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Modeling Evapotranspiration Response to Climatic Forcings Using Data-Driven Techniques in Grassland Ecosystems

Modeling Evapotranspiration Response to Climatic Forcings Using Data-Driven Techniques in... Hindawi Advances in Meteorology Volume 2018, Article ID 1824317, 18 pages https://doi.org/10.1155/2018/1824317 Research Article Modeling Evapotranspiration Response to Climatic Forcings Using Data-Driven Techniques in Grassland Ecosystems 1,2 1,2 Xianming Dou andYongguoYang Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process of Ministry of Education, China University of Mining and Technology, Xuzhou 221116, China School of Resources and Geosciences, China University of Mining and Technology, Xuzhou 221116, China Correspondence should be addressed to Yongguo Yang; yongguoyang@hotmail.com Received 6 November 2017; Revised 9 February 2018; Accepted 15 March 2018; Published 22 April 2018 Academic Editor: Harry D. Kambezidis Copyright © 2018 Xianming Dou and Yongguo Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Remarkable progress has been made over the last decade toward characterizing the mechanisms that dominate the exchange of water vapor between the biosphere and the atmosphere. This is attributed partly to the considerable development of machine learning techniques that allow the scientific community to use these advanced tools for approximating the nonlinear processes aec ff ting the variation of water vapor in terrestrial ecosystems. Three novel machine learning approaches, namely, group method of data handling, extreme learning machine (ELM), and adaptive neurofuzzy inference system (ANFIS), were developed to simulate and forecast the daily evapotranspiration (ET) at four different grassland sites based on the ux fl tower data using the eddy covariance method. es Th e models were compared with the extensively utilized data-driven models, including artificial neural network, generalized regression neural network, and support vector machine (SVM). Moreover, the influences of internal functions on their corresponding models (SVM, ELM, and ANFIS) were investigated together. It was demonstrated that most developed models did good job of simulating and forecasting daily ET at the four sites. In addition to strengths of robustness and simplicity, the newly proposed methods achieved the estimates comparable to those of the conventional approaches and accordingly can be used as promising alternatives to traditional methods. It was further discovered that the generalization performance of the ELM, ANFIS, and SVM models strongly depended on their respective internal functions, especially for SVM. 1. Introduction relatively essential for understanding the responses of ET to different environmental forces and oer ff ing precise ET Grasslands coverapproximately 13%ofgloballandsurface budgets for solving the issue of water resource allocation [1]. It is universally acknowledged that grassland ecosystems and management. Eddy covariance technique has been con- play a crucial role in global water and carbon budgets as sidered as a reliable approach and is being used extensively well as energy balances [2, 3]. In grassland ecosystems, the to measure grassland ET in different climates [7]. A large interrelations between atmosphere and evapotranspiration amount of data from numerous flux tower sites, including ET (ET), consisting of transpiration and evaporation from the and other micrometeorological variables, have been collected soil and plant systems, are closely related to ecosystem andarchivedinglobalfluxnetworkinrecentyears [8,9], productivity, particularly in arid and semiarid regions [4]. providing a solid foundation for obtaining helpful knowledge Their dynamical interactions between biophysical and bio- of the underlying mechanisms influencing the variation of geochemical processes are substantially affected by a variety ET across various time scales from hourly to interannual. of environmental driving factors, such as climate change, However, accurately estimating ET of grassland ecosystems nutrient deposition, and increased atmospheric CO [4–6]. remains a great challenge due to the limited understanding of Therefore, measuring and estimating ET in grasslands are how ET responds to human practical activities (e.g., land use 2 Advances in Meteorology change, grazing, and fertilization) and climate extreme events the strengths and shortcomings of each method and provide (e.g., extreme precipitation, wind storms, droughts, and heat helpful suggestions for the relevant researchers. waves). It is a widely accepted fact that the ability of all the above-mentioned methods is strongly aeff cted by their cor- A broad range of approaches are presently utilized to responding inner parameters [24]. However, very few studies model and predict terrestrial ET at various spatial levels have reported the roles of different intrinsic parameters for from ecosystem to regional or global level. es Th e methods each approach in characterizing the actual behavior of the can be commonly grouped into three categories: remote addressed problems, especially for the relatively new meth- sensing-based [10, 11], physically based [12, 13], and data- ods, ANFIS and ELM, even though these approaches have driven [14, 15]. Among these approaches, physically based been widely applied in other fields. For example, although techniques are universally used by both the ecological and several recent studies have examined the effects of different hydrological communities, due to their distinct advantage membership functions on ANFIS for various hydrological of oer ff ing a physical insight into the complex hydrological time series prediction [25–27], it remains unclear how the process controlling the temporal and spatial variation of ET. ANFIS model is influenced by different identification algo- However, temporal and spatial heterogeneity of land surface rithms for fuzzy inference system (FIS) generation for the characteristics strongly affects the underlying processes of present application. In fact, when establishing these models ongoing water vapor exchange, which considerably increases in practical applications, these intrinsic algorithms in most the complexity of elucidating the hydrological relationship studies are commonly determined by random selection or between land and the atmosphere and subsequently impedes trial-and-error procedure, which may limit, to some extent, the pursuit of obtaining accurate physically based models. the ability of related models. Accordingly, it is certainly worth Data-driven methods have been receiving increasing examining the impacts of inner parameters on SVM, ANFIS, attention in the last decade for ET simulation and prediction and ELM for predicting ET, which is also another major task at different terrestrial ecosystems. Numerous previous studies for the current research. have reported the ability of machine learning techniques Considering the presently existing above-mentioned in the prediction of ET at terrestrial ecosystems [16, 17]. It issues, the novelty of this paper lies in the use of three has been demonstrated that these approaches are capable of state-of-the-art data-driven methods for estimating daily ET eeff ctively seizing most useful information stored in the avail- basedontheavailableeddycovariancemeasurementsat able data (e.g., the measurements based on eddy covariance four different grassland sites. More specicfi ally, the novelty method), without depending on any complex underlying of this paper is threefold as follows. First, we probe into knowledge about the evolving process of ET. Nevertheless, the feasibility and effectiveness of three modern data-driven to the best of our knowledge, most studies focused primarily models, including GMDH, ELM, and ANFIS, for modeling on using three ubiquitous approaches, namely, artificial neu- and predicting the ET at the daily time scale. Second, we ral network (ANN), generalized regression neural network investigate whether these newly proposed models have the (GRNN), and support vector machine (SVM). potential to sufficiently complement or replace the con- In recent years, many novel machine learning techniques ventionally recognized methods, ANN, GRNN, and SVM. have been proposed for handling the complex nonlinear Finally, we particularly focus on evaluating the impacts of problems, such as adaptive neurofuzzy inference system intrinsic algorithms involved in each model (SVM, ELM, and (ANFIS), extreme learning machine (ELM), and group ANFIS) on their respective generalization ability. method of data handling (GMDH). eTh generalization ability of these advanced approaches has been extensively acknowl- 2. Materials and Methods edged in forecasting the environmental and climatological variables. More particularly, these methods have been widely 2.1. Site Description and Data Used. In this study, four grass- applied in the nonlinear time series prediction in several var- land ecosystems were used to explore the modeling capability ious branches of hydrology, such as reference ET forecasting of the proposed models. These sites are situated in different [18, 19], evaporation prediction [20, 21], and soil moisture countries. The details of each site are shown in Table 1. estimation [22, 23]. However, comparatively few attempts to eTh ywereselectedfor thepresentstudymainlydue to apply these state-of-the-art approaches have been made to their continuous multiyear measurements of water vapor u fl x date for estimating the ET at terrestrial ecosystems based on (ET) with the eddy covariance technique. In addition, the the eddy covariance data. measurements of other variables were also undertaken at In addition, all the techniques, including the conventional these sites, primarily including CO ux, fl energy ux fl es (latent ANN, GRNN, and SVM methods, and the relative novel heat and sensible heat), and meteorological variables. The methods (ELM, ANFIS, and GMDH) proposed by this study utilized instruments and processing procedures of related remarkably differ in terms of their structures, principles, data at each site have been, respectively, reported in previous and parameters. And, therefore, their generalization ability studiesasshown inTable1. should be different in theory. For this reason, regarding Statistical parameters of daily measurements utilized in their practical application in the present study, systematically this study during at least 6-year period for all the sites are evaluating the ability of all the methods for ET prediction giveninTable 2. As showninthetable, theannualmeanair ∘ ∘ is particularly important with the objective of ensuring the temperature (𝑇 )changes from 6.48 CatCA-Letto10.20 C predictive accuracy. Besides, it is also beneficial to identify at HU-Bug; the annual mean soil temperature (𝑇 ) is between 𝑠 Advances in Meteorology 3 Table 1: Site characteristics used in this study. Site Latitude Longitude Elevation MAT TAP Climate Period Reference AT-Neu 47.12 11.32 970 6.68 669 Temperate 2004–2009 Wohlfahrt et al. [28] CA-Let 49.71 −112.94 951 6.48 1095 boreal 1999–2007 Flanagan et al. [29] DE-Gri 50.95 13.51 385 8.35 934 Temperate 2004–07, 2009-10 Hussain et al. [30] HU-Bug 46.69 19.60 140 10.20 499 Temperate 2003–2008 Carvalhais et al. [31] Note. MAT and TAP denote the mean annual temperature and total annual precipitation, respectively, and they are calculated based on the time period (period ∘ −1 column). The units of elevation, MAT, and TAP are m, C, and mm year ,respectively. ∘ ∘ 7.35 CatCA-Letand10.84 C at HU-Bug; the annual mean point out that the generalization ability of SVM method −2 −1 considerably depends on the choice of kernel function. net radiation (𝑅 )rangesfrom4.24molm day at AT-Neu −2 −1 eTh re are many alternative kernel algorithms, such as radial to 6.17 mol m day at CA-Let; the annual mean relative basis function (RBF), polynomial, sigmoid, exponential, humidity (𝑅 ) varies from 60.40% at CA-Let to 79.80% at Laplacian, and rational quadratic. eTh rfi st three kernel AT-Neu. eTh other statistical characteristics of these variables functions are commonly used for SVM models and therefore are also summarized. Furthermore, Table 2 also presents were compared and assessed in this study. As a matter of the correlation coefficients between ET and environmental convenience, the SVM models with the kernel functions, variables. It can be clearly seen that almost all the variables at RBF, polynomial, and sigmoid, were hereinafter referred to the four sites have strong correlation with ET. The variables, as SVM-RBF, SVM-Poly, and SVM-Sig, respectively. For a 𝑇 ,𝑇 ,and𝑅 , show strong positive correlation with ET, while 𝑎 𝑠 𝑛 given case, the critical internal parameters involved in the 𝑅 presents negative correlation with ET. Daily available training process, including the cost factor, the slack factor, measurements for at least six years were divided into three and the related parameter of respective kernel algorithm, parts. At each site, the first 4-year dataset was utilized for were carefully obtained through the grid search approach. All training, the h year dataset was used for validation with the SVM models applied in the present research were per- the intention of preventing overtraining or overtfi ting of the formed according to LIBSVM software written by MATLAB training dataset, and the remaining dataset was employed for programming language [36]. predicting. 2.2.3. Adaptive Neurofuzzy Inference System. ANFIS has 2.2. Data-Driven Techniques received much attention for modeling and predicting the hydrological time series (e.g., evaporation, groundwater level, 2.2.1. Artificial Neural Network. ANN model performance and stream-flow) in recent years. Hence, this method has depends on parallel information processing system involved been widely recognized as a promising alternative tool to in a multilayer network, and the model is capable of trans- traditional data-driven techniques for mapping the nonlinear forming helpful information from the input data into knowl- relationship between independent and dependent variables edge through artificial neurons which are directly linked in different research efi lds. Selecting a reasonable FIS is to active synapses with a set of weights related to different an important precondition for successfully elucidating the variables[32]. Itsultimategoalistoestablish thenonlin- nonlinear processes underlying a given problem, when estab- ear relationship between input (independent) variables and lishing an ANFIS model. Presently, Takagi and Sugeno [37] output (dependent) variables. In this study, a feed-forward method is extensively adopted in diverse research areas, ANN with a single hidden layer was used and its parameters and, in particular, its powerful ability in estimating various were updated using the backpropagation learning algorithm hydrological variables has been proved by accumulating lines with the intention of minimizing the error between the target of evidence to date. Accordingly, Takagi and Sugeno-based values and the calculated values derived from the network. ANFIS models were developed by the present work for all When designing ANN models in this study, hyperbolic tan- the applied cases. To achieve an optimum AFNIS model, gent sigmoid and linear algorithms were selected as transfer two types of parameters, namely, the antecedent parameters functions for hidden layer and output layer, respectively, with which influence the effectiveness of the applied membership the purpose of generating output results from each neuron. function and the consequent parameters which determine In addition, the determination of other key parameters and the quality of the system output, need to be optimized functions, such as the number of nodes of hidden layer and appropriately. eTh hybrid learning procedure is the most training functions, was also taken into account based on the commonly utilized to adjust the antecedent and consequent trial-and-error approach. parameters using the gradient descent and least squares 2.2.2. Support Vector Machine. eS Th VMapproachisan methods, respectively. In addition, of particular interest is the important soft computing method and has been utilized in impacts of different identification algorithms for generating many research efi lds. eTh detail of theory about SVM can FISs on the ability of developed ANFIS models. eTh current be foundinVapnik[33]and itsadvancesinthe practical research also attempts to address this issue. As a convenience, applications can be found in some recent reviews [33–35]. the ANFIS models with three extensively used identification Based on the accumulated experience, it is noteworthy to algorithms, namely, grid partitioning, subtractive clustering, fift 4 Advances in Meteorology fl 𝑎 𝑛 𝑠 𝑎 𝑛 𝑠 𝑎 𝑛 𝑠 𝑎 𝑛 𝑠 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑅 𝑅 𝑅 𝑅 𝑅 𝑅 𝑅 𝑅 𝑇 Table 2: Daily statistical parameters of ux tower measured environmental variables including air temperature ( ), net radiation ( ), relative humidity ( ), soil temperature ( ), and evapotranspiration (ET) in the whole period. Period Variable mean max min sd ku sk 6.68 22.96 −17.63 8.19 2.24 −0.29 0.80 4.24 16.51 −6.44 5.33 1.97 0.16 0.88 AT-Neu 79.80 99.98 44.36 10.98 2.52 −0.46 −0.59 8.71 21.28 −2.56 6.86 1.50 0.01 0.78 ET 1.29 6.78 −0.32 1.33 2.75 0.87 1.00 6.48 28.57 −31.89 10.37 3.10 −0.58 0.59 6.17 19.18 −15.83 5.91 1.93 0.38 0.76 CA-Let 60.40 99.04 16.94 16.48 2.18 0.04 −0.19 7.35 24.52 −10.06 7.99 1.81 0.18 0.61 ET 0.81 5.96 −0.50 1.01 6.68 1.92 1.00 8.35 27.83 −18.02 7.80 2.37 −0.25 0.76 5.08 19.76 −4.25 5.34 2.17 0.55 0.90 DE-Gri 77.98 100.00 39.22 10.60 2.63 −0.31 −0.63 9.68 24.32 −0.84 6.10 1.83 0.03 0.75 ET 0.96 4.50 −0.61 0.98 3.33 1.04 1.00 10.20 30.15 −18.72 8.98 2.28 −0.22 0.72 5.81 18.26 −3.90 5.38 1.88 0.39 0.83 HU-Bug 76.28 99.66 38.88 12.01 2.61 −0.38 −0.46 10.84 26.03 −3.11 7.21 1.78 0.05 0.70 ET 1.28 5.96 −0.06 1.10 3.68 1.08 1.00 ∘ −2 ∘ −1 Note.Theunits of , , , ,andET are C, mol m , %, C, and mm day ,respectively. , , , , ,and refer to the mean, maximum, minimum, standard deviation, kurtosis, and ℎ mean max min sd ku sk skewness of each variable, respectively. refers to the correlation coefficient between each variable and ET. Advances in Meteorology 5 and fuzzy c-means clustering, were abbreviated as ANFIS- 2.2.6. Group Method of Data Handling. GMDH approach Grid, ANFIS-SC, and ANFIS-FCM, respectively. as a typical inductive high-order regression-type algorithm is commonly subsumed under the category of feed-forward 2.2.4. General Regression Neural Network. GRNN proposed neural network [43]. The architecture of this heuristic non- by Specht [38] based on nonlinear regression theory is widely linear method is established automatically based on self- utilized for function approximation. It is closely associated organization learning algorithm, which is significantly differ- with the radial basis function neural network, but there ent from other machine learning algorithms. Moreover, the exists a slight distinction between these two networks in GMDH method can conquer the limitation of requiring prior knowledge regarding a given problem, and redundant input terms of topological structure. The GRNN model as a one- pass learning method is designed by using a highly parallel variables can be eliminated eecti ff vely during the learning. framework. In fact, the number of neurons in all the layers is Besides, the GMDH is highly robust to noise data and thus is strongly dependent upon the number of the used variables as not aeff cted by the existing outliers in the training samples. well as the sample size of a given training dataset, and thus In a well-developed GMDH network, the neuron in each these neurons do not require adjustment during the learning. hidden layer is individually connected by two inputs and a In addition to this, another noteworthy advantage of the singleoutput andactsasatransferfunction forrepresenting GRNN approach over other data-driven techniques is that the the results generated by the two neurons from the previous GRNN model does not need much time to select its internal layer. Mathematically, each neuron is represented by using algorithms or parameters, apart from the smoothing factor a quadratic polynomial equation with vfi e weights and one that highly aeff cts the model generalization performance. At bias. Ultimately, the well-trained network can be expressed by using an explicit high-order polynomial function in present, there is no standard, universally accepted method for determining the optimal smoothing factor with the aim of relation to all the neurons reserved in the network. All the guaranteeing the forecasting precision of the GRNN model. weighting coefficients involved in this iterative function are In this study, the proper smoothing factor that was set calculated by a common least square method. More details ranging from 0.01 to 1 was obtained by using an iterative aboutGMDHmethodcan be foundinIvakhnenko[43]and algorithm. Moreover, to prevent the overtt fi ing, fourfold Barzegar et al. [44]. cross validation was utilized in the training. Further details regarding the principle of the GRNN approach can be found 2.3. Model Structure and Evaluation. It is clear from Table 2 in Raghavendra and Deka [34] and Yaseen et al. [39]. that each environmental variable has high linear correlation with ET. er Th efore, these variables ( 𝑇 ,𝑇 ,𝑅 ,𝑅 )wereused 𝑎 𝑠 𝑛 ℎ 2.2.5. Extreme Learning Machine. ELM rfi stly proposed by as inputs for all the proposed data-driven models. Before the Huang et al. [40] is a relatively new, modern data-driven training of each applied model, the input variables and ET technique and has been successfully applied to deal with the were normalized to a range between 0 and 1. MATLAB so-ft nonlinear problems in diverse areas during the last few years. ware (version 8.2, R2013b) was utilized for the development The developed ELM method has a topological architecture of of the models and the related statistical analysis of estimated single-hidden-layer feed-forward neural network. Its number results. of hidden nodes can be randomly gained, and their relevant 2 In this study, the coefficient of determination ( 𝑅 ), Nash- parameters (weights and biases) do not need to be tuned as Sutcliffe efficiency (NSE), root mean square error (RMSE), these properties have been demonstrated to be independent and mean absolute error (MAE) were considered as statistical of the training dataset. By contrast, for the traditional back- indices for measuring the performance of the developed propagation based ANN approach, almost all the parameters data-driven models. These statistical indices are, respectively, are highly problem-dependent and should be carefully set expressed as below: or optimized by a common, time-consuming trial-and-error process. Moreover, the powerful approximation ability of the ELM approach has been strongly supported by several ∑ (ET − ET)(ET − ET ) [ ] 𝑖=1 𝑜,𝑖 𝑜 𝑚,𝑖 𝑚 lines of evidence [39, 41]. eTh fundamental principle of ELM 2 [ ] 𝑅 = , [ ] approach can be found in more detail in Huang et al. [40]. 2 2 𝑁 𝑁 ∑ (ET − ET) ∑ (ET − ET ) 𝑜,𝑖 𝑜 𝑚,𝑖 𝑚 Furthermore, it should be emphasized that appropri- 𝑖=1 𝑖=1 [ ] ate activation function is of importance for guaranteeing 𝑁 2 the modeling and generalization performance of the ELM ∑ (ET − ET ) 𝑖=1 𝑜,𝑖 𝑚,𝑖 method [42]. eTh sigmoid, sine, and hard limit algorithms NSE=1− , ∑ (ET − ET) are the three common types of activation functions applied 𝑖=1 𝑜,𝑖 𝑜 (1) for the hidden layer. The influences of different activation functions on the modeling ability of developed ELM models were evaluatedbythisstudy.Forthesakeofconvenience, RMSE= ∑(ET − ET ), 𝑜,𝑖 𝑚,𝑖 theELMmodelswiththesigmoid,sine, andhardlimitalgo- 𝑖=1 rithms were abbreviatedasELM-Sig,ELM-Sin,and ELM- Hard, respectively. Moreover, the linear activation function 𝑁 󵄨 󵄨 󵄨 󵄨 MAE= ∑ ET − ET , was adopted for the output layer for all the developed ELM 󵄨 󵄨 𝑜,𝑖 𝑚,𝑖 󵄨 󵄨 𝑖=1 models. 6 Advances in Meteorology where ET and ET denote the observed and modeled values The performance of the applied data-driven models for 𝑜 𝑚 estimating ET over the training, validation, and prediction of daily ET, respectively; ET and ET are the means of 𝑜 𝑚 periods at CA-Let site is shown in Table 4. As can be seen observed and modeled values, respectively;𝑁 is the number from the table, the ANN model performs the best on the of observed values. Regarding the physical significance of whole, followed by the ANFIS-SC and ANFIS-Grid models. these indicators, the𝑅 was used to measure the proportion The SVM-Sig model provides the worst accuracy among the of total variance in the observed ET that is explained by the twelve models. Based on the 𝑅 ,NSE,RMSE, andMAE modeled ET. For a perfect model, the𝑅 is expectedtobe metrics, the overall performance of these applied models in close to unity. However, this index is limited because it is the prediction period can be ranked as follows: ANN, ANFIS- calculated based on the linear relationships between observed SC, ANFIS-Grid, ANFIS-FCM, SVM-RBF, ELM-Sin, ELM- and simulated values and is sensitive to outliers. Alternatively, Sig, SVM-Poly, GRNN, GMDH, ELM-Hard, and SVM-Sig. the NSE represents the level of agreement between observed Figure 2illustrates themeasuredand predictedETbythe and simulated ET and can offer useful knowledge about optimal models for each approach in the prediction stage at the relative estimation of the generalization performance CA-Let site. As shown in the figure, the ANN, ANFIS-SC, and for a given model. It is sensitive to differences in mea- SVM-RBF models have higher𝑅 and lower RMSE than other sured and calculated means and variances and accordingly models. In addition, the tfi lines of these three models are was employed in the present investigation. Moreover, other closer to their respective ideal lines (1 : 1 line), in comparison valuable information involving the predictive ability of the with the other models. developed models can also be provided by the RMSE and MAE indicators. Therefore, these performance criteria were Comparisons of the applied models are made in Table 5 employed together to obtain helpful insight into the efficiency for modeling daily ET at DE-Gri site. Unlike the previous of the developed models. sites, the ELM-Sin model has better accuracy than the other models in terms of the used indices. eTh ranks of the estimated models in the prediction stage are: ELM-Sin, 3. Results ELM-Sig, ANN, ANFIS-Grid, GRNN, GMDH, ANFIS-FCM, ANFIS-SC, SVM-RBF, ELM-Hard, SVM-Poly, and SVM-Sig. The performance indices, including 𝑅 ,NSE,RMSE,and Figure 3 illustrates the estimates of the optimal models for MAE, areemployedtoevaluatetheaccuracyoftheutilized ET simulation in the prediction phase at DE-Gri site. It is models in predicting the daily ET in this study.𝑅 and IA with apparent from the gfi ure that the tfi line of the ANFIS-Grid larger values and RMSE and MAE with smaller values imply model is closer to the ideal line (1 : 1 line), while the ELM-Sin higher model efficiency. Table 3 shows the estimated results of model has the highest𝑅 and provides less scattered estimates all machine learning models (ANN, GRNN, GMDH, ELM, than the other models, which has also been conrm fi ed in ANFIS, and SVM) for ET over the training, validation, and Table 5. prediction periods at AT-Neu site. As can be seen from Table 6 summarizes the accuracy of the applied models Table 3, the ANFIS-SC model gives the best performance in thepredictionofETinthepredictionperiod,withthehighest for forecasting daily ET in the prediction phase at HU-Bug site. It can be clearly seen from the table that the GMDH values of𝑅 (0.9379) andNSE (0.9355) andthe lowest valueof −1 −1 model achieves the best precision among the developed RMSE (0.3308 mm day )and MAE(0.2260mm day ). And twelve models. Based on the utilized performance indicators, the ELM-Sin model provides the inferior results in terms of the overall model efficiency of these models in the prediction 𝑅 ,NSE,RMSE, andMAE.TheSVM-Sig modelperformsthe period canberankedasfollows:GMDH,ELM-Sig,ELM-Sin, worst among the twelve models. According to the𝑅 ,NSE, ANN, ANFIS-SC, SVM-RBF, ANFIS-FCM, ANFIS-Grid, RMSE, and MAE metrics, the overall performance ranks GRNN, SVM-Poly, ELM-Hard, and SVM-Sig. The scatterplot of these developed models in the prediction period can be comparisons of the estimated methods with their respective summarized as follows: ANFIS-SC, ELM-Sin, ANFIS-FCM, optimal parameters are made in Figure 4 over the prediction ANN, ELM-Sig, GMDH, SVM-RBF, ANFIS-Grid, GRNN, stage at HU-Bug site. As shown from the gfi ure, the slope and ELM-Hard, SVM-Poly, and SVM-Sig. bias values of the tfi line equation of both the ANFIS-SC and eTh comparisons of daily ET observed and predicted ELM-Sig models are closer to those of their corresponding by using the data-driven models over the prediction period exactlines(1 : 1line,slope:1,andbias:0),comparedwiththose in the form of scatter plot at AT-Neu site are shown in of the other models. However, the GMDH model seems to be Figure 1. As a convenience, the scattered estimates of the more successful than the other models from the𝑅 and RMSE optimal ELM, ANFIS, and SVM models are exclusively viewpoints. compared with those of the ANN, GRNN, and GMDH In order to provide insights into the over- and underes- models. As illustrated in Figure 1, the tfi line of the SVM- timation of the used data-driven models in predicting daily RBF model is closer to the ideal line (1 : 1 line) than those of ET, the measured and modeled values by the best models for the other models, considering the corresponding equations each site in the whole period are demonstrated in Figure 5. of tl fi ines. However, it canbeseenfromFigure1and It is evident from the figure that the modeled values of these Table 3 that the ANFIS-SC model seems to have slightly best models for each site can closely follow the corresponding higher𝑅 value than the other models and obtains similar observed ones, which is previously confirmed in Tables 3–6. scattered estimates to those of the ANN and ELM-Sin models. However, the peak values during the growing season in the Advances in Meteorology 7 Th Table 3: Comparisons of data-driven model performances for evapotranspiration among the training, validation and prediction periods at AT-Neu sit e. Training Validation Prediction Model 2 2 2 NSE RMSE MAE NSE RMSE MAE NSE RMSE MAE ANN 0.9298 0.9294 0.3551 0.2321 0.9407 0.9375 0.3318 0.2203 0.9355 0.9338 0.3350 0.2278 GRNN 0.9596 0.9595 0.2689 0.1635 0.9134 0.9118 0.3943 0.2640 0.9207 0.9186 0.3714 0.2473 GMDH 0.9271 0.9270 0.3610 0.2442 0.9246 0.9220 0.3707 0.2464 0.9356 0.9320 0.3394 0.2342 ELM-Sig 0.9256 0.9256 0.3644 0.2430 0.9265 0.9249 0.3639 0.2461 0.9355 0.9328 0.3376 0.2322 ELM-Sin 0.9278 0.9278 0.3591 0.2332 0.9302 0.9283 0.3554 0.2415 0.9365 0.9344 0.3335 0.2242 ELM-Hard 0.8762 0.8762 0.4702 0.3365 0.8814 0.8811 0.4577 0.3394 0.9043 0.9031 0.4053 0.2836 ANFIS-Grid 0.9407 0.9407 0.3255 0.2121 0.9237 0.9230 0.3684 0.2585 0.9247 0.9219 0.3639 0.2436 ANFIS-SC 0.9373 0.9373 0.3347 0.2138 0.9318 0.9304 0.3503 0.2402 0.9379 0.9355 0.3308 0.2260 ANFIS-FCM 0.9376 0.9376 0.3338 0.2151 0.9380 0.9358 0.3363 0.2314 0.9369 0.9343 0.3338 0.2282 SVM-RBF 0.9387 0.9373 0.3347 0.1928 0.9333 0.9328 0.3440 0.2357 0.9338 0.9321 0.3392 0.2286 SVM-Poly 0.8357 0.8321 0.5476 0.4007 0.8351 0.8341 0.5406 0.4287 0.8746 0.8696 0.4701 0.3579 SVM-Sig 0.5948 0.5061 0.9391 0.7203 0.5113 0.4352 0.9976 0.7997 0.5910 0.5063 0.9149 0.7275 −1 Note. e units of RMSE and MAE are mm day . 8 Advances in Meteorology 1 : 1 6 6 4 4 y = 0.8927x + 0.1772 2 2 y = 0.9016x + 0.1503 R = 0.9207 R = 0.9355 RMS% = 0.3714 0 0 RMS% = 0.3350 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (a) (b) 6 6 4 4 2 2 y = 0.9041x + 0.1596 y = 0.8791x + 0.1671 R = 0.9356 R = 0.9365 0 0 RMS% = 0.3394 RMS% = 0.3335 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (c) (d) 6 6 4 4 y = 0.8984x + 0.1617 2 2 y = 0.9248x + 0.1454 R = 0.9379 R = 0.9338 0 0 RMS% = 0.3308 RMS% = 0.3392 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (e) (f) Figure 1: Comparisons of daily ET between eddy covariance measured and simulated by data-driven models in the prediction period at AT-Neu site. (a) ANN model; (b) GRNN model; (c) GMDH model; (d) ELM-Sin model; (e) ANFIS-SC model; and (f) SVM-RBF model. prediction period appear to be appreciably underestimated by isthefactthatits learning speed is showntobeextremely the optimal models for all the sites, especially for CA-Let site, faster than that of other data-driven approaches, partly which is also consistent with the scatter plots in Figures 1–4. because the number of hidden nodes of an ELM model can be randomly determined. In addition, its related parameters (weights and biases) need not be tuned as these properties 4. Discussion are problem-independent and thus are not clearly associated In the following subsections, we concentrated primarily on with the applied training dataset. discussing the generalization ability of all data-driven models Furthermore, with the advances in machine learning in for forecasting daily ET and then on exploring the effects recent years, a number of new machine learning methods, of dieff rent internal functions on the ELM, ANFIS, and such as relevance vector machine [45], M5 model tree [46], SVM models. Finally, we also pointed out some potential and genetic programming [47], have been proposed and improvements for the follow-up work. successfully applied in other diverse efi lds, such as forecasting Our estimates demonstrated that all the examined mod- of meteorological time series (e.g., air temperature and els, including ANN, GRNN, GMDH, ELM, ANFIS, and precipitation) and prediction of water resource variables SVM, can seize the nonlinear relationship between ET and (e.g., rainfall–runo,ff groundwater level, and drought). Con- environmental variables according to the combination of sequently, it is also important to investigate the feasibility four dieff rent performance criteria. Moreover, our modeling and effectiveness of these new approaches in dealing with the results also conrfi med that the new computational intelli- present ET estimation, which will be undertaken in our future gence techniques (GMDH, ELM, and ANFIS) were capable work. of effectively acquiring the seasonal and interannual variation in ET driven by the environmental variables. More impor- Our modeling results also showed that an obvious differ- tantly, these three methods had significant superiority over ence existed within each method (ELM, ANFIS, and SVM) with various internal functions in terms of predictive perfor- conventional methods in terms of robustness and simplicity. Specifically, of particular interest regarding the ELM method mance. Therefore, selecting appropriate internal function for −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) Advances in Meteorology 9 Th Table 4: Comparisons of data-driven model performances for evapotranspiration among the training, validation and prediction periods at CA-Let sit e. Training Validation Prediction Model 2 2 2 NSE RMSE MAE NSE RMSE MAE NSE RMSE MAE ANN 0.7593 0.7590 0.3791 0.2541 0.8553 0.7671 0.5690 0.3546 0.7859 0.7334 0.5911 0.3607 GRNN 0.8417 0.8176 0.3298 0.1997 0.8112 0.6472 0.7002 0.4096 0.7415 0.6307 0.6957 0.3919 GMDH 0.6673 0.6673 0.4454 0.3036 0.8303 0.6887 0.6577 0.4018 0.6931 0.6343 0.6922 0.4134 ELM-Sig 0.7159 0.7159 0.4115 0.2821 0.8038 0.7045 0.6409 0.4057 0.7469 0.6907 0.6367 0.3913 ELM-Sin 0.7163 0.7163 0.4113 0.2805 0.8423 0.7570 0.5811 0.3582 0.7530 0.6998 0.6272 0.3787 ELM-Hard 0.5615 0.5615 0.5113 0.3602 0.6843 0.5572 0.7845 0.4758 0.6013 0.5446 0.7725 0.4733 ANFIS-Grid 0.7820 0.7820 0.3605 0.2418 0.8480 0.7869 0.5443 0.3473 0.7805 0.7380 0.5859 0.3527 ANFIS-SC 0.7691 0.7691 0.3711 0.2495 0.8467 0.7712 0.5639 0.3507 0.7855 0.7311 0.5936 0.3492 ANFIS-FCM 0.7649 0.7649 0.3744 0.2532 0.8628 0.7879 0.5429 0.3405 0.7805 0.7287 0.5962 0.3554 SVM-RBF 0.7936 0.7912 0.3528 0.2111 0.8453 0.7668 0.5693 0.3418 0.7762 0.7225 0.6030 0.3577 SVM-Poly 0.6888 0.6772 0.4387 0.2888 0.8489 0.7824 0.5500 0.3326 0.7528 0.7053 0.6214 0.3676 SVM-Sig 0.0244 −0.0790 290.02 241.69 0.0616 −0.1655 263.96 225.25 0.0226 −0.0104 298.60 248.78 −1 Notes. e unit of RMSE and MAE is mm day . 10 Advances in Meteorology 6 6 1 : 1 4 4 2 2 y = 0.6073x + 0.2295 y = 0.5030x + 0.2370 R = 0.7859 0 0 R = 0.7415 RMS% = 0.5911 RMS% = 0.6957 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (a) (b) 6 6 4 4 2 2 y = 0.5700x + 0.2810 y = 0.5195x + 0.2921 2 R = 0.7530 R = 0.6931 0 0 RMS% = 0.6272 RMS% = 0.6922 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (c) (d) 6 6 4 4 2 2 y = 0.6019x + 0.2366 y = 0.6101x + 0.1976 2 2 R = 0.7762 R = 0.7855 0 0 RMS% = 0.5936 RMS% = 0.6030 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (e) (f) Figure 2: Comparisons of daily ET between eddy covariance measured and simulated by data-driven models in the prediction period at CA-Let site. (a) ANN model; (b) GRNN model; (c) GMDH model; (d) ELM-Sin model; (e) ANFIS-SC model; and (f) SVM-RBF model. each method is essential with the objective of achieving the of ANFIS techniques in other different fields have concen- best modeling ability. It is highly recommended that different trated mainly on evaluating the roles of the membership internal functions for each method should be evaluated functions under grid partitioning algorithm. It should be in advance, when these methods are used for regression mentioned that selecting appropriate membership function and classicfi ation problems. More specicfi ally in the present and determining its optimal number may effectively improve study, for ANFIS method, the evaluated three algorithms for the performance of grid partitioning based ANFIS model. generating FISs had noticeable eeff cts on the performance of In conclusion, our study has broaden the scope of ANFIS ANFIS on the whole. We found that, among the three various research and provided deep insights into the application of ANFIS models, the ANFIS model with the subtractive clus- ANFIS method. In the follow-up work, we will investigate tering algorithm performed the best at AT-Neu, CA-Let, and together the capability of the aforementioned algorithms HU-Bug sites, while grid partitioning based ANFIS model (subtractive clustering, grid partitioning, and fuzzy c-means generated the optimal estimates at DE-Gri site. er Th efore, clustering), as well as different types of membership functions there was no omnipotent algorithm that was appropriate under grid partitioning algorithm. for all the cases. In addition, Cobaner [48] investigated According to the predictive capability and efficiency of the ability of two different ANFIS methods, respectively, SVM, it was found from our results that remarkable difference based on the subtractive clustering and grid partitioning existed among three different kernel functions (sigmoid, algorithms, in estimating reference ET using daily climatic polynomial, and RBF), which has been also confirmed data, and found that subtractive clustering based ANFIS by the previous studies in other fields [49–51]. Moreover, model achieved more plausible precision with fewer amounts our estimates indicated that the RBF kernel function for of computation in comparison with grid partitioning based SVM method performed better than the other two kernel ANFIS model. Moreover, to the best of our knowledge, functions (sigmoid and polynomial) in the prediction of most studies comparing the performance of different types daily ET. It concurred with the findings from numerous −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) Advances in Meteorology 11 Table 5: Comparisons of data-driven model performances for evapotranspiration among the training, validation, and prediction periods at DE-Gri si te. Training Validation Prediction Model 2 2 2 NSE RMSE MAE NSE RMSE MAE NSE RMSE MAE ANN 0.8633 0.8630 0.3470 0.2426 0.9341 0.8927 0.3411 0.2336 0.9623 0.9341 0.2769 0.1942 GRNN 0.8612 0.8603 0.3504 0.2487 0.9294 0.8814 0.3587 0.2478 0.9585 0.9292 0.2871 0.2058 GMDH 0.8396 0.8396 0.3755 0.2707 0.9326 0.8724 0.3719 0.2573 0.9619 0.9253 0.2949 0.2121 ELM-Sig 0.8535 0.8535 0.3589 0.2580 0.9358 0.8885 0.3478 0.2347 0.9669 0.9392 0.2659 0.1920 ELM-Sin 0.8546 0.8546 0.3575 0.2522 0.9477 0.9066 0.3182 0.2203 0.9711 0.9398 0.2646 0.1896 ELM-Hard 0.8012 0.8012 0.4180 0.2911 0.8926 0.8724 0.3720 0.2662 0.9053 0.8765 0.3791 0.2534 ANFIS-Grid 0.8772 0.8772 0.3285 0.2304 0.9173 0.8713 0.3735 0.2447 0.9574 0.9334 0.2785 0.1961 ANFIS-SC 0.8637 0.8637 0.3461 0.2427 0.9230 0.8716 0.3732 0.2397 0.9501 0.9088 0.3258 0.2167 ANFIS-FCM 0.8636 0.8636 0.3462 0.2439 0.9244 0.8744 0.3691 0.2378 0.9500 0.9099 0.3238 0.2159 SVM-RBF 0.8638 0.8633 0.3466 0.2306 0.9196 0.8796 0.3614 0.2332 0.9407 0.9002 0.3408 0.2092 SVM-Poly 0.7885 0.7852 0.4345 0.3221 0.7629 0.7043 0.5662 0.3879 0.8461 0.8199 0.4578 0.3407 SVM-Sig 0.0170 −0.0682 43.738 37.467 0.0001 −0.3639 37.708 31.554 0.1190 −0.2045 45.388 39.515 −1 Note.TheunitofRMSEand MAEismmday . 12 Advances in Meteorology 1 : 1 4 4 2 2 y = 0.7911x + 0.1870 y = 0.8010x + 0.1517 R = 0.9585 R = 0.9623 0 0 RMS% = 0.2871 RMS% = 0.2769 −1 012345 −1 012345 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (a) (b) 4 4 2 2 y = 0.7979x + 0.1693 y = 0.7834x + 0.1411 R = 0.9619 R = 0.9711 RMS% = 0.2949 RMS% = 0.2646 −1 012345 −1 012345 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (c) (d) 4 4 2 2 y = 0.7535x + 0.1708 y = 0.8033x + 0.1501 R = 0.9574 R = 0.9407 0 0 RMS% = 0.2785 RMS% = 0.3408 −1 01234 5 −1 01234 5 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (e) (f) Figure 3: Comparisons of daily ET between eddy covariance measured and simulated by data-driven models in the prediction period at DE-Gri site. (a) ANN model; (b) GRNN model; (c) GMDH model; (d) ELM-Sin model; (e) ANFIS-Grid model; and (f) SVM-RBF model. studies, showing the superiority of RBF over the other such as rainfall and runoff time series forecasting. In brief, kernel functions in solving the regression problems [52–54]. theELMtechniquecan be apromising alternativetoolto For example, Zounemat-Kermani et al. [55] evaluated the traditional methods for dealing with the regression issue in capability of SVM model with four different kernel functions the current research as well as the gap-filling problem of (linear, polynomial, sigmoid, and RBF) for forecasting daily ETfluxmeasuredbythe eddy covariance technique. Onthe suspended sediment concentrations and further pointed out other hand, relatively less attention has been drawn toward that the RBF for SVM model was the best choice for modeling exploring the eeff cts of various activation functions (e.g., sine, hydrological phenomena. Mohammadi et al. [56] investi- sigmoid, and hard limit activation function) in the hidden gated the ability of two different types of SVM models based layer on the generalization ability of ELM. In the present on polynomial and RBF kernel functions in forecasting the study, our results demonstrated that the sine and sigmoid horizontal global solar radiation and found that RBF for SVM activation functions for ELM models played the similar roles was highly competent for predicting daily horizontal global in estimating the daily ET and dramatically outperformed solar radiation in comparison with polynomial function. the hard limit activation function. eTh refore, it is important As a relatively new method, ELM exhibited strong to emphasize that the sine and sigmoid activation functions modeling accuracy in predicting daily ET, which has been are recommended as the optimal options for establishing the verified by previous studies for other applications, such as ELMmodelsforET forecasting. reference ET prediction [57] and stream-flow forecasting Furthermore, many recent studies have found that select- [39]. In particular, a very noteworthy aspect was that the ing an appropriate training function is vitally essential for ELM method presented a remarkable advantage against assuring the predictive ability and reliability of ANN in other other data-driven approaches with respect to computational fields [59–61]. Despite the fact that ANN has been recognized time and efficiency due to its simple network structure and as the most popular method to simulate the ET as well nontuned mechanism [58], which is a beneficial contribution asthecarbonfluxes at ecosystemlevel basedonthe eddy to the solution of some real-time forecasting problems, covariance-measured data [62–64], the influences of various −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) Advances in Meteorology 13 Th Table 6: Comparisons of data-driven model performances for evapotranspiration among the training, validation, and prediction periods at HU-Bug si te. Training Validation Prediction Model 2 2 2 NSE RMSE MAE NSE RMSE MAE NSE RMSE MAE ANN 0.8765 0.8764 0.3955 0.2636 0.8038 0.8023 0.4474 0.3022 0.7969 0.7907 0.5018 0.3635 GRNN 0.9043 0.9041 0.3483 0.2284 0.7412 0.7333 0.5196 0.3581 0.7519 0.7395 0.5598 0.3895 GMDH 0.8135 0.8135 0.4858 0.3303 0.7773 0.7770 0.4752 0.3315 0.8165 0.8143 0.4727 0.3272 ELM-Sig 0.8467 0.8467 0.4405 0.3030 0.7625 0.7563 0.4967 0.3566 0.8155 0.8087 0.4797 0.3402 ELM-Sin 0.8521 0.8521 0.4327 0.2910 0.7823 0.7807 0.4712 0.3352 0.8134 0.8075 0.4813 0.3449 ELM-Hard 0.7113 0.7113 0.6045 0.4539 0.6425 0.6291 0.6128 0.4577 0.7045 0.7017 0.5991 0.4478 ANFIS-Grid 0.8921 0.8921 0.3695 0.2556 0.7178 0.7008 0.5504 0.3605 0.7595 0.7414 0.5578 0.3774 ANFIS-SC 0.8721 0.8721 0.4024 0.2705 0.7761 0.7713 0.4811 0.3407 0.7893 0.7784 0.5164 0.3752 ANFIS-FCM 0.8679 0.8679 0.4089 0.2760 0.7709 0.7655 0.4873 0.3376 0.7726 0.7636 0.5333 0.3801 SVM-RBF 0.8917 0.8897 0.3737 0.2323 0.7529 0.7511 0.5020 0.3404 0.7699 0.7671 0.5294 0.3739 SVM-Poly 0.7451 0.7392 0.5745 0.3901 0.7344 0.7286 0.5241 0.3737 0.7266 0.7237 0.5765 0.4114 SVM-Sig 0.0049 −0.0610 218.15 178.95 0.0193 −0.0991 201.38 168.64 0.0090 −0.0053 207.32 171.67 −1 Note. e unit of RMSE and MAE is mm day . 14 Advances in Meteorology 6 6 1 : 1 4 4 2 2 y = 0.8481x + 0.2141 y = 0.8670x + 0.1858 R = 0.7519 R = 0.7969 0 0 RMS% = 0.5598 RMS% = 0.5018 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (a) (b) 6 6 4 4 2 2 y = 0.8883x + 0.1680 y = 0.8521x + 0.1728 R = 0.8155 R = 0.8165 0 0 RMS% = 0.4797 RMS% = 0.4727 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (c) (d) 6 6 4 4 2 2 y = 0.8795x + 0.1359 y = 0.8089x + 0.2289 R = 0.7893 R = 0.7699 0 0 RMS% = 0.5164 RMS% = 0.5294 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (e) (f) Figure 4: Comparisons of daily ET between eddy covariance measured and simulated by data-driven models in the prediction period at HU-Bug site. (a) ANN model; (b) GRNN model; (c) GMDH model; (d) ELM-Sig model; (e) ANFIS-SC model; and (f) SVM-RBF model. training algorithms on the ANN performance have never benchmarks in order to compare their capability. Moreover, been examined to date. Consequently, special attention will this study also focused on investigating the influences of be given to the evaluation of the modeling abilities of ANN internal functions on their corresponding models (ELM, models with a variety of training algorithms for predicting ANFIS, and SVM) in terms of the generalization performance ET and carbon u fl xes in our follow-up work. on the basis of a set of statistical indices (𝑅 ,NSE,RMSE, and MAE). 5. Conclusions To summarize, the primary findings in the present study can be enumerated as follows: In recent years, many attempts mainly involving the use of soft computing modeling approaches have been made to sim- (1) It has been discovered that all the models developed in ulateand forecast theETinterrestrial ecosystems.However, this study were capable of mapping the nonlinear pro- the lack of comprehensive comparative researches related to cesses of governing the variation of the ET between these state-of-the-art modeling techniques largely hinders the biosphere and the atmosphere at the ecosystem their applicability and popularity, primarily owing to the level, and these novel models (GMDH, ELM, and confusion in what approach should be appropriately chosen ANFIS) produced estimates comparable to those of from a variety of data-driven methods in the practical appli- the conventional models. cations. To overcome this hindrance, the current research first (2) Considering the robustness and simplicity, these attempted to investigate the suitability and effectiveness of novel approaches can be used as promising alter- three newly proposed methods, GMDH, ELM, and ANFIS, natives to traditional methods for modeling and for estimating daily ET at four different grassland sites based forecasting daily ET. on the eddy covariance-measured data. In addition to these techniques, three traditional soft computing techniques, (3) ep Th redictiveaccuracyoftheSVM,ELM,andANFIS including ANN, GRNN, and SVM, were also employed as models was strongly dependent on their respective −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) Advances in Meteorology 15 −1 2004 2005 2006 2007 2008 2009 Measured Modeled (a) −1 1999 2000 2001 2002 2003 2004 2005 2006 2007 Measured Modeled (b) −1 2004 2005 2006 2007 2009 2010 Measured Modeled (c) −1 2003 2004 2005 2006 2007 2008 Measured Modeled (d) Figure 5: Eddy covariance measured and simulated daily ET by their respective best models for the four sites in the whole period. (a) For AT-Neu site using ANFIS-SC model; (b) for CA-Let site using ANN model; (c) for DE-Gri site using ELM-Sin model; and (d) for HU-Bug site using GMDH model. internal functions, especially for SVM. Three different It should be noted that all the data-driven modeling kernel functions for the SVM method were together techniques strongly driven by a large amount of data are tested and the results suggested that the RBF kernel oen ft argued because the intrinsic mechanisms of these well- function substantially outperformed both the polyno- trained models are still not able to be represented explicitly. mial and sigmoid kernel functions. Accordingly, this argument is very likely to decrease the (4) eTh ELM models with the sigmoidal and sine activa- credibility of these techniques and further impede their tion functions generated the similar modeling accu- applications. Notwithstanding this limitation, our present racy andwereappreciably superior to theELMmodel investigation does suggest that these data-driven methods with the hard limit function. based on soft computing can effectively complement phys- ically based models, broaden the horizon of ecological, (5) For the ANFIS method, the algorithms for generating FISs had noticeable eeff cts on the performance of climatological, and hydrologic researchers, and therefore ANFIS method. The optimal algorithm can be deter- contribute to the estimates of regional and global water mined according to a trial-and-error procedure. resources under climate change. −1 −1 −1 −1 ET (mm daS ) ET (mm daS ) ET (mm daS ) ET (mm daS ) 16 Advances in Meteorology Conflicts of Interest [12] A.Polhamus,J.B.Fisher,andK.P.Tu,“Whatcontrolsthe error structure in evapotranspiration models?” Agricultural and eTh authors declare that there are no conflicts of interest. Forest Meteorology,vol.169,pp. 12–24,2013. [13] R.K.Vinukollu,E.F.Wood,C.R.Ferguson,andJ.B.Fisher, “Global estimates of evapotranspiration for climate studies Acknowledgments using multi-sensor remote sensing data: Evaluation of three This work was financially supported by the Natural Science process-based approaches,” Remote Sensing of Environment,vol. 115, no. 3, pp. 801–823, 2011. Fund of China (no. 41672324) and the Priority Academic [14] Y. Chen,J.Xia,S.Lianget al., “Comparisonofsatellite- Program Development of Jiangsu Higher Education Institu- based evapotranspiration models over terrestrial ecosystems in tions. The present research used the eddy covariance data China,” Remote Sensing of Environment,vol.140,pp.279–293, acquired and shared by the CarboEurope and Fluxnet- Canada Research Networks. eTh authors would like to thank [15] F. 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Modeling Evapotranspiration Response to Climatic Forcings Using Data-Driven Techniques in Grassland Ecosystems

Advances in Meteorology , Volume 2018: 18 – Apr 22, 2018

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Copyright © 2018 Xianming Dou and Yongguo Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract

Hindawi Advances in Meteorology Volume 2018, Article ID 1824317, 18 pages https://doi.org/10.1155/2018/1824317 Research Article Modeling Evapotranspiration Response to Climatic Forcings Using Data-Driven Techniques in Grassland Ecosystems 1,2 1,2 Xianming Dou andYongguoYang Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process of Ministry of Education, China University of Mining and Technology, Xuzhou 221116, China School of Resources and Geosciences, China University of Mining and Technology, Xuzhou 221116, China Correspondence should be addressed to Yongguo Yang; yongguoyang@hotmail.com Received 6 November 2017; Revised 9 February 2018; Accepted 15 March 2018; Published 22 April 2018 Academic Editor: Harry D. Kambezidis Copyright © 2018 Xianming Dou and Yongguo Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Remarkable progress has been made over the last decade toward characterizing the mechanisms that dominate the exchange of water vapor between the biosphere and the atmosphere. This is attributed partly to the considerable development of machine learning techniques that allow the scientific community to use these advanced tools for approximating the nonlinear processes aec ff ting the variation of water vapor in terrestrial ecosystems. Three novel machine learning approaches, namely, group method of data handling, extreme learning machine (ELM), and adaptive neurofuzzy inference system (ANFIS), were developed to simulate and forecast the daily evapotranspiration (ET) at four different grassland sites based on the ux fl tower data using the eddy covariance method. es Th e models were compared with the extensively utilized data-driven models, including artificial neural network, generalized regression neural network, and support vector machine (SVM). Moreover, the influences of internal functions on their corresponding models (SVM, ELM, and ANFIS) were investigated together. It was demonstrated that most developed models did good job of simulating and forecasting daily ET at the four sites. In addition to strengths of robustness and simplicity, the newly proposed methods achieved the estimates comparable to those of the conventional approaches and accordingly can be used as promising alternatives to traditional methods. It was further discovered that the generalization performance of the ELM, ANFIS, and SVM models strongly depended on their respective internal functions, especially for SVM. 1. Introduction relatively essential for understanding the responses of ET to different environmental forces and oer ff ing precise ET Grasslands coverapproximately 13%ofgloballandsurface budgets for solving the issue of water resource allocation [1]. It is universally acknowledged that grassland ecosystems and management. Eddy covariance technique has been con- play a crucial role in global water and carbon budgets as sidered as a reliable approach and is being used extensively well as energy balances [2, 3]. In grassland ecosystems, the to measure grassland ET in different climates [7]. A large interrelations between atmosphere and evapotranspiration amount of data from numerous flux tower sites, including ET (ET), consisting of transpiration and evaporation from the and other micrometeorological variables, have been collected soil and plant systems, are closely related to ecosystem andarchivedinglobalfluxnetworkinrecentyears [8,9], productivity, particularly in arid and semiarid regions [4]. providing a solid foundation for obtaining helpful knowledge Their dynamical interactions between biophysical and bio- of the underlying mechanisms influencing the variation of geochemical processes are substantially affected by a variety ET across various time scales from hourly to interannual. of environmental driving factors, such as climate change, However, accurately estimating ET of grassland ecosystems nutrient deposition, and increased atmospheric CO [4–6]. remains a great challenge due to the limited understanding of Therefore, measuring and estimating ET in grasslands are how ET responds to human practical activities (e.g., land use 2 Advances in Meteorology change, grazing, and fertilization) and climate extreme events the strengths and shortcomings of each method and provide (e.g., extreme precipitation, wind storms, droughts, and heat helpful suggestions for the relevant researchers. waves). It is a widely accepted fact that the ability of all the above-mentioned methods is strongly aeff cted by their cor- A broad range of approaches are presently utilized to responding inner parameters [24]. However, very few studies model and predict terrestrial ET at various spatial levels have reported the roles of different intrinsic parameters for from ecosystem to regional or global level. es Th e methods each approach in characterizing the actual behavior of the can be commonly grouped into three categories: remote addressed problems, especially for the relatively new meth- sensing-based [10, 11], physically based [12, 13], and data- ods, ANFIS and ELM, even though these approaches have driven [14, 15]. Among these approaches, physically based been widely applied in other fields. For example, although techniques are universally used by both the ecological and several recent studies have examined the effects of different hydrological communities, due to their distinct advantage membership functions on ANFIS for various hydrological of oer ff ing a physical insight into the complex hydrological time series prediction [25–27], it remains unclear how the process controlling the temporal and spatial variation of ET. ANFIS model is influenced by different identification algo- However, temporal and spatial heterogeneity of land surface rithms for fuzzy inference system (FIS) generation for the characteristics strongly affects the underlying processes of present application. In fact, when establishing these models ongoing water vapor exchange, which considerably increases in practical applications, these intrinsic algorithms in most the complexity of elucidating the hydrological relationship studies are commonly determined by random selection or between land and the atmosphere and subsequently impedes trial-and-error procedure, which may limit, to some extent, the pursuit of obtaining accurate physically based models. the ability of related models. Accordingly, it is certainly worth Data-driven methods have been receiving increasing examining the impacts of inner parameters on SVM, ANFIS, attention in the last decade for ET simulation and prediction and ELM for predicting ET, which is also another major task at different terrestrial ecosystems. Numerous previous studies for the current research. have reported the ability of machine learning techniques Considering the presently existing above-mentioned in the prediction of ET at terrestrial ecosystems [16, 17]. It issues, the novelty of this paper lies in the use of three has been demonstrated that these approaches are capable of state-of-the-art data-driven methods for estimating daily ET eeff ctively seizing most useful information stored in the avail- basedontheavailableeddycovariancemeasurementsat able data (e.g., the measurements based on eddy covariance four different grassland sites. More specicfi ally, the novelty method), without depending on any complex underlying of this paper is threefold as follows. First, we probe into knowledge about the evolving process of ET. Nevertheless, the feasibility and effectiveness of three modern data-driven to the best of our knowledge, most studies focused primarily models, including GMDH, ELM, and ANFIS, for modeling on using three ubiquitous approaches, namely, artificial neu- and predicting the ET at the daily time scale. Second, we ral network (ANN), generalized regression neural network investigate whether these newly proposed models have the (GRNN), and support vector machine (SVM). potential to sufficiently complement or replace the con- In recent years, many novel machine learning techniques ventionally recognized methods, ANN, GRNN, and SVM. have been proposed for handling the complex nonlinear Finally, we particularly focus on evaluating the impacts of problems, such as adaptive neurofuzzy inference system intrinsic algorithms involved in each model (SVM, ELM, and (ANFIS), extreme learning machine (ELM), and group ANFIS) on their respective generalization ability. method of data handling (GMDH). eTh generalization ability of these advanced approaches has been extensively acknowl- 2. Materials and Methods edged in forecasting the environmental and climatological variables. More particularly, these methods have been widely 2.1. Site Description and Data Used. In this study, four grass- applied in the nonlinear time series prediction in several var- land ecosystems were used to explore the modeling capability ious branches of hydrology, such as reference ET forecasting of the proposed models. These sites are situated in different [18, 19], evaporation prediction [20, 21], and soil moisture countries. The details of each site are shown in Table 1. estimation [22, 23]. However, comparatively few attempts to eTh ywereselectedfor thepresentstudymainlydue to apply these state-of-the-art approaches have been made to their continuous multiyear measurements of water vapor u fl x date for estimating the ET at terrestrial ecosystems based on (ET) with the eddy covariance technique. In addition, the the eddy covariance data. measurements of other variables were also undertaken at In addition, all the techniques, including the conventional these sites, primarily including CO ux, fl energy ux fl es (latent ANN, GRNN, and SVM methods, and the relative novel heat and sensible heat), and meteorological variables. The methods (ELM, ANFIS, and GMDH) proposed by this study utilized instruments and processing procedures of related remarkably differ in terms of their structures, principles, data at each site have been, respectively, reported in previous and parameters. And, therefore, their generalization ability studiesasshown inTable1. should be different in theory. For this reason, regarding Statistical parameters of daily measurements utilized in their practical application in the present study, systematically this study during at least 6-year period for all the sites are evaluating the ability of all the methods for ET prediction giveninTable 2. As showninthetable, theannualmeanair ∘ ∘ is particularly important with the objective of ensuring the temperature (𝑇 )changes from 6.48 CatCA-Letto10.20 C predictive accuracy. Besides, it is also beneficial to identify at HU-Bug; the annual mean soil temperature (𝑇 ) is between 𝑠 Advances in Meteorology 3 Table 1: Site characteristics used in this study. Site Latitude Longitude Elevation MAT TAP Climate Period Reference AT-Neu 47.12 11.32 970 6.68 669 Temperate 2004–2009 Wohlfahrt et al. [28] CA-Let 49.71 −112.94 951 6.48 1095 boreal 1999–2007 Flanagan et al. [29] DE-Gri 50.95 13.51 385 8.35 934 Temperate 2004–07, 2009-10 Hussain et al. [30] HU-Bug 46.69 19.60 140 10.20 499 Temperate 2003–2008 Carvalhais et al. [31] Note. MAT and TAP denote the mean annual temperature and total annual precipitation, respectively, and they are calculated based on the time period (period ∘ −1 column). The units of elevation, MAT, and TAP are m, C, and mm year ,respectively. ∘ ∘ 7.35 CatCA-Letand10.84 C at HU-Bug; the annual mean point out that the generalization ability of SVM method −2 −1 considerably depends on the choice of kernel function. net radiation (𝑅 )rangesfrom4.24molm day at AT-Neu −2 −1 eTh re are many alternative kernel algorithms, such as radial to 6.17 mol m day at CA-Let; the annual mean relative basis function (RBF), polynomial, sigmoid, exponential, humidity (𝑅 ) varies from 60.40% at CA-Let to 79.80% at Laplacian, and rational quadratic. eTh rfi st three kernel AT-Neu. eTh other statistical characteristics of these variables functions are commonly used for SVM models and therefore are also summarized. Furthermore, Table 2 also presents were compared and assessed in this study. As a matter of the correlation coefficients between ET and environmental convenience, the SVM models with the kernel functions, variables. It can be clearly seen that almost all the variables at RBF, polynomial, and sigmoid, were hereinafter referred to the four sites have strong correlation with ET. The variables, as SVM-RBF, SVM-Poly, and SVM-Sig, respectively. For a 𝑇 ,𝑇 ,and𝑅 , show strong positive correlation with ET, while 𝑎 𝑠 𝑛 given case, the critical internal parameters involved in the 𝑅 presents negative correlation with ET. Daily available training process, including the cost factor, the slack factor, measurements for at least six years were divided into three and the related parameter of respective kernel algorithm, parts. At each site, the first 4-year dataset was utilized for were carefully obtained through the grid search approach. All training, the h year dataset was used for validation with the SVM models applied in the present research were per- the intention of preventing overtraining or overtfi ting of the formed according to LIBSVM software written by MATLAB training dataset, and the remaining dataset was employed for programming language [36]. predicting. 2.2.3. Adaptive Neurofuzzy Inference System. ANFIS has 2.2. Data-Driven Techniques received much attention for modeling and predicting the hydrological time series (e.g., evaporation, groundwater level, 2.2.1. Artificial Neural Network. ANN model performance and stream-flow) in recent years. Hence, this method has depends on parallel information processing system involved been widely recognized as a promising alternative tool to in a multilayer network, and the model is capable of trans- traditional data-driven techniques for mapping the nonlinear forming helpful information from the input data into knowl- relationship between independent and dependent variables edge through artificial neurons which are directly linked in different research efi lds. Selecting a reasonable FIS is to active synapses with a set of weights related to different an important precondition for successfully elucidating the variables[32]. Itsultimategoalistoestablish thenonlin- nonlinear processes underlying a given problem, when estab- ear relationship between input (independent) variables and lishing an ANFIS model. Presently, Takagi and Sugeno [37] output (dependent) variables. In this study, a feed-forward method is extensively adopted in diverse research areas, ANN with a single hidden layer was used and its parameters and, in particular, its powerful ability in estimating various were updated using the backpropagation learning algorithm hydrological variables has been proved by accumulating lines with the intention of minimizing the error between the target of evidence to date. Accordingly, Takagi and Sugeno-based values and the calculated values derived from the network. ANFIS models were developed by the present work for all When designing ANN models in this study, hyperbolic tan- the applied cases. To achieve an optimum AFNIS model, gent sigmoid and linear algorithms were selected as transfer two types of parameters, namely, the antecedent parameters functions for hidden layer and output layer, respectively, with which influence the effectiveness of the applied membership the purpose of generating output results from each neuron. function and the consequent parameters which determine In addition, the determination of other key parameters and the quality of the system output, need to be optimized functions, such as the number of nodes of hidden layer and appropriately. eTh hybrid learning procedure is the most training functions, was also taken into account based on the commonly utilized to adjust the antecedent and consequent trial-and-error approach. parameters using the gradient descent and least squares 2.2.2. Support Vector Machine. eS Th VMapproachisan methods, respectively. In addition, of particular interest is the important soft computing method and has been utilized in impacts of different identification algorithms for generating many research efi lds. eTh detail of theory about SVM can FISs on the ability of developed ANFIS models. eTh current be foundinVapnik[33]and itsadvancesinthe practical research also attempts to address this issue. As a convenience, applications can be found in some recent reviews [33–35]. the ANFIS models with three extensively used identification Based on the accumulated experience, it is noteworthy to algorithms, namely, grid partitioning, subtractive clustering, fift 4 Advances in Meteorology fl 𝑎 𝑛 𝑠 𝑎 𝑛 𝑠 𝑎 𝑛 𝑠 𝑎 𝑛 𝑠 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑅 𝑅 𝑅 𝑅 𝑅 𝑅 𝑅 𝑅 𝑇 Table 2: Daily statistical parameters of ux tower measured environmental variables including air temperature ( ), net radiation ( ), relative humidity ( ), soil temperature ( ), and evapotranspiration (ET) in the whole period. Period Variable mean max min sd ku sk 6.68 22.96 −17.63 8.19 2.24 −0.29 0.80 4.24 16.51 −6.44 5.33 1.97 0.16 0.88 AT-Neu 79.80 99.98 44.36 10.98 2.52 −0.46 −0.59 8.71 21.28 −2.56 6.86 1.50 0.01 0.78 ET 1.29 6.78 −0.32 1.33 2.75 0.87 1.00 6.48 28.57 −31.89 10.37 3.10 −0.58 0.59 6.17 19.18 −15.83 5.91 1.93 0.38 0.76 CA-Let 60.40 99.04 16.94 16.48 2.18 0.04 −0.19 7.35 24.52 −10.06 7.99 1.81 0.18 0.61 ET 0.81 5.96 −0.50 1.01 6.68 1.92 1.00 8.35 27.83 −18.02 7.80 2.37 −0.25 0.76 5.08 19.76 −4.25 5.34 2.17 0.55 0.90 DE-Gri 77.98 100.00 39.22 10.60 2.63 −0.31 −0.63 9.68 24.32 −0.84 6.10 1.83 0.03 0.75 ET 0.96 4.50 −0.61 0.98 3.33 1.04 1.00 10.20 30.15 −18.72 8.98 2.28 −0.22 0.72 5.81 18.26 −3.90 5.38 1.88 0.39 0.83 HU-Bug 76.28 99.66 38.88 12.01 2.61 −0.38 −0.46 10.84 26.03 −3.11 7.21 1.78 0.05 0.70 ET 1.28 5.96 −0.06 1.10 3.68 1.08 1.00 ∘ −2 ∘ −1 Note.Theunits of , , , ,andET are C, mol m , %, C, and mm day ,respectively. , , , , ,and refer to the mean, maximum, minimum, standard deviation, kurtosis, and ℎ mean max min sd ku sk skewness of each variable, respectively. refers to the correlation coefficient between each variable and ET. Advances in Meteorology 5 and fuzzy c-means clustering, were abbreviated as ANFIS- 2.2.6. Group Method of Data Handling. GMDH approach Grid, ANFIS-SC, and ANFIS-FCM, respectively. as a typical inductive high-order regression-type algorithm is commonly subsumed under the category of feed-forward 2.2.4. General Regression Neural Network. GRNN proposed neural network [43]. The architecture of this heuristic non- by Specht [38] based on nonlinear regression theory is widely linear method is established automatically based on self- utilized for function approximation. It is closely associated organization learning algorithm, which is significantly differ- with the radial basis function neural network, but there ent from other machine learning algorithms. Moreover, the exists a slight distinction between these two networks in GMDH method can conquer the limitation of requiring prior knowledge regarding a given problem, and redundant input terms of topological structure. The GRNN model as a one- pass learning method is designed by using a highly parallel variables can be eliminated eecti ff vely during the learning. framework. In fact, the number of neurons in all the layers is Besides, the GMDH is highly robust to noise data and thus is strongly dependent upon the number of the used variables as not aeff cted by the existing outliers in the training samples. well as the sample size of a given training dataset, and thus In a well-developed GMDH network, the neuron in each these neurons do not require adjustment during the learning. hidden layer is individually connected by two inputs and a In addition to this, another noteworthy advantage of the singleoutput andactsasatransferfunction forrepresenting GRNN approach over other data-driven techniques is that the the results generated by the two neurons from the previous GRNN model does not need much time to select its internal layer. Mathematically, each neuron is represented by using algorithms or parameters, apart from the smoothing factor a quadratic polynomial equation with vfi e weights and one that highly aeff cts the model generalization performance. At bias. Ultimately, the well-trained network can be expressed by using an explicit high-order polynomial function in present, there is no standard, universally accepted method for determining the optimal smoothing factor with the aim of relation to all the neurons reserved in the network. All the guaranteeing the forecasting precision of the GRNN model. weighting coefficients involved in this iterative function are In this study, the proper smoothing factor that was set calculated by a common least square method. More details ranging from 0.01 to 1 was obtained by using an iterative aboutGMDHmethodcan be foundinIvakhnenko[43]and algorithm. Moreover, to prevent the overtt fi ing, fourfold Barzegar et al. [44]. cross validation was utilized in the training. Further details regarding the principle of the GRNN approach can be found 2.3. Model Structure and Evaluation. It is clear from Table 2 in Raghavendra and Deka [34] and Yaseen et al. [39]. that each environmental variable has high linear correlation with ET. er Th efore, these variables ( 𝑇 ,𝑇 ,𝑅 ,𝑅 )wereused 𝑎 𝑠 𝑛 ℎ 2.2.5. Extreme Learning Machine. ELM rfi stly proposed by as inputs for all the proposed data-driven models. Before the Huang et al. [40] is a relatively new, modern data-driven training of each applied model, the input variables and ET technique and has been successfully applied to deal with the were normalized to a range between 0 and 1. MATLAB so-ft nonlinear problems in diverse areas during the last few years. ware (version 8.2, R2013b) was utilized for the development The developed ELM method has a topological architecture of of the models and the related statistical analysis of estimated single-hidden-layer feed-forward neural network. Its number results. of hidden nodes can be randomly gained, and their relevant 2 In this study, the coefficient of determination ( 𝑅 ), Nash- parameters (weights and biases) do not need to be tuned as Sutcliffe efficiency (NSE), root mean square error (RMSE), these properties have been demonstrated to be independent and mean absolute error (MAE) were considered as statistical of the training dataset. By contrast, for the traditional back- indices for measuring the performance of the developed propagation based ANN approach, almost all the parameters data-driven models. These statistical indices are, respectively, are highly problem-dependent and should be carefully set expressed as below: or optimized by a common, time-consuming trial-and-error process. Moreover, the powerful approximation ability of the ELM approach has been strongly supported by several ∑ (ET − ET)(ET − ET ) [ ] 𝑖=1 𝑜,𝑖 𝑜 𝑚,𝑖 𝑚 lines of evidence [39, 41]. eTh fundamental principle of ELM 2 [ ] 𝑅 = , [ ] approach can be found in more detail in Huang et al. [40]. 2 2 𝑁 𝑁 ∑ (ET − ET) ∑ (ET − ET ) 𝑜,𝑖 𝑜 𝑚,𝑖 𝑚 Furthermore, it should be emphasized that appropri- 𝑖=1 𝑖=1 [ ] ate activation function is of importance for guaranteeing 𝑁 2 the modeling and generalization performance of the ELM ∑ (ET − ET ) 𝑖=1 𝑜,𝑖 𝑚,𝑖 method [42]. eTh sigmoid, sine, and hard limit algorithms NSE=1− , ∑ (ET − ET) are the three common types of activation functions applied 𝑖=1 𝑜,𝑖 𝑜 (1) for the hidden layer. The influences of different activation functions on the modeling ability of developed ELM models were evaluatedbythisstudy.Forthesakeofconvenience, RMSE= ∑(ET − ET ), 𝑜,𝑖 𝑚,𝑖 theELMmodelswiththesigmoid,sine, andhardlimitalgo- 𝑖=1 rithms were abbreviatedasELM-Sig,ELM-Sin,and ELM- Hard, respectively. Moreover, the linear activation function 𝑁 󵄨 󵄨 󵄨 󵄨 MAE= ∑ ET − ET , was adopted for the output layer for all the developed ELM 󵄨 󵄨 𝑜,𝑖 𝑚,𝑖 󵄨 󵄨 𝑖=1 models. 6 Advances in Meteorology where ET and ET denote the observed and modeled values The performance of the applied data-driven models for 𝑜 𝑚 estimating ET over the training, validation, and prediction of daily ET, respectively; ET and ET are the means of 𝑜 𝑚 periods at CA-Let site is shown in Table 4. As can be seen observed and modeled values, respectively;𝑁 is the number from the table, the ANN model performs the best on the of observed values. Regarding the physical significance of whole, followed by the ANFIS-SC and ANFIS-Grid models. these indicators, the𝑅 was used to measure the proportion The SVM-Sig model provides the worst accuracy among the of total variance in the observed ET that is explained by the twelve models. Based on the 𝑅 ,NSE,RMSE, andMAE modeled ET. For a perfect model, the𝑅 is expectedtobe metrics, the overall performance of these applied models in close to unity. However, this index is limited because it is the prediction period can be ranked as follows: ANN, ANFIS- calculated based on the linear relationships between observed SC, ANFIS-Grid, ANFIS-FCM, SVM-RBF, ELM-Sin, ELM- and simulated values and is sensitive to outliers. Alternatively, Sig, SVM-Poly, GRNN, GMDH, ELM-Hard, and SVM-Sig. the NSE represents the level of agreement between observed Figure 2illustrates themeasuredand predictedETbythe and simulated ET and can offer useful knowledge about optimal models for each approach in the prediction stage at the relative estimation of the generalization performance CA-Let site. As shown in the figure, the ANN, ANFIS-SC, and for a given model. It is sensitive to differences in mea- SVM-RBF models have higher𝑅 and lower RMSE than other sured and calculated means and variances and accordingly models. In addition, the tfi lines of these three models are was employed in the present investigation. Moreover, other closer to their respective ideal lines (1 : 1 line), in comparison valuable information involving the predictive ability of the with the other models. developed models can also be provided by the RMSE and MAE indicators. Therefore, these performance criteria were Comparisons of the applied models are made in Table 5 employed together to obtain helpful insight into the efficiency for modeling daily ET at DE-Gri site. Unlike the previous of the developed models. sites, the ELM-Sin model has better accuracy than the other models in terms of the used indices. eTh ranks of the estimated models in the prediction stage are: ELM-Sin, 3. Results ELM-Sig, ANN, ANFIS-Grid, GRNN, GMDH, ANFIS-FCM, ANFIS-SC, SVM-RBF, ELM-Hard, SVM-Poly, and SVM-Sig. The performance indices, including 𝑅 ,NSE,RMSE,and Figure 3 illustrates the estimates of the optimal models for MAE, areemployedtoevaluatetheaccuracyoftheutilized ET simulation in the prediction phase at DE-Gri site. It is models in predicting the daily ET in this study.𝑅 and IA with apparent from the gfi ure that the tfi line of the ANFIS-Grid larger values and RMSE and MAE with smaller values imply model is closer to the ideal line (1 : 1 line), while the ELM-Sin higher model efficiency. Table 3 shows the estimated results of model has the highest𝑅 and provides less scattered estimates all machine learning models (ANN, GRNN, GMDH, ELM, than the other models, which has also been conrm fi ed in ANFIS, and SVM) for ET over the training, validation, and Table 5. prediction periods at AT-Neu site. As can be seen from Table 6 summarizes the accuracy of the applied models Table 3, the ANFIS-SC model gives the best performance in thepredictionofETinthepredictionperiod,withthehighest for forecasting daily ET in the prediction phase at HU-Bug site. It can be clearly seen from the table that the GMDH values of𝑅 (0.9379) andNSE (0.9355) andthe lowest valueof −1 −1 model achieves the best precision among the developed RMSE (0.3308 mm day )and MAE(0.2260mm day ). And twelve models. Based on the utilized performance indicators, the ELM-Sin model provides the inferior results in terms of the overall model efficiency of these models in the prediction 𝑅 ,NSE,RMSE, andMAE.TheSVM-Sig modelperformsthe period canberankedasfollows:GMDH,ELM-Sig,ELM-Sin, worst among the twelve models. According to the𝑅 ,NSE, ANN, ANFIS-SC, SVM-RBF, ANFIS-FCM, ANFIS-Grid, RMSE, and MAE metrics, the overall performance ranks GRNN, SVM-Poly, ELM-Hard, and SVM-Sig. The scatterplot of these developed models in the prediction period can be comparisons of the estimated methods with their respective summarized as follows: ANFIS-SC, ELM-Sin, ANFIS-FCM, optimal parameters are made in Figure 4 over the prediction ANN, ELM-Sig, GMDH, SVM-RBF, ANFIS-Grid, GRNN, stage at HU-Bug site. As shown from the gfi ure, the slope and ELM-Hard, SVM-Poly, and SVM-Sig. bias values of the tfi line equation of both the ANFIS-SC and eTh comparisons of daily ET observed and predicted ELM-Sig models are closer to those of their corresponding by using the data-driven models over the prediction period exactlines(1 : 1line,slope:1,andbias:0),comparedwiththose in the form of scatter plot at AT-Neu site are shown in of the other models. However, the GMDH model seems to be Figure 1. As a convenience, the scattered estimates of the more successful than the other models from the𝑅 and RMSE optimal ELM, ANFIS, and SVM models are exclusively viewpoints. compared with those of the ANN, GRNN, and GMDH In order to provide insights into the over- and underes- models. As illustrated in Figure 1, the tfi line of the SVM- timation of the used data-driven models in predicting daily RBF model is closer to the ideal line (1 : 1 line) than those of ET, the measured and modeled values by the best models for the other models, considering the corresponding equations each site in the whole period are demonstrated in Figure 5. of tl fi ines. However, it canbeseenfromFigure1and It is evident from the figure that the modeled values of these Table 3 that the ANFIS-SC model seems to have slightly best models for each site can closely follow the corresponding higher𝑅 value than the other models and obtains similar observed ones, which is previously confirmed in Tables 3–6. scattered estimates to those of the ANN and ELM-Sin models. However, the peak values during the growing season in the Advances in Meteorology 7 Th Table 3: Comparisons of data-driven model performances for evapotranspiration among the training, validation and prediction periods at AT-Neu sit e. Training Validation Prediction Model 2 2 2 NSE RMSE MAE NSE RMSE MAE NSE RMSE MAE ANN 0.9298 0.9294 0.3551 0.2321 0.9407 0.9375 0.3318 0.2203 0.9355 0.9338 0.3350 0.2278 GRNN 0.9596 0.9595 0.2689 0.1635 0.9134 0.9118 0.3943 0.2640 0.9207 0.9186 0.3714 0.2473 GMDH 0.9271 0.9270 0.3610 0.2442 0.9246 0.9220 0.3707 0.2464 0.9356 0.9320 0.3394 0.2342 ELM-Sig 0.9256 0.9256 0.3644 0.2430 0.9265 0.9249 0.3639 0.2461 0.9355 0.9328 0.3376 0.2322 ELM-Sin 0.9278 0.9278 0.3591 0.2332 0.9302 0.9283 0.3554 0.2415 0.9365 0.9344 0.3335 0.2242 ELM-Hard 0.8762 0.8762 0.4702 0.3365 0.8814 0.8811 0.4577 0.3394 0.9043 0.9031 0.4053 0.2836 ANFIS-Grid 0.9407 0.9407 0.3255 0.2121 0.9237 0.9230 0.3684 0.2585 0.9247 0.9219 0.3639 0.2436 ANFIS-SC 0.9373 0.9373 0.3347 0.2138 0.9318 0.9304 0.3503 0.2402 0.9379 0.9355 0.3308 0.2260 ANFIS-FCM 0.9376 0.9376 0.3338 0.2151 0.9380 0.9358 0.3363 0.2314 0.9369 0.9343 0.3338 0.2282 SVM-RBF 0.9387 0.9373 0.3347 0.1928 0.9333 0.9328 0.3440 0.2357 0.9338 0.9321 0.3392 0.2286 SVM-Poly 0.8357 0.8321 0.5476 0.4007 0.8351 0.8341 0.5406 0.4287 0.8746 0.8696 0.4701 0.3579 SVM-Sig 0.5948 0.5061 0.9391 0.7203 0.5113 0.4352 0.9976 0.7997 0.5910 0.5063 0.9149 0.7275 −1 Note. e units of RMSE and MAE are mm day . 8 Advances in Meteorology 1 : 1 6 6 4 4 y = 0.8927x + 0.1772 2 2 y = 0.9016x + 0.1503 R = 0.9207 R = 0.9355 RMS% = 0.3714 0 0 RMS% = 0.3350 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (a) (b) 6 6 4 4 2 2 y = 0.9041x + 0.1596 y = 0.8791x + 0.1671 R = 0.9356 R = 0.9365 0 0 RMS% = 0.3394 RMS% = 0.3335 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (c) (d) 6 6 4 4 y = 0.8984x + 0.1617 2 2 y = 0.9248x + 0.1454 R = 0.9379 R = 0.9338 0 0 RMS% = 0.3308 RMS% = 0.3392 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (e) (f) Figure 1: Comparisons of daily ET between eddy covariance measured and simulated by data-driven models in the prediction period at AT-Neu site. (a) ANN model; (b) GRNN model; (c) GMDH model; (d) ELM-Sin model; (e) ANFIS-SC model; and (f) SVM-RBF model. prediction period appear to be appreciably underestimated by isthefactthatits learning speed is showntobeextremely the optimal models for all the sites, especially for CA-Let site, faster than that of other data-driven approaches, partly which is also consistent with the scatter plots in Figures 1–4. because the number of hidden nodes of an ELM model can be randomly determined. In addition, its related parameters (weights and biases) need not be tuned as these properties 4. Discussion are problem-independent and thus are not clearly associated In the following subsections, we concentrated primarily on with the applied training dataset. discussing the generalization ability of all data-driven models Furthermore, with the advances in machine learning in for forecasting daily ET and then on exploring the effects recent years, a number of new machine learning methods, of dieff rent internal functions on the ELM, ANFIS, and such as relevance vector machine [45], M5 model tree [46], SVM models. Finally, we also pointed out some potential and genetic programming [47], have been proposed and improvements for the follow-up work. successfully applied in other diverse efi lds, such as forecasting Our estimates demonstrated that all the examined mod- of meteorological time series (e.g., air temperature and els, including ANN, GRNN, GMDH, ELM, ANFIS, and precipitation) and prediction of water resource variables SVM, can seize the nonlinear relationship between ET and (e.g., rainfall–runo,ff groundwater level, and drought). Con- environmental variables according to the combination of sequently, it is also important to investigate the feasibility four dieff rent performance criteria. Moreover, our modeling and effectiveness of these new approaches in dealing with the results also conrfi med that the new computational intelli- present ET estimation, which will be undertaken in our future gence techniques (GMDH, ELM, and ANFIS) were capable work. of effectively acquiring the seasonal and interannual variation in ET driven by the environmental variables. More impor- Our modeling results also showed that an obvious differ- tantly, these three methods had significant superiority over ence existed within each method (ELM, ANFIS, and SVM) with various internal functions in terms of predictive perfor- conventional methods in terms of robustness and simplicity. Specifically, of particular interest regarding the ELM method mance. Therefore, selecting appropriate internal function for −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) Advances in Meteorology 9 Th Table 4: Comparisons of data-driven model performances for evapotranspiration among the training, validation and prediction periods at CA-Let sit e. Training Validation Prediction Model 2 2 2 NSE RMSE MAE NSE RMSE MAE NSE RMSE MAE ANN 0.7593 0.7590 0.3791 0.2541 0.8553 0.7671 0.5690 0.3546 0.7859 0.7334 0.5911 0.3607 GRNN 0.8417 0.8176 0.3298 0.1997 0.8112 0.6472 0.7002 0.4096 0.7415 0.6307 0.6957 0.3919 GMDH 0.6673 0.6673 0.4454 0.3036 0.8303 0.6887 0.6577 0.4018 0.6931 0.6343 0.6922 0.4134 ELM-Sig 0.7159 0.7159 0.4115 0.2821 0.8038 0.7045 0.6409 0.4057 0.7469 0.6907 0.6367 0.3913 ELM-Sin 0.7163 0.7163 0.4113 0.2805 0.8423 0.7570 0.5811 0.3582 0.7530 0.6998 0.6272 0.3787 ELM-Hard 0.5615 0.5615 0.5113 0.3602 0.6843 0.5572 0.7845 0.4758 0.6013 0.5446 0.7725 0.4733 ANFIS-Grid 0.7820 0.7820 0.3605 0.2418 0.8480 0.7869 0.5443 0.3473 0.7805 0.7380 0.5859 0.3527 ANFIS-SC 0.7691 0.7691 0.3711 0.2495 0.8467 0.7712 0.5639 0.3507 0.7855 0.7311 0.5936 0.3492 ANFIS-FCM 0.7649 0.7649 0.3744 0.2532 0.8628 0.7879 0.5429 0.3405 0.7805 0.7287 0.5962 0.3554 SVM-RBF 0.7936 0.7912 0.3528 0.2111 0.8453 0.7668 0.5693 0.3418 0.7762 0.7225 0.6030 0.3577 SVM-Poly 0.6888 0.6772 0.4387 0.2888 0.8489 0.7824 0.5500 0.3326 0.7528 0.7053 0.6214 0.3676 SVM-Sig 0.0244 −0.0790 290.02 241.69 0.0616 −0.1655 263.96 225.25 0.0226 −0.0104 298.60 248.78 −1 Notes. e unit of RMSE and MAE is mm day . 10 Advances in Meteorology 6 6 1 : 1 4 4 2 2 y = 0.6073x + 0.2295 y = 0.5030x + 0.2370 R = 0.7859 0 0 R = 0.7415 RMS% = 0.5911 RMS% = 0.6957 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (a) (b) 6 6 4 4 2 2 y = 0.5700x + 0.2810 y = 0.5195x + 0.2921 2 R = 0.7530 R = 0.6931 0 0 RMS% = 0.6272 RMS% = 0.6922 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (c) (d) 6 6 4 4 2 2 y = 0.6019x + 0.2366 y = 0.6101x + 0.1976 2 2 R = 0.7762 R = 0.7855 0 0 RMS% = 0.5936 RMS% = 0.6030 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (e) (f) Figure 2: Comparisons of daily ET between eddy covariance measured and simulated by data-driven models in the prediction period at CA-Let site. (a) ANN model; (b) GRNN model; (c) GMDH model; (d) ELM-Sin model; (e) ANFIS-SC model; and (f) SVM-RBF model. each method is essential with the objective of achieving the of ANFIS techniques in other different fields have concen- best modeling ability. It is highly recommended that different trated mainly on evaluating the roles of the membership internal functions for each method should be evaluated functions under grid partitioning algorithm. It should be in advance, when these methods are used for regression mentioned that selecting appropriate membership function and classicfi ation problems. More specicfi ally in the present and determining its optimal number may effectively improve study, for ANFIS method, the evaluated three algorithms for the performance of grid partitioning based ANFIS model. generating FISs had noticeable eeff cts on the performance of In conclusion, our study has broaden the scope of ANFIS ANFIS on the whole. We found that, among the three various research and provided deep insights into the application of ANFIS models, the ANFIS model with the subtractive clus- ANFIS method. In the follow-up work, we will investigate tering algorithm performed the best at AT-Neu, CA-Let, and together the capability of the aforementioned algorithms HU-Bug sites, while grid partitioning based ANFIS model (subtractive clustering, grid partitioning, and fuzzy c-means generated the optimal estimates at DE-Gri site. er Th efore, clustering), as well as different types of membership functions there was no omnipotent algorithm that was appropriate under grid partitioning algorithm. for all the cases. In addition, Cobaner [48] investigated According to the predictive capability and efficiency of the ability of two different ANFIS methods, respectively, SVM, it was found from our results that remarkable difference based on the subtractive clustering and grid partitioning existed among three different kernel functions (sigmoid, algorithms, in estimating reference ET using daily climatic polynomial, and RBF), which has been also confirmed data, and found that subtractive clustering based ANFIS by the previous studies in other fields [49–51]. Moreover, model achieved more plausible precision with fewer amounts our estimates indicated that the RBF kernel function for of computation in comparison with grid partitioning based SVM method performed better than the other two kernel ANFIS model. Moreover, to the best of our knowledge, functions (sigmoid and polynomial) in the prediction of most studies comparing the performance of different types daily ET. It concurred with the findings from numerous −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) Advances in Meteorology 11 Table 5: Comparisons of data-driven model performances for evapotranspiration among the training, validation, and prediction periods at DE-Gri si te. Training Validation Prediction Model 2 2 2 NSE RMSE MAE NSE RMSE MAE NSE RMSE MAE ANN 0.8633 0.8630 0.3470 0.2426 0.9341 0.8927 0.3411 0.2336 0.9623 0.9341 0.2769 0.1942 GRNN 0.8612 0.8603 0.3504 0.2487 0.9294 0.8814 0.3587 0.2478 0.9585 0.9292 0.2871 0.2058 GMDH 0.8396 0.8396 0.3755 0.2707 0.9326 0.8724 0.3719 0.2573 0.9619 0.9253 0.2949 0.2121 ELM-Sig 0.8535 0.8535 0.3589 0.2580 0.9358 0.8885 0.3478 0.2347 0.9669 0.9392 0.2659 0.1920 ELM-Sin 0.8546 0.8546 0.3575 0.2522 0.9477 0.9066 0.3182 0.2203 0.9711 0.9398 0.2646 0.1896 ELM-Hard 0.8012 0.8012 0.4180 0.2911 0.8926 0.8724 0.3720 0.2662 0.9053 0.8765 0.3791 0.2534 ANFIS-Grid 0.8772 0.8772 0.3285 0.2304 0.9173 0.8713 0.3735 0.2447 0.9574 0.9334 0.2785 0.1961 ANFIS-SC 0.8637 0.8637 0.3461 0.2427 0.9230 0.8716 0.3732 0.2397 0.9501 0.9088 0.3258 0.2167 ANFIS-FCM 0.8636 0.8636 0.3462 0.2439 0.9244 0.8744 0.3691 0.2378 0.9500 0.9099 0.3238 0.2159 SVM-RBF 0.8638 0.8633 0.3466 0.2306 0.9196 0.8796 0.3614 0.2332 0.9407 0.9002 0.3408 0.2092 SVM-Poly 0.7885 0.7852 0.4345 0.3221 0.7629 0.7043 0.5662 0.3879 0.8461 0.8199 0.4578 0.3407 SVM-Sig 0.0170 −0.0682 43.738 37.467 0.0001 −0.3639 37.708 31.554 0.1190 −0.2045 45.388 39.515 −1 Note.TheunitofRMSEand MAEismmday . 12 Advances in Meteorology 1 : 1 4 4 2 2 y = 0.7911x + 0.1870 y = 0.8010x + 0.1517 R = 0.9585 R = 0.9623 0 0 RMS% = 0.2871 RMS% = 0.2769 −1 012345 −1 012345 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (a) (b) 4 4 2 2 y = 0.7979x + 0.1693 y = 0.7834x + 0.1411 R = 0.9619 R = 0.9711 RMS% = 0.2949 RMS% = 0.2646 −1 012345 −1 012345 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (c) (d) 4 4 2 2 y = 0.7535x + 0.1708 y = 0.8033x + 0.1501 R = 0.9574 R = 0.9407 0 0 RMS% = 0.2785 RMS% = 0.3408 −1 01234 5 −1 01234 5 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (e) (f) Figure 3: Comparisons of daily ET between eddy covariance measured and simulated by data-driven models in the prediction period at DE-Gri site. (a) ANN model; (b) GRNN model; (c) GMDH model; (d) ELM-Sin model; (e) ANFIS-Grid model; and (f) SVM-RBF model. studies, showing the superiority of RBF over the other such as rainfall and runoff time series forecasting. In brief, kernel functions in solving the regression problems [52–54]. theELMtechniquecan be apromising alternativetoolto For example, Zounemat-Kermani et al. [55] evaluated the traditional methods for dealing with the regression issue in capability of SVM model with four different kernel functions the current research as well as the gap-filling problem of (linear, polynomial, sigmoid, and RBF) for forecasting daily ETfluxmeasuredbythe eddy covariance technique. Onthe suspended sediment concentrations and further pointed out other hand, relatively less attention has been drawn toward that the RBF for SVM model was the best choice for modeling exploring the eeff cts of various activation functions (e.g., sine, hydrological phenomena. Mohammadi et al. [56] investi- sigmoid, and hard limit activation function) in the hidden gated the ability of two different types of SVM models based layer on the generalization ability of ELM. In the present on polynomial and RBF kernel functions in forecasting the study, our results demonstrated that the sine and sigmoid horizontal global solar radiation and found that RBF for SVM activation functions for ELM models played the similar roles was highly competent for predicting daily horizontal global in estimating the daily ET and dramatically outperformed solar radiation in comparison with polynomial function. the hard limit activation function. eTh refore, it is important As a relatively new method, ELM exhibited strong to emphasize that the sine and sigmoid activation functions modeling accuracy in predicting daily ET, which has been are recommended as the optimal options for establishing the verified by previous studies for other applications, such as ELMmodelsforET forecasting. reference ET prediction [57] and stream-flow forecasting Furthermore, many recent studies have found that select- [39]. In particular, a very noteworthy aspect was that the ing an appropriate training function is vitally essential for ELM method presented a remarkable advantage against assuring the predictive ability and reliability of ANN in other other data-driven approaches with respect to computational fields [59–61]. Despite the fact that ANN has been recognized time and efficiency due to its simple network structure and as the most popular method to simulate the ET as well nontuned mechanism [58], which is a beneficial contribution asthecarbonfluxes at ecosystemlevel basedonthe eddy to the solution of some real-time forecasting problems, covariance-measured data [62–64], the influences of various −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) Advances in Meteorology 13 Th Table 6: Comparisons of data-driven model performances for evapotranspiration among the training, validation, and prediction periods at HU-Bug si te. Training Validation Prediction Model 2 2 2 NSE RMSE MAE NSE RMSE MAE NSE RMSE MAE ANN 0.8765 0.8764 0.3955 0.2636 0.8038 0.8023 0.4474 0.3022 0.7969 0.7907 0.5018 0.3635 GRNN 0.9043 0.9041 0.3483 0.2284 0.7412 0.7333 0.5196 0.3581 0.7519 0.7395 0.5598 0.3895 GMDH 0.8135 0.8135 0.4858 0.3303 0.7773 0.7770 0.4752 0.3315 0.8165 0.8143 0.4727 0.3272 ELM-Sig 0.8467 0.8467 0.4405 0.3030 0.7625 0.7563 0.4967 0.3566 0.8155 0.8087 0.4797 0.3402 ELM-Sin 0.8521 0.8521 0.4327 0.2910 0.7823 0.7807 0.4712 0.3352 0.8134 0.8075 0.4813 0.3449 ELM-Hard 0.7113 0.7113 0.6045 0.4539 0.6425 0.6291 0.6128 0.4577 0.7045 0.7017 0.5991 0.4478 ANFIS-Grid 0.8921 0.8921 0.3695 0.2556 0.7178 0.7008 0.5504 0.3605 0.7595 0.7414 0.5578 0.3774 ANFIS-SC 0.8721 0.8721 0.4024 0.2705 0.7761 0.7713 0.4811 0.3407 0.7893 0.7784 0.5164 0.3752 ANFIS-FCM 0.8679 0.8679 0.4089 0.2760 0.7709 0.7655 0.4873 0.3376 0.7726 0.7636 0.5333 0.3801 SVM-RBF 0.8917 0.8897 0.3737 0.2323 0.7529 0.7511 0.5020 0.3404 0.7699 0.7671 0.5294 0.3739 SVM-Poly 0.7451 0.7392 0.5745 0.3901 0.7344 0.7286 0.5241 0.3737 0.7266 0.7237 0.5765 0.4114 SVM-Sig 0.0049 −0.0610 218.15 178.95 0.0193 −0.0991 201.38 168.64 0.0090 −0.0053 207.32 171.67 −1 Note. e unit of RMSE and MAE is mm day . 14 Advances in Meteorology 6 6 1 : 1 4 4 2 2 y = 0.8481x + 0.2141 y = 0.8670x + 0.1858 R = 0.7519 R = 0.7969 0 0 RMS% = 0.5598 RMS% = 0.5018 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (a) (b) 6 6 4 4 2 2 y = 0.8883x + 0.1680 y = 0.8521x + 0.1728 R = 0.8155 R = 0.8165 0 0 RMS% = 0.4797 RMS% = 0.4727 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (c) (d) 6 6 4 4 2 2 y = 0.8795x + 0.1359 y = 0.8089x + 0.2289 R = 0.7893 R = 0.7699 0 0 RMS% = 0.5164 RMS% = 0.5294 0 246 0 246 −1 −1 Measured ET (mm daS ) Measured ET (mm daS ) (e) (f) Figure 4: Comparisons of daily ET between eddy covariance measured and simulated by data-driven models in the prediction period at HU-Bug site. (a) ANN model; (b) GRNN model; (c) GMDH model; (d) ELM-Sig model; (e) ANFIS-SC model; and (f) SVM-RBF model. training algorithms on the ANN performance have never benchmarks in order to compare their capability. Moreover, been examined to date. Consequently, special attention will this study also focused on investigating the influences of be given to the evaluation of the modeling abilities of ANN internal functions on their corresponding models (ELM, models with a variety of training algorithms for predicting ANFIS, and SVM) in terms of the generalization performance ET and carbon u fl xes in our follow-up work. on the basis of a set of statistical indices (𝑅 ,NSE,RMSE, and MAE). 5. Conclusions To summarize, the primary findings in the present study can be enumerated as follows: In recent years, many attempts mainly involving the use of soft computing modeling approaches have been made to sim- (1) It has been discovered that all the models developed in ulateand forecast theETinterrestrial ecosystems.However, this study were capable of mapping the nonlinear pro- the lack of comprehensive comparative researches related to cesses of governing the variation of the ET between these state-of-the-art modeling techniques largely hinders the biosphere and the atmosphere at the ecosystem their applicability and popularity, primarily owing to the level, and these novel models (GMDH, ELM, and confusion in what approach should be appropriately chosen ANFIS) produced estimates comparable to those of from a variety of data-driven methods in the practical appli- the conventional models. cations. To overcome this hindrance, the current research first (2) Considering the robustness and simplicity, these attempted to investigate the suitability and effectiveness of novel approaches can be used as promising alter- three newly proposed methods, GMDH, ELM, and ANFIS, natives to traditional methods for modeling and for estimating daily ET at four different grassland sites based forecasting daily ET. on the eddy covariance-measured data. In addition to these techniques, three traditional soft computing techniques, (3) ep Th redictiveaccuracyoftheSVM,ELM,andANFIS including ANN, GRNN, and SVM, were also employed as models was strongly dependent on their respective −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) −1 −1 −1 Modeled ET (mm daS ) Modeled ET (mm daS ) Modeled ET (mm daS ) Advances in Meteorology 15 −1 2004 2005 2006 2007 2008 2009 Measured Modeled (a) −1 1999 2000 2001 2002 2003 2004 2005 2006 2007 Measured Modeled (b) −1 2004 2005 2006 2007 2009 2010 Measured Modeled (c) −1 2003 2004 2005 2006 2007 2008 Measured Modeled (d) Figure 5: Eddy covariance measured and simulated daily ET by their respective best models for the four sites in the whole period. (a) For AT-Neu site using ANFIS-SC model; (b) for CA-Let site using ANN model; (c) for DE-Gri site using ELM-Sin model; and (d) for HU-Bug site using GMDH model. internal functions, especially for SVM. Three different It should be noted that all the data-driven modeling kernel functions for the SVM method were together techniques strongly driven by a large amount of data are tested and the results suggested that the RBF kernel oen ft argued because the intrinsic mechanisms of these well- function substantially outperformed both the polyno- trained models are still not able to be represented explicitly. mial and sigmoid kernel functions. Accordingly, this argument is very likely to decrease the (4) eTh ELM models with the sigmoidal and sine activa- credibility of these techniques and further impede their tion functions generated the similar modeling accu- applications. Notwithstanding this limitation, our present racy andwereappreciably superior to theELMmodel investigation does suggest that these data-driven methods with the hard limit function. based on soft computing can effectively complement phys- ically based models, broaden the horizon of ecological, (5) For the ANFIS method, the algorithms for generating FISs had noticeable eeff cts on the performance of climatological, and hydrologic researchers, and therefore ANFIS method. The optimal algorithm can be deter- contribute to the estimates of regional and global water mined according to a trial-and-error procedure. resources under climate change. −1 −1 −1 −1 ET (mm daS ) ET (mm daS ) ET (mm daS ) ET (mm daS ) 16 Advances in Meteorology Conflicts of Interest [12] A.Polhamus,J.B.Fisher,andK.P.Tu,“Whatcontrolsthe error structure in evapotranspiration models?” Agricultural and eTh authors declare that there are no conflicts of interest. Forest Meteorology,vol.169,pp. 12–24,2013. 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