Comparative study of different wavelets for developing parsimonious Volterra model for rainfall-runoff simulation

Although the Volterra models are non-parsimonious ones, they are being used because they can mimic dynamics of complex systems. However, applying and identification of the Volterra models using data may result in overfitting problem and uncertainty. In this investigation we evaluate capability of different wavelet forms for decomposing and compressing the Volterra kernels in order to overcome this problem by reducing the number of the model coefficients to be estimated and generating smooth kernels. A simulation study on a rainfall?runoff process over the Cache River watershed showed that the method performance is successful due to multi-resolution capacity of the wavelet analysis and high capability of the Volterra model. The results also revealed that db2 and sym2 wavelets have the same high potential in improving the linear Volterra model performance. However, QS wavelet was more successful in yielding smooth kernels. Moreover, the probability of overfitting while identifying the nonlinear Volterra model may be less than the linear model.