Modular Wavelet–Extreme Learning Machine: a New Approach for Forecasting Daily Rainfall

A rainfall forecasting method based on coupling wavelet analysis and a novel artificial neural network technique called extreme learning machine (ELM) is proposed. In this way, the unique characteristics of each technique are combined to capture different patterns in the data. At first, wavelet analysis is used to decompose rainfall time series into wavelet coefficients, and then the wavelet coefficients are used as inputs into the ELM model to forecast rainfall. The accuracy of the model is further improved using a modular learning approach. In the modular learning, an innovative approach to determine the optimum number of clusters entitled threshold cluster number is introduced. The relative performances of the proposed models are compared with the single ELM model for three cases consisting of one daily rainfall series from Iran (Kharjeguil station), one daily rainfall series from India (Ajmer station) and one daily rainfall series from the United States (Barton Pond station). The correlation coefficient (r), root mean square errors (RMSE) and Nash–Sutcliffe efficiency coefficient (NS) statistics are used as the comparing criteria. The comparison results indicate that the proposed modular wavelet–ELM method could significantly increase the forecast accuracy and perform much better than both the wavelet–ELM and single ELM. Moreover, three case study results indicate the importance of determining the optimum number of clusters based on the new concept of threshold cluster number in order to achieve optimum forecast results.