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Quantifying contributions to polar warming amplification in an idealized coupled general circulation model

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Abstract

An idealized coupled general circulation model is used to demonstrate that the surface warming due to the doubling of CO2 can still be stronger in high latitudes than in low latitudes even without the negative evaporation feedback in low latitudes and positive ice-albedo feedback in high latitudes, as well as without the poleward latent heat transport. The new climate feedback analysis method formulated in Lu and Cai (Clim Dyn 32:873–885, 2009) is used to isolate contributions from both radiative and non-radiative feedback processes to the total temperature change obtained with the coupled GCM. These partial temperature changes are additive and their sum is convergent to the total temperature change. The radiative energy flux perturbations due to the doubling of CO2 and water vapor feedback lead to a stronger warming in low latitudes than in high latitudes at the surface and throughout the entire troposphere. In the vertical, the temperature changes due to the doubling of CO2 and water vapor feedback are maximum near the surface and decrease with height at all latitudes. The simultaneous warming reduction in low latitudes and amplification in high latitudes by the enhanced poleward dry static energy transport reverses the poleward decreasing warming pattern at the surface and in the lower troposphere, but it is not able to do so in the upper troposphere. The enhanced vertical moist convection in the tropics acts to amplify the warming in the upper troposphere at an expense of reducing the warming in the lower troposphere and surface warming in the tropics. As a result, the final warming pattern shows the co-existence of a reduction of the meridional temperature gradient at the surface and in the lower troposphere with an increase of the meridional temperature gradient in the upper troposphere. In the tropics, the total warming in the upper troposphere is stronger than the surface warming.

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Acknowledgments

The authors are in debts to Drs. Max J. Suarez and Qiang Fu for providing the source codes of the dynamical core and radiation transfer model used in this study. The computations were made at the high performance computing facility at the Florida State University. We are grateful for constructive comments from Dr. K.-K. Tung and from two anonymous reviewers. This work is supported by grants from the NOAA/Office of Global Programs (GC04-163 and GC06-038) and from the National Science Foundation (ATM-0833001).

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Correspondence to Ming Cai.

Appendix: Online calculations of convergence of non-radiative energy fluxes

Appendix: Online calculations of convergence of non-radiative energy fluxes

In addition to radiative energy fluxes, there are non-radiative energy fluxes associated with turbulent heat fluxes at the surface, vertical convective processes, frictional process, and large-scale (vertical and horizontal) advective processes. Unlike the radiative energy fluxes, these non-radiative energy flux terms (except surface heat fluxes and frictional terms) are not explicitly needed during model integrations because changes in momentum fields are directly related to force rather than energy. Because our feedback analysis is built on the energy balance equation, we need to compute and output the non-radiative energy flux terms as diagnostic variables during model integrations. We apply the tendency method to obtain the remaining non-radiative energy flux convergence terms at each grid point and each time step during model integrations without using spatial finite difference approximations as follows:

The energy flux convergence due to the vertical and horizontal advective tendencies provided from the dynamical core, Q lg_dyn, is calculated according to

$$ Q^{\rm \lg \_dyn} = {\frac{{(mc_{p} T + m{\frac{{{\mathbf{v}}^{2} }}{2}})^{\rm after\_advection} - (mc_{p} T + m{\frac{{{\mathbf{v}}^{2} }}{2}})^{\rm before\_advection} }}{2\Updelta t}} $$
(9)

where m is the atmospheric mass occupying at the grid point; T and v are its temperature and velocity (c p is the air heat capacity at constant pressure); and 2Δt is the physical time interval for the leap-frog time integration scheme. The terms with superscripts “before_advection” and “after_advection” are evaluated, respectively, before and after the dynamical tendencies are updated during model integrations.

There are numerical filters applied to all atmospheric variables after the advective tendency updating to control the numerical modes resulting from the time integration with advective tendencies. We have explicitly diagnosed for the loss of kinetic energy due to numerical filtering (numerical filters do not lead to a loss of potential energy since potential energy is linearly proportional to temperature) according to.

$$ D_{\rm num\_filter} = {\frac{{(m{\frac{{{\mathbf{v}}^{2} }}{2}})^{\rm after\_num\_filter} - (m{\frac{{{\mathbf{v}}^{2} }}{2}})^{\rm before\_num\_filter} }}{2\Updelta t}} $$
(10)

The terms with superscripts “before_num_filter” and “after_num_filter” are evaluated, respectively, before and after the filter subroutines are called during model integrations. We then update the temperature at the same grid point with the change equal to \( - 2\Updelta tD_{\rm num\_filter} /(mc_{p} ) \). As a result, there is no energy loss in our model due to numerical filters, as discussed in Sect. 2 of the main text.

The kinetic energy loss due to the frictional terms specified in (2) is diagnosed as

$$ D_{\rm fric} = {\frac{{(m{\frac{{{\mathbf{v}}^{2} }}{2}})^{\rm after\_fric} - (m{\frac{{{\mathbf{v}}^{2} }}{2}})^{\rm before\_fric} }}{2\Updelta t}} $$
(11)

The terms with superscripts “before_fric” and “after_fric” are evaluated, respectively, before and after the friction terms are applied during model integrations. We then calculate

$$ F_{D} = - \sum\nolimits_{\sigma } {} D_{\rm fric} $$
(12)

where \( \sum\nolimits_{\sigma } {} \)represents a summation over all layers above the ground. As indicated in (4), the term F D is used as a heating term at the surface layer in order to ensure the energy conservation of the climate system.

The energy flux convergence associated with the dry convection adjustment scheme (1) is calculated according to

$$ Q^{\rm conv} = {\frac{{(\rm mc_{p} T)^{\rm after\_conv} - (\rm mc_{p} T)^{\rm before\_conv} }}{2\Updelta t}} $$
(13)

The terms with superscripts “before_conv” and “after_conv” are evaluated, respectively, before and after the convection adjustment subroutine is called during model integrations. Note that the energy flux convergence associated with convective transport of moist and momentum is not included in our simple coupled GCM.

The accuracy of these online calculations of non-radiative radiative energy flux convergence terms can be checked independently although some of them are never used explicitly during model integrations or they are only for the diagnostics purpose. The accuracy of (A5) is ensured by confirming that the vertical summation of Q conv is zero. Two conditions need to be met for an accurate estimate of Q lg_dyn: (1) the vertical summation of Q lg_dyn is equal to the net radiative flux at the TOA at each location after a longtime averaging and (2) the global mean of the vertical summation of Q lg_dyn is equal to zero at each time step. The global condition that the global mean of the longtime mean net radiative flux at the TOA is equal to zero (which is calculated from radiation model alone) is an indicator of the accuracy of (A2–A4). Finally, the longtime mean balance among all of radiative and non-radiative energy flux terms at each location is the ultimate validation of the accuracies of all energy flux term calculations. We have verified that these conditions are all met satisfactorily with errors less than few tenth W m−2.

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Lu, J., Cai, M. Quantifying contributions to polar warming amplification in an idealized coupled general circulation model. Clim Dyn 34, 669–687 (2010). https://doi.org/10.1007/s00382-009-0673-x

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