Reference Evapotranspiration Models Research Articles

Reference Evapotranspiration Modeling Using Artificial Intelligence-Based Approaches: A Bibliometric Analysis

A bibliometric analysis was performed over the period 1992–2023, to pinpoint important trends, emphasis, and geographic distribution of international reference evapotranspiration (ETo) modeling research using intelligence-based approaches. Data was mined from the databases of the online version of Web of Science. The data was analyzed using the Excel program, and the bibliometric mapping was performed using the VOSviewer software. A total of 1148 articles met the required criteria. The findings indicated that the number of articles had increased rapidly over the past five years and that English was the prevalent language (99.5%). Researchers in 99 countries have published in this field of research. China ranked first with 356 articles (31.0%), followed by the United States of America with 193 articles (16.8%). Egypt and Saudi Arabia are two of the top 15 countries in the world. These articles were published in 289 journals; the Journal of Hydrology was the most productive journal (95 articles, 8.3%), followed by Computers and Electronics in Agriculture (67, 5.8%). The most productive author is Kisi Ozgur from Turkey (68 articles, 4.2%). Taking into account all the institutions working on ETo modeling (1555 institutions), the Chinese Academy of Science was ranked first (80 articles, 7.0%), followed by the Egyptian Knowledge Bank (55 articles, 4.8%). Artificial neural networks and machine learning were the most commonly used intelligence-based approaches for ETo modeling. Reinforcement learning was the least popular technique for ETo modeling, which could be due to its complexity and data requirements.

Predictive Modeling and Comparative Analysis of Reference Evapotranspiration with Machine Learning Algorithms

Accurate estimation of reference evapotranspiration (ET0) is crucial for a multitude of applications, encompassing drought detection, irrigation scheduling, water resource management, and disaster risk reduction. This investigation utilized the FAO-PM equation for ET0 estimation and subsequently incorporated meteorological variables as input variables with machine learning (ML) models to enhance ET0 predictions. The dataset was bifurcated into training and testing data segments. Four distinct machine learning models were deployed in this study, namely Random Forest (RF), Support Vector Machine (SVM), Gradient Boosting Machine (GBM), and Linear Regression (LR). The performance of these models was evaluated using various statistical indices, including Mean Absolute Error (MAE), Mean Sum of Error (MSE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and the coefficient of determination (R2), to pinpoint the most efficacious ML algorithm. After conducting a comprehensive analysis involving both training and testing data, the results unequivocally identify GBM with MAE values of 0.054 and 0.077, MSE values of 0.005 and 0.011, MAPE values of 0.014 and 0.022, RMSE values of 0.072 and 0.107, and an R2 value of 0.096 and 0.092 during training and testing, respectively. This model has been selected as the optimal choice for precise ET0 estimation within the study region. Subsequently, SVM, RF, and LR follow as alternatives in terms of performance, in descending order.

Estimating cucumber crop coefficients under different greenhouse microclimatic conditions

This study aimed to determine cucumber crop coefficients under different greenhouse microclimatic conditions, parameterizing the Priestley-Taylor reference evapotranspiration model. Crop evapotranspiration was directly measured with the use of lysimeters, and crop coefficients were computed following the two-step climate FAO 56 methodology. Greenhouse compartments (i.e., cooled or uncooled) showed reference evapotranspiration differences of up to 12% in an autumn-winter crop. The results presented cucumber crop coefficient values from the initial to the late-season growth stages from 0.45 to 0.94 depending on the greenhouse climate. Based on the greenhouse hourly microclimatic variation of KC, it is recommended not to apply a KC as a constant for transpiration estimation even at greenhouses located within the same region Regression analysis relating crop coefficients with leaf area revealed very high correlation coefficients for the equations tested. The results indicated that evapotranspiration can be modeled satisfactory based on a significant relationship between crop coefficient and simple measurements of the leaf area index (i.e., KC = 0.447 × LAI).

Evaluation and Modelling of Reference Evapotranspiration Using Different Machine Learning Techniques for a Brazilian Tropical Savanna

Meteorological elements can affect the environment and cultures differently and may alter the natural development process contributing significantly to climate change. Meteorological variables of the Brazilian Pantanal were studied and used to determine evapotranspiration with fewer variables. It was found that artificial intelligence can substantially improve environmental modeling when alternative prediction techniques are used, resulting in lower project costs and more reliable results. This work tried to find the best combination by comparing machine learning techniques such as artificial neural networks, random forests, and support vector machines. A new model was created that depends on fewer climatic variables compared to the Penman–Monteith method (the standard method for estimating reference evapotranspiration) and can efficiently describe the reference evapotranspiration. Machine learning techniques are highly efficient for modeling environmental systems since they can process large amounts of data and find the best interactions between the parameters involved. In addition, more than 98% accuracy was obtained using fewer variables compared to the standard method when artificial neural networks are utilized.

Remotely Sensed and Empirical Reference Evapotranspiration Models to Derive Crop Coefficients for Pistachios in the Central Basin of Iran

Remotely Sensed and Empirical Reference Evapotranspiration Models to Derive Crop Coefficients for Pistachios in the Central Basin of Iran

Investigation of Valiantzas’ Simplified forms of FAO56 Penman-Monteith Reference Evapotranspiration Models in a semi-arid region

The performance of sixteen Valiantzas’ reference evapotranspiration models was investigated using the meteorological data obtained from Agricultural Engineering College and Research Institute, Kumulur, Lalgudi Taluk of Tiruchirapalli district, which is a semi-arid region located in Tamil Nadu, India. The Valiantzas’ reference evapotranspiration was compared with the globally used FAO56 Penman-Monteith method. The indexes used for comparison are coefficient of determination (R2), Standard Error Estimate (SEE) and long-term average ratio (RT). The Valiantzas’ models requiring complete dataset performed excellently in this station. The models not requiring wind speed data also performed equally well in this station and exhibited a fairly good correlation with FAO56-PM method. The other formulae accounting for local average wind conditions, reduced set formulae with temperature and relative humidity data alone and reduced set formulae with temperature and radiation data alone also performed well in this station. The investigation showed fair accuracy of Valiantzas’ Models and hence researchers can use these models in the absence of availability of the complete dataset.

Modeling reference evapotranspiration using machine learning and remote sensing techniques for semi-arid subtropical climate of Indian Punjab

Abstract A study was carried out to develop and evaluate the performance of different machine learning (ML) models for predicting reference evapotranspiration (ET0). The models included multiple linear regression (MLR), least square-support vector machine (LS-SVM), artificial neural networks (ANNs) and adaptive neuro-fuzzy inference system (ANFIS). The daily meteorological data for 50 years (1970–2019) were used to estimate ET0 using FAO-ET calculator. The FAO-ET calculator was compared with ML models to investigate the best-fit ML model for predicting ET. Thereafter, ET predicted by the best-fit ML model was compared with satellite (Moderate Resolution Imaging Spectroradiometer – MODIS) ET, which was finally mapped to a larger landscape (over entire Punjab and Haryana). Modeling of ET0 was best performed through LS-SVM followed by ANN2, ANN1, ANFIS10, ANFIS2, MLR and ANFIS9 models. Among developed models, coefficient of determination (R2) value varied from 0.800 to 0.998, being highest (0.998) under LS-SVM model. MODIS overestimated ET when compared with LS-SVM having R2 and root mean square error (RMSE) values of 0.73 and 3.95 mm, respectively. After applying the bias correction factor, R2 and RMSE were 0.74 and 1.19 mm, respectively. The ML and satellite-based ET estimation would be useful for timely water budgeting to manage the water scarcity problems from local to regional levels.

Modelling reference evapotranspiration using principal component analysis and machine learning methods under different climatic environments

AbstractReference evapotranspiration (ETo) is a complex process in the hydrologic cycle that influences several hydrologic parameters. Although several methods have been developed to model ETo, a reliable method that can use limited climatic input parameters for data‐limited regions is still limited. This study evaluated four machine learning (ML) methods: M5 pruned (M5P) tree, sequential minimal optimization (SMO), radial basis function neural regression (RBFNreg) and multilinear regression (MLR). The major objective of this study was to identify the best approach to estimate ETo with minimum input data in five stations (Multan, Jacobabad, Faisalabad, Islamabad and Skardu) located in Pakistan. The datasets of these stations comprised maximum and minimum temperatures (Tmax, Tmin), average relative humidity (RHavg), average wind speed (Ux), and sunshine hours (n) variables. Two scenarios were used for ETo modelling. In the first scenario, five climatic variables were used as inputs to estimate ETo as obtaining full climatic parameters is the biggest challenge in developing countries. Principal component analysis (PCA) was used as a clustering technique in the second scenario to reduce the climatic input parameters. The PCA results indicated that Tmax, Tmin and n were identified as effective inputs for ETo estimation. Based on statistical indicators, the M5P tree outperformed the other applied ML methods in estimating ETo under various climatic environments. This study recommends focusing on areas with high ETo values and adequate irrigation scheduling of crops to achieve water sustainability.

Development of machine learning-based reference evapotranspiration model for the semi-arid region of Punjab, India

Evapotranspiration (ET) is a critical element of the hydrological cycle, and its proper assessment is essential for irrigation scheduling, agricultural and hydro-meteorological studies, and water budget estimation. It is computed for most applications as a product of reference crop evapotranspiration (ET0) and crop coefficient, notably using the well-known two-step method. Accurate predictions of reference evapotranspiration (ET0) using limited meteorological inputs are critical in data-constrained circumstances. Due to the unavailability and heterogeneity of broad parameters of the FAO PM method, it becomes a major constraint for accurately estimating ET0. To overcome the complexity of calculation, the present study was focused on developing a Random Forest-based (RF) ET0 model to estimate the crop ET for the semi-arid region of northwest India. The RF-based model was developed by focusing on the easily available data at the farm level. For comparative study existing models like Hargreaves–Samani, Modified Penman and modified Hargreaves–Samani were used to estimate the ET0. The models' calibration and validation were done using meteorological data collected from the weather station of Punjab Agricultural University for 21 years (1990–2010) and nine years (2011–2019), respectively, and the FAO PM model was taken as a standard. The mean absolute error (MAE) and root-mean-square error (RMSE) were found to be least as 0.95 mm/d and 1.32 mm/d, respectively for the developed RF model, with an r2 value of 0.92. The seasonal ET0 estimated by modified Hargreaves–Samani (MHS) and RF were found as 498.3, 482.1 mm in rabi season and 755, 744.8 mm in kharif season respectively, whereas the annual ET0 was 1380.2 and 1355.7 mm respectively. The predicted ET0 values by RF-based model were used for irrigation scheduling of two growing seasons (2020–2021) of maize and wheat crops. The outcome of the field trial also demonstrates that there was no appreciable yield drop in the crop when compared to irrigation scheduling by the FAO PM model, demonstrating the applicability of the developed model for irrigation in the semiarid region of the Punjab in India.

Modification of the radiation-based Abtew reference evapotranspiration model under humid climate, Northeast India

Abstract This study aimed to improve the Abtew model for reference evapotranspiration (ET0) calculation in Northeast India using seven temperature-based solar radiation models. The temperature-based models require only air temperature as input data, which can be easily measured in most locations worldwide. The performance of the improved Abtew models (A1-A7), along with the Stephen Stewart model (SS), the Irmak model (Ir), and the modified Turc model (MT), was evaluated under the climatic conditions of Dibrugarh, Northeast India, using statistical indices such as mean absolute error (MAE), root mean square error (RMSE), standard error (SE), coefficient of correlation (r), coefficient of determination (R2), and index of agreement (D). The results showed that the seven improved Abtew models (RMSE = 0.40–0.53 mm/day; D = 0.81–0.93) outperformed the four physical models (RMSE = 0.43–2.77 mm/day; D = 0.49–0.91) for the ET0 estimate at Dibrugarh. The statistical analysis identified that the A6 model ranked highest for Dibrugarh. This study highlights the significant improvement in ET0 estimation accuracy by utilizing temperature-based solar radiation models in the Abtew model. Therefore, we strongly recommend using the A6 model to estimate ET0, which requires only temperature data as input, for estimating ET0 under the climatic conditions of Dibrugarh, Northeast India.

Selection of alternate reference evapotranspiration models based on multi-criteria decision ranking for semiarid climate

Selection of alternate reference evapotranspiration models based on multi-criteria decision ranking for semiarid climate

Predictive Modelling of Reference Evapotranspiration Using Machine Learning Models Coupled with Grey Wolf Optimizer

Mismanagement of fresh water is a primary concern that negatively impacts agricultural productivity. Judicious use of water in agriculture is possible by estimating the optimal requirement. The present practice of estimating crop water requirements is using reference evapotranspiration (ET0) values, which is considered a standard method. Hence, predicting ET0 is vital in allocating and managing available resources. In this study, different machine learning (ML) algorithms, namely random forests (RF), extreme gradient boosting (XGB), and light gradient boosting (LGB), were optimized using the naturally inspired grey wolf optimizer (GWO) viz. GWORF, GWOXGB, and GWOLGB. The daily meteorological data of 10 locations falling under humid and sub-humid regions of India for different cross-validation stages were employed, using eighteen input scenarios. Besides, different empirical models were also compared with the ML models. The hybrid ML models were found superior in accurately predicting at all the stations than the conventional and empirical models. The reduction in the root mean square error (RMSE) from 0.919 to 0.812 mm/day in the humid region and 1.253 mm/day to 1.154 mm/day in the sub-humid region was seen in the least accurate model using the hyperparameter tuning. The RF models have improved their accuracies substantially using the GWO optimizer than LGB and XGB models.

Modelling of Reference Evapotranspiration using Neural Network and Regression Approaches for Semi-humid Region of Sikkim

This study compared the applicability of multiple linear regression (MLR) and artificial neural network (ANN) approaches for estimating the weekly reference evapotranspiration (ET0) in a semi-humid area of Tadong in Gangtok district of Sikkim state in India. Daily meteorological data (1991 - 2020) were used for developing MLR and ANN model using various combinations of meteorological data. Predicted ET0 values were compared with the FAO-56 Penman Monteith (PM) equation estimated ET0. The coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), and Nash Sutcliffe efficiency (NSE) were used to assess the performance of MLR and ANN models. For ANN model, one hidden layer and four neurons was found as the best ANN architecture. ANN-4 model with inputs parameters of maximum air temperature (Tmax), minimum air temperature (Tmin), maximum relative humidity (RHmax), minimum relative humidity (RHmin), and sunshine hours (SSH) had the smallest RMSE (0.609 mm.day-1 and 0.880 mm.day-1), MAE (0.473 mm.day-1 and 0.551mm.day-1) and the highest R2 (0.752 and 0.657) and NSE (0.782 and 0.696) during training and testing phases, respectively. The MLR-4 model with same combination of input parameters (Tmax, Tmin, RHmax, RHmin, SSH) resulted in smallest RMSE (0.704 mm.day-1 and 0.714 mm.day-1), MAE (0.562 mm.day-1and 0.583 mm.day-1); and the highest R2 (0.679 and 0.602) and NSE (0.708 and 0.597) during training and testing phase, respectively. Study also showed increase in model performance of ANN and MLR models with increase in number of meteorological parameters. All the ANN models gave comparable results, but ANN 4 model resulted in higher prediction accuracy for the sub-humid region of Tadong in Gangtok district of North-east India. The developed ANN-4 model could be helpful for preparing irrigation schedules and planning, and management of water resources in the data scarce northeast region of India and other identical climatic regions.

Empirical equation for estimating sunshine hours, and comparison of reference evapotranspiration models in temperate Kashmir Valley, India

Empirical equation for estimating sunshine hours, and comparison of reference evapotranspiration models in temperate Kashmir Valley, India

Generalized Daily Reference Evapotranspiration Models Based on a Hybrid Optimization Algorithm Tuned Fuzzy Tree Approach

Reference evapotranspiration (ET0) is an important driver in managing scarce water resources and making decisions on real-time and future irrigation scheduling. Therefore, accurate prediction of ET0 is crucial in the water resources management discipline. In this study, the prediction of ET0 was performed by employing several optimization algorithms tuned Fuzzy Inference System (FIS) and Fuzzy Tree (FT) models, for the first time, whose generalization capability was tested using data from other stations. The FISs and FTs were developed through parameters tuning using Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Pattern Search (PS), and their combinations. The FT was developed by combining several FIS objects that received ranked meteorological variables. A total of 50 FIS and FT models were developed and the model ranking was performed utilizing Shannon’s Entropy (SE). Evaluation outcomes revealed the superiority of the hybrid PSO-GA tuned Sugeno type 1 FT model (with R = 0.929, NRMSE = 0.169, accuracy = 0.999, NS = 0.856, and IOA = 0.985) over others. For evaluating the generalization capability of the best model, three different parts of datasets (all-inclusive, 1st half, and 2nd half) of the five test stations were evaluated. The proposed hybrid PSO-GA tuned Sugeno type 1 FT model performed similarly well, according to the findings, on the datasets of the test stations. The study concluded that the hybrid PSO-GA tuned Sugeno type 1 FT approach, which was composed of several standalone FIS objects, was suitable for predicting daily ET0 values.

Evaluation of Machine Learning Models for Daily Reference Evapotranspiration Modeling Using Limited Meteorological Data in Eastern Inner Mongolia, North China

Background: Water shortages limit agricultural production in arid and semiarid regions around the world. The accurate estimation of reference evapotranspiration (ET0) is of the utmost importance for computing crop water requirements, agricultural water management, and irrigation scheduling design. However, due to the combination of insufficient meteorological data and uncertain inputs, the accuracy and stability of the ET0 prediction model were different to varying degrees. Methods: Six machine learning models were proposed in the current study for daily ET0 estimation. Information on the weather, such as the maximum and minimum air temperatures, solar radiation, relative humidity, and wind speed, during the period 1960~2019 was obtained from eighteen stations in the northeast of Inner Mongolia, China. Three input combinations were utilized to train and test the proposed models and compared with the corresponding empirical equations, including two temperature-based, three radiation-based, and two humidity-based empirical equations. To evaluate the ET0 estimation models, two strategies were used: (1) in each weather station, we trained and tested the proposed machine learning model, and then compared it with the empirical equations, and (2) using the K-means algorithm, all weather stations were sorted into three groups based on their average climatic features. Then, each station tested the machine learning model trained using the other stations within the group. Three statistical indicators, namely, determination coefficient (R2), root mean square error (RMSE), and mean absolute error (MAE), were used to evaluate the performance of the models. Results: The results showed the following: (1) The temperature-based temporal convolutional neural network (TCN) model outperformed the empirical equations in the first strategy, as shown by the TCN’s R2 values being 0.091, 0.050, and 0.061 higher than those of empirical equations; the RMSE of the TCN being significantly lower than that of empirical equations by 0.224, 0.135, and 0.159 mm/d; and the MAE of the TCN being significantly lower than that of empirical equations by 0.208, 0.151, and 0.097 mm/d, and compared with the temperature-based empirical equations, the TCN model markedly reduced RMSE and MAE while increasing R2 in the second strategy. (2) In comparison to the radiation-based empirical equations, all machine learning models reduced RMSE and MAE, while significantly increasing R2 in both strategies, particularly the TCN model. (3) In addition, in both strategies, all machine learning models, particularly the TCN model, enhanced R2 and reduced RMSE and MAE significantly when compared to humidity-based empirical equations. Conclusions: When the radiation or humidity characteristics were added to the given temperature characteristics, all the proposed machine learning models could estimate ET0, and its accuracy was higher than the calibrated empirical equations external to the training study area, which makes it possible to develop an ET0 estimation model for cross-station data with similar meteorological characteristics to obtain a satisfactory ET0 estimation for the target station.

Modelling reference evapotranspiration using gene expression programming and artificial neural network at Pantnagar, India

Evapotranspiration is an essential component of the hydrological cycle that is of particular interest for water resource planning. Its quantification is helpful in irrigation scheduling, water balance studies, water allocation, etc. Modelling of reference evapotranspiration (ET0) using both gene expression programming (GEP) and artificial neural network (ANN) techniques was done using the daily meteorological data of the Pantnagar region, India, from 2010 to 2019. A total of 15 combinations of inputs were used in developing the ET0 models. The model with the least number of inputs consisted of maximum and minimum air temperatures, whereas the model with the highest number of inputs consisted of maximum air temperature, minimum air temperature, mean relative humidity, number of sunshine hours, wind speed at 2 m height and extra-terrestrial radiation as inputs and with ET0 as the output for all the models. All the GEP models were developed for a single functional set and pre-defined genetic operator values, while the best structure in each ANN model was found based on the performance during the testing phase. It was found that ANN models were superior to GEP models for the estimation purpose. It was evident from the reduction in RMSE values ranging from 2 % to 56 % during training and testing phases in all the ANN models compared with GEP models. The ANN models showed an increase of about 0.96 % to 9.72 % of R2 value compared to the respective GEP models. The comparative study of these models with multiple linear regression (MLR) depicted that the ANN and GEP models were superior to MLR models.

Comparison of Fourteen Reference Evapotranspiration Models With Lysimeter Measurements at a Site in the Humid Alpine Meadow, Northeastern Qinghai-Tibetan Plateau.

Evapotranspiration is a key component in the terrestrial water cycle, and accurate evapotranspiration estimates are critical for water irrigation management. Although many applicable evapotranspiration models have been developed, they are largely focused on low-altitude regions, with less attention given to alpine ecosystems. In this study, we evaluated the performance of fourteen reference evapotranspiration (ET0) models by comparison with large weight lysimeter measurements. Specifically, we used the Bowen ratio energy balance method (BREB), three combination models, seven radiation-based models, and three temperature-based models based on data from June 2017 to December 2018 in a humid alpine meadow in the northeastern Qinghai–Tibetan Plateau. The daily actual evapotranspiration (ETa) data were obtained using large weighing lysimeters located in an alpine Kobresia meadow. We found that the performance of the fourteen ET0 models, ranked on the basis of their root mean square error (RMSE), decreased in the following order: BREB > Priestley-Taylor (PT) > DeBruin-Keijman (DK) > 1963 Penman > FAO-24 Penman > FAO-56 Penman–Monteith > IRMAK1 > Makkink (1957) > Makkink (1967) > Makkink > IRMAK2 > Hargreaves (HAR) > Hargreaves1 (HAR1) > Hargreaves2 (HAR2). For the combination models, the FAO-24 Penman model yielded the highest correlation (0.77), followed by 1963 Penman (0.75) and FAO-56 PM (0.76). For radiation-based models, PT and DK obtained the highest correlation (0.80), followed by Makkink (1967) (0.69), Makkink (1957) (0.69), IRMAK1 (0.66), and IRMAK2 (0.62). For temperature-based models, the HAR model yielded the highest correlation (0.62), HAR1, and HAR2 obtained the same correlation (0.59). Overall, the BREB performed best, with RMSEs of 0.98, followed by combination models (ranging from 1.19 to 1.27 mm day−1 and averaging 1.22 mm day−1), radiation-based models (ranging from 1.02 to 1.42 mm day−1 and averaging 1.27 mm day−1), and temperature-based models (ranging from 1.47 to 1.48 mm day−1 and averaging 1.47 mm day−1). Furthermore, all models tended to underestimate the measured ETa during periods of high evaporative demand (i.e., growing season) and overestimated measured ETa during low evaporative demand (i.e., nongrowing season). Our results provide new insights into the accurate assessment of evapotranspiration in humid alpine meadows in the northeastern Qinghai–Tibetan Plateau.

Modern Techniques to Modeling Reference Evapotranspiration in a Semiarid Area Based on ANN and GEP Models

Evapotranspiration (ET) is a significant aspect of the hydrologic cycle, notably in irrigated agriculture. Direct approaches for estimating reference evapotranspiration (ET0) are either difficult or need a large number of inputs that are not always available from meteorological stations. Over a 6-year period (2006–2011), this study compares Feed Forward Neural Network (FFNN), Radial Basis Function Neural Network (RBFNN), and Gene Expression Programming (GEP) machine learning approaches for estimating daily ET0 in a meteorological station in the Lower Cheliff Plain, northwest Algeria. ET0 was estimated using the FAO-56 Penman–Monteith (FAO56PM) equation and observed meteorological data. The estimated ET0 using FAO56PM was then used as the target output for the machine learning models, while the observed meteorological data were used as the model inputs. Based on the coefficient of determination (R2), root mean square error (RMSE), and Nash–Sutcliffe efficiency (EF), the RBFNN and GEP models showed promising performance. However, the FFNN model performed the best during training (R2 = 0.9903, RMSE = 0.2332, and EF = 0.9902) and testing (R2 = 0.9921, RMSE = 0.2342, and EF = 0.9902) phases in forecasting the Penman–Monteith evapotranspiration.

Performance evaluation of geospatially assisted reference evapotranspiration models

Performance evaluation of geospatially assisted reference evapotranspiration models