Accurate reference evapotranspiration estimation with limited data for sustainable irrigation in eastern Morocco: a machine learning approach

Reference evapotranspiration (ETo) is essential for irrigation practices and the management of water resources and plays a vital role in agricultural and hydro-meteorological studies. The FAO-56 Penman-Monteith (PM) equation, recommended as the sole standard method of calculating ETo by the Food and Agriculture Organization of the United Nations (FAO), is the most commonly used and accurate model to determine the ETo and evaluate ETo equations. However, it requires many meteorological variables, often restricting its applicability in regions with poor or missing meteorological observations. Many empirical and semi-empirical equations have been developed to predict the ET0 from numerous meteorological data. The FAO-24 Pan method is commonly used worldwide to estimate ETo because it is simple and requires only pan coefficients. However, pan coefficients (Kpan) should be determined accurately to estimate ET0 using the FAO-24 Pan method. As the accuracy and reliability of the Kpan models can be different from one location to another, they should be tested or calibrated for different climates and surrounding conditions. In this study, the performance of the eight Kpan models was evaluated using 22-year daily climate data for the summer growing season in Adana, which has a Mediterranean climate in Turkey. The results showed that the mean seasonal pan coefficients estimated by all Kpan models differed significantly at a 1% significance level from those observed by FAO-56 PM according to the two-tail z test. In the study, ETo values estimated by Kpan models were compared against those obtained by the FAO-56 PM equation. The seasonal and monthly performance of Kpan models was varied, and the Wahed & Snyder model presented the best performance for ETo estimates at the seasonal scale. (RMSE = 0.550 mm d−1; MAE = 0.425 mm d−1; MBE = −0.378 mm d−1; RE = 0.134). In addition, it showed a good performance in estimating ETo on a monthly scale. The Orang model showed the lowest performance in estimating ETo among all models, with a very high relative error on the seasonal scale. (RMSE = 1.867 mm d−1; MAE = 1.806 mm d−1; MBE = −1.806 mm d−1; RE = 0.455). In addition, it showed the poorest performance on a monthly scale. Hence, the Wahed & Snyder model can be considered to estimate ETo under Adana region conditions after doing the necessary calibration.

The current study aims to improve the performance of simple methods for the estimation of daily reference evapotranspiration (ET0) in humid East China, namely Priestley–Taylor 1972 (P-T 1972), Hargreaves–Samani 1985 (H-S 1985) and Turc 1961 (TU 1961). These methods were evaluated and calibrated based on well-watered grass lysimeter experiments. The FAO-56 Penman–Monteith equation (FAO-56 PM) is the best method, and the radiation-based methods (TU 1961 and P-T 1972) perform much better than the temperature-based method (H-S 1985). In the simple methods, the coefficients are calibrated to: 1.34 for P-T 1972; 0.0186, 23.47 and 17.06 for TU 1961; and 0.0027 and 0.449 for H-S 1985. The locally calibrated TU 1961 and P-T 1972 perform much better than the original, with either the observed ET0r or the ET0c obtained by FAO-56 PM as standard. However, local calibration does not significantly improve the performance of the H-S 1985 method. In humid East China, FAO-56 PM is the best method for daily ET0 calculation. TU 1961, especially if locally calibrated, is the optimal choice as a simple substitute for FAO-56 PM when solar radiation is available. Otherwise, serious local calibration is strongly recommended before applying H-S 1985 for daily ET0 estimation.

Accurate determination of grass-reference evapotranspiration (ETo) is very important for agricultural, hydrological, and environmental studies, especially under increasing water scarcity and climate mitigation conditions. The FAO-56 Penman-Monteith (FAO-PM) model is renowned for being the most accurate model; however, it requires a full climate data set that is not always available at all weather stations, especially in most of the developing countries. Thus, using ETo models that require a reduced set of climate data continues to be an important alternative in such cases. The objectives of this study were to (1) evaluate the FAO-56 Penman-Monteith equation to estimate ETo with limited climate data, and (2) evaluate two of the latest ETo equations developed by Valiantzas. Climatic variables, including maximum and minimum air temperature, maximum and minimum relative humidity, solar radiation, and wind speed were collected from eight weather stations across Burkina Faso. The results showed that when solar radiation data were missing, solar radiation estimation from maximum and minimum daily air temperatures generated accurate estimates of ETo, with regression slope from 0.98 to 1.04, root mean squared error (RMSE) less than 0.60 mm/day, and low mean biased error (MBE) within the range of −0.18–0.02 mm/day. In the case of lacking relative humidity data, the RMSE and MBE varied from 0.07 to 0.47 mm/day and from −0.45 to 0.22 mm/day, respectively, and the regression slope varied from 0.90 to 1.14, and the coefficient of determination (R2) ranged from 0.77 to 0.92. In the case of missing wind speed, the method that used long-term average wind speed (ETo-um) resulted in the best estimates, especially for lower ETo rates (ETo<6 mm/day) as compared to the method (ETo-w2) that adopted the default wind speed of 2 m/s. Indeed the ETo-w2 method overestimated ETo from 4 to 35%. With the ETo-um method, RMSE varied from 0.43 to 0.57 mm/day and the MBE varied from −0.05 to 0.04 mm/day whereas the (ETo-w2) method had the RMSE ranging from 0.59 to 2.11 mm/day and the MBE ranging from 0.26 to 1.90 mm/day. The FAO-PM equation had the least accurate performance when only temperature data is available. The Valiantzas 1 equation that uses only air temperature and relative humidity data was not suitable and is not recommended for use in Burkina Faso climatic conditions. The Valiantzas 2 equation with full climatic data resulted in good ETo estimates relative to the FAO-PM ETo with full data under the Burkina Faso climate conditions; however, the FAO-PM equation is recommended because of limitations of the Valiantzas 2 equation under limited data conditions.

Dynamics of reference evapotranspiration in the Bolivian highlands (Altiplano)

Estimation of evapotranspiration (ET) for alpine meadow areas in the Tibetan Plateau (TP) is essential for water resource management. However, observation data has been limited due to the extreme climates and complex terrain of this region. To address these issues, four representative methods, Penman-Monteith (PM), Priestley-Taylor (PT), Hargreaves-Samani (HS), and Mahringer (MG) methods, were adopted to estimate ET, which were then compared with ET measured using Eddy Covariance (EC) for five alpine meadow sites during the growing seasons from 2010 to 2014. And each site was measured for one growing season during this period. The results demonstrate that the PT method outperformed at all sites with a coefficient of determination (R2) ranging from 0.76 to 0.94 and root mean square error (RMSE) ranging from 0.41 to 0.62 mm d-1. The PM method showed better performance than HS and MG methods, and the HS method produced relatively acceptable results with higher R2 (0.46) and lower RMSE (0.89 mm d-1) compared to MG method with R2 of 0.16 and RMSE of 1.62 mm d-1, while MG underestimated ET at all alpine meadow sites. Therefore, the PT method, being the simpler approach and less data dependent, is recommended to estimate ET for alpine meadow areas in the Tibetan Plateau. The PM method produced reliable results when available data were sufficient, and the HS method proved to be a complementary method when variables were insufficient. On the contrary, the MG method always underestimated ET and is, thus, not suitable for alpine meadows. These results provide a basis for estimating ET on the Tibetan Plateau for annual data collection, analysis, and future studies.

Evapotranspiration (ET) has been the focus of research for decades as it is the key to improving water resources management. This study addresses the estimation of daily reference evapotranspiration (ET₀) using machine learning (ML) models with limited meteorological data in newly developed agricultural areas in Egypt. The study tested five methods for selecting key input features to compare the performance of 20 ML models across 14 stations using available daily meteorological data from 1943 to 2024. The modified FAO Penman-Monteith (PM) method was used to estimate ET₀ as a benchmark for evaluating the performance of ML models. The Categorical Boosting (CatBoost) regressor achieved the highest performance across all stations when using the complete feature dataset and maintained high performance with three features. Furthermore, the results showed consistent success of CatBoost, Light Gradient Boosting Machine (LightGBM), and Gradient Boosting Machine (GB) when two features, selected by Sequential Forward Selection (SFS) method, were used. This highlights the feature selection method's ability to capture the most important meteorological variables, making it a valuable tool for improving ET₀ prediction in different agroclimatic regions. In addition, wind speed (U) and maximum temperature (Tmax) were identified as critical predictors of daily ET₀ in Egypt. This approach offers a practical solution for improving water management in newly reclaimed desert areas, not only in Egypt but also in other regions with similar climatic conditions.

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.

Short-term forecasting of daily reference evapotranspiration using the reduced-set Penman-Monteith model and public weather forecasts

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.

The hydrological cycle should be scrutinized and investigated under recent climate change scenarios to ensure global water management and to increase its utilization. Although the FAO proposed the use of the Penman–Monteith (PM) equation worldwide to predict evapotranspiration (ET), which is one of the most crucial components of the hydrological cycle, its complexity and time-consuming nature, have led researchers to examine alternative methods. In this study, the performances of numerous temperature-driven ET methods were examined relative to the PM using daily climatic parameters from central stations in 11 districts of the Kahramanmaras province. Owing to its geographical location and other influencing factors, the city has a degraded Mediterranean climate with varying elevation gradients, while its meteorological patterns (i.e., temperature and precipitation) deviate from those of the main Mediterranean climate. A separate evaluation was performed via ten different statistical metrics, and spatiotemporal ET variability was reported for the districts. This study revealed that factors such as altitude, terrain features, slope, aspect geography, solar radiation, and climatic conditions significantly impact capturing reference values, in addition to temperature. Moreover, an assessment was conducted in the region to evaluate the effect of modified ET formulae on simulations. It can be drawn as a general conclusion that the Hargreaves–Samani and modified Blaney–Criddle techniques can be utilized as alternatives to PM in estimating ET, while the Schendel method exhibited the lowest performance throughout Kahramanmaras.

Evapotranspiration estimation by two different neuro-fuzzy inference systems

The accuracy of an adaptive neurofuzzy computing technique in estimation of reference evapotranspiration ( ET0 ) is investigated in this paper. The daily climatic data, solar radiation, air temperature, relative humidity, and wind speed from two stations, Pomona and Santa Monica, in Los Angeles, Calif., are used as inputs to the neurofuzzy model to estimate ET0 obtained using the FAO-56 Penman–Monteith equation. In the first part of the study, a comparison is made between the estimates provided by the neurofuzzy model and those of the following empirical models: The California Irrigation Management System, Penman, Hargreaves, and Ritchie. In this part of the study, the empirical models are calibrated using the standard FAO-56 PM ET0 values. The estimates of the neurofuzzy technique are also compared with those of the calibrated empirical models and artificial neural network (ANN) technique. Mean-squared errors, mean-absolute errors, and determination coefficient statistics are used as comparing criteria f...

This paper provides an overview of the research carried out over the last 25 years on the FAO56 single and basal crop coefficients of subtropical and tropical orchards and plantations of cactus pear, dragon fruit, fig, jujube, passion fruit, pomegranate, cape gooseberry, cherimoya, guava, longan, lychee, mango, papaya, acerola, carambola, cashew, cacao, coffee, jaboticaba, jatropha, macadamia, açai palm, coconut, date palm, guayule, oil palm, peach palm, ramie and rubber tree. The main objective of this review is to update standard single crop coefficients (Kc) and basal crop coefficients (Kcb) and complete the Kc and Kcb values tabulated in FAO56. Kc is the ratio between the non-stressed crop evapotranspiration (ETc) and the grass reference evapotranspiration (ETo), and Kcb is the ratio between the crop transpiration (Tc) and the ETo. When selecting and analysing the literature, only studies that used the FAO Penman–Monteith equation, or another equation well related to the former to compute ETo were considered, while ETc or Tc were obtained from accurate field measurements on crops under pristine (non-stress cropping conditions) or eustress (“good stress”) conditions. Articles meeting these conditions were selected to provide data for updating Kc and Kcb under standard conditions. The related description of orchards and plantations refers to crop cultivar and rootstock, irrigation systems and scheduling, planting spacing, fraction of ground cover (fc) by the crops, crop height (h), crop age and training systems, as Kc and Kcb values depend on these characteristics. To define the standard Kc and Kcb values of the selected crops, the values collected in the literature were compared with previously tabulated standard Kc and Kcb values. The updated tabulated values are transferable to other locations and climates and can be used to calculate and model crop water requirements, primarily for irrigation planning and scheduling, and thereby supporting of improved water use and savings, which is the overall aim of the current review.

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.

A total of 11 empirical evapotranspiration equations were developed by Hargreaves (1975), Hargreaves (1985), Makkink, Turc, Priestley–Taylor, Jensen–Haise, Doorenbos and Pruitt, Abtew, McGuinness and Bordne, Rohwer and Blaney–Criddle. These were compared with pan evaporation data measured at 10 stations in Gansu Province, northwest China. The comparison was first made using the default values in each of the 11 equations, and then redone using calibrated coefficient values. The calibration was made for all 11 equations using the climatic index Pa/Pg. The results show that using default coefficient values resulted in large errors for all equations. The largest error was found in the comparison results of the Turc, and McGuinness and Bordne equations. The Turc and Jensen–Haise equations should be used to estimate the daily evapotranspiration (ET) under the conditions of Tmean &gt; 0 and Tmean &gt; −3°C, respectively, when applied to northwest China. Based on the comparison results of before and after recalibration, the Doorenbos and Pruitt method is more suitable to the arid, semiarid and wet regions in northwest China. The accuracy of the results for determining monthly ET greatly improved when calibrated coefficient values were introduced to the 11 equations, except for McGuinness and Bordne, Abtew, and Blaney–Criddle, which need to be recalibrated using two parameters. Thus, it can be concluded that calibration can be used to modify evapotranspiration equations with multi‐station data to improve the accuracy of evapotranspiration estimates in northwest China. Copyright © 2009 John Wiley &amp; Sons, Ltd.