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LAMONT-DOHERTY EARTH OBSERVATORY
THE EARTH INSTITUTE AT COLUMBIA UNIVERSITY
Drought Research
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Thermodynamic and dynamic mechanisms for large-scale changes in the hydrological cycle in response to global warming
Richard Seager, Naomi Naik
Lamont-Doherty Earth Observatory
and
Gabriel Vecchi
Geophysical Fluid Dynamics Laboratory

January 2010

Drying and a poleward expansion of the subtropics and wetting in the deep tropics and mid to high latitudes are robust model projections of climate change forced by rising greenhouse gases. These can be summed up as 'rich getting richer' or 'dry getting drier and wet getting wetter' to first order, although the meridional expansion of the subtropical dry zones is an interesting second order effect. Despite the robustness of these projections - robust in the sense that all climate models produce these changes - the mechanisms for the change are not yet fully understood. This is in part because it requires analyzing the moisture budget within the models used as part of the Intergovernmental Panel on Climate Change Assessment Report 4 (IPCC AR4) using daily data and taking great care with vertical integrals etc. That is, it involves a lot of data and tedious calculation. However we just did it for the 15 models that had saved all the needed data and looking at 2046-65 relative to 1960-2000. The results are described in a recent paper in Journal of Climate (link) by Seager, Naik and Vecchi.

The change in precipitation minus evaporation (P-E) averaged across these 15 models shows the expected tropical wetting, subtropical drying and expansion, and wetting at higher latitudes. The change in P-E is contributed to by changes in moisture convergence or divergence by the time mean flow and moisture convergence or divergence by the high frequency flow variations within transient eddies (storm systems). However, changes in the mean flow moisture divergence or convergence can occur because of changes in moisture itself or changes in the flow. We calculated the contributions of each. That is, we calculated the change in moisture convergence or divergence that would occur if the circulation remained at 20th Century values but humidity changed. This we refer to as the 'thermodynamic' component (TH) contribution to changes in P-E. And then we calculated the change in moisture divergence or convergence that would occur if the humidity remained at 20th Century values but the circulation changed. This we refer to as the 'mean circulation dynamic' (MCD) contribution to changes in P-E.

This was all done for two half years, October through March and April through September. These results are shown in Figures 1 and 2. The change in P-E is actually closely approximated by the change in the thermodynamic component. All we are seeing here is the effect of rising specific humidity: as the atmosphere warms and can hold more water vapor the existing patterns of water vapor transport intensify making wet areas wetter and dry areas drier. The mean circulation dynamic component is also important. Under global warming the mean tropical circulation weakens and, hence, this dynamic term tends to reduce the spatial contrast in P-E. This effect is, however, smaller than the thermodynamic effect of rising humidity. More interesting and important are the bands of dynamic drying that occur on the poleward flanks of the subtropical dry zones that act to expand them poleward. The change in transient eddy moisture flux also dries the subtropics and is primarily responsible for the wetting of the mid and high latitudes. This represents a strengthening of the existing pattern of poleward transient eddy moisture flux.


Figure 1
Figure 1. The multi-model ensemble mean, change in the moisture budget for October to March of 2046-2065 minus 1961-2000. Shown are change in P-E (top left), change in mean flow moisture convergence due to change in specific humidity alone (top right), the change in mean flow moisture convergence due to change in mean circulation alone (bottom left) and the change in transient eddy moisture flux convergence (bottom right). Units are mm/day.



Figure 2
Figure 2. Same as Figure 1 but for the April to September half year.

We also broke the changes in moisture divergence and convergence into parts related to changes in moisture advection and parts related to changes in divergent or convergent flow. This was done for both the thermodynamic and dynamic contributions to give advective and divergent contributions to each. Results are shown in Figures 3 and 4. The part of the thermodynamic term due to changes in moisture advection is quite easy to understand: because of the nonlinearity of the Clausius-Clapeyron equation even a uniform warming, with fixed relative humidity, causes specific humidity to rise more in warmer regions than in cooler regions intensifying moisture gradients. Hence existing patterns of moisture advection intensify as humidity rises: more drying in the trade winds and moistening at higher latitudes.


Figure 3
Figure 3. Decomposition of the change in the multi-model ensemble mean, thermodynamic and dynamic contributions to the change in the moisture budget for October to March of 2046-2065 minus 1961-2000. Shown are change in moisture advection due to changes in humidity (top left), change in convergence of moisture by the mean flow due to changes in humidity (top right), the change in moisture advection due to changes in mean circulation (bottom left) and the change in convergence of moisture due to changes in the mean circulation (bottom right). Units are mm/day.



Figure 4
Figure 4. Same as Figure 3 but for the April to September half year.

Even simpler is the contribution to the thermodynamic term related to the divergent or convergent flow operating on a moister atmosphere. This term leads to more drying in regions of current day moisture divergence (like the subtropics) and more moistening in regions of current day moisture convergence (like the Intertropical Convergence Zone and monsoons). The change in moisture advection due to changes in flow is quite spatially complex. More simple is the change in moisture convergence or divergence due to changes in mass convergence or divergence. This term clearly shows the weakening of the tropical circulation and increased convergence over the equatorial Pacific Ocean where the multi-model ensemble mean shows SST warming. This term also shows the drying on the poleward flanks of the subtropical dry zones as low level divergence increases there.

The changes in low level divergence, and their 20th Century values, are shown in Figure 5. This shows the weakening of the tropical circulation but also increased low level divergence on the poleward flanks of the subtropical low level divergence regions. This is indicative of a poleward shift of the meridional circulation cells that is in itself related to a poleward expansion of the Hadley Cell and poleward shift of the mid-latitude storm tracks. To date there is no well accepted explanation for why these dynamical changes occur, even as they are robust predictions of models in response to rising greenhouse gases.


Figure 5
Figure 5. The 20th Century divergence at 925mb (colors) and the 21st Century change (contours) for the October through March (top) and April through September (bottom) half years. The divergence has been multiplied by 106 with units of per sec.

The thermodynamic contribution to changing P-E can be further simplified. So far we have evaluated this with the actual model projected change in humidity. A simpler calculation is to evaluate it assuming that the relative humidity remains fixed at 20th Century values but the atmosphere warms as projected. Figures 6 and 7 show the actual thermodynamic contribution to changes in P-E, the part due to changes in specific humidity according to unchanged relative humidity and the part due to changes in relative humidity. Clearly the thermodynamic contribution is dominated by temperature change with fixed relative humidity.


Figure 6
Figure 6. The 21st Century change in the P-E tendency for the October through March half year due to changes in specific humidity (top) and the contribution with fixed relative humidity (middle) and variations in relative humidity (bottom). Units are mm/day.



Figure 7
Figure 7.Same as 6 but for the April through September half year.

The zonal means of the breakdown in the moisture budget are shown in Figure 8 together with the neglected cross product and surface gradient terms and the residual imbalance. Alas, it is unavoidable that errors in these calculations leave a notable imbalance. However it does not impact the large scale structures of the changes in the hydrological cycle.


Figure 8
Figure 8. The annual and zonal mean change in P-E and contributions from the thermodynamic term, TH, mean circulation dynamics term, MCD, and transient eddy moisture flux convergence, TE (top). In the lower panel the changes in the annual and zonal mean nonlinear term (NL) and the surface boundary term (S), as well as the residual between the change in P-E and the sum of the five contributing terms, are shown. Units are mm/day.

All of this provides a quite complete accounting of model projections of change in P-E. A large part of this occurs utterly simply from rising specific humidity in a warming atmosphere. But circulation changes are also important as are increases in the poleward moisture flux by transient eddies. These changes add up to a simple conclusion: wet areas will get wetter and dry areas will get drier while the semi-arid zones of the subtropics will expand poleward. The relative simplicity of the underlying mechanisms and their root cause in aspects of large scale circulation and moisture transport that we feel climate models handle well, makes us more certain that these changes will actually occur in the future. Of course we do need to pin down why the circulation changes occur. But even as we do that the world needs to plan for a changed hydrological cycle in a warmer world with both wetting and drying regions facing serious adaptation problems.



REFERENCES
  • Seager, R., N. Naik and G.A. Vecchi, 2010: Thermodynamic and dynamic mechanisms for large-scale changes in the hydrological cycle in response to global warming. J. Climate, 23: 4651-4668. PDF

 
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