Estimating Reference Crop Evapotranspiration Research Articles

Comparison of potential evapotranspiration methods in Ethiopia

The Food and Agricultural Organization method for estimating reference crop evapotranspiration (ETo), FAO56, is the standard method across the globe. Daily ETo estimated using seventeen potential evapotranspiration (PET) methods that has less data requirments were compared with FAO56 at five sites in Ethiopia (Bahir Dar, Bale Robe, Hawassa, Metehara, and Nazareth). The average rank of five model validation metrics namely standard deviation, RMSE, MAPE, NSE, and correlation were used to compare the methods. By taking the areal average ETo and PET, ten methods, Wen, Ant, Pen, Mak, PT, Ha5, Ha4, Tho, Rad, and Enk, having correlation > 0.57 and MAPE < 28% were ranked 1st to 10th, respectively. Also, at each site, the above ten PET methods were compared. By taking the average ranks of the five sites, Wen, Pen, Ant, PT, and Mak & Ha5 ranked 1st to 5th, respectively. Wen & Ant methods which are applied in Ethiopia for the first time had shown the best performance.

Parameterization of the Ångström–Prescott formula based on machine learning benefit estimation of reference crop evapotranspiration with missing solar radiation data

AbstractAccurately estimated reference evapotranspiration (ET0) is essential to regional water management. The FAO recommends coupling the Penman–Monteith (P‐M) model with the Ångström–Prescott (A‐P) formula as the standard method for ET0 estimation with missing Rs measurements. However, its application is usually restricted by the two fundamental coefficients (a and b) of the A‐P formula. This paper proposes a new method for estimating ET0 with missing Rs by combining machine learning with physical‐based P‐M models (PM‐ET0). The benchmark values of the A‐P coefficients were first determined at the daily, monthly, and yearly scales, and further evaluated in Rs and ET0 estimates at 80 national Rs measuring stations. Then, three empirical models and four machine‐learning methods were evaluated in estimating the A‐P coefficients. Machine learning methods were also used to estimate ET0 (ML‐ET0) to compare with the PM‐ET0. Finally, the optimal estimation method was used to estimate the A‐P coefficients for the 839 regular weather stations for ET0 estimation without Rs measurement for China. The results demonstrated a descending trend for coefficient a from northwest to southeast China, with larger values in cold seasons. However, coefficient b showed the opposite distribution as the coefficient a. The FAO has recommended a larger a but a smaller b for southeast China, which produced the region's largest Rs and ET0 estimation errors. Additionally, the A‐P coefficients calibrated at the daily scale obtained the best estimation accuracy for both Rs and ET0, and slightly outperformed the monthly and yearly coefficients without significant difference in most cases. The machine learning methods outperformed the empirical methods for estimating the A‐P coefficients, especially for the sites with extreme values. Further, ML‐ET0 outperformed the PM‐ET0 with yearly A‐P coefficients but underperformed those with daily and monthly ones. This study indicates an exciting potential for combining machine learning with physical models for estimating ET0. However, we found that using the A‐P coefficients with finer time scales is unnecessary to deal with the missing Rs measurements.

Estimating reference crop evapotranspiration using improved convolutional bidirectional long short-term memory network by multi-head attention mechanism in the four climatic zones of China

Accurate reference crop evapotranspiration (ET0) estimation is essential for agricultural water management, crop productivity, and irrigation systems. As the standard ET0 estimation method, the Penman-Monteith equation has been widely recommended worldwide. However, its application is still restricted to comprehensive meteorological data deficiency, making the exploration of alternative simpler models for acceptable ET0 estimation highly meaningful. Concerning the aforementioned requirement, this study developed the novel deep learning model (MA-CNN-BiLSTM), which incorporates Multi-Head Attention mechanism (MA), Convolutional Neural Network (CNN), and Bidirectional Long Short-Term Memory network (BiLSTM) as intricate relationship processor, feature extractor, and regression component, to estimate ET0 based on radiation-based (Rn-based), humidity-based (RH-based), and temperature-based (T-based) input combinations at 600 stations during 1961–2020 throughout China under internal and external cross-validation strategies. Besides, through a comparative evaluation among MA-CNN-BiLSTM, CNN-BiLSTM, BiLSTM, LSTM, Multivariate Adaptive Regression Splines (MARS), and empirical models, the result indicated that MA-CNN-BiLSTM achieved superior precision, with values of Determination Coefficient (R2), Nash–Sutcliffe efficiency coefficient (NSE), Relative Root Mean Square Error (RRMSE), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE) ranging 0.877–0.972, 0.844–0.962, 0.129–0.292, 0.294–0.644 mm d−1, 0.244–0.566 mm d−1 for internal strategy and 0.797–0.927, 0.786–0.920, 0.162–0.335, 0.409–0.969 mm d−1, 0.294–0.699 mm d−1 for external strategy. Specifically, Rn-based MA-CNN-BiLSTM excelled in the temperate continental zone (TCZ) and mountain plateau zone (MPZ), while RH-based MA-CNN-BiLSTM yielded best precision in others. Furthermore, the internal strategy was superior to external strategy by 2.74–106.04% for R2, 1.11–120.49% for NSE, 1.41–40.27% for RRMSE, 1.68–45.53% for RMSE, and 1.21–38.87% for MAE, respectively. In summary, the main contribution of the present study is the proposal of a novel LSTM-type ET0 model (MA-CNN-BiLSTM) to cope with various data-missing scenarios throughout China, which can provide effective support for decision-making in regional agriculture water management.

Estimating reference crop evapotranspiration using optimized empirical methods with a novel improved Grey Wolf Algorithm in four climatic regions of China

Accurate estimation of reference crop evapotranspiration (ETo) is crucial for agricultural water management. As the simplified alternatives of the Penman-Monteith equation, empirical methods have been widely recommended worldwide. However, its application is still limited to parameters localization varied with geographical and climatic conditions, therefore developing an excellent optimization algorithm for calibrating parameters is very necessary. Regarding the above requirement, the present study developed a novel improved Grey Wolf Algorithm (MDSL-GWA) to optimize the most recommended ones among three types of ETo methods. After the optimization performance comparison among Least Square Method (LSM), Genetic Algorithm (GA), Grey Wolf Algorithm (GWA), and MDSL-GWA in four climatic regions of China, this study found that the Priestley-Taylor (PT) method was the best radiation-based (Rn-based) method and achieved better performance in temperate continental region (TCR), mountain plateau region (MPR), and temperate monsoon region (TMR) than other types. While the temperature-based (T-based) Hargreaves-Samani (HS) method performed best in subtropical monsoon region (SMR), further attaching better performance among the same type in TMR and TCR, while the Oudin method was the best T-based method in MPR. Moreover, the Romanenko method was better humidity-based (RH-based) in TCR and MPR, whereas the Brockamp-Wenner method exhibited higher in SMR and TMR. Furthermore, despite intelligence optimization algorithms significantly enhancing original ETo methods, the MDSL-GWA achieved best performance and outperformed other algorithms by 4.5–29.6% in determination coefficient (R2), 4.7–27.3% in nash-sutcliffe efficient (NSE), 3.7–44.4% in relative root mean square error (RRMSE), and 3.1–56.2% in mean absolute error (MAE), respectively. After optimization, the MDSL-GWA-PT was the most recommended ETo method in TMR, TCR, and MPR, and the median values of R2, NSE, RRMSE, and MAE ranged 0.907–0.958, 0.887–0.925, 0.083–0.103, and 0.115–0.162 mm, respectively. In SMR, the MDSL-GWA-HS produced the best ETo estimates, with median values of R2, NSE, RRMSE, and MAE being 0.876, 0.843, 0.112, and 0.146 mm, respectively. In summary, this study recommended the best ETo method and algorithms using accessible data in four climatic regions of China, which is helpful for decision-making in effective management and utilization of regional agricultural water resources.

Scaling solar-induced chlorophyll fluorescence by using VPD0.5 improves the simulation of reference crop evapotranspiration in the arid and semiarid regions of northern China

Accurately estimating reference crop evapotranspiration (ET0) is crucial for decision-making regarding irrigation, improving farmland water use efficiency, planning water resources, and simulating the global water cycle. However, because traditional ET0 estimation models often require a large number of meteorological parameters as input variables, their application potential is limited, especially when simulating arid and semiarid regions where meteorological data are lacking. Therefore, it is still very challenging to estimate ET0 at large scales in arid and semiarid areas. In this study, we first proposed a semi-mechanistic model for estimating ET0 by deriving the relationship between canopy conductance to water vapor (gw) and solar-induced chlorophyll fluorescence (SIF) based on Fick's law and the light use efficiency (LUE) model, combining theories on optimal stomatal behaviour. Second, the relationship between SIF × VPD0.5 (VPD0.5: 0.5-power of the vapor pressure deficit) and ET0 in the model was verified at the site scale. On this basis, the semi-mechanistic model was applied to three machine learning models to simulate ET0. Four statistical indicators, including the coefficient of determination (R2), root mean square error (RMSE), normalized root mean square error (NRMSE) and mean absolute error (MAE), were used to verify the model performance and screen out the optimal model. Finally, the optimal model was compared with five traditional empirical models. The results showed that (1) the relationship between ET0 and the product of SIF and the 0.5-power vapor pressure deficit (SIF × VPD0.5) was closer than the relationship between ET0 and SIF at the site scale. (2) Compared to the case in which SIF was used as the only input variable, three machine learning models performed better when SIF was scaled using VPD0.5 as the input variable, and the random forest regression (RFR) model in which SIF × VPD0.5 was the input variable was the optimal model (ET0opt). (3) The total mean value of ET0 at 22 sites simulated by ET0opt is 15.46 mm/4 days. The total mean ET0 value for the 22 sites calculated by the five traditional empirical models vary from 10.70 mm/4 days to 20.96 mm/4 days, while our results were in this range and close to their mean value. Our study provides a valuable reference basis for large-scale ET0 estimations using remote sensing in arid and semiarid areas.

Management of irrigation water in Al-Baha, Saudi Arabia, using a simple alternative to the Penman–Monteith equation

Estimating reference crop evapotranspiration (ETo) is very important in the planning and scheduling of irrigation water. A simple method for the estimation of ETo is needed, with fewer meteorological factors that are required for estimation using the Penmen–Monteith equation (PME). The aim of this study was to manage irrigation water in the Al-Baha region of Saudi Arabia using a simple equation to estimate ETo based on air temperature as an effective alternative to the PME. Four simple temperature-dependent equations proposed by Thornthwaite, Blaney-Criddle, Hamon and Linacre were selected for analysis. Of these four equations, the Linacre equation (LE) was found to be best for estimating ETo. Although the ETo rate was overestimated when using the LE compared with the PME, it had the lowest error percentage (9.55%) and the highest R2 (0.97). After deducing a new and accurate equation based on the LE with the ability to estimate the ETo rate, the modified LE produced values closest to the results obtained using the PME for the Al-Baha region. It can thus be relied upon for estimating irrigation needs in the Al-Baha region with the irrigation systems used in the region.

Prediction Model for Reference Crop Evapotranspiration Based on the Back-propagation Algorithm with Limited Factors

The precise estimation of reference crop evapotranspiration (ETO) is vital for regional and irrigation water resource management. It is also beneficial to the rational allocation of regional water resources and alleviates the disparity between water supply and demand. This study accurately estimates the ETO of 14 meteorological stations in southern China. Five neural network models (extreme learning machine [ELM], back-propagation neural network [BP], ant colony optimization [ACO]-BP, bird swarm algorithm [BSA]-BP, and cat swarm optimization [CSO]-BP) were introduced to predict ETO with limited factors using different methods. The results demonstrated that models involving T (average, maximum, and minimum air temperature), sunshine duration (n), and relative humidity (RH) exhibited the highest accuracy of all studied combinations; the role of T, n, RH, wind speed (U2) and average atmospheric pressure (AP) regarding ETO gradually decreased. These three biological heuristic algorithms (ACO, BSA, and CSO) each significantly enhanced the capability of the BP model. The accuracy and computational cost of the CSO-BP model are better than those built by other algorithms. Therefore, it is strongly recommended to use the CSO-BP model for ETO estimation in southern China. This result serves as a reference for a more accurate estimation of ETO for future irrigation decision-making and water resource management in southern China.

Modeling Daily Reference Evapotranspiration from Climate Variables: Assessment of Bagging and Boosting Regression Approaches

The increasing frequency of droughts and floods due to climate change has severely affected water resources across the globe in recent years. An optimal design for the scheduling and management of irrigation is thus urgently needed to adapt agricultural activities to the changing climate. The accurate estimation of reference crop evapotranspiration (ET0), a vital hydrological component of the water balance and crop water need, is a tiresome task if all the relevant climatic variables are unavailable. This study investigates the potential of four ensemble techniques for estimating precise values of the daily ET0 at representative stations in 10 agro-climatic zones in the state of Karnataka, India, from 1979 to 2014. The performance of these models was evaluated by using several combinations of climatic variables as inputs by using tenfold cross-validation. The outcomes indicated that predictions of ET0 by all four ensemble models based on all climatic variables were the most accurate in comparison with other input combinations. The random forest regressor was found to deliver the best performance among the four models on all measures considered (Nash–Sutcliffe efficiency, 1.0, root-mean-squared error, 0.016 mm/day, and mean absolute error, 0.011 mm/day). However, it incurred the highest computational cost, whereas the computational cost of the bagging model for linear regression was the lowest. The extreme gradient-boosting model delivered the most stable performance with a modified training dataset. The work here shows that these models can be recommended for daily ET0 estimation based on the users’ interests.

Improvement of reference crop evapotranspiration estimates using limited data for the Brazilian Cerrado

Evapotranspiration (ET) is a key component of the hydrological cycle. Therefore, adequately estimating it is crucial to improving water resource planning and management.One of the most affordable methods of estimating ET is first to estimate reference crop evapotranspiration (ETo) and later associate it to crop and soil coefficients. The FAO Kc-ETo approach can be used only when ETo is computed with the FAO Penman-Monteith equation. However, low data availability may restict the equations used to estimate ETo. In this study, we assess and calibrate common methods used to estimate ETo under such conditions of limited data availability. Based on the annual calibration, the Makkink (NSE = 0.85) outperformed the Priestley-Taylor (NSE = 0.73), Hargreaves-Samani (NSE = 0.56), and Penman-Monteith temperature approach (NSE = 0.58). The seasonal calibration of parameters showed no significant improvement to the methods assessed (ΔNSE ≤ 0.01), except for the Priestley-Taylor (ΔNSE = 0.06). The performance of temperature-based equations was particularly limited due to the performance of the equation adopted to estimate global solar radiation. Thus, improving the representation of global solar radiation for limited data availability can also play a key role in improving ETo prediction.

Calibration and Evaluation of Empirical Methods to Estimate Reference Crop Evapotranspiration in West Texas

Evapotranspiration is an essential component of the hydrologic cycle, and its accurate quantification is crucial for managing crop water requirements and the operation of irrigation systems. Evapotranspiration data is key to hydrological and water management research investigations, including studying the impact of various climatic factors on crop water requirements. It has been estimated as the product of the reference crop evapotranspiration and crop coefficient. Daily reference crop evapotranspiration (ETo) can be determined by several methods and equations. The Food and Agriculture Organization Penman-Monteith equation requires complete weather data, whereas empirical equations such as Hargreaves and Samani, Valiantzas, Priestley-Taylor, Makkink, and Stephens-Stewart require limited weather data. This work evaluated different empirical equations for West Texas using the standard FAO Penman-Monteith method and calibrated their parameters to improve ETo estimation. Detailed meteorological data from West Texas Mesonet and high resolution (800 m) Parameter-elevation Regressions on Independent Slopes Model (PRISM) datasets from 2007 to 2016 were used. Daily ETo calculated using the standard FAO Penman-Monteith equation was compared to ETo estimated based on different empirical methods. The results show that all original empirical equations underestimated ETo. Calibration improved the performance of tested equations; however, there seems to be underestimation of ETo in the 8–16 mm range. Overall, the monthly Hargreaves and Samani equation with either original or calibrated values of its parameters outperformed all tested models. This equation seems to be a reasonable estimator, especially under limited weather data conditions.

Estimating FAO Blaney-Criddle b-Factor Using Soft Computing Models

FAO Blaney-Criddle has been generally an accepted method for estimating reference crop evapotranspiration. In this regard, it is inevitable to estimate the b-factor provided by the Food and Agriculture Organization (FAO) of the United Nations Irrigation and Drainage Paper number 24. In this study, five soft computing methods, namely random forest (RF), M5 model tree (M5), support vector regression with the polynomial function (SVR-poly), support vector regression with radial basis function kernel (SVR-rbf), and random tree (RT), were adapted to estimate the b-factor. And Their performances were also compared. The suitable hyper-parameters for each soft computing method were investigated. Five statistical indices were deployed to evaluate their performance, i.e., the coefficient of determination (r2), the mean absolute relative error (MARE), the maximum absolute relative error (MXARE), the standard deviation of the absolute relative error (DEV), and the number of samples with an error greater than 2% (NE &gt; 2%). Findings reveal that SVR-rbf gave the highest performance among five soft computing models, followed by the M5, RF, SVR-poly, and RT. The M5 also derived a new explicit equation for b estimation. SVR-rbf provided a bit lower efficacy than the radial basis function network but outperformed the regression equations. Models’ Applicability for estimating monthly reference evapotranspiration (ETo) was demonstrated.

Optimized empirical model based on whale optimization algorithm for simulate daily reference crop evapotranspiration in different climatic regions of China

The accurate estimation of reference crop evapotranspiration (ET0) is of great significance to improve agricultural water use efficiency and optimize regional water resources management. At present, the applicability evaluation system of ET0 models is still lacking in several climate regions in China, leading to the confusion in application of the ET0 model in some specific regions. In this study, the daily meteorological data of 84 representative stations in four climate regions of China during the past 30 years (1991–2019) were selected to evaluate the ET0 simulation results of twelve empirical models (four temperature models, five radiation models, and three hybrid models) on the daily scale, and the optimal models suitable for each climate region were screened. Whale optimization algorithm (WOA) was used to optimize the optimal model to improve the simulation accuracy, and the ET0 results were compared with those predicted by extreme learning machine (ELM). The results showed that the estimation accuracy of the hybrid model was the best throughout China, followed by the radiation model, and the temperature model was relatively poor, with R2 ranges of 0.77–0.88, 0.60–0.86, and 0.58–0.82, respectively. Among the temperature-based models, Hargreaves-Samani and Improve Baier-Robertson model had the highest accuracy, with R2 of 0.80 and 0.79. Among the radiation-based models, Priestley-Taylor and Jensen-Haise models had the best accuracy, with R2 of 0.82 and 0.79. Among the hybrid models, Penman model had the highest accuracy, with R2 of 0.84. The accuracy of Hargreaves-Samani and Improve Baier-Robertson model in SMZ climate region was higher than TCZ, TMZ, and MPZ, and the accuracy of Jensen-Haise model in TCZ was the highest. The estimation accuracy of Priestley-Taylor and Penman models was similar in SMZ, TCZ, TMZ and MPZ. Using WOA to optimize the optimal temperature, radiation, and hybrid models, the prediction accuracy was improved by 12.05 %, 11.06 %, and 10.46 %, which were higher than the result of ELM model, with R2 of 0.90, 0.91, 0.95 and 0.90, respectively. Therefore, it is recommended to adopt WOA to optimize the empirical model to estimate the ET0 all over China.

Prediction Model for Daily Reference Crop Evapotranspiration Based on Hybrid Algorithm in Semi-Arid Regions of China

The accurate estimation of reference crop evapotranspiration (ETO) plays an important role in guiding regional water resource management and crop water content research. In order to improve the accuracy of ETO prediction in regions with missing data, this study used the partial correlation analysis method to select factors that have a large impact on ETO as input combinations to construct ETO estimation models for typical stations in semi-arid regions of China. A biological heuristic optimization algorithm (Golden Eagle optimization algorithm (GEO) and Sparrow optimization algorithm (SSA)) and Extreme Learning Machine model (ELM) were combined to improve the estimation accuracy. The results showed that Ra was the primary factor affecting the ETO model, with an importance range of 0.187–0.566. Compared with the independent ELM model, the hybrid model has higher accuracy and stability. The estimated value of the SSA-ELM model under five-factor input condition (Ra, RH, Tmax, Tmin, U2) is closest to the standard value calculated by FAO56 PM: RMSE = 0.067–0.085, R2 = 0.998–0.999, MAE = 0.050–0.066 and NSE = 0.998–0.999. In general, the combination of a partial correlation analysis algorithm and a hybrid model can be used to estimate ETO with high accuracy under the condition of reducing input factors. Use of the first five factors extracted from the partial correlation analysis algorithm as input to build an ETO estimation model based on SSA-ELM in China’s semi-arid regions is recommended, which can also provide a reference for ETO estimation in similar regions.

Splitting and Length of Years for Improving Tree-Based Models to Predict Reference Crop Evapotranspiration in the Humid Regions of China

To improve the accuracy of estimating reference crop evapotranspiration for the efficient management of water resources and the optimal design of irrigation scheduling, the drawback of the traditional FAO-56 Penman–Monteith method requiring complete meteorological input variables needs to be overcome. This study evaluates the effects of using five data splitting strategies and three different time lengths of input datasets on predicting ET0. The random forest (RF) and extreme gradient boosting (XGB) models coupled with a K-fold cross-validation approach were applied to accomplish this objective. The results showed that the accuracy of the RF (R2 = 0.862, RMSE = 0.528, MAE = 0.383, NSE = 0.854) was overall better than that of XGB (R2 = 0.867, RMSE = 0.517, MAE = 0.377, NSE = 0.860) in different input parameters. Both the RF and XGB models with the combination of Tmax, Tmin, and Rs as inputs provided better accuracy on daily ET0 estimation than the corresponding models with other input combinations. Among all the data splitting strategies, S5 (with a 9:1 proportion) showed the optimal performance. Compared with the length of 30 years, the estimation accuracy of the 50-year length with limited data was reduced, while the length of meteorological data of 10 years improved the accuracy in southern China. Nevertheless, the performance of the 10-year data was the worst among the three time spans when considering the independent test. Therefore, to improve the daily ET0 predicting performance of the tree-based models in humid regions of China, the random forest model with datasets of 30 years and the 9:1 data splitting strategy is recommended.

Resolving data-hungry nature of machine learning reference evapotranspiration estimating models using inter-model ensembles with various data management schemes

Over the past decade, there has been an increasing research on the use of machine learning tools for estimating reference crop evapotranspiration (ETo). However, due to the data-hungry nature of the machine learning models, all of these researches are not suitable for regions with limited data supply. This study aims to provide a breakthrough for the bottleneck through coupling of the inter-model ensemble with various data management schemes. The Bayesian modeling approach and a non-linear neural ensemble based inter-model ensemble (BMA-E and NNE-E) were developed locally with data from five different meteorological stations in the Peninsular Malaysia. The NNE-E was found to be highly robust spatially, whereby it can be used to estimate daily ETo accurately at other stations, even though with reduced input meteorological parameters. However, the performances of the locally trained models were found wanting and were fluctuating violently. This was resolved through creating a data pool that include the data from all stations and developing a universal NNE. By following the proposed scheme of things, the daily ETo can be easily estimated across the whole Peninsular Malaysia. This being, without the need for historical data and new models at estimation site.

Prediction model for daily reference crop evapotranspiration based on hybrid algorithm and principal components analysis in Southwest China

Accurately estimating reference crop evapotranspiration (ETo) is crucial for water resource management and precise irrigation. The FAO-56 Penman–Monteith model has the highest accuracy in terms of ETo prediction, but its application is restricted by a lack of complete meteorological data. To develop a high accuracy prediction model for ETo with incomplete meteorological data, this study used four principal component analysis methods (i.e. path analysis, stepwise linear regression analysis, logistic regression analysis and factor analysis) to determine few factors that strongly affect ETo as the input to established the ETo model with machine learning (ML). The prediction model for ETo was established using support vector machine (SVM), gradient boosting decision tree (GBDT), particle swarm optimisation (PSO)- SVM, and PSO-GBDT algorithms. This study demonstrated that SVM, GBDT, PSO-SVM and PSO-GBDT models can maintain the highest accuracy by using the five most important affect factors extracted on the basis of path analysis (PA) as input, for various models, the precision ranges of NSE, R2, RMSE, MAE, and GPI were approximately 0.53–0.70, 0.63–0.84, 0.27–0.47, 0.27–0.69, and 0.72–1.01 respectively. The accuracy of SVM and GBDT significantly improved through optimisation using PSO. When inputting the top five factors of importance extracted by PA algorithm in each model, the SVM and GBDT model optimized by PSO algorithm increased the average value of GPI by 17.74% and 46.71% respectively. When inputting the top five factors extracted by the PA algorithm in PSO-GBDT, the average value of NSE, R2, RMSE and MAE is 22.37%, 2.83%, 9.05% and 6.84% higher than that of PSO-SVM, and the GPI is 8.30% higher than that of PSO-SVM. This study shows that the ETo prediction model constructed by the PSO-GBDT algorithm can obtain the highest accuracy when the top five factors extracted by the PA algorithm are used as input. This provides a reference for ETo estimation in Southwest China.

Extreme learning machine for reference crop evapotranspiration estimation: Model optimization and spatiotemporal assessment across different climates in China

Accurate estimation of reference crop evapotranspiration (ETo) is critical for quantifying crop water requirements and irrigation schedule design. This study proposed two optimization methods, i.e., particle swarm optimization (PSO) and genetic algorithm (GA), to determine the input weights and hidden biases of extreme learning machine (ELM), and developed two novel hybrid GA-ELM and PSO-ELM models for ETo estimations with limited input data. A temporal and spatial scanning strategy that can avoid misleading or partially valid results was applied to train and test the models, using daily climatic data during 1994–2016 from 96 meteorological stations across various climates of China. The results revealed that GA-ELM and PSO-ELM could quantify ETo on daily, monthly, and annual time scales, with GA-ELM (with model efficiency ranging from 0.80 to 0.97) performing better than PSO-ELM (with model efficiency ranging from 0.70 to 0.93) in all climates. The temperature-based GA-ELM only with air temperature data as forcing input has relatively accurate ETo estimates across different environments, and can be recommended as an alternative method when radiation data are not available. Spatial assessment reveals that the machine learning models trained by external data also offer accurate ETo estimates, confirming the applicability of models for ETo estimations elsewhere without the model training or when local data for model training are unavailable. Overall, the GA-ELM model provides accurate ETo estimates on various time scales and exhibits superior performance than the PSO-ELM model, and thus can be recommended for ETo estimations using limited data as model forcing in different climates of China. Our work presents a novel method for accurate ETo estimations with limited data, which has practical implications in regional agricultural water management.

Comparison of four bio-inspired algorithms to optimize KNEA for predicting monthly reference evapotranspiration in different climate zones of China

Accurate estimation of reference crop evapotranspiration (ET0) is of great significance to crop water use and agricultural water resources management. This study evaluated the performance of four bio-inspired algorithm optimized kernel-based nonlinear extension of Arps decline (KNEA) models, namely KNEA with grasshopper optimization algorithm (GOA-KNEA), KNEA with grey wolf optimizer algorithm (GWO-KNEA), KNEA with particle swarm optimization algorithm (PSO-KNEA), and KNEA with salp swarm algorithm (SSA-KNEA), on estimating monthly ET0 across China. Monthly meteorological data [including maximum air temperature (Tmax), minimum air temperature (Tmin), extra-terrestrial solar radiation (Ra), relative humidity (RH), global solar radiation (Rs), wind speed (U)] during 1966–2015 from 51 weather stations across the seven different climate zones of China were used for model training and testing. Four different combinations of meteorological data were applied as model input, and results from the FAO-56 Penman-Monteith formula were used as a control. Results showed that the GWO-KNEA model overall performed better than the other three coupling models, of which the GWO-KNEA2 model (i.e., the model with input combination 2) was the best (on average R2 = 0.9814, RMSE = 0.2143 mm d−1). The convergence rate and the population size of the GWO-KNEA model were also superior to the other three models. Among input combinations, models with combination 2 had the best overall performance, while models with combination 3 were the worst on average. In terms of the importance of each meteorological parameter contributing to model accuracy, Rs was greater than Ra, RH, or U. Among different climate zones, station specific models in the semi-arid steppe of Inner Mongolia showed the best estimating performance in general, while models in the Qinghai-Tibetan Plateau overall performed relatively poorly. The GOA-KNEA and SSA-KNEA models with the combination 4 showed large increases (29.7% and 28.7%, respectively), indicating a problem of overfitting. Conversely, the GWO-KNEA model was the most stable model with the smallest increase in RMSE during the testing phase (4.4–15.7%) among all models. In summary, taking the model's estimation accuracy, stability, convergence rate, and climate environment into account, our results suggest that GWO-KNEA would be a suitable model for estimating ET0 in different climate zones of China and the most practical input combination would be combination 2.

Comparison of neural network models for estimation of reference crop evapotranspiration

Reference evapotranspiration (ETo) is important component in calculation of crop water requirements, climatological and hydrological studies. However, it is a nonlinear dynamic and complex process. Artificial neural network (ANN) techniques are powerful to accurately map complex and nonlinear input output relationships. Penman-Monteith (P-M) model is sole standard method for estimation of ETo but it requires many kinds of weather data. Hence it was planned to test an ANN technique for estimating the ETo with limited and full data for Kolhapur region, Maharashtra, India. The five ANN models were developed by different combinations of meteorological parameters as neurons in input layer with varying neurons in middle layer and one neuron in the output layer i.e. ETo by P-M method. These are ANN1 (Pan evaporation); ANN2 (Tmax. and Tmin.); ANN3 (Tmax.,Tmin and SSH); ANN4 (Tmax., Tmin., RHmax., RHmin., and SSH) and ANN5 (Tmax., Tmin., RHmax., RHmin., SSH and WS). During training mode, it was observed that ANN5 model showed the best values of all performance measures i.e. correlation coefficient (0.997), index of agreement (0.998), efficiency coefficient (0.993),root mean square error (0.100), mean absolute error (0.059), mean absolute percentage error (2.076) due to full data. Under limited data condition, it was observed that the results of all performance measure (ANN1 to ANN4) models varied in the range as correlation coefficient (0.929 to 0.967), index of agreement (0.962 to 0.983), root mean square error (0.317 to 0.460), mean absolute error (0.194 to 0.297), mean absolute percentage error (6.027 to 9.679) and efficiency coefficient (0.863 to 0.934) in training mode. It can be seen that all limited data models demonstrate relatively very close performances based on statistical criteria. Similar kind of close differences for each performance measure were observed during validation stage of all ANN models. Results indicated that all ANN models satisfy performance criteria well in training and validation mode and can be generalized for prediction of ETo values. Overall, the performance suggests that ANN models can be an accepted for accurate prediction of ETo values for Kolhapur region as per data availability.

Improved Hargreaves Model Based on Multiple Intelligent Optimization Algorithms to Estimate Reference Crop Evapotranspiration in Humid Areas of Southwest China

Reference crop evapotranspiration (ET0) is an important indicator for precise regulation of crop water content, irrigation forecast formulation, and regional water resources management. The Hargreaves model (HG) is currently recognized as the simplest and most effective ET0 estimation model. To further improve the prediction accuracy of the HG model, this study is based on the data of 98 meteorological stations in southwest China (1961–2019), using artificial bee colony (ABC), differential evolution (DE) and particle swarm optimization (PSO) algorithms to calibrate the HG model globally. The standard ET0 value was calculated by FAO-56 Penman–Monteith (PM) model. We compare the calculation accuracy of 3 calibrated HG models and 4 empirical models commonly used (Hargreaves, Priestley–Taylor, Imark–Allen and Jensen–Hais). The main outcomes demonstrated that on a daily scale, the calibrated HG models (R2 range 0.74–0.98) are more accurate than 4 empirical models (R2 range 0.55–0.84), and ET0-PSO-HG has the best accuracy, followed by ET0-ABC-HG and ET0-DE-HG, with average R2 of 0.83, 0.82 and 0.80, average RRMSE of 0.23 mm/d, 0.25 mm/d and 0.26 mm/d, average MAE of 0.52 mm/d, 0.53 mm/d and 0.57 mm/d, and average GPI of 0.17, 0.05, and 0.04, respectively; on a monthly scale, ET0-PSO-HG also has the highest accuracy, followed by ET0-ABC-HG and ET0-DE-HG, with median R2 of 0.96, 0.95 and 0.94, median RRMSE of 0.16 mm/d, 0.17 mm/d and 0.18 mm/d respectively, median MAE of 0.46 mm/d, 0.50 mm/d, and 0.55 mm/d, median GPI of 1.12, 0.44 and 0.34, respectively. The calibrated HG models (relative error of less than 10.31%) are also better than the four empirical models (relative error greater than 16.60%). Overall, the PSO-HG model has the most accurate ET0 estimation on daily and monthly scales, and it can be suggested as the preferred model to predict ET0 in humid regions in southwest China regions.