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

Outline Gill’s model: Response of tropical atmosphere to focused diabatic

heating Response to symmetric and asymmetric forcing Other solutions Conclusions

Lindzen and Nigam’s model: Response of the tropical atmosphere to SST gradients Observations Model assumptions/the back-pressure effect Solutions Conclusions

Gill’s Model

Forcing: Heating of a limited area at or near the Equator such as over the Indonesian region

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

Gill’s model formulation and assumptions 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 Forcing ~O(1) Rigid lid at Z=D

1(2.6)

21

(2.12) 2

(2.8)

(2.9)

pu yv

xp

yuy

u vp Q

x y

w p Q

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.

Walker circulation is 5x that of Hadley cells

Symmetric Response in the heating region

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.

(4.11) 0

(4.12)

u vy v

x y

v yQ

Divergence is balanced by the advection of planetary vorticity: Sverdrop Relation

Response to asymmetric forcing about the Equator (positive north, negative south) Mixed planetary-gravity wave response which has no effect

outside the forcing region, since they don’t propagate 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

Cross-equatorial flow from High to Low pressure Zonally integrated solution yields dominant Hadley Cell with

rising motion in NH and low-level poleward westerly flow.

Heating mostly north of the Equator: combined solution

Symmetric response (Equatorial easterlies) evident to east of forcing region

Upward vertical motion associated with heating dominates to north

Westerlies west of forcing between 0<y<2 Easterlies south of Equator both east and west of

forcing region Low in NH, High in SH Zonally integrated solution shows dominant

Hadley Cell circulation 70% of Walker Cell

Summary

Walker circulation driven only by the response to symmetric heating

Hadley circulation driven by the heating region and region to west (asymmetric heating)

Effect of large topographic barriers– “Squashing” of pressure contours and low-level

jets by boundary

Lindzen and Nigam 1987 : Response of tropical atmosphere

to SST gradients

Theory Observations and Assumptions Model Model solutions Analysis of Sensitivities Zonally symmetric model Conclusions

Theory

Observational and model evidence that precipitation anomalies in tropics associated with SSTA and low-level moisture covergence rather than evaporation anomalies

Authors investigate whether SST variations forcing of pressure gradients, which contribute to low-level convergence

Observations and Assumptions

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 Analyzed eddy virtual temperature fields up to

700mb. High degree of vertical correlation.

The Model

'

1

's

's

o

(1) ( , , ) 1

zonally averaged surface temperature

0.003 , vertical lapse rate

height in m

T Eddy component of surface temperature

TEddy variation of static stabil

H

s so

s

ZT z T z T

H

T

Km

z

o

ity

geopotential height

H 3000 , 0.30

Z

m

Assumption: = (T) (2 ) [2 ]ob nT

The model continued'

2 2

' 3s

(3) ( , , ) (2 )( ) ( )( )2

where T , 1.225 , 288 , 1/ ,

o sT o s T T

o

s s o o o

g n Tp Z p g nT Z Z Z Z

H

T T kgm T K n T

1

The linearized horizontal momentum equations are:

2(6b) 1

cos 2 3

2(7 ) 1

2 3

where / ~ (2.5 )

0.61( , ) ( , ) 1 wh

1

o s

o s

d oc

vs s

nH TgfV U

a

nH Tgb fU V

a

C V H days

qT T

q

ere q is specific humdity

Forcing: FGGE 1000mb summertime virtual temperature field.

Model Solution with Fixed Lid

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

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.

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

Zonal Gradient=0

Meridional Gradient=0

Analysis of sensitivities

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, . Conclusion: The momentum balance in the

model’s tropics is essentially geostrophic to within a few degrees of the Equator

Analysis of sensitivities 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

Argues against a simple momentum balance between friction and the pressure gradient force in the tropics

Analysis of sensitivities

How sensitive are the model solutions to the value of the adjustment timescale, c? c10 minutes or less: Stronger flow and excessive

convergence

– c ~3hr: flow and convergence fields weakened

30 min < c< 1hr: cumulus development time

Zonally symmetric model

Objective: Determine the surface forced component of the lower tropospheric Hadley circulation through the use of a coupled model

Retain only the zonal mean terms of the back pressure version of the model

(12 )

(12 ) (2 )2

( cos ) (12c)

cos

o ss o

o c

a fV U

nH Thb fU nT n H V

H Vh

a

Conclusions

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)

Momentum balance in model’s tropics is essentially geostrophic except within a few degrees of Equator

Conclusions

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.

Although zonal gradients in SST are smaller than their meridional counterparts, they can be of regionally dominant such as in the SPCZ.

The net eddy tropical convergence has important contributions from both the Beta convergence and Laplacian of the net pressure fields terms

The surface temperature field contribute importantly to the mean meridional circulation

References

Gill, A.E., 1980, Some simple solutions for heat-induced tropical circulation, Quart. J. R. Met. Soc. 106, pp. 447-462

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