# Pan Evaporation Estimation in Uttarakhand and Uttar Pradesh States, India: Validity of an Integrative Data Intelligence Model

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## Abstract

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_{m}). A new artificial intelligent (AI) model called the co-active neuro-fuzzy inference system (CANFIS) was developed for monthly EP

_{m}estimation at Pantnagar station (located in Uttarakhand State) and Nagina station (located in Uttar Pradesh State), India. The proposed AI model was trained and tested using different percentages of data points in scenarios one to four. The estimates yielded by the CANFIS model were validated against several well-established predictive AI (multilayer perceptron neural network (MLPNN) and multiple linear regression (MLR)) and empirical (Penman model (PM)) models. Multiple statistical metrics (normalized root mean square error (NRMSE), Nash–Sutcliffe efficiency (NSE), Pearson correlation coefficient (PCC), Willmott index (WI), and relative error (RE)) and graphical interpretation (time variation plot, scatter plot, relative error plot, and Taylor diagram) were performed for the modeling evaluation. The results of appraisal showed that the CANFIS-1 model with six input variables provided better NRMSE (0.1364, 0.0904, 0.0947, and 0.0898), NSE (0.9439, 0.9736, 0.9703, and 0.9799), PCC (0.9790, 0.9872, 0.9877, and 0.9922), and WI (0.9860, 0.9934, 0.9927, and 0.9949) values for Pantnagar station, and NRMSE (0.1543, 0.1719, 0.2067, and 0.1356), NSE (0.9150, 0.8962, 0.8382, and 0.9453), PCC (0.9643, 0.9649, 0.9473, and 0.9762), and WI (0.9794, 0.9761, 0.9632, and 0.9853) values for Nagina stations in all applied modeling scenarios for estimating the monthly EP

_{m}. This study also confirmed the supremacy of the proposed integrated GT-CANFIS model under four different scenarios in estimating monthly EP

_{m}. The results of the current application demonstrated a reliable modeling methodology for water resource management and sustainability.

## 1. Introduction

_{m}) using direct measurement can be a tedious, expensive, and time-consuming task [10]. Therefore, the introduction of robust and reliable intelligent models is a hot topic in the field of hydrology [11].

_{m}is highly non-linear and non-stationary and associated with several climatic factors (i.e., air temperature, dew point temperature, relative humidity, wind speed, sunshine hours, and solar radiation). Recently, several non-linear hybrid or simple artificial intelligent (AI) models have been employed for modeling various hydrological components [12,13,14,15,16,17,18,19]. Over the past decades, applications of AI models have demonstrated their feasibility as efficient tools for estimating daily and monthly pan evaporation using easily measured climatic variables [20,21,22,23,24,25,26,27]. Another essential development in the computer aid base has been the integration of standalone AI models and nature-inspired optimization algorithms for obtaining more reliable hybrid intelligent models [28,29,30,31].

_{m}at Tabriz (Iran) and Antalya (Turkey) stations. The results revealed that the MLPNN model outperformed the other models at both stations. Kisi and Heddam [32] investigated the comparative potential of multivariate adaptive regression spline (MARS), M5 Tree, modified Hargreaves–Samani (MHS), Stephens–Stewart (SS), and multiple linear regression (MLR) models for modeling the monthly EP

_{m}using only T

_{max}and T

_{min}data of three hydrometeorological stations in Turkey. The results disclosed that the MARS model achieved a superior prediction accuracy in comparison to the other models. Sebbar et al. [21] employed extreme learning machine (ELM) with online sequential (ELM_OS) and optimal pruned (ELM_OP) techniques to predict the monthly EP

_{m}at Ain Dalia and Zit Emba stations located in Algeria. The obtained results indicated the high prediction accuracy of the ELM_OS model in comparison to the ELM_OP model. Majhi et al. [22] evaluated the ability of deep long short-term memory cell (Deep-LSTM) and MLPNN models for modeling the daily pan evaporation in India. The compared results evidenced the capacity of the Deep-LSTM model performance in comparison to that of the MLPNN model. Lu et al. [23] estimated the daily evaporation over multiple regions in China using M5 Tree, random forest (RF), and gradient boosting decision tree (GBDT) models. They found that the GBDT model outperformed the other models.

_{m}in different climates of China using extreme learning machine (ELM), artificial neural network embedded with particle swarm optimization (PSO-ANN), genetic algorithm (GA-ANN), and Stephens–Stewart (SS) models. The results of the modeling comparison demonstrated that the ELM, PSO-ANN, and GA-ANN models provided better estimates than the SS model. Furthermore, several advanced models have been developed for modeling multiple scales of the pan evaporation process across the globe [28,34,35,36,37,38,39,40,41,42]. In accordance with the literature, the exploration of new versions of AI models is still an ongoing research area. Therefore, the current research investigated the potential of a newly explored AI model (i.e., the co-active neuro-fuzzy inference system (CANFIS)), as a widespread approximator for any non-linear occupation. The foremost excellence of the CANFIS model is evidenced by pattern-dependent coefficients (weights) among the consequent and premise layers [43]. Although there have been several studies focused on establishing a robust and reliable predictive model, few have focused on improving the models’ accuracy. The current research can contribute to prediction performance improvement based on the incorporation of the best selection of input variables. The implementation of the CANFIS model was advanced by integrating a non-linear input selection approach called the Gamma test (GT), in order to identify the input attributes correlating to the targeted predicted variable.

## 2. Case Study and Data Description

_{max}and T

_{min}), wind speed (WS), relative humidity at 7:00 a.m. (RH-1) and 2:00 p.m. (RH-2), bright sunshine hours (SSH), and monthly pan evaporation (EP

_{m}) were obtained from observatories located at the Pantnagar Crop Research Centre (PCRC), Uttarakhand, and Rice Research Station Nagina, Bijnor district in Uttar Pradesh State, India. Figure 2a,b illustrates the climatic parameters measured from January 2009 to December 2016 (eight year period) at both stations using a box and whisker plot, which presents statistics on the minimum value, first quartile, median, third quartile, and maximum value for climatic parameters (reading from lower to upper values). Additionally, Table 1 reports the brief statistical properties of climatic variables intended for both stations. The statistical characteristics reveal the platykurtic (−) and leptokurtic (+) nature of the climatic variables at both stations. Table 2 shows the correlations between the monthly EP

_{m}and other climatic variables for both stations. It can be observed from Table 2 that all of the six variables (T

_{min}, T

_{max}, RH-1, RH-2, WS, and SSH) have significant correlations with the EP

_{m}at a 5% significance level.

## 3. Methodology

#### 3.1. Gamma Test (GT)

_{ratio}approach the minimum, it indicates the goodness of input variables [47,56]. The V

_{ratio}is computed using the following expression:

_{ratio}, and Γ), to estimate the monthly EP

_{m}at Pantnagar and Nagina stations.

#### 3.2. Co-Active Neuro-Fuzzy Inference System (CANFIS) Model

#### 3.3. Multilayer Perceptron Neural Network (MLPNN) Model

_{ij}and W

_{jk}). The appropriate weights are adjusted to minimize the error between the observed and predicted output through back propagation encountered from right to left, as depicted in Figure 4.

_{m}). Data normalization was conducted with the hyperbolic-tangent (tanh) activation function (ranges from −1 to 1). As recommended by previous studies, the maximum number of neurons contained in the hidden layer was projected through the 2n + 1 idea, where n is the number of input variables [59]. Training of the MLPNN model was terminated over a 0.001 threshold value after 1000 epochs in NeuroSolutions 5.0 software. The framework of the MLPNN model designed in this study was built to incorporate all of the six input climate variables collected.

#### 3.4. Multiple Linear Regression (MLR) Model

_{1}, X

_{2}, …… X

_{n}are the independent variables; and ${\beta}_{0},{\beta}_{1},{\beta}_{2}$………${\beta}_{k}$ are the regression coefficients.

#### 3.5. Penman Model (PM)

^{2}/month), $\Delta $ is the slope of the saturation vapor pressure–air temperature curve (kPa/°C), $\gamma $ indicates the psychrometric constant (kPa/°C), and ${E}_{a}$ is the aerodynamic function (mm/month) and computed using Equation (5):

#### 3.6. Modeling Scenarios

- Scenario-1 contains 25% data for training (January 2009 to December 2010) and 75% data for testing (January 2011 to December 2016).
- Scenario-2 contains 50% data for training (January 2009 to December 2012) and 50% data for testing (January 2013 to December 2016).
- Scenario-3 contains 75% data for training (January 2009 to December 2014) and 25% data for testing (January 2015 to December 2016).
- Scenario-4 contains 75% data for training (January 2011 to December 2016) and 25% data for testing (January 2009 to December 2010).

_{m}estimation at the two study locations.

#### 3.7. Performance Appraisal Indicators

- Pearson correlation coefficient [54,56,70]:$$PCC=\frac{{\sum}_{\mathrm{i}=1}^{\mathrm{N}}\left({X}_{obs,i}-\overline{{X}_{obs}}\right)\left({Y}_{est,i}-\overline{{Y}_{est}}\right)}{\sqrt{{\sum}_{\mathrm{i}=1}^{\mathrm{N}}{({X}_{obs,i}-\overline{{X}_{obs}})}^{2}{\sum}_{\mathrm{i}=1}^{\mathrm{N}}{({Y}_{est,i}-\overline{{Y}_{est}})}^{2}}}$$
- Relative error [66,73]:$$RE=\frac{\left({X}_{obs,i}-{Y}_{est,i}\right)}{\left({X}_{obs,i}\right)}\times 100,$$
_{m}values for the ith dataset, respectively; $\overline{{X}_{obs}}$ and $\overline{{Y}_{est}}$ are the mean observed and estimated monthly EP_{m}values for ith dataset, respectively; and N is the number of observations.

## 4. Application Results and Analysis

#### 4.1. Optimal Input Variable Selection Using GT

_{m}at the Pantnagar and Nagina meteorological stations (Table 3). To complete this, the feasibility of the GT approach was adopted to identify the related input combinations that are crucial to building predictive models. The statistical results of GT are reported in Table 4 for both stations. Based on the GT results in Table 4, and with a fixed mask example (111111), the minimum values of Γ = 0.0017, A = 0.0665, SE = 0.0013, and V

_{ratio}= 0.0070 were obtained for Pantnagar station (Figure 6a), while the minimum values of Γ = 0.0112, A = 0.0395, SE = 0.0024, and V

_{ratio}= 0.0448 were obtained for Nagina station (Figure 6b). The mask demonstrated the incorporation of the six input variables for estimating the EP

_{m}. Hence, the following input variables were utilized for EP

_{m}estimation (i.e., T

_{max}, T

_{min}, RH-1, RH-2, WS, and SSH) at Pantnagar and Nagina stations, respectively. It is worth mentioning that including the WS variable as an input parameter provides a better score compared to the SSH (compare the Gamma scores of T

_{max}, RH-2, WS and T

_{max}, RH-2, SSH; or scores of T

_{max}, WS and T

_{max}, SSH in Table 4), according to the Gamma test, at both stations. This is in direct agreement with the correlations between WS or SSH and EP

_{m}given in Table 2.

#### 4.2. Estimation of EP_{m} under Different Scenarios at Pantnagar Station

_{max}, T

_{min}, RH-1, RH-2, WS, and SSH) was used for training and testing the applied methods (CANFIS, MLPNN, and MLR) under four different scenarios based on the performance evaluation indicators (NRMSE, NSE, PCC, and WI). The values of NRMSE, NSE, PCC, and WI in the four different scenarios in the testing phase are summarized in Table 5, which indicate that in scenario-1, the NRMSE (mm/month) = 0.1364, 0.1404, and 0.1402; NSE = 0.9439, 0.9406, and 0.9408; PCC = 0.9790, 0.9751, and 0.9758; and WI = 0.9860, 0.9857, and 0.9851 for the CANFIS-1, MLPNN-1 (with the structure of 6 inputs-9 processing elements-1 output), and MLR-1 models, respectively. In scenario-2 (Table 5), the NRMSE (mm/month) = 0.0904, 0.0920, and 0.1110; NSE = 0.9736, 0.9726, and 0.9602; PCC = 0.9872, 0.9857, and 0.9818; and WI = 0.9934, 0.9932, and 0.9903 for the CANFIS-1, MLPNN-1 (6-11-1), and MLR-1 models, respectively. Under scenario-3 (Table 5), the NRMSE (mm/month) = 0.0947, 0.0993, and 0.1085; NSE = 0.9703, 0.9674, and 0.9611; PCC = 0.9877, 0.9874, and 0.9831; and WI = 0.9927, 0.9918, and 0.9905 for the CANFIS-1, MLPNN-1 (6-10-1) and MLR-1 models, respectively. In the case of scenario-4 (Table 5), the NRMSE (mm/month) = 0.0898, 0.1021, and 0.1056; NSE = 0.9799, 0.9740, and 0.9721; PCC = 0.9922, 0.9877, and 0.9885; and WI = 0.9949, 0.9934, and 0.9927 for the CANFIS-1, MLPNN-1 (6-9-1), and MLR-1 models, respectively. In order to validate the results of the CANFIS, MLPNN, and MLR models, a comparison with the PM was made for all scenarios. As Table 5 clearly shows, the CANFIS-1 models out-performed the other models in all four scenarios, followed by the MLPNN-1 models. Therefore, the CANFIS-1 models followed the best statistical criteria (i.e., maximum rate of WI, PCC, and NSE, and minimum rate of NRMSE) for the testing period and were selected as the best among the three models. Likewise, the performance of PM was found to be the worst in all scenarios for monthly EP

_{m}estimation at the Pantnagar station.

_{m}values obtained by CANFIS-1, MLPNN-1, MLR-1, and PM models under scenarios one to four during the testing period at Pantnagar. In the scatter plots, the regression line (RL) provides the coefficient of determination (R

^{2}) for all four scenarios. In scenario-1, the R

^{2}= 0.9584, 0.9508, 0.9542, and 0.2951; scenario-2, the R

^{2}= 0.9745, 0.9736, 0.9639, and 2721; scenario-3, the R

^{2}= 0.9756, 0.9750, 0.9666, and 3203; and scenario-4, the R

^{2}= 0.9845, 0.9756, 0.9771, and 0.2953, for the CANFIS-1, MLPNN-1, MLR-1, and PM models during the testing phase, respectively. Besides, scenarios one to four demonstrated that the regression line is above the 1:1 line, and this means that the PM model under these scenarios highly overestimated the magnitude of the monthly EP

_{m}values at Pantnagar station.

_{m}values of the CANFIS-1, MLPNN-1, MLR-1, and PM models in the four different scenarios over the testing period are illustrated in Figure 8a–d. As reported in Figure 8a–d, the RE percentage was limited to between +40 and −20 for the first scenario. The highest RE% was experienced using the Penman model (PM). However, the minimum relative error percentage was obtained for the CANFIS model, and it was limited to ±10, with some observations reaching ±20. Greater spreading of the RE for all prescribed models seemed to occur at the peak value of monthly EP

_{m}. It can also be observed from Figure 8, together with Figure 7, that the models’ accuracy varies over diverse scenarios and this suggests the use of various scenarios in evaluating the potential of AI models, as also discussed by Kisi and Heddam [32].

_{m}values yielded by the CANFIS-1, MLPNN-1, MLR-1, and PM models under scenarios one to four during the testing period at Pantnagar station through a Taylor diagram (TD), which is a polar plot for acquiring a visual judgment of model performance based on the coefficient of correlation, standard deviation, and root mean square error (RMSE). Figure 9a–d shows that the estimates provided by the CANFIS-1 model in all four scenarios are very close to the observed values of monthly EP

_{m}. Henceforth, the CANFIS-1 model with T

_{max}, T

_{min}, RH-1, RH-2, WS, and SSH climatic parameters can be cast for monthly EP

_{m}estimation at Pantnagar station.

#### 4.3. Estimation of EP_{m} under Different Scenarios at Nagina Station

_{max}, T

_{min}, RH-1, RH-2, WS, and SSH) during the testing period under four different scenarios. Nagina station in scenario-1 (Table 6) achieved NRMSE values ranging from 0.1543 to 0.1866 and NSE/PCC (WI) values ranging from 0.9150 to 0.8758/0.9643 to 0.9437 (0.9794 to 0.9698) for the CANFIS-1, MLPNN-1 (6-10-1), and MLR-1 models, respectively. In scenario-2 (Table 6), the NRMSE values ranged from 0.1719 to 0.2299 and NSE/PCC (WI) values ranged from 0.8962 to 0.8144/0.9649 to 0.9346 (0.9761 to 0.9579) for the CANFIS-1, MLPNN-1 (6-10-1), and MLR-1 models, respectively. In the case of scenario-3 (Table 6), the NRMSE values ranged from 0.2067 to 0.2939 and NSE/PCC (WI) values ranged from 0.8382 to 0.6729/0.9473 to 0.9049 (0.9632 to 0.9313), while in scenario-4, the NRMSE values ranged from 0.1356 to 0.1621 and NSE/PCC (WI) values ranged from 0.9453 to 0.9219/0.9762 to 0.9666 (0.853 to 0.9789), for the CANFIS-1, MLPNN-1 (6-10-1), and MLR-1 models, respectively. A comparison of the CANFIS, MLPNN, and MLR models against the PM for all scenarios exposed the better performance of the CANFIS model, followed by the MLPNN and MLR models. As Table 6 clearly indicates, the CANFIS-1 models out-performed the other models in all four scenarios, followed by the MLPNN-1 models. Therefore, CANFIS-1 followed the best statistical criteria (i.e., minimum values = NRMSE, and maximum values = NSE, PCC, and WI) during the testing period and was selected as the best of the three models. Hence, the models’ estimation accuracies show variations over the four scenarios and increasing the training data length generally improves the models’ exactness in estimation of the monthly EP

_{m}, as also discussed by Kisi and Heddam [32].

_{m}values obtained by the CANFIS-1, MLPNN-1, MLR-1, and Penman models under scenarios one to four during the testing period at Nagina station. In scenario-1, the R

^{2}is 0.9299, 0.9201, 0.8905, and 0.2879; scenario-2, the R

^{2}is 0.9311, 0.8999, 0.8735, and 0.2863; scenario-3, the R

^{2}is 0.8973, 0.8550, 0.8188, and 0.2944; and scenario-4, the R

^{2}is 0.9529, 0.9498, 0.9343, and 0.3911 for the CANFIS-1, MLPNN-1, MLR-1, and PM models during the testing phase, respectively. In addition, the scenarios one, two, and three demonstrated that the regression line (RL) is above the 1:1 line for all of the methods and this means that the CANFIS-1, MLPNN-1, and MLR-1 models under these scenarios slightly over-predict, while in scenario-4, they under-predict, the monthly EP

_{m}values at Nagina station. Moreover, scenarios one to four verified that the Penman model highly over-estimates the EP

_{m}values. Therefore, the use of various data splitting scenarios is recommended when testing data-driven methods in the estimation of EP

_{m}.

_{m}values for all applied predictive models for Nagina station is displayed in Figure 11a–d for the four different scenarios over the testing period. Figure 11a–d shows that the RE percentage was between +25 and −50 for the first scenario. The maximum RE% was experienced for the Penman model. Apparently, the best performance based on this metric was attained for the CANFIS model and for the fourth scenario. The relative error percentage was limited to ±15 for about 80% of the testing phase of modeling. Conversely, the rest of the data observations ranged by ±20%. Therefore, extreme spreading of the RE for the peak value of the monthly EP

_{m}was detected for all prescribed models.

_{m}values yielded through the CANFIS-1, MLPNN-1, MLR-1, and Penman models under scenarios one to four during the testing period. Figure 12a–d shows that the CANFIS-1 model in all four scenarios is closer to the observed values of monthly EP

_{m}compared to the other applied models. Therefore, the CANFIS-1 model with T

_{max}, T

_{min}, RH-1, RH-2, WS, and SSH climatic variables at Nagina station can be employed for monthly EP

_{m}estimation.

#### 4.4. Comparison and Discussion

_{m}was estimated at Pantnagar and Nagina stations under four different scenarios by employing the CANFIS, MLPNN, and MLR models in conjunction with GT, which revealed the appropriate input variable combination for this task. The results produced by the CANFIS model were validated against the MLPNN and MLR models using several statistical metrics and visual interpretations. The CANFIS model optimized with the Takagi–Sugeno–Kang (TSK) fuzzy inference system, hyperbolic-tangent (tanh) activation function, delta bar delta algorithm, and Gaussian membership functions demonstrated a substantial predictability performance of the modeled evaporation process. This was observed for all of the investigated modeling scenarios.

_{m}process is usually highly associated with major uncertainties of climatic variability. Therefore, proposing the CANFIS model was an excellent idea for addressing this complex climate process. For this region, it was evidenced that the incorporation of all related available hydrological information was highly crucial for modeling the monthly EP

_{m}. This was due to the high stochasticity of the monthly EP

_{m}, which is very much influenced by different climate attributes. Decadal research on pan evaporation estimation has shown the wide applications of AI models. Through validation against literature studies [28,74,75,76,77,78,79], the present implementation of the CANFIS model confirmed its predictability capacity using statistical metrics.

## 5. Conclusions

_{m}using the Gamma test. The second phase of modeling was employed to estimate the value of monthly EP

_{m}using different AI models, including CANFIS and MLPNN at Pantnagar station (located in Uttarakhand State) and Nagina station (located in Uttar Pradesh State), India. Owing to the fact that different span data can influence the efficiency of the applied AI models, several scenarios were investigated, applying different training and testing data set spans. For validation purposes, the predictability potential of CANFIS and MLPNN were evaluated against the classical multiple linear regression and traditional Penman model. The modeling procedure was inspected using multiple statistical metrics (i.e., normalized root mean square error, Nash–Sutcliffe efficiency, Pearson correlation coefficient, Willmott index, and relative error). In addition, graphical inspections were performed, including a time variation plot, scatter plot, relative error percentage graph, and Taylor diagram. The findings of the research evidenced the capacity of the CANFIS-1 model for estimating monthly-scale pan evaporation incorporating all of the weather information, including the minimum and maximum air temperature, morning and afternoon relative humidity, wind speed, and sunshine hours. The superiority of the CANFIS-1 model was observed for all examined scenarios and at both Pantnagar and Nagina stations. Additionally, the performance of the traditional Penman model was found to be the worst in all scenarios for estimating the monthly EP

_{m}at both stations. Overall, the result of the current research demonstrated the feasibility of the CANFIS model as a newly developed data-intelligent approach for simulating pan evaporation in the Indian region, where it can be applied for several water resource engineering applications.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Mbangiwa, N.C.; Savage, M.J.; Mabhaudhi, T. Modelling and measurement of water productivity and total evaporation in a dryland soybean crop. Agric. For. Meteorol.
**2019**, 266–267, 65–72. [Google Scholar] [CrossRef] - Sayl, K.N.; Muhammad, N.S.; Yaseen, Z.M.; El-shafie, A. Estimation the Physical Variables of Rainwater Harvesting System Using Integrated GIS-Based Remote Sensing Approach. Water Resour. Manag.
**2016**, 30, 3299–3313. [Google Scholar] [CrossRef] - Sanikhani, H.; Kisi, O.; Maroufpoor, E.; Yaseen, Z.M. Temperature-based modeling of reference evapotranspiration using several artificial intelligence models: Application of different modeling scenarios. Theor. Appl. Climatol.
**2019**, 135, 449–462. [Google Scholar] [CrossRef] - Zhao, G.; Gao, H. Estimating reservoir evaporation losses for the United States: Fusing remote sensing and modeling approaches. Remote Sens. Environ.
**2019**, 226, 109–124. [Google Scholar] [CrossRef] [Green Version] - Deo, R.C.; Samui, P. Forecasting Evaporative Loss by Least-Square Support-Vector Regression and Evaluation with Genetic Programming, Gaussian Process, and Minimax Probability Machine Regression: Case Study of Brisbane City. J. Hydrol. Eng.
**2017**, 22, 05017003. [Google Scholar] [CrossRef] - Salman, S.A.; Shahid, S.; Ismail, T.; Ahmed, K.; Wang, X.-J. Selection of climate models for projection of spatiotemporal changes in temperature of Iraq with uncertainties. Atmos. Res.
**2018**, 213, 509–522. [Google Scholar] [CrossRef] - Wang, K.; Liu, X.; Tian, W.; Li, Y.; Liang, K.; Liu, C.; Li, Y.; Yang, X. Pan coefficient sensitivity to environment variables across China. J. Hydrol.
**2019**, 572, 582–591. [Google Scholar] [CrossRef] - Tabari, H.; Talaee, P.H.; Abghari, H. Utility of coactive neuro-fuzzy inference system for pan evaporation modeling in comparison with multilayer perceptron. Meteorol. Atmos. Phys.
**2012**, 116, 147–154. [Google Scholar] [CrossRef] - Friedrich, K.; Grossman, R.L.; Huntington, J.; Blanken, P.D.; Lenters, J.; Holman, K.D.; Gochis, D.; Livneh, B.; Prairie, J.; Skeie, E.; et al. Reservoir Evaporation in the Western United States: Current Science, Challenges, and Future Needs. Bull. Am. Meteorol. Soc.
**2017**, 99, 167–187. [Google Scholar] [CrossRef] - Ali Ghorbani, M.; Kazempour, R.; Chau, K.-W.; Shamshirband, S.; Taherei Ghazvinei, P. Forecasting pan evaporation with an integrated artificial neural network quantum-behaved particle swarm optimization model: A case study in Talesh, Northern Iran. Eng. Appl. Comput. Fluid Mech.
**2018**, 12, 724–737. [Google Scholar] [CrossRef] - Jing, W.; Yaseen, Z.M.; Shahid, S.; Saggi, M.K.; Tao, H.; Kisi, O.; Salih, S.Q.; Al-Ansari, N.; Chau, K.-W. Implementation of evolutionary computing models for reference evapotranspiration modeling: Short review, assessment and possible future research directions. Eng. Appl. Comput. Fluid Mech.
**2019**, 13, 811–823. [Google Scholar] [CrossRef] [Green Version] - Yaseen, Z.M.; El-shafie, A.; Jaafar, O.; Afan, H.A.; Sayl, K.N. Artificial intelligence based models for stream-flow forecasting: 2000–2015. J. Hydrol.
**2015**, 530, 829–844. [Google Scholar] [CrossRef] - Danandeh Mehr, A.; Nourani, V.; Kahya, E.; Hrnjica, B.; Sattar, A.M.A.; Yaseen, Z.M. Genetic programming in water resources engineering: A state-of-the-art review. J. Hydrol.
**2018**, 566, 643–667. [Google Scholar] [CrossRef] - Nourani, V.; Hosseini Baghanam, A.; Adamowski, J.; Kisi, O. Applications of hybrid wavelet–Artificial Intelligence models in hydrology: A review. J. Hydrol.
**2014**, 514, 358–377. [Google Scholar] [CrossRef] - Fahimi, F.; Yaseen, Z.M.; El-shafie, A. Application of soft computing based hybrid models in hydrological variables modeling: A comprehensive review. Theor. Appl. Climatol.
**2016**, 128, 875–903. [Google Scholar] [CrossRef] - Yaseen, Z.M.; Sulaiman, S.O.; Deo, R.C.; Chau, K.-W. An enhanced extreme learning machine model for river flow forecasting: State-of-the-art, practical applications in water resource engineering area and future research direction. J. Hydrol.
**2018**, 569, 387–408. [Google Scholar] [CrossRef] - Fotovatikhah, F.; Herrera, M.; Shamshirband, S.; Ardabili, S.F.; Piran, J. Mechanics Survey of computational intelligence as basis to big flood management: Challenges, research directions and future work. Eng. Appl. Comput. Fluid Mech.
**2018**, 2060, 411–437. [Google Scholar] - Salih, S.Q.; Sharafati, A.; Ebtehaj, I.; Sanikhani, H.; Siddique, R.; Deo, R.C.; Bonakdari, H.; Shahid, S.; Yaseen, Z.M. Integrative stochastic model standardization with genetic algorithm for rainfall pattern forecasting in tropical and semi-arid environments. Hydrol. Sci. J.
**2020**, 65, 1145–1157. [Google Scholar] [CrossRef] - Hai, T.; Sharafati, A.; Mohammed, A.; Salih, S.Q.; Deo, R.C.; Al-Ansari, N.; Yaseen, Z.M. Global Solar Radiation Estimation and Climatic Variability Analysis Using Extreme Learning Machine Based Predictive Model. IEEE Access
**2020**, 8, 12026–12042. [Google Scholar] [CrossRef] - Qasem, S.N.; Samadianfard, S.; Kheshtgar, S.; Jarhan, S.; Kisi, O.; Shamshirband, S.; Chau, K.-W. Modeling monthly pan evaporation using wavelet support vector regression and wavelet artificial neural networks in arid and humid climates. Eng. Appl. Comput. Fluid Mech.
**2019**, 13, 177–187. [Google Scholar] [CrossRef] [Green Version] - Sebbar, A.; Heddam, S.; Djemili, L. Predicting Daily Pan Evaporation (Epan) from Dam Reservoirs in the Mediterranean Regions of Algeria: OPELM vs OSELM. Environ. Process.
**2019**, 6, 309–319. [Google Scholar] [CrossRef] - Majhi, B.; Naidu, D.; Mishra, A.P.; Satapathy, S.C. Improved prediction of daily pan evaporation using Deep-LSTM model. Neural Comput. Appl.
**2019**, 31, 1–15. [Google Scholar] [CrossRef] - Lu, X.; Ju, Y.; Wu, L.; Fan, J.; Zhang, F.; Li, Z. Daily pan evaporation modeling from local and cross-station data using three tree-based machine learning models. J. Hydrol.
**2018**, 566, 668–684. [Google Scholar] [CrossRef] - Eray, O.; Mert, C.; Kisi, O. Comparison of multi-gene genetic programming and dynamic evolving neural-fuzzy inference system in modeling pan evaporation. Hydrol. Res.
**2017**, 49, 1221–1233. [Google Scholar] [CrossRef] - Adnan, R.M.; Malik, A.; Kumar, A.; Parmar, K.S.; Kisi, O. Pan evaporation modeling by three different neuro-fuzzy intelligent systems using climatic inputs. Arab. J. Geosci.
**2019**, 12, 606. [Google Scholar] [CrossRef] - Moazenzadeh, R.; Mohammadi, B.; Shamshirband, S.; Chau, K. Coupling a firefly algorithm with support vector regression to predict evaporation in northern Iran. Eng. Appl. Comput. Fluid Mech.
**2018**, 12, 584–597. [Google Scholar] [CrossRef] [Green Version] - Salih, S.Q.; Sharafati, A.; Khosravi, K.; Faris, H.; Kisi, O.; Tao, H.; Ali, M.; Yaseen, Z.M. River suspended sediment load prediction based on river discharge information: Application of newly developed data mining models. Hydrol. Sci. J.
**2019**, 65, 624–637. [Google Scholar] [CrossRef] - Ghorbani, M.A.; Deo, R.C.; Yaseen, Z.M.; HKashani, M.; Mohammadi, B. Pan evaporation prediction using a hybrid multilayer perceptron-firefly algorithm (MLP-FFA) model: Case study in North Iran. Theor. Appl. Climatol.
**2018**, 133, 1119–1131. [Google Scholar] [CrossRef] - Feng, Y.; Jia, Y.; Zhang, Q.; Gong, D.; Cui, N. National-scale assessment of pan evaporation models across different climatic zones of China. J. Hydrol.
**2018**, 564, 314–328. [Google Scholar] [CrossRef] - Sharafati, A.; Tafarojnoruz, A.; Shourian, M.; Yaseen, Z.M. Simulation of the depth scouring downstream sluice gate: The validation of newly developed data-intelligent models. J. Hydro Environ. Res.
**2020**, 29, 20–30. [Google Scholar] [CrossRef] - Mohammed, M.; Sharafati, A.; Al-Ansari, N.; Yaseen, Z.M. Shallow Foundation Settlement Quantification: Application of Hybridized Adaptive Neuro-Fuzzy Inference System Model. Adv. Civ. Eng.
**2020**, 2020, 1–14. [Google Scholar] [CrossRef] [Green Version] - Kisi, O.; Heddam, S. Evaporation modelling by heuristic regression approaches using only temperature data. Hydrol. Sci. J.
**2019**, 64, 653–672. [Google Scholar] [CrossRef] - Shiri, J. Evaluation of a neuro-fuzzy technique in estimating pan evaporation values in low-altitude locations. Meteorol. Appl.
**2019**, 26, 204–212. [Google Scholar] [CrossRef] [Green Version] - Deo, R.C.; Ghorbani, M.A.; Samadianfard, S.; Maraseni, T.; Bilgili, M.; Biazar, M. Multi-layer perceptron hybrid model integrated with the firefly optimizer algorithm for windspeed prediction of target site using a limited set of neighboring reference station data. Renew. Energy
**2018**, 116, 309–323. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A.; Kisi, O. Monthly pan-evaporation estimation in Indian central Himalayas using different heuristic approaches and climate based models. Comput. Electron. Agric.
**2017**, 143, 302–313. [Google Scholar] [CrossRef] - Rezaie-Balf, M.; Kisi, O.; Chua, L.H.C. Application of ensemble empirical mode decomposition based on machine learning methodologies in forecasting monthly pan evaporation. Hydrol. Res.
**2019**, 50, 498–516. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A.; Kisi, O. Daily Pan Evaporation Estimation Using Heuristic Methods with Gamma Test. J. Irrig. Drain. Eng.
**2018**, 144, 04018023. [Google Scholar] [CrossRef] - Salih, S.Q.; Allawi, M.F.; Yousif, A.A.; Armanuos, A.M.; Saggi, M.K.; Ali, M.; Shahid, S.; Al-Ansari, N.; Yaseen, Z.M.; Chau, K.-W. Viability of the advanced adaptive neuro-fuzzy inference system model on reservoir evaporation process simulation: Case study of Nasser Lake in Egypt. Eng. Appl. Comput. Fluid Mech.
**2019**, 13, 878–891. [Google Scholar] [CrossRef] [Green Version] - Wang, L.; Kisi, O.; Zounemat-Kermani, M.; Gan, Y. Comparison of six different soft computing methods in modeling evaporation in different climates. Hydrol. Earth Syst. Sci. Discuss.
**2016**, 20, 1–51. [Google Scholar] [CrossRef] - Wang, L.; Niu, Z.; Kisi, O.; Li, C.; Yu, D. Pan evaporation modeling using four different heuristic approaches. Comput. Electron. Agric.
**2017**, 140, 203–213. [Google Scholar] [CrossRef] - Wang, L.; Kisi, O.; Zounemat-Kermani, M.; Li, H. Pan evaporation modeling using six different heuristic computing methods in different climates of China. J. Hydrol.
**2017**, 544, 407–427. [Google Scholar] [CrossRef] - Wang, L.; Kisi, O.; Hu, B.; Bilal, M.; Zounemat-Kermani, M.; Li, H. Evaporation modelling using different machine learning techniques. Int. J. Climatol.
**2017**, 37, 1076–1092. [Google Scholar] [CrossRef] - Aytek, A. Co-active neurofuzzy inference system for evapotranspiration modeling. Soft Comput.
**2009**, 13, 691–700. [Google Scholar] [CrossRef] - Stefánsson, A.; Končar, N.; Jones, A.J. A note on the gamma test. Neural Comput. Appl.
**1997**, 5, 131–133. [Google Scholar] [CrossRef] - Moghaddamnia, A.; Ghafari Gousheh, M.; Piri, J.; Amin, S.; Han, D. Evaporation estimation using artificial neural networks and adaptive neuro-fuzzy inference system techniques. Adv. Water Resour.
**2009**, 32, 88–97. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A. Comparison of soft-computing and statistical techniques in simulating daily river flow: A case study in India. J. Soil Water Conserv.
**2018**, 17, 192–199. [Google Scholar] [CrossRef] - Ashrafzadeh, A.; Malik, A.; Jothiprakash, V.; Ghorbani, M.A.; Biazar, S.M. Estimation of daily pan evaporation using neural networks and meta-heuristic approaches. ISH J. Hydraul. Eng.
**2018**, 24, 1–9. [Google Scholar] [CrossRef] - Kakaei Lafdani, E.; Moghaddam Nia, A.; Ahmadi, A. Daily suspended sediment load prediction using artificial neural networks and support vector machines. J. Hydrol.
**2013**, 478, 50–62. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A.; Kisi, O.; Shiri, J. Evaluating the performance of four different heuristic approaches with Gamma test for daily suspended sediment concentration modeling. Environ. Sci. Pollut. Res.
**2019**, 26, 22670–22687. [Google Scholar] [CrossRef] - Remesan, R.; Shamim, M.A.; Han, D.; Mathew, J. Runoff prediction using an integrated hybrid modelling scheme. J. Hydrol.
**2009**, 372, 48–60. [Google Scholar] [CrossRef] - Goyal, M.K. Modeling of Sediment Yield Prediction Using M5 Model Tree Algorithm and Wavelet Regression. Water Resour. Manag.
**2014**, 28, 1991–2003. [Google Scholar] [CrossRef] - Rashidi, S.; Vafakhah, M.; Lafdani, E.K.; Javadi, M.R. Evaluating the support vector machine for suspended sediment load forecasting based on gamma test. Arab. J. Geosci.
**2016**, 9, 583. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A.; Piri, J. Daily suspended sediment concentration simulation using hydrological data of Pranhita River Basin, India. Comput. Electron. Agric.
**2017**, 138, 20–28. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A. Pan Evaporation Simulation Based on Daily Meteorological Data Using Soft Computing Techniques and Multiple Linear Regression. Water Resour. Manag.
**2015**, 29, 1859–1872. [Google Scholar] [CrossRef] - Piri, J.; Amin, S.; Moghaddamnia, A.; Keshavarz, A.; Han, D.; Remesan, R. Daily pan evaporation modeling in a hot and dry climate. J. Hydrol. Eng.
**2009**, 14, 803–811. [Google Scholar] [CrossRef] - Singh, A.; Malik, A.; Kumar, A.; Kisi, O. Rainfall-runoff modeling in hilly watershed using heuristic approaches with gamma test. Arab. J. Geosci.
**2018**, 11, 261. [Google Scholar] [CrossRef] - Jang, J.-S.R.; Sun, C.-T.; Mizutani, E. Neuro-Fuzzy and Soft Computing A Computational Approach to Learning and Machine Intelligence; Prentice-Hall: Upper Saddle River, NJ, USA, 1997. [Google Scholar]
- Haykin, S. Neural Networks—A Comprehensive Foundation, 2nd ed.; Prentice-Hall: Upper Saddle River, NJ, USA, 1999; pp. 26–32. [Google Scholar]
- Yaseen, Z.M.; El-Shafie, A.; Afan, H.A.; Hameed, M.; Mohtar, W.H.M.W.; Hussain, A. RBFNN versus FFNN for daily river flow forecasting at Johor River, Malaysia. Neural Comput. Appl.
**2015**, 27, 1533–1542. [Google Scholar] [CrossRef] - Ghorbani, M.A.; Asadi, H.; Makarynskyy, O.; Makarynska, D.; Yaseen, Z.M. Augmented chaos-multiple linear regression approach for prediction of wave parameters. Eng. Sci. Technol. Int. J.
**2017**, 20, 1180–1191. [Google Scholar] [CrossRef] - Penman, H.L. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. Lond. A
**1948**, 193, 120–145. [Google Scholar] - Penman, H.L. Evaporation: An introductory survey. J. Agric. Sci.
**1956**, 9, 9–29. [Google Scholar] - Allen, R.G.; Pereira, L.S.; Raes, D.; Smith, M. Crop evapotranspiration: Guidelines for computing crop requirements. FAO Irrig. Drain. Pap.
**1998**, 56, 300. [Google Scholar] - Taylor, K.E. Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res. Atmos.
**2001**, 106, 7183–7192. [Google Scholar] [CrossRef] - Shiri, J. Improving the performance of the mass transfer-based reference evapotranspiration estimation approaches through a coupled wavelet-random forest methodology. J. Hydrol.
**2018**, 561, 737–750. [Google Scholar] [CrossRef] - Tao, H.; Diop, L.; Bodian, A.; Djaman, K.; Ndiaye, P.M.; Yaseen, Z.M. Reference evapotranspiration prediction using hybridized fuzzy model with firefly algorithm: Regional case study in Burkina Faso. Agric. Water Manag.
**2018**, 208, 140–151. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A.; Ghorbani, M.A.; Kashani, M.H.; Kisi, O.; Kim, S. The viability of co-active fuzzy inference system model for monthly reference evapotranspiration estimation: Case study of Uttarakhand State. Hydrol. Res.
**2019**, 50, 1623–1644. [Google Scholar] [CrossRef] [Green Version] - Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Khosravi, K.; Mao, L.; Kisi, O.; Yaseen, Z.M.; Shahid, S. Quantifying Hourly Suspended Sediment Load Using Data Mining Models: Case Study of a Glacierized Andean Catchment in Chile. J. Hydrol.
**2018**, 65, 624–637. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A.; Singh, R.P. Application of Heuristic Approaches for Prediction of Hydrological Drought Using Multi-scalar Streamflow Drought Index. Water Resour. Manag.
**2019**, 33, 3985–4006. [Google Scholar] [CrossRef] - Willmott, C.J. On the validation of models. Phys. Geogr.
**1981**, 2, 184–194. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A. Meteorological drought prediction using heuristic approaches based on effective drought index: A case study in Uttarakhand. Arab. J. Geosci.
**2020**, 13, 276. [Google Scholar] [CrossRef] - Yaseen, Z.M.; Awadh, S.M.; Sharafati, A.; Shahid, S. Complementary data-intelligence model for river flow simulation. J. Hydrol.
**2018**, 567, 180–190. [Google Scholar] [CrossRef] - Keskin, M.E.; Terzi, Ö.; Taylan, D. Estimating daily pan evaporation using adaptive neural-based fuzzy inference system. Theor. Appl. Climatol.
**2009**, 98, 79–87. [Google Scholar] [CrossRef] - Sanikhani, H.; Kisi, O.; Nikpour, M.R.; Dinpashoh, Y. Estimation of Daily Pan Evaporation Using Two Different Adaptive Neuro-Fuzzy Computing Techniques. Water Resour. Manag.
**2012**, 26, 4347–4365. [Google Scholar] [CrossRef] - Keskin, M.E.; Terzi, Ö. Artificial Neural Network Models of Daily Pan Evaporation. J. Hydrol. Eng.
**2006**, 11, 65–70. [Google Scholar] [CrossRef] - Shirsath, P.B.; Singh, A.K. A Comparative Study of Daily Pan Evaporation Estimation Using ANN, Regression and Climate Based Models. Water Resour. Manag.
**2010**, 24, 1571–1581. [Google Scholar] [CrossRef] - Goyal, M.K.; Bharti, B.; Quilty, J.; Adamowski, J.; Pandey, A. Modeling of daily pan evaporation in sub tropical climates using ANN, LS-SVR, Fuzzy Logic, and ANFIS. Expert Syst. Appl.
**2014**, 41, 5267–5276. [Google Scholar] [CrossRef] - Malik, A.; Kumar, A.; Kim, S.; Kashani, M.H.; Karimi, V.; Sharafati, A.; Ghorbani, M.A.; Al-Ansari, N.; Salih, S.Q.; Yaseen, Z.M. Modeling monthly pan evaporation process over the Indian central Himalayas: Application of multiple learning artificial intelligence model. Eng. Appl. Comput. Fluid Mech.
**2020**, 14, 323–338. [Google Scholar] [CrossRef] [Green Version] - Mirjalili, S.; Gandomi, A.H.; Mirjalili, S.Z.; Saremi, S.; Faris, H.; Mirjalili, S.M. Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Adv. Eng. Softw.
**2017**, 114, 163–191. [Google Scholar] [CrossRef]

**Figure 1.**The coordinates of the investigated meteorological stations in Uttarakhand State and Uttar Pradesh State, India.

**Figure 7.**Comparison plots of observed and estimated monthly pan-evaporation values yielded by the CANFIS-1, MLPNN-1, MLR-1, and PM models in (

**a**) scenario-1, (

**b**) scenario-2, (

**c**) scenario-3, and (

**d**) scenario-4 during the testing period at Pantnagar station.

**Figure 8.**Relative error (RE) percentage distribution of the CANFIS-1, MLPNN-1, MLR-1, and PM models for (

**a**) scenario-1, (

**b**) scenario-2, (

**c**) scenario-3, and (

**d**) scenario-4 during the testing period at Pantnagar station.

**Figure 9.**Taylor diagram (TD) of observed and estimated monthly evaporation obtained by the CANFIS-1, MLPNN-1, MLR-1, and PM models in (

**a**) scenario-1, (

**b**) scenario-2, (

**c**) scenario-3, and (

**d**) scenario-4 during the testing period at Pantnagar station.

**Figure 10.**Comparison plots of observed and estimated monthly pan-evaporation values yielded by the CANFIS-1, MLPNN-1, and MLR-1 models in (

**a**) scenario-1, (

**b**) scenario-2, (

**c**) scenario-3, and (

**d**) scenario-4 during the testing period at Nagina station.

**Figure 11.**RE percentage distribution of the CANFIS-1, MLPNN-1, MLR-1, and PM models in (

**a**) scenario-1, (

**b**) scenario-2, (

**c**) scenario-3, and (

**d**) scenario-4 during the testing period at Nagina station.

**Figure 12.**Taylor plot of observed and estimated monthly evaporation obtained by the CANFIS-1, MLPNN-1, MLR-1, and PM models in (

**a**) scenario-1, (

**b**) scenario-2, (

**c**) scenario-3, and (

**d**) scenario-4 during the testing period at Nagina station.

Station/Climatic Variable | Statistical Parameters | ||||||
---|---|---|---|---|---|---|---|

Minimum | Maximum | Mean | Std | Skewness | Kurtosis | ||

Pantnagar | T_{min} (^{o}C) | 5.80 | 26.30 | 17.27 | 7.07 | −0.15 | −1.55 |

T_{max} (^{o}C) | 16.50 | 40.10 | 29.94 | 5.88 | −0.48 | −0.54 | |

RH-1 (%) | 59.00 | 96.00 | 84.30 | 9.72 | −1.23 | 0.21 | |

RH-2 (%) | 19.00 | 77.00 | 51.38 | 15.04 | −0.16 | −0.99 | |

WS (km/h) | 2.10 | 9.90 | 5.09 | 1.90 | 0.37 | −0.43 | |

SSH (h) | 2.60 | 9.90 | 6.58 | 1.92 | −0.21 | −0.90 | |

EP_{m} (mm) | 1.00 | 11.40 | 4.43 | 2.65 | 0.91 | −0.16 | |

Nagina | T_{min} (^{o}C) | 5.40 | 26.50 | 16.84 | 7.40 | −0.14 | −1.55 |

T_{max} (^{o}C) | 16.10 | 40.10 | 29.14 | 5.94 | −0.47 | −0.54 | |

RH-1 (%) | 20.20 | 99.00 | 88.90 | 12.34 | −2.44 | 9.08 | |

RH-2 (%) | 23.00 | 81.00 | 55.03 | 14.63 | −0.04 | −0.89 | |

WS (km/h) | 1.00 | 7.00 | 3.77 | 1.52 | 0.21 | −0.92 | |

SSH (h) | 2.80 | 10.10 | 6.98 | 1.86 | −0.28 | −0.79 | |

EP_{m} (mm) | 0.90 | 8.40 | 3.71 | 2.03 | 0.52 | −0.76 |

Station/Climatic Variable | T_{min} | T_{max} | RH-1 | RH-2 | WS | SSH | EP_{m} | |
---|---|---|---|---|---|---|---|---|

Pantnagar | T_{min} | 1.00 | ||||||

T_{max} | 0.84 * | 1.00 | ||||||

RH-1 | −0.47 * | −0.79 * | 1.00 | |||||

RH-2 | 0.21 * | −0.35 * | 0.65 * | 1.00 | ||||

WS | 0.57 * | 0.62 * | −0.75 * | −0.23 * | 1.00 | |||

SSH | 0.12 | 0.58 * | −0.64 * | −0.80 * | 0.28 * | 1.00 | ||

EP_{m} | 0.63 * | 0.88 * | −0.95 * | −0.52 * | 0.82 * | 0.59 * | 1.00 | |

Nagina | T_{min} | 1.00 | ||||||

T_{max} | 0.85 * | 1.00 | ||||||

RH-1 | −0.48 * | −0.70 * | 1.00 | |||||

RH-2 | 0.23 * | −0.26 * | 0.55 * | 1.00 | ||||

WS | 0.50 * | 0.54 * | −0.61 * | −0.18 | 1.00 | |||

SSH | 0.21 * | 0.61 * | −0.60 * | −0.74 * | 0.38 * | 1.00 | ||

EP_{m} | 0.73 * | 0.88 * | −0.82 * | −0.37 * | 0.77 * | 0.64 * | 1.00 |

**Table 3.**Contribution of different climatic variables to the composition of the seven models at the study stations.

Climatic Variables | CANFIS/MLPNN/MLR | ||||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | |

T_{min} | √ | ||||||

T_{max} | √ | √ | √ | √ | √ | √ | √ |

RH-1 | √ | ||||||

RH-2 | √ | √ | √ | ||||

WS | √ | √ | √ | √ | |||

SSH | √ | √ | √ | √ |

Various Input Combinations | GT Statistic | |||||
---|---|---|---|---|---|---|

Γ | A | SE | Vratio | Mask | ||

Pantnagar | T_{min}, T_{max}, RH-1, RH-2, WS, SSH | 0.0017 | 0.0665 | 0.0013 | 0.0070 | 111111 |

T_{max}, WS, SSH | 0.0109 | 0.0905 | 0.0023 | 0.0436 | 010011 | |

T_{max}, RH-2, WS | 0.0050 | 0.1375 | 0.0031 | 0.0199 | 010110 | |

T_{max}, RH-2, SSH | 0.0105 | 0.1548 | 0.0071 | 0.0419 | 010101 | |

T_{max}, WS | 0.0119 | 0.1934 | 0.0031 | 0.0476 | 010010 | |

T_{max}, SSH | 0.0118 | 0.3441 | 0.0042 | 0.0474 | 010001 | |

T_{max} | 0.0156 | 0.3202 | 0.0024 | 0.0623 | 010000 | |

Nagina | T_{min}, T_{max}, RH-1, RH-2, WS, SSH | 0.0112 | 0.0395 | 0.0024 | 0.0448 | 111111 |

T_{max}, WS, SSH | 0.0179 | 0.0704 | 0.0048 | 0.0718 | 010011 | |

T_{max}, RH-2, WS | 0.0163 | 0.0821 | 0.0047 | 0.0652 | 010110 | |

T_{max}, RH-2, SSH | 0.0189 | 0.1528 | 0.0058 | 0.0756 | 010101 | |

T_{max}, WS | 0.0163 | 0.2786 | 0.0047 | 0.0653 | 010010 | |

T_{max}, SSH | 0.0247 | 0.2652 | 0.0071 | 0.0989 | 010001 | |

T_{max} | 0.0370 | 0.3576 | 0.0055 | 0.1479 | 010000 |

**Table 5.**Normalized root mean square error (NRMSE), Nash–Sutcliffe efficiency (NSE), Pearson correlation coefficient (PCC), and Willmott index (WI) values of CANFIS, MLPNN, multiple linear regression (MLR), and Penman model (PM) models during the testing period at Pantnagar station under four different scenarios.

Model | Structure | Testing Period | ||||
---|---|---|---|---|---|---|

NRMSE (mm/month) | NSE | PCC | WI | |||

Scenario-1 | CANFIS-1 | Bell-3 | 0.1364 | 0.9439 | 0.9790 | 0.9860 |

MLPNN-1 | 6-9-1 | 0.1404 | 0.9406 | 0.9751 | 0.9857 | |

MLR-1 | - | 0.1402 | 0.9408 | 0.9768 | 0.9851 | |

PM | - | 0.9585 | −1.7672 | 0.8047 | 0.5590 | |

Scenario-2 | CANFIS-1 | Gauss-2 | 0.0904 | 0.9736 | 0.9872 | 0.9934 |

MLPNN-1 | 6-11-1 | 0.0920 | 0.9726 | 0.9867 | 0.9932 | |

MLR-1 | - | 0.1110 | 0.9602 | 0.9818 | 0.9903 | |

PM | - | 0.9871 | −2.1474 | 0.8224 | 0.5486 | |

Scenario-3 | CANFIS-1 | Gauss-3 | 0.0947 | 0.9703 | 0.9877 | 0.9927 |

MLPNN-1 | 6-10-1 | 0.0993 | 0.9674 | 0.9874 | 0.9918 | |

MLR-1 | - | 0.1085 | 0.9611 | 0.9831 | 0.9905 | |

PM | - | 0.9994 | −2.3051 | 0.8511 | 0.5416 | |

Scenario-4 | CANFIS-1 | Gauss-2 | 0.0898 | 0.9799 | 0.9922 | 0.9949 |

MLPNN-1 | 6-9-1 | 0.1021 | 0.9740 | 0.9877 | 0.9934 | |

MLR-1 | - | 0.1056 | 0.9721 | 0.9885 | 0.9927 | |

PM | - | 0.9168 | −1.1016 | 0.8103 | 0.5957 |

**Table 6.**NRMSE, NSE, PCC, and WI values of the CANFIS, MLPNN, and MLR models during the testing period at Nagina station under four different scenarios.

Model | Structure | Testing Period | ||||
---|---|---|---|---|---|---|

NRMSE (mm/month) | NSE | PCC | WI | |||

Scenario-1 | CANFIS-1 | Gauss-3 | 0.1543 | 0.9150 | 0.9643 | 0.9794 |

MLPNN-1 | 6-10-1 | 0.1813 | 0.8827 | 0.9592 | 0.9723 | |

MLR-1 | - | 0.1866 | 0.8758 | 0.9437 | 0.9698 | |

PM | 1.3464 | −5.4677 | 0.8507 | 0.4585 | ||

Scenario-2 | CANFIS-1 | Gauss-2 | 0.1719 | 0.8962 | 0.9649 | 0.9761 |

MLPNN-1 | 6-10-1 | 0.1899 | 0.8734 | 0.9486 | 0.9699 | |

MLR-1 | - | 0.2299 | 0.8144 | 0.9346 | 0.9579 | |

PM | 1.3989 | −5.8728 | 0.8470 | 0.4493 | ||

Scenario-3 | CANFIS-1 | Gauss-2 | 0.2067 | 0.8382 | 0.9473 | 0.9632 |

MLPNN-1 | 6-10-1 | 0.2281 | 0.8031 | 0.9247 | 0.9552 | |

MLR-1 | - | 0.2939 | 0.6729 | 0.9049 | 0.9313 | |

PM | 1.3907 | −6.3213 | 0.8158 | 0.4291 | ||

Scenario-4 | CANFIS-1 | Gauss-2 | 0.1356 | 0.9453 | 0.9762 | 0.9853 |

MLPNN-1 | 6-10-1 | 0.1477 | 0.9351 | 0.9746 | 0.9820 | |

MLR-1 | - | 0.1621 | 0.9219 | 0.9666 | 0.9789 | |

PM | 1.1789 | −3.1294 | 0.8961 | 0.5362 |

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**MDPI and ACS Style**

Malik, A.; Rai, P.; Heddam, S.; Kisi, O.; Sharafati, A.; Salih, S.Q.; Al-Ansari, N.; Yaseen, Z.M.
Pan Evaporation Estimation in Uttarakhand and Uttar Pradesh States, India: Validity of an Integrative Data Intelligence Model. *Atmosphere* **2020**, *11*, 553.
https://doi.org/10.3390/atmos11060553

**AMA Style**

Malik A, Rai P, Heddam S, Kisi O, Sharafati A, Salih SQ, Al-Ansari N, Yaseen ZM.
Pan Evaporation Estimation in Uttarakhand and Uttar Pradesh States, India: Validity of an Integrative Data Intelligence Model. *Atmosphere*. 2020; 11(6):553.
https://doi.org/10.3390/atmos11060553

**Chicago/Turabian Style**

Malik, Anurag, Priya Rai, Salim Heddam, Ozgur Kisi, Ahmad Sharafati, Sinan Q. Salih, Nadhir Al-Ansari, and Zaher Mundher Yaseen.
2020. "Pan Evaporation Estimation in Uttarakhand and Uttar Pradesh States, India: Validity of an Integrative Data Intelligence Model" *Atmosphere* 11, no. 6: 553.
https://doi.org/10.3390/atmos11060553