ABSTRACT
In rainfall–runoff modeling, the wavelet-based artificial neural network (WANN) model, which links wavelet transform to an artificial neural network (ANN) in order to capture multiscale features of the process as well as to forecast the runoff values, is a beneficial method. For any hydrological process with long-term historical data, which enjoys the WANN method as a modeling tool, numerous inputs should be imposed to ANNs in order to model the process. Applying numerous inputs, without paying attention to their importance in the model, may lead to essential decline in WANN model performance. Therefore, efficient methods are needed to determine dominant data as model inputs. In this chapter, two mathematical concepts (i.e., self-organizing maps [SOMs] and entropy) were used as feature extraction methods for modeling the rainfall–runoff process of the Delaney Creek and Payne Creek Subbasins located in Florida, USA, with distinct hydrogeomorphological characteristics. Firstly, in order to handle the multifrequency characteristic of the process, both rainfall and runoff time series were decomposed into several subseries by wavelet transform. Subsequently, dominant subseries were extracted via SOM- and entropy-based criteria to be imposed into a feed-forward neural network (FFNN) model to predict runoff values in daily and monthly scales. To have better interpretation about the model efficiency, the results of two proposed models (wavelet–SOM–FFNN [WSNN] and wavelet–entropy–FFNN [WENN]) were compared with autoregressive integrated moving average with exogenous input (ARIMAX) and ad hoc FFNN methods, without any data preprocessing. The results proved that conjunction of employed feature extraction methods and the WANN approach could improve model efficiency. In monthly modeling, the WSNN and WENN showed lower performance compared with daily models. This might be due to the few numbers of subseries utilized in monthly preprocessing, which SOMs could not organize properly, and in the WENN model, this might be due to involvement of more uncertainty in the monthly data, which could be distinguished via entropy, as a measure of randomness and uncertainty.
