Towards a stochastic model of rainfall for radar hydrology

Abstract

In order to investigate to what extent rainfall fluctuations observed with different types of instruments reflect the properties of the rainfall process itself and to what extent they are merely instrumental artefacts we are in the process of developing a stochastic model of rainfall. The starting point for the development of the model has been the notion that at the spatial and temporal scales associated with many types of surface rainfall measurements, rainfall is a discrete process describing the arrival of raindrops of different sizes at the ground. A fundamental question is whether this raindrop arrival process can be considered a homogeneous (Poisson) process or whether it behaves as a clustering (or possibly even scaling) process, as has recently been proposed in the literature. We have tested the classical Poisson homogeneity hypothesis in rainfall on a 35 min time series of 10 s raindrop size spectra collected with a 50 cm2 optical disdrometer. The rain rates calculated from the spectra indicated roughly uncorrelated fluctuations around a constant mean rain rate of about 3.5 mm h-1. Two types of analysis of the drop counts were carried out, a global analysis taking into account all drops regardless of their size and an analysis considering the drop counts in the 16 0.21 mm diameter intervals separately. The first type of analysis revealed that even for the more or less stationary time series under consideration the total raindrop arrival rate was overdispersed with respect to the homogeneous Poisson process. The second type of analysis demonstrated that this rejection of the homogeneity hypothesis could be attributed entirely to raindrops with diameters smaller than 1.14 mm. Although these drops account for 66% of the raindrop concentration in the air and 55% of the raindrop arrival rate at the ground, they only account for 14% of the rain rate and 2% of the radar reflectivity factor (on the basis of the mean drop size distribution during the experiment). In other words, although clustering may be a significant phenomenon for the smallest raindrops, the analyzed data seem to indicate that for moderate rain rates the arrival rate fluctuations of the raindrops which contribute most to rain rate and radar reflectivity factor behave according to Poisson statistics.