The reliable quantification of daily evapotranspiration (ET) over vast croplands is a quest in many scholarly works aimed at the precise practice of water resources management. Remote sensing–based empirical and nonempirical models were developed to overcome largescale quantification issues, which are usually experienced when using conventional approaches for the estimation of ET. The surface energy balance system (SEBS) model was used to quantify the daily ET in the arid/semiarid over Wadi AdDwaser, Saudi. SEBS input variables are parametrically sensitive and climatic dependent, and the model input/output dependencies are of high comprehensibility; therefore, the optimization analysis of SEBS input/output parameters is the target of the current research. SEBS inputs reciprocal inconsistencies were determined using the artificial neural network analysis, while the output dependencies on the daily ET estimation were mapped. Results demonstrated that the temperature and relative humidity are the most sensitive parameters to be considered in the routine crop monitoring procedure. SEBS output thematic maps showed the robust proportional correlation between the daily ET and the conducted temperature map. Moreover, the estimated daily ET was inversely correlated with the estimated cold sensible heat fluxes. The findings suggest systematic monitoring and forecasting procedures for efficient watersaving management plans in Saudi Arabia.
The estimation of daily evapotranspiration (ET) using the remote sensing data was successfully applied to the last decade of agricultural studies. The remote sensing data were continuously developed and improved to enclose the farinfrared and shortwave infrared as crucial segments of the electromagnetic spectrum [1,2]. The latter two segments showed extensive importance in waterrelated scholarly studies rather in atmospheric water studies at the top of atmosphere level [3,4] or at the top of canopy (TOC) level [5,6]. The TOC applications of remote sensing covered the soil/water relationships as well as the water/crop relationships [7,8].
The substantial quantification of the ET exploiting remote sensing imagery proved significantly the quantum involvement of the sensible heat fluxes interacted with the TOC water vapor in largescale agricultural practices [9,10]. Nevertheless, the implementation of the adopted algorithms is valid solely in localscale practices, while the largescale agricultural practices are used to encounter droughts due to the interactions of surface geometry and heat flux fluctuation, besides the lack of meteorological data consistency [11,12].
Empirical and nonempirical algorithms to quantify the daily ET were lately developed to serve purposes and different spatial configuration settings [13,14]. Those physical models were heavily dependent on the physical parameters of the surrounding environments, and therefore, the biological parameters were less involved [15,16]. The most recently developed algorithms to quantify the daily ET showed the synergy between the physical and the biological parameters in a single biophysical algorithm performance [17,18,19,20].
One of the current and bestperforming calculations to estimate ET is the semiempirical SEBS model founded by Su [21]. SEBS considers not only a diverse range of land surfaces but also the physical and biological parameters that were conducted from two European Space Agency sensors: Advanced AlongTrack Scanning Radiometer (AATSR) and MEdium Resolution Imaging Spectrometer (MERIS) symbolism.
Optimization analysis could convey a significant determination to the hesitation in multiinput measurement uncertainties. It is a functional strategy to analyze the intuitive relationship between detached frameworks [23]. The optimization analysis procedures and its executions are discussed in the studies by Ficici et al. [24] and Kunnan and Carr [25]. The procedure of the comprehensive study generally examines the most extreme, least, and the mean desirability parameters for singular observations considering the reality that the desirability analysis and its transformations led to a forecasted retort into nonscaled values [26,27,28].
The artificial neural network (ANN) analysis was developed by Jo et al. [29]. The backpropagation method was the conceptual development of ANN to be implemented extensively after [30] the neural network training procedure. The uses of ANN are comprehensively and successfully applied in several fields related to hydrology and water resources management. Related fields to water quality assessment and water resources management were discussed in the previous studies [31,32,33,34,35].
The objectives of the research are the realization of the SEBS algorithm over a largescale agricultural practice in an arid environment and then to thematically map SEBS outputs. Consequently, an optimization analysis of SEBS input parameters will be exercised to comprehend SEBS inputs reciprocal inconsistencies using the ANN analysis. Finally, the SEBS model output dependencies are assessed against the estimated ET over Wadi AdDwaser, Saudi Arabia.
Wadi Adwaser is a typical example of an arid environment located in Saudi Arabia. Wadi Adwaser is located at 44°43′ latitude and 20°29′ longitude, which is at an approximate distance of 600 km southwest of Riyadh, the capital city of Saudi Arabia (Figure 1). The major activity in Wadi AdDwaser is agriculture. More than 1,20,000 hectares of the designated study area is used for Alfalfa crop production as a wholeyear fodder [36]. The main irrigation system is the pivot sprinklers connected to water pumps. These are deepwell pumps that convey groundwater continuously to the sprinklers. The extensive use of the groundwater resources in Wadi AdDwaser led to a drastic drop in the groundwater level and irrecoverable soil salinity problems [37]. The mean annual temperature in the designated study area is around 37°C with huge variations between the maximum temperatures of 45°C and the minimum temperature closely to 3°C. The mean annual rainfall is reported to be less than 18 mm with mostly sunny day’s long solar radiation [38].
The use of the SEBS calculation necessitates input parameters from four remote sensing images that can be acquired from three unique informational collections: (1) two datasets of AATSR images acquired in March and June 2012, (2) two datasets of MERIS images acquired in synchronization with the AATSR images and the total number of the remote sensing datasets is four images, and (3) meteorological data, as entirely mentioned in the studies by Su [18] and Elhag et al. [10]. The meteorological data utilized in the current study are incorporated in the form of 10year monthly average temperature, relative humidity, wind speed, and solar radiation to ensure the meteorological stability of the used data [22,40]. The information was gathered amid August 2012 (Table 1).
Month  Minimum temperature  Maximum temperature  Humidity  Wind  Sun expo.  Radiation 

(°C)  (°C)  (%)  (km/day)  (h)  (MJ/m²/day)  
January  3.7  25.2  40  346  7.4  15.7 
February  5.8  28.6  34  302  8.2  18.5 
March  9.4  32.9  28  302  8.7  21.3 
April  12.8  37.9  27  302  8.9  23.0 
May  17.8  42.8  16  302  7.1  20.6 
June  19.8  45.1  11  259  8.1  22.0 
July  21  45.5  13  346  6.5  19.6 
August  25.1  45.4  13  302  6.3  19.1 
September  17.5  42.8  15  259  7.7  20.2 
October  12.5  37.7  21  216  7.8  18.5 
November  7.5  31.1  29  259  8.5  17.4 
December  4.9  26.5  37  216  6.6  14.1 
Average  13.1  36.8  24  284  7.6  19.2 
SEBS comprises a sequence of examination practices for the assurance of the surface physical and biophysical parameters to be initially assessed. These parameters are albedo, emissivity factor, maximum and minimum temperature, and vegetation possibilities. Finally, a model for the assurance of the evaporative fraction estimation based on meteorological restriction conditions to the wet/dry weather limit was adopted [18]. The SEBS essential conditions are as follows:
The pixel conditions representing the dry (Hdry) and the wet (Hwet) metrological settings are controlled by the actual sensible heat fluxes. The Hdry and the Hwet pixel values are determined by equation sequence under the hypothesis of having a comprehensive wet condition [10]. Therefore, the daily ET estimation (E_{daily}) is estimated as follows:
A total number of 52 ground truth standardized Penman–Monteith ET data were collected uniformly to verify the daily ET conducted in the current study using an SEBS model. The lysimeter technique was carried out according to Liu and Wang [41] with ±0.025 calibrated accuracy. The calibration procedure was principally based on placing double infiltrometers of Taylor [42].
The reason for utilizing the optimization analysis is to simultaneously enhance the model forecasts considering numerous conditions. Optimization analysis is a standout practice found among the most wellknown methodologies used to expand a few progressions of response [23]. In a general sense, the desirability analysis changes over the information capacities into (0,1) scale to enhance the model forecasting in terms of optimization. Derringer and Suich [23] reported that the optimization analysis is based on three procedural approaches.
Maximization analysis:
Minimization analysis:
Overall desirability:
The ANN analysis was implemented in the current study to decompose the interconnected relationships of the input parameters for the better comprehensive standing of the problem. In this study, the neural analysis was carried out based on the study by Monahan [43].
The neural network regression method can be conducted as follows:
Such neural network settings can function under only one hidden layer to avoid the model overfitting [44]. The
To limit the model predictions between 0 and 1, the concluding productions must be in a linear relationship. The skiplayer diagram of the neural network analysis is shown in Figure 2.
The following is the equation for the skiplayer ANN for regression:
It ought to be evident that these approaches are exceedingly parameterized and subsequently will tend to overfit the investigated datasets. Crossvalidation is a consequent practice to ensure that the prescient execution of the neural network analysis is satisfactory.
The skiplayer neural network analysis is conducted as follows:
However, this model tends to overfit its training datasets. Therefore, assurance of the satisfactory execution of the ANNs demonstrates is an unquestionable requirement. Five distinct evaluation criteria are utilized to decide the optimum fit: the Pearson correlation coefficient of connection (R), the root mean square error (RMSE), the mean absolute deviation (MAD), the negative loglikelihood, and finally the unconditional sum of squares (SSE). Essentially, RMSE is the preferred analyzed parameter for comparability explanations. RMSE can be calculated as follows:
Univariate statistical analysis is performed to find mean, standard deviation, number, sum, quantile, maximum, minimum, and N missing functions. These functions run across columns or rows. The statistic is computed for each row across the series of rows. The quantile function was performed to evaluate the conducted values, ascendingly in the tabulate manner, of the 2D image data from 0 to 1 according to Cheng and Parzen [45] as follows:
Regression analysis was carried out to investigate the reliance of the conducted daily ET on the albedo, temperature Hdry, and Hwet outputs. The scatter plot matrix was conducted using the restricted maximum likelihood equation (RMLE) function according to the study by Robert and Gene Hwang [46] as follows:
To understand the conceptual framework of the study under investigation, SEBS input/output diagram shown in Figure 3 indicates that the main inputs of SEBS model are meteorological data combined with certain remote sensing imagery. Conversely, the output data are mainly thermal maps where each of which is used for different data measures. The inconsistency process starts with the problem definition utilizing the collected problemsolving information. Consequently, the analysis matrix can be performed with different weights of criteria in a comparable mode [47,48]. Throughout the normalization methods, the weights were transformed into a uniform scale value between 0 and 1. The value function converts the implementation of an option into a weighted score, which represents the degree to which a decision objective is matched [49].
The application of the SEBS model over the designated study area has produced 21 different output thematic maps related to surface energy fluxes. The actual daily ET and the evaporative fraction thematic maps were demonstrated caused by their relative significance to the study purposes. According to the regression equation demonstrated in Figure 4 (Y = 3.939 ln(x) − 1.4319 and R^{2} = 0.8189), the application of the SEBS model over the study area is significantly correlated with the ground truth data measurements collected from the lysimeter.
The idea behind drawing the best fit line assumes that the data are scattered along a line that represents the least squares regression error. This equation is of substantial sensible use because the water balance information is required for the irrigation requirements in the study area or under similar conditions. Therefore, the actual daily ET values were verified using real data in situ measurements.
Consequential information could be collected from remote sensing data only when the inadequacy conditions are considered. Inadequacy conditions for the application of the SEBS model primarily depend on the surface roughness [18], the planetary boundary layer [50], and land use land cover type [51,52].
The frequency distribution of daily ET values over the study area illustrated in Figure 5 has a mean frequency peak value at 2.4 mm, corresponding to the temperature distribution value of 322 K.
Table 2 and Figure 6 show the Gaussian analysis of the Jackknife predicated model and the desirability function on SEBS input data. Results show insignificance difference in SEBS input desirability in terms of temperature in general (Figure 6a–c). According to Table 2, −2*loglikelihood values for the maximum, minimum, and average temperatures were estimated to be closer to 83 with marginal variation [53].
Jackknife predicted model  

Theta  μ  σ²  −2*loglikelihood  
SEBS inputs  
Maximum temperature  31.4  13.5  22.5  82.4 
Minimum temperature  20.7  28.3  27.1  83.9 
Average temperature  26.8  20.9  24.3  83.1 
Relative humidity  13.6  0.7  0.0  −30.7 
Wind speed  100  1.3  0.0  −6.7 
Solar radiation  2.6  1957.3  322469.6  199.8 
Finally, solar radiations in Figure 6f show arbitrary Gaussian behavior with −2*loglikelihood value estimated to be 199.8, which is the highest value among SEBS input parameters. A higher Gaussian value indicates that the role of solar radiation in SEBS daily ET in the Wadi AdDwaser is still understudied [39,54]. Such a correlation needs to be considered in water conservation plants in arid environments [55].
The ANN analysis of a hidden layer, eight nodes, and hyperbolic refraction stimulation function was performed under specific conditions for each temporal dataset. These settings were sensibly practiced to limit the overfitting of the used algorithm, and ANN findings are presented in Table 3.
Training measures  Validation measures  Predication profiler  

Maximum temperature  R^{2}  0.73244  R^{2}  0.62325 

RMSE  2.44274  RMSE  2.76878  
Mean absolute deviation  2.04149  Mean absolute deviation  2.41238  
−loglikelihood  20.8085  −loglikelihood  12.1867  
SSE  53.7028  SSE  38.3308  
Sum frequency  9  Sum frequency  5  
Minimum temperature  R^{2}  0.84119  R^{2}  0.84231  
RMSE  1.95751  RMSE  2.09276  
Mean absolute deviation  1.69674  Mean absolute deviation  1.78596  
−loglikelihood  18.8155  −loglikelihood  10.7871  
SSE  34.4865  SSE  21.8982  
Sum frequency  9  Sum frequency  5  
Average temperature  R^{2}  0.79173  R^{2}  0.75405  
RMSE  2.19008  RMSE  2.4088  
Mean absolute deviation  1.86911  Mean absolute deviation  2.09916  
−loglikelihood  19.8259  −loglikelihood  11.4903  
SSE  43.168  SSE  29.0117  
Sum frequency  9  Sum frequency  5  
Relative humidity  R^{2}  0.83576  R^{2}  0.81527  
RMSE  0.02941  RMSE  0.0499  
Mean absolute deviation  0.02292  Mean absolute deviation  0.0321  
−loglikelihood  −18.967  −loglikelihood  −7.8937  
SSE  0.00779  SSE  0.01245  
Sum frequency  9  Sum frequency  5  
Wind speed  R^{2}  0.00082  R^{2}  −0.0269  
RMSE  0.20227  RMSE  0.16364  
Mean absolute deviation  0.15755  Mean absolute deviation  0.14555  
−loglikelihood  −1.6130  −loglikelihood  −1.9558  
SSE  0.36821  SSE  0.13389  
Sum frequency  9  Sum frequency  5  
Solari radiation  R^{2}  0.98032  R^{2}  0.98621  
RMSE  63.5153  RMSE  72.3797  
Mean absolute deviation  44.4785  Mean absolute deviation  56.3246  
−loglikelihood  50.132  −loglikelihood  28.5043  
SSE  36307.8  SSE  26194.1  
Sum frequency  9  Sum frequency  5 
Based on RMSE and –loglikelihood, the dataset of April showed that relative humidity followed by wind speed was used to descend the neural network classification parameters. The significant variables obtained from the analysis imply their importance to determine their influence on the SEBS estimation [44]. Temperature (minimum, average, and maximum, correspondingly) came in second in the significance order, while solar radiation ranked the last. This could be explained due to the close range of the wind speed and the relative humidity variations within the collected data from the different meteorological stations. On the contrary, solar radiation showed the highest range of input data variability [56,57].
According to the Gaussian analysis with −2*loglikelihood value of −6.708327, the wind speed was the least desirably function that affects the SEBS algorithm to conduct the daily ET within the selected study area as shown in Figure 6e [40,58].
The daily ET showed uneven −loglikelihood values with SEBS input parameters integrated together for satisfactory results [59]. Each parameter value was multiplied to its corresponded layer, and then the layers were overlaid all together to be introduced to the final optimization process [55].
The spatial distribution of daily ET values varies over Wadi AdDwaser. The extreme daily ET findings are situated at the West and East side of the study area, while in the central region of the Wadi AdDwaser, the daily ET findings are ranged from low to medium. The mean daily ET was estimated to be around 2.4 mm/day, with an extreme value reached to 9 mm/day (Figure 7). The range of the estimated daily ET, evaporative fraction, and other heat fluxes indices is presented in Table 4.
Daily_Evap  Relative_Evap  Albedo  Temp  Hdry  Hwet  

Minimum  0.3242  0.1997  0.1787  258.8811  42871.4548  4355.4284 
Maximum  8.9951  0.9532  0.7247  341.6599  131850.2985  45843.4828 
Mean  4.6521  0.8927  0.3533  320.6427  100361.5447  10746.6688 
Sigma  0.5836  0.0211  0.0502  3.3124  7818.0457  1856.7539 
Median  4.6803  0.8944  0.3632  320.8219  98774.0922  10432.7801 
Coefficient variation  0.2341  0.0402  0.2635  0.0202  0.1602  0.5292 
P75 threshold  4.9878  0.9002  0.3952  322.2586  104800.7300  11405.1564 
P80 threshold  5.0624  0.9017  0.3973  322.5819  106224.3915  11648.2505 
P85 threshold  5.1556  0.9032  0.4005  323.0670  108003.9684  11972.3759 
P90 threshold  5.2767  0.9061  0.4037  323.7137  111029.2491  12539.5954 
Maximum error  0.0093  0.0015  0.0011  0.1617  88.9788  81.0314 
The estimation of the daily ET values was not performed over the agricultural practices of the study area only, and it was also extended over the peripheral bare soils to estimate the potential ET values instead of the actual values. The tendency of the algorithm to estimate the potential ET over noncroplands is the reason behind the higher daily ET values (Table 4). This shift from the mean values of the daily ET was due to the absence of the biological parameters, especially the leaf area index (LAI) found using the MERIS sensor and the daily estimation is based on only the physical parameters found from the AATSR and the meteorological data [10,36].
Following the daily ET mapping, the evaporative fraction was also mapped in along with surface temperature, surface albedo, and the hot and the cold heat fluxes at the TOC level. The coefficient of variation was precisely used in the present study to assess the SEBS output inconsistencies (Table 4). The smallest coefficient was pointed out by the surface temperature (0.02), while the daily ET values and the corresponded albedo values showed robust dependencies of 0.234 and 0.263, respectively.
The performed regression analysis (Table 5) showed two distinctive behaviors of the estimated daily ET and each of the surface temperature and the heat fluxes as shown in Figure 8. The estimated daily ET showed persistent correlation with the surface albedo and the hot heat fluxes, while it was proportionally correlated with the surface temperature and inversely correlated with the cold heat fluxes [15,18,60,61].
Regression function  R^{2}  

Daily ET against surface albedo  0.005X + 1.984  0.43 
Daily ET against Hdry fluxes  −0.004X − 1.843  0.42 
Daily ET against Hwet fluxes  −2.79 ln(x) − 3.523  0.89 
Daily ET against surface temperature  2.84 ln(x) − 3.754  0.88 
The correlation established between the estimated daily ET and either the surface temperature or the cold heat fluxes was logical in principle, and it proves the efficiency of the SEBS model as well as the output intrarelationships [62,63,64]. Meanwhile, the surface albedo and the hot heat fluxes seemed to be less significant in SEBS output inconsistencies [44,65]. Accordingly, effective watersaving plans shall continuously monitor surface temperature variations to ensure their validity particularly in arid regions where the water resource management plans are always questioned of its sustainability [10,66].
The use of the SEBS input/output inconsistencies is to develop and disseminate information about conditionspecific management approaches that are considered to be profitable and practical for agricultural practices and the supply chain [67,68]. The use of the meteorological data for SEBS model performance is to estimate the daily ET on an accurate manner to minimize the overfit of the estimation using a single month data [22,69,70].
SEBS was used in the arid environments of Wadi AdDwaser to estimate the daily ET. The algorithm estimated daily ET values are within the empirical range of 1.2–8.9 mm/day. The desirability function as well as the ANN analysis show the significant importance of input datasets used to investigate and examine the SEBS input parameters over the designated study area. Temperature and relative humidity are significant parameters and must be considered and regularly monitored for water quality management plans in the selected study area. Further temporal data analysis is required to identify the trend of the solar radiation role. The current investigation is a biophysical evaluation that delivers information that could be used by farmers to enhance their cropping pattern. Furthermore, the outcomes could be valuable for other investigators who could use these results for diverse studies. For future considerations, a greater number of factors such as soil, climate, irrigation facilities, and socioeconomic shall be taken into consideration.
This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. (G651551440). The authors, therefore, acknowledge with thanks, DSR technical and financial support.
Conflict of interest: The author declares that there is no conflict of interest regarding the publication of this article.
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