The theoretical relationship between precipitate water vapour in the atmosphere &amp; surface humidity has been investigated. By introducing the concept of a lapse parameter alpha, a method has been devised for estimation of precipitable water vapour. Results have been compared for six Indian Stations for which upper air data were available

Aggarwal, B. K.

Garg, O. P.

Majumdar, N. C.

English

Defence Science Journal

WATER VAPOUR CONTENT OF THE ATMOSPHERE IN RELATION TO SURFACE HUMIDITY N. C. WJUMDAR, O.P. GARG Defence Science Laboratory, Delhi & B. K. AGGARWAL M. M, H. College, Ghaziabad (Received 7 February 19'77) The theoretical relationship betweenprecipitablewater vapour in the atmc sphere & surface humidity has been ir- vestigated. By introducing the concept of a lapse parameter a, a metnod has been devised for estimation of precipi- table water vapour. Results have been compared for six Indian Stations for which upper air data were available. Atmospherio water vapour plays an important role in all thermodynamic processes in the atmos- phere, particularly in the absorption of radiation, both solar-and terrestrial. Water vapour has absorp- tion bands in the short infra-red spectrum of solar radiation, and much stronger absorption bands in the long infra-red spectrum of terrestriakradiation. Quantitative estimate of the total water vapour content of the atmosphere is essential for the study of atmospheric heat balance, specially at the earth-air in- terface. Besides its obvious importance in agricultural meteorology, it is also needed for .the study of 'atmospheric turbidity', which is responsible for the variation in total attenuation of solar radiation dur- ing its passage through the atmosphere. The water vapour content of the atmosphere between any two isobaric layers is, as a rule, expres- sed in terms of 'Precipitable water', which is simply the depth of liquid water which would be for- lmed if the vapour contained in a vertical column of ail of uniform cross section between the fwo pres- sure levels, were all condensed. The piecipitable watel W,2, between preseure levels, p, end p,, is usually expreaeed in cm or in gm/cm2, assuming density of water to  be 1 gm/cm3. Total preeipitable water in the entire atmosphere above pressure level p, can be obtained with fi =: 0. - . Very little work seems to have been carried out so far, for reliable estimation of W in, respect of Indian stations. Mukerjed has estimated W by the 'Xummatbn method', based on radiosonde data, from ground surface upto the highest level of observation, i.e. 600 mb. Anantha Krishna et a12 have extra- polated the observed data upto 200 mb level. Apart from the high degree of u~certainty associated with t h e  method of extrapolation used, the data used were not considered t o  be suBciently reliable in view of poor performance at sub-zero temperatures, of humidity sensors used in those days in radiosonde equip- ment. Moreover, the highest level of observation being only 600 mb, estimation of total prwipitable w a t e ~  based on such data, cannot be relied upon. Robinson3 has also stated that water content sound- ings are, in general, not as reliable as pressure and temperature soundings. Things have, however, im- proved since then, and data arc now available upto 400 or 350 mb in respect of quite a number of Indian stations. In the present paper, attempt has been made t o  investigate the theoretical relationship between precipitable water and surface humidity, with a view to  exploring the possibilities of using the latter for esi$mating the former. This was considered worth while because upper-air data are not available for a very large number of Indian stations. , T H E O R E T I C A L  D E R I V A T I O N  O F  T H E  R E L A T I O N S H I P  B E T W E E N  P R E C I P I T A B L E  W A T E R  A N D  S U R F A C E  H U M I D I T Y  , Both atmospher'ic pressure, p,-and partial vapour pressure, e, are found to fall almost exponentially with height, although the latter falls at a rela,tively?aster rate, so that more than 99% of the total water vapour content is confined within the troposphere. We have, therefore, defined a lapse parameter, a, by the following equation de -- a~ - d  - e P (1) I DEF. SCI. J., VOL. 27, OCTOBER 1977 which means that the relative change in vapour pressure is d times that in 'atmospheric pressure. a', thus represents the vertical moisture profile relative to total pressure. Ineegration of eqn. (1) yields log e = a log p c c (2) " 01' ez/e1 = ( ~ 2 1 ~ 1 ) ~  (3) where pl and p, ale two specified pressure levels, and el and e, are the corresponding vapour pressures, Equation (2) shows that log e plotted against log p  shauld give a straight line: with slope 'a'. Fig. 1 gives such a plot in respect of six Indian stationl~, based on uppei. air data4. The stations and the months were so chosen as t o  cover a wide range of humidiky and pressure-bvels. It will be seen that a is not a constant but varies between 2.90 and 3.83. Now, precipitable water, d W, within a layer of thickness dh  at a height his given by - d W  = pw dh  -(4) where p, is the density of water vapour in that layer. - . J The pressure drop d p  across the laye1 is dp - - p g d h = - - ( p a  + p,)gdh where p is the density of moist air and pa, that of dry air at the same height and q is the acceleration due t o  gravity. Bence, 1 T ( P a  f I Substituting this value in eqn. (4), we obtaia Since under practical circumstances, e is very small compared to  p, even at pound level, the perfect gas equation may be reasonably @plied t o  dry air as well as the vapour component. Thus we can write, - p - e  = . p a R a T  1 (6) and e = PU R, T * (7) where (p - e) is the partial pressure of dry air, T, the absolute temperature, and R, and R, are the constants for &y air and water-vapow: respectively. Dividing eqn (6) by eqn (7), we obtain - Ra - (-)=-. 9 Pw RW ' whence, - - 0.622e ( , ? P , ) =  p - 0.378e (8) This follows from the fact that Ra/R, =,,Ma Ma,= 0.622 where Mw is the molecular weight of water v%pour+(18.016) and M,  is the effective molecular weight of dry air (28.97). Prom a scrutiny of climatological data for all Indian Stations5, it is observed that 0.378 e a t  ground level never exceeds 1.7% of the total pressure even under extreme conditions, the value decreasing with height. No significant error will, therefore, be introduced by simplifying equation (8) t o  the form - Pw - 0.622 e Pu + Pw P Substitution of this value ?n eqn. (5) gives, 0.622 e dp . - dW = - 9 P (9) * However, in meteorological practice, pressures are always expressed in millibars (1 mb = 108 dynes/cm2). Since g varies very little within the troposphere, a constant value of 980 cm/sec2 may be assumed without any significant error. , - Equatios (9), thus reduces t o  From (3), we have e = .el (P/PI)~ (11) bB'. ~ C I .  J., VOL. 27, OCTO~X~R 1977b where el and p1 correspor_ld t o  the initial level. Substitution of this valuein (lo), gives 1 0-636 el (mb) dW - . pa-1. dp PP , Integration of this equation between limits p1 and p2 gives the precipitable water, W12, between thesc two levels, so that l WI2 = 0.635 a el (mb) [ - (pdpl)a 1 (12) - The total precipitable water, W, inthe entire atmosphere above the ground surface, can be obtained by puttiug, pl = po and e, -- eo at the ground suiface, andfi t3 0. . . .- H p c e  ' 0,636 w=-- a (mb) cna ' (13) and, the precipitable water, Wp, from pound level upto any specified level, p, will be given by / 0.635 eo (mb) w, = a > [ 1 -- (p i~ i j "  j (14) In orde~ t o  avoid ~om~utationa2 work, two nomograms have been pre&red and presented in Figures 2 and 3. The former gives total prkcipitable water W for given values of ground vapour pressure, eo, and lapse parameter, g: The latter gives the'correction factor [l - (p/pO)u] for given values of p/po and a in order to  estimate W9 upto to  the highest level of observation. ,. [ V A L I D A T I O K  O F  P R O P O S E D  M E T H O D  The upper a i ~  data of six Indian stations, based on which Pig. 1 has been prepared, have been utilis- .. ed .for testing the validity of the proposed method of estimation of grmipitable water. For each sta- tion, the lapse par~meter, a, is given by the slope of the corresponding line in Pig. 1. Then, with the - help of the two nomograms in Pigs. 2 and 3, Wp wt+s estimated upto the highest,level of observation. T O T A L  P R E C ~ P I T A D L E  WATER VAGOU~\W) f r ~ ,  1 m m - 4  N W r l n p  9 2 ? : :$  ", b b , 0 0 0  0 0 - ?, 2% 9 9 -  N W b i n  in I 0  0 0 0  0 0 0  0 0 0.0 I 1 I i . i i l l I l i ~ ~ . ~ ~  l l ~ ~ ~ ~ ~ 1 ~ ~ i ~ ~ ~ ~ ~ ~ l ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~  1 1  LJ I 1 i - SUFIFACE VAPOUR PRESSURE (e,) -mb - N b ~ 0 .  * .. Llll~lllljllll/;lll/li~~llllUI L A P S E  P A R A M E T E R  (d) Fig. 2-Nomogram for estimation of total precipitable water yapour ( W &om surfabe vapour pressure e, and lapse parameter -a). 200 M ~ J W D ~  : et. al. : W&r Vapour of Atmosphere / CORRECTION FACTOR - , 0 '0 '0 P a r r r u a E  RATIO [ P , ~ ~ ]  - A W . . b o b  L b b v . --. [ I  I - - t I I I Fig. 3-Nomogram for evaluation of correction factor for preoipitable water vapour W from ground pressure level p. to any  pressure level p. . W p  was also independently computed $om &he same data by the conventional summation method'. , According t o  this methhd, the local atmosphere is visualised as made up of rt finite l a , y e ~  defined by iso- baric levels, p, (ground), pl, p2. . . . . . . . . . . . . . .pa. Then, t o  a first approximation, the precipitablc water, W,, in the rth layer, accordhg to  equation (10) will be given by - (15) where Mr. the average value of e /p  in the rth layer, I Hence total precipitable water, ,WO*, will be given by - Here, the last or the qth layer is bounded above by the highest level of observation, so that pa is p, and Won is Wp as given by eqn. (14). Values of precipitable water estimated from surface vapour pressure according t o  the prepsed method have been compared with those computed by the 'summation method' described abova, in Fig. 4, from which one may be able to  judge the closeness of agreement. . DISCUSSION It will be appreciated that the introduction of the concept of lapse p r a m e t e ~ ,  a, amounts to an ideali- sation'of the real atmosphere. Actually, the vertical moisture profile has been found tb  depart consider- ably from the assumed picture in a number of cases. . Even then, it has been found possible to  estimate precipitahle water from surface humidity with reasonable accuracy from the mean slopeof the graph bet- ween log e and log p. It follows, therefore, that even if the lapse parameter varies from layer to  layer, K,  as defined in this paper, should serve the purpoke of . estimating ' precipitable water, being an integra- ted average for the whole atmosphere. DEB. Sa. J., BOL. 27, ~ C T O B B I ~  1977 Attempts have been made in the past to esti- mate precipitable water from surface humidity. For emmple, Hann's fbrmula, namely, W=0.25 0,m6 is still being used3. This formula = I - is based on the extrapolation of the ground water 0 1 vapour pressure eomb and gives the total water 2 -  * I  content of the atmosphere, W, in om. of preci- pitable water vapour. This formula may be subject t o  systematic errors of more than 30% at same places. According to  (13), Hann's formula assumes a constant value of 2.54 for a which' is much lower tbtt tke values obtained from Fig. I., and should, thereforb, yield much higher NEW DELW values of W. Y Charts are also available6, from which preci- 0 3 t 7 2 5 ; pitable water can be calculated as a function of I p  cm.. COMPUTED FROM UPPER A I R  OAT* dew point temperatinre at lCOO mb. These ale based om t6e-&&%mption of a pseudo-adiabatic Fig. 4-Comparison between proposed method for e~tinirut~ion lapse rate in the atmosphere. Values obtained of precipitable water w p  Cm from surface humidity from these charts are also higher than ' . and com uted value from upper' air data by con- ventiouay suhmation method. - those computed from upper air data. Reitan7 as proposed an empirical formula for prediction of precipitable water from surface dew hl- point. This a so suffers from similar drawbacks as discussed above in so far as it fails to  consider the variation of a and yields much higher values than those obtained by actual computation from upper air data. It appears, therefore, t i a t  the method proposed in this paier is likely t o  give more reliable informa- tion, particularly because, a has been found to  vary between 2.90 and 3-83 for the six stations investi- gated so far. The authors are grateful t o  Dr., A.K. Sreedhar, Director, Defence Science Laboratory, Delhi, for his permission t o  publish this paper. R E F E R E N C E S  1. MUKERJI, T.K., Ind.. J .  Met. &. GPeophys. 13 (1962), 371. 2. ANANTHAKRISRNAN, R., Mary M Selvan & Chellappa R., Ind. J. Met. & Geophys, I 6  (1965), 371. 3. ROBINBOX, N., 'Solar Radiation' (Elsevier Publishing Company, London), 1966, 115. 4. Aerological Data of India (India Meteorological Department, New Delhi), June & December 1969. 6. Climatological Tables ef Observatories in India, (India Meteorological Departmert, New Delhi), 1931-1960. > 6. ~rnithsonian%eteorolo~ical Tables, (Smithsonian Institution Press, Washington), 1971, 327. \ 7. REITAN, Clayton H. J. App. Met., 2 (1963), 776. 

Water Vapour Content of the Atmosphere in Relation to Surface Humidity

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Water Vapour Content of the Atmosphere in Relation to Surface Humidity

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