# Forecasting Long-Series Daily Reference Evapotranspiration Based on Best Subset Regression and Machine Learning in Egypt

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

## Abstract

**:**

_{o}), a crucial step in the hydrologic cycle, is essential for system design and management, including the balancing, planning, and scheduling of agricultural water supply and water resources. When climates vary from arid to semi-arid, and there are problems with a lack of meteorological data and a lack of future information on ET

_{o}, as is the case in Egypt, it is more important to estimate ET

_{o}precisely. To address this, the current study aimed to model ET

_{o}for Egypt’s most important agricultural governorates (Al Buhayrah, Alexandria, Ismailiyah, and Minufiyah) using four machine learning (ML) algorithms: linear regression (LR), random subspace (RSS), additive regression (AR), and reduced error pruning tree (REPTree). The Climate Forecast System Reanalysis (CFSR) of the National Centers for Environmental Prediction (NCEP) was used to gather daily climate data variables from 1979 to 2014. The datasets were split into two sections: the training phase, i.e., 1979–2006, and the testing phase, i.e., 2007–2014. Maximum temperature (T

_{max}), minimum temperature (T

_{min}), and solar radiation (SR) were found to be the three input variables that had the most influence on the outcome of subset regression and sensitivity analysis. A comparative analysis of ML models revealed that REPTree outperformed competitors by achieving the best values for various performance matrices during the training and testing phases. The study’s novelty lies in the use of REPTree to estimate and predict ET

_{o}, as this algorithm has not been commonly used for this purpose. Given the sparse attempts to use this model for such research, the remarkable accuracy of the REPTree model in predicting ET

_{o}highlighted the rarity of this study. In order to combat the effects of aridity through better water resource management, the study also cautions Egypt’s authorities to concentrate their policymaking on climate adaptation.

## 1. Introduction

_{o}) using various meteorological data. The World Meteorological Organization (WMO) and the International Commission on Irrigation and Drainage (ICID) introduced the model as a reliable method for estimating ET

_{o}, and it was also approved as a suitable alternative to lysimeter data by the ICID [1]. One of the most significant issues in hydrology and agriculture is ET

_{o}modeling, which allows for the prediction of future values of this variable. In fact, the forecast of this variable tells us how much water the plant will need in the future. This method is quite successful and is used in the region to schedule crop irrigation. Increased demand for limited water resources, climate change, and certain agricultural commodities have all pointed to the need for better ways to make efficient use of the water resources at our fingertips as well as distribute them at the right time and through the right channel to produce premium food [2]. Certain management actions, crop characteristics, weather conditions, land type, and field operations are all key variables that influence the ET

_{o}process [3].

_{o}is critical in determining agricultural irrigation requirements on a regional and global scale, preparing water budgets, and assessing the impact of various climatic changes [4]. Significant problems arise when ET

_{o}modeling is tried to estimate accurately using available meteorological data at different gauging stations [5]. A precise measurement of the ET

_{o}serves a variety of purposes including not only the research of climate change and the evaluation of water resources but also the efficient monitoring and forecasting of droughts as well as the correct use and development of water resources [6]. Machine learning (ML) models based on robust algorithms are now being used to map nonlinear processes employing input and output (target) variables. Raza et al. [7] examined research publications on ET

_{o}estimation published in the last eight years (2012–2020) for accuracy, structure, and usefulness. The presented studies’ main goal is to establish an alternative ML model to the FAO-PM56 since it requires a substantial quantity of climatic data as input, which is not accessible at many stations, especially in developing countries. As a result, designing ML models employing all of the usable data comparable to FAO-PM56 is not worthwhile. Moreover, a limited number of studies have investigated the development of a generalized ET

_{o}model for accurate ET

_{o}estimation in all stations within a region, such as Raza et al. [8]. This is particularly important in developing countries since climatic data from most stations are either missing or unavailable owing to technical challenges and a lack of technology. As a result, developing an ET

_{o}model with fewer climatic inputs (such as temperature data) should be enough.

_{o}modeling for this purpose. Utilizing alternative ML models, it may be possible to incorporate such inputs (simultaneously) into the daily ET

_{o}estimation.

_{o}in the study area of Egypt using daily time-scale data. As a result, this study aims to (i) investigate the historical distributions of ET

_{o}from 1979 to 2014, (ii) evaluate the performance and accuracy of ML algorithms in daily ET

_{o}estimation, and (iii) select the optimal ET

_{o}ML model based on statistical metrics results. These data are essential for understanding the influence of climate change on ET

_{o}in the study region.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The Alexandria governorate is located in the northern part of the country, directly on the Mediterranean Sea, making it one of the most important harbors in Egypt. The Alexandria governorate is located about 188.6 km northwest of Cairo and covers an area of 2818 km

^{2}. The Ismailiyah governorate is one of the Canal Zone governorates of Egypt. Located in the northeastern part of the country, it covers an area of 5066 km

^{2}and is about 122.5 km away from Cairo. The Minufiyah governorate is located in the Nile Delta’s northern part, north of Cairo. It covers about 2543 km

^{2}. The population of Al Buhayrah, Alexandria, Ismailiyah, and Minufiyah governorates are estimated by the Central Agency for Public Mobilization and Statistics in Egypt (CAPMAS) [32] to be 6,723,269; 5,469,480; 1,419,631; and 4,640,003 people per capita on 1 January 2022.

#### 2.2. Datasets Description

## 3. Methodology

_{o}estimation methodology in the study (Figure 3) is based on the following: (i) collection of daily databases; (ii) data preparation and selection of the best variables; (iii) application of four forecasting machine learning models: linear regression (LR), additive regression (AR), random subspace (RSS), and reduced error pruning tree (REPTree); (iv) training and testing of developed models; (v) evaluation of the results obtained based on RMSE, R

^{2}, MAE, and RRSE; (vi) selection of the best developed model for ET

_{o}prediction; and finally, (vii) the end of the process. The four forecasting machine learning models used in this study are discussed below:

#### 3.1. Machine Learning (ML) Models

#### 3.1.1. Random Subspace (RSS)

_{i}(i = 1, …, n) in the training sample set X = [X1; …; Xn] is defined as a p-dimensional vector Xi = (x

_{i1}, x

_{i2}, …, x

_{ip}) and defined by p features. Then, r < p features are randomly selected from the p-dimensional dataset X. Consequently, the modified training set X

_{˜b}= X

^{˜b}

_{1}, X

^{˜b}

_{2}…, X

^{˜b}

_{n}, is composed of r-dimensional training incidences. After this step, classifiers are built into the random subspaces X

^{˜b}and aggregated by utilizing a majority voting. Therefore, the RSS is implemented in the following way [35]:

- Repeat for b = 1, 2, …, B;
- Choose an r-dimensional random subspace Xb˜;
- from the original p-dimensional feature space X;
- Build a classifier C
^{b}(x) (with a decision boundary C^{b}(x) = 0) in Xb˜; - Aggregate classifiers C
^{b}(x), b = 1, 2, …, B, by utilizing majority voting for the final decision.

#### 3.1.2. Additive Regression (AR)

#### 3.1.3. Reduced Error Pruning Tree (REPTree)

#### 3.1.4. Linear Regression (LR)

#### 3.2. Performance Metrics

_{i}is the observed values, and Y

_{i}is the estimated values; $\stackrel{-}{X}$ is the mean of observed values in X variables; $\stackrel{-}{Y}$ is the mean of estimated values in Y variables.

## 4. Results

#### 4.1. Analysis of Best Subset Regression for Determining Best Input Combinations

^{2}, adjusted R

^{2}, Mallows’ Cp, Akaike’s AIC, Schwarz’s SBC, and Amemiya’s PC, whose results are shown in Table 2. It can be inferred that four input variables, i.e., T

_{max}, T

_{min}, RH, and SR (displayed in bold), were identified as the best input combination given they had the lowest values of Mallows’ Cp (4.195) and Amemiya’s PC (0.033) and the highest value of R

^{2}(0.967) and adjusted R

^{2}(0.967) amid all input combinations.

_{o}, for example, 0.907 with T

_{max}, 0.806 with T

_{mean}, and 0.923 with SR. To take advantage of long-term time-series datasets for ET

_{o}, the present study categorized the complete dataset into two sets, of which the first segment comprised 75% of the dataset for training purposes (for the training period 1979–2006), while the second segment comprised 25% for validation/testing purposes (for the testing period 2007–2014) of the models.

#### 4.2. Sensitivity Analysis

_{o}with greater accuracy. Findings from regression analysis on all input variables are summarized in Table 3. It can be inferred in terms of absolute standard coefficients that the variables such as T

_{max}(0.649), T

_{min}(−0.205), RH (−0.005), and SR (0.525) are the most influential input variables. These standardized coefficients of input variables for sensitivity analysis for ET

_{o}are further demonstrated in Figure 5.

#### 4.3. Comparison of ML Algorithms for ET_{o} Estimation

_{o}was estimated by implementing four ML algorithms, i.e., linear regression (LR), random subspace (RSS), additive regression (AR), and reduced error pruning tree (REPTree). To evaluate the performances of the applied algorithm, five performance indicators were employed, i.e., mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), root relative squared error (RRSE), and correlation coefficient (R). The best performance of the models was identified based on the higher value for r (close to one) and lower values for MAE, RMSE, RAE, and RRSE (close to zero). Table 3 shows the general trend for these performance indicators corresponding to each model. Following the aforementioned performance quantification criteria, the model REPTree was observed as the best model during both the training and testing phase, followed by the LR model (Table 4). This implied that the REPTree model has the potential to estimate the ET

_{o}with greater accuracy as compared with other algorithms. In the training phase, the model REPTree yielded the highest value for r (0.99) and lowest values for MAE (0.21), RMSE (0.28), RAE (3.45%), and RRSE (4.01%); during the testing phase also, the model REPTree yielded the highest value for r (0.99) and lowest values for MAE (0.28), RMSE (0.37), RAE (4.13%), and RRSE (4.72%), as shown in Table 4. The changes in the values for these performance indicators between the training and testing phases were found insignificant; thus, the model was considered suitable for the present study site. Following REPTree, the model LR was the second-best performing model, as in the training phase, the model LR yielded a higher value for r (0.98) and lower values for MAE (1.00), RMSE (1.30), RAE (16.66%), and RRSE (18.47%); during the testing phase also, the model LR yielded a higher value for r (0.98) and lower values for MAE (1.10), RMSE (1.37), RAE (16.28%), and RRSE (17.70%).

_{o}data and scattered plots showing the whole testing dataset of observed vs. estimated ET

_{o}values were developed for the LR, RSS, AR, and REPTree models throughout the testing phase. The regression line, as shown in the scatter plot, was used for the assessment of model performance. The R

^{2}value was assessed to be 0.9867 for the LR model, 0.9838 for the RSS model, 0.9644 for the AR model, and 0.9989 for the REPTree model. All the models (except for REPTree) underestimated the ET

_{o}prediction, as the models were observed located below the best-fit 1:1 line. Nevertheless, the REPtree model was observed located nearest to the best-fit 1:1 line. In coherence to the inference made in the previous section, the model REPTree here, too, was implied as the best model for estimating the daily ET

_{o}for the present study site. For this, an additional sample time-series and scatter plot is shown in Figure 6e, indicating a higher correlation (similar to the entire time-series and scatter plot of REPTree) for the most recent study year.

## 5. Discussion

_{o}variable. Considering the findings of this study, it can be broadly inferred that all the four ML algorithm-based models, i.e., LR, RSS, AR, and REPTree, developed in this study more or less demonstrated their predictive capabilities in estimating ET

_{o}. Through a comparative analysis, this study suggested REPTree as the most suitable model for advancing further investigation in the study area. The model REPTree was observed to outclass other models based on satisfying all criteria for performance indicators, as the indicators obtained the most-appropriate values (lowest for MAE, RMSE, RAE, and RRSE and highest for r). These results were further supported by the findings from time-series and scattered plots (refer to Figure 6) as well as from radar chart (Figure 7) and Taylor diagram (Figure 8) developed for comparing the four ML algorithms. They comprehensively indicated REPTree as the best model for the prediction of ET

_{o}, followed by LR, while the model AR was comparatively found to be the worst-performing model for the present study site.

_{o}. In addition, the present study determined REPTree as the most suitable model among the models developed to estimate the same. Both these inferences are against the ongoing trend, where researchers have primarily focused on estimating ET

_{o}using other machine learning algorithms. Many studies in recent times have been conducted to estimate hydrologic variables such as pan evaporation, evapotranspiration, etc., from across the globe using ML algorithms. Sattari et al. [52] successfully evaluated the deep learning-based gated recurrent units (GRUs) and tree-based models for estimating ET

_{o}as a case study in Turkey. They found GRUs as the best- and REPTree as the worst-performing model. Kushwaha et al. [53] examined the performance of the four meta-heuristic algorithms, i.e., support vector machine (SVM), random tree (RT), REPTree, and RSS, for simulating daily pan evaporation at two different locations in north India and observed the greater suitability of the model SVM for prediction compared to the others. Nhu et al. [54] predicted the daily water level of Zrebar Lake in Iran using M5P, random forest (RF), random tree (RT), and REPTree algorithms, wherein their results indicated a good prediction capability for all the developed models other than REPTree. Furthermore, if the literature focusing ET

_{o}estimation using ML algorithms is only considered, no recent studies are found to employ the model REPTree. For example, Salam and Islam [55] evaluated the potential of RT, bagging, and RS ensemble learning algorithms for ET

_{o}prediction in Bangladesh. In that, their study found the model RT to outperform other models while estimating daily ET

_{o}. Tikhamarine et al. [56] explored the potential of support vector regression (SVR) integrated with grey wolf optimizer (SVR-GWO) for ET

_{o}estimation in the north of Algeria and concluded its suitability in the study stations. Kisi et al. [57] developed a radial-basis M5 model tree (RM5Tree) for ET

_{o}prediction in Turkey and evaluated it better than the traditional M5 model tree. Bai et al. [58] evaluated four ensemble ET models (EEMs) that use different ML classifiers such as K-nearest neighbors, RF, SVM, and multi-layer perception neural network (MLP). Their study found that ML-based EEMs outperformed individual ET and conventional EEMs. Granata [20] assessed the M5P tree, bagging, RF, and SVR for how precise an ET

_{o}prediction could be obtained in central Florida by developing models in a varying combination of influencing variables. Mehdizadeh et al. [9] successfully evaluated gene expression programming (GEP), SVM, and multivariate adaptive regression splines (MARS) in estimating ET

_{o}in Iran. Their results shown that the MARS had the best performance in the weather-data-based scenarios. Ferreira et al. [10] estimated daily ET

_{o}in Brazil using ANN and SVM. They found that the ANN and SVM models outperformed the empirical equations studied. Fan et al. [19] successfully evaluated random forest (RF), M5Tree, gradient boosting decision tree (GBDT), and extreme gradient boosting (XGBoost) for estimating daily ET

_{o}in China. According to the results, the ELM and SVM models achieved the best combination of prediction accuracy and stability. The XGBoost and GBDT models performed similarly to the SVM and ELM models in terms of accuracy and stability but with significantly lower computation time. Bellido-Jiménez et al. [59] successfully evaluated MLP, generalized regression neural network (GRNN), extreme learning machine (ELM), SVM, RF, and XGBoost for estimating daily ET

_{o}in Spain. Their findings revealed that GRNN and ELM had the lowest computation time, while MLP and ELM were generally the models with the better performances. In general, all the aforementioned studies jointly concluded through their various model assessments that, other than REPTree, the entire presently developed model in this study was observed to be one of the suitable models among many machine-learning-algorithm-based models for estimating hydrologic variables, especially the ET

_{o}.

_{o}investigated in the present study. Hence, knowledge of ML algorithms becomes paramount, especially when applying certain algorithms; for example, REPTree is limited while estimating ET

_{o}. Such a study allows estimating the future magnitudes, thereby informing the concerned authorities and administrators to orient their policymaking towards more specific climate-resilient pathways.

## 6. Conclusions

_{o}) for four sites in Egypt (Al Buhayrah, Alexandria, Ismailiyah, and Minufiyah governorates). In order to achieve this, daily climate data variables (including minimum and maximum temperatures, humidity, wind speed, vapor pressure deficit, and solar radiation) for the studied regions over 36 years from 1979 to 2014 were collected from the National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR). In addition, the best subset regression analysis was used to determine the best input combinations of meteorological parameters for calculating the ET

_{o}. Sensitivity analysis was carried out and included all input variables in determining the most influential input variables to predict the ET

_{o}with greater accuracy. The following findings were obtained:

- -
- The results showed that the best input combination for the ET
_{o}model was determined as four input combinations (T_{max}/T_{min}/RH/SR) with high R^{2}(0.967) and high Adj-R^{2}(0.967) and MSE of 1.727; - -
- The most sensitive input variables to predict the ET
_{o}with greater accuracy were T_{max}, T_{min}, and SR; - -
- The REPTree model generated the best results with the highest value for r (0.99) and the lowest values for MAE (0.21), RMSE (0.28), RAE (3.45%), and RRSE (4.01%) during the training phase; it also generated the highest value for r (0.99) and the lowest values for MAE (0.28), RMSE (0.37), RAE (4.13%), and RRSE during the testing phase (4.72%);
- -
- The AR model generated the worst results with R = 0.9595, MAE = 1.5914, RMSE = 1.9876, RAE = 26.25%, and RRSE = 28.22% during the training phase.

_{o}. The study’s novelty lies in using REPTree to estimate and predict ET

_{o}, as this algorithm has not been commonly used for this purpose. This finding is important given the urgent need to better understand hydrological variables in light of climate change and land-use transformations. The study underscores the importance of machine learning algorithms in predicting ET

_{o}and their potential for estimating future magnitudes to guide climate-resilient policymaking. The study’s results have broader implications beyond ET

_{o}prediction, as machine learning algorithms have been increasingly employed in hydrologic research. The study contributes to the growing literature on using machine learning algorithms to estimate hydrologic variables such as evapotranspiration, pan evaporation, and water levels. The study’s findings suggest that researchers should consider using REPTree rather than other commonly used algorithms for ET

_{o}prediction. In summary, this study highlights the significance of using REPTree in hydrologic research and its potential for predicting ET

_{o}. The study’s results underscore the importance of machine learning algorithms in guiding climate-resilient policymaking in the face of ongoing climate change and land-use transformations. This research could be useful for managing the water resources in the study area.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Allen, R.G.; Pereira, L.S.; Raes, D.; Smith, M. Crop Evapotranspiration-Guidelines for Computing Crop Water Requirements-Fao Irrigation and Drainage Paper 56; FAO: Rome, Italy, 1998; Volume 300, p. D05109. Available online: http://www.climasouth.eu/sites/default/files/FAO%2056.pdf (accessed on 1 October 2022).
- Dhillon, R.; Rojo, F.; Upadhyaya, S.K.; Roach, J.; Coates, R.; Delwiche, M. Prediction of plant water status in almond and walnut trees using a continuous leaf monitoring system. Precis. Agric.
**2019**, 20, 723–745. [Google Scholar] [CrossRef] - Sharma, S.; Regulwar, D.G. Prediction of evapotranspiration by artificial neural network and conventional methods. Int. J. Eng. Res.
**2016**, 5, 184–187. [Google Scholar] - Nouri, H.; Beecham, S.; Kazemi, F.; Hassanli, A.M.; Anderson, S. Remote sensing techniques for predicting evapotranspiration from mixed vegetated surfaces. Hydrol. Earth Syst. Sci. Discuss.
**2013**, 10, 3897–3925. [Google Scholar] [CrossRef] - Lu, G.; Wu, Z.; He, H. Hydrological Cycle and Quantity Forecast; Science Press: Beijing, China, 2010. (In Chinese) [Google Scholar]
- Jun-Fang, Z.H.A.O.; Jian-Ping, G.U.O.; Zhang, Y.H.; Jing-Wen, X.U. Advances in research of impacts of climate change on agriculture. Chin. J. Agrometeorol.
**2010**, 31, 200. [Google Scholar] - Raza, A.; Hu, Y.; Shoaib, M.; Abd Elnabi, M.K.; Zubair, M.; Nauman, M.; Syed, N.R. A Systematic Review on Estimation of Reference Evapotranspiration under Prisma Guidelines. Pol. J. Environ. Stud.
**2021**, 30, 5413–5422. [Google Scholar] [CrossRef] - Raza, A.; Shoaib, M.; Baig, M.A.I.; Ahmad, S.; Khan, M.M.; Ullah, M.K.; Hashim, S. Comparative study of powerful predictive modeling techniques for modeling monthly reference evapotranspiration in various climatic regions. Fresenius Environ. Bull.
**2021**, 30, 7490–7513. [Google Scholar] - Mehdizadeh, S.; Behmanesh, J.; Khalili, K. Using MARS, SVM, GEP and empirical equations for estimation of monthly mean reference evapotranspiration. Comput. Electron. Agric.
**2017**, 139, 103–114. [Google Scholar] [CrossRef] - Ferreira, L.B.; da Cunha, F.F. New approach to estimate daily reference evapotranspiration based on hourly temperature and relative humidity using machine learning and deep learning. Agric. Water Manag.
**2020**, 234, 106113. [Google Scholar] [CrossRef] - Guo, X.; Sun, X.; Ma, J. Prediction of daily crop reference evapotranspiration (ET
_{o}) values through a least-squares support vector machine model. Hydrol. Res.**2011**, 42, 268–274. [Google Scholar] [CrossRef] - Traore, S.; Luo, Y.; Fipps, G. Deployment of artificial neural network for short-term forecasting of evapotranspiration using public weather forecast restricted messages. Agric. Water Manag.
**2016**, 163, 363–379. [Google Scholar] [CrossRef] - Valipour, M.; Gholami Sefidkouhi, M.A.; Raeini-Sarjaz, M.; Guzman, S.M. A hybrid data-driven machine learning technique for evapotranspiration modeling in various climates. Atmosphere
**2019**, 10, 311. [Google Scholar] [CrossRef] [Green Version] - Mattar, M.A. Using gene expression programming in monthly reference evapotranspiration modeling: A case study in Egypt. Agric. Water Manag.
**2018**, 198, 28–38. [Google Scholar] [CrossRef] - Gocic, M.; Petković, D.; Shamshirband, S.; Kamsin, A. Comparative analysis of reference evapotranspiration equations modelling by extreme learning machine. Comput. Electron. Agric.
**2016**, 127, 56–63. [Google Scholar] [CrossRef] - Abdullah, S.S.; Malek, M.A.; Abdullah, N.S.; Kisi, O.; Yap, K.S. Extreme learning machines: A new approach for prediction of reference evapotranspiration. J. Hydrol.
**2015**, 527, 184–195. [Google Scholar] [CrossRef] - Raza, A.; Shoaib, M.; Faiz, M.A.; Baig, F.; Khan, M.M.; Ullah, M.K.; Zubair, M. Comparative assessment of reference evapotranspiration estimation using conventional method and machine learning algorithms in four climatic regions. Pure Appl. Geophys.
**2020**, 177, 4479–4508. [Google Scholar] [CrossRef] - Raza, A.; Shoaib, M.; Khan, A.; Baig, F.; Faiz, M.A.; Khan, M.M. Application of non-conventional soft computing approaches for estimation of reference evapotranspiration in various climatic regions. Theor. Appl. Climatol.
**2020**, 139, 1459–1477. [Google Scholar] [CrossRef] - Fan, J.; Yue, W.; Wu, L.; Zhang, F.; Cai, H.; Wang, X.; Lu, X.; Xiang, Y. Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily reference evapotranspiration using limited meteorological data in different climates of China. Agric. For. Meteorol.
**2018**, 263, 225–241. [Google Scholar] [CrossRef] - Granata, F. Evapotranspiration evaluation models based on machine learning algorithms—A comparative study. Agric. Water Manag.
**2019**, 217, 303–315. [Google Scholar] [CrossRef] - Elbeltagi, A.; Raza, A.; Hu, Y.; Al-Ansari, N.; Kushwaha, N.L.; Srivastava, A.; Zubair, M. Data intelligence and hybrid metaheuristic algorithms-based estimation of reference evapotranspiration. Appl. Water Sci.
**2022**, 12, 152. [Google Scholar] [CrossRef] - Feng, Y.; Cui, N.; Gong, D.; Zhang, Q.; Zhao, L. Evaluation of random forests and generalized regression neural networks for daily reference evapotranspiration modelling. Agric. Water Manag.
**2017**, 193, 163–173. [Google Scholar] [CrossRef] - Feng, Y.; Peng, Y.; Cui, N.; Gong, D.; Zhang, K. Modeling reference evapotranspiration using extreme learning machine and generalized regression neural network only with temperature data. Comput. Electron. Agric.
**2017**, 136, 71–78. [Google Scholar] [CrossRef] - Fang, W.; Huang, S.; Huang, Q.; Huang, G.; Meng, E.; Luan, J. Reference evapotranspiration forecasting based on local meteorological and global climate information screened by partial mutual information. J. Hydrol.
**2018**, 561, 764–779. [Google Scholar] [CrossRef] - Saggi, M.K.; Jain, S. Reference evapotranspiration estimation and modeling of the Punjab Northern India using deep learning. Comput. Electron. Agric.
**2019**, 156, 387–398. [Google Scholar] [CrossRef] - Huang, G.; Wu, L.; Ma, X.; Zhang, W.; Fan, J.; Yu, X.; Zeng, W.; Zhou, H. Evaluation of CatBoost method for prediction of reference evapotranspiration in humid regions. J. Hydrol.
**2019**, 574, 1029–1041. [Google Scholar] [CrossRef] - Torres, A.F.; Walker, W.R.; McKee, M. Forecasting daily potential evapotranspiration using machine learning and limited climatic data. Agric. Water Manag.
**2011**, 98, 553–562. [Google Scholar] [CrossRef] - Tang, D.; Feng, Y.; Gong, D.; Hao, W.; Cui, N. Evaluation of artificial intelligence models for actual crop evapotranspiration modeling in mulched and non-mulched maize croplands. Comput. Electron. Agric.
**2018**, 152, 375–384. [Google Scholar] [CrossRef] - Walls, S.; Binns, A.D.; Levison, J.; MacRitchie, S. Prediction of actual evapotranspiration by artificial neural network models using data from a Bowen ratio energy balance station. Neural Comput. Appl.
**2020**, 32, 14001–14018. [Google Scholar] [CrossRef] - Nourani, V.; Elkiran, G.; Abdullahi, J. Multi-station artificial intelligence based ensemble modeling of reference evapotranspiration using pan evaporation measurements. J. Hydrol.
**2019**, 577, 123958. [Google Scholar] [CrossRef] - Tabari, H.; Martinez, C.; Ezani, A.; Hosseinzadeh Talaee, P. Applicability of support vector machines and adaptive neurofuzzy inference system for modeling potato crop evapotranspiration. Irrig. Sci.
**2013**, 31, 575–588. [Google Scholar] [CrossRef] - CAPMAS (Central Agency for Public Mobilization and Statistics). Egypt in Figures: Population. 2022. Available online: https://www.capmas.gov.eg/Pages/StaticPages.aspx?page_id=5035# (accessed on 15 October 2022).
- Ayaz, A.; Rajesh, M.; Singh, S.K.; Rehana, S. Estimation of reference evapotranspiration using machine learning models with limited data. AIMS Geosci.
**2021**, 7, 268–290. [Google Scholar] [CrossRef] - Ho, T.K. The random subspace method for constructing decision forests. IEEE Trans. Pattern Anal. Mach. Intell.
**1998**, 20, 832–844. [Google Scholar] - Yaman, M.A.; Subasi, A.; Rattay, F. Comparison of random subspace and voting ensemble machine learning methods for face recognition. Symmetry
**2018**, 10, 651. [Google Scholar] [CrossRef] [Green Version] - Skurichina, M.; Duin, R.P. Bagging, boosting and the random subspace method for linear classifiers. Pattern Anal. Appl.
**2002**, 5, 121–135. [Google Scholar] [CrossRef] - Xia, C.; Pan, Z.; Polden, J.; Li, H.; Xu, Y.; Chen, S. Modelling and prediction of surface roughness in wire arc additive manufacturing using machine learning. J. Intell. Manuf.
**2022**, 33, 1467–1482. [Google Scholar] [CrossRef] - Ravikumar, P.; Lafferty, J.; Liu, H.; Wasserman, L. Sparse additive models. J. R. Stat. Soc. Ser. B
**2009**, 71, 1009–1030. [Google Scholar] [CrossRef] - Hastie, T.; Tibshirani, R. Generalized Additive Models. Stat. Sci.
**1986**, 6, 15–51. [Google Scholar] [CrossRef] - Laanaya, F.; St-Hilaire, A.; Gloaguen, E. Water temperature modelling: Comparison between the generalized additive model, logistic, residuals regression and linear regression models. Hydrol. Sci. J.
**2017**, 62, 1078–1093. [Google Scholar] [CrossRef] - Fu, J.C.; Huang, H.Y.; Jang, J.H.; Huang, P.H. River Stage Forecasting Using Multiple Additive Regression Trees. Water Resour. Manag.
**2019**, 33, 4491–4507. [Google Scholar] [CrossRef] - Senthil Kumar, A.R.; Ojha, C.S.P.; Goyal, M.K.; Singh, R.D.; Swamee, P.K. Modeling of Suspended Sediment Concentration at Kasol in India Using ANN, Fuzzy Logic, and Decision Tree Algorithms. J. Hydrol. Eng.
**2012**, 17, 394–404. [Google Scholar] [CrossRef] - Witten, I.H.; Frank, E. Data mining: Practical machine learning tools and techniques with Java implementations. Acm Sigmod Record
**2002**, 31, 76–77. [Google Scholar] [CrossRef] - Quinlan, J. Simplifying decision trees. Int. J. Man-Mach. Stud.
**1987**, 27, 221–234. [Google Scholar] [CrossRef] [Green Version] - Bharti, B.; Pandey, A.; Tripathi, S.K.; Kumar, D. Modelling of runoff and sediment yield using ANN, LS-SVR, REPTree and M5 models. Hydrol. Res.
**2017**, 48, 1489–1507. [Google Scholar] [CrossRef] [Green Version] - Breiman, L. Bagging predictors. Mach. Learn.
**1996**, 24, 123–140. [Google Scholar] [CrossRef] [Green Version] - Joseph, K.S.; Ravichandran, T. A comparative evaluation of software effort estimation using REPTree and K* in handling with missing values. Aust. J. Basic Appl. Sci.
**2012**, 6, 312–317. [Google Scholar] - Pérez-Domínguez, L.; Garg, H.; Luviano-Cruz, D.; García Alcaraz, J.L. Estimation of Linear Regression with the Dimensional Analysis Method. Mathematics
**2022**, 10, 1645. [Google Scholar] [CrossRef] - Hothorn, T.; Bretz, F.; Westfall, P. Simultaneous inference in general parametric models. Biom. J. J. Math. Methods Biosci.
**2008**, 50, 346–363. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, M.; Hu, S.; Ge, Y.; Heuvelink, G.B.; Ren, Z.; Huang, X. Using multiple linear regression and random forests to identify spatial poverty determinants in rural China. Spat. Stat.
**2020**, 42, 100461. [Google Scholar] [CrossRef] - Park, J.Y.; Phillips, P.C. Statistical inference in regressions with integrated processes: Part 2. Econom. Theory
**1989**, 5, 95–131. [Google Scholar] [CrossRef] [Green Version] - Sattari, M.T.; Apaydin, H.; Shamshirband, S. Performance evaluation of deep learning-based gated recurrent units (GRUs) and tree-based models for estimating ET
_{o}by using limited meteorological variables. Mathematics**2020**, 8, 972. [Google Scholar] [CrossRef] - Kushwaha, N.L.; Rajput, J.; Elbeltagi, A.; Elnaggar, A.Y.; Sena, D.R.; Vishwakarma, D.K.; Mani, I.; Hussein, E.E. Data intelligence model and meta-heuristic algorithms-based pan evaporation modelling in two different agro-climatic zones: A case study from northern India. Atmosphere
**2021**, 12, 1654. [Google Scholar] [CrossRef] - Nhu, V.H.; Shahabi, H.; Nohani, E.; Shirzadi, A.; Al-Ansari, N.; Bahrami, S.; Miraki, S.; Geertsema, M.; Nguyen, H. Daily water level prediction of Zrebar Lake (Iran): A comparison between M5P, random forest, random tree and reduced error pruning trees algorithms. ISPRS Int. J. Geo-Inf.
**2020**, 9, 479. [Google Scholar] [CrossRef] - Salam, R.; Islam, A.R.M.T. Potential of RT, Bagging and RS ensemble learning algorithms for reference evapotranspiration prediction using climatic data-limited humid region in Bangladesh. J. Hydrol.
**2020**, 590, 125241. [Google Scholar] [CrossRef] - Tikhamarine, Y.; Malik, A.; Souag-Gamane, D.; Kisi, O. Artificial intelligence models versus empirical equations for modeling monthly reference evapotranspiration. Environ. Sci. Pollut. Res.
**2020**, 27, 30001–30019. [Google Scholar] [CrossRef] [PubMed] - Kisi, O.; Keshtegar, B.; Zounemat-Kermani, M.; Heddam, S.; Trung, N.T. Modeling reference evapotranspiration using a novel regression-based method: Radial basis M5 model tree. Theor. Appl. Climatol.
**2021**, 145, 639–659. [Google Scholar] [CrossRef] - Bai, Y.; Zhang, S.; Bhattarai, N.; Mallick, K.; Liu, Q.; Tang, L.; Im, J.; Guo, L.; Zhang, J. On the use of machine learning based ensemble approaches to improve evapotranspiration estimates from croplands across a wide environmental gradient. Agric. For. Meteorol.
**2021**, 298, 108308. [Google Scholar] [CrossRef] - Bellido-Jiménez, J.A.; Estévez, J.; García-Marín, A.P. New machine learning approaches to improve reference evapotranspiration estimates using intra-daily temperature-based variables in a semi-arid region of Spain. Agric. Water Manag.
**2021**, 245, 106558. [Google Scholar] [CrossRef] - Arnell, N.W.; Gosling, S.N. The impacts of climate change on river flood risk at the global scale. Clim. Change
**2016**, 134, 387–401. [Google Scholar] [CrossRef] [Green Version] - Khadke, L.; Pattnaik, S. Impact of initial conditions and cloud parameterization on the heavy rainfall event of Kerala (2018). Model. Earth Syst. Environ.
**2021**, 7, 2809–2822. [Google Scholar] [CrossRef] - Meza, I.; Siebert, S.; Döll, P.; Kusche, J.; Herbert, C.; Eyshi Rezaei, E.; Nouri, H.; Gerdener, H.; Popat, E.; Frischen, J.; et al. Global-scale drought risk assessment for agricultural systems. Nat. Hazards Earth Syst. Sci.
**2020**, 20, 695–712. [Google Scholar] [CrossRef] [Green Version] - Sazib, N.; Mladenova, I.; Bolten, J. Leveraging the google earth engine for drought assessment using global soil moisture data. Remote Sens.
**2018**, 10, 1265. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Location of the study area (Al Buhayrah, Alexandria, Ismailiyah, and Minufiyah governorates) in Egypt.

**Figure 2.**Demonstration of time series of each input variable used for developing ML models for simulating the evapotranspiration process.

**Figure 6.**Time-series plots (

**left**) represent observed and modeled ET

_{o}data, and scattered plots (

**right**) represent the entire testing dataset of observed versus estimated ET

_{o}values during the testing phase for the models ((

**a**) LR, (

**b**) RSS, (

**c**) AR, (

**d**) and (

**e**) RETree).

**Table 1.**Statistical analysis of climate data variables from 1979 to 2014 in the governorates of Al Buhayrah, Alexandria, Ismailiyah, and Minufiyah.

Governorate | Metrics | T_{max}(°C) | T_{min}(°C) | T_{mean}(°C) | P (mm) | WS (Km/h) | RH (%) | SR (kWh/m ^{2}) | ET_{o} (mm/day) |
---|---|---|---|---|---|---|---|---|---|

Al Buhayrah | Maximum | 47.59 | 26.38 | 35.09 | 40.50 | 9.14 | 0.98 | 30.68 | 34.01 |

Minimum | 8.17 | −2.69 | 6.36 | 0.00 | 0.75 | 0.11 | 0.00 | 0.00 | |

Average | 27.52 | 13.89 | 20.71 | 0.34 | 3.29 | 0.64 | 20.45 | 13.05 | |

Std. deviation | 6.81 | 5.28 | 5.72 | 1.50 | 0.92 | 0.10 | 7.84 | 6.83 | |

Variance | 46.40 | 27.84 | 32.70 | 2.24 | 0.84 | 0.01 | 61.53 | 46.70 | |

Skewness | −0.21 | −0.20 | −0.15 | 8.84 | 0.96 | −0.98 | −0.51 | −0.06 | |

Kurtosis | −0.93 | −0.97 | −1.20 | 118.55 | 2.43 | 2.41 | −0.89 | −1.13 | |

Alexandria | Maximum | 43.43 | 29.82 | 35.15 | 32.97 | 12.88 | 0.94 | 30.49 | 29.83 |

Minimum | 9.35 | 2.72 | 7.87 | 0.00 | 1.20 | 0.10 | 0.00 | 0.00 | |

Average | 26.11 | 15.98 | 21.04 | 0.38 | 4.52 | 0.64 | 20.48 | 11.28 | |

Std. deviation | 6.06 | 4.81 | 5.18 | 1.53 | 1.35 | 0.10 | 7.82 | 5.83 | |

Variance | 36.72 | 23.17 | 26.82 | 2.33 | 1.83 | 0.01 | 61.13 | 33.98 | |

Skewness | −0.19 | −0.08 | −0.12 | 7.69 | 1.01 | −1.43 | −0.53 | −0.06 | |

Kurtosis | −0.93 | −1.09 | −1.21 | 83.65 | 2.33 | 3.14 | −0.84 | −1.03 | |

Ismailiyah | Maximum | 47.76 | 27.64 | 35.59 | 33.74 | 4.98 | 0.96 | 30.74 | 32.82 |

Minimum | 7.06 | −0.14 | 5.83 | 0.00 | 0.49 | 0.07 | 0.00 | 0.00 | |

Average | 28.81 | 12.78 | 20.79 | 0.18 | 1.70 | 0.59 | 20.71 | 14.49 | |

Std. deviation | 7.50 | 4.57 | 5.74 | 1.03 | 0.43 | 0.12 | 7.33 | 7.62 | |

Variance | 56.18 | 20.87 | 32.95 | 1.06 | 0.18 | 0.01 | 53.75 | 58.14 | |

Skewness | −0.24 | −0.11 | −0.15 | 13.61 | 1.44 | −0.72 | −0.42 | 0.02 | |

Kurtosis | −1.03 | −0.96 | −1.18 | 281.36 | 5.21 | 0.97 | −0.98 | −1.24 | |

Minufiyah | Maximum | 48.09 | 25.30 | 35.55 | 60.28 | 6.38 | 0.97 | 31.06 | 34.41 |

Minimum | 6.77 | −2.23 | 5.29 | 0.00 | 0.62 | 0.09 | 0.00 | 0.00 | |

Average | 29.42 | 12.84 | 21.13 | 0.16 | 2.36 | 0.57 | 20.92 | 15.00 | |

Std. deviation | 7.74 | 5.34 | 6.28 | 1.01 | 0.63 | 0.13 | 7.43 | 7.82 | |

Variance | 59.94 | 28.52 | 39.43 | 1.02 | 0.39 | 0.02 | 55.18 | 61.21 | |

Skewness | −0.23 | −0.23 | −0.17 | 25.06 | 0.78 | −0.36 | −0.44 | −0.02 | |

Kurtosis | −1.07 | −1.00 | −1.23 | 1134.97 | 1.95 | 0.37 | −0.97 | −1.28 |

No. of Variables | Variables | MSE | R^{2} | Adjusted R^{2} | Mallows’ Cp | Akaike’s AIC | Schwarz’s SBC | Amemiya’s PC |
---|---|---|---|---|---|---|---|---|

1 | SR | 7.670 | 0.853 | 0.853 | 178,771.227 | 105,837.493 | 105,855.209 | 0.147 |

2 | T_{max}/SR | 2.773 | 0.947 | 0.947 | 31,471.556 | 52,988.983 | 53,015.557 | 0.053 |

3 | T_{max}/T_{mean}/SR | 1.728 | 0.967 | 0.967 | 26.095 | 28,408.184 | 28,443.616 | 0.033 |

4 | T_{max}/T_{mean}/RH/SR | 1.727 | 0.967 | 0.967 | 4.195 | 28,386.287 | 28,430.577 | 0.033 |

5 * | T_{max}/T_{min}/RH/SR | 1.727 | 0.967 | 0.967 | 4.195 | 28,386.287 | 28,430.577 | 0.033 |

6 | T_{max}/T_{min}/WS/RH/SR | 1.727 | 0.967 | 0.967 | 6.000 | 28,388.092 | 28,441.240 | 0.033 |

Source | Value | Standard Error | t | Pr > |t| | Lower Bound (95%) | Upper Bound (95%) |
---|---|---|---|---|---|---|

T_{max} | 0.649 | 0.002 | 366.370 | <0.0001 | 0.646 | 0.653 |

T_{min} | −0.205 | 0.001 | −167.137 | <0.0001 | −0.208 | −0.203 |

T_{mean} | 0.000 | 0.000 | ||||

WS | 0.000 | 0.000 | ||||

RH | −0.005 | 0.001 | −4.889 | <0.0001 | −0.007 | −0.003 |

SR | 0.525 | 0.001 | 414.793 | <0.0001 | 0.523 | 0.527 |

**Table 4.**Performance metrics for the models developed during the training and testing phase for ET

_{o}estimation.

ML Algorithms | Training Phase | Testing Phase | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

MAE | RMSE | RAE (%) | RRSE (%) | r | MAE | RMSE | RAE (%) | RRSE (%) | r | |

LR | 1.0099 | 1.3011 | 16.6612 | 18.4732 | 0.9828 | 1.1050 | 1.3717 | 16.2809 | 17.7032 | 0.9849 |

RSS | 1.3673 | 1.7407 | 22.5558 | 24.7149 | 0.9757 | 1.6727 | 2.1425 | 24.6466 | 27.6511 | 0.9838 |

AR | 1.5913 | 1.9876 | 26.2524 | 28.2209 | 0.9595 | 1.6378 | 2.0703 | 24.1312 | 26.7191 | 0.9644 |

REPTree | 0.2095 | 0.2828 | 3.4565 | 4.0159 | 0.9992 | 0.2806 | 0.3659 | 4.1344 | 4.7224 | 0.9989 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Elbeltagi, A.; Srivastava, A.; Al-Saeedi, A.H.; Raza, A.; Abd-Elaty, I.; El-Rawy, M.
Forecasting Long-Series Daily Reference Evapotranspiration Based on Best Subset Regression and Machine Learning in Egypt. *Water* **2023**, *15*, 1149.
https://doi.org/10.3390/w15061149

**AMA Style**

Elbeltagi A, Srivastava A, Al-Saeedi AH, Raza A, Abd-Elaty I, El-Rawy M.
Forecasting Long-Series Daily Reference Evapotranspiration Based on Best Subset Regression and Machine Learning in Egypt. *Water*. 2023; 15(6):1149.
https://doi.org/10.3390/w15061149

**Chicago/Turabian Style**

Elbeltagi, Ahmed, Aman Srivastava, Abdullah Hassan Al-Saeedi, Ali Raza, Ismail Abd-Elaty, and Mustafa El-Rawy.
2023. "Forecasting Long-Series Daily Reference Evapotranspiration Based on Best Subset Regression and Machine Learning in Egypt" *Water* 15, no. 6: 1149.
https://doi.org/10.3390/w15061149