Time series prediction of seasonal precipitation in Iran, using data-driven models: a comparison under different climatic conditions

Seasonal total precipitation is one of the important meteorological variables and its prediction is useful for the supply of water to different sectors. This study aims to compare Seasonal Autoregressive Integrated Moving Average (SARIMA), Multilayer Perceptron (MLP), Adaptive Neuro-Fuzzy Inference System-Subtractive Clustering (ANFIS-SC), and ANFIS-Fuzzy Cluster Means (ANFIS-FCM) for the prediction of seasonal precipitation. The precipitation data were obtained for the 1951–2018 period from 8 stations located in different climatic zones of Iran. The stations and their climates are Anzali (per-humid moderate climate), Babolsar (humid moderate climate), Kermanshah (semi-arid cold climate), Shiraz (semi-arid moderate climate), Bushehr (arid warm climate), Shahroud (arid cold climate), Isfahan (extra-arid cold climate), and Zahedan (extra-arid moderate climate). The time-lagged precipitation as input for all models was chosen using the autocorrelation function (ACF), and the data were divided into two periods: 1951–2001 for training (75%) and 2002–2018 for testing (25%). Based on the evaluation criteria (root mean squared error [RMSE], normalized root mean squared error [NRMSE], Wilmott Index [WI], Akaike Information Criterion [AIC], and Bayesian Information Criterion [BIC]), results showed that the SARIMA stochastic model was more accurate than the artificial intelligence methods and had the least over- and under-estimations. MLs exhibited good prediction accuracy, but ANFIS-FCM had a little higher accuracy. Consequently, due to the high accuracy and simplicity, the stochastic model is reported as the best predictor for seasonal precipitation in all climates. In terms of the R2 values, the models showed better fitting in wet and normal years than in drought years. Further, the model predictions were more accurate in per-humid and humid areas than in arid and extra-arid climates. Also, the NRMSE values were in the range of 0.1 and 0.2, which indicated that SARIMA’s performance was medium and well. A significant result of this study was that results for different climates based on RMSE were completely opposite to those based on NRMSE, WI, and R2. This contrast was caused by the neglect of data range in the RMSE equation, so it is not a good choice to compare the results under different climates and it is better to use its normalized form “NRMSE.”