The downscaling of rain gauge time-series

Kevin S. Paulson & Paul D. Baxter

This paper develops a downscaling algorithm capable of producing ensembles of rain rate time-series, with integration times as short at 10 seconds, consistent with a time-series of rain rates with integration times as long as 6 hours. The algorithm is based on a stochastic multiplicative cascade using beta distributions as the random generator. The statistics of these cascades are developed in the paper. The cascade requires two parameters at each of a geometric progression of scales. These parameters are estimated from one gauge-year of rain gauge data, with a 10 second integration period, collected in the Southern UK. The statistical moments up to third order, of nine gauge-years of data, are calculated for integration times in the range 10 seconds to 6 hours. These data are compared with time-series derived by accumulating 10 second data to larger integration times, and then downscaling using the proposed algorithm.

Keywords: rain, rain gauge, downscaling, multifractal, multiplicative cascade