Hybrid Wavelet Neuro-Fuzzy Approach for Rainfall-Runoff Modeling

Abstract

The ability of wavelet transform (WT) to simultaneously deal with both the spectral and temporal information contained within time series data makes it popular to use in modeling the rainfall-runoff process over a catchment. This study explores the potential of hybrid Wavelet Co-Active Neuro Fuzzy Inference System (WCANFIS) models for simulating the transformation of rainfall-runoff process in the Baihe catchment located in China. The study investigates the selection of suitable settings for wavelet-based neuro-fuzzy rainfall-runoff models. These settings include the choice of a suitable wavelet function and the number of decomposition levels to be employed. For the development of wavelet neuro-fuzzy rainfall-runoff models, the input rainfall data is transformed by using the Discrete Wavelet Transformation (DWT). Ten different wavelet functions including the simple mother wavelet Haar; db2, db4, and db8 wavelet functions from the most popular wavelet family Daubechies; the Sym2, Sym4, Sym8 wavelets with sharp peaks; Coif2, Coif4 wavelets; and the discrete meyer (dmey) wavelet functions are used in this study. The study also investigates 10 input vectors in order to compare the two approaches of input vector selection to be used in conjunction with the WCANFIS models. The five input vectors are selected using the most common approach in which selection of the input vector comprising of the sequential time series data. Using this approach, the first input vector contains only lag-one day time series data and then modifying the input vector by successively adding one more lag time series into input vector and this continues up to a specific lag time (lag-5 day in the present study). The remaining five input vector combinations are selected on the basis of cross-correlation analysis. The performance of the developed WCANFIS models are compared with the simple Co-active Neuro Fuzzy Inference System (CANFIS) models developed without WT and a total of 101 models are investigated in this study. The study reveals that the WCANFIS models performed better with the parsimonious input vector containing lagged time rainfall series having poor correlation with the observe runoff. The developed hybrid WCANFIS models performed best with the db8 mother wavelet function at the maximum possible decomposition level.