Multiple kernel fusion: a novel approach for lake water depth modeling

Abstract

Multiple kernel fusion (MKF) refers to the task of combining multiple sources of information in the Hilbert space for improved performance. Very often the combined kernel is formed as a linear composition of multiple base kernels where the combination weights are learned from the data. As the first application of an MKF approach in hydrological modeling, lake water depth as one of the pivot factors in the reservoir analysis is simulated by considering different hydro-meteorological variables. The role of each individual input parameter is initially investigated by applying a kernel regression approach. We then illustrate the utility of an MKF formalism which learns kernel combination of weights to yield an optimal composition for kernel regression. A set of 40-year data collected from 27 groundwater and streamflow stations and 7 meteorological stations for precipitation and evaporation parameters in the vicinity of Lake Urmia are utilized for model development. Both visual and quantitative statistical performance criteria illustrate a superior performance for the MKF approach compared to kernel ridge regression (KRR), the support vector regression (SVR), back propagation neural network (BPNN) and auto regressive (AR) models. More specifically, while each individual input parameter fails to provide an ac curate prediction for lake water depth modeling, an optimal combination of all input parameters incorporating the groundwater level, streamflow, precipitation and evaporation via a multiple kernel learning approach en hances the predictive performance of the model accuracy in the multiple scenarios. The promising results (RMSE= 0.098 m; R2 = 0.987; NSE = 0.986) may motivate the application of a MKF approach towards solving alternative and complex hydrological problems.