Evaluation of an inverse distance weighting method for patching daily and dekadal rainfall over the Free State Province, South Africa

Abstract

Climate data recorded by national meteorological agencies is either incomplete or faulty for some periods due to a number of reasons. Multi-functional utilization of climate data in complete form necessitates the filling of these gaps. In this study an inverse distance weighting (IDW) method was used to estimate rainfall utilizing neighbouring station data in the Free State Province of South Africa. Six weather stations evenly distributed across the province, and with data for 1950 to 2008, were used to evaluate this patching IDW approach at daily and dekadal time steps. Coefficient of determination (r²), mean absolute error (MAE) and mean bias error (MBE) were the statistics used in the assessment. Firstly, the study conducted a sensitivity analysis of the IDW exponent (p) which showed that the best results are obtained when p is either 2 or 2.5. The estimated values at all six stations were highly correlated with the measured rainfall data with an overall r² value exceeding 0.70 for both daily and dekadal estimates. MAE showed low miscalculations with values with an average of 1 mm per day and 4.4 mm per dekad. MBE was very low for both daily and dekadal evaluations but the disaggregated data showed underestimation of the IDW mostly for daily rainfall exceeding 10 mm. Thus, IDW methodology proved to be an acceptable approach for estimating both daily and dekadal rainfall in the Free State Province.

Keywords: estimation, missing data, neighbouring stations