Uncertainty-based rainfall network design using a fuzzy spatial interpolation method

The importance of optimization of rain gauge stations locations is critical given that rainfall data is central to various water-related studies. As rainfall data has vagueness in nature, fuzzy set theory can describe uncertainties existing in rainfall data. In this paper, we develop a framework to rainfall network design that combines fuzzy concepts and a deterministic spatial interpolation method known as Fuzzy Inverse Distance Weighted (FIDW). It addresses two important issues: (1) the assessment of two types of fuzzy mathematical approaches known as Fuzzy Standard IDW (FS-IDW) and Fuzzy Modified IDW (FM-IDW); (2) the comparison of the FIDW with spatial and spatiotemporal network designs using Ordinary Kriging (OK), known as OK-S and OK-ST, respectively. We consider four objective functions (OF): interval-based Estimation Error Variance Types 1 and 2 (EEVT1, EEVT2), Mean Square Error (MSE) and Coefficient of Determination (R²). Four scenarios of number of removed stations including 5, 10, 15 and 20 are also analysed via statistical indicators. Firstly, the FIDW parameters (power and radius) are optimized for each OF. Then, we resort to a Genetic Algorithm (GA) to solve these OFs. Percentage of similarity between optimal removed station in both FIDW methods (FS-IDW and FM-IDW) is higher than OK-ST method. Between FIDW methods, FM-IDW yields better results. Statistical results of four removed stations (5, 10, 15 and 20 rain gauge stations) show that the highest variation in estimation accuracy is from 5 to 20 removed stations which belongs to EEVT1 OF and is around 30%.