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Reference crop evapotranspiration (ET0) is a crucial variable for estimating the ecological water demand of vegetation. Under climate change, the trends of ET0 change vary in different regions. The study of spatial and temporal variations in ET0 and attribution analysis at the regional scale is more conducive to the regional agricultural water management and ecological water demand estimation under the changing environment. We analyzed the change trend, spatial distribution and the contribution of meteorological factors to annual ET0 change of the Fenwei Plain during a historical period (1985-2015) and a future period (2030-2060) based on the latest climate data and high-precision grid data from the Sixth International Coupled Model Intercomparison Project (CMIP6). The results showed that the meteorological data from CMIP6 could be used for the prediction of ET0 after bias correction, and that the prediction accuracy of the multi-model ensemble approach (R2 of 82.9%, RMSE of 14.9 mm) was higher than that of a single climate model. ET0 in the Fenwei Plain showed a significant decreasing trend in the historical period, but a non-significant increasing and significant increasing trend in the future period under the SSP245 and SSP585 scenarios, respectively. The vapor pressure deficit had the largest contribution to the ET0 change in both the historical and future periods, and was the primary meteorological factor affecting the ET0 change in the Fenwei Plain under the climate change. Solar radiation and wind speed were important meteorological factors affecting the ET0 change in the historical period, while temperature and wind speed were the important meteorological factors affecting the ET0 change in the future period. The meteorological factors that had great contribution to ET0 change were due to the larger multi-year relative change rates, rather than the high sensitivity of these meteorological factors to ET0. The ET0 of the plain under the SSP245 and SSP585 scenarios increased by 4.2% and 3.1% in the future period, respectively, compared with the historical period. The differences in the spatial distribution of the result were mainly from the eastern and western regions of the plain. Based on the high-precision spatial and temporal distribution of ET0, the spatial and temporal data could be used as a reference for the development of various adaptation for climate change in the Fenwei Plain.

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Recycled wastewater effluent irrigation and implementing limited irrigation rates are two promising strategies for water conservation in agriculture. However, one major challenge is the accumulation and translocation of Pharmaceutical and Personal Care Products (PPCPs) from recycled water to crops. This study investigated the effects of UV persulfate (UV/PS) treatment of recycled water and limited irrigation rate on PPCPs accumulation and physiological responses of St. Augustine turfgrass via a 14-week field trial. Carbamazepine (CBZ), sulfamethoxazole (SMX), triclosan (TCS), fluoxetine (FLX) and diclofenac (DCF) were spiked at 0.1-1.5 µg/L into recycled water and two limited irrigation rates corresponding to 60 % and 80 % of reference Evapotranspiration (ETo) were applied. Results showed that UV/PS removed 60 % of CBZ and > 99 % of other PPCPs from recycled water. Irrigation with UV/PS treated recycled water resulted in approximately a 60 % reduction in CBZ accumulation and complete removal of SMX, DCF, FLX and TCS in both turfgrass leaves and roots. A more limited irrigation rate at 60 % ETo resulted in a higher accumulation of CBZ accumulation compared to 80 % ETo. Similarly, the canopy temperature increased under 60 % ETo irrigation rate compared to 80 % ETo, suggesting that turfgrass under 60 % ETo was more prone to water stress. Applying a 60 % ETo irrigation rate was not sufficient to maintain the turfgrass quality in the acceptable range. A negative correlation between the visual quality and cumulative mass of PPCPs in turfgrass leaves at different irrigation rates was observed, yet irrigation rate was the major driver of turfgrass overall quality and health. Insights from this study will help to integrate recycled water with treatment and limited irrigation, thereby enhancing agricultural water reuse practices.

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Background: Reference evapotranspiration (ETo), which is used as the basic data in many studies within the scope of hydrology, meteorology, irrigation and soil sciences, can be estimated by using the evaporation (Epan) measured from the class-A pan evaporimeter. However, this method requires reliable pan coefficients (Kp). Many empirical models are used to estimate Kp coefficients. The reliability of these models varies depending on climatic and environmental conditions. Therefore, they need to be tested in the local conditions where they will be used. In this study, conducted in Kahramanmaras, which has a semi-arid Mediterranean climate in Turkey during the July-October periods of 2020 and 2021, aimed to determine the usability levels of six Kp models in estimating daily and monthly average ETo. Methods: The Kp coefficients estimated by the models were multiplied with the daily Epan values, and the daily average ETo values were estimated on the basis of the model. The daily Epan values were measured using an ultrasonic sensor sensitive to the water surface placed on the class-A pan evaporimeter. The ultrasonic sensor was managed by a programmable logic controller (PLC). To enable the sensor to be managed by PLC, a software was prepared using the CODESYS programming language and uploaded to the PLC. The daily average ETo values determined by the FAO-56 Penman-Monteith equation were accepted as actual values. The ETo values estimated by the Kp models were compared with the actual ETo values using the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE) and determination coefficient (R2) statistical approaches. Results: The Wahed & Snyder outperformed the other models in estimating daily (MAE = 0.78 mm day-1, MAPE = 14.40%, RMSE = 0.97 mm day-1, R2 = 0.82) and monthly (MAE = 0.32 mm day-1, MAPE = 5.88%, RMSE = 0.32 mm day-1, R2 = 0.99) average ETo. FAO-56 showed the nearest performance to Wahed & Snyder. The Snyder model presented the worst performance in estimating daily (MAE = 2.09 mm day-1, MAPE = 37.53%, RMSE = 2.36 mm day-1, R2 = 0.82) and monthly (MAE = 1.83 mm day-1, MAPE = 31.82%, RMSE = 1.87 mm day-1, R2 = 0.99) average ETo. It has been concluded that none of the six Kp models can be used to estimate the daily ETo in Kahramanmaras located in the Mediterranean-Southeastern Anatolian transitional zone, and only Wahed & Snyder and FAO-56 can be used to estimate the monthly ETo without calibration.

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Reference evapotranspiration (ET0) estimation is crucial for efficient irrigation planning, optimized water management and ecosystem modeling, yet it presents significant challenges, particularly when meteorological data availability is limited. This study utilized remote sensing data of land surface temperature (LST), day of year, and latitude, and employed a machine learning approach (i.e., random forest) to develop an improved remote sensing ET0 model. The model performed excellently in 567 meteorological stations in China with an R2 of 0.97, RMSE of 0.40, MBE of 0.00, and MAPE of 0.11 compared to the FAO-PM ET0; it also performed well globally, yielding an average R2 of 0.97 and RMSE of 0.43 across 120 sites in mid-latitude (20°-50°) regions. This model demonstrates simplicity, accuracy, robust and generalization, holding great potential for widespread application, especially in the large-scale, high-resolution estimation of ET0. This study will contribute to advancements in water resources management, agricultural planning, and climate change studies.

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Soil moisture is an important component of the hydrological cycle and a key mediator between land surface and atmospheric interactions. Although substantial progress has been made in remote sensing of soil moisture at different spatial scales, the shallow penetration depth of remote sensors greatly limits their utility for applications in meteorological modelling and hydrological studies where the critical variable of interest is the root-zone soil moisture content. Therefore, this study assesses the relationship between soil moisture at the surface (10 cm) and in lower soil layers (20, 40, 60, 80, 100, and 120 cm) under varying climates, soils, and crop types. Cross-correlation analysis is applied to daily in-situ soil moisture measurements from 4712 locations in agricultural lands across the contiguous United States. Our analysis demonstrates that zero-day lag always produced the highest correlation between 10 cm soil moisture and soil moisture in the lower layers. In addition, a positive and strong relationship between 10 and 20 cm soil moisture (r = 0.84) was observed, while the relationships between 10 and 40 cm soil moisture were moderate (r = 0.52). The decline in cross-correlation continued to the deeper soil layers, which indicated that, on a daily timescale, the surface soil moisture gradually becomes decoupled with soil moisture at greater depths. Therefore, our research suggests that the estimation of soil moisture in the soil layers up to 40 cm based on surface soil moisture is most promising. However, the influence of climate, crop type, and soil texture on the strength of relationships between surface and lower layers makes the prediction difficult. The comparatively weak relationship between precipitation and soil moisture (0.09-0.32), as well as the relationship between reference evapotranspiration (ETo) and soil moisture (-0.19-0.18), in this study can be attributed to scale mismatching from different data sources.

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Reference evapotranspiration (ET0 ) is a significant parameter for efficient irrigation scheduling and groundwater conservation. Different machine learning models have been designed for ET0 estimation for specific combinations of available meteorological parameters. However, no single model has been suggested so far that can handle diverse combinations of available meteorological parameters for the estimation of ET0. This article suggests a novel architecture of an improved hybrid quasi-fuzzy artificial neural network (ANN) model (EvatCrop) for this purpose. EvatCrop yielded superior results when compared with the other three popular models, decision trees, artificial neural networks, and adaptive neuro-fuzzy inference systems, irrespective of study locations and the combinations of input parameters. For real-field case studies, it was applied in the groundwater-stressed area of the Terai agro-climatic region of North Bengal, India, and trained and tested with the daily meteorological data available from the National Centres for Environmental Prediction from 2000 to 2014. The precision of the model was compared with the standard Penman-Monteith model (FAO56PM). Empirical results depicted that the model performances remarkably varied under different data-limited situations. When the complete set of input parameters was available, EvatCrop resulted in the best values of coefficient of determination (R2 = 0.988), degree of agreement (d = 0.997), root mean square error (RMSE = 0.183), and root mean square relative error (RMSRE = 0.034).

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Reference evapotranspiration (ETo) has a significant role in water resource planning and management as well as analysis of crop production and other agricultural tasks. Methods for estimating ETo may require diurnal/monthly assessments to perceive the consequences of climatic changes on local regions. The spatial and temporal patterns of ETo were analyzed in the current work using data from 340 weather stations in Iran. The entropy theory was used to assess the uncertainty of the utilized variables and the modified Kendall test was applied for temporal trend analysis. The interpolation (e.g., kriging) and ordinary least squares (OLS) methods were used for spatio-temporal ETo classification/modeling. The spatial analysis demonstrated that the OLS method with a good fit measure (R2 = 0.985) successfully simulated the spatial relationships of ETo with climatic parameters. After examining error indices, the cokriging method with an exponential variogram was introduced as the best method of seasonal and annual ETo classification in Iran. Spatially and temporally calculated ETo patterns using modified Hargreaves (MHGR) and MODIS methods closely resembled the standard FAO Penman-Monteith (FPM-56) method, all indicating a gradual increase in ETo. MHGR and MODIS methods serve as suitable alternatives for estimating ETo in various climatic regions of Iran, provided data availability.

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Accurate and reliable estimation of Reference Evapotranspiration (ETo) is crucial for water resources management, hydrological processes, and agricultural production. The FAO-56 Penman-Monteith (FAO-56PM) approach is recommended as the standard model for ETo estimation; nevertheless, the absence of comprehensive meteorological variables at many global locations frequently restricts its implementation. This study compares shallow learning (SL) and deep learning (DL) models for estimating daily ETo against the FAO-56PM approach based on various statistic metrics and graphic tool over a coastal Red Sea region, Sudan. A novel approach of the SL model, the Catboost Regressor (CBR) and three DL models: 1D-Convolutional Neural Networks (1D-CNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU) were adopted and coupled with a semi-supervised pseudo-labeling (PL) technique. Six scenarios were developed regarding different input combinations of meteorological variables such as air temperature (Tmin, Tmax, and Tmean), wind speed (U2), relative humidity (RH), sunshine hours duration (SSH), net radiation (Rn), and saturation vapor pressure deficit (es-ea). The results showed that the PL technique reduced the systematic error of SL and DL models during training for all the scenarios. The input combination of Tmin, Tmax, Tmean, and RH reflected higher performance than other combinations for all employed models. The CBR-PL model demonstrated good generalization abilities to predict daily ETo and was the overall superior model in the testing phase according to prediction accuracy, stability analysis, and less computation cost compared to DL models. Thus, the relatively simple CBR-PL model is highly recommended as a promising tool for predicting daily ETo in coastal regions worldwide which have limited climate data.

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The reference evapotranspiration (ETo) is considered one of the primary variables for water resource management, irrigation practices, agricultural and hydro-meteorological studies, and modeling different hydrological processes. Therefore, an accurate prediction of ETo is essential. A large number of empirical methods have been developed by numerous scientists and specialists worldwide to estimate ETo from different climatic variables. The FAO56 Penman-Monteith (PM) is the most accepted and accurate model to estimate ETo in various environments and climatic conditions. However, the FAO56-PM method requires radiation, air temperature, air humidity, and wind speed data. In this study in Adana Plain, which has a Mediterranean climate for the summer growing season, using 22-year daily climatic data, the performance of the FAO56-PM method was evaluated with different combinations of climatic variables when climatic data were missing. Additionally, the performances of Hargreaves-Samani (HS) and HS (A&G) equations were assessed, and multiple linear regression models (MLR) were developed using different combinations of climatic variables. The FAO56-PM method could accurately estimate daily ETo when wind speed (U) and relative humidity (RH) data were unavailable, using the procedures suggested by FAO56 Paper (RMSEs were smaller than 0.4 mm d-1, and percent relative errors (REs) were smaller than 9%). Hargreaves-Samani (A&G) and HS equations could not estimate daily ETo accurately according to the statistical indices (RMSEs = 0.772-0.957 mm d-1; REs (%) = 18.2-22.6; R2 = 0.604-0.686, respectively). On the other hand, MLR models' performance varied according to a combination of different climatic variables. According to t-stat and p values of independent variables for MLR models, solar radiation (Rs) and sunshine hours (n) variables had more effect on estimating ETo than other variables. Therefore, the models that used Rs and n data estimated daily ETo more accurately than the others. RMSE values of the models that used Rs were between 0.288 to 0.529 mm d-1; RE(%) values were between 6.2%-11.5% in the validation process. RMSE values of the models that used n were between 0.457 to 0.750 mm d-1; RE(%) values were between 9.9%-16.3% in the validation process. The models based only on air temperature had the worst performance (RMSE = 1.117 mm d-1; RE(%) = 24.2; R2 = 0.423).

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In this study, stochastic gradient boosting (SGB), a commonly-adopted soft computing method, was used to estimate reference evapotranspiration (ETo) for the Adiyaman region of southeastern Türkiye. The FAO-56-Penman-Monteith method was used to calculate ETo, which we then estimated using SGB with maximum temperature, minimum temperature, relative humidity, wind speed, and solar radiation obtained from a meteorological station.•The calculated ETo time series values were decomposed into sub-series using Singular Spectrum Analysis (SSA) to enhance prediction accuracy.•Each sub-series was trained with the first 70% of observations and tested with the remaining 30% via SGB. Final prediction values were obtained by collecting all series predictions.•Three lag times were taken into account during the predictions, and both short-term and long-term ETo values were estimated using the proposed framework. The results were tested with respect to root mean square error (RMSE) and Nash-Sutcliffe efficiency (NSE) indicators for ensuring whether the model produced statically acceptable outcomes.

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In this study, the predictive power of three different machine learning (ML)-based approaches, namely, multi-gene genetic programming (MGGP), M5 model trees (M5Tree), and K-nearest neighbor algorithm (KNN), for long-term monthly reference evapotranspiration (ET0) prediction were investigated. The input data consist of monthly solar radiation (Rs), maximum air temperature (Tmax), and wind speed (Ws) derived from 163 meteorological stations in Turkey. Different input combinations were created and analyzed. The model's performance was evaluated using criteria such as Nash-Sutcliffe efficiency, Kling-Gupta efficiency, relative root mean squared error, mean absolute percentage error, and determination coefficient. Moreover, Taylor, radar, and boxplot diagrams were created. It was determined that the MGGP model outperformed both the M5Tree and the KNN models. The equation obtained from the MGGP model, for the best-performed combination of Rs-Tmax-Ws, was presented. The best weather conditions were obtained as 0.029 to 31.814 MJ/m2, - 5.8 to 45.7 °C, and 0.140 to 5.086 m/s for Rs, Tmax, and Ws, respectively. It was also found that the Rs was the most potent input variable for ET0 estimation while Ws was the weakest.

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The accurate estimation of reference evapotranspiration (ET0) is crucial for water resource management and crop water requirements. This study aims to develop an efficient and accurate model to estimate the monthly ET0 in the Jialing River Basin, China. For this purpose, a relevance vector machine, complex extreme learning machine (C-ELM), extremely randomized trees, and four empirical equations were developed. Monthly climatic data including mean air temperature, solar radiation, relative humidity, and wind speed from 1964 to 2014 were used as inputs for modeling. A total comparison was made between all constructed models using four statistical indicators, i.e., the coefficient of determination (R2), Nash efficiency coefficient (NSE), root mean square error (RMSE) and mean absolute error (MAE). The outcome of this study revealed that the Hargreaves equation (R2 = 0.982, NSE = 0.957, RMSE = 7.047 mm month-1, MAE = 5.946 mm month-1) had better performance than the other empirical equations. All machine learning models generally outperformed the studied empirical equations. The C-ELM model (R2 = 0.995, NSE = 0.995, RMSE = 2.517 mm month-1, MAE = 1.966 mm month-1) had the most accurate estimates among all generated models and can be recommended for monthly ET0 estimation in the Jialing River Basin, China.

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[This corrects the article DOI: 10.3389/fpls.2022.854196.].

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Reference evapotranspiration (ETo) is a variable that helps determine atmospheric pressure on living (reference) grass to release water into the atmosphere. For this purpose, four main driving forces: air temperature, air humidity, solar radiation, and wind speed need to be measured over the well-watered reference grass. The relative influence of these driving forces is region and climate-specific, with daily and seasonal variations. A clear understanding of the dynamic interactions of ETo's driving factors can illuminate the water and energy cycles of the earth and assist modelers with more accurate predictions of ETo. In this study, Pearson correlation, mutual information, and random forest feature importance analyses have been used to evaluate the relative importance of meteorological driving forces of ETo in California. To better understand the interrelations of these variables, 1,365,823 daily data samples from 237 standardized weather stations for 36 years have been clustered into homogeneous climatic zones and analyzed. To compensate for the effects of seasonality, feature importance analysis is also conducted on seasonal and monthly clustered data. Moreover, seasonal and annual trends of ETo and its driving factors are investigated for California and homogeneous zones using the Mann-Kendall test. Our findings reveal that for annually clustered data, solar radiation is the most influential driving factor of ETo in California. However, analysis of seasonal and monthly clustered data shows that vapor pressure deficit is the most informative factor during the summer and spring, while solar radiation is more important during the colder seasons. Results of trend analysis don't suggest a consistent monotonic trend for ETo and other variables for different seasons and zones. However, it is shown that agricultural regions with heavy irrigation dependence like the Central Valley are getting warmer and drier, especially during the irrigation season. This can adversely affect the water resources, agriculture industry, and food production of California, and modeling efforts like this can be very informative for future water resources management.

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The Southeastern Anatolian Region of Turkey is located in semi arid climate zone and therefore requires an efficient water use. Well-planned irrigation with optimum water required by the crops is essential for the limited water resources of the region. The numerical tool CROPWAT of the Food and Agriculture Organization (FAO) was used for modelling efficient irrigation of local crops pistachio, olive, almond and grape without reducing the yield. Local climatic, soil, plant and rainfall information were used as inputs to CROPWAT model to predict the reference evapotranspiration (ETo) values. The crop water requirement (CWR) for pistachio, olive, almond, and grape was calculated as 1,294.0 mm, 659.4 mm, 790.2 mm, and 752.0 mm, respectively, The number of irrigation needed during growth stages was determined as eight for pistachio, three for olive, six for almond and five for grape.

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Reference evapotranspiration (ET0), as one important variable in climatology, hydrology, and agricultural science, plays an important role in the terrestrial hydrological cycle and agricultural irrigation. However, the ET0 estimation process is inaccurate due to the lack of weather stations and historical data. In this study, a new method of ET0 estimation was proposed to improve the ET0 estimation performance in regions with limited data. Four empirical models with different data requirements, Albrecht, Hargreaves-Samani, Priestley-Taylor, and Penman, were applied and optimized the parameters by the Shuffled Complex Evolution-University of Arizona algorithm with the ET0 calculated by the Penman-Monteith model as the reference value at 600 meteorological stations in China. Two machine learning models, Random Forest (RF) and Multiple Linear Regression (MLR) were used to establish the regionalization of the parameter of the empirical model. The result showed that parameter optimization could significantly improve ET0 estimation in different climate regions of China. The Penman model has the strongest physical foundation and the highest estimation accuracy, followed by the Hargeaves-Samani and Priestley-Taylor model. The mass-transfer-based model, Albrecht, could only estimate regional ET0 efficiently after parameter optimization. Based on the more advanced RF machine learning regionalization method that considers complex linear relationships of variables, ET0 estimation in regions lacking data could be improved efficiently. Machine learning could be used to describe the ET0 model parameters in different regions because of the similarity. The combination of machine learning and empirical model could provide a new method for ET0 estimation in data deficient regions.

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Evapotranspiration is an important quantity required in many applications, such as hydrology and agricultural and irrigation planning. Reference evapotranspiration is particularly important, and the prediction of its variations is beneficial for analyzing the needs and management of water resources. In this paper, we explore the predictive ability of hybrid ensemble learning to predict daily reference evapotranspiration (RET) under the semi-arid climate by using meteorological datasets at 12 locations in the Andalusia province in southern Spain. The datasets comprise mean, maximum, and minimum air temperatures and mean relative humidity and mean wind speed. A new modified variant of the grey wolf optimizer, named the PRSFGWO algorithm, is proposed to maximize the ensemble learning's prediction accuracy through optimal weight tuning and evaluate the proposed model's capacity when the climate data is limited. The performance of the proposed approach, based on weighted ensemble learning, is compared with various algorithms commonly adopted in relevant studies. A diverse set of statistical measurements alongside ANOVA tests was used to evaluate the predictive performance of the prediction models. The proposed model showed high-accuracy statistics, with relative root mean errors lower than 0.999% and a minimum R2 of 0.99. The model inputs were also reduced from six variables to only two for cost-effective predictions of daily RET. This shows that the PRSFGWO algorithm is a good RET prediction model for the semi-arid climate region in southern Spain. The results obtained from this research are very promising compared with existing models in the literature.

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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.

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The importance of daily data on reference evapotranspiration (ET0) has increased in recent years due to its relevance in planning and decision making regarding irrigated agriculture, water production, and forest restoration. Facing the scarcity of this information measured in loco, the study of interpolation methods capable of representing ET0 becomes important. Therefore, this study aimed to evaluate the adequacy of the Random Forest (RF) method in the spatialization of ET0 in the watersheds of the Mid-South region of the Espírito Santo State, located within the Atlantic Forest biome, Brazil. From this study, it was found that the RF method is the most suitable one for ET0 spatialization when compared to the Angular distance weighting (ADW) and the inverse distance weighting (IDW) techniques. Also, the spatializations carried out by this method were transformed into databases in a grid format and made available online. Furthermore, the RF database was also compared to other ET0 grid databases, and it was concluded that the RF database also carried out a better performance than the other ones.

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Accurate simulation of evapotranspiration is of substantial importance to hydrology, ecology, agriculture, and water resources management. Evapotranspiration is equal to the fraction of potential evapotranspiration (PET) constrained by soil water. PET can be calculated from meteorological observations with a wide global distribution and high density. However, it is necessary to determine how to accurately simulate daily evapotranspiration through PET. We have developed a non-linear function for simulating evapotranspiration through PET constrained by soil water at daily scale. The evaluation results show that the accuracy of the evapotranspiration simulation using the non-linear function was higher than that of linear relations and complementary relationship (CR) methods. In the temperature-based PET equations, the Hargreaves-Samani equation was the closest to the Penman-Monteith calculation values. The simulation accuracy of the CR methods obviously improved after parameter calibration. The accuracy has a large variability at the global scale. Daily evapotranspiration can be simulated with PET data in some regions with a high accuracy (Nash and Sutcliffe efficiency coefficient > 0.60), including most regions of Eurasia, eastern and southern North America, and northern South America. However, other regions showed a poor performance (Nash and Sutcliffe efficiency coefficient < 0.20), including western North America, the Mediterranean region, and the eastern and western coastal regions of Australia. Our results indicate that the accurate simulation of daily evapotranspiration can be achieved based on meteorological data in most regions of the world. Owing to the wide distribution of global meteorological observations, the accurate simulation of the daily evapotranspiration method proposed in this study can be applied in other regions across the globe.

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