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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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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 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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Yuriy P. Krasovskiy and Peter H. Stone

Abstract

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

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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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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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Peter H. Stone and Mao-Sung Yao

Abstract

Vertical eddy fluxes of heat are calculated from simulations with a variety of climate models, ranging from three-dimensional GCMs to a one-dimensional radiative-convective model. The models’ total eddy flux in the lower troposphere is found to agree well with Hantel's analysis from observations, but in the mid- and upper troposphere the models’ values are systematically 30% to 50% smaller than Hantel's. The models nevertheless give very good results for the global temperature profile, and the reason for the discrepancy is unclear. The model results show that the manner in which the vertical eddy flux is carried is very sensitive to the parameterization of moist convection. When a moist adiabatic adjustment scheme with a critical value for the relative humidity of 100% is used, the vertical transports by large-scale eddies and small-scale convection on a global basis are equal; but when a penetrative convection scheme is used, the large-scale flux on a global basis is only about one-fifth to one-fourth the small-scale flux. Comparison of the model results with observations indicates that the results with the latter scheme are more realistic. However, even in this case, in mid- and high latitudes the large and small-scale vertical eddy fluxes of heat are comparable in magnitude above the planetary boundary layer.

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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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Xiaoli Wang, Peter H. Stone, and Jochem Marotzke

Abstract

A global ocean general circulation model of idealized geometry, combined with an atmospheric model based on observed transports of heat, momentum, and moisture, is used to explore the sensitivity of the global conveyor belt circulation to the surface freshwater fluxes, in particular the effects of meridional atmospheric moisture transports. The numerical results indicate that the equilibrium strength of the North Atlantic Deep Water (NADW) formation increases as the global freshwater transports increase. However, the global deep water formation—that is, the sum of the NADW and the Southern Ocean Deep Water formation rates—is relatively insensitive to changes of the freshwater flux.

Perturbations to the meridional moisture transports of each hemisphere identify equatorially asymmetric effects of the freshwater fluxes. The results are consistent with box model results that the equilibrium NADW formation is primarily controlled by the magnitude of the Southern Hemisphere freshwater flux. However, the results show that the Northern Hemisphere freshwater flux has a strong impact on the transient behavior of the North Atlantic overturning. Increasing this flux leads to a collapse of the conveyor belt circulation, but the collapse is delayed if the Southern Hemisphere flux also increases. The perturbation experiments also illustrate that the rapidity of collapse is affected by random fluctuations in the wind stress field.

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