Diagnostic study of a monsoon depressionby Geostrophic Baroclinic Model~

K. Y. IUO and S. H.\'L\~IAS [

l , '~l ;l ule of Tropical. JJdcnrolnY:J, Poo/J"

(Rereit."l 8 .1[ar.', WaS)

,:\BSTH.\t 'T . \'e-t-tiCl'I t'lllocit.iOM a t s..-)II. ':'uu. :,(MJ/lull :JIJII.1Il b lm r fa l't.'!i , "*"'.d"tt....1'" ith ll.UlOIl!l'l "'1I ,II'l'n'&!'iiull 1m \ " 1""1\,""Iculated IIlAkinJ/: II~ ' t ~ra -t-k-vc l ~l'f ~trul'h ic ha.rndinic 1lI . ...lel , Tho region u( up ward \"l'rticnl n ·l"eiti"!f agn.....8 we'll" itht ill' n'lo\'iun nf r,uuf"lI.

'1'111' co n tri bu t iun>o ")'the \'urti cil y nd n ·(,t iull a nd d iwrgr-nce k rlll lS in th e \ "rl icit)"\'(IIlI\ t i,," )Ill\!' 1"'\'11 c\"ltl llah'l l ,l\u,ltill' i lll p(lrta.lll·l~ of t h odive r gen ce tcr ut in I oruiulutin g a uuuicrb-al urodcl for the Ulll1}lWon i,. h~lught out,

2. List of symbols

V Geostrophic wind velocity

{ Relative geost rophic vorti cit y

f o Standard value of the Coriuli e pnnuueter

'" Geopotent ialZ Height of a ll isobari c sur face

1jJ Stream function for d ie nondivenrentcomponent of veloci ty

tip r I' " I I fw ..= Jl III ivmuu C lange 0 prc,' ...ure

I. Introduction

'l'he genernl synopti c features of monsoon do­pres....iom.. hnve been studied in the past by severa lworkers (Auanthakrishnun and Bhat ia 1iJ6(l,Koteswarum and George 1958 nnd 19GO, Kotas­warum and Uno 190:1, ~[a ln rku r 19H and 1950,Pisharoty and ..\J-Ilflili 195i nnd Rno andJnyaraman1958), Also, u preliminary attempt to forecnst thefiOO ·ntl. pattern in the case of the monsoon depres­siun hy graphical technique.' was mad e by Das endBu>.e(liJ58). In tb is paper, a diaguosti c st udy of thodepression hue been at tempted by lUI merical me­thod s making U~ of 1\ 4-level geostrophic haro ­clinic model .

Tlw thermodynamic energy equation fur ,,«lil\lJa~

tic motion is given hy

( I)

J (.I , lJ) .Tacohian operator

(aA alJa.. ay

Unit vecto r in the vert ical

" 'ind speed in the Xedirec tiun

'Viml speed in the Y~tl i rect ionv

k

"

3. Basic Equallons

Ali the bu..sic equation of motion, We adopted t he(Iua!ii~geo~truphic system proposed hy Chnrney(1918). III this system t he Coriolis parameter i.rcgnrded as COILQ,t8Ilt except when it is difforentiat ­t"4 1 with respect to latitude, several terms in thevorticity equation (the vertical advect ion tum, t hetwist ing term) are omitted, the divergence equationis replaced by the geostrophio relation, and themeasure of stat ic stability in the thermodynami cequation is t reated 8S a function only of pre- sure.Since the Hossby Number is estimated to he about11 ·1 over India, while it is abou t (l'1 ill the middlelut itudcs, the quusi-ueostrophic system ofequnt ionsi~ likelv to vield It'ss accurat e results in 10\\ lat itudost han in file middle latitudes. SliII tl ro qunsi­gool'ltropllie system lias been used ~(l that it J1111y

serve RB II first approximation. The equatiou« usedin thiKstudy are us follows.

Tho vort icity equation is given hy-

ae + v. \l ({ +f) = f . VW~t iJ1'

Sta tic stability

Potent ial t emperat ur e

Specifie volume

Isoba ric gradien t operutui (i ~ + j ~)"x ~yv

9

CI

ct.

v' Lnp luciun ll Jll'CatOI' ( a' a' )- + ­ax' ay' (~) + V. V (a.p) + ClW = 0.11' ai'

(2)