Rainfall-runoff modeling through regression in the reproducing kernel Hilbert space algorithm

In this study, Regression in the Reproducing Kernel Hilbert Space (RRKHS) technique which is a non-linear regression approach formulated in the reproducing kernel Hilbert space (RRKHS) is applied for rainfall-runoff (R-R) modeling for the first time. The RRKHS approach is commonly applied when the data to be modeled is highly non-linear, and consequently, the common linear approaches fail to provide satisfactory performance. The calibration and verification processes of the RRKHS for one- and mull-day ahead forecasting R-R models were demonstrated using daily rainfall and streamflow measurement from a mountainous catchment located in the Black Sea region, Turkey. The efficacy of the new approach in each forecasting scenario was compared with those of other benchmarks, namely radial basis function artificial neural network and multivariate adaptive regression splines. The results illustrate the superiority of the RRKHS approach to its counterparts in terms of different performance indices. The range of relative peak error (PE) is found as 0.009-0.299 for the best scenario of the RRKHS model, which illustrates the high accuracy of RRKHS in peak streamflow estimation. The superior performance of the RRKHS model may be attributed to its formulation in a very high (possibly infinite) dimensional space which facilitates a more accurate regression analysis. Based on the promising results of the current study, it is expected that the proposed approach would be applied to other similar environmental modeling problems.