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## Abstract

The two-layer model is used to study how horizontal shear in a baroclinic zonal flow affects the structure of growing baroclinic waves. The solution is simplified by assuming that the radius of deformation is small compared to the planetary scale. The method of solution yields results for waves near neutral stability. For these waves, solutions are found for many different wind profiles. These solutions show: 1) that the waves have a natural meridional scale equal to the radius of deformation, the same as the zonal scale; 2) that the wave perturbation in the lower atmosphere is primarily confined to regions where the vertical shear of the unperturbed zonal flow is greatest; and 3) the horizontal eddy stresses always transport momentum against the horizontal gradient of the zonal flow. Thus, the baroclinic waves tend to increase the intensity of any jets present in the unperturbed zonal flow, no matter what their number or position, and they are accompanied by horizontal shearing and stretching deformation wind fields which are of comparable strength.

## Abstract

The two-layer model is used to study how horizontal shear in a baroclinic zonal flow affects the structure of growing baroclinic waves. The solution is simplified by assuming that the radius of deformation is small compared to the planetary scale. The method of solution yields results for waves near neutral stability. For these waves, solutions are found for many different wind profiles. These solutions show: 1) that the waves have a natural meridional scale equal to the radius of deformation, the same as the zonal scale; 2) that the wave perturbation in the lower atmosphere is primarily confined to regions where the vertical shear of the unperturbed zonal flow is greatest; and 3) the horizontal eddy stresses always transport momentum against the horizontal gradient of the zonal flow. Thus, the baroclinic waves tend to increase the intensity of any jets present in the unperturbed zonal flow, no matter what their number or position, and they are accompanied by horizontal shearing and stretching deformation wind fields which are of comparable strength.

## Abstract

The authors introduce a four-box interhemispheric model of the meridional overturning circulation. A single box represents high latitudes in each hemisphere, and in contrast to earlier interhemispheric box models, low latitudes are represented by two boxes—a surface box and a deep box—separated by a thermocline in which a balance is assumed between vertical advection and vertical diffusion. The behavior of the system is analyzed with two different closure assumptions for how the low-latitude upwelling depends on the density contrast between the surface and deep low-latitude boxes. The first is based on the conventional assumption that the diffusivity is a constant, and the second on the assumption that the energy input to the mixing is constant.

There are three different stable equilibrium states that are closely analogous to the three found by Bryan in a single-basin interhemispheric ocean general circulation model. One is quasi-symmetric with downwelling in high latitudes of both hemispheres, and two are asymmetric solutions, with downwelling confined to high latitudes in one or the other of the two hemispheres. The quasi-symmetric solution becomes linearly unstable for strong global hydrological forcing, while the two asymmetric solutions do not.

The qualitative nature of the solutions is generally similar for both the closure assumptions, in contrast to the solutions in hemispheric models. In particular, all the stable states can be destabilized by finite amplitude perturbations in the salinity or the hydrological forcing, and transitions are possible between any two states. For example, if the system is in an asymmetric state, and the moisture flux into the high-latitude region of downwelling is slowly increased, for both closure assumptions the high-latitude downwelling decreases until a critical forcing is reached where the system switches to the asymmetric state with downwelling in the opposite hemisphere. By contrast, in hemispheric models with the energy constraint, the downwelling increases and there is no loss of stability.

## Abstract

The authors introduce a four-box interhemispheric model of the meridional overturning circulation. A single box represents high latitudes in each hemisphere, and in contrast to earlier interhemispheric box models, low latitudes are represented by two boxes—a surface box and a deep box—separated by a thermocline in which a balance is assumed between vertical advection and vertical diffusion. The behavior of the system is analyzed with two different closure assumptions for how the low-latitude upwelling depends on the density contrast between the surface and deep low-latitude boxes. The first is based on the conventional assumption that the diffusivity is a constant, and the second on the assumption that the energy input to the mixing is constant.

There are three different stable equilibrium states that are closely analogous to the three found by Bryan in a single-basin interhemispheric ocean general circulation model. One is quasi-symmetric with downwelling in high latitudes of both hemispheres, and two are asymmetric solutions, with downwelling confined to high latitudes in one or the other of the two hemispheres. The quasi-symmetric solution becomes linearly unstable for strong global hydrological forcing, while the two asymmetric solutions do not.

The qualitative nature of the solutions is generally similar for both the closure assumptions, in contrast to the solutions in hemispheric models. In particular, all the stable states can be destabilized by finite amplitude perturbations in the salinity or the hydrological forcing, and transitions are possible between any two states. For example, if the system is in an asymmetric state, and the moisture flux into the high-latitude region of downwelling is slowly increased, for both closure assumptions the high-latitude downwelling decreases until a critical forcing is reached where the system switches to the asymmetric state with downwelling in the opposite hemisphere. By contrast, in hemispheric models with the energy constraint, the downwelling increases and there is no loss of stability.

## 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.

## 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.

## Abstract

An experiment has been designed to test the predictions of nongeostrophic baroclinic stability theory. The apparatus is similar to the conventional rotating annulus experiments, except that the vertical temperature difference can be controlled as well as the horizontal temperature difference. Therefore, the Richardson number can be decreased by heating the bottom of the annulus relative to the top. The first qualitative observations derived from the experiment are described and are found to agree well with the theory. With no vertical temperature difference applied, the motion consists of a conventional baroclinic instability superimposed on the basic thermal wind. As the fluid is destabilized symmetric instabilities first appear superimposed on the baroclinic instability. As further destabilization occurs the symmetric instabilities completely replace the baroclinic instability, and are themselves subsequently replaced by small-scale, nonsymmetric instabilities.

## Abstract

An experiment has been designed to test the predictions of nongeostrophic baroclinic stability theory. The apparatus is similar to the conventional rotating annulus experiments, except that the vertical temperature difference can be controlled as well as the horizontal temperature difference. Therefore, the Richardson number can be decreased by heating the bottom of the annulus relative to the top. The first qualitative observations derived from the experiment are described and are found to agree well with the theory. With no vertical temperature difference applied, the motion consists of a conventional baroclinic instability superimposed on the basic thermal wind. As the fluid is destabilized symmetric instabilities first appear superimposed on the baroclinic instability. As further destabilization occurs the symmetric instabilities completely replace the baroclinic instability, and are themselves subsequently replaced by small-scale, nonsymmetric instabilities.

## Abstract

The GISS global general circulation model has been used to simulate July conditions, in a manner analogous to the previously described January simulation. Sea surface temperatures, ice cover, snow line and soil moisture were assigned values based on climatological data for July, and the integration was started from real data for 18 June 1973. Because of the realistic initial condition, the model rapidly approached a quasi-steady state. Mean statistics were computed for the simulated calendar month of July, and compared with climatological data, mainly for the Northern Hemisphere troposphere. Qualitatively, the model-generated energy cycle, distributions of winds, temperature, humidity and pressure, dynamical transports, diabatic heating, evaporation, precipitation and cloud cover are all realistic. Quantitatively, the July simulation, like the January simulation, tends to underestimate the strength of the mean meridional circulations, the eddy activity and some of the associated transports. The July simulation of zonal mean temperature and zonal wind fields is superior to the January simulation in the Northern Hemisphere because of the absence of the polar night jet, and the decreased importance of large-scale dynamical heating and cooling in summer.

In order to assess the model's ability to simulate seasonal differences, the July and January simulations were compared with each other and with climatological data on seasonal changes. The model simulates accurately the northward displacement of the mid-latitude jets, the low-latitude Hadley cells, the tropical rain belt, the trade winds, and the ITCZ in July compared to January, the reversal of the Indian monsoon, and the weakening of the zonal meridional circulations and the decline of eddy activity in the summer. The simulated seasonal differences in the Southern Hemisphere are much less pronounced than in the Northern Hemisphere as expected.

From a climatological point of view, there are three particular aspects of the model's simulations that need to be improved: 1) arctic regions in January are as much as 10°K too cold, because of the model's underestimate of the dynamical transports of heat into high latitudes; 2) the simulation of the climatological fields in the vicinity of the Himalayas and Southeast Asia is noticeably poorer than in other areas—for example, in Southeast Asia in the July simulation the rainfall is half the observed amount; and 3) the global albedo in July is too high when compared to satellite-derived values (0.35 vs 0.26), at least partially because the model-simulated deep, penetrating cumulus clouds occur too frequently in July.

## Abstract

The GISS global general circulation model has been used to simulate July conditions, in a manner analogous to the previously described January simulation. Sea surface temperatures, ice cover, snow line and soil moisture were assigned values based on climatological data for July, and the integration was started from real data for 18 June 1973. Because of the realistic initial condition, the model rapidly approached a quasi-steady state. Mean statistics were computed for the simulated calendar month of July, and compared with climatological data, mainly for the Northern Hemisphere troposphere. Qualitatively, the model-generated energy cycle, distributions of winds, temperature, humidity and pressure, dynamical transports, diabatic heating, evaporation, precipitation and cloud cover are all realistic. Quantitatively, the July simulation, like the January simulation, tends to underestimate the strength of the mean meridional circulations, the eddy activity and some of the associated transports. The July simulation of zonal mean temperature and zonal wind fields is superior to the January simulation in the Northern Hemisphere because of the absence of the polar night jet, and the decreased importance of large-scale dynamical heating and cooling in summer.

In order to assess the model's ability to simulate seasonal differences, the July and January simulations were compared with each other and with climatological data on seasonal changes. The model simulates accurately the northward displacement of the mid-latitude jets, the low-latitude Hadley cells, the tropical rain belt, the trade winds, and the ITCZ in July compared to January, the reversal of the Indian monsoon, and the weakening of the zonal meridional circulations and the decline of eddy activity in the summer. The simulated seasonal differences in the Southern Hemisphere are much less pronounced than in the Northern Hemisphere as expected.

From a climatological point of view, there are three particular aspects of the model's simulations that need to be improved: 1) arctic regions in January are as much as 10°K too cold, because of the model's underestimate of the dynamical transports of heat into high latitudes; 2) the simulation of the climatological fields in the vicinity of the Himalayas and Southeast Asia is noticeably poorer than in other areas—for example, in Southeast Asia in the July simulation the rainfall is half the observed amount; and 3) the global albedo in July is too high when compared to satellite-derived values (0.35 vs 0.26), at least partially because the model-simulated deep, penetrating cumulus clouds occur too frequently in July.

## Abstract

Several experiments are described in which the sub-grid-scale vertical eddy viscosity in the GISS global general circulation model was varied. The results show that large viscosities suppress large-scale eddies in middle and high latitudes, but enhance the circulation in the tropical Hadley cell and increase the extent of the tropical easterlies. Comparison with observations shows that the GISS model requires eddy viscosities ∼1 m^{2}/s or less to give realistic results for middle and high latitudes, and eddy viscosities ∼100 m^{2}/s to give realistic results for low latitudes. A plausible mechanism for the implied increase in small-scale mixing in low latitudes is cumulus convection.

## Abstract

Several experiments are described in which the sub-grid-scale vertical eddy viscosity in the GISS global general circulation model was varied. The results show that large viscosities suppress large-scale eddies in middle and high latitudes, but enhance the circulation in the tropical Hadley cell and increase the extent of the tropical easterlies. Comparison with observations shows that the GISS model requires eddy viscosities ∼1 m^{2}/s or less to give realistic results for middle and high latitudes, and eddy viscosities ∼100 m^{2}/s to give realistic results for low latitudes. A plausible mechanism for the implied increase in small-scale mixing in low latitudes is cumulus convection.

## Abstract

Direct temperature measurements are reported for two rotating annulus experiments. One shows the flow pattern interpreted by Stone *et al*. as a manifestation of symmetric baroclinic (inertial) instability, and the other shows the flow pattern typical of baroclinic waves. The mean value of the Richardson number in the former experiment is found to he 0.62. This value agrees with theoretical expectations for a symmetric haroclinic instability regime and thus verifies the original interpretation of the flow pattern. The mean value of the Richardson number in the baroclinic wave experiment is 83. In the symmetric instability experiment the thermal fields and Richardson number are not steady, but show a cyclic variation.

## Abstract

Direct temperature measurements are reported for two rotating annulus experiments. One shows the flow pattern interpreted by Stone *et al*. as a manifestation of symmetric baroclinic (inertial) instability, and the other shows the flow pattern typical of baroclinic waves. The mean value of the Richardson number in the former experiment is found to he 0.62. This value agrees with theoretical expectations for a symmetric haroclinic instability regime and thus verifies the original interpretation of the flow pattern. The mean value of the Richardson number in the baroclinic wave experiment is 83. In the symmetric instability experiment the thermal fields and Richardson number are not steady, but show a cyclic variation.

## Abstract

The sensitivity of the ocean’s climate to the diapycnal diffusivity in the ocean is studied for a global warming scenario in which CO_{2} increases by 1% yr^{−1} for 75 yr. The thermohaline circulation slows down for about 100 yr and recovers afterward, for any value of the diapycnal diffusivity. The rates of slowdown and of recovery, as well as the percentage recovery of the circulation at the end of 1000-yr integrations, are variable, but a direct relation with the diapycnal diffusivity cannot be found. At year 70 (when CO_{2} has doubled) an increase of the diapycnal diffusivity from 0.1 to 1.0 cm^{2} s^{−1} leads to a decrease in surface air temperature of about 0.4 K and an increase in sea level rise of about 4 cm. The steric height gradient is divided into thermal component and haline component. It appears that, in the first 60 yr of simulated global warming, temperature variations dominate the salinity ones in weakly diffusive models, whereas the opposite occurs in strongly diffusive models.

The analysis of the vertical heat balance reveals that deep-ocean heat uptake is due to reduced upward isopycnal diffusive flux and parameterized-eddy advective flux. Surface warming, induced by enhanced CO_{2} in the atmosphere, leads to a reduction of the isopycnal slope, which translates into a reduction of the above fluxes. The amount of reduction is directly related to the magnitude of the isopycnal diffusive flux and parameterized-eddy advective flux at equilibrium. These latter fluxes depend on the thickness of the thermocline at equilibrium and hence on the diapycnal diffusion. Thus, the increase of deep-ocean heat uptake with diapycnal diffusivity is an indirect effect that the latter parameter has on the isopycnal diffusion and parameterized-eddy advection.

## Abstract

The sensitivity of the ocean’s climate to the diapycnal diffusivity in the ocean is studied for a global warming scenario in which CO_{2} increases by 1% yr^{−1} for 75 yr. The thermohaline circulation slows down for about 100 yr and recovers afterward, for any value of the diapycnal diffusivity. The rates of slowdown and of recovery, as well as the percentage recovery of the circulation at the end of 1000-yr integrations, are variable, but a direct relation with the diapycnal diffusivity cannot be found. At year 70 (when CO_{2} has doubled) an increase of the diapycnal diffusivity from 0.1 to 1.0 cm^{2} s^{−1} leads to a decrease in surface air temperature of about 0.4 K and an increase in sea level rise of about 4 cm. The steric height gradient is divided into thermal component and haline component. It appears that, in the first 60 yr of simulated global warming, temperature variations dominate the salinity ones in weakly diffusive models, whereas the opposite occurs in strongly diffusive models.

The analysis of the vertical heat balance reveals that deep-ocean heat uptake is due to reduced upward isopycnal diffusive flux and parameterized-eddy advective flux. Surface warming, induced by enhanced CO_{2} in the atmosphere, leads to a reduction of the isopycnal slope, which translates into a reduction of the above fluxes. The amount of reduction is directly related to the magnitude of the isopycnal diffusive flux and parameterized-eddy advective flux at equilibrium. These latter fluxes depend on the thickness of the thermocline at equilibrium and hence on the diapycnal diffusion. Thus, the increase of deep-ocean heat uptake with diapycnal diffusivity is an indirect effect that the latter parameter has on the isopycnal diffusion and parameterized-eddy advection.

## Abstract

The transient response of both surface air temperature and deep ocean temperature to an increasing external forcing strongly depends on climate sensitivity and the rate of the heat mixing into the deep ocean, estimates for both of which have large uncertainty. In this paper a method for estimating rates of oceanic heat uptake for coupled atmosphere–ocean general circulation models from results of transient climate change simulations is described. For models considered in this study, the estimates vary by a factor of 2½. Nevertheless, values of oceanic heat uptake for all models fall in the range implied by the climate record for the last century. It is worth noting that the range of the model values is narrower than that consistent with observations and thus does not provide a full measure of the uncertainty in the rate of oceanic heat uptake.

## Abstract

The transient response of both surface air temperature and deep ocean temperature to an increasing external forcing strongly depends on climate sensitivity and the rate of the heat mixing into the deep ocean, estimates for both of which have large uncertainty. In this paper a method for estimating rates of oceanic heat uptake for coupled atmosphere–ocean general circulation models from results of transient climate change simulations is described. For models considered in this study, the estimates vary by a factor of 2½. Nevertheless, values of oceanic heat uptake for all models fall in the range implied by the climate record for the last century. It is worth noting that the range of the model values is narrower than that consistent with observations and thus does not provide a full measure of the uncertainty in the rate of oceanic heat uptake.