Precipitation deficit causes meteorological drought, and its continuation appears as other different types of droughts including hydrological, agricultural, economic, and social droughts. Multivariate Standardized Precipitation Index (MSPI) can show the drought status from the perspective of different drought types simultaneously. Forecasting multivariate droughts can provide good information about the future status of a region and will be applicable for the planners of different water divisions. In this study, the MLP model and its hybrid form with the Imperialistic Competitive Algorithm (MLP‐ICA) have been investigated for the first time in multivariate drought studies. For this purpose, two semi‐arid stations of western Iran were selected, and their precipitation data were provided from the Iranian Meteorological Organization (IRIMO), during the period of 1988–2017. MSPI was calculated in 5‐time windows of the multivariate drought, including MSPI_3–6 (drought in perspectives of soil moisture and surface hydrology simultaneously), MSPI_6–12 (hydrological and agricultural droughts simultaneously), MSPI_3–12 (soil moisture, surface hydrology, and agricultural droughts simultaneously), MSPI_12–24 (drought in perspectives of agriculture and groundwater simultaneously), and MSPI_24–48 (socio‐economical droughts). The results showed acceptable performances in forecasting multivariate droughts. In both stations, the larger time windows (MSPI_12–24 and MSPI_24–48) had better predictions than the smaller ones (MSPI_3–6, MSPI_6–12, and MSPI_3–12). Generally, it can be reported that, by decreasing the size of the time window, the gradual changes of the index give way to sudden jumps. This causes weaker autocorrelation and consequently weaker predictions, e.g., forecasting droughts from the perspective of soil moisture and surface hydrology simultaneously (MSPI_3–6). The hybrid MLP‐ICA shows stronger prediction results than the simple MLP model in all comparisons. The ICA optimizer could averagely improve MLP’s accuracy by 28.5%, which is a significant improvement. According to the evaluations (RMSE = 0.20; MAE = 0.15; R = 0.95), the results are hopeful for simultaneous forecasting of different drought types and can be tested for other similar areas.

Evapotranspiration is one of the most important hydro-climatological components which directly affects agricultural productions. Therefore, its forecasting is critical for water managers and irrigation planners. In this study, adaptive neuro-fuzzy inference system (ANFIS) model has been hybridized by differential evolution (DE) optimization algorithm as a novel approach to forecast monthly reference evapotranspiration (ET0). Furthermore, this model has been compared with the classic stochastic time series model. For this, the ET0 rates were calculated on a monthly scale during 1995–2018, based on FAO-56 Penman–Monteith equation and meteorological data including minimum air temperature, maximum air temperature, mean air temperature, minimum relative humidity, maximum relative humidity & sunshine duration. The investigation was performed on 6 stations in different climates of Iran, including Bandar Anzali & Ramsar (per-humid), Gharakhil (sub-humid), Shiraz (semi-arid), Ahwaz (arid), and Yazd (extra-arid). The models’ performances were evaluated by the criteria percent bias (PB), root mean squared error (RMSE), normalized RMSE (NRMSE), and Nash-Sutcliff (NS) coefficient. Surveys confirm the high capability of the hybrid ANFIS-DE model in monthly ET0 forecasting; so that the DE algorithm was able to improve the accuracy of ANFIS, by 16% on average. Seasonal autoregressive integrated moving average (SARIMA) was the most suitable pattern among the time series stochastic models and superior to its competitors, ANFIS and ANFIS-DE. Consequently, the SARIMA was suggested more appropriate for monthly ET0 forecasting in all the climates, due to its simplicity and parsimony. Comparison between the different climates confirmed that the climate type significantly affects the forecasting accuracies: it’s revealed that all the models work better in extra-arid, arid and semi-arid climates, than the humid and per-humid areas.

Evaporation is one of the main components of the hydrological cycle, and its estimation is crucial and important for water resources management issues. Access to a reliable estimator tool for evaporation simulation is important in arid and semi-arid areas such as Iran, which lose more than 70% of their received precipitation by evaporation. Current research employs the Bayesian Regularization (BR) and Scaled Conjugate Gradient (SCG) algorithms for training the Multilayer Perceptron (MLP) model (as MLP-BR and MLP-SCG) and comparing their performance with the Levenberg–Marquardt (LM) algorithm (as MLP-LM). For this purpose, 16 meteorological variables were used on a daily scale; including temperature (5 variables), air pressure (4 variables), and relative humidity (6 variables) as input data sets, and pan evaporation as the target variable of the MLP model. The surveys were conducted during the period of 2006–2021 in Fars Province in Iran, which is a semi-arid region and has many natural lakes. Various combinations of input-target pairs were tested by several learning algorithms, resulting in seven input scenarios: (1) temperature-based (T), (2) pressure-based (F), (3) humidity-based (RH), (4) temperature–pressure-based (T-F), (5) temperature–humidity-based (T-RH), (6) pressure–humidity-based (F-RH) and (7) temperature–pressure–humidity-based (T-F-RH). The results indicated the relative superiority of the three-component scenario of T-F-RH, and a considerable weakness in the single-component scenario of RH compared with others. The best performance with a root mean square error (RMSE) equal to 1.629 and 1.742 mm per day and a Wilmott Index (WI) equal to 0.957 and 0.949 (respectively for validation and test periods) belonged to the MLP-BR model. Additionally, the amount of R² (greater than 84%), Nash-Sutcliff efficiency (greater than 0.8) and normalized RMSE (less than 0.1) all indicate the reliability of the estimates provided for the daily pan evaporation. In the comparison between the studied training algorithms, two algorithms, BR and SCG, in most cases, showed better performance than the powerful and common LM algorithm. The obtained results suggest that future researchers in this field consider BR and SCG training algorithms for the supervised training of MLP for the numerical estimation of pan evaporation by the MLP model.