atmosphere heat and freshwater exchanges are calculated as residuals of the steady-state atmospheric budgets.

Owing to the ocean component’s weak heat transport, the model has too strong a meridional SST gradient when driven with observed atmospheric meridional transports. When the latter are made interactive, the conveyor belt circulation collapses. A flux adjustment is introduced in which the efficiency of the atmospheric transports is lowered to match the too low efficiency of the ocean component.

The feedbacks between the THC and both the atmospheric heat and moisture transports are positive, whether atmospheric transports are interactive in the Northern Hemisphere, the Southern Hemisphere, or both. However, the feedbacks operate differently in the Northern and Southern Hemispheres, because the Pacific THC dominates in the Southern Hemisphere, and deep water formation in the two hemispheres is negatively correlated. The feedbacks in the two hemispheres do not necessarily reinforce each other because they have opposite effects on low-latitude temperatures. The model is qualitatively similar in stability to one with conventional “additive” flux adjustment, but quantitatively more stable.

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