The influence of evaporation and drop-interactions on a rainshaft

Abstract

Calculations have been made of the variations with fall-depth z of the liquid water content, L, rainfall rate, p, radar reflectivity, Z, drop concentration, NT, and raindrop size distribution n(r), within a steady-state rainshaft as a result of the evaporation and interaction of the drops. The interactions were described by a generalized stochastic equation which takes account, as described by Brazier-Smith, Jennings and Latham (1973), of the variation of coalescence efficiency ε with drop radii R, γ and the fact that satellite drops are produced when drops separate after collision. The relative humidity is assumed to fall linearly from 100 per cent at cloud base (z = 0, T = 8°C) with a gradient β. The lapse rate within the rainshaft was taken to be 8°C km−1 and the initial size distribution was generally given by the Marshall-Palmer equation. Calculations were made for 3 different situations in order to isolate the physical processes which most affect the rainfall: (1), evaporation without interaction; (2) interaction without evaporation; (3) both interaction and evaporation. The calculations for Case (1) indicate that the numbers of drops in all size classes are diminished with increasing Z̄, with a preferential reduction at the small-radius end of the spectrum. In Case (2) the interactions of the raindrops introduce considerable detail into n(r), with bimodal curves associated with satellite drop production, the highly efficient consumption of small drops by larger ones and the variations of ε and fall-velocity V with drop-radius γ. The main feature of the calculations for Case (3) is the rǒle of coalescence in preserving within the spectrum a considerable amount of liquid water that would otherwise be lost by evaporation. For example, whereas the rainwater content at z = 1·5 km for β = 20 per cent km−1 and Lo = 1·0 gm m−3 is 0·28 gm m−3 if interactions are absent, their presence elevates L to 0·57 gm m−3 at this level. This retention effect is significant for all values considered of β, L, p, and the initial slope of the raindrop size distribution (varied from half to twice that of the Marshall-Palmer equation). It is also found that the structure introduced into the size distributions as a result of interactions is partially smoothed out by evaporation, which replaces a substantial proportion of the smallest drops consumed by coalescence.