Some limiting forms of the poisson distribution of annual station precipitation

Abstract

Annual station precipitation is represented as a seasonally stationary Poisson arrival process in terms of three constituent random variables: season length, number of storms, and storm depth, and the distribution of the annual total is derived. The contribution of each constituent variable to variance of the annual total precipitation is determined, and limiting distributions of the latter are derived by letting each contribution vanish separately. In humid climates it is shown that the storm depth variability predominates, giving a distribution which is closely normal. In arid climates the number of storms controls and gives a highly skewed distribution. All cases are compared with observations.