Industrial waste significantly impacts water and soil quality, restricting their suitability for agricultural and domestic use. This study investigates the distribution of heavy metals (HMs) in groundwater and soils across the Shazand plain under different irrigation methods and rainfed farming systems. It evaluates the Total Hazard Quotient (THQ) and Carcinogenic Risk (TCR) associated with HMs for both children and adults, considering exposure through ingestion, dermal contact, and inhalation. A total of 104 samples were collected, comprising water samples from wells and boreholes, and soil samples. Concentrations of Pb, Cd, Cr, Ni, Hg, Zn, and Cu were analyzed using atomic absorption spectrometry, and the data were assessed using descriptive and inferential statistics. The highest average concentrations of HMs in groundwater samples were observed for Cr (19 µg l⁻¹) and Zn (22.8 µg l⁻¹). In soil samples, Cr (35.28 µg g⁻¹) and Zn (216.52 µg g⁻¹) exhibited the highest values. The Total Hazard Index (HI) indicated a high risk across different age groups, ranging from moderate to very high in the study areas. The Soil Pollution Load Index (PLI) was 18.22 in rainfed farming and 71.17 in irrigated farming, indicating severe HM contamination across the site. Carcinogenic health risks from HMs exceeded acceptable levels, with children showing greater vulnerability compared to adults. This research underscores the urgent need for effective environmental management strategies to mitigate HM contamination, safeguard public health, and ensure sustainable agricultural practices in industrialized regions.

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 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.