The study aimed to evaluate the accuracy of empirical equations (Hargreaves-Samani; HS, Irmak; IR and Dalton; DT) and multivariate linear regression models (MLR1–6) for estimating reference evapotranspiration (ET_Ref) in different climates of Iran based on the Köppen method including arid desert (Bw), semiarid (Bs), humid with mild winters (C), and humid with severe winters (D). For this purpose, climatic data of 33 meteorological stations during 30 statistical years 1990–2019 were used with a monthly time step. Based on various meteorological data (minimum and maximum temperature, relative humidity, wind speed, solar radiation, extraterrestrial radiation, and vapor pressure deficit), in addition to 6 multivariate linear regression models and three empirical equations were used as MLR1, MLR2, and HS (temperature-based), MLR3 and IR (radiation-based), MLR4, MLR5 and DT (mass transfer-based), and MLR6 (combination-based) were also used to estimate the reference evapotranspiration. The results of these models were compared using the root mean square error (RMSE), mean absolute error (MAE), scatter index (SI), determination coefficient (R²), and Nash-Sutcliffe efficiency (NSE) statistical criteria with the evapotranspiration results of the FAO₅₆ Penman-Monteith reference as target data. All MLR models gave better results than empirical equations. The results showed that the simplest regression model (MLR1) based on the minimum and maximum temperature data was more accurate than the empirical equations. The lowest and highest accuracy related to the MLR6 model and HS empirical equation with RMSE was 10.8–15.1 mm month⁻¹ and 22–28.3 mm month⁻¹, respectively. Also, among all the evaluated equations, radiation-based models such as IR in Bw and Bs climates with MAE = 8.01–11.2 mm month⁻¹ had higher accuracy than C and D climates with MAE = 13.44–14.48 mm month⁻¹. In general, the results showed that the ability of regression models was excellent in all climates from Bw to D based on SI < 0.2.

This study aims to determine the crucial variables for predicting agricultural drought in various climates of Iran by employing feature selection methods. To achieve this, two databases were used, one consisting of ground-based measurements and the other containing six reanalysis products for temperature (T), root zone soil moisture (SM), potential evapotranspiration (PET), and precipitation (P) variables during the 1987–2019 period. The accuracy of the global database data was assessed using statistical criteria in both single- and multi-product approaches for the aforementioned four variables. In addition, five different feature selection methods were employed to select the best single condition indices (SCIs) as input for the support vector regression (SVR) model. The superior multi-products based on time series (SMT) showed increased accuracy for P, T, PET, and SM variables, with an average 47%, 41%, 42%, and 52% reduction in mean absolute error compared to SSP. In hyperarid climate regions, PET condition index was found to have high relative importance with 40% and 36% contributions to SPEI-3 and SPEI-6, respectively. This suggests that PET plays a key role in agricultural drought in hyperarid regions because of very low precipitation. Additionally, the accuracy results of different feature selection methods show that ReliefF outperformed other feature selection methods in agricultural drought modeling. The characteristics of agricultural drought indicate the occurrence of drought in 2017 and 2018 in various climates in Iran, particularly arid and semi-arid climates, with five instances and an average duration of 12 months of drought in humid climates.

This study examines the effectiveness of various quantile regression (QR) and machine learning (ML) methodologies developed for analyzing the relationship between meteorological parameters and daily reference evapotranspiration (ET_ref) across diverse climates in Iran spanning from 1987 to 2022. The analyzed models include D-vine copula-based quantile regression (DVQR), multivariate linear quantile regression (MLQR), Bayesian model averaging quantile regression (BMAQR), as well as machine learning algorithms such as extreme learning machine (ELM), random forest (RF), M5 model Tree (M5Tree), least squares support vector regression algorithm (LSSVR), and extreme gradient boosting (XGBoost). Additionally, empirical equations (EEs) such as Baier and Robertson (BARO), Jensen and Haise (JEHA), and Penman (PENM) models were considered. While the EEs demonstrated acceptable performance, the QR and ML models exhibited superior accuracy. Among these, the MLQR model displayed the highest accuracy compared to DVQR and BMAQR models. Moreover, LSSVR, XGBoost, and M5Tree models outperformed ELM and RF models. Notably, LSSVR, XGBoost, and MLQR models exhibited comparable performance (R2 and NSE > 0.92, MBE and RMSE < 0.5, and SI > 0.05) to M5Tree and BMAQR models across all climates. Importantly, these models significantly outperformed EEs, DVQR, ELM, and RF models in all climates. In conclusion, high-dimensional QR and ML models are recommended as promising alternatives for accurately estimating daily ET_ref in diverse global climate conditions.

Drought assessment is inherently complex, particularly under the influences of climate change, which complicates long-term forecasting. This study introduces a novel hybrid deep learning model, Deep Feedforward Natural Networks (DFFNN), enhanced by War Strategy Optimization (WSO), aimed at forecasting the Standardized Precipitation Evapotranspiration Index (SPEI) for lead times of one, three, six, nine, and twelve months. Key parameters of the DFFNN, including the number of neurons and layers, learning rate, training function, and weight initialization, were optimized using the WSO algorithm. The model’s performance was validated against two established optimizers: Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). Evaluations were conducted at two synoptic stations with distinct climatic conditions in Iran. Results demonstrated that the WSO-DFFNN model achieved superior performance for SPEI 12 (t + 1) with a correlation coefficient (r) of 0.9961 and Normalized Root Mean Square Error (NRMSE) of 0.1028; for SPEI 12 (t + 3) with r = 0.8856 and NRMSE = 0.1833; for SPEI 12 (t + 6) with r = 0.8573 and NRMSE = 0.2203; for SPEI 12 (t + 9) with r = 0.7951 and NRMSE = 0.2479; and for SPEI 12 (t + 12) with r = 0.7840 and NRMSE = 0.3279 at the Chabahar station. Additionally, the WSO-DFFNN model outperformed for SPEI 12 (t + 1) with r = 0.9118 and NRMSE = 0.1704; for SPEI 12 (t + 3) with r = 0.8386 and NRMSE = 0.2048; for SPEI 12 (t + 6) with r = 0.7602 and NRMSE = 0.2919; for SPEI 12 (t + 9) with r = 0.6379 and NRMSE = 0.2843; and for SPEI 12 (t + 12) with r = 0.6044 and NRMSE = 0.3463 at the Anzali station. The results obtained from this study have the potential to improve drought management strategies.

To accurately manage water resources, a precise prediction of reference evapotranspiration (ET_ref) is necessary. The best empirical equations to determine ET_ref are usually the temperature-based Baier and Robertson (BARO), the radiation-based Jensen and Haise (JEHA), and the mass transfer-based Penman (PENM) ones. Two machine learning (ML) models were used: least squares support vector regression (LSSVR) and ANFIS optimized using the particle swarm optimization algorithm (ANFPSO). These models were applied to the daily ET_ref at 100 synoptic stations for different climates of Iran. Performance of studied models was evaluated by the correlation coefficient (R), coefficient of determination (R²), mean absolute error (MAE), root mean square error (RMSE), scatter index (SI) and the Nash-Sutcliffe efficiency (NSE). The combination-based ML models (LSSVR4 and ANFPSO4) had the lowest error (RMSE = 0.34-2.85 mm d^-1) and the best correlation (R = 0.66-0.99). The temperature-based empirical relationships had more precision than the radiation- and mass transfer-based empirical equations.