Prediction model for reference crop evapotranspiration based on the back-propagation algorithm with limited factors

Prediction model for reference crop evapotranspiration based on the back-propagation algorithm with limited factors | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Prediction model for reference crop evapotranspiration based on the back-propagation algorithm with limited factors Long Zhao, Liwen Xing, Yuhang Wang, Ningbo Cui, Hanmi Zhou, Yi Shi, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1671161/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Feb, 2023 Read the published version in Water Resources Management → Version 1 posted 5 You are reading this latest preprint version Abstract The accurate estimation of reference crop evapotranspiration (ET O ) is vital for regional water and irrigation water resource management and is beneficial to the rational allocation of regional water resources, and alleviates the disparity between water supply and demand. This study accurately estimates the ET O of 14 meteorological stations in southern China. Five neural network models (back-propagation neural network [BP], extreme learning machine [ELM], ant colony optimization [ACO]-BP, bird swarm algorithm [BSA]-BP, cat swarm optimization [CSO]-BP) were introduced to predict ET O with limited factors using different methods. The results demonstrated that models inputting T (maximum, minimum and average 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 (U 2 ) and average atmospheric pressure (AP) in relation to ET O gradually decreased. All the three biological heuristic algorithms effectively improved the performance 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 ET O prediction in southern China. This result provided a reference for the more accurate prediction of ET O for future irrigation decision-making and water resource management in southern China. Back-propagation neural network Hybrid optimization algorithm Reference evapotranspiration Southern China Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1 Introduction The reference crop evapotranspiration (ET O ) is critical in determining crop water requirements (Gocić and Arab Amiri 2021). To obtain accurate ET O for agricultural water management, the Food and Agriculture Organization (FAO) suggested the use of the Penman-Monteith (Cunha et al. 2021 Maqsood et al. 2022 ) model (FAO-56 PM). FAO-56 PM is a semi-empirical and semi-physical model for ET O calculations but requires multiple input parameters, such as the maximum (T max ), minimum (T min ), average temperature (T ave ), average wind speed (U), relative humidity (RH) and sunshine duration (n). However, many areas lack modern weather stations, and comprehensive meteorological data can be challenging, so it is difficult to estimate the ET O accurately. Therefore, improving ET O simulation accuracy has become a research highlight of recent studies without input data. Many studies have recently constructed simple input models for ET O prediction, such as temperature-based and radiation-based models (Rodrigues et al. 2021). Although empirical models have been widely employed for estimating ET O , they are challenging to handle intricacy and nonlinear relationships between independent and dependent variables. With the development of artificial intelligence technology, machine learning (ML) for managing nonlinear problems has improved model performance considerably (Zhao et al. 2021 ). Zhang et al. ( 2018 ) tested the adaptability of an ET O model constructed using three ML algorithms, namely the support vector machine (SVM), back-propagation neural network (BP) and adaptive neuro-fuzzy inference system (ANFIS), and the results demonstrated that the models have good applicability for predicting ET O . Wu et al. (2019a) evaluated eight ML models for predicting daily ET O with a small number of meteorological parameters in different climatic regions of China. They found that SVM models have high accuracy and stability. Bellido-Jiménez et al. ( 2020 ) selected several temperatures-based ML models to estimate ET O in the semi-arid region of Andalusia, and the results showed that extreme learning machine (ELM) models have high performance in predicting ET O . The ML models have satisfactory performances with single input factors, and numerous studies have reported that the accuracy of ML models is generally higher than that of empirical models in estimating ET O . Zhu et al. ( 2020 ) successfully predicted daily ET O with limited meteorological data using different ML models along with six empirical models (Priestley-Taylor, Makkink, Imark, Hargreaves-Samani (HS), Dalton and Trabert), achieving satisfying results. dos Santos Farias et al. ( 2020 ) studied the performance of ML models and empirical models in a Brazilian agricultural frontier with limited meteorological data, and ML models show a better performance than empirical models with the same climatological variables. However, ML algorithms can be problematic, and the algorithm parameters are not necessarily optimal, limiting the constructed model's prediction accuracy. Many scholars have employed optimization algorithms for ML algorithms. The results showed that RBFN is helpful in ML models estimating ET O with different input parameters. Wu et al. ( 2019b ) applied four bio-inspired algorithms to improve the accuracy of ELM models. They found that hybrid ELM models exhibited greater improvements in daily ET O prediction. Ahmadi et al. ( 2021 ) employed a novel model via intelligent water drops and support vector regression to predict ET O . Results showed that it performed best among all ML models and empirical models. The optimization algorithms have improved ML models to estimate ET O , and the hybrid optimization algorithm was recommended to improve the ML models to estimate ET O . Along with another optimization algorithm, research has frequently reported that the three optimization algorithms of ant colony optimization (ACO), bird swarm algorithm (BSA) and cat swarm optimization (CSO) exhibit more favorable optimization effects. Wang et al. ( 2020 ) indicated that optimization with BSA markedly improved the performance of the SVM model compared with particle swarm optimization (PSO) and the genetic algorithm (GA); however, the BSA had higher stability and robustness. Huang et al. ( 2020 ) observed that CSO resulted in higher accuracy than PSO in predicting rock fragmentation. Southern China is a crucial grain production area. This region is largely subject to a tropical monsoon climate with abundant rainfall. Its topographical conditions are complex; precipitation's climatic conditions and temporal and spatial distribution in different regions differ considerably. Therefore, the efficient use of agricultural water in the southern region is crucial. This paper inputs various parameter combinations into BP, ELM, ACO-BP, BSA-BP and CSO-BP models to construct an ET O prediction model for typical stations in southern China. The study aims were as follows: (1) to determine the influence of different input combinations on daily ET O prediction, (2) to develop five ML models (BP, ELM, ACO-BP, BSA-BP and CSO-BP) for daily ET O prediction with limited factors and (3) to compare the prediction accuracy and adaptability of the five models in southern China. 2 Materials And Methods 2.1 Study area and data sets This study analyzed data from 14 stations (Wenjiang, Kunming, Wuhan, Shapingba, Changsha, Guiyang, Nanjing, Hefei, Hangzhou, Nanchang, Xiamen, Guangzhou, Nanning and Haikou) in southern China (Fig. 1 : 18–35°N, 98–122°E), with a subtropical, tropical monsoon climate. Because of the monsoon effects, the annual precipitation variation in southern China is large. The availability of water resources is changeable; the high rainfall in summer and autumn and the low rainfall in winter and spring can lead to summer waterlogging and spring droughts, respectively. The meteorological data used in this study were extracted from the China Meteorological Data Network ( http://data.cma.cn/ ) daily dataset from 1960 to 2019 and included T, U, n, RH and average atmospheric pressure (AP). The datasets of the 14 stations were of high quality. The k-fold method is used to divide the data set, which randomly divides the data into two subsets, i.e., the Training and Testing dataset. The k value is set to 10; that is, the data is divided into ten parts, and nine parts are taken in turn as training, one part is used for testing, and the average of the results is taken as the estimation (Fan et al. 2018 ). 2.2 FAO-56 PM equation The daily ET O is calculated using the following FAO-56 PM equation: $$\text{E}{\text{T}_\text{O}}=\frac{{0.408\Delta (Rn - G)+\gamma \frac{{900}}{{{T_{mean}}+273}}{U_2}({e_s} - {e_a})}}{{\Delta +\gamma (1+0.34{U_2})}}$$ 1 Where \({\Delta }\) is the slope of the vapor pressure curve (kPa ℃ −1 ), \({R}_{n}\) is the solar net radiation (MJ m − 2 day − 1 ), \(G\) is the soil heat flux density (MJ m − 2 day − 1 ), \(\gamma\) is the psychrometric constant (kPa °C − 1 ), \({T}_{mean}\) is the mean air temperature (°C), \({U}_{2}\) is the wind speed at 2 m (m/s), \({e}_{s}\) is saturated vapor pressure (kPa), \({e}_{a}\) is the actual vapor pressure (kPa). 2.3 Different machine learning for predicting daily reference crop evapotranspiration This study uses eleven combinations (Table 1 ) based on different meteorological data inputs for different ML models to predict the daily ET O . Various studies have indicated that temperature factors T (average, maximum and minimum temperature) affect ET O (Xing et al. 2016 ). Therefore, T is selected for the first three inputs of the model in this study. A flowchart of the daily ET O prediction process applied in this study is depicted in Fig. 2 . To address the shortcomings of the traditional BP algorithm, this applies the ACO, BSA and CSO algorithms to optimize the initial weights of the BP algorithm, and the BP algorithm is established with the respective optimization models, after this referred to as the ACO-BP, BSA-BP and CSO-BP algorithms. The program code is written in MATLAB software, version R2020b. All the simulations were performed in a computer with Intel® Core TM i7-10700K CPU @ 3.80 GHz and 16 GB RAM. 2.3.1 Back-Propagation neural network The BP algorithm, also known as the error back-propagation algorithm, is a multilayer forward neural network. The function of a finite number of discontinuous points is approximated through an input layer and an output layer, and several hidden layers. Effectively solve the learning problem of the hidden layer neuron connection weights. More details can be found in Yan et al. (2020). 2.3.2 Extreme learning machine The ELM is a learning algorithm based on single hidden layer feedforward neural networks that can directly approximate nonlinear mapping with input data; this is useful for many natural and artificial methods that are difficult to manage using classical parameterization methods. With the presence of the neural networks in the models, the hidden layer node parameters of the algorithm can be randomly or artificially provided without adjustment; the learning speed is fast, and generalizability is high. For more information about the ELM model refer to Huang et al. ( 2006 ). 2.3.3 Ant colony optimization algorithm ACO is an intelligent optimization algorithm that simulates ant colony foraging behavior. Ants communicate through pheromones when searching for food; the shorter the path, the greater the concentration of information and the probability of choosing the path. Over time, more ants choose the shorter path from the food source to the ant nest. Based on this natural phenomenon, the ACO algorithm exhibits high robustness, parallelism and favorable characteristics, and can determine a globally optimal solution quickly. More details about the ACO can be found in (Laura et al. 2008 ; Fakhar et al. 2018). 2.3.4 Bird swarm algorithm The BSA optimizes the BP neural network through the following steps (Elif et al. 2020): The global search capability of the BSA is utilized to optimize the initial weights and thresholds the BP neural network. Each group of decision variables is contained in the spatial position of each bird in the flock. The fitness function is used to measure the superiority of the individual’s spatial position. An individual’s spatial position is continuously updated using behavioral strategies such as those related to foraging, vigilance, and flying until the foraging process of the flock is optimized. For details on the algorithm, please refer to Meng et al ( 2016 ) 2.3.5 Cat swarm optimization algorithm CSO (Lin et al. 2016 ) is a swarm intelligence algorithm proposed by observing the behavior of cats, which consists of tracking mode and finding mode. It optimizes the BP neural network's input and hidden layers, the connection weights between the hidden and output layers, and the threshold for each layer. The details can be found in (Chu et al. 2006 ). 2.4 Model prediction evaluation The coefficient of determination (R 2 ), relative root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe coefficient (NSE) and Global performance indicator (GPI)were used to evaluate the performances of the models (Feng et al. 2018 ; Agrawal et al. 2022 ). $$\text{R}\text{M}\text{S}\text{E}=\sqrt {\frac{1}{n}\mathop \sum \limits_{{i=1}}^{n} {{\left( {{Y_i} - {X_i}} \right)}^2}}$$ 2 $${\text{R}^2}=\frac{{{{\left[ {\mathop \sum \nolimits_{{i=1}}^{n} \left( {{X_i} - \bar {X}} \right)\left( {{Y_i} - \bar {Y}} \right)} \right]}^2}}}{{\mathop \sum \nolimits_{{i=1}}^{n} {{\left( {{X_i} - \bar {X}} \right)}^2}\mathop \sum \nolimits_{{i=1}}^{n} {{\left( {{Y_i} - \bar {Y}} \right)}^2}}}$$ 3 $$\text{M}\text{A}\text{E}=\frac{1}{n}\mathop \sum \limits_{{i=1}}^{n} \left| {{y_i} - {x_i}} \right|$$ 4 $$\text{N}\text{S}\text{E}=1 - \frac{{\mathop \sum \nolimits_{{i=1}}^{n} {{\left( {{X_i} - {Y_i}} \right)}^2}}}{{\mathop \sum \nolimits_{{i=1}}^{n} {{\left( {{Y_i} - \bar {Y}} \right)}^2}}}$$ 5 $$\text{G}\text{P}\text{I}={\alpha _j}\mathop \sum \nolimits_{{i=1}}^{4} (\mathop T\nolimits_{j} - \mathop {\bar {T}}\nolimits_{j} )$$ 6 where \({X}_{i}\) and \({Y}_{i}\) are the simulated and measured values, respectively; n is the number of measured values; \(\stackrel{-}{ x}\) and \(\stackrel{-}{y}\) the means of the simulated and measured values. \({T}_{j}\) is the normalized value of the RMSE, MAE, R 2 and NSE, \({\stackrel{\text{̄}}{\text{T}}}_{j}\) is the median of the corresponding parameter when \({T}_{j}\) is the RMSE and MAE, \({\alpha }_{j}\) is − 1, or 1 otherwise. The closer R 2 is to 1, the more accurate the prediction ability of the model, and the smaller the value of the MAE and RMSE, the smaller the simulation error. The closer the NSE is to 1, the higher the model quality and credibility. The higher the GPI, the more effective the overall simulation effect of the model. 3 Results And Discussion 3.1 Evaluation of different meteorological data combinations for daily reference crop evapotranspiration prediction The performance of the different daily ET O estimation models using different meteorological data combinations is presented in Table 1 . The CSO-BP model showed the best accuracy performance across all input combinations, but the BP model performed poorly in accuracy. When three factors are input, the mean ranges of RMSE, R 2 , MAE and NSE of the constructed model are 0.586–0.745 mm d − 1 , 0.774–0.842, 0.445–0.571 mm d − 1 and 0.750–0.842, respectively. When adding an input factor, the model accuracy is improved. The highest accuracy is C3, indicating that the influence of n is greater than that of other factors. Combined with the input of only the temperature factor, it can be known that as input, the meteorological factors that have the greatest impact on the model are in descending order of T, n, RH, U 2 and AP. Four input factors, the mean ranges of RMSE, R 2 , MAE and NSE of the constructed model are 0.391–0.708 mm d − 1 , 0.792–0.930, 0.293–0.547 mm d − 1 and 0.774–0.930, respectively. When five factors are input, the mean ranges of RMSE, R 2 , MAE and NSE of the constructed model are 0.326–0.697 mm d − 1 , 0.805–0.952, 0.249–0.548 mm d − 1 and 0.776–0.952, respectively. A fifth input factor is introduced to generate the most accurate input combination C11, compared to other combinations; it can be seen that the contribution of n to ET O is higher than the superposition of other factors, and a consistent conclusion can be obtained for RH. The variable analysis heatmap obtained by performing a Pearson correlation analysis matrix on the input is shown in Fig. 3 . The overall results in the southern region show that other factors except RH and AP are positively correlated with ETo. The absolute value of the correlation is the largest for T max and the smallest for AP, which is consistent with the results obtained by the different input models constructed above. This study confirmed that the ML models with T, n and RH factor inputs exhibited the optimal performance for daily ET O prediction. The meteorological factors, as input, that revealed the most influence on the model are, in descending order, T, n, RH, U 2 and AP. Through the different divisions of the factor input combination, it can produce less input, which is better than adding more input. It is significant in terms of reducing input requirements and reducing computational costs. After revealing the influence of variables on the model results, consistent results can be obtained by using Pearson correlation analysis. Therefore, correlation analysis is recommended to verify variable selection, and feature selection algorithms can be used to study input factors in follow-up research further. Table 1 The performance of machine learning models with different combinations of input parameters Input RMSE (mm d − 1 ) R 2 MAE (mm d − 1 ) NSE GPI C1: T BP1 0.745 0.774 0.571 0.750 -0.591 ELM1 0.631 0.824 0.478 0.823 0.095 ACO-BP1 0.603 0.834 0.457 0.834 0.251 BSA-BP1 0.602 0.835 0.454 0.835 0.237 CSO-BP1 0.586 0.842 0.445 0.842 0.329 C2: T, RH BP2 0.690 0.829 0.547 0.785 -0.203 ELM2 0.524 0.875 0.395 0.875 0.701 ACO-BP2 0.509 0.883 0.382 0.883 0.780 BSA-BP2 0.512 0.882 0.384 0.882 0.794 CSO-BP2 0.500 0.887 0.374 0.887 0.841 C3: T, n BP3 0.645 0.856 0.508 0.812 0.088 ELM3 0.417 0.921 0.303 0.918 1.284 ACO-BP3 0.398 0.928 0.297 0.928 1.374 BSA-BP3 0.399 0.929 0.299 0.929 1.369 CSO-BP3 0.391 0.930 0.293 0.930 1.399 C4: T, U 2 BP4 0.696 0.792 0.537 0.777 -0.325 ELM4 0.580 0.851 0.436 0.851 0.408 ACO-BP4 0.539 0.867 0.407 0.867 0.532 BSA-BP4 0.555 0.862 0.420 0.861 0.609 CSO-BP4 0.522 0.875 0.394 0.875 0.705 C5: T, AP BP5 0.708 0.802 0.547 0.774 -0.341 ELM5 0.615 0.835 0.466 0.834 0.205 ACO-BP5 0.593 0.841 0.446 0.841 0.257 BSA-BP5 0.602 0.836 0.451 0.835 0.309 CSO-BP5 0.543 0.864 0.407 0.864 0.588 C6: T, n, U 2 BP6 0.618 0.881 0.488 0.824 0.271 ELM6 0.347 0.946 0.264 0.946 1.607 ACO-BP6 0.335 0.949 0.255 0.949 1.645 BSA-BP6 0.339 0.948 0.259 0.948 1.660 CSO-BP6 0.332 0.951 0.252 0.951 1.682 C7: T, n, AP BP7 0.618 0.877 0.486 0.823 0.258 ELM7 0.395 0.929 0.294 0.929 1.385 ACO-BP7 0.385 0.933 0.287 0.933 1.431 BSA-BP7 0.385 0.932 0.288 0.932 1.435 CSO-BP7 0.376 0.935 0.280 0.935 1.476 C8: T, RH, U 2 BP8 0.661 0.830 0.512 0.801 -0.053 ELM8 0.481 0.896 0.362 0.895 0.944 ACO-BP8 0.461 0.904 0.343 0.904 1.036 BSA-BP 0.465 0.902 0.345 0.902 1.054 CSO-BP8 0.453 0.907 0.336 0.907 1.100 C9: T, U 2 , AP BP9 0.697 0.805 0.547 0.776 -0.313 ELM9 0.565 0.857 0.429 0.856 0.474 ACO-BP9 0.538 0.869 0.405 0.869 0.590 BSA-BP9 0.545 0.865 0.407 0.865 0.628 CSO-BP9 0.517 0.877 0.389 0.877 0.733 C10: T, RH, n BP10 0.566 0.900 0.455 0.851 0.538 ELM10 0.339 0.948 0.261 0.948 1.641 ACO-BP10 0.332 0.951 0.253 0.951 1.664 BSA-BP10 0.335 0.950 0.257 0.950 1.679 CSO-BP10 0.326 0.952 0.249 0.952 1.703 C11: T, RH, AP BP11 0.687 0.851 0.548 0.785 -0.139 ELM11 0.523 0.877 0.394 0.877 0.717 ACO-BP11 0.501 0.887 0.373 0.887 0.817 BSA-BP11 0.506 0.885 0.376 0.884 0.845 CSO-BP11 0.489 0.893 0.362 0.893 0.916 Note: best statistical indicators among all models are marked in bold. 3.2 Statistical performance of different machine learning models for daily reference crop evapotranspiration prediction The accuracy comparison of five different ML models in the southern region is shown in Fig. 4 . The information given in the figure shows differences in the performance of different models. In terms of RMSE and MAE, the BP model has the highest median line, followed by ELM, indicating that the ELM algorithm is better than BP. However, the optimized BP model shows better accuracy than ELM in model evaluation. The CSO-BP midline is the lowest, indicating that the results are the most satisfactory among all models. In comparison, the ACO-BP accuracy is slightly better than that of BSA-BP. R 2 and NSE are opposite to RMSE and MAE in the evaluation model; that is, the higher the median line, the better the model accuracy, and R 2 and NSE give the same results as RMSE and MAE when evaluating five models. The medians of RMSE, R 2 , MAE and NSE of CSO-BP were 0.446 mm d − 1 , 0.905, 0.333 mm d − 1 and 0.905, respectively. The medians of RMSE, R 2 , MAE and NSE of ACO-BP were 0.468 mm d − 1 , 0.900, 0.346 mm d − 1 and 0.900, respectively. The medians of RMSE, R 2 , MAE and NSE of BSA-BP were 0.473 mm d − 1 , 0.899, 0.348 mm d − 1 and 0.899, respectively. The medians of RMSE, R 2 , MAE and NSE of ELM were 0.487 mm d − 1 , 0.893, 0.362 mm d − 1 and 0.892, respectively. The medians of RMSE, R 2 , MAE and NSE of BP were 0.687 mm d − 1 , 0.851, 0.533 mm d − 1 and 0.805, respectively. Compared with the BP model, the most satisfactory CSO-BP model has a 34.979% and 37.659% reduction in the median of RMSE and MAE and a 6.425% and 12.435% improvement in R2 and NSE, respectively. Table 2 lists the average calculation cost (time used for calculation) for the different models. The results show that the average time consumed by the BP model with different combinations of factors is at most 0.67 s. The ELM model had the lowest time cost among the five models, and the time cost of varying input factors ranged from 0.02 to 0.03 s. Among the three hybrid models, the time costs of the ACO-BP and BSA-BP were relatively close at 32.38 to 45.13 s and 37.25 to 45.51 s, respectively; that of the CSO-BP was the lowest among the hybrid models, with an average running time of 4.14 to 7.25 s. In the BP algorithm, the gradient descent method requires multiple iterations to modify the weights and thresholds, and the training speed is therefore slow. Zhang et al. ( 2018 ) combined remote sensing data with an ML algorithm and applied the BP machine algorithm to establish an ET O estimation model of spatial distribution. The results revealed that the BP algorithm had lower prediction accuracy for ET O prediction than models such as the artificial neural network, SVM and ANFIS. The BP model sinks into the local optimum easily and cannot reach the global minimum. The ELM algorithm does not require weights or threshold adjustment during the training process. Still, it only adjusts the number of neurons in the hidden layer to obtain the only optimal solution. Therefore, the accuracy of the ELM model is higher than that of the BP model. Optimization algorithms can markedly improve the simulation accuracy of ML models. Arora et al. ( 2021 ) used the ANIFS algorithm to optimize the GA to predict flood sensitivity, significantly improving the model’s accuracy with the optimized algorithm. This study used ACO, BSA and CSO to optimize the BP model. Among the three hybrid models, CSO-BP had the highest accuracy. These optimization algorithms show satisfactory optimization results for the BP model. CSO-BP is more accurate than the other two optimization algorithms, mainly because the CSO algorithm has a dynamic grouping mechanism to avoid the algorithm falling into local optimum. The optimization algorithm has the advantages of fewer control parameters, fast convergence speed and high robustness, and the optimized model has higher accuracy. The other two optimization algorithms may face being trapped in local optima and slow to converge, affecting their performance (Zhang et al. 2020 ). Table 2 Computational costs of the different models with different parameter combinations (s) Input BP ELM ACO-BP BSA-BP CSO-BP C1 0.60 ± 0.25 0.02 ± 0.01 35.53 ± 1.12 37.25 ± 4.52 4.14 ± 0.62 C2 0.50 ± 0.11 0.03 ± 0.02 41.61 ± 1.64 37.63 ± 5.31 4.62 ± 0.59 C3 0.53 ± 0.17 0.03 ± 0.01 38.42 ± 1.25 40.99 ± 4.65 4.72 ± 0.63 C4 0.55 ± 0.16 0.03 ± 0.01 39.18 ± 4.28 39.31 ± 5.06 4.76 ± 0.51 C5 0.58 ± 0.17 0.03 ± 0.00 36.13 ± 0.98 41.67 ± 4.57 4.68 ± 1.03 C6 0.48 ± 0.10 0.03 ± 0.00 32.47 ± 1.18 39.17 ± 5.42 5.20 ± 1.46 C7 0.55 ± 0.17 0.03 ± 0.01 32.33 ± 1.26 38.18 ± 4.76 7.25 ± 1.57 C8 0.67 ± 0.22 0.03 ± 0.01 33.61 ± 0.81 45.51 ± 3.97 6.51 ± 0.89 C9 0.57 ± 0.28 0.03 ± 0.01 45.12 ± 2.36 38.23 ± 4.12 5.92 ± 0.74 C10 0.43 ± 0.10 0.03 ± 0.01 45.12 ± 2.90 41.36 ± 6.45 6.38 ± 0.86 C11 0.47 ± 0.12 0.03 ± 0.01 33.52 ± 4.07 42.67 ± 4.31 6.32 ± 0.68 3.3 Comparison of reference crop evapotranspiration models by GPI To use as little meteorological data as possible to build a prediction model for ET O and to evaluate the generalizability of the model, we used the meteorological data of 14 meteorological stations to construct a model based on five types of machine learning (BP, ELM, ACO-BP, BSA-BP, CSO-BP) prediction model. Although four evaluation metrics are used, none of them can be used individually to judge the performance of the selected model. Therefore, this study further applied the performance of the GPI comprehensive evaluation model in predicting ET O , and the results are shown in Fig. 5 . The red dot in the figure represents the GPI value of the model. The larger the value, the better the model fitting effect. To show the model fitting effect more clearly, the surface and projection are used to represent the accuracy changes of different models visually. Overall, the GPI value of Fig. 5 (e) CSO-BP is higher than other models, indicating that its simulation effect is better the ACO-BP model had slightly better prediction accuracy than the BSA-BP model. At the same time, both of them outperformed the ELM models with the worse performance by the original BP. In the 11 input combinations constructed by introducing different inputs based on temperature, it is observed that when two types of factors are input, the GPI value calculated by introducing n (C3) is the highest, which BP, ELM, ACO-BP, BSA-BP and CSO-BP had an average of 0.088, 1.284, 1.374, 1.369 and 1.399, respectively. When three different factors were input, the temperature-based input introduced n and RH models (C11) with the highest accuracy. BP, ELM, ACO-BP, BSA-BP and CSO-BP had an average of 0.538, 1.641, 1.679, 1.664 and 1.703, respectively. Combining the GPI results of different models with 11 input combinations, it can be seen that the contributions of different input factors to ET O prediction are in descending order of T, n, RH, U 2 and AP. The higher GPI value in the coastal area maybe because the temperature difference in the coastal area is smaller than that in the inland area, and temperature is the biggest factor affecting the prediction, which makes the model accuracy higher than that in the inland area. Among the 14 stations in the southern region, the ET O prediction of the five ML algorithms exhibited high accuracy in areas such as Wenjiang and Shapingba. In terms of GPI, BP, ELM, ACO-BP, BSA-BP and CSO-BP had average of 0.744 (ranging 0.010–1.620), 1.414 (ranging 0.926–1.938), 1.332 (ranging 0.836–1.900), 1.389 (ranging 0.916–1.926) and 1.531 (ranging 0.954–1.960), respectively. But low accuracy in some southern coastal areas such as Xiamen and Guangzhou. In terms of GPI, BP, ELM, ACO-BP, BSA-BP and CSO-BP had average of -0.960 (ranging − 1.928–0.390), 0.210 (ranging − 1.326–1.439), 0.361 (ranging − 1.053–1.468), 0.311 (ranging − 1.066–1.471) and 0.451 (ranging − 1.022–1.501), respectively. The different climatic conditions of these weather stations may have contributed to the differences in the accuracy of ETo estimates. The study shows satisfactory accuracy with less data input. It can better predict ET O in southern China and recommends the CSO-BP (T, n and RH) model because of its accuracy, stability, and computational efficiency. However, this study only covers part of China, and the global promotion of the established model needs to be studied. The study shows that the prediction accuracy of sites with different climatic characteristics is quite different. There is no free lunch theorem proving that a single algorithm cannot perform satisfactorily on all problems. Therefore, the next step can apply this model to different climate zones region to find more suitable climatic conditions. Further, by optimizing the optimization model, the performance of the model in terms of accuracy and computational cost can be improved. 4 Conclusion In this study, limited factors were input into the BP, ELM, ACO-BP, BSA-BP and CSO-BP models to construct an ET O prediction model at 14 stations in southern China. The results demonstrated the following: (1) With the input of T, n and RH factors, ET O prediction models achieved the highest accuracy. The meteorological factors as input with the most influence on the model were, in descending order, T, n, RH, U 2 and AP. (2) The accuracy of the ELM model was higher than that of the unoptimized BP model. The ELM model had the lowest time costs of all five prediction models (0.02–0.03 s). The three algorithms (ACO, BSA and CSO) exerted satisfactory optimization effects on the BP model. The CSO-BP model had the highest accuracy, with mean values of 0.326 to 0.586, 0.842 to 0.952, 0.249 to 0.445, 0.842 to 0.952 and 0.329 to 1.703 for RMSE, R 2 , MAE, NSE and GPI, respectively. The time cost of the CSO-BP model was much lower than that of the other two hybrid models. (3) Five ET O models (BP, ELM, ACO-BP, CSO-BP and BSA-BP) exhibited high accuracy at most of the 14 stations in southern China, particularly in Wenjiang and Shapingba; in coastal areas (Xiamen and Guangzhou), however, they had slightly lower accuracy. Declarations Acknowledgments We would like to thank the National Climatic Centre of the China Meteorological Administration for providing the climate database used in this study. Ethical Approval Not applicable. Consent to Participate All authors give their consent to participate. Consent to Publish All authors give their consent to publish. Author contributions H.Zhou: Validation, L.Xing: Methodology and Writing, L.Zhao: Conceptualization and Writing, N.Cui: Conceptualization, S.Chen: Data curation, X.Zhao: Data curation, Y.Shi: Methodology, Y.Wang: Methodology and Writing, Z.Li: Data curation. Funding This work was supported by National Natural Science Foundation of China (51922072, 51779161,51009101), Key R&D and Promotion Projects in Henan Province (Science and Technology Development) (No. 222102110452), the Fundamental Research Funds for the Central Universities (2019CDPZH-10), PhD research start up the foundation of Henan University of Science and Technology (No. 13480025 and No. 13480033) and Key Scientific Research Projects of Colleges and Universities in Henan Province(22B416002). Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Availability of data and materials Available upon request. References Agrawal Y, Kumar M, Ananthakrishnan S, Kumarapuram G (2022) Evapotranspiration Modeling Using Different Tree Based Ensembled Machine Learning Algorithm. Water Resour Manage 36:1025–1042. https://doi.org/10.1007/s11269-022-03067-7 Arora A, Arabameri A, Pandey M, Siddiqui MA, Bhardwaj A (2021) Optimization of state-of-the-art fuzzy-metaheuristic ANFIS-based machine learning models for flood susceptibility prediction mapping in the Middle Ganga Plain, India. Sci Total Environ 750:141565. https://doi.org/10.1016/j.scitotenv.2020.141565 Zhu B, Feng Y, Gong D, Jiang S, Zhao L, Cui N (2020) Hybrid particle swarm optimization with extreme learning machine for daily reference evapotranspiration prediction from limited climatic data. Comput Electron Agric 173:105430. https://doi.org/10.1016/j.compag.2020.105430 Cunha AC, Gabriel Filho LRA, Tanaka AA, Goes BC, Putti FF (2021) Influence Of The Estimated Global Solar Radiation On The Reference Evapotranspiration Obtained Through The Penman-Monteith Fao 56 Method. Agric Water Manage 243:106491. https://doi.org/10.1016/j.agwat.2020.106491 Chu S, Tsai P, Pan J (2006) Cat Swarm Optimization. Lecture Notes in Computer Science. https://doi.org/10.1007/11801603_94 Altay EV, Alatas B (2020) Bird swarm algorithms with chaotic mapping. Artif Intell Rev 53(2):1373–1414. https://doi.org/10.1007/s10462-019-09704-9 Abbas F, Fan P (2018) Clustering-based reliable low-latency routing scheme using ACO method for vehicular networks. Veh Commun 12:66–74. https://doi.org/10.1016/j.vehcom.2018.02.004 dos Santos Farias DB, Althoff D, Rodrigues LN, Filgueiras R (2020) Performance evaluation of numerical and machine learning methods in estimating reference evapotranspiration in a Brazilian agricultural frontier. Theoret Appl Climatol 142(3):1481–1492. https://doi.org/10.1007/s00704-020-03380-4 Ahmadi F, Mehdizadeh S, Mohammadi B, Pham QB, DOAN TNC (2021) Application of an artificial intelligence technique enhanced with intelligent water drops for monthly reference evapotranspiration estimation. Agric Water Manage 244:106622. https://doi.org/10.1016/j.agwat.2020.106622 Gocić M, Amiri MA (2021) Reference Evapotranspiration Prediction Using Neural Networks and Optimum Time Lags. Water Resour Manage 35:1913–1926. https://doi.org/10.1007/s11269-021-02820-8 Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501. https://doi.org/10.1016/j.neucom.2005.12.126 Huang J, Asteris PG, Pasha MKS, Mohammed AS, Hasanipanah M (2020) A new auto-tuning model for predicting the rock fragmentation: a cat swarm optimization algorithm. Engineering with Computers 2020:1–12. https://doi.org/10.1007/s00366-020-01207-4 Zhang J, Xia K, He Z, Fan S (2020) Dynamic Multi-Swarm Differential Learning Quantum Bird Swarm Algorithm and Its Application in Random Forest Classification Model. Comput Intell Neurosci 6858541:24. https://doi.org/10.1155/2020/6858541 Bellido-Jiménez JA, Estévez J, García-Marín AP (2020) New machine learning approaches to improve reference evapotranspiration estimates using intra-daily temperature-based variables in a semi-arid region of Spain. Agric Water Manage 245:106558. https://doi.org/10.1016/j.agwat.2020.106558 Fan J, Yue W, Wu L, Zhang F, Cai H, Wang X, Lu X, Xiang Y (2018) Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily reference evapotranspiration using limited meteorological data in different climates of China. Agric For Meteorol 263:225–241. https://doi.org/10.1016/j.agrformet.2018.08.019 Lin K, Zhang K, Huang Y, Hung J, Yen N (2016) Feature selection based on an improved cat swarm optimization algorithm for big data classification. J Supercomputing 72(8):3210–3221. https://doi.org/10.1007/s11227-016-1631-0 Laura R, Matteo B, Gianluca R (2008) On ant routing algorithms in ad hoc networks with critical connectivity. Ad Hoc Netw 6(6):827–859. https://doi.org/10.1016/j.adhoc.2007.07.003 Wu L, Fan J (2019a) Comparison of neuron-based, kernel-based, tree-based and curve-based machine learning models for predicting daily reference evapotranspiration. PLoS ONE 14(5):0217520. https://doi.org/10.1371/journal.pone.0217520 Wu L, Zhou H, Ma X, Fan J, Zhang F (2019b) Daily reference evapotranspiration prediction based on hybridized extreme learning machine model with bio-inspired optimization algorithms: Application in contrasting climates of China. J Hydrol 577:123960. https://doi.org/10.1016/j.jhydrol.2019.123960 Zhao L, Zhao X, Zhou H, Wang X, Xing X (2021) Prediction model for daily reference crop evapotranspiration based on hybrid algorithm and principal components analysis in Southwest China. Comput Electron Agric 190:106424. https://doi.org/10.1016/j.compag.2021.106424 Rodrigues GC, Braga RP (2021) Estimation of Reference Evapotranspiration during the Irrigation Season Using Nine Temperature-Based Methods in a Hot-Summer Mediterranean Climate. Agriculture 11(2):124. https://doi.org/10.3390/agriculture11020124 Wang S, Liu S, Che X, Wang Z, Zhang J, Kong D (2020) Recognition of polycyclic aromatic hydrocarbons using fluorescence spectrometry combined with bird swarm algorithm optimization support vector machine. Spectrochim Acta Part A Mol Biomol Spectrosc 224:117404. https://doi.org/10.1016/j.saa.2019.117404 Meng X, Gao X, Lu L, Yu L, Zhang H (2016) A new bio-inspired optimisation algorithm: Bird Swarm Algorithm. J Exp Theor Artif Intell 28(4):673–687. https://doi.org/10.1080/0952813X.2015.1042530 Maqsood J, Farooque AA, Abbas F, Esau T, Wang X, Acharya B, Afzaal H (2022) Application of Artificial Neural Networks to Project Reference Evapotranspiration Under Climate Change Scenarios. Water Resour Manage 36:835–851. https://doi.org/10.1007/s11269-021-02997-y Meng X, Gao X, Lu L, Liu Y, Zhang H (2016) A new bio-inspired optimisation algorithm: Bird Swarm Algorithm. J Exp Theor Artif Intell 28(4):673–687. https://doi.org/10.1080/0952813X.2015.1042530 Xing X, Liu Y, Zhao W, Kang D, Yu M, Ma X (2016) Determination of dominant weather parameters on reference evapotranspiration by path analysis theory. Comput Electron Agric 120(22):10–16. http://dx.doi.org/10.1016/j.compag.2015.11.001 Feng Y, Jia Y, Zhang Q, Gong D, Cui N (2018) National-scale assessment of pan evaporation models across different climatic zones of China. J Hydrol 564:314–328. https://doi.org/10.1016/j.jhydrol.2018.07.013 Zhang Z, Gong Y, Wang Z (2018) Accessible remote sensing data based reference evapotranspiration estimation modelling. Agric Water Manage 210:59–69. https://doi.org/10.1016/j.agwat.2018.07.039 Supplementary Files Highlights.docx Cite Share Download PDF Status: Published Journal Publication published 01 Feb, 2023 Read the published version in Water Resources Management → Version 1 posted Editorial decision: Minor revisions 02 Dec, 2022 Reviewers agreed at journal 19 Jun, 2022 Reviewers invited by journal 17 Jun, 2022 Editor assigned by journal 19 May, 2022 First submitted to journal 19 May, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1671161","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":114396029,"identity":"6bc6412c-16c6-4dd9-b98e-ca41263bb4e1","order_by":0,"name":"Long Zhao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+UlEQVRIiWNgGAWjYBACAx4GA2YgLQPEjI9hohLEaOEBYmZjBiiLaC1s0kRpMec5vPlzQY0ND790+7XqgprD9vYMzAdv8zDY5eHSYtnbVmA841gaj+ScM2W3Zxw7nNjDwJZszcOQXIzTYed5DJJ52A7zGNzISbsNZCTwMPCYSfMwHEhswKPlMM8/iJZiIMOeh4H/G34tZ3sMm3nbQFrSjzEDGYw9DDxs+LWcOVbMzNsH9MuMHGZp3r70xJ7DbMaWcwyS8WhJ3vyZ55uNHL9E+kMgw9qevb354Y03FXY4tSABHgMIzQw2irB6IGB/QJSyUTAKRsEoGHkAAASwTlo9DiYDAAAAAElFTkSuQmCC","orcid":"","institution":"Henan University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Long","middleName":"","lastName":"Zhao","suffix":""},{"id":114396030,"identity":"f3022c9e-8e1c-49ef-aa11-37f142bc7fba","order_by":1,"name":"Liwen Xing","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Liwen","middleName":"","lastName":"Xing","suffix":""},{"id":114396031,"identity":"40f0c997-c394-4f9a-aa59-2a3400342771","order_by":2,"name":"Yuhang Wang","email":"","orcid":"","institution":"Henan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yuhang","middleName":"","lastName":"Wang","suffix":""},{"id":114396032,"identity":"bfef27f4-2a21-4bfe-9a0f-403b729f9d92","order_by":3,"name":"Ningbo Cui","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Ningbo","middleName":"","lastName":"Cui","suffix":""},{"id":114396033,"identity":"08eb5fd3-f414-460b-be50-eb989798a4b9","order_by":4,"name":"Hanmi Zhou","email":"","orcid":"","institution":"Henan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Hanmi","middleName":"","lastName":"Zhou","suffix":""},{"id":114396034,"identity":"61d1822b-04cb-4177-8658-fb417d19455a","order_by":5,"name":"Yi Shi","email":"","orcid":"","institution":"Henan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Shi","suffix":""},{"id":114396035,"identity":"c8f466d1-0d75-4ac7-9e4c-daafc48234e9","order_by":6,"name":"Sudan Chen","email":"","orcid":"","institution":"Henan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Sudan","middleName":"","lastName":"Chen","suffix":""},{"id":114396036,"identity":"fb78e450-2aa5-4b73-a786-af175be92cec","order_by":7,"name":"Xinbo Zhao","email":"","orcid":"","institution":"Henan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xinbo","middleName":"","lastName":"Zhao","suffix":""},{"id":114396037,"identity":"08cdd99a-3265-4445-a336-4b317f8113ff","order_by":8,"name":"Zhe Li","email":"","orcid":"","institution":"Henan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Zhe","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2022-05-19 00:38:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1671161/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1671161/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11269-022-03423-7","type":"published","date":"2023-02-01T18:37:01+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":23233286,"identity":"36c182af-ccc4-4033-8df2-c0f5f6184dde","added_by":"auto","created_at":"2022-06-29 14:57:46","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":181863,"visible":true,"origin":"","legend":"\u003cp\u003e\tGeographical distribution of the meteorological stations in southern China \u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-1671161/v1/25a5ed39f602d63a73d8d9ea.png"},{"id":23233020,"identity":"ec171660-d4d9-4cf1-8c63-4239e58801ce","added_by":"auto","created_at":"2022-06-29 14:52:46","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":326154,"visible":true,"origin":"","legend":"\u003cp\u003e\tFlow chart of ET\u003csub\u003eO\u003c/sub\u003e predicting used in this study\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-1671161/v1/26074c61b003e4d416675090.png"},{"id":23233022,"identity":"8c1dfef1-4147-41a7-880f-d3da5ff0cfb3","added_by":"auto","created_at":"2022-06-29 14:52:46","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1036156,"visible":true,"origin":"","legend":"\u003cp\u003eHeatmap of Pearson correlation analysis between input features and ET\u003csub\u003eO\u003c/sub\u003e in southern China\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-1671161/v1/7638939c8055398e4a9bc455.png"},{"id":23233024,"identity":"449c02bb-4208-4688-ac1f-1ab59c21091a","added_by":"auto","created_at":"2022-06-29 14:52:46","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":972141,"visible":true,"origin":"","legend":"\u003cp\u003eBoxplots of overall accuracy performance of different models\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-1671161/v1/c24c3f8975c2c3413c6b6aa7.png"},{"id":23233025,"identity":"51e77297-b773-4290-a28d-5386ff0d0bf0","added_by":"auto","created_at":"2022-06-29 14:52:46","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":4955047,"visible":true,"origin":"","legend":"\u003cp\u003eComparing the accuracy of five models at sites and different input combinations via GPI (a) BP, (b) ELM, (c) ACO-BP, (d) BSA-BP, (e) CSO-BP\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-1671161/v1/fed68e70186ddb5c84408612.png"},{"id":44718409,"identity":"46aa5ce0-5ab0-4890-b68a-cdef88699131","added_by":"auto","created_at":"2023-10-16 18:46:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2636996,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1671161/v1/61db0c3a-8e46-464a-865b-1ec78e851f45.pdf"},{"id":23233287,"identity":"53ef4ac2-20c9-49bf-b240-e5ad4d0df722","added_by":"auto","created_at":"2022-06-29 14:57:46","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":16569,"visible":true,"origin":"","legend":"","description":"","filename":"Highlights.docx","url":"https://assets-eu.researchsquare.com/files/rs-1671161/v1/2782edf1a2fe5ad85dd92ed3.docx"}],"financialInterests":"","formattedTitle":"Prediction model for reference crop evapotranspiration based on the back-propagation algorithm with limited factors","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe reference crop evapotranspiration (ET\u003csub\u003eO\u003c/sub\u003e) is critical in determining crop water requirements (Gocić and Arab Amiri 2021). To obtain accurate ET\u003csub\u003eO\u003c/sub\u003e for agricultural water management, the Food and Agriculture Organization (FAO) suggested the use of the Penman-Monteith (Cunha et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e Maqsood et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) model (FAO-56 PM). FAO-56 PM is a semi-empirical and semi-physical model for ET\u003csub\u003eO\u003c/sub\u003e calculations but requires multiple input parameters, such as the maximum (T\u003csub\u003emax\u003c/sub\u003e), minimum (T\u003csub\u003emin\u003c/sub\u003e), average temperature (T\u003csub\u003eave\u003c/sub\u003e), average wind speed (U), relative humidity (RH) and sunshine duration (n). However, many areas lack modern weather stations, and comprehensive meteorological data can be challenging, so it is difficult to estimate the ET\u003csub\u003eO\u003c/sub\u003e accurately. Therefore, improving ET\u003csub\u003eO\u003c/sub\u003e simulation accuracy has become a research highlight of recent studies without input data.\u003c/p\u003e \u003cp\u003eMany studies have recently constructed simple input models for ET\u003csub\u003eO\u003c/sub\u003e prediction, such as temperature-based and radiation-based models (Rodrigues et al. 2021). Although empirical models have been widely employed for estimating ET\u003csub\u003eO\u003c/sub\u003e, they are challenging to handle intricacy and nonlinear relationships between independent and dependent variables. With the development of artificial intelligence technology, machine learning (ML) for managing nonlinear problems has improved model performance considerably (Zhao et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Zhang et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) tested the adaptability of an ET\u003csub\u003eO\u003c/sub\u003e model constructed using three ML algorithms, namely the support vector machine (SVM), back-propagation neural network (BP) and adaptive neuro-fuzzy inference system (ANFIS), and the results demonstrated that the models have good applicability for predicting ET\u003csub\u003eO\u003c/sub\u003e. Wu et al. (2019a) evaluated eight ML models for predicting daily ET\u003csub\u003eO\u003c/sub\u003e with a small number of meteorological parameters in different climatic regions of China. They found that SVM models have high accuracy and stability. Bellido-Jim\u0026eacute;nez et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) selected several temperatures-based ML models to estimate ET\u003csub\u003eO\u003c/sub\u003e in the semi-arid region of Andalusia, and the results showed that extreme learning machine (ELM) models have high performance in predicting ET\u003csub\u003eO\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eThe ML models have satisfactory performances with single input factors, and numerous studies have reported that the accuracy of ML models is generally higher than that of empirical models in estimating ET\u003csub\u003eO\u003c/sub\u003e. Zhu et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) successfully predicted daily ET\u003csub\u003eO\u003c/sub\u003e with limited meteorological data using different ML models along with six empirical models (Priestley-Taylor, Makkink, Imark, Hargreaves-Samani (HS), Dalton and Trabert), achieving satisfying results. dos Santos Farias et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) studied the performance of ML models and empirical models in a Brazilian agricultural frontier with limited meteorological data, and ML models show a better performance than empirical models with the same climatological variables.\u003c/p\u003e \u003cp\u003eHowever, ML algorithms can be problematic, and the algorithm parameters are not necessarily optimal, limiting the constructed model's prediction accuracy. Many scholars have employed optimization algorithms for ML algorithms. The results showed that RBFN is helpful in ML models estimating ET\u003csub\u003eO\u003c/sub\u003e with different input parameters. Wu et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019b\u003c/span\u003e) applied four bio-inspired algorithms to improve the accuracy of ELM models. They found that hybrid ELM models exhibited greater improvements in daily ET\u003csub\u003eO\u003c/sub\u003e prediction. Ahmadi et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) employed a novel model via intelligent water drops and support vector regression to predict ET\u003csub\u003eO\u003c/sub\u003e. Results showed that it performed best among all ML models and empirical models. The optimization algorithms have improved ML models to estimate ET\u003csub\u003eO\u003c/sub\u003e, and the hybrid optimization algorithm was recommended to improve the ML models to estimate ET\u003csub\u003eO\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eAlong with another optimization algorithm, research has frequently reported that the three optimization algorithms of ant colony optimization (ACO), bird swarm algorithm (BSA) and cat swarm optimization (CSO) exhibit more favorable optimization effects. Wang et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) indicated that optimization with BSA markedly improved the performance of the SVM model compared with particle swarm optimization (PSO) and the genetic algorithm (GA); however, the BSA had higher stability and robustness. Huang et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) observed that CSO resulted in higher accuracy than PSO in predicting rock fragmentation.\u003c/p\u003e \u003cp\u003eSouthern China is a crucial grain production area. This region is largely subject to a tropical monsoon climate with abundant rainfall. Its topographical conditions are complex; precipitation's climatic conditions and temporal and spatial distribution in different regions differ considerably. Therefore, the efficient use of agricultural water in the southern region is crucial. This paper inputs various parameter combinations into BP, ELM, ACO-BP, BSA-BP and CSO-BP models to construct an ET\u003csub\u003eO\u003c/sub\u003e prediction model for typical stations in southern China. The study aims were as follows: (1) to determine the influence of different input combinations on daily ET\u003csub\u003eO\u003c/sub\u003e prediction, (2) to develop five ML models (BP, ELM, ACO-BP, BSA-BP and CSO-BP) for daily ET\u003csub\u003eO\u003c/sub\u003e prediction with limited factors and (3) to compare the prediction accuracy and adaptability of the five models in southern China.\u003c/p\u003e"},{"header":"2 Materials And Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Study area and data sets\u003c/h2\u003e \u003cp\u003eThis study analyzed data from 14 stations (Wenjiang, Kunming, Wuhan, Shapingba, Changsha, Guiyang, Nanjing, Hefei, Hangzhou, Nanchang, Xiamen, Guangzhou, Nanning and Haikou) in southern China (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e: 18\u0026ndash;35\u0026deg;N, 98\u0026ndash;122\u0026deg;E), with a subtropical, tropical monsoon climate. Because of the monsoon effects, the annual precipitation variation in southern China is large. The availability of water resources is changeable; the high rainfall in summer and autumn and the low rainfall in winter and spring can lead to summer waterlogging and spring droughts, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe meteorological data used in this study were extracted from the China Meteorological Data Network (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://data.cma.cn/\u003c/span\u003e\u003cspan address=\"http://data.cma.cn/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) daily dataset from 1960 to 2019 and included T, U, n, RH and average atmospheric pressure (AP). The datasets of the 14 stations were of high quality. The k-fold method is used to divide the data set, which randomly divides the data into two subsets, i.e., the Training and Testing dataset. The k value is set to 10; that is, the data is divided into ten parts, and nine parts are taken in turn as training, one part is used for testing, and the average of the results is taken as the estimation (Fan et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 FAO-56 PM equation\u003c/h2\u003e \u003cp\u003eThe daily ET\u003csub\u003eO\u003c/sub\u003e is calculated using the following FAO-56 PM equation:\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\text{E}{\\text{T}_\\text{O}}=\\frac{{0.408\\Delta (Rn - G)+\\gamma \\frac{{900}}{{{T_{mean}}+273}}{U_2}({e_s} - {e_a})}}{{\\Delta +\\gamma (1+0.34{U_2})}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\Delta }\\)\u003c/span\u003e \u003c/span\u003e is the slope of the vapor pressure curve (kPa ℃\u003csup\u003e\u0026minus;1\u003c/sup\u003e),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({R}_{n}\\)\u003c/span\u003e \u003c/span\u003e is the solar net radiation (MJ m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(G\\)\u003c/span\u003e \u003c/span\u003e is the soil heat flux density (MJ m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003eday\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\gamma\\)\u003c/span\u003e \u003c/span\u003e is the psychrometric constant (kPa \u0026deg;C\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({T}_{mean}\\)\u003c/span\u003e \u003c/span\u003e is the mean air temperature (\u0026deg;C),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({U}_{2}\\)\u003c/span\u003e \u003c/span\u003e is the wind speed at 2 m (m/s),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({e}_{s}\\)\u003c/span\u003e \u003c/span\u003e is saturated vapor pressure (kPa),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({e}_{a}\\)\u003c/span\u003e \u003c/span\u003e is the actual vapor pressure (kPa).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Different machine learning for predicting daily reference crop evapotranspiration\u003c/h2\u003e \u003cp\u003eThis study uses eleven combinations (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) based on different meteorological data inputs for different ML models to predict the daily ET\u003csub\u003eO\u003c/sub\u003e. Various studies have indicated that temperature factors T (average, maximum and minimum temperature) affect ET\u003csub\u003eO\u003c/sub\u003e (Xing et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Therefore, T is selected for the first three inputs of the model in this study. A flowchart of the daily ET\u003csub\u003eO\u003c/sub\u003e prediction process applied in this study is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. To address the shortcomings of the traditional BP algorithm, this applies the ACO, BSA and CSO algorithms to optimize the initial weights of the BP algorithm, and the BP algorithm is established with the respective optimization models, after this referred to as the ACO-BP, BSA-BP and CSO-BP algorithms. The program code is written in MATLAB software, version R2020b. All the simulations were performed in a computer with Intel\u0026reg; Core \u003csup\u003eTM\u003c/sup\u003e i7-10700K CPU @ 3.80 GHz and 16 GB RAM.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1 Back-Propagation neural network\u003c/h2\u003e \u003cp\u003eThe BP algorithm, also known as the error back-propagation algorithm, is a multilayer forward neural network. The function of a finite number of discontinuous points is approximated through an input layer and an output layer, and several hidden layers. Effectively solve the learning problem of the hidden layer neuron connection weights. More details can be found in Yan et al. (2020).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2 Extreme learning machine\u003c/h2\u003e \u003cp\u003eThe ELM is a learning algorithm based on single hidden layer feedforward neural networks that can directly approximate nonlinear mapping with input data; this is useful for many natural and artificial methods that are difficult to manage using classical parameterization methods. With the presence of the neural networks in the models, the hidden layer node parameters of the algorithm can be randomly or artificially provided without adjustment; the learning speed is fast, and generalizability is high. For more information about the ELM model refer to Huang et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.3.3 Ant colony optimization algorithm\u003c/h2\u003e \u003cp\u003eACO is an intelligent optimization algorithm that simulates ant colony foraging behavior. Ants communicate through pheromones when searching for food; the shorter the path, the greater the concentration of information and the probability of choosing the path. Over time, more ants choose the shorter path from the food source to the ant nest. Based on this natural phenomenon, the ACO algorithm exhibits high robustness, parallelism and favorable characteristics, and can determine a globally optimal solution quickly. More details about the ACO can be found in (Laura et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Fakhar et al. 2018).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.3.4 Bird swarm algorithm\u003c/h2\u003e \u003cp\u003eThe BSA optimizes the BP neural network through the following steps (Elif et al. 2020): The global search capability of the BSA is utilized to optimize the initial weights and thresholds the BP neural network. Each group of decision variables is contained in the spatial position of each bird in the flock. The fitness function is used to measure the superiority of the individual\u0026rsquo;s spatial position. An individual\u0026rsquo;s spatial position is continuously updated using behavioral strategies such as those related to foraging, vigilance, and flying until the foraging process of the flock is optimized. For details on the algorithm, please refer to Meng et al (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e)\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e2.3.5 Cat swarm optimization algorithm\u003c/h2\u003e \u003cp\u003eCSO (Lin et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) is a swarm intelligence algorithm proposed by observing the behavior of cats, which consists of tracking mode and finding mode. It optimizes the BP neural network's input and hidden layers, the connection weights between the hidden and output layers, and the threshold for each layer. The details can be found in (Chu et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Model prediction evaluation\u003c/h2\u003e \u003cp\u003eThe coefficient of determination (R\u003csup\u003e2\u003c/sup\u003e), relative root mean square error (RMSE), mean absolute error (MAE), Nash\u0026ndash;Sutcliffe coefficient (NSE) and Global performance indicator (GPI)were used to evaluate the performances of the models (Feng et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Agrawal et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\text{R}\\text{M}\\text{S}\\text{E}=\\sqrt {\\frac{1}{n}\\mathop \\sum \\limits_{{i=1}}^{n} {{\\left( {{Y_i} - {X_i}} \\right)}^2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${\\text{R}^2}=\\frac{{{{\\left[ {\\mathop \\sum \\nolimits_{{i=1}}^{n} \\left( {{X_i} - \\bar {X}} \\right)\\left( {{Y_i} - \\bar {Y}} \\right)} \\right]}^2}}}{{\\mathop \\sum \\nolimits_{{i=1}}^{n} {{\\left( {{X_i} - \\bar {X}} \\right)}^2}\\mathop \\sum \\nolimits_{{i=1}}^{n} {{\\left( {{Y_i} - \\bar {Y}} \\right)}^2}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\text{M}\\text{A}\\text{E}=\\frac{1}{n}\\mathop \\sum \\limits_{{i=1}}^{n} \\left| {{y_i} - {x_i}} \\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\text{N}\\text{S}\\text{E}=1 - \\frac{{\\mathop \\sum \\nolimits_{{i=1}}^{n} {{\\left( {{X_i} - {Y_i}} \\right)}^2}}}{{\\mathop \\sum \\nolimits_{{i=1}}^{n} {{\\left( {{Y_i} - \\bar {Y}} \\right)}^2}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\text{G}\\text{P}\\text{I}={\\alpha _j}\\mathop \\sum \\nolimits_{{i=1}}^{4} (\\mathop T\\nolimits_{j} - \\mathop {\\bar {T}}\\nolimits_{j} )$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{i}\\)\u003c/span\u003e\u003c/span\u003e are the simulated and measured values, respectively; \u003cem\u003en\u003c/em\u003e is the number of measured values;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{ x}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{y}\\)\u003c/span\u003e\u003c/span\u003e the means of the simulated and measured values.\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{j}\\)\u003c/span\u003e\u003c/span\u003e is the normalized value of the RMSE, MAE, R\u003csup\u003e2\u003c/sup\u003e and NSE, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\stackrel{\\text{̄}}{\\text{T}}}_{j}\\)\u003c/span\u003e\u003c/span\u003e is the median of the corresponding parameter when \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T}_{j}\\)\u003c/span\u003e\u003c/span\u003e is the RMSE and MAE, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha }_{j}\\)\u003c/span\u003e\u003c/span\u003e is \u0026minus;\u0026thinsp;1, or 1 otherwise. The closer R\u003csup\u003e2\u003c/sup\u003e is to 1, the more accurate the prediction ability of the model, and the smaller the value of the MAE and RMSE, the smaller the simulation error. The closer the NSE is to 1, the higher the model quality and credibility. The higher the GPI, the more effective the overall simulation effect of the model.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results And Discussion","content":"\u003cdiv class=\"Section2\" id=\"Sec13\"\u003e\n \u003ch2\u003e3.1 Evaluation of different meteorological data combinations for daily reference crop evapotranspiration prediction\u003c/h2\u003e\n \u003cp\u003eThe performance of the different daily ET\u003csub\u003eO\u003c/sub\u003e estimation models using different meteorological data combinations is presented in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The CSO-BP model showed the best accuracy performance across all input combinations, but the BP model performed poorly in accuracy. When three factors are input, the mean ranges of RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE and NSE of the constructed model are 0.586\u0026ndash;0.745 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 0.774\u0026ndash;0.842, 0.445\u0026ndash;0.571 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 0.750\u0026ndash;0.842, respectively.\u003c/p\u003e\n \u003cp\u003eWhen adding an input factor, the model accuracy is improved. The highest accuracy is C3, indicating that the influence of n is greater than that of other factors. Combined with the input of only the temperature factor, it can be known that as input, the meteorological factors that have the greatest impact on the model are in descending order of T, n, RH, U\u003csub\u003e2\u003c/sub\u003e and AP. Four input factors, the mean ranges of RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE and NSE of the constructed model are 0.391\u0026ndash;0.708 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 0.792\u0026ndash;0.930, 0.293\u0026ndash;0.547 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 0.774\u0026ndash;0.930, respectively. When five factors are input, the mean ranges of RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE and NSE of the constructed model are 0.326\u0026ndash;0.697 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 0.805\u0026ndash;0.952, 0.249\u0026ndash;0.548 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 0.776\u0026ndash;0.952, respectively. A fifth input factor is introduced to generate the most accurate input combination C11, compared to other combinations; it can be seen that the contribution of n to ET\u003csub\u003eO\u003c/sub\u003e is higher than the superposition of other factors, and a consistent conclusion can be obtained for RH.\u003c/p\u003e\n \u003cp\u003eThe variable analysis heatmap obtained by performing a Pearson correlation analysis matrix on the input is shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e. The overall results in the southern region show that other factors except RH and AP are positively correlated with ETo. The absolute value of the correlation is the largest for T\u003csub\u003emax\u003c/sub\u003e and the smallest for AP, which is consistent with the results obtained by the different input models constructed above.\u003c/p\u003e\n \u003cp\u003eThis study confirmed that the ML models with T, n and RH factor inputs exhibited the optimal performance for daily ET\u003csub\u003eO\u003c/sub\u003e prediction. The meteorological factors, as input, that revealed the most influence on the model are, in descending order, T, n, RH, U\u003csub\u003e2\u003c/sub\u003e and AP. Through the different divisions of the factor input combination, it can produce less input, which is better than adding more input. It is significant in terms of reducing input requirements and reducing computational costs. After revealing the influence of variables on the model results, consistent results can be obtained by using Pearson correlation analysis. Therefore, correlation analysis is recommended to verify variable selection, and feature selection algorithms can be used to study input factors in follow-up research further.\u003c/p\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe performance of machine learning models with different combinations of input parameters\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003eRMSE (mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003eMAE (mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003eNSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003eGPI\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC1: T\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.745\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.774\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.571\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.750\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e-0.591\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.631\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.824\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.478\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.823\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.095\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.603\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.834\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.457\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.834\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.251\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.602\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.835\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.454\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.835\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.237\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.586\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.842\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.445\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.842\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.329\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC2: T, RH\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.690\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.829\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.547\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.785\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e-0.203\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.524\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.875\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.395\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.875\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.701\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.509\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.883\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.382\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.883\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.780\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.512\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.882\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.384\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.882\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.794\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.887\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.374\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.887\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.841\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC3: T, n\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.645\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.856\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.508\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.812\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.088\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.417\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.921\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.303\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.918\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.284\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.398\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.928\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.297\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.928\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.374\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.399\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.929\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.299\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.929\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.369\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.391\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.930\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.293\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.930\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.399\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC4: T, U\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.696\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.792\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.537\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.777\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e-0.325\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.580\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.851\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.436\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.851\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.408\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.539\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.867\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.407\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.867\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.532\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.555\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.862\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.420\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.861\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.609\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.522\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.875\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.394\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.875\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.705\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC5: T, AP\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.708\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.802\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.547\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.774\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e-0.341\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.615\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.835\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.466\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.834\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.205\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.593\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.841\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.446\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.841\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.257\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.602\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.836\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.451\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.835\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.309\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.543\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.864\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.407\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.864\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.588\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC6: T, n, U\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.618\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.881\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.488\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.824\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.271\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.347\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.946\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.264\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.946\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.607\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.335\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.949\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.255\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.949\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.645\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.259\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.660\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.332\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.951\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.252\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.951\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.682\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC7: T, n, AP\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.618\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.877\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.486\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.823\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.258\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.395\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.929\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.294\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.929\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.385\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.385\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.933\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.287\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.933\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.431\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.385\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.932\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.288\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.932\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.435\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.376\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.935\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.280\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.935\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.476\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC8: T, RH, U\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.661\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.830\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.512\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.801\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e-0.053\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.481\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.896\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.362\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.895\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.944\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.461\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.904\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.343\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.904\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.036\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.465\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.902\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.902\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.054\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.453\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.907\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.907\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC9: T, U\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e, \u003cstrong\u003eAP\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.697\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.805\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.547\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.776\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e-0.313\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.565\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.857\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.429\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.856\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.474\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.538\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.869\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.405\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.869\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.590\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.545\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.865\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.407\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.865\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.628\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.517\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.877\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.389\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.877\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.733\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC10: T, RH, n\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 26.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 8.8%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 24.9333%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 5.2%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" style=\"width: 9.6%;\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBP10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.566\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.900\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.455\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.851\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.538\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.261\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.641\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.332\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.951\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.951\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.664\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.335\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.950\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.257\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.950\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e1.679\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.326\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.952\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.249\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.952\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.703\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eC11: T, RH, AP\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eBP11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.687\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.851\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.548\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.785\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e-0.139\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eELM11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.523\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.877\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.394\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.877\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.717\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eACO-BP11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.501\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.887\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.373\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.887\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.817\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eBSA-BP11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.506\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.885\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.376\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.884\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.845\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" style=\"width: 24.5333%;\"\u003e\n \u003cp\u003eCSO-BP11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 26.9333%;\"\u003e\n \u003cp\u003e0.489\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 8.8%;\"\u003e\n \u003cp\u003e0.893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 24.9333%;\"\u003e\n \u003cp\u003e0.362\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 5.2%;\"\u003e\n \u003cp\u003e0.893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" style=\"width: 9.6%;\"\u003e\n \u003cp\u003e0.916\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eNote: best statistical indicators among all models are marked in bold.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec14\"\u003e\n \u003ch2\u003e3.2 Statistical performance of different machine learning models for daily reference crop evapotranspiration prediction\u003c/h2\u003e\n \u003cp\u003eThe accuracy comparison of five different ML models in the southern region is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. The information given in the figure shows differences in the performance of different models. In terms of RMSE and MAE, the BP model has the highest median line, followed by ELM, indicating that the ELM algorithm is better than BP. However, the optimized BP model shows better accuracy than ELM in model evaluation. The CSO-BP midline is the lowest, indicating that the results are the most satisfactory among all models. In comparison, the ACO-BP accuracy is slightly better than that of BSA-BP. R\u003csup\u003e2\u003c/sup\u003e and NSE are opposite to RMSE and MAE in the evaluation model; that is, the higher the median line, the better the model accuracy, and R\u003csup\u003e2\u003c/sup\u003e and NSE give the same results as RMSE and MAE when evaluating five models. The medians of RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE and NSE of CSO-BP were 0.446 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 0.905, 0.333 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 0.905, respectively. The medians of RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE and NSE of ACO-BP were 0.468 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 0.900, 0.346 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 0.900, respectively. The medians of RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE and NSE of BSA-BP were 0.473 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 0.899, 0.348 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 0.899, respectively. The medians of RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE and NSE of ELM were 0.487 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 0.893, 0.362 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 0.892, respectively. The medians of RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE and NSE of BP were 0.687 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 0.851, 0.533 mm d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 0.805, respectively. Compared with the BP model, the most satisfactory CSO-BP model has a 34.979% and 37.659% reduction in the median of RMSE and MAE and a 6.425% and 12.435% improvement in R2 and NSE, respectively.\u003c/p\u003e\n \u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e lists the average calculation cost (time used for calculation) for the different models. The results show that the average time consumed by the BP model with different combinations of factors is at most 0.67 s. The ELM model had the lowest time cost among the five models, and the time cost of varying input factors ranged from 0.02 to 0.03 s. Among the three hybrid models, the time costs of the ACO-BP and BSA-BP were relatively close at 32.38 to 45.13 s and 37.25 to 45.51 s, respectively; that of the CSO-BP was the lowest among the hybrid models, with an average running time of 4.14 to 7.25 s.\u003c/p\u003e\n \u003cp\u003eIn the BP algorithm, the gradient descent method requires multiple iterations to modify the weights and thresholds, and the training speed is therefore slow. Zhang et al. (\u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e) combined remote sensing data with an ML algorithm and applied the BP machine algorithm to establish an ET\u003csub\u003eO\u003c/sub\u003e estimation model of spatial distribution. The results revealed that the BP algorithm had lower prediction accuracy for ET\u003csub\u003eO\u003c/sub\u003e prediction than models such as the artificial neural network, SVM and ANFIS. The BP model sinks into the local optimum easily and cannot reach the global minimum. The ELM algorithm does not require weights or threshold adjustment during the training process. Still, it only adjusts the number of neurons in the hidden layer to obtain the only optimal solution. Therefore, the accuracy of the ELM model is higher than that of the BP model. Optimization algorithms can markedly improve the simulation accuracy of ML models. Arora et al. (\u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e) used the ANIFS algorithm to optimize the GA to predict flood sensitivity, significantly improving the model\u0026rsquo;s accuracy with the optimized algorithm.\u003c/p\u003e\n \u003cp\u003eThis study used ACO, BSA and CSO to optimize the BP model. Among the three hybrid models, CSO-BP had the highest accuracy. These optimization algorithms show satisfactory optimization results for the BP model. CSO-BP is more accurate than the other two optimization algorithms, mainly because the CSO algorithm has a dynamic grouping mechanism to avoid the algorithm falling into local optimum. The optimization algorithm has the advantages of fewer control parameters, fast convergence speed and high robustness, and the optimized model has higher accuracy. The other two optimization algorithms may face being trapped in local optima and slow to converge, affecting their performance (Zhang et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab2\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eComputational costs of the different models with different parameter combinations (s)\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBP\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eELM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eACO-BP\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBSA-BP\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCSO-BP\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.60\u0026thinsp;\u0026plusmn;\u0026thinsp;0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.02\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e35.53\u0026thinsp;\u0026plusmn;\u0026thinsp;1.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e37.25\u0026thinsp;\u0026plusmn;\u0026thinsp;4.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.14\u0026thinsp;\u0026plusmn;\u0026thinsp;0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.50\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e41.61\u0026thinsp;\u0026plusmn;\u0026thinsp;1.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e37.63\u0026thinsp;\u0026plusmn;\u0026thinsp;5.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.62\u0026thinsp;\u0026plusmn;\u0026thinsp;0.59\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e38.42\u0026thinsp;\u0026plusmn;\u0026thinsp;1.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e40.99\u0026thinsp;\u0026plusmn;\u0026thinsp;4.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.72\u0026thinsp;\u0026plusmn;\u0026thinsp;0.63\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.55\u0026thinsp;\u0026plusmn;\u0026thinsp;0.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39.18\u0026thinsp;\u0026plusmn;\u0026thinsp;4.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39.31\u0026thinsp;\u0026plusmn;\u0026thinsp;5.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.76\u0026thinsp;\u0026plusmn;\u0026thinsp;0.51\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.58\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e36.13\u0026thinsp;\u0026plusmn;\u0026thinsp;0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e41.67\u0026thinsp;\u0026plusmn;\u0026thinsp;4.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.68\u0026thinsp;\u0026plusmn;\u0026thinsp;1.03\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.48\u0026thinsp;\u0026plusmn;\u0026thinsp;0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e32.47\u0026thinsp;\u0026plusmn;\u0026thinsp;1.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39.17\u0026thinsp;\u0026plusmn;\u0026thinsp;5.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.20\u0026thinsp;\u0026plusmn;\u0026thinsp;1.46\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.55\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e32.33\u0026thinsp;\u0026plusmn;\u0026thinsp;1.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e38.18\u0026thinsp;\u0026plusmn;\u0026thinsp;4.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.25\u0026thinsp;\u0026plusmn;\u0026thinsp;1.57\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.67\u0026thinsp;\u0026plusmn;\u0026thinsp;0.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e33.61\u0026thinsp;\u0026plusmn;\u0026thinsp;0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e45.51\u0026thinsp;\u0026plusmn;\u0026thinsp;3.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.51\u0026thinsp;\u0026plusmn;\u0026thinsp;0.89\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.57\u0026thinsp;\u0026plusmn;\u0026thinsp;0.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e45.12\u0026thinsp;\u0026plusmn;\u0026thinsp;2.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e38.23\u0026thinsp;\u0026plusmn;\u0026thinsp;4.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.92\u0026thinsp;\u0026plusmn;\u0026thinsp;0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.43\u0026thinsp;\u0026plusmn;\u0026thinsp;0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e45.12\u0026thinsp;\u0026plusmn;\u0026thinsp;2.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e41.36\u0026thinsp;\u0026plusmn;\u0026thinsp;6.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.38\u0026thinsp;\u0026plusmn;\u0026thinsp;0.86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.47\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e33.52\u0026thinsp;\u0026plusmn;\u0026thinsp;4.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e42.67\u0026thinsp;\u0026plusmn;\u0026thinsp;4.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.32\u0026thinsp;\u0026plusmn;\u0026thinsp;0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec15\"\u003e\n \u003ch2\u003e3.3 Comparison of reference crop evapotranspiration models by GPI\u003c/h2\u003e\n \u003cp\u003eTo use as little meteorological data as possible to build a prediction model for ET\u003csub\u003eO\u003c/sub\u003e and to evaluate the generalizability of the model, we used the meteorological data of 14 meteorological stations to construct a model based on five types of machine learning (BP, ELM, ACO-BP, BSA-BP, CSO-BP) prediction model. Although four evaluation metrics are used, none of them can be used individually to judge the performance of the selected model. Therefore, this study further applied the performance of the GPI comprehensive evaluation model in predicting ET\u003csub\u003eO\u003c/sub\u003e, and the results are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. The red dot in the figure represents the GPI value of the model. The larger the value, the better the model fitting effect. To show the model fitting effect more clearly, the surface and projection are used to represent the accuracy changes of different models visually. Overall, the GPI value of Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e (e) CSO-BP is higher than other models, indicating that its simulation effect is\u003c/p\u003e\n \u003cp\u003ebetter the ACO-BP model had slightly better prediction accuracy than the BSA-BP model. At the same time, both of them outperformed the ELM models with the worse performance by the original BP. In the 11 input combinations constructed by introducing different inputs based on temperature, it is observed that when two types of factors are input, the GPI value calculated by introducing n (C3) is the highest, which BP, ELM, ACO-BP, BSA-BP and CSO-BP had an average of 0.088, 1.284, 1.374, 1.369 and 1.399, respectively. When three different factors were input, the temperature-based input introduced n and RH models (C11) with the highest accuracy. BP, ELM, ACO-BP, BSA-BP and CSO-BP had an average of 0.538, 1.641, 1.679, 1.664 and 1.703, respectively. Combining the GPI results of different models with 11 input combinations, it can be seen that the contributions of different input factors to ET\u003csub\u003eO\u003c/sub\u003e prediction are in descending order of T, n, RH, U\u003csub\u003e2\u003c/sub\u003e and AP. The higher GPI value in the coastal area maybe because the temperature difference in the coastal area is smaller than that in the inland area, and temperature is the biggest factor affecting the prediction, which makes the model accuracy higher than that in the inland area. Among the 14 stations in the southern region, the ET\u003csub\u003eO\u003c/sub\u003e prediction of the five ML algorithms exhibited high accuracy in areas such as Wenjiang and Shapingba. In terms of GPI, BP, ELM, ACO-BP, BSA-BP and CSO-BP had average of 0.744 (ranging 0.010\u0026ndash;1.620), 1.414 (ranging 0.926\u0026ndash;1.938), 1.332 (ranging 0.836\u0026ndash;1.900), 1.389 (ranging 0.916\u0026ndash;1.926) and 1.531 (ranging 0.954\u0026ndash;1.960), respectively. But low accuracy in some southern coastal areas such as Xiamen and Guangzhou. In terms of GPI, BP, ELM, ACO-BP, BSA-BP and CSO-BP had average of -0.960 (ranging \u0026minus;\u0026thinsp;1.928\u0026ndash;0.390), 0.210 (ranging \u0026minus;\u0026thinsp;1.326\u0026ndash;1.439), 0.361 (ranging \u0026minus;\u0026thinsp;1.053\u0026ndash;1.468), 0.311 (ranging \u0026minus;\u0026thinsp;1.066\u0026ndash;1.471) and 0.451 (ranging \u0026minus;\u0026thinsp;1.022\u0026ndash;1.501), respectively. The different climatic conditions of these weather stations may have contributed to the differences in the accuracy of ETo estimates.\u003c/p\u003e\n \u003cp\u003eThe study shows satisfactory accuracy with less data input. It can better predict ET\u003csub\u003eO\u003c/sub\u003e in southern China and recommends the CSO-BP (T, n and RH) model because of its accuracy, stability, and computational efficiency. However, this study only covers part of China, and the global promotion of the established model needs to be studied. The study shows that the prediction accuracy of sites with different climatic characteristics is quite different. There is no free lunch theorem proving that a single algorithm cannot perform satisfactorily on all problems. Therefore, the next step can apply this model to different climate zones region to find more suitable climatic conditions. Further, by optimizing the optimization model, the performance of the model in terms of accuracy and computational cost can be improved.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4 Conclusion","content":"\u003cp\u003eIn this study, limited factors were input into the BP, ELM, ACO-BP, BSA-BP and CSO-BP models to construct an ET\u003csub\u003eO\u003c/sub\u003e prediction model at 14 stations in southern China. The results demonstrated the following:\u003c/p\u003e \u003cp\u003e(1) With the input of T, n and RH factors, ET\u003csub\u003eO\u003c/sub\u003e prediction models achieved the highest accuracy. The meteorological factors as input with the most influence on the model were, in descending order, T, n, RH, U\u003csub\u003e2\u003c/sub\u003e and AP.\u003c/p\u003e \u003cp\u003e(2) The accuracy of the ELM model was higher than that of the unoptimized BP model. The ELM model had the lowest time costs of all five prediction models (0.02\u0026ndash;0.03 s). The three algorithms (ACO, BSA and CSO) exerted satisfactory optimization effects on the BP model. The CSO-BP model had the highest accuracy, with mean values of 0.326 to 0.586, 0.842 to 0.952, 0.249 to 0.445, 0.842 to 0.952 and 0.329 to 1.703 for RMSE, R\u003csup\u003e2\u003c/sup\u003e, MAE, NSE and GPI, respectively. The time cost of the CSO-BP model was much lower than that of the other two hybrid models.\u003c/p\u003e \u003cp\u003e(3) Five ET\u003csub\u003eO\u003c/sub\u003e models (BP, ELM, ACO-BP, CSO-BP and BSA-BP) exhibited high accuracy at most of the 14 stations in southern China, particularly in Wenjiang and Shapingba; in coastal areas (Xiamen and Guangzhou), however, they had slightly lower accuracy.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u0026nbsp;\u003c/strong\u003eWe would like to thank the National Climatic Centre of the China Meteorological Administration for providing the climate database used in this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Participate\u003c/strong\u003e All authors give their consent to participate.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Publish\u003c/strong\u003e All authors give their consent to publish.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eH.Zhou: Validation,\u0026nbsp;L.Xing: Methodology and\u0026nbsp;Writing, L.Zhao: Conceptualization and\u0026nbsp;Writing,\u0026nbsp;N.Cui: Conceptualization, S.Chen: Data curation, X.Zhao: Data curation, Y.Shi: Methodology,\u0026nbsp;Y.Wang:\u0026nbsp;Methodology\u0026nbsp;and\u0026nbsp;Writing, Z.Li:\u0026nbsp;Data curation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e This work was supported by National Natural Science Foundation of China (51922072, 51779161,51009101), Key R\u0026amp;D and Promotion Projects in Henan Province (Science and Technology Development) (No. 222102110452), the Fundamental Research Funds for the Central Universities (2019CDPZH-10), PhD research start up the foundation of Henan University of Science and Technology (No. 13480025 and No. 13480033) and Key Scientific Research Projects of Colleges and Universities in Henan Province(22B416002).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u0026nbsp;\u003c/strong\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u0026nbsp;\u003c/strong\u003eAvailable upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAgrawal Y, Kumar M, Ananthakrishnan S, Kumarapuram G (2022) Evapotranspiration Modeling Using Different Tree Based Ensembled Machine Learning Algorithm. Water Resour Manage 36:1025\u0026ndash;1042. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11269-022-03067-7\u003c/span\u003e\u003cspan address=\"10.1007/s11269-022-03067-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eArora A, Arabameri A, Pandey M, Siddiqui MA, Bhardwaj A (2021) Optimization of state-of-the-art fuzzy-metaheuristic ANFIS-based machine learning models for flood susceptibility prediction mapping in the Middle Ganga Plain, India. Sci Total Environ 750:141565. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.scitotenv.2020.141565\u003c/span\u003e\u003cspan address=\"10.1016/j.scitotenv.2020.141565\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhu B, Feng Y, Gong D, Jiang S, Zhao L, Cui N (2020) Hybrid particle swarm optimization with extreme learning machine for daily reference evapotranspiration prediction from limited climatic data. Comput Electron Agric 173:105430. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compag.2020.105430\u003c/span\u003e\u003cspan address=\"10.1016/j.compag.2020.105430\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCunha AC, Gabriel Filho LRA, Tanaka AA, Goes BC, Putti FF (2021) Influence Of The Estimated Global Solar Radiation On The Reference Evapotranspiration Obtained Through The Penman-Monteith Fao 56 Method. Agric Water Manage 243:106491. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.agwat.2020.106491\u003c/span\u003e\u003cspan address=\"10.1016/j.agwat.2020.106491\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChu S, Tsai P, Pan J (2006) Cat Swarm Optimization. Lecture Notes in Computer Science. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/11801603_94\u003c/span\u003e\u003cspan address=\"10.1007/11801603_94\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAltay EV, Alatas B (2020) Bird swarm algorithms with chaotic mapping. Artif Intell Rev 53(2):1373\u0026ndash;1414. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10462-019-09704-9\u003c/span\u003e\u003cspan address=\"10.1007/s10462-019-09704-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbbas F, Fan P (2018) Clustering-based reliable low-latency routing scheme using ACO method for vehicular networks. Veh Commun 12:66\u0026ndash;74. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.vehcom.2018.02.004\u003c/span\u003e\u003cspan address=\"10.1016/j.vehcom.2018.02.004\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003edos Santos Farias DB, Althoff D, Rodrigues LN, Filgueiras R (2020) Performance evaluation of numerical and machine learning methods in estimating reference evapotranspiration in a Brazilian agricultural frontier. Theoret Appl Climatol 142(3):1481\u0026ndash;1492. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00704-020-03380-4\u003c/span\u003e\u003cspan address=\"10.1007/s00704-020-03380-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAhmadi F, Mehdizadeh S, Mohammadi B, Pham QB, DOAN TNC (2021) Application of an artificial intelligence technique enhanced with intelligent water drops for monthly reference evapotranspiration estimation. Agric Water Manage 244:106622. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.agwat.2020.106622\u003c/span\u003e\u003cspan address=\"10.1016/j.agwat.2020.106622\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGocić M, Amiri MA (2021) Reference Evapotranspiration Prediction Using Neural Networks and Optimum Time Lags. Water Resour Manage 35:1913\u0026ndash;1926. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11269-021-02820-8\u003c/span\u003e\u003cspan address=\"10.1007/s11269-021-02820-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489\u0026ndash;501. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.neucom.2005.12.126\u003c/span\u003e\u003cspan address=\"10.1016/j.neucom.2005.12.126\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuang J, Asteris PG, Pasha MKS, Mohammed AS, Hasanipanah M (2020) A new auto-tuning model for predicting the rock fragmentation: a cat swarm optimization algorithm. Engineering with Computers 2020:1\u0026ndash;12. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00366-020-01207-4\u003c/span\u003e\u003cspan address=\"10.1007/s00366-020-01207-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang J, Xia K, He Z, Fan S (2020) Dynamic Multi-Swarm Differential Learning Quantum Bird Swarm Algorithm and Its Application in Random Forest Classification Model. Comput Intell Neurosci 6858541:24. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1155/2020/6858541\u003c/span\u003e\u003cspan address=\"10.1155/2020/6858541\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBellido-Jim\u0026eacute;nez JA, Est\u0026eacute;vez J, Garc\u0026iacute;a-Mar\u0026iacute;n AP (2020) New machine learning approaches to improve reference evapotranspiration estimates using intra-daily temperature-based variables in a semi-arid region of Spain. Agric Water Manage 245:106558. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.agwat.2020.106558\u003c/span\u003e\u003cspan address=\"10.1016/j.agwat.2020.106558\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFan J, Yue W, Wu L, Zhang F, Cai H, Wang X, Lu X, Xiang Y (2018) Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily reference evapotranspiration using limited meteorological data in different climates of China. Agric For Meteorol 263:225\u0026ndash;241. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.agrformet.2018.08.019\u003c/span\u003e\u003cspan address=\"10.1016/j.agrformet.2018.08.019\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLin K, Zhang K, Huang Y, Hung J, Yen N (2016) Feature selection based on an improved cat swarm optimization algorithm for big data classification. J Supercomputing 72(8):3210\u0026ndash;3221. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11227-016-1631-0\u003c/span\u003e\u003cspan address=\"10.1007/s11227-016-1631-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLaura R, Matteo B, Gianluca R (2008) On ant routing algorithms in ad hoc networks with critical connectivity. Ad Hoc Netw 6(6):827\u0026ndash;859. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.adhoc.2007.07.003\u003c/span\u003e\u003cspan address=\"10.1016/j.adhoc.2007.07.003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu L, Fan J (2019a) Comparison of neuron-based, kernel-based, tree-based and curve-based machine learning models for predicting daily reference evapotranspiration. PLoS ONE 14(5):0217520. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0217520\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0217520\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu L, Zhou H, Ma X, Fan J, Zhang F (2019b) Daily reference evapotranspiration prediction based on hybridized extreme learning machine model with bio-inspired optimization algorithms: Application in contrasting climates of China. J Hydrol 577:123960. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jhydrol.2019.123960\u003c/span\u003e\u003cspan address=\"10.1016/j.jhydrol.2019.123960\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao L, Zhao X, Zhou H, Wang X, Xing X (2021) Prediction model for daily reference crop evapotranspiration based on hybrid algorithm and principal components analysis in Southwest China. Comput Electron Agric 190:106424. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compag.2021.106424\u003c/span\u003e\u003cspan address=\"10.1016/j.compag.2021.106424\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRodrigues GC, Braga RP (2021) Estimation of Reference Evapotranspiration during the Irrigation Season Using Nine Temperature-Based Methods in a Hot-Summer Mediterranean Climate. Agriculture 11(2):124. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/agriculture11020124\u003c/span\u003e\u003cspan address=\"10.3390/agriculture11020124\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang S, Liu S, Che X, Wang Z, Zhang J, Kong D (2020) Recognition of polycyclic aromatic hydrocarbons using fluorescence spectrometry combined with bird swarm algorithm optimization support vector machine. Spectrochim Acta Part A Mol Biomol Spectrosc 224:117404. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.saa.2019.117404\u003c/span\u003e\u003cspan address=\"10.1016/j.saa.2019.117404\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMeng X, Gao X, Lu L, Yu L, Zhang H (2016) A new bio-inspired optimisation algorithm: Bird Swarm Algorithm. J Exp Theor Artif Intell 28(4):673\u0026ndash;687. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/0952813X.2015.1042530\u003c/span\u003e\u003cspan address=\"10.1080/0952813X.2015.1042530\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMaqsood J, Farooque AA, Abbas F, Esau T, Wang X, Acharya B, Afzaal H (2022) Application of Artificial Neural Networks to Project Reference Evapotranspiration Under Climate Change Scenarios. Water Resour Manage 36:835\u0026ndash;851. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11269-021-02997-y\u003c/span\u003e\u003cspan address=\"10.1007/s11269-021-02997-y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMeng X, Gao X, Lu L, Liu Y, Zhang H (2016) A new bio-inspired optimisation algorithm: Bird Swarm Algorithm. J Exp Theor Artif Intell 28(4):673\u0026ndash;687. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/0952813X.2015.1042530\u003c/span\u003e\u003cspan address=\"10.1080/0952813X.2015.1042530\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXing X, Liu Y, Zhao W, Kang D, Yu M, Ma X (2016) Determination of dominant weather parameters on reference evapotranspiration by path analysis theory. Comput Electron Agric 120(22):10\u0026ndash;16. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://dx.doi.org/10.1016/j.compag.2015.11.001\u003c/span\u003e\u003cspan address=\"10.1016/j.compag.2015.11.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFeng Y, Jia Y, Zhang Q, Gong D, Cui N (2018) National-scale assessment of pan evaporation models across different climatic zones of China. J Hydrol 564:314\u0026ndash;328. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jhydrol.2018.07.013\u003c/span\u003e\u003cspan address=\"10.1016/j.jhydrol.2018.07.013\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang Z, Gong Y, Wang Z (2018) Accessible remote sensing data based reference evapotranspiration estimation modelling. Agric Water Manage 210:59\u0026ndash;69. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.agwat.2018.07.039\u003c/span\u003e\u003cspan address=\"10.1016/j.agwat.2018.07.039\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Back-propagation neural network, Hybrid optimization algorithm, Reference evapotranspiration, Southern China ","lastPublishedDoi":"10.21203/rs.3.rs-1671161/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1671161/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe accurate estimation of reference crop evapotranspiration (ET\u003csub\u003eO\u003c/sub\u003e) is vital for regional water and irrigation water resource management and is beneficial to the rational allocation of regional water resources, and alleviates the disparity between water supply and demand. This study accurately estimates the ET\u003csub\u003eO\u003c/sub\u003e of 14 meteorological stations in southern China. Five neural network models (back-propagation neural network [BP], extreme learning machine [ELM], ant colony optimization [ACO]-BP, bird swarm algorithm [BSA]-BP, cat swarm optimization [CSO]-BP) were introduced to predict ET\u003csub\u003eO\u003c/sub\u003e with limited factors using different methods. The results demonstrated that models inputting T (maximum, minimum and average 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 (U\u003csub\u003e2\u003c/sub\u003e) and average atmospheric pressure (AP) in relation to ET\u003csub\u003eO\u003c/sub\u003e gradually decreased. All the three biological heuristic algorithms effectively improved the performance 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 ET\u003csub\u003eO\u003c/sub\u003e prediction in southern China. This result provided a reference for the more accurate prediction of ET\u003csub\u003eO\u003c/sub\u003e for future irrigation decision-making and water resource management in southern China.\u003c/p\u003e","manuscriptTitle":"Prediction model for reference crop evapotranspiration based on the back-propagation algorithm with limited factors","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-06-29 14:52:44","doi":"10.21203/rs.3.rs-1671161/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Minor revisions","date":"2022-12-02T06:22:51+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2022-06-19T05:37:13+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-06-17T14:45:31+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-05-20T01:20:23+00:00","index":"","fulltext":""},{"type":"submitted","content":"Water Resources Management","date":"2022-05-19T06:16:24+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"49b56acc-3aea-4094-a0b4-a9e2eaac4640","owner":[],"postedDate":"June 29th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T18:43:30+00:00","versionOfRecord":{"articleIdentity":"rs-1671161","link":"https://doi.org/10.1007/s11269-022-03423-7","journal":{"identity":"water-resources-management","isVorOnly":false,"title":"Water Resources Management"},"publishedOn":"2023-02-01 18:37:01","publishedOnDateReadable":"February 1st, 2023"},"versionCreatedAt":"2022-06-29 14:52:44","video":"","vorDoi":"10.1007/s11269-022-03423-7","vorDoiUrl":"https://doi.org/10.1007/s11269-022-03423-7","workflowStages":[]},"version":"v1","identity":"rs-1671161","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1671161","identity":"rs-1671161","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}