Large Scale Dynamics of the Tropical Atmosphere At. Sci. 575

 

0. The sequence on atmosphere-ocean interactions

 

1. Tropical Observations

 

            Handouts

            Annual cycle (Mitchell and Wallace, 1992)

 

2. The role of the tropics

 

On time scales less than decadal, the only effects of SST on the rest of the globe are from the tropics

 

Sterl and Hazeleger, 2005

 

Thermal forcing (organized by SST but not caused by SST) to rest of globe. Forcing effects determined by location and magnitude of forcing and transmission properties of atmosphere.

 

Divergence crucial to tropics and large

 

Trenberth et al, 2000

 

Tropical ocean participates in effects of tropics on rest of globe through oceanic heat transport and through ENSO.

 

 

3. Tropical Thermodynamics

 

Notes from Cane and Sarachik, 2006

 

4. Tropical Divergence

 

In midlatitudes: quasi-geostrophy gives: f:ζ:δ = 1:R0:R02

 

In the tropics, the divergence is of the same order as the vorticity.

 

In the tropics, divergence is thermally forced by the latent heat released in cumulonimbus: 

 

wN2 Å Q

 

Reed and Recker, 1971

 

5. How clouds heat.

 

Yanai, Esbensen and Chu, 1973)

 

6. Convective Boundary Layers

 

            Tennekes, 1973

 

7. The maintenance of the vertical stratification---Radiative-Convective Equilibrium

 

Sarachik, 1978; 1985

 

8. A 2d Example of Thermal Forcing--The Hadley Circulation

 

Schneider and Lindzen, 1978,

Schneider, 1978

 

9. Thermal Forcing by an isolated heat source

 

            Matsuno (1966); Gill (1980

            Lindzen (1967)

            Wu et al. (1999,2000,2001)

            Chiang et al (2001)

 

10. How SST determines the location of the thermal sources:

 

            Lindzen and Nigam. 1987

            Battisti et al., 1999

Neelin, 1989

 

11. Teleconecting to higher latitudes

 

            Trenberth et al., 1998.

 

12. The Walker Circulation

 

            Geisler, 1981

 

13 Recap

 

            Notes from Cane and Sarachik, 2006

 

References:

 

Battisti, D. S., E. S. Sarachik, and A. C. Hirst, 1999: A Consistent Model for the Large-Scale Steady Surface Atmospheric Circulation in the Tropics. J. Climate, 12, 2956-2964.

 

Chiang, J. C. H., S. E. Zebiak, and M. A. Cane, 2001: Relative roles of elevated heating and surface temperature gradients in driving anomalous surface winds over tropical oceans. J Atmos. Sci., 58, 1371-1394.

 

Geisler, J.E., 1981: A linear model of the Walker circulation. J. Atmos. Sci., 38, 1390-1400.

 

Gill, A. E., 1980: Some simple solutions for heat induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106, 447–462

 

Lindzen, R. D, 1967: Planetary waves on beta-planes. Mon. Wea. Rev., 95, 441-451.

 

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.

 

Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial area. J. Met. Soc. Japan, 44, 25-43.

 

Mitchell, T.P. and J.M. Wallace, 1992: The annual cyucle in equatorial convection and sea surface temperature. J. Clim., 5, 1140-1156.

 

Neelin, J.D., 1989: On the interpretation of the Gill model. J. Atmos. Sci.,46, 2466–2468.

 

Reed, R. J. and E..Recker. 1971: Structure and Properties of Synoptic-Scale Wave Disturbances in the Equatorial Western Pacific. J.Atmos. Sci., 28, 1117–1133.

 

Sarachik, E. S., 1978: Tropical sea surface temperature: An interactive one-dimensional atmosphere‑ocean model, Dyn. Atmos.& Oceans., 2, 455‑469.

 

Sarachik, E. S., 1985: A simple theory for the vertical structure of the tropical atmosphere. Pure Appl. Geophys., 123, 261–271.

 

Schneider, E.K., 1977: Axially symmetric steady-state models of the basic

state for instability and climate studies. Part II. Nonlinear calculations. J. Atmos. Sci., 34, 280-297.

 

Schneider, E.K., and R. S. Lindzen, 1977a: A discussion of the parameterization of momentum exchange by cumulus convection. J. Geophys. Res., 81, 3158-3160.

 

Schneider, E.K., and R. S. Lindzen, 1977b: Axially symmetric steady-state models of the basic state for instability and climate studies. I. Linearized calculations. J. Atmos. Sci., 34, 263-279.

 

Sterl, A. and W. Hazeleger, 2005: The relative roles of tropical and extratropical forcing  on atmospheric variability. Geophys. Res. Lett., 32, doi: 10.1029/2005GL023757.

 

Tennekes. H., 1973: A model for the dynamics of the inversion above a convective boundary layer. J. Atmos. Sci., 30, 558–567.

 

Trenberth, K. E., G. W. Branstator, D. Karoly, A. Kumar, N.-C. Lau, and C. Ropelewski. 1998: Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperatures. J. Geophys.  Res., 103 (C7), 14,291–14,324.

 

Trenberth, K.E., D.P. Stepaniak, and J.M. Caron, 2000: The global monsoon as seen through the divergent atmospheric circulation. J. Climate, 13, 3969-3993.

 

Wu, Z., E.S. Sarachik, and D.S. Battisti, 1999: Thermally forced surface winds on an equatorial beta-plane. J. Atmos. Sci., 56, 2029-2037.

 

Wu, Z., D.S. Battisti, and E.S. Sarachik 2000a: Rayleigh Friction, Newtonian Cooling, and the Linear Response to Steady Tropical Heating. J. Atmos. Sci., 57, 1937-1957.

 

Wu, Z., E.S. Sarachik, and D.S. Battisti, 2000b: The vertical structure of convective heating and the three-dimensional structure of the forced circulation in the tropics. J. Atmos. Sci., 57, 2169-2187.

 

Wu, Z., E.S. Sarachik, and D.S. Battisti, 2001: Thermally driven tropical circulations under Rayleigh friction and Newtonian cooling: Analytic solutions. J. Atmos. Sci., 58, 724-741.

 

Yanai, M., S. Esbensen and J-H. Chu. 1973: Determination of bulk properties of tropical cloud clusters from large-scale heat and moisture budgets. J. Atmos. Sci., 30, 611–627.

Some Numbers

 

Radius of Earth  6370 km

 

Area of Earth  0.51x1015 m2

 

Solar Constant 1367 W/m2

 

Area covered by Oceans   0.36x1015 m2

 

Heat capacity of Water    Cpw = 1cal/gmK = 4.19 x103 J/kgK

 

Heat Capacity of Dry Air            Cpa = 0.24 cal/gmK = 1.0x103 J/kgK

 

Density of Air at surface 1.23 kg/m3

 

Density of Water 1gm/cm3 = 103 kg/m3  = 1 tonne/m3

 

1 year has 3.15x107 sec (which can be remembered as ¹ x107 sec)

 

Latent heat of water L = 2.5 x 106 J/kgK

 

Universal Gas Constant R = 8.31x103 J/Kmol

 

Gravity at Sea Level  g=9.81m/s2

 

Stefan-Boltzman Constant  σ=5.67 x 10-8 J/m2K4s

 

 

Derived Quantities:

 

The mass of a water column of area 1m2 area and 10 m deep is 10 tonnes

 

The mass of the total air column exerting 1020hPa at surface is about 10 tonnes

 

50 W/m2 into a column of area 1m2 of water 50 meters deep heats the column 1K in 50 days (ÒThe 50-50-50 ruleÓ)

 

100 W/m2 into a unit column of water 100 m deep heats that column 0.6K/mo.

 

100 W/m2 into a unit column of air to the top of the atmosphere heats the air column 0.8K/day

 

It takes 29W/m2 to evaporate 1mm/day of water from the surface.

 

For the mean temperature of surface of the earth, T=15¼C=288K, σT4 = 390 W/m2 For T=300K, σT4 = 459 W/m2