The Development of Raindrop-size Distributions and Implications Related to the Physics of Precipitation

Abstract

Computations of the changes of the raindrop-size distributions with distance fallen are made with a computer. With the assumption of a steady mass flux of raindrops just below the melting level, changes brought about in the distribution through coalescence among raindrops, by accretion of cloud droplets, and by evaporation are considered. The numerical procedures which are used remove all restraints on the form of the initial raindrop-size distribution and on the properties of the cloud and the atmosphere through which the drops are falling. Raindrop-size distributions may frequently be expressed satisfactorily by a function of the form:where D is the drop diameter, NDdD the number of drops of diameter between D and D + dD in unit volume of space, N0 the value of ND for D = 0, and Λ is the magnitude of the slope of the distribution. It is found that an initial distribution having a relatively large slope is considerably modified by the processes of coalescence, accretion and evaporation. Whereas the number of smaller drops is markedly depleted by each process, the number of larger drops is increased by coalescence and accretion but is decreased by evaporation. A distribution with a relatively small slope is only slightly modified by the three processes. By considering raindrop-size distributions with various slopes but equal rainfall intensity, it is found that the depletion of cloud liquid water content increases as the slope of the distribution becomes larger. The amount of evaporation also increases as the slope of the distribution increases. A procedure is presented whereby the raindrop-size distribution at the melting level can be deduced. This is possible by combining the information obtained from the computations of the change in the distribution below the melting level with the observed distribution at the ground. One study of this type for the light rain of 31 July 1961 at Flagstaff, Ariz., shows that the observed distribution at the surface must develop from a distribution aloft which has more large drops and fewer small drops than indicated by the Marshall and Palmer distribution.