In this research, three different evolutionary algorithms (EAs), namely, particle swarm optimization (PSO), genetic algorithm (GA) and differential evolution (DE), are integrated with the adaptive neuro-fuzzy inference system (ANFIS) model. The developed hybrid models are proposed to forecast rainfall time series. The capability of the proposed evolutionary hybrid ANFIS was compared with the conventional ANFIS in forecasting monthly rainfall for the Pahang watershed, Malaysia. To select the optimal model, sixteen different combinations of six different lag attributes taking into account the effect of monthly, seasonal, and annual history were considered. The performances of the forecasting models were assessed using various forecasting skill indicators. Moreover, an uncertainty analysis of the developed forecasting models was performed to evaluate the ability of the hybrid ANFIS models. The bound width of 95% confidence interval (d-factor) and the percentage of observed samples which was enveloped by 95% forecasted uncertainties (95PPU) were used for this purpose. The results indicated that all the hybrid ANFIS models performed better than the conventional ANFIS and for all input combinations. The obtained results showed that the models with best input combinations had the (95PPU and d-factor) values of (91.67 and 1.41), (91.03 and 1.41), (89.74 and 1.42), and (88.46 and 1.43) for ANFIS-PSO, ANFIS-GA, ANFIS-DE, and the conventional ANFIS, respectively. Based on the 95PPU and d-factor, it is concluded that all hybrid ANFIS models have an acceptable degree of uncertainty in forecasting monthly rainfall. The results of this study proved that the hybrid ANFIS with an evolutionary algorithm is a reliable modeling technique for forecasting monthly rainfall.

A unit hydrograph (UH) of a watershed may be viewed as the unit pulse response function of a linear system. In recent years, the use of probability distribution functions (pdfs) for determining a UH has received much attention. In this study, a nonlinear optimization model is developed to transmute a UH into a pdf. The potential of six popular pdfs, namely two-parameter gamma, two-parameter Gumbel, two-parameter log-normal, two-parameter normal, three-parameter Pearson distribution, and two-parameter Weibull is tested on data from the Lighvan catchment in Iran. The probability distribution parameters are determined using the nonlinear least squares optimization method in two ways: (1) optimization by programming in Mathematica; and (2) optimization by applying genetic algorithm. The results are compared with those obtained by the traditional linear least squares method. The results show comparable capability and performance of two nonlinear methods. The gamma and Pearson distributions are the most successful models in preserving the rising and recession limbs of the unit hydographs. The log-normal distribution has a high ability in predicting both the peak flow and time to peak of the unit hydrograph. The nonlinear optimization method does not outperform the linear least squares method in determining the UH (especially for excess rainfall of one pulse), but is comparable.

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