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The evaporation of raindrops
Author(s) -
Best A. C.
Publication year - 1952
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49707833608
Subject(s) - radius , drop (telecommunication) , relative humidity , humidity , evaporation , atmosphere (unit) , physics , thermodynamics , meteorology , telecommunications , computer security , computer science
The evaporation of a single drop of water as it falls through an atmosphere in which the lapse rate is 6·5°C/km and the surface temperature either 15°C or 41°C is examined. By making certain justified assumptions, it is shown that the change in surface area of a large drop (i.e., with radius exceeding 0·15 mm) as it falls from height z 1 to z 2 is proportional to (1 — f ) 1·13 exp (— lz ) where 100 f is the relative humidity and l is a constant. Values are given for the constant of proportionality and for l . If the drop has a radius less than 0·15 mm the change in volume of the drop is proportional to (1 — f ) 1·062 exp (— lz ). These results are then used to assess the effect of evaporation on the size and size distribution of raindrops falling through a constant atmosphere. It is shown that if the size distribution of raindrops at some initial height is given by 1 — F = exp [ — (2 a / b ) n ] where F is the fraction of liquid water comprised by drops with radius less than a , and b and n are constants, then evaporation will lead to a change in the values of b and n but will not affect the general validity of the formula. As the rain falls through the non‐saturated air the distributive index n tends to a value between 3·5 and 4·0 whether it was greater or less than such a value initially. If the initial value of n is less than 3·0 the scale diameter b increases as a result of evaporation. If the initial value of n exceeds about 3·5 the scale diameter decreases. The effect of evaporation upon the radar response from falling rain is also examined. In the last part of the paper the effect of the evaporation of rain into air which is initially unsaturated is considered. It is shown that the air temperature tends to a steady value and the relative humidity to 100 per cent. The excess of temperature above the steady‐state value and the deficit of relative humidity below 100 per cent decrease exponentially to zero with time. The depression of the steady‐state temperature below the initial temperature is a function only of the initial temperature and relative humidity and a table is given showing the value of the steady‐state temperature for nine different sets of initial conditions. The rate at which the final state is approached depends however only upon the rate of rainfall and a formula is derived for this dependence.