Water vapour fluxes computed across different walls of the triangular volume of peninsular India, bounded by Trivandrum, Bombay and Nagpur, were used to compute the net flux convergence on a monthly mean basis for the months June through September for the years 1967-72. The precipitation rates over the region were computed by using the flux convergence values and the equation of continuity for water vapour and were compared with the actual rainfall. The agreement between the computed precipitation and actual rainfall was found to be fairly close

Bavadekar, SN

Mooley, DA

Ministry of Earth Sciences, Government of India

Tellus (1978), 30,537-541 
Computation of the average precipitation over the western 
part of peninsular India during the summer monsoon from 
the continuity equation for atmespheric water vapour 
By S .  N. BAVADEKAR and D. A. MOOLEY, Indian Institute of Tropical Meteorology, Pune-5, India 
(Manuscript received November 29,1977; in final form June 30, 1978) 
ABSTRACT 
Water vapour fluxes computed across different walls of the triangular volume of peninsular 
India, bounded by Trivandrum, Bombay and Nagpur, were used to compute the net flux 
convergence on a monthly mean basis for the months June through September for the years 
1967-72. The precipitation rates over the region were computed by using the flux convergence 
values and the equation of continuity for water vapour and were compared with the actual 
rainfall. The agreement between the computed precipitation and actual rainfall was found 
to be fairly close. 
1. Introduction 
Saha and Bavadekar (1973) computed the water 
vapour fluxes across different walls of the rec- 
tangular volume over the Arabian Sea during the 
summer monsoon months of 1963 and 1964 and 
suggested that the major influx of water vapour 
in the volume over the Arabian Sea was by the 
cross equatorial flow (i.e. across the wall 42OE to 
75O E) and the major outflux was across the section 
wall parallel to the west coast of India (equator to 
26' N). 
The onshore fluxes over the west coast of India 
were further studied by Saha and Bavadekar 
(1977) for the 9 years 1964-72 for the summer 
monsoon months and were correlated with the rain- 
fall along the west coast of India and also over 
peninsular India bounded by Trivandrum, Bombay 
and Nagpur. The correlation coefficients were 0.87 
for the west coast section (Trivandrum to Bombay) 
and 0.85 for the peninsular region and these were 
statistically significant at the 1% level. In the 
present investigation precipitation values computed 
by the water vapour budget method for western 
peninsular India are compared with the actual 
rainfall over the region. 
2. Continuity equation of the atmospheric 
water vapour 
The equation of continuity of water vapour used 
for the computation of the average precipitation 
rate R, for the western part of peninsular India 
i s  given as: 
R =-- lr V .  (q?)dp + E 
g 
whereY\, 
g '3is the acceleration due to gravity 
q the mixing ratio of water vapour 
V the vector wind 
E the rate of evapotranspiration 
p b , p ,  the pressures at the bottom and top of 
the section wall, respectively. 
--* 
The first term on the right-hand side represents 
the flux convergence of water vapour and contains 
the contributions due to time mean flow and tran- 
sient eddies. The sum total of the flux convergence 
of water vapour and the evapotranspiration E is 
realized as the average precipitation over the 
region. 
Tellus 30 (1 978), 6 
538 S. N. BAVADEKAR AND D. A. MOOLEY 
3. Data and methods of analysis 
The positions of the radiosonde and pilot balloon 
stations used for the purpose of computations are 
shown in Fig. 1. As mentioned before, the data 
for the summer monsoon months June through 
September and for the years 1967 to 1972 were 
used for the computation of water vapour fluxes. 
2 6  i 
i 
t 
5 * t 4 I 1 L l _ L . I J  5y, 
70.E 7 5' 8 O'E 
Fig. 1. Triangular portion of peninsular India showing 
the positions of the radiosonde, pilot balloon and 
rainfall stations. 
The details regarding the sections of triangular 
region, height of the station above mean sea level, 
length segments, etc., are given in Table 1. 
The top of the section wall was assumed at 
450 mb and bottom at the surface of the earth. 
The pressure interval was 50 mb. The procedure 
for analysis to fill up the data gap for the moisture 
parameter, etc., is similar to that given by Saha 
and Bavadekar (1977). 
3.1. Calculations of moisture flux 
The water vapour fluxes are computed across 
the section walls of the triangular region (Fig. 1) 
of peninsular India. The expression for computing 
the net flux, F,,  normal to the section wall is 
1 + ( V q  + u'q') sin /3) AL Ap 
where 
L is the length of the section 
AL convenient length segments 
Ap convenient pressure interval 
u, u components of the daily wind velocity, u 
positive towards the east and u positive 
towards the north 
p the angle of inclination of the section with 
the meridian. 
Table 1. Length of the segments used in three sections for  the computation of water uapourjluxes 
Station height above Length of segments 
Stations m.s.1. in metres RS/PB* inkm 
Trivandrum to Trivandrum 64 RS Trivandrum to 14" N 530 
Bombay section Cochin 03 PB 
Mangalore 22 PB 
Goa 55 RS 14O N to Bombay 600 
Bombay 14 RS 
Bombay to Nagpur Bombay 14 RS Bombay to 76' E 330 
section Aurangabad 600 PB 76O E to Nagour 3 10 
Nagpur 300 RS 
Nagpur to Nagpur 300 RS Nagpur to Hyderabad 370 
Trivandrum section Hyderabad 600 PB Hyderabad to Bangalore 450 
Bangalore 950 RS Bangalore to Trivandrum 450 
Trivandrum 64 RS 
* RS-radiosonde station; PB-pilot balloon station. 
Tellus 30 (1 978), 6 
AVERAGE PRECIPITATION OVER THE WESTERN PART OF PENINSULAR INDIA 
Table 2.  Budget of moisturejuxes and actual precipitation (unit: 10'' kg day-') 
Year 
Month 1967 1968 1969 1970 1971 1972 
June FD 
E 
RC 
R ,  
July FD 
E 
Rc 
R ,  
August FD 
E 
RC 
Ra 
September FD 
E 
Rc 
R ,  
0.24 
0.16 
0.40 
0.44 
0.53 
0.17 
0.70 
0.66 
- 
0.16 
0.27 
-0.02 
0.16 
0.14 
0.24 
- 
0.19 
0.16 
0.35 
0.44 
0.35 
0.17 
0.52 
0.64 
0.09 
0.16 
0.25 
0.25 
0.16 
0.16 
0.32 
0.30 
0.15 
0.16 
0.3 1 
0.4 1 
0.3 1 
0.17 
0.48 
0.58 
0.06 
0.16 
0.22 
0.27 
- 
0.16 
0.3 7 
- 
0.59 
0.16 
0.75 
0.55 
0.47 
0.17 
0.64 
0.48 
0.46 
0.16 
0.62 
0.62 
0.10 
0.16 
0.26 
0.27 
0.32 
0.16 
0.48 
0.52 
0.22 
0.17 
0.39 
0.4 1 
0.18 
0.16 
0.34 
0.34 
0.28 
0.16 
0.44 
0.26 
0.30 
0.16 
0.46 
0.4 1 
0.16 
0.17 
0.33 
0.40 
0.26 
0.16 
0.42 
0.20 
0.10 
0.16 
0.26 
0.14 
FD: Flux convergence; E: evapotranspiration; R,: computed precipitation; R,: actual precipitation. 
- Not computed due to lack of data. 
The other symbols are explained previously. 
Bar and prime denote time mean (i.e. mean for 
the month) and eddy components, respectively. 
Expression (2) can be split into two parts, giving 
the contributions due to time mean flow and tran- 
sient fluctuations separately. The contribution due 
to transient fluctuations is very small and can 
be neglected. 
With the help of computed fluxes normal to the 
section wall, the flux convergence term is obtained. 
These values are tabulated in Table 2. If the 
influx of the water vapour into the triangular 
volume is greater than the outflux, there is net 
flux convergence of water vapour and therefore 
the positive values are interpreted as flux 
convergence. 
3.2. Estimation of evapotranspiration 
The actual evapotranspiration E over the 
region was not readily available for the required 
period. The charts for the potential evapotranspira- 
tion PE over the Indian region have been prepared 
on a monthly basis (Rao et al., 1971). The average 
daily potential evapotranspiration was estimated 
from these charts for the monsoon months. The 
539 
actual evapotranspiration E is obtained by 
comparing the actual rainfall R, with potential 
evapotranspiration and using the following criteria: 
E = PE; 
and 
E = R, - storage rate - run off if R, < PE 
if R, > PE 
In most of the cases R, was found to be greater 
than PE, and hence the evaporation was assumed 
to be at the rate of PE. Year to year variations of 
E are thus disregarded in this study. 
4. Results 
From the computation of water vapour fluxes, 
it is observed that the influx into the area takes 
place across the sections Trivandrum-Bombay and 
Bombay-Nagpur. The major contribution is due to 
to the Trivandrum-Bombay section. The average 
daily fluxes in this section also show an increasing 
trend from June to July. The values drop in 
August and are lowest in September. This is 
consistent as far as the normal progress of the 
Tellus 30 (1 978), 6 
540 S. N. BAVADEKAR AND D. A. MOOLEY 
Table 3. Zonal and meridional components of water vapourfluxes for  June 1971 and 1972 (unit: 
lo5 kg m-' day-') 
Zonal flux (positive towards east) 
June 1971 June 1972 June 1971 June 1972 
Mean Eddy Mean Eddy Mean Eddy Mean Eddy 
Meridional flux (positive towards north) 
Trivandrum 396.4 -4.1 234.1 7.6 -137.3 2.1 -168.9 1.2 
Goa 321.8 -0.7 138.5 6.5 -60.4 4.1 -36.0 11.0 
Bombay 350.6 5.0 159.5 -1.9 82.9 8.8 71.8 12.6 
Nagpur 255.5 -3.7 - 82.6 -14.0 -71.5 -4.9 -88.2 22.7 
Bangalore 290.3 * 130.7 * 0.9 * 34.4 * 
* Not computed. 
monsoon over the country is concerned and is 
found in almost every year except for the year 
1971, when the maximum was found in June. The 
section Bombay-Nagpur is oriented more or less 
in the direction of the monsoon flow and has a 
small normal component to the section wall and 
hence does not show such systematic behaviour. 
The outflux given by the Trivandrum-Nagpur 
section shows systematic behaviour similar to the 
Trivandrum-Bombay section. 
The section Trivandrum-Bombay was also 
investigated to find out the vertical distribution of 
water vapour fluxes in various layers from the 
surface to 450 mb. On an average the maximum 
contribution of 19% is made by the layer 900 to 
850 mb. The layer from the surface up to 700 mb 
contributes 86% and only 14% contribution is 
due to the layer above 700 mb. The latter contribu- 
tion, though insignificant (see also Section 4.2), is 
comparable to the magnitude of the precipitation. 
4.1. Zonal and meridionaljuxes of water vapour 
Zonal and meridional components of water 
vapour fluxes, both due to time mean flow and 
transient fluctuations, are presented in Table 3 
for the month of June for the years 1971 and 1972. 
The monsoon behaviour was contrasting in nature 
for these months. The progress of the monsoon 
during June 1971 was very rapid, except for the 
break period during the second week of the month. 
The monsoon, however, revived in the third week 
and advanced in north-west India by the last week. 
The advance of the monsoon during the year 1971 
over different parts of the country was generally 
a week or 10 days ahead of the normal date of 
onset. In 1972, the south-west monsoon advanced 
temporarily over the south peninsula towards the 
end of the second week of May, but again retreated 
during the third week of May. It revived over 
Kerala by as late as 18 June. In general the 
advance of the monsoon over the peninsula and 
north-west India was delayed by 10 to 15 days in 
this year. 
Comparing the zonal and meridional components 
of the fluxes, it is observed that the zonal flux was 
considerably smaller during June 1972 than in June 
1971 at all the radiosonde stations. The eddy fluxes 
are generally small in magnitude. At Bombay the 
meridional flux is southerly and is weaker during 
June 1972, whereas the northerly meridional flux, 
shown by Trivandrum, strengthened in June 1972. 
Goa, which is in between the two stations, shows 
the northerly meridional flux to be weaker in 
magnitude than Trivandrum and Bombay. The 
orography on the west coast is probably respon- 
sible for the typical distribution of meridional fluxes 
as mentioned above. 
4.2. Flux convergence and precipitation 
The vertical profile of the flux convergence was 
obtained for all the years but they are presented 
only for the years 1971 and 1972 in Table 4. There 
is strong flux convergence in the lower layer up to 
about 850 mb followed by divergence aloft. the 
maximum value of flux divergence is near the 
800 mb level and then decreases aloft rapidly and 
even changes sign with small fluctuations. The 
strong convergence in the lower layer is mostly 
due to the presence of the orographic barrier 
(Western Ghats) along the west coast of India. 
Tellus 30 (1 978), 6 
AVERAGE PRECIPITATION OVER THE WESTERN PART OF PENINSULAR INDIA 54 1 
Table 4. Values of moisture JIux convergence at direrent isobaric surfaces for  the years 1971-1972 
(unit: 1O'O kgday;')  
Level 
Year 1000 950  900 850 800 750 700 650  600  550 500 450 
1971 June 510 250 -076 -168 -089 -063 -033 +019 +021 -019 -009 
July 455 239 -093 -161 -101 -058 -041 -025 -011 -012 -002 
August 379 131 -119 -131 -087 -040 -002 +007 +007 003 001 
September 230 172 035 -064 -048 -035 -014 008  018 022  015 
1972 June 232 165 -031 -049 -029 -018 005 001 -008 -010 -015 
July 477 245 -125 -225 -143 -046 -012 -010 -020 -022 -017 
August 393 119 -076 -081 -020 004 017 -020 -037 -017 -004 
September 096 042 -002 -017 009 008  -009 -014 -001 009 009 
The west coast stations, therefore, always get 
more precipitation compared to the stations on the 
leeward side of the Ghats. 
From the comparison of total influx and pre- 
cipitation it is found that, on an average, about 
13 % of the total infiux over the triangular volume 
is converted into precipitation. The contribution 
due to flux convergence is 8% and that due to 
evapotranspiration is 5 YO. These figures indicate 
that abundant moisture supply is available through- 
out the summer monsoon period but only a small 
fraction of it is converted into precipitation. 
5. Concluding remarks 
The budget method of computing the precipi- 
tation has some limitations. The limitations are due 
to the inadequate network of radiosonde stations 
over the region under consideration and also due 
to lack of knowledge of the actual evapotran- 
spiration. The flux divergence term is the small 
difference of two large terms of total influx and out- 
flux and requires proper and careful analysis of 
wind and mixing ratios. The computed precipitation 
rates, in spite of these limitations, are fairly close to 
actual rainfall. 
6. Acknowledgements 
The authors' grateful thanks are due to Mrs 
M. S. Naik and Shri R. M. Khaladkar who 
assisted in processing of data and Shri A. 
Girijavallabhan who typed the manuscript. 
REFERENCES 
Rao, K. N., George, C. J. and Ramasastri, K. S. 1971. the northern summer. Quart. J. R. Met. SOC. 99, 
Saha, K. R. and Bavadekar, S. N. 1977. Moisture flux 
across the west coast of India and rainfall during 
the southwest monsoon. Quart. J. R .  Met. SOC. 103, 
370-374. 
Potential evapotranspiration (PE) over India, 273-278. 
Scientific Report No. 136, India Met. Department. 
Saha, K. R. and Bavadekar,'S. N. 1973. Water vapour 
budget and precipitation over the Arabian sea during 
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HEPA3PbIBHOCTH AJIX ATMOCQEPHOTO BOARHOrO IIAPA 
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HarnypoM, PaCC'UiTbIBanHCb H HCnOnb30BZUIWCb AJIR peZUIbHbIMH OCaAKaMH. HaffseHo AOBOJIbHO TeCHOe 
PaCIreTOB ITOJlHOfi AHBepreHUHn nOTOKa Ha OCHOBe COrnaCUe MeXW BblYUCJleHHblMH W PWJIbHbIMH 
CpeAHeMeCR'iHblX AaHHbIX AJIR MKRUeB C HIOHR no OCaKaMH. 
CeATR6Pb 1967-72rr. CKOPOCTH OCaAKOB HaA 3 T 0 9  
Tellus 30 (1 978), 6 


Computation of the average precipitation over the western part of the peninsular India during summer monsoon from the continuity equation for atmospheric water vapour

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Computation of the average precipitation over the western part of the peninsular India during summer monsoon from the continuity equation for atmospheric water vapour

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Ministry of Earth Sciences, Government of India