Comparison of kriging methods in rainfall estimation based on entropy‑copula (case study: Simineh river, lake Urmia Basin, Iran)

Abstract

Abstract This research has examined the performance of universal, simple, and ordinary kriging methods for estimating rainfall at a fixed point using the daily rainfall statistics of 14 stations around the Simineh River basin in the time series of 1988–2017. In order to make a correct comparison and provide acceptable results close to the reality, first the quality and value of the data of the rain gauge stations inside the basin have been evaluated through the Entropy-Copula approach. Then, the rainfall estimation has been done in the coordinates of the location of the best rain gauge station. The results of examining the mutual effect of the stations revealed the efficiency of more than 92% of the simulation approach with the R-vine copula in all stations. Comparison of entropy with multivariate regression method and entropy with R-vine copula indicated that the use of copula in entropy improves all evaluation indicators. As an example, RMSE and NSE at Dashband Bukan station improved by 41% and 4%, respectively, using the Entropy- Copula approach. By running entropy, Bukan Dashband station with N(i) = 0.016 was chosen as the best station. Estimation of daily rainfall using kriging methods for 2017 in the GIS environment based on the R2 criterion showed the superiority of the ordinary kriging method with R2 = 0.67. For monthly rainfall, simple kriging with R2 = 0.75 was superior to the other two methods. For annual rainfall, the ordinary kriging method was superior to the other two methods with R2 = 0.61. The comparison of GIS and MATLAB results based on the three indicators RMSE, NS, and MAE revealed the compatibility of GIS and MATLAB results. Comparing the results of daily rainfall estimation based on 30-year daily data at Dashband Bukan station with the observational data of this station based on all evaluation criteria indicated that the ordinary kriging method outperformed the other two methods. The universal kriging method had a better performance than the simple one. RMSE value for ordinary kriging was 2.422, simple kriging was 2.603, and global kriging was 2.527. Similarly, R2 in estimation with ordinary kriging was 0.68, simple 0.63, and universal 0.65. Therefore, the ordinary kriging method can be appraised as suitable for daily rainfall estimation.