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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.

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.

In developing countries, the demand for food has increased with significant increases in population. Greater demands are therefore being placed on the agricultural sector to increase production. This has led to increased soil erosion, especially in arid and semi-arid regions. The aim of this study was to simulate runoff and erosion on soils of three different wheat agroecosystems (rainfed farming, traditional irrigation, and industrial irrigation systems). The effect of variations in soil texture, slopes (1, 3 and 5%) and rainfall intensity (10, 25 and 40 mm h−1) on runoff volume, runoff coefficient, sediment concentrations, and sediment loss (soil erosion) were recorded for soils from each management system. Soil chemical properties (pH, EC) and organic matter were not significantly related to soil erosion. Analysis of variance showed significant differences in soil erosion and runoff coefficients when slopes were increased from 1 to 5 percent. The highest soil erosion was recorded on a slope of 5% with a rainfall intensity of 40 mm h−1, and the lowest on a slope of 1% with a rainfall intensity of 10 mm h−1. Of the three management systems, the highest runoff volume, runoff coefficient, sediment concentration and soil erosion occurred on soils from the traditional irrigation treatment, with a soil texture of sandy loam, slopes of 5% and rainfall intensity of 40 mm h−1. Results of the study indicated that the influence of slope and rainfall intensity on runoff volume, runoff coefficient, sediment concentration and soil erosion varies with soil texture and agroecosystem. These results can be usefully applied to agricultural land use planning and water management systems for reducing soil erosion at regional and on-farm levels.

In this study, the least square support vector machines (LS-SVM) method was used to predict the longitudinal dispersion coefficient (DL) in natural streams in comparison with the empirical equations in various datasets. To do this, three datasets of field data including hydraulic and geometrical characteristics of different rivers, with various statistical characteristics, were applied to evaluate the performance of LS-SVM and 15 empirical equations. The LS-SVM was evaluated and compared with developed empirical equations using statistical indices of root mean square error (RMSE), standard error (SE), mean bias error (MBE), discrepancy ratio (DR), Nash-Sutcliffe efficiency (NSE) and coefficient of determination (R2). The results demonstrated that LS-SVM method has a high capability to predict the DL in different datasets with RMSE = 58–82 m2 s−1, SE = 24–39 m2 s−1, MBE = −1.95–2.6 m2 s−1, DR = 0.08–0.13, R2 = 0.76–0.88, and NSE = 0.75–0.87 as compared with previous empirical equations. It can be concluded that the proposed LS-SVM model can be successfully applied to predict the DL for a wide range of river characteristics.

Drought is one of the most complex phenomena in the world; so, proper management is very important in monitoring and reducing its damage. For this purpose, Standard Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI), and Reconnaissance Drought Index (RDI) indices were used to analyze the intensity and frequency of drought in the coastal wet, mountain, semi-mountain, semi-desert, desert, and coastal desert climates of Iran in four seasons, separately: autumn, winter, spring, and summer. Forty-three synoptic stations with a common statistical period of 50 years (1969–2019) were selected. The results showed that the trend of drought in winter and summer is increasing in all studied climates. The comparison of the results in the trend analysis of the drought showed the same trend, but the SPEI index compared to the other indicators showed a quicker response to changes in drier climates. The highest correlation (0.80–0.99) between SPI-RDI and SPEI-RDI indices in coastal desert, mountain, and semi-mountain climates and the lowest correlation (0.34) between SPI-SPEI and SPEI-RDI indices in semi-desert, desert, and coastal desert climates were obtained. SPI-RDI variations showed similar values in colder climates. The SPEI is based on precipitation and temperature data, and it has the advantage of combining multi-scalar character with the capacity to include the effects of temperature variability in the drought assessment. Thus, SPEI is recommended as a suitable index for studying and identifying the effect of climate change on drought conditions.

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 (ETRef) 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.

The accurate estimation of reference evapotranspiration (ETref) is a crucial component for modeling hydrological and ecological cycles. The goal of this study was the calibration of 32 empirical equations used to determine ETref in the three classes of temperature-based, solar radiation–based, and mass transfer–based evapotranspiration. The calibration was based on measurements taken between the years 1990 and 2019 at 41 synoptic stations located in very dry, dry, semidry, and humid climates of Iran. The performance of the original and calibrated empirical equations compared to the PM-FAO56 equation was evaluated based on model evaluation techniques including the coefficient of determination (R2), the root mean square error (RMSE), the average percentage error (APE), the mean bias error (MBE), the index of agreement (D), and the scatter index (SI). The results show that the calibrated Baier and Robertson equation for temperature-based models, the Jensen and Haise equation for solar radiation–based models, and the Penman equation for mass transfer–based models performed better than the original empirical equations. The calibrated equations had, respectively, an average R2 = 0.73, 0.67, and 0.78; RMSE = 35.14, 35.02, and 30.20 mm year-1; and MBE = − 5.6, − 3.89, and 2.57 mm year-1. The original empirical equations had values of average R2 = 0.60, 0.37, and 0.65; RMSE = 68.34, 66.98, and 52.62 mm year-1; and MBE = − 5.75, 4.26, and 8.99 mm year-1, respectively. The calibrated empirical equations for very dry climate (e.g., Zabol, Zahedan, Bam, Iranshahr, and Chabahar stations) also significantly reduced the SI value from SI > 0.3 (poor class) to SI < 0.1 (excellent class). Therefore, the calibrated empirical equations are highly recommended for estimating ETref in different climates.

After precipitation, reference evapotranspiration (ET O ) plays a crucial role in the hydrological cycle as it quantifies water loss. ET O significantly impacts the water balance and holds great importance at the basin level because of the spatial distribution of managing water resources. Large scale teleconnection indices (LSTIs) play a vital role by influencing climatic variables and can be pivotal in determining ET O and its predictive variables. This study aimed to model and forecast annual ET O in Iran’s basins by utilizing LSTIs and employing various machine learning models (MLMs) such as least squares support vector machine, generalized regression neural network, multi-linear regression (MLR), and multi-layer perceptron (MLP). Initially, climate data from 122 synoptic stations covering six and 30, main and sub basins were collected, and annual ET O values were computed using the Food and Agriculture Organization 56 (PMF 56) Penman–Monteith equation. The correlations between these values and 37 LSTIs were examined within lead times ranging from 7 to 12 months. Through a stepwise approach, the most influential predictor indices (LSTIs) were selected as input datasets for the MLMs. The findings revealed the significant influence of factors such as carbon dioxide (CO 2 ), Atlantic multidecadal oscillation, Atlantic Meridional Mode, and East Atlantic on annual ET O . Overall, all MLMs performed well in terms of the Scatter Index during both training and testing phases across all sub-basins. Furthermore, the MLP and MLR models displayed superior performance compared to other models in the training and testing evaluations based on various assessment metrics.

Accurate forecasting of dissolved oxygen (DO) levels is vital for river ecosystem health. A novel methodology, MVMD-TSA-GPR, combines Multivariate Variational Mode Decomposition (MVMD), the Tunicate Swarm Algorithm (TSA), and Gaussian Process Regression (GPR) to improve DO level predictions. This study also incorporated Generalized Additive Model and Regression Bagged Ensemble (RBE) for 1- and 3-month forecasts using monthly data (1974–2023) from 16 water quality parameters across five Mississippi River basin sites. Key predictors identified through cross-correlation include lagged values and parameters like water temperature, discharge, pH, total phosphorus, potassium, and sulfate, which significantly influence DO levels. The MVMD-TSA-GPR model outperformed others, especially at site 5, showing substantial improvements in accuracy with decreased RMSE values across various scenarios. Model ranking via the Taylor Diagram indicated MVMD-TSA-GPR had the highest performance, followed by MVMD-TSA-RBE and others. Notably, the GPR model’s RMSE at site 3 decreased from 2.11 to 1.01 (109% reduction) for the 1-month forecast, while at site 4 for the 3-month forecast, it dropped from 1.85 to 1.04 (106% reduction). The results revealed that the MVMD-TSA-GPR model demonstrated the highest performance for DO (t + 1), achieving R = 0.90, PBIAS = 0.73%, and WI = 0.804, as well as for DO (t + 3), with R = 0.88, PBIAS = 0.54%, and WI = 0.779, at the Lower Mississippi site during the test phase. Additionally, the MVMD-TSA-RBE model excelled for DO (t + 1) in the Missouri River at the Hermann site, achieving R = 0.91, PBIAS = 0.86%, and WI = 0.805 during the test phase. These results underscore the effectiveness of the MVMD-TSA hybrid approach. Interpretative analysis using SHapley Additive exPlanations (SHAP) revealed water temperature, pH, and potassium as key factors affecting DO levels. The speed and accuracy of MVMD-TSA-GPR make it a promising tool for monitoring river water quality.

Precipitation forecasts are of high significance for different disciplines. In this study, precipitation was forecasted using a wide range of teleconnection signals across different precipitation regimes. For this purpose, four sophisticated machine learning algorithms, i.e., the Generalized Regression Neural Network (GRNN), the Multi-Layer Perceptron (MLP), the Multi-Linear Regression (MLR), and the Least Squares Support Vector Machine (LSSVM), were applied to forecast seasonal and annual precipitation in 1- to 6-months lead times. To classify precipitation regimes, precipitation was clustered using percentiles. The indices quantifying El Niño-Southern Oscillation (ENSO) phasing showed the highest association with autumn, spring, and annual precipitation over the studied areas. The MLP and LSSVM algorithms provided satisfactory forecasts for almost all cases. However, our results indicated that the performance of LSSVM decreased in testing data, implying the tendency of this algorithm towards overfitting. The MLP showed a more balanced performance for the training and testing sets. Consequently, MLP seems best suited to be used for forecasting precipitation in our study area. The modeling algorithms provided less reliable forecasts for the regions corresponding to the 10–40th percentiles, mostly located in hyper-arid and arid environments. This underscores the inherent difficulty of precipitation forecasting in the hyper-arid and arid areas, wherein precipitation is very erratic and sparsely distributed. Our findings illustrate that clustering precipitation regimes to consider microclimate seems vital for reliable precipitation forecasting. Moreover, the results seem useful to design preventive drought/flood risk management strategies and to improve food-water security in Iran.