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. The methodology considers two basic assumptions. • The rainfall data of missing period have similar statistical properties to the data from available periods. Fairly large amounts of data exist to generalize the parameters from the available periods to the points with no data. The assumption is also supported by the fact that, for the studied stations, the first and second halves of the available datasets possess similar statistical properties. • Spatial correlations exist among rainfall occurrence and amounts of neighboring stations. The fact is reasonable as fairly negative relationship were observed between correlation of daily rainfall and distances among the studied stations. Once the PG distributions were decided, samples were generated with the parameters of respective stations. The generated data for a station is completely random in nature and independent of the rainfall amounts of neighboring stations. To match the data, first the rainfall amount of the region is estimated as the weighted mean of rainfall amounts from four closest stations. Weights were taken as the inverse of the distances of the neighboring stations from the target station. Days were sorted from driest to wettest on the basis of the mean rainfall amounts of neighboring stations, and finally, the generated data were matched. Instead of using two separate models for generating continuous data (rainfall depth) with exact zero (no rainfall), the proposed method use a single model to model both components of daily rainfall simultaneously. The method resolves the problem of overestimating non-zero rainfall amount that arises while using traditional interpolation methods. However, the method may not work well when the neighboring stations are not close to the target station.