Filling gaps in daily rainfall data: a statistical approach

Abstract

Daily rainfall data are one of the basic inputs in hydrological and ecological modeling and in assessing water quality. However, most data series are too short to perform reliable and meaningful analyses and possess significant number of missing records. The study focuses on developing a methodology to fill the gaps in daily rainfall series considering data of twenty rainfall stations from Brahmani Basin, Rachi, India. A probabilistic approach is adopted to generate data for filling on missing points. The Poisson-gamma (PG) distributions were explored in the study as they possess useful properties to simultaneously model both the continuous (rainfall depth) and discrete (rainfall occurrence) components of daily rainfall. First, the PG distributions were fitted to the daily rainfall data of targeted stations and the parameters were estimated. The models were compared with the widely used inverse distance interpolation method. To compare the fit of the models, a dataset of size equal to the size of the observed dataset were generated. The means and percentages of days with no rainfall of observed and simulated datasets were very similar. However, PG distributions slightly overestimate the 95th percentile and underestimate the variance and 99th percentile. This indicates that the models do not capture well the extremely heavy rainfall events; hence, the PG distributions need to modify to capture better the extreme events. However, with respect to all statistics, the PG model performs better than the inverse distance interpolation method.