Application of Statistical, Fuzzy and Perceptron Neural Networks in Drought Forecasting (Case Study: Gonbad-e Kavous Station)

Due to economic, social, and environmental perplexities associated with drought, it is considered as one of the most complex natural hazards. To investigate the beginning along with analyzing the direct impacts of drought; the significance of drought monitoring must be highlighted. Regarding drought management and its consequences alleviation, drought forecasting must be taken into account (11). The current research employed multi-layer perceptron (MLP), adaptive neuro-fuzzy inference system (ANFIS), radial basis function (RBF) and general regression neural network (GRNN). It is interesting to note that, there has not been any record of applying GRNN in drought forecasting.
Throughout this paper, Standard Precipitation Index (SPI) was the basis of drought forecasting. To do so, the precipitation data of Gonbad Kavous station during the period of 1972-73 to 2006-07 were used. To provide short-term, mid-term, and long-term drought analysis; SPI for 1, 3, 6, 9, 12, and 24 months was evaluated. SPI evaluation benefited from four statistical distributions, namely, Gamma, Normal, Log-normal, and Weibull along with Kolmogrov-Smirnov (K-S) test. Later, to compare the capabilities of four utilized neural networks for drought forecasting; MLP, ANFIS, RBF, and GRNN were applied. MLP as a multi-layer network, which has a sigmoid activation function in hidden layer plus linear function in output layer, can be considered as a powerful regressive tool. ANFIS besides adaptive neuro networks, employed fuzzy logic. RBF, the foundation of radial basis networks, is a three-layer network with Gaussian function in its hidden layer, and a linear function in the output layer. GRNN is another type of RBF which is used for radial basis regressive problems. The performance criteria of the research were as follows: Correlation (R2), Root Mean Square Error (RMSE), Mean Absolute Error (MAE).
Results According to statistical distribution analysis, the optimal precipitation distribution in many cases was not Gamma distribution. The various time-scales of SPI revealed that, at least in 50% of the events, Gamma was not the selected distribution. Throughout the drought forecasting on the basis of SPI time-series with four aforementioned networks, 80% of the data was allocated to the training process whilst the rest of them considered for the test process. The proper parameters of the networks were chosen via trial and error. Moreover, Cross-validation was used to overcome the over-estimation. The results revealed that the long-term SPIs outdid the others. Performance of the networks promoted with increases in time scales of SPI. In other words, the performance criteria improved proportional to the increases in the time-scales. Based on the Table 3, the least and best performance were contributed to SPI1 and SPI24, respectively. In this regard, R2 of MLP for observed and estimated values of SPI vitiated from 0.009 to 0.949. Similar to MLP, correlation of ANFIS, RBF, and GRNN increased from 0.021 to 0.925, 0.263 to 0.953, and 0.210 to 0.955. Comparison of observed and estimated mean values via Z test indicated that null hypothesis of equal mean observed and estimated values was only rejected for SPI1 with α=0.01. Hence, except SPI1 forecasting, the all other scenarios have remained the mean of observed time series which highlighted the robustness of artificial intelligence in drought forecasting.
The main objective of the ongoing research was monitoring and forecasting of drought based upon various time scales of SPI. In doing so, the precipitation data of Gonbad Kavous station during the period of 1972-73 to 2006-07 were used. Based on K-S test, the best statistical distribution test for different time scales of SPI evaluation was chosen, and then, the SPI was calculated based on the most fitted distribution. After generating the time-series, MLP, ANFIS, RBF, and GRNN were applied for drought forecasting. According to the findings, the lowest performance of forecasting belonged to SPI1 where its RBF’s best performance for R2, RMSE, and MAE were 0.263, 0.806, and 0.989. Furthermore, increases in SPI time-scale promoted the performance of networks. Thus, the worst and best performance belonged to SPI1 and SPI24, respectively. Among the utilized models, ANFIS stood superior to the others, and GRNN followed up after it.