Climatic Characteristics and Modeling Evaluation of Pan Evapotranspiration over Henan Province, China

: Pan evapotranspiration (E) is an important physical parameter in agricultural water resources research. Many climatic factors a ﬀ ect E, and one of the essential challenges is to model or predict E utilizing limited climatic parameters. In this study, the performance of four di ﬀ erent artiﬁcial neural network (ANN) algorithms i.e., multiple hidden layer back propagation (MBP), generalized regression neural network (GRNN), probabilistic neural networks (PNN), and wavelet neural network (WNN) and one empirical model namely Stephens–Stewart (SS) were employed to predict monthly E. Long-term climatic data (i.e., 1961–2013) was used for the validation of the proposed model in the Henan province of China. It was found that di ﬀ erent models had diverse prediction accuracies in various geographical locations, MBP model outperformed other models over almost all stations (maximum R 2 = 0.96), and the WNN model was the best over two sites, the accuracies of the ﬁve models ranked as MBP, WNN, GRNN, PNN, and SS. The performances of WNN and GRNN were almost the same, ﬁve-input ANN models provided better accuracy than the two-input (solar radiation (R o ) and air temperature (T)) SS empirical model (R 2 = 0.80). Similarly. the two-input ANN models (maximum R 2 = 0.83) also generally performed better than the two-input (R o and T) SS empirical model. The study could reveal that the above ANN models can be used to predict E successfully in hydrological modeling over Henan Province. monthly mean values of the solar radiation (Ro), relative (RH), wind speed (W), pan evapotranspiration abilities of four di ﬀ erent ANN models, MBP, GRNN, PNN, and WNN, and one empirical SS model in modeling E utilizing di ﬀ erent meteorological dataset combinations of Ro, T, H, W, and RH in Henan Province from 1961–2013. The climatic dataset obtained from 14 stations in di ﬀ erent geographical locations were used as inputs for training and testing in Henan Province. The results of this study could be applied practically in the ﬁeld of regional evaporation calculation. This study concluded that:


Introduction
The transfer mechanism between liquid water and water vapor is known as evapotranspiration. The change in water vapor pressure decides the characteristics of evapotranspiration [1,2]. In the fields of water resource information acquisition and irrigation system designing, pan evapotranspiration had become a fundamental physical variable [3]. Many climatic factors can influence the change of pan evapotranspiration including temperature, solar radiation, wind speed, and relative humidity. Few studies aimed at the quantitative influence of different climatic parameters on the changes of pan evapotranspiration in different regions [4][5][6][7][8][9]. Therefore, it is necessary to accurately estimate and predict pan evapotranspiration utilizing climatic parameters in the study of hydrological modeling and water resources management.  Table 1). The monthly mean values of the solar radiation (Ro), relative humidity (RH), wind speed (W), air temperature (T), pan evapotranspiration (E), and sunshine duration (H) were used in this study for 53 years (from 1961 to 2013). The device of pan evapotranspiration is U20 type evaporator with a diameter of 0.20 m, depth of 0.10 m. The datasets were obtained from the China meteorological information center [26][27][28].  Table 1). The monthly mean values of the solar radiation (Ro), relative humidity (RH), wind speed (W), air temperature (T), pan evapotranspiration (E), and sunshine duration (H) were used in this study for 53 years (from 1961 to 2013). The device of pan evapotranspiration is U20 type evaporator with a diameter of 0.20 m, depth of 0.10 m. The datasets were obtained from the China meteorological information center [26][27][28].

Multiple Hidden Layer Back-Propagation (BP) Neural Network (MBP)
The back-propagation (BP) neural network was a feedforward neural network [29]. The main characteristic of the BP neural network was that the signal was forward feedback and the error was backpropagation. Prior to transmission, the input signal was processed step by step from the input layer to the hidden layer. Neurons state of each layer affected only the next layer. If the result layer did not get the desired output, the weight and threshold were adjusted based on the prediction error. BP neural network prediction results were constantly close to the expected forecast results.
The BP neural network was composed of an input layer, a hidden layer, and output layer. Hidden layers can be divided into a haploid hidden layer and multiple hidden layers according to the number of layers. Multiple hidden layers consisted of multiple single hidden layers. The multi-hidden layer had stronger generalization ability and higher prediction accuracy. The selection of hidden layer amounts should consider the network precision and training time comprehensively. For a simpler mapping relationship, the single hidden layer can be selected to improve the accuracy of the network. For complex mapping relationships, multiple hidden layers can be selected. In that regard, the multiple hidden layer BP neural network (MBP) was utilized in the current study.

Generalized Regression Neural Network (GRNN)
The generalized regression neural network (GRNN) was one of the radial base neural networks [30,31]. The GRNN had strong nonlinear mapping capability and a flexible network structure. The GRNN had higher fault tolerance and robustness. It was suitable for solving nonlinear problems. The GRNN had obvious advantages in approximation ability and learning speed. The GRNN can be converged to the optimal return along with the increase of samples. In addition, the GRNN can also deal with unstable data. Therefore, the GRNN had been widely used in signal processing, configurable analysis, and control decision system.

Probabilistic Neural Networks (PNN)
The probability neural network (PNN) was a feedforward neural network developed based on radial-based function [32,33]. Its theoretical foundation was the Bayesian minimum risk criterion and the probability of Parzen windows. The layers of the PNN were made up of input patterns, sum layers, and output layers. In practice, it had advantages of adopting a linear learning algorithm to complete the nonlinear problems with high precision. The corresponding weight of PNN was the distribution of design samples. The PNN network did not require drilling and can meet the real-time processing requirements.

Wavelet Neural Network (WNN)
The wavelet neural network (WNN) was based on the BP neural network topology. It was a feedforward recursive network with little pokey functions as the hidden nodes [34,35]. The wavelet base function used in this study was the Morlet wavelet function. It was similar to the BP neural network weight correction algorithm. It used a gradient correction method to calculate network weight and wavelet base function parameters and obtain the desired results of the wavelet neural network closer.

Stephens and Stewart Model (SS)
The Stephens and Stewart (SS) model was a simple linear regression function [10]. The equation can be indicated as E = Ro·(a 1 + b 1 ·T), where a 1 and b 1 are decided by training data utilizing the least square method.
Land 2020, 9, 229 5 of 14 (4) where, N represents the number of variables, and the Em and the E O are the modeled and observed values of pan evapotranspiration, respectively.    The units of Ro, T, H, W, and E are MJm −2 , °C, hour, ms −1 , and mm/day, respectively; M, S, V, Skew, min, max represent the mean, standard deviation, variance, skewness, minimum, and maximum values, respectively. R represents the correlation between E and the relevant meteorological factor.

Prediction Results of Different ANN Models
This study tried different combinations of inputs. Table 3 provides an input combination for each model. Table S1 shows that the training and test results of MBP, GRNN, PNN, WNN, and SS models for predicting E of San menxia and Lu shi stations. From the table, the models with whole meteorological variables (Ro, T, H, W, and RH) had the optimum accuracy. In predicting E of San menxia, the WNN model is superior to other models. MBP model is superior to other models in the prediction of E at Lu shi. During the testing phase, the precision of the model was as follows WNN, GRNN, MBP, PNN, and SS in San menxia station. The accuracy level of the soft computing model in the test period was MBP, WNN, GRNN, PNN, and SS in Lu shi station. These accuracy levels are calculated based on the R 2 , RMSE, MAE, EN standards. Here, the WNN has the optimal precision, and the SS has the lowest precision at San menxia station. Additionally, MBP has the optimal precision while the SS also has the lowest precision in Lu shi. By comparing the simple two-input SS   Figure 3. Seasonal variation trend of meteorological variables in each station.

Prediction Results of Different ANN Models
This study tried different combinations of inputs. Table 3 provides an input combination for each model. Table S1 shows that the training and test results of MBP, GRNN, PNN, WNN, and SS models for predicting E of San menxia and Lu shi stations. From the table, the models with whole meteorological variables (Ro, T, H, W, and RH) had the optimum accuracy. In predicting E of San menxia, the WNN model is superior to other models. MBP model is superior to other models in the prediction of E at Lu shi. During the testing phase, the precision of the model was as follows WNN, GRNN, MBP, PNN, and SS in San menxia station. The accuracy level of the soft computing model in the test period was MBP, WNN, GRNN, PNN, and SS in Lu shi station. These accuracy levels are calculated based on the R 2 , RMSE, MAE, E N standards. Here, the WNN has the optimal precision, and the SS has the lowest precision at San menxia station. Additionally, MBP has the optimal precision while the SS also has the lowest precision in Lu shi. By comparing the simple two-input SS (R o and T) model, the artificial neural network (ANN) models had better precision than the SS. Additionally, the two-input ANN computing models seem to have the same precision as the SS model in predicting E at San menxia and Lu shi stations. Table S2 shows the precision of applying models to predict E at Xi xia and Zheng zhou stations. Similar to Lu shi station, the all-weather input mode usually provides the best accuracy. The accuracy and optimal MBP model of Xi xia and Zheng zhou station in predicting E are better than the other models. The precisions ranks are MBP, GRNN, WNN, PNN, and SS. The precision of the two-input ANN models in predicting E at Xi xia and Zheng zhou station was the same as that of the SS model.  Table S3 provides the statistical data of the ANN model for predicting E at Baofeng and Nan yang stations. At Baofeng station, the performance of the five-input modes was the best, and the performance of the MBP model was better than that of other models. The accuracy ranks of models were as follows: MBP, WNN, GRNN, PNN, and SS. In Nan yang station, three-input MBP and two-input WNN models have better performance than their corresponding five-input models. The behavior of the GRNN is better than other models. The precision of the models is ranked as follows: GRNN, WNN, SS, MBP, and PNN. Obviously, compared with the two-input ANN model of Nan yang station, the effect of the SS model is poor. Table S4 reveals the results of Xin yang and An yang stations. It can be seen from those models with intact weather data that they usually have optimal accuracies. The WNN model has better behavior than the other models in Xin yang according to RMSE, MAE, R 2 , and E N . The rankings are WNN, MBP, GRNN, SS, and PNN in Xin yang. The MBP model has better behavior than others in An yang according to RMSE, MAE, R 2 , and E N . The rankings are MBP, GRNN, WNN, PNN, and SS in An yang. The SS model has the same precision as the two-input ANN models in predicting E at Xin yang and An yang station. Table S5 shows the veracity of predicting E of Xin xiang and Shang qiu stations by using the ANN and experiential models. Similar to the previous stations, usually five-input models had optimal precisions, and the performance of the MBP model is superior to other models in RMSE, MAE, R 2 , and E N statistics. Accuracies of models in the test stage are ranked as follows: MBP, GRNN, WNN, PNN, and SS in both Xin xiang and Shang qiu stations. The accuracies of the MBP, GRNN, PNN, WNN, and SS models are shown in Table S6 for prediction E of Xu chang and Xi hua stations. Like previous sites, the five-input model typically provides the best performance. The five-input MBP model is both greater than the other models in Xu chang and Xi hua stations. The rankings of precisions are MBP, WNN, GRNN, SS, and PNN in Xu chang station. Additionally, in the Xi hua station, the accuracies are ranked as follows: MBP, WNN, GRNN, PNN, and SS. The comparison between the two-input models and SS model showed that the SS model had the same precision as other two-input ANN models in the test stage. Table S7 provides the test accuracy of models for predicting E at Zhu madian and Gushi stations. In the two stations, the five-input ANN models also had the best precisions according to MAE, RMSE, R 2 , and E N index. The MBP model had optimal performance compared to the other models in predicting E at Zhu madian and Gushi stations. The performance ranks of the models both are MBP, GRNN, WNN, SS, and PNN at Zhu madian and Gushi stations. The comparison of two-input ANN models and SS models indicated that the two-input ANN models and SS models had similar performances. General precisions of models are shown in Table 4. The MBP model had much better scores than the other methods in predicting E and the final precisions are ranked as follows: MBP, WNN, GRNN, PNN, and SS. Additionally, the performance of GRNN and WNN were almost the same. Table 4. Accuracy rank a of the soft computing models in estimating pan evapotranspiration (E). 1  San menxia  3  2  4  1  5  Western part  2  Lu shi  1  3  4  2  5  Western part  3  Xi xia  1  3  4  2  5  Western part  4  Zheng zhou  1  2  4  3  5  Central part  5  Baofeng  1  3  4  2  5  Central part  6  Nan yang  4  1  5  2  3  Central part  7  Xin yang  2  3  5  1  4 Central part 8

Stations MBP GRNN PNN WNN SS Region
An  Figure 4 shows the comparison of models utilizing all stations database. Better accuracy appeared in five-input models. The MBP model was better than the other models. The precisions were ranked MBP, WNN, GRNN, PNN, and SS. Two-input MBP, WNN, GRNN models perform inferior to the SS model; the SS model has lower precision than the five-input ANN models (Figure 4 and Table 5). In Figure 4, all the ANN computing models generally have good generalization ability. The generalized MBP model was also tested at every site ( Table 5). The results showed that the five-input MBP model had a high generalization ability based on RMSE, MAE, R 2 , and E N index.

Discussion
The Ro, T, and H were much better at modeling E than other variables in San menxia station. Table 2 shows the value of R also confirms this. Ro, T, and H parameters of Xi xia station also had a good performance in modeling E and is also shown in Table 2. In the Lu shi station, the Ro and T parameters were proved to be more valid in modeling E than H. This was because Ro (R = 0.94) had a higher correlation with E than H (R = 0.64) at Lu shi station. Ro proved to be the most valid variable

Discussion
The Ro, T, and H were much better at modeling E than other variables in San menxia station. Table 2 shows the value of R also confirms this. Ro, T, and H parameters of Xi xia station also had a good performance in modeling E and is also shown in Table 2. In the Lu shi station, the R o and T parameters were proved to be more valid in modeling E than H. This was because R o (R = 0.94) had a higher correlation with E than H (R = 0.64) at Lu shi station. R o proved to be the most valid variable in modeling E at Nan yang, Xin yang, Xu chang, and Gushi stations, which is also confirmed by the high R values. Models with W (or RH) generally provided worse results than those with R o input. Adding W input generally decreased the model accuracies at Zheng zhou and BaoFeng stations (R = 0.21 in Zheng zhou and R = 0.33 in BaoFeng). Similar to the San menxia and Xi xia stations, the R o input was found to be better at modeling E than the other input variables at An yang, Xin xiang, Shang qiu, Xi hua, and Zhu madian stations. Similar to the An yang and Xin xiang stations, the R o variable had higher correlations with E (see Table 2) than H, W, and RH at Xi hua and Zhu madian stations. The T variable also provided better accuracy than the H, W, and RH in predicting E here. Figure 4 also indicates that the R o was the most useful variable in predicting E based on the all stations dataset. It is noteworthy that T and H input parameters were better. W and RH input parameters were worst. It was also indicated that only T or H input was deficient for high precision modeling E. The model behaviors were becoming better generally with the increase of input parameter amounts, which indicated that all meteorological variables had positive influences on modeling E in most of the stations of Henan Province. Some underestimations of ANN models also existed. Different geographical locations and climates may be the reason.
In short, ANN models with whole meteorological variables (R o , T, H, W, and RH) generally had the best precision. This indicated that all these parameters are required for the best E model. The R o was the most useful variable in modeling E from the all stations dataset. Then, T and H inputs parameters were better. W and RH input parameters were worst. Adding W or RH inputs into models usually weakens their precisions in modeling E in the all stations dataset. This reveals that the complicated nonlinear relationship between W (RH) and E cannot be shown from the ANN models we tested in this study. Two-input (R o and T) ANN models usually provide better precision than the SS model in the all stations dataset. This told us that R o and T can be preferred in some areas where obtaining the data of the other variables (H, W, and RH) are difficult.
Many ANN models, such as multi-layer perceptron (MLP), generalized regression neural network (GRNN), fuzzy genetic (FG), least-square support vector machine (LSSVM), multivariate adaptive regression spline (MARS), and adaptive neuro-fuzzy inference systems with grid partition (ANFIS-GP) have different accuracies in different climates. For example, the GRNN model performed better in Tibetan Plateau [2], however, SS models are preferred for some climatic zones such as BJ (Beijing), CQ (Chongqing), and HK (Haikou) stations [2] compared to the complex nonlinear models. Previous studies showed that ANN models are accurate, but their time efficiency is a little slower than the SS model. The adaptive neuro-fuzzy inference system (ANFIS) and ANN evaporation models also showed good performance when limited climatic parameters were used in the USA [3]. Shirsath et al. [9] also showed that ANN had slightly better performance than multiple linear regression (MLR) models, Penman, Priestley-Taylor, and SS [10]. Shiri et al. [10] showed that the gene expression programming (GEP) model was more accurate than empirical-physical models with improvements of adding gene thinking in the model [11]. It has been found that ANN worked very well at the study site in estimating evaporation in the hot and dry region [13]. The optimal COMBINE-GRNNM-GA method also had a good performance in predicting pan evaporation in the Republic of Korea by combining the advantages of both [17]. Comparing with ANN, the least squares-support vector, regression (LS-SVR), fuzzy logic, and adaptive neuro-fuzzy inference system (ANFIS) models revealed that machine learning models outperform the traditional Hargreaves and Samani method (HGS) and SS empirical methods [18]. We should choose appropriate ANN models in different regions of different climatic types. Such as, Ro, T, and H are the most useful variable of MBP in predicting E that we can choose in Henan Province (subtropical temperate continental climate). In the future, novel genetic algorithms of ANNs can be tried in predicting E, such as a stacking model that makes synergetic use of multiple ANN models can create more accurate and robust models [36,37]. Therefore, the ANN models of predicting pan evaporation have the advantage of efficiency and accuracy.

Conclusions
This study explored the abilities of four different ANN models, MBP, GRNN, PNN, and WNN, and one empirical SS model in modeling E utilizing different meteorological dataset combinations of Ro, T, H, W, and RH in Henan Province from 1961-2013. The climatic dataset obtained from 14 stations in different geographical locations were used as inputs for training and testing in Henan Province. The results of this study could be applied practically in the field of regional evaporation calculation. This study concluded that: (a) ANN models with five-inputs generally have better accuracies (maximum R 2 = 0.96). The five-input ANN models provided better accuracy than the two-input (R o and T) SS empirical model (R 2 = 0.80). Additionally, the two-input ANN models (maximum R 2 = 0.83) also generally performed better than the two-input (R o and T) SS empirical model (R 2 = 0.80).
(b) The accuracies of the applied models rank as MBP (rank index: 20), WNN (rank index: 32), GRNN (rank index: 33), PNN (rank index: 61), and SS (rank index: 64). The MBP models are the most appropriate for predicting E using limited climatic inputs in different geographical locations and climatic zones in Henan Province. The performances of WNN and GRNN were almost the same.
(c) R o seems to be the most important parameter in predicting E at most stations, while T and H inputs parameters were better. W and RH input parameters were worst. Adding W or RH inputs into models generally can increase model accuracies in predicting E.
Supplementary Materials: The following are available online at http://www.mdpi.com/2073-445X/9/7/229/s1, Table S1: Statistics of different models at San menxia and Lu shi station, Table S2: Statistics of different models at Xi xia and Zheng zhou station, Table S3: Statistics of different models at Bao feng and Nan yang station, Table S4: Statistics of different models at Xin yang and An yang station, Table S5: Statistics of different models at Xin xiang and Shang qiu station, Table S6: Statistics of different models at Xu chang and Xi hua station, Table S7: Statistics of different models at Zhu madian and Gu shi station.