Evaluation of Five Equations for Short-Term Reference Evapotranspiration Forecasting Using Public Temperature Forecasts for North China Plain

Demand control in agriculture enhances water efficiency by optimizing resource utilization. Among the primary causes of water loss are evaporation and transpiration, making their accurate estimation crucial for effective water management. This study aims to determine the most precise potential evaporation and transpiration (ET0) estimation method using data from 18 synoptic stations. The methods evaluated include Ivanov, Thornthwaite, Blaney-Criddle (BC), Priestley-Taylor, Makkink, Turc, and Hargreaves- Samani (HS). Two analytical approaches were employed: evaluation criteria and multi-criteria decision-making (MCDM) techniques, incorporating the Analytic Hierarchy Process (AHP), VIKOR, and Shannon entropy methods. The rankings derived from these methods were further refined through integration techniques such as averaging, Copeland, and Borda methods. Among the evaluated methods, HS and BC performed best based on evaluation criteria. The relative root mean square error (RMSE) reduction from HS to other methods was 82.92% for Ivanov, 72.45% for Thornthwaite, 39.16% for BC, 37.39% for Priestley-Taylor, 26.64% for Makkink, and 68.54% for Turc. Notably, the Shannon entropy and AHP rankings aligned, consistently placing BC and HS at the top. In integrated ranking approaches, the Copeland and Borda methods yielded identical results, with BC, HS, Makkink, and Turc achieving high rankings. Priestley-Taylor and Ivanov were ranked equally in the averaging method, whereas Thornthwaite ranked lowest. The Ivanov method consistently placed last in Copeland and Borda rankings. Considering similarity criteria values exceeding 0.8, the BC method is particularly effective in wet and semi-arid climates, while the HS method demonstrates reliability across all three climate zones studied.

Assessment of reference evapotranspiration forecasting in the Mediterranean climate of Central Chile using the ASCE standardized Penman-Monteith equation, the Hargreaves-Samani equation, and weather predictions from the Global Forecast System model

This work aimed to estimate and compare two simplified methods to estimate the reference evapotranspiration – Eto, Hargreaves-Samani (HS) and FAO-Blaney-Criddle, (BC) to the Penman-Monteith-FAO (PM) method. The results of the estimates were obtained on the basis of climatic data available at each location under study, using Irriplus software. The cities of interest for the study were selected according to the representativeness of the characteristics of the region between the main brazilian producing centers of coffee: Cerrado, East, South and Zona da Mata of Minas Gerais state, west and southwest of Bahia state, and the cities chosen were Araguari, Patrocinio, Caratinga, Lavras, Varginha, Vicosa, in Minas Gerais state, and Vitoria da Conquista and Barreiras, Bahia state. In all locations, HS equation best fit to the equation of PM, this being recommended for irrigation management in conditions of limited availability of climate data.

A long-term (30 year) historical analysis of turfgrass monthly net irrigation requirements for southeast USA is analyzed and discussed in this paper. The process involved gathering weather data for ten locations in Florida plus one in Alabama, from 1980 through 2009, and data quality. Available weather data included maximum and minimum temperature, maximum and minimum relative humidity, wind speed, and rainfall. Solar radiation was estimated using the Hargreaves–Samani equation, and coefficients were calibrated for every location. Reference evapotranspiration (ETos) was calculated using the ASCE-EWRI standardized reference evapotranspiration equation. Net irrigation was estimated using a daily soil–water balance. Variability in soil types and root depth was taken into account during the simulations, and three sets of monthly K c values from the literature were applied from north through south Florida. Results showed that the calibrated Hargreaves–Samani adjustment coefficients varied from 0.14 in Tallahassee to 0.24 in Key West, with an inland average value of 0.15, and a coastal average value of 0.18. The calculated ETos ranged from 1,296 mm year−1 in Tallahassee to 1,658 mm year−1 in Miami. The estimated net irrigation ranged from 423 mm year−1 in Mobile, AL, to 1,063 mm year−1 in Key West, FL. The number of irrigation events per year varied from 25 in Mobile to 161 in Key West. May and December were the months with the highest and lowest net irrigation requirements, respectively.

Climate change may have strong impacts on water resources in developing countries. In North Africa, many dams and reservoirs have been built to secure water availability in the context of a strong inter-annual variability of precipitation. The goal of this study is to evaluate climate change impacts on surface water resources for the largest dams in Algeria, Morocco and Tunisia using high-resolution (12 km) regional climate models (RCM) simulations. To evaluate the atmospheric demand (evapotranspiration), two approaches are compared: The direct use of actual evaporation simulated by the RCMs, or estimation of reference evapotranspiration computed with the Hargreaves-Samani (HAR) equation, relying on air temperature only, and the FAO-Penman Monteith (PM) equation, computed with temperature, wind, radiation and relative humidity. Results showed a strong convergence of the RCM simulations towards increased temperature and a decrease in precipitation, in particular during spring and the western part of North Africa. A decrease in actual evapotranspiration, highly correlated to the decrease in precipitations, is observed throughout the study area. On the opposite, an increase in reference evapotranspiration is observed, with similar changes between HAR and PM equations, indicating that the main driver of change is the temperature increase. Since the catchments are rather water-limited than energy-limited, despite opposite projections for actual and reference evapotranspiration a decrease of water availability is projected for all basins under all scenarios, with a strong east-to-west gradient. The projected decrease is stronger when considering reference evapotranspiration rather than actual evaporation. These pessimistic future projections are an incentive to adapt the current management of surface water resources to future climatic conditions.

Standardized precipitation evapotranspiration index (SPEI) is an acknowledged drought monitoring index, and the evapotranspiration (ET) used to calculated SPEI is obtained based on the Thornthwaite (TH) model. However, the SPEI calculated based on the TH model is overestimated globally, whereas the more accurate ET derived from the Penman–Monteith (PM) model recommended by the Food and Agriculture Organization of the United Nations is unavailable due to the lack of a large amount of meteorological data at most places. Therefore, how to improve the accuracy of ET calculated by the TH model becomes the focus of this study. Here, a revised TH (RTH) model is proposed using the temperature (T) and precipitable water vapor (PWV) data. The T and PWV data are derived from the reanalysis data and the global navigation satellite system (GNSS) observation, respectively. The initial value of ET for the RTH model is calculated based on the TH model, and the time series of ET residual between the TH and PM models is then obtained. Analyzed results reveal that ET residual is highly correlated with PWV and T, and the correlate coefficient between PWV and ET is −0.66, while that between T and ET for cases of T larger or less than 0 °C are −0.54 and 0.59, respectively. Therefore, a linear model between ET residual and PWV/T is established, and the ET value of the RTH model can be obtained by combining the TH-derived ET and estimated ET residual. Finally, the SPEI calculated based on the RTH model can be obtained and compared with that derived using PM and TH models. Result in the Loess Plateau (LP) region reveals the good performance of the RTH-based SPEI when compared with the TH-based SPEI over the period of 1979–2016. A case analysis in April 2013 over the LP region also indicates the superiority of the RTH-based SPEI at 88 meteorological and 31 GNSS stations when the PM-based SPEI is considered as the reference.

Comparison of hourly and daily reference crop evapotranspiration equations across seasons and climate zones in Australia

ABSTRACTIn the North China Plain (NCP), the assessment of water surplus or deficit (WSD), which is calculated as precipitation minus reference evapotranspiration (ET0), holds significant implications for water resource management and agricultural irrigation decision‐making, given the region's long‐standing severe shortage of water resources. However, the magnitude, trend and climatic drivers of WSD remain poorly understood in the NCP. This study analysed the spatial and temporal characteristics of WSD, and quantified the contribution of climatic factors to WSD based on the sensitivity and contribution rate analysis methods with climatic data from 75 meteorological stations. The result showed that: (1) Annual WSD decreased mainly in northeastern NCP and increased significantly in southern NCP during 1961–2022. Annual WSD increased slightly from 1961 to 2022 at a rate of 1.63 mm a−2 mainly due to the more significant decrease (−1.88 mm a−2) in ET0 compared to precipitation (−0.25 mm a−2). (2) In terms of the sensitivity of WSD to climatic factors, relative humidity had the highest sensitivity, followed by net radiation, wind speed, precipitation and average air temperature. (3) Significant declines of wind speed were the most dominant factor affecting WSD variation in most part of NCP during most of a year, and net radiation of four stations in the western high‐elevation regions played the most important role. This study enhances comprehension of the impact of climate change on WSD in the NCP and provides a reference for improving management of agricultural water resources under NCP's evolving climatic conditions.

Dynamics of reference evapotranspiration in the Bolivian highlands (Altiplano)

Assessing forecast performance of daily reference evapotranspiration: A comparison of equations, machine and deep learning using weather forecasts

An accurate estimation of Evapotranspiration (ET) is an important issue in hydrology, water resources management and irrigation scheduling. There are a wide range of methods for estimation of ET, among which, machine learning techniques and remote sensing-based approaches demonstrated more reasonable results. Accordingly, this study attempts to compare the capability of two developed models of Gene-Expression Programming (GEP) and Surface Energy Balance Algorithm for Land (SEBAL) in estimation of ET, at four different climate types of Temperate-Warm (T-W), Wet-Warm (W-W), Arid-Cold (A-C), and Arid-Warm (A-W). In this way, a-two year of daily records as weather variables (i.e., maximum and minimum temperature, dew-point temperature, vapor pressure, saturated vapor pressure, relative humidity, 24-h rainfall, sunshine hours, and wind speed) were considered as input variables, whereas ET values were computed as output variable (observed ET) by using FAO Penman–Monteith-56 method. After development of two predictive models, the statistical results were compared with well-known Hargreaves–Samani method. The results showed that while Hargreaves–Samani equation could not yield remarkable results in any of the climates, GEP and SEBAL demonstrated accurate predictions. In this way, GEP was the superior model in T-W (R2 = 0.902 and RMSE = 0.713 mm/day) and A-W (R2 = 0.951 and RMSE = 0.634 mm/day) climates but it dropped a bit in two other climates. However, SEBAL not only had the best performance in both climates of W-W (R2 = 0.967 and RMSE = 0.515 mm/day) and A-C (R2 = 0.990 and RMSE = 0.720 mm/day), but also demonstrated good predictions in T-W and A-W climates. Therefore, SEBAL is recommended as the best model for estimation of ET in all climate types.

Study regionAmu Darya River Basin (ADRB), Central Asia. Study focusReference-evapotranspiration (ETo) is the most prominent variable for agriculture water-resource management. The Penman-Monteith (PM) equation has been accepted as universal-standard for estimating ETo but it requires extensive climatic-variables. The PM alternative Hargreaves-Samani (HS) equation inadequately estimates ETo with an average error of RMSE 1.84 mm/day, NSE 0.27, and MAE 0.61 mm/day, respectively, in the ADRB. New hydrological insight for the regionThe present study proposes the calibration of original HS-equation based on actual vapor pressure and linear regression to estimate daily ETo at 114 meteorological stations in the ADRB. The locally-calibrated HS-equation coefficient (C) was found variated-widely across the different climatic-conditions and months, ranging from 0.0025 to 0.0186, due to hyper-aridity conditions in the study area. Compared with proposed methods by other studies, the modified-HS equation and empirical-coefficient using newly-proposed variable leads to a significant reduction of the average root means square error and mean absolute error by about 55 % and 52 %, respectively, demonstrates their feasibility and accuracy in the ADRB, Central Asia. In-addition, the modified-HS-equation based on climatic zones were found to be more accurate and comprehensive than geographical localizations. The modified-HS equation and empirical-coefficient using newly-proposed variable and approach is suitable to estimate ETo in a data scarce region (e.g., ADRB), when only temperatures, solar radiation and vapor pressure data are available.

Daily reference evapotranspiration (ETo) is an essential component of the hydrologic processes of surface water generation from precipitation. Iraq suffers from a scarcity of surface water due to the erection of many dams on the Tigris and Euphrates Rivers by neighboring countries on upstream locations along these rivers. Therefore, ETo values should be measured more accurately in Iraq. In this study, the Penman–Monteith (PM) equation was used as the benchmark to calculate the standard values of ETo for 103 stations in Iraq using a daily meteorological data set from 2010 to 2019 (5 years each for calibration and validation periods). Three forms of the Hargreaves–Samani (HS) equation were evaluated for estimating the ETo values. The first two equations have common and optimum coefficient sets (HSC and HSO equations, respectively). The third equation is proposed in this study and modifies the HS equation by incorporating a wind speed variable with an optimum coefficient set (HSW equation). The coefficients of the HSO and HSW equations were optimized in terms of the Nash–Sutcliffe efficiency (NSE) coefficient and the coefficient of determination (R2) using the shuffled complex evolution (SCE) optimization method. The respective success rates of ETo estimation during the calibration and validation periods are 37% and 39% when using the HSC equation, 96% and 95% with the HSO equation, and 100% and 100% with the HSW equation. Results indicated that the HSO and HSW equations enhance the estimation of ETo values relative to the HSC equation, and the HSW equation performs best among the three. Therefore, incorporating the wind speed in the HS equation with the optimum coefficient set increases the robustness of its predictive capacity for all regions of Iraq, including those with high altitudes.

The Penman–Monteith equation (FAO-56) is accepted as the standard model for estimating reference evapotranspiration (ETo). However, the major obstacle to using FAO-56 widely is that it requires numerous climatic data. The Hargreaves–Samani (HS) method is frequently used for the calculation of ETo since it is based on measurements of daily minimum and maximum air temperature alone. Those are commonly recorded at many meteorological stations throughout the world. It is the objective of this paper to evaluate the quality of HS and calibrate the coefficients of this method for different climates as represented by the Köppen classification. Estimated values are compared with Penman–Monteith ETo values in terms of the coefficient of efficiency Ceff as well as the root mean square error, the mean absolute error and the Bayes information criterion. The Penman–Monteith equation for ETo (FAO-56) is based on physics and known to provide best estimates of ETo. The results of our work show that the correlation between long-term monthly means of HS and FAO-56 can be improved significantly by introducing climate-class specific coefficients.

Accurate estimation of daily reference evapotranspiration (ETo) is essential for effective irrigation scheduling, improved water-use efficiency, and sustainable crop production in arid and semi-arid regions. Although the FAO-56 Penman–Monteith equation (ETo PM ) is widely accepted as the reference method, its reliance on complete meteorological data limits its applicability in data-scarce agricultural systems such as those in eastern Morocco. This study proposes a practical solution for daily ETo estimation under data-limited conditions by evaluating machine learning approaches against traditional empirical models. Daily climatic data (2001–2025) were collected from airport meteorological stations, NASA POWER reanalysis, and on-farm sensors at four representative locations in Eastern Morocco (Oujda, Berkane, Taourirt, and Figuig). ETo was computed using the ETo PM equation. Three ML algorithms—Support Vector Regression (SVR), Random Forest (RF), and Extreme Gradient Boosting (XGBoost)—were developed under multiple input scenarios guided by feature-importance analysis, which identified solar radiation (Rsn), maximum temperature (Tmax), and relative humidity (RH) as dominant predictors. To ensure realistic evaluation and avoid information leakage, a strict chronological split was applied, using 2001–2018 for training and 2019–2025 for independent testing. The best ML configurations were then compared with widely used empirical ETo equations (Hargreaves–Samani, Jensen–Haise, Priestley–Taylor, Makkink, and Turc). Results showed that XGBoost consistently outperformed SVR and RF, achieving the best balance between accuracy and computational efficiency. The three-input configuration (Rsn + Tmax + RH) produced near-reference performance across all locations ( R 2 = 0.976; RMSE < 0.55 mm day −1 ; training time ≈ 4.48 s; RAM ≈ 0.13 MB), while the reduced two-input configuration (Rsn + Tmax) maintained reliable performance ( R 2 = 0.936; RMSE ≈ 0.60 mm day −1 ; training time ≈ 0.33 s; RAM ≈ 0.13 MB). In contrast, empirical approaches exhibited poor predictive capability and weak transferability, with negative R 2 values and substantially larger errors (RMSE generally > 4 mm day −1 , exceeding 7 mm day −1 in the weakest formulations). Overall, this machine learning–based framework provides a robust and operational alternative for daily ETo estimation in eastern Morocco, supporting efficient irrigation scheduling, improved agricultural water management, enhanced crop productivity, and sustainable agriculture in arid and semi-arid regions.