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Abstract
The Hadley cell of a virtually dry snowball Earth atmosphere under equinox insolation is studied in a comprehensive atmospheric general circulation model. In contrast to the Hadley cell of modern Earth, momentum transport by dry convection, which is modeled as vertical diffusion of momentum, is important in the upper branch of the snowball Earth Hadley cell. In the zonal momentum balance, mean meridional advection of mean absolute vorticity is not only balanced by eddies but also by vertical diffusion of zonal momentum. Vertical diffusion also contributes to the meridional momentum balance by decelerating the Hadley cell through downgradient mixing of meridional momentum between its upper and lower branches. When vertical diffusion of momentum is suppressed in the upper branch, the Hadley cell strengthens by a factor of about 2. This is in line with the effect of vertical diffusion in the meridional momentum balance but in contrast with its effect in the zonal momentum balance. Neither axisymmetric Hadley cell theories based on angular momentum conservation nor eddy-permitting Hadley cell theories that neglect vertical diffusion of momentum are applicable to the snowball Earth Hadley cell. Because the snowball Earth Hadley cell is a particular realization of a dry Hadley cell, these results show that an appropriate description of dry Hadley cells should take into account vertical transport of momentum by dry convection.
Abstract
The Hadley cell of a virtually dry snowball Earth atmosphere under equinox insolation is studied in a comprehensive atmospheric general circulation model. In contrast to the Hadley cell of modern Earth, momentum transport by dry convection, which is modeled as vertical diffusion of momentum, is important in the upper branch of the snowball Earth Hadley cell. In the zonal momentum balance, mean meridional advection of mean absolute vorticity is not only balanced by eddies but also by vertical diffusion of zonal momentum. Vertical diffusion also contributes to the meridional momentum balance by decelerating the Hadley cell through downgradient mixing of meridional momentum between its upper and lower branches. When vertical diffusion of momentum is suppressed in the upper branch, the Hadley cell strengthens by a factor of about 2. This is in line with the effect of vertical diffusion in the meridional momentum balance but in contrast with its effect in the zonal momentum balance. Neither axisymmetric Hadley cell theories based on angular momentum conservation nor eddy-permitting Hadley cell theories that neglect vertical diffusion of momentum are applicable to the snowball Earth Hadley cell. Because the snowball Earth Hadley cell is a particular realization of a dry Hadley cell, these results show that an appropriate description of dry Hadley cells should take into account vertical transport of momentum by dry convection.
Abstract
To examine the long-term stability of Arctic and Antarctic sea ice, idealized simulations are carried out with the climate model ECHAM5/Max Planck Institute Ocean Model (MPI-OM). Atmospheric CO2 concentration is increased over 2000 years from preindustrial levels to quadrupling, is then kept constant for 5940 years, is afterward decreased over 2000 years to preindustrial levels, and is finally kept constant for 3940 years.
Despite these very slow changes, the sea ice response significantly lags behind the CO2 concentration change. This lag, which is caused by the ocean's thermal inertia, implies that the sea ice equilibrium response to increasing CO2 concentration is substantially underestimated by transient simulations. The sea ice response to CO2 concentration change is not truly hysteretic and is in principle reversible.
The authors find no lag in the evolution of Arctic sea ice relative to changes in annual-mean Northern Hemisphere surface temperature. The summer sea ice cover changes linearly with respect to both CO2 concentration and temperature, while the Arctic winter sea ice cover shows a rapid transition to a very low sea ice coverage. This rapid transition of winter sea ice is associated with a sharply enhanced ice–albedo feedback and a sudden onset of convective-cloud feedback in the Arctic.
The Antarctic sea ice cover retreats continuously without any rapid transition during the warming. Compared to Arctic sea ice, Antarctic sea ice shows a much more strongly lagged response to changes in CO2 concentration. It even lags behind the surface temperature change, which is caused by a different response of ocean deep convection during the warming and the cooling periods.
Abstract
To examine the long-term stability of Arctic and Antarctic sea ice, idealized simulations are carried out with the climate model ECHAM5/Max Planck Institute Ocean Model (MPI-OM). Atmospheric CO2 concentration is increased over 2000 years from preindustrial levels to quadrupling, is then kept constant for 5940 years, is afterward decreased over 2000 years to preindustrial levels, and is finally kept constant for 3940 years.
Despite these very slow changes, the sea ice response significantly lags behind the CO2 concentration change. This lag, which is caused by the ocean's thermal inertia, implies that the sea ice equilibrium response to increasing CO2 concentration is substantially underestimated by transient simulations. The sea ice response to CO2 concentration change is not truly hysteretic and is in principle reversible.
The authors find no lag in the evolution of Arctic sea ice relative to changes in annual-mean Northern Hemisphere surface temperature. The summer sea ice cover changes linearly with respect to both CO2 concentration and temperature, while the Arctic winter sea ice cover shows a rapid transition to a very low sea ice coverage. This rapid transition of winter sea ice is associated with a sharply enhanced ice–albedo feedback and a sudden onset of convective-cloud feedback in the Arctic.
The Antarctic sea ice cover retreats continuously without any rapid transition during the warming. Compared to Arctic sea ice, Antarctic sea ice shows a much more strongly lagged response to changes in CO2 concentration. It even lags behind the surface temperature change, which is caused by a different response of ocean deep convection during the warming and the cooling periods.
Abstract
Three methods are analyzed for the design of ocean observing systems to monitor the meridional overturning circulation (MOC) in the North Atlantic. Specifically, a continuous monitoring array to monitor the MOC at 1000 m at different latitudes is “deployed” into a numerical model. The authors compare array design methods guided by (i) physical intuition (heuristic array design), (ii) sequential optimization, and (iii) global optimization. The global optimization technique can recover the true global solution for the analyzed array design, while gradient-based optimization would be prone to misconverge. Both global optimization and heuristic array design yield considerably improved results over sequential array design. Global optimization always outperforms the heuristic array design in terms of minimizing the root-mean-square error. However, whether the results are physically meaningful is not guaranteed; the apparent success might merely represent a solution in which misfits compensate for each other accidentally. Testing the solution gained from global optimization in an independent dataset can provide crucial information about the solution’s robustness.
Abstract
Three methods are analyzed for the design of ocean observing systems to monitor the meridional overturning circulation (MOC) in the North Atlantic. Specifically, a continuous monitoring array to monitor the MOC at 1000 m at different latitudes is “deployed” into a numerical model. The authors compare array design methods guided by (i) physical intuition (heuristic array design), (ii) sequential optimization, and (iii) global optimization. The global optimization technique can recover the true global solution for the analyzed array design, while gradient-based optimization would be prone to misconverge. Both global optimization and heuristic array design yield considerably improved results over sequential array design. Global optimization always outperforms the heuristic array design in terms of minimizing the root-mean-square error. However, whether the results are physically meaningful is not guaranteed; the apparent success might merely represent a solution in which misfits compensate for each other accidentally. Testing the solution gained from global optimization in an independent dataset can provide crucial information about the solution’s robustness.
Abstract
The literature offers conflicting findings about which regions contribute most to increases in the global radiative feedback after a forcing increase. This paper explains the disagreement by discriminating between two common definitions of the local feedback, which use either local temperature or global temperature as their basis. Although the two definitions of feedback have been previously compared in aquaplanet models with slab oceans, here the definitions are compared for the first time in an atmosphere–ocean general circulation model (MPI-ESM1.2) integrated over four doublings of atmospheric CO2 concentrations. Large differences between the definitions can be seen in all feedbacks, but especially in the temperature and water vapor feedbacks. Differences of up to 10 W m−2 K−1 over the Southern Ocean can be explained by the pattern of surface warming, which weights the local feedbacks and reduces their contribution to the global mean. This finding is, however, dependent on the resolution of analysis, because the local-temperature definition is mathematically inconsistent across spatial scales. Furthermore, attempts to estimate the effect of “pattern weighting” by separating local feedbacks and warming patterns at the gridcell level fail, because the radiative change in key tropical regions is also determined by tropospheric stability via the global circulation. These findings indicate that studies of regional feedback change are more sensitive to methodological choices than previously thought, and that the tropics most likely dominate regional contributions to global radiative feedback change on decadal to centennial time scales.
Significance Statement
Radiative feedbacks are processes that either intensify or damp global surface warming. We compare two ways to define local radiative feedbacks in a climate model and find that the choice of definition drastically impacts the results. Differences in feedback between the definitions are up to 10 W m−2 K−1 over the Southern Ocean; by comparison, the estimate of the true global feedback is around −1 W m−2 K−1. Also, one of the definitions is mathematically inconsistent across different scales of spatial aggregation. Our findings matter because they help to reconcile disagreement in previous studies about which regions dominate global radiative feedback change in model simulations of global warming.
Abstract
The literature offers conflicting findings about which regions contribute most to increases in the global radiative feedback after a forcing increase. This paper explains the disagreement by discriminating between two common definitions of the local feedback, which use either local temperature or global temperature as their basis. Although the two definitions of feedback have been previously compared in aquaplanet models with slab oceans, here the definitions are compared for the first time in an atmosphere–ocean general circulation model (MPI-ESM1.2) integrated over four doublings of atmospheric CO2 concentrations. Large differences between the definitions can be seen in all feedbacks, but especially in the temperature and water vapor feedbacks. Differences of up to 10 W m−2 K−1 over the Southern Ocean can be explained by the pattern of surface warming, which weights the local feedbacks and reduces their contribution to the global mean. This finding is, however, dependent on the resolution of analysis, because the local-temperature definition is mathematically inconsistent across spatial scales. Furthermore, attempts to estimate the effect of “pattern weighting” by separating local feedbacks and warming patterns at the gridcell level fail, because the radiative change in key tropical regions is also determined by tropospheric stability via the global circulation. These findings indicate that studies of regional feedback change are more sensitive to methodological choices than previously thought, and that the tropics most likely dominate regional contributions to global radiative feedback change on decadal to centennial time scales.
Significance Statement
Radiative feedbacks are processes that either intensify or damp global surface warming. We compare two ways to define local radiative feedbacks in a climate model and find that the choice of definition drastically impacts the results. Differences in feedback between the definitions are up to 10 W m−2 K−1 over the Southern Ocean; by comparison, the estimate of the true global feedback is around −1 W m−2 K−1. Also, one of the definitions is mathematically inconsistent across different scales of spatial aggregation. Our findings matter because they help to reconcile disagreement in previous studies about which regions dominate global radiative feedback change in model simulations of global warming.
Abstract
A low-resolution coupled ocean–atmosphere general circulation model (OAGCM) is used to study the characteristics of the large-scale ocean circulation and its climatic impacts in a series of global coupled aquaplanet experiments. Three configurations, designed to produce fundamentally different ocean circulation regimes, are considered. The first has no obstruction to zonal flow, the second contains a low barrier that blocks zonal flow in the ocean at all latitudes, creating a single enclosed basin, while the third contains a gap in the barrier to allow circumglobal flow at high southern latitudes.
Warm greenhouse climates with a global average air surface temperature of around 27°C result in all cases. Equator-to-pole temperature gradients are shallower than that of a current climate simulation. While changes in the land configuration cause regional changes in temperature, winds, and rainfall, heat transports within the system are little affected. Inhibition of all ocean transport on the aquaplanet leads to a reduction in global mean surface temperature of 8°C, along with a sharpening of the meridional temperature gradient. This results from a reduction in global atmospheric water vapor content and an increase in tropical albedo, both of which act to reduce global surface temperatures.
Fitting a simple radiative model to the atmospheric characteristics of the OAGCM solutions suggests that a simpler atmosphere model, with radiative parameters chosen a priori based on the changing surface configuration, would have produced qualitatively different results. This implies that studies with reduced complexity atmospheres need to be guided by more complex OAGCM results on a case-by-case basis.
Abstract
A low-resolution coupled ocean–atmosphere general circulation model (OAGCM) is used to study the characteristics of the large-scale ocean circulation and its climatic impacts in a series of global coupled aquaplanet experiments. Three configurations, designed to produce fundamentally different ocean circulation regimes, are considered. The first has no obstruction to zonal flow, the second contains a low barrier that blocks zonal flow in the ocean at all latitudes, creating a single enclosed basin, while the third contains a gap in the barrier to allow circumglobal flow at high southern latitudes.
Warm greenhouse climates with a global average air surface temperature of around 27°C result in all cases. Equator-to-pole temperature gradients are shallower than that of a current climate simulation. While changes in the land configuration cause regional changes in temperature, winds, and rainfall, heat transports within the system are little affected. Inhibition of all ocean transport on the aquaplanet leads to a reduction in global mean surface temperature of 8°C, along with a sharpening of the meridional temperature gradient. This results from a reduction in global atmospheric water vapor content and an increase in tropical albedo, both of which act to reduce global surface temperatures.
Fitting a simple radiative model to the atmospheric characteristics of the OAGCM solutions suggests that a simpler atmosphere model, with radiative parameters chosen a priori based on the changing surface configuration, would have produced qualitatively different results. This implies that studies with reduced complexity atmospheres need to be guided by more complex OAGCM results on a case-by-case basis.
Abstract
As a contribution to a detailed evaluation of Intergovernmental Panel on Climate Change (IPCC)-type coupled climate models against observations, this study analyzes Arctic sea ice parameters simulated by the Max-Planck-Institute for Meteorology (MPI-M) fully coupled climate model ECHAM5/Max-Planck-Institute for Meteorology Hamburg Primitive Equation Ocean Model (MPI-OM) for the period from 1980 to 1999 and compares them with observations collected during field programs and by satellites. Results of the coupled run forced by twentieth-century CO2 concentrations show significant discrepancies during summer months with respect to observations of the spatial distribution of the ice concentration and ice thickness. Equally important, the coupled run lacks interannual variability in all ice and Arctic Ocean parameters. Causes for such big discrepancies arise from errors in the ECHAM5/MPI-OM atmosphere and associated errors in surface forcing fields (especially wind stress). This includes mean bias pattern caused by an artificial circulation around the geometric North Pole in its atmosphere, as well as insufficient atmospheric variability in the ECHAM5/MPI-OM model, for example, associated with Arctic Oscillation/North Atlantic Oscillation (AO/NAO). In contrast, the identical coupled ocean–ice model, when driven by NCEP–NCAR reanalysis fields, shows much increased skill in its ice and ocean circulation parameters. However, common to both model runs is too strong an ice export through the Fram Strait and a substantially biased heat content in the interior of the Arctic Ocean, both of which may affect sea ice budgets in centennial projections of the Arctic climate system.
Abstract
As a contribution to a detailed evaluation of Intergovernmental Panel on Climate Change (IPCC)-type coupled climate models against observations, this study analyzes Arctic sea ice parameters simulated by the Max-Planck-Institute for Meteorology (MPI-M) fully coupled climate model ECHAM5/Max-Planck-Institute for Meteorology Hamburg Primitive Equation Ocean Model (MPI-OM) for the period from 1980 to 1999 and compares them with observations collected during field programs and by satellites. Results of the coupled run forced by twentieth-century CO2 concentrations show significant discrepancies during summer months with respect to observations of the spatial distribution of the ice concentration and ice thickness. Equally important, the coupled run lacks interannual variability in all ice and Arctic Ocean parameters. Causes for such big discrepancies arise from errors in the ECHAM5/MPI-OM atmosphere and associated errors in surface forcing fields (especially wind stress). This includes mean bias pattern caused by an artificial circulation around the geometric North Pole in its atmosphere, as well as insufficient atmospheric variability in the ECHAM5/MPI-OM model, for example, associated with Arctic Oscillation/North Atlantic Oscillation (AO/NAO). In contrast, the identical coupled ocean–ice model, when driven by NCEP–NCAR reanalysis fields, shows much increased skill in its ice and ocean circulation parameters. However, common to both model runs is too strong an ice export through the Fram Strait and a substantially biased heat content in the interior of the Arctic Ocean, both of which may affect sea ice budgets in centennial projections of the Arctic climate system.
Abstract
Simple proem models have been developed to investigate the role of atmosphere-ocean feedbacks in the stability of the current mode of the thermohaline circulation in the North Atlantic. A positive feedback between the meridional atmospheric transport of moisture and the high-latitude sinking thermohaline circulation (EMT feedback) has been found to help destabilize the latter. The minimum perturbation required to shut off the high-latitude sinking is considerably smaller when this feedback is included. Also, the high-latitude sinking is shut off much faster with this feedback than without it, given a perturbation of the same magnitude. There is also a strong positive feedback between atmospheric heat transport and the thermohaline circulation, but this can be modeled accurately on the global scale by using a properly tuned Newtonian cooling law for the surface beat flux. Idealized flux adjustment experiments suggest that the sensitivity of the real climate is not represented well in coupled atmosphere-ocean general circulation models that require 0(1) adjustments in the surface fluxes of heat and freshwater to simulate the current climate.
Abstract
Simple proem models have been developed to investigate the role of atmosphere-ocean feedbacks in the stability of the current mode of the thermohaline circulation in the North Atlantic. A positive feedback between the meridional atmospheric transport of moisture and the high-latitude sinking thermohaline circulation (EMT feedback) has been found to help destabilize the latter. The minimum perturbation required to shut off the high-latitude sinking is considerably smaller when this feedback is included. Also, the high-latitude sinking is shut off much faster with this feedback than without it, given a perturbation of the same magnitude. There is also a strong positive feedback between atmospheric heat transport and the thermohaline circulation, but this can be modeled accurately on the global scale by using a properly tuned Newtonian cooling law for the surface beat flux. Idealized flux adjustment experiments suggest that the sensitivity of the real climate is not represented well in coupled atmosphere-ocean general circulation models that require 0(1) adjustments in the surface fluxes of heat and freshwater to simulate the current climate.
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.
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.
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.
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.
Abstract
The implications are investigated of representing ocean gyre circulations by a diffusion term in the Stommel and Rooth box models of the thermohaline circulation (THC) in one and two hemispheres, respectively. The approach includes mostly analytical solution and study of the bifurcation structure, but also numerical integration and feedback analysis. Sufficient diffusion (gyre strength) eliminates multiple equilibria from either model, highlighting the need for accurate gyre circulation strength in general circulation models (GCMs) when considering the potential for abrupt climate change associated with THC shutdown.
With diffusion, steady-state flow strength in the Rooth model depends on freshwater forcing (i.e., implied atmospheric water vapor transport) in both hemispheres, not only on that in the upwelling hemisphere, as in the nondiffusive case. With asymmetric freshwater forcing, two solutions (strong stable and weak unstable) are found with sinking in the hemisphere with stronger forcing and one solution with sinking in the other hemisphere. Under increased freshwater forcing the two solutions in the hemisphere with stronger forcing meet in a saddle-node bifurcation (if diffusion is sufficiently strong to prevent a subcritical Hopf bifurcation first), followed by flow reversal. Thus, the bifurcation structure with respect to freshwater forcing of the diffusive Rooth model of two-hemisphere THC is similar to that of the Stommel model of single-hemisphere THC, albeit with a very different dynamical interpretation. Gyre circulations stabilize high-latitude sinking in the Stommel model. In the Rooth model, gyre circulations only stabilize high-latitude sinking if the freshwater forcing is weaker in the sinking hemisphere than in the upwelling hemisphere, by an amount that increases with diffusion. The values of diffusion and freshwater forcing at which qualitative change in behavior occurs correspond to the range of the values used in and obtained with GCMs, suggesting that this analysis can provide a conceptual foundation for analyzing the stability of the interhemispheric THC, and also for the potential of the Atlantic THC to undergo abrupt change.
Abstract
The implications are investigated of representing ocean gyre circulations by a diffusion term in the Stommel and Rooth box models of the thermohaline circulation (THC) in one and two hemispheres, respectively. The approach includes mostly analytical solution and study of the bifurcation structure, but also numerical integration and feedback analysis. Sufficient diffusion (gyre strength) eliminates multiple equilibria from either model, highlighting the need for accurate gyre circulation strength in general circulation models (GCMs) when considering the potential for abrupt climate change associated with THC shutdown.
With diffusion, steady-state flow strength in the Rooth model depends on freshwater forcing (i.e., implied atmospheric water vapor transport) in both hemispheres, not only on that in the upwelling hemisphere, as in the nondiffusive case. With asymmetric freshwater forcing, two solutions (strong stable and weak unstable) are found with sinking in the hemisphere with stronger forcing and one solution with sinking in the other hemisphere. Under increased freshwater forcing the two solutions in the hemisphere with stronger forcing meet in a saddle-node bifurcation (if diffusion is sufficiently strong to prevent a subcritical Hopf bifurcation first), followed by flow reversal. Thus, the bifurcation structure with respect to freshwater forcing of the diffusive Rooth model of two-hemisphere THC is similar to that of the Stommel model of single-hemisphere THC, albeit with a very different dynamical interpretation. Gyre circulations stabilize high-latitude sinking in the Stommel model. In the Rooth model, gyre circulations only stabilize high-latitude sinking if the freshwater forcing is weaker in the sinking hemisphere than in the upwelling hemisphere, by an amount that increases with diffusion. The values of diffusion and freshwater forcing at which qualitative change in behavior occurs correspond to the range of the values used in and obtained with GCMs, suggesting that this analysis can provide a conceptual foundation for analyzing the stability of the interhemispheric THC, and also for the potential of the Atlantic THC to undergo abrupt change.
