1. Simple tropical models and their relationship to GCMs Adam Sobel, Columbia Chris Bretherton, U. Washington

2. All aspects of tropical climate depend on tightly coupled feedbacks between convection, clouds, radiation, SST, surface fluxes… In characterizing feedbacks, useful to look at local relationships between different physical variables (scatter plots) – takes out geography Observed relationships can be used to constrain models of all sorts In GCMs, relationships can be diagnosed and compared to obs, and to other GCMs In simple models, relationships can be put in via bulk parameters, and sensitivity relatively easily understood – may help to interpret GCM biases?

3. E.g. water vapor path vs. precip, from satellite microwave

4. Normalizing to saturated WVP (mass-weighted column mean RH) gives better fit

5. Sensitive test for GCMs: CCM3.6 too much rain at low wvp (shallow cloud regions?)

6. Longwave cloud forcing (TOA), CCM3.6

7. Shortwave not as good -> coupled model errors

8. Simple models Neelin-Zeng “Quasi-equilibrium tropical circulation model” (QTCM) Single baroclinic mode for temperature, moisture, wind, + barotropic mode for wind Betts-Miller type convection Underlying construction (single mode etc.) similar to models by Raymond, Emanuel, others QTCM is good bridge between GCMs, simple models We work with further reductions of QTCM (assumed symmetries etc.)

9. Idealized Walker circulation (Bretherton & Sobel 2002) 1-dimensional (longitude) domain, sinusoidal SST, no rotation Temperature assumed constant in x, but unknown QTCM vertical structures Convective scheme: hard adjustment or “strict quasi-equilibrium” Convective greenhouse feedback on radiative cooling R=R clr – rP, r=0.2 Fixed surface wind speed & exchange coeff.

10. Equations u is baroclinic, has sign of upper trop. wind In convective regions, q=T. Gross moist stability M=M s – M q. A q is constant coef. P diagnosed from moist static energy plus (1).

11. System is very sensitive to cloud- radiative feedback parameter

12. And also gross moist stability (Neelin & Held 1987; Yu et al. 1998; Raymond 2000). r modifies “effective GMS” vertical motions efficiently inefficiently export/import energy Radiative cooling larger smaller

13. Same system with ocean mixed layer (Sobel 2003; Peters & Bretherton 2004) set SWCF=LWCF (both linear in precip as before) Finite conv adj time P=(q-T)/  Forcing is background sfc rad +ocean heat xport divergence, linear in x Now size of convective region much less dependent on r, because SWCF counteracts LWCF by cooling the surface; but other parts of the solution, such as SST in convective region, are sensitive to r For large r can get instability to coupled oscillations on intraseasonal/subannual time scale (Sobel & Gildor 2004)

14. Insights In these models, moisture is key horizontally varying fields. Controls precip, and through that, CRF. Key parameters are gross moist stability, and the constants relating WVP and CRF to precip

15. How is this relevant to biases in GCMs? Sensitivity to parameters such as r, GMS, convective time scale (WVP vs. precip) in simple models is relatively straightforward to understand. These same parameters can be diagnosed from GCMs. We can thus place the GCM in the parameter space of the simple model, which might – if the simple model has enough of the right stuff in it - give us some insight into why the GCM behaves as it does. Would be especially interesting to compare these parameters in several different GCMs.