1. The Atmospheric Response to Changes in Tropical Sea Surface Temperatures An overview of Gill, A.E., 1980, Some simple solutions for heat- induced tropical circulation and Lindzen, R.S. and S. Nigam, 1987, On the Role of Sea Surface Temperature Gradients in Forcing Low-level Winds and Convergence in the Tropics Ann Gravier AT 750 19 Nov 2002

2. Outline l Gill’s model: Response of tropical atmosphere to focused diabatic heating l Response to symmetric and asymmetric forcing l Other solutions l Conclusions l Lindzen and Nigam’s model: Response of the tropical atmosphere to SST gradients l Observations l Model assumptions/the back-pressure effect l Solutions l Conclusions

3. Gill’s Model n Forcing: Heating of a limited area at or near the Equator such as over the Indonesian region n Responses: – Eastward propagating Kelvin waves, creating easterly tradewinds, and producing a Walker-type circulation, with rising over the source and sinking to the east – Slower (1/3) westward propagating planetary wave, of lesser extent producing a region of surface westerlies such as observed over the Indian Ocean

4. Gill’s model formulation and assumptions n Linear for small perturbations on a resting atmosphere Non-dimensional forced shallow water equations on equatorial  plane where f =  y Dissipative processes for friction and cooling =  small n Forcing ~O(1) n Rigid lid at Z=D

5. Response to symmetric forcing about the Equator (and x=0) Kelvin wave response travels eastward at unit speed and decays with time (at  ) and space (  ) – Note from (4.3) response is only in u, p and w (easterlies, downward vertical motion, and troughing at the Equator for x>2. Planetary wave response travels westward at 1/3 KW and decays spatially at 3  - From (4.8), the PW response has a meridional response which enables cyclonic motion on both sides of the Equator and relative ridging at the Equator west of the heating region. n Walker circulation is 5x that of Hadley cells

6. Symmetric Response in the heating region n Forcing in the region |x|<L (heating region) – As z increases,  goes to zero, from (4.8) w>0 (upward motion) and v>0 for y>0 and v<0 for y<0 (poleward motion-away from heat source) – Relationship is elucidated by vorticity eqn taken in limit  goes to zero. Divergence is balanced by the advection of planetary vorticity: Sverdrop Relation

9. Response to asymmetric forcing about the Equator (positive north, negative south) n Mixed planetary-gravity wave response which has no effect outside the forcing region, since they don’t propagate n Westward moving planetary wave response in u, v, p, and w per (5.6). – No response to east OUTSIDE heating region (x>2) – Upward (downward) vertical motion north (south) of Equator; cyclone to north and anticyclone to south n Cross-equatorial flow from High to Low pressure n Zonally integrated solution yields dominant Hadley Cell with rising motion in NH and low-level poleward westerly flow.

12. Heating mostly north of the Equator: combined solution n Symmetric response (Equatorial easterlies) evident to east of forcing region n Upward vertical motion associated with heating dominates to north n Westerlies west of forcing between 0<y<2 n Easterlies south of Equator both east and west of forcing region n Low in NH, High in SH n Zonally integrated solution shows dominant Hadley Cell circulation 70% of Walker Cell

15. Summary n Walker circulation driven only by the response to symmetric heating n Hadley circulation driven by the heating region and region to west (asymmetric heating) n Effect of large topographic barriers – “Squashing” of pressure contours and low-level jets by boundary

16. Lindzen and Nigam 1987 : Response of tropical atmosphere to SST gradients n Theory n Observations and Assumptions n Model n Model solutions n Analysis of Sensitivities n Zonally symmetric model n Conclusions

17. Theory n Observational and model evidence that precipitation anomalies in tropics associated with SSTA and low- level moisture covergence rather than evaporation anomalies n Authors investigate whether SST variations forcing of pressure gradients, which contribute to low-level convergence

18. Observations and Assumptions n Lower troposphere over tropical oceans is vertically well-mixed to about 700mb – Presence of trade-wind inversion (2-3km) – Isolates lower part of atmosphere from effects of upper atmosphere n Analyzed eddy virtual temperature fields up to 700mb. High degree of vertical correlation.

20. The Model

21. The model continued

22. Forcing: FGGE 1000mb summertime virtual temperature field.

23. Model Solution with Fixed Lid

24. The “back-pressure” effect Problem: Unrealistic simulation of zonal and meridional velocities and associated eddy convergence at equator. Sensitivity of near equatorial winds to small variations in equatorial pressure field. – On timescales of less than the cumulus cloud development time (~1hr), in nature, the winds make small-scale adjustments in that finite time to “correct” pressure (decrease the pressure gradient, and thereby the convergence). Therefore before vertical mass flux occurs, there is a horizontal redistribution of mass within the trade inversion

25. The “back-pressure” effect Original model instantaneously takes up any convergence by cumulonimbus mass flux Improved model: To include this back pressure effect, authors incorporate mechanism that allows variations in high of lid (height perturbations) within a specified adjustment or relaxation time, 30 min.

27. Analysis of sensitivities Is the low-level tropical flow forced by the zonal or meridional gradients of SST or both? Meridional gradients are ~2X zonal gradients Separately set zonal/meridional eddy SST gradients=0 Results in Figs. 7a and 7b: Convergence forced by zonal gradients~meridional gradients. Dominance appears regional Conclusion: East-west gradients in low-level flow and convergence over tropical Pacific are forced not only by zonal gradients in SST, but also by zonal variations in the meridional SST gradient field

28. Zonal Gradient=0 Meridional Gradient=0

29. Analysis of sensitivities n What is the essential horizontal momentum balance? – Recall that the momentum balance is between the Coriolis force, the eddy temperature (pressure) gradient and friction. – Tested sensitivity to Rayleigh friction coefficient, . n Conclusion: The momentum balance in the model’s tropics is essentially geostrophic to within a few degrees of the Equator

30. Analysis of sensitivities n How important is the contribution of “beta convergence” to the total convergence over tropical oceans? – Eqn 11c. First term on RHS includes effects of geostrophic convergence and friction term. Other major term is essentially Laplacian of net pressure field. – The beta convergence term is important because it largely determines the sign of the convergence field and compensates for the Laplacian term (opposite sign) in the near-Equatorial region. Fig. 9 n Argues against a simple momentum balance between friction and the pressure gradient force in the tropics

32. Analysis of sensitivities How sensitive are the model solutions to the value of the adjustment timescale,  c ? –  c  10 minutes or less: Stronger flow and excessive convergence –  c ~3hr: flow and convergence fields weakened 30 min <  c < 1hr: cumulus development time

33. Zonally symmetric model n Objective: Determine the surface forced component of the lower tropospheric Hadley circulation through the use of a coupled model n Retain only the zonal mean terms of the back pressure version of the model

35. Conclusions n SSTs and their associated gradients are an important forcing mechanism of low-level tropical flow and convergence. Low-level forcing is differential heating by SSTs of trade cumulus layer (not latent heat release). The net eddy tropical convergence is very sensitive to near-Equatorial pressure gradients: To attain a realistic simulation, the Cb mass flux exiting the trade inversion layer must be allowed time to adjust to the horizontal convergence in a finite time (  c ) n Momentum balance in model’s tropics is essentially geostrophic except within a few degrees of Equator

36. Conclusions n Longitudinal gradients in low-level flow and convergence over the tropical Pacific are forced not only by zonal gradients in SST, but also by zonal variations in the meridional SST gradient field. n Although zonal gradients in SST are smaller than their meridional counterparts, they can be of regionally dominant such as in the SPCZ. n The net eddy tropical convergence has important contributions from both the Beta convergence and Laplacian of the net pressure fields terms n The surface temperature field contribute importantly to the mean meridional circulation

37. References l Gill, A.E., 1980, Some simple solutions for heat-induced tropical circulation, Quart. J. R. Met. Soc. 106, pp. 447-462 l Lindzen, R.S. and S. Nigam, 1987, On the Role of Sea Surface Temperature Gradients in Forcing Low-level Winds and Convergence in the Tropics, J. Atmos. Sci., 44, 2418-2436