# Performance Evaluation of Five Machine Learning Algorithms for Estimating Reference Evapotranspiration in an Arid Climate

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## Abstract

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_{o}) calculation. Despite this, the PMF cannot be employed when meteorological variables are constrained; therefore, alternative models for ET

_{o}estimation requiring fewer variables must be chosen, which means that they perform at least as well as, if not better than, the PMF in terms of accuracy and efficiency. This study evaluated five machine learning (ML) algorithms to estimate ET

_{o}and compared their results with the standardized PMF. For this purpose, ML models were trained using monthly time series climatic data. The created ML models underwent testing to determine ET

_{o}under varying meteorological input combinations. The results of ML models were compared to assess their accuracy and validate their performance using several statistical indicators, errors (root-mean-square (RMSE), mean absolute error (MAE)), model efficiency (NSE), and determination coefficient (R

^{2}). The process of evaluating ML models involved the utilization of radar charts, Smith graphs, heatmaps, and bullet charts. Based on our findings, satisfactory results have been obtained using RBFFNN based on M12 input combinations (mean temperature (T

_{mean}), mean relative humidity (RH

_{mean}), sunshine hours (Sh)) for ET

_{o}estimation. The RBFFNN model exhibited the most precise estimation as RMSE obtained values of 0.30 and 0.22 during the training and testing phases, respectively. In addition, during training and testing, the MAE values for this model were recorded as 0.15 and 0.17, respectively. The highest R

^{2}and NSE values were noted as 0.98 and 0.99 for the RBFNN during performance analysis, respectively. The scatter plots and spatial variations of the RBFNN and PMF in the studied region indicated that the RBFNN had the highest efficacy (R

^{2}, NSE) and lowest errors (RMSE, MAE) as compared with the other four ML models. Overall, our study highlights the potential of ML models for ET

_{o}estimation in the arid region (Jacobabad), providing vital insights for improving water resource management, helping climate change research, and optimizing irrigation scheduling for optimal agricultural water usage in the region.

## 1. Introduction

_{o}) is a basic factor in the empirical models. The difficulty in ascertaining the ET for each individual crop is the underlying factor contributing to this issue. Hence, indirect methods are used to estimate ET

_{o}and crop coefficients, which are further utilized to quantify ET for individual crops of interest. The Penman–Monteith (PMF) approach, first introduced by Allen in 1998 and subsequently validated in several climatic conditions [4,6], is now endorsed by the Food and Agriculture Organisation (FAO) of the United Nations and the American Society of Civil Engineers (ASCE) committee. In order to complete PMF ET

_{o}calculations, it is important to possess a comprehensive meteorological data collection for several places around the globe. Although the relative importance, interdependence, and interrelationships among the components were previously unclear, recent studies provided ML-based projections of the PMF ET

_{o}using a substantial amount of meteorological data [7,8]. Ravindran et al. [9] employed the PMF using the available meteorological data to calculate ET

_{o}and then compared it with a deep neural network (DNN) model that only takes sun radiation (Rn) as an input parameter [9]. Zhou et al. [10] investigated the efficacy of machine learning (ML) models, namely deep factorization machine (DeepFM), gradient boosting with categorical feature support (CatBoost), light gradient boosting (LightGBM), extreme gradient boosting (XGBoost), and gradient boosting decision tree (GBDT), for estimating the ET

_{o}. Basagaoglu et al. [7] determined that Rn is the most important meteorological variable for determining ET

_{o}in a semi-arid location. However, sunshine hours (Sh) might be substituted when Rn is unavailable. The analyses of previous studies revealed that Sh exhibits a closer association with Rn than the other meteorological variables and can be used in the absence of Rn [11,12,13]. The current study used the Sh variable in the analysis for ET

_{o}estimation because of the deficiency in the Rn factor.

_{o}estimation using the PMF is the unavailability of several meteorological variables and uncertainty in collected data [14,15]. Despite the availability of critical climatic variables, a scarcity of automated weather stations installed at specific sites necessitates the presence of climatic data in numerous locations. Additionally, the use of obsolete weather stations raises issues with data quality. Data calibration is required since the sensor’s inconsistent performance exposes several variances. In this scenario, the inconsistency of ET

_{o}estimates opens the door for developing alternative techniques that use fewer inputs to calculate ET

_{o}similarly or at least approach the PMF.

_{o}estimates because of the frequent absence of meteorological variables [16,17,18,19]. Despite this, ML based on various algorithms (cuckoo, water wave optimization, coactive neuro-fuzzy inference system, decision support system) has become popular for ET

_{o}modeling in comparison with empirical equations (the PMF, Hargreaves, Turc, Jensen–Haise, Hargreaves–Samani) using limited climatic data [20,21,22,23,24,25,26,27,28]. The ML models provided good output (ET

_{o}) that approached the corresponding empirical equation (PMF) because the optimal selection of input variables against the output factor by adding or eliminating an input variable is considered the main advantage in increasing the efficacy of input versus output relation [29,30,31,32,33,34,35].

_{o}modeling using ML has gained significant attention in recent academic studies, raising interest among hydrologists and meteorologists across different countries. Yin et al. [36] calculated daily ET

_{o}in a Hilly interior watershed in northwest China and found support vector machines (SVMs) worked best using daily meteorological data. Wen et al. [37] compared ML with four empirical models in an arid region of China and found temperatures (minimum and maximum) as effective parameters for ET

_{o}estimation. Wang et al. [38] analyzed the efficacy of two ML models, namely gene expression programming (GEP) and artificial neural networks (ANNs), in the Karst area of Guangxi Province located in China, for calculating daily ET

_{o}. The research showed that ML outperformed with fewer meteorological inputs. Sanikhani et al.’s [39] study showed that the monthly ET

_{o}in the Isparta and Antalya region (Turkey) was successfully quantified by employing ML models using limited (temperature) data. In an arid region (Sistan and Baluchestan Province) of Iran, Pour et al. [40] used ML with varying input climatic combinations and found that the ML model (SVM) exhibited superior performance in comparison with the other models for the estimation of ET

_{o}. In Jiangxi Province (China), Wu et al. [41] examined the efficacy of ML models using cross-station and synthetic data to measure monthly mean daily ET

_{o}and concluded that tree-based ML outperformed other models. Daily ET

_{o}using limited climatic data was estimated by Saggi and Jain [42] in Punjab province, India. They found deep learning exhibited superior performance compared with the other models. Similarly, Shiri et al. [43] found good performance of ML for ET

_{o}estimation using 29 weather stations in Iran. Tikhamarine et al. [44] compared five ANN-based meta-heuristic algorithms (gray wolf optimizer, multiverse optimizer, particle swarm optimizer, whale optimization algorithm, ant lion optimizer) to estimate monthly ET

_{o}using limited data in the Uttarakhand State (Himalayan Region) of India and found that gray wolf optimizer performed well in comparison with the targeted empirical (valiantzas) model. Likewise, Ferreira et al. [45] found that the performance of ML (ANN, GEP) models was good and close to the PMF with minimal climate data in several regions of Brazil. Granata [46] estimated ET

_{o}using climate data collected from eddy covariance (EC) flux tower stations set up at a location (Floral City) in central Florida with a humid subtropical environment and found that the chosen ML models were capable of ET

_{o}modeling with limited input data in the studied area. Keshtegar et al. [47] compared tree-based and ANN-based ML models with polynomial chaos expansion and the response surface method in the Mediterranean region (Isparta and Antalya) of Turkey for estimating ET

_{o}. Likewise, Nourani et al. [48] estimated ET

_{o}using climatic data in different climatic regions across five countries (Turkey, NC, Iraq, Iran and Libya) by employing ML ensemble based models and found ANN based ML performed good in comparison to other models. Shiri [49] used limited climatic input in ML models for estimating ET

_{o}in an arid region of Iran, and comparison results with six empirical equations showed the supremacy of the chosen ML model.

_{o}estimation using ML under Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines and suggested the comparison of ML algorithms for ET

_{o}using fewer inputs, especially in developing countries (Pakistan) due to the lack of climatic data. When conventional methods (like the PMF) cannot be used because of excessive input demands or the unavailability of climatic parameters like Rn [36,37,38,39,40,41,42,43,44,45,46,47,48,49], the task of improving methods that rely on fewer climatic inputs and developing ML models for ET

_{o}estimation with minimal climatic records becomes of great relevance. Kushwaha et al. [51] concluded that ML might capture time series data without discretization when handled correctly and be able to estimate ET

_{o}accurately. Similar findings were obtained by Wu et al. [52] in the Poyang Lake basin in southern China, Roy et al. [53] in the Gazipur District in Bangladesh, Ahmadi et al. [54] in the arid and semi-arid climate of Iran, Sattari et al. [55] in the Corum province of Turkey, and Malik et al. [56] in the Uttarakhand State of India in comparison with the empirical (PMF) method for ET

_{o}modeling.

_{o}modeling based on ML algorithms using less climatic data, the current study explores five ML algorithms’ performances for estimating ET

_{o}in the arid region (Jacobabad) of Sindh province, Pakistan. The main goal of this study is to determine effective climatic variables for ET

_{o}estimation. In the current study, a total of 17 different input models were initially formulated based on different combinations made by using the meteorological inputs which are mainly used in the PMF for ET

_{o}estimation. We tried to accurately estimate ET

_{o}with limited climatic data and the best input combination to calculate ET

_{o}, which can be used as an alternative to the PMF in Jacobabad. The novelty of this study is that a comparison of five ML algorithms, namely Iterative dichotomizer (ID3), gradient boosting (GB), Random forest (RF), multilayer neural network (MLNN), and radial basis function neural network (RBFNN), for ET

_{o}estimation using less climatic data is not yet explored in an arid region (Jacobabad) of Pakistan. In a nutshell, the following are three objectives of this study:

- ET
_{o}estimation using five ML (ID3, GB, RF, MLNN, and RBFNN) algorithms. - Identifying an effective combination of meteorological inputs for ET
_{o}estimation. - Performance evaluation of ML algorithms through visualization (radar, heatmap, bullet, and Smith graphs) based on different statistical indices to determine the best one among them.

_{o}retrieved from the ML model may be interpolated into monthly and yearly ET

_{o}maps depicting ET

_{o}variations over the studied area. Agronomists, hydrologists, and agricultural engineers may use the ET

_{o}maps to more accurately determine the water needed to irrigate the crops (via drip and spray irrigation).

## 2. Study Area and Dataset

_{min}) exhibited an initial increase from January to July, followed by a slow decline until December. The observed pattern in Tmax was consistent, as shown in Figure 2a. The fluctuation in seasons can be attributed to the solar radiation emitted by the sun, as depicted in Figure 2a. Sh witnessed the summer’s peak and the beginning of winter’s decline. The variable RH

_{mean}exhibited a relationship with both T

_{max}and T

_{min}, as it was seen that the periods of elevated air temperature coincided with the highest levels of humidity. According to the data presented in Figure 2a, the average relative humidity (RH

_{mean}) exhibited its maximum values throughout July to September, which can be attributed to the impact of wind, and there could be much more important meteorological reasons, such as the atmospheric circulation pattern together with the surrounding ocean and topography of the selected regions. During the summer season, it can be observed from Figure 2a that there is an upward trend between wind speed and humidity levels in the air. The summer months exhibited the most notable rise in average and maximum humidity levels. In addition, Figure 2b indicates cyclical conditions of climatic variables starting from 1 January to 31 December for the years 1987 to 2016.

#### Physical–Geographical Conditions

## 3. Study Methodology

#### 3.1. PMF

_{o}using meteorological input values. The PMF approach was used to determine the value of ET

_{o}in this software (Weblink: https://www.fao.org/land-water/databases-and-software/cropwat/en/, access date, 20 September 2023). The PMF developed by Allen et al. [4] in 1998 determines ET

_{o}values based on a combination of meteorological and aerodynamic parameters (es, ea, e

_{min}, e

_{max}, Δ, G, and Ɣ). The mathematical notation of the PMF is described as follows:

_{o}is measured in mm/day; R

_{n}= net radiation at the surface (MJ/m

^{2}/day);

^{2}/day); T

_{mean}= air temperature at 2 m height (°C);

_{s}= saturation vapor pressure (kPa); e

_{a}= actual vapor pressure (kPa);

_{s}is saturation vapor pressure (kPa); Ws = wind speed.

#### 3.2. Proposed ML Framework

_{o}was used as the benchmark for output (ET

_{o}) values when chosen ML algorithms were applied. For this purpose, we used Waikato Environment for Knowledge Analysis (WEKA) software version 3.9.4. It is a collection of machine learning algorithms for data mining tasks. It contains tools for data preparation, classification, regression, clustering, association rules mining, and visualization. It is an open-source software issued under the GNU General Public License (weblink: https://www.cs.waikato.ac.nz/ml/weka/, accessed date, 5 August 2023). Weka was used in this study, and the following steps were implemented. The dataset used was pre-processed in the first step (1). The data file was prepared in comma-separated values (CSV) file format (2), and it was uploaded to Weka software by using the import feature (3). The optimal parameters related to ML algorithms were selected (4), data were classified (5), and the nearest neighbor was chosen as the estimation function (6). In the cross-validation process, K-means clustering was utilized (7), association rules were performed (8), and, in the last step, the model was evaluated (9). A schematic framework of the ML models suggested for ET

_{o}estimation is shown in Figure 3.

#### 3.2.1. Iterative Dichotomizer (ID3)

_{b}is the information gain for the k-wise classified function.

#### 3.2.2. Gradient Boosting (GB)

_{o}+ B

_{1}× T

_{1}(X) + B

_{2}× T

_{2}(X)………………+ B

_{m}× T

_{m}(X)

_{o}is the starting value in the series, X is the vector of “pseudo-residual” values remaining at this point in the series, T

_{x}(X) represents the trees fitted to the pseudo-residuals (here, x = 1, 2, 3…….m), B

_{x}is the coefficient of the tree node predicted values (here, x = 1, 2, 3…….m).

_{o}value was predicted by averaging the values from the various subsets.

#### 3.2.3. Random Forest (RF)

- Climatic variables were chosen as predictors/inputs.
- The sample data constituted 70% of the total dataset, separated using the randomization function.
- Analysis was performed using dataset (OOB), and residual values were stored separately.
- The ET
_{o}obtained from each tree as output was gathered and stored. - The mean values of the output variable (ET
_{o}) were computed as a whole.

_{o}. Table 2 overviews the best possible ID3, GB, and RF parameters.

#### 3.2.4. Multilayer Neural Network (MLNN)

_{o}using the MLNN:

- Climate-related input variables were chosen as predictors.
- Sigmoid and linear activation functions were used in the input-hidden and hidden-output layers.
- The weight connection between interconnected neurons was adjusted via the adoption of a back-propagation procedure.
- The kernel functions utilized were Traditional Conjugate Gradient (TCG) and Scaled Conjugate Gradient (SCG).
- The ET
_{o}was estimated as an output.

#### 3.2.5. Radial Basis Function Neural Network (RBFNN)

_{o}.

#### 3.2.6. Selection of Meteorological Input Combinations

_{min}, T

_{max}, RH

_{mean}, Ws, and Sh for ET

_{o}estimation. When M2 is used to estimate ET

_{o}, ML algorithms (ID3, GB, RF, MLNN, and RBFNN) with the RH

_{mean}and Sh variables are considered as inputs. Likewise, Table 3 provides information on the other 15 input combinations (M1 through M17) in the same format as M1 and M2. Previous research evaluated the performance of the ML algorithms using various statistical criteria [40,41,42,43,44,45,46,47,48,49,50]. The ML algorithms’ performance using all 17 input combinations was measured using the statistical indices root-mean-square error (RMSE), determination coefficient (R2), mean absolute error (MAE), mean bias error (MBE), and Nash–Sutcliffe efficiency (NSE).

_{obs}, ET

_{est}, $\overline{{ET}_{obs}\text{}}$, and $\overline{{ET}_{est}}$ are the observed, estimated, average observed, and average estimated ET

_{o}, respectively, and n represents total records.

^{2}is the goodness-of-fit parameter, which may be from 0 to 1. It is a number between −1 and 1 that has no dimensions. A correlation coefficient near 1 indicates a strong association. The MSE calculates the average squared deviation between observed and anticipated values. When comparing errors between experimental and anticipated values, the root-mean-square error (RMSE) is often utilized. Model performance improves when the MSE, RMSE, and NRMSE values decrease. The NSE index is a regularly used goodness of fit statistic to evaluate a model’s effectiveness. The NSE may be measured from −1 to 1. Lower RMSE and MAE values and greater R

^{2}and NSE values indicate a superior model.

## 4. Study Results

^{2}, MAE, and NSE). The 30-year, 360-record dataset was split into training (252 records) and testing sets (108 records). Each ML model’s performance accuracy over all seventeen scenarios was evaluated using the testing set. The training set was utilized for calibration and model development. The ET

_{o}estimated with the PMF was used as the standard for assessment of both decision-based and neural network-based ML algorithms.

_{1}= T

_{min}, T

_{max}, RH

_{mean}, W

_{s}, S

_{h}to M

_{17}= T

_{mean}, W

_{s}) to determine their impact on ET

_{o}prediction. The performance of ET

_{o}prediction was evaluated by adding and removing different meteorological variables. The interpretation of the performances was based on a combination of statistical indicators and graphical approaches. Figure 8 presents the performance evaluation of ML models using bullet charts. The structure of statistical metrics for each model in the training and testing phases is provided. It is worth mentioning that all the ML models created attained high levels of accuracy. Nevertheless, after scrutinizing the NSE and R2 values, it can be deduced that the RBFNN algorithms and the M12 and M13 combinations showed the highest precision. Likewise, examining the RMSE and MAE values, it was concluded that the M12 combination exhibited the lowest error rate and yielded the most precise prediction results using the RBFNN ML algorithms.

^{2}and NSE values. However, the highest prediction for ET

_{o}was achieved using RBFFNN algorithms. When evaluating ML model performances based on RMSE and MAE error metrics, the suitable input combination was found to be M12. Additionally, the model combinations M1, M11, M12, and M13 stand out for their low RMSE and MAE and high accuracy (NSE and R

^{2}) as compared with other input combinations. Furthermore, when the optimal algorithm is considered, the RBFNN algorithm was tested to yield the highest prediction performance. According to this, the optimal model has RMSE values of 0.30 during training and 0.22 during testing. Additionally, the MAE values for this model are 0.15 during training and 0.17 during testing. When examining the R

^{2}and NSE values, they were observed to be 0.98 during the training phase and 0.99 during the testing phase.

_{o}prediction using radar charts. When evaluating the R

^{2}and NSE values, it is observed that the models M1, M5, M6, M7, M11, M12, M13, and M14 exhibit high prediction accuracy, with the RBFNN algorithm achieving the highest accuracy. The GB algorithm is also successful as a second-degree model. On the other hand, the highest error (RMSE and MAE) was obtained with the ID3 algorithm. When performing a performance analysis based on RMSE values to determine the optimal model for ET

_{o}prediction, the RBFNN model emerges as the model with the lowest error. The second-best ML model is identified as GB, followed by GB and ID3. Additionally, analyzing the MAE values reveals that the algorithm with the lowest error is the RBFNN, while the second-best ML model was RF, followed by GB and ID3. Overall, RMSE and MAE obtained the highest in the case of ID3 ML algorithms.

^{2}, NSE) and error (MAE, RMSE) of the applied ML models. The Smith chart is a particular kind of impedance chart that has parallel series of lines. Lines in the first set, called constant resistance lines, display mutual tangency along the right side of the horizontal diameter and form circles. Constant resistance (j) circles are the conventional name for these spherical formations. The values of the resistances represented by the j circles are shown on the horizontal diameter where the circles connect with the line. The circle of positive resistance is shown on the top side of the horizontal line, while the circle of negative resistance is shown on the bottom side of the horizontal line. It is observed in Figure 10 that statistical indices (R

^{2}, NSE, MAE, and RMSE) of the ML models lie on the top side of the horizontal line, which corresponds to the positive value ranging between 0 and 1. In addition, it was noted that the RBFNN approaches 1 for R

^{2}and NSE while MAE and RMSE decline to 0, indicating the superior performance of the RBFNN as compared with other applied ML models.

_{o}estimated with the RBFNN using the M12 input combination (best model) and standardized PMF in the training and testing phases over the studied region. It is clearly observed in Figure 11 that RBNN trailed well with the PMF and could be used in cases of limited climatic input data. In addition, Figure 13 indicates temporal variation in ET

_{o}estimated with the RBFNN and PMF from 1986 to 2016 in the training and testing phases. It can be concluded that the RBFNN algorithms performed well and coincide with the ET

_{o}values of the PMF.

## 5. Study Discussion

_{o}values. Accordingly, the RBFFNN model had the highest accuracy and ID3 showed the weakest prediction success. It was deduced that the Tmean, RHmean, and Ws input variables had the highest effect on ET

_{o}estimation. Pal and Deswal [57] employed the M5 model tree method to model daily ET

_{o}in the climatic data of Davis station, which California maintains. The inputs for the model were solar radiation, average air temperature, average relative humidity, and average wind speed. The M5 model tree model successfully predicted meteorological data and ET

_{o}values, as evidenced by the results of this research. The outputs of this research support the presented study. The study conducted by Vaz et al. [58] employed machine learning and deep neural networks to construct a model for evapotranspiration, utilizing only a limited number of weather variables, including temperature, humidity, and wind. The presented research coincides with this research, as both establish the Random forest algorithm’s potential to provide satisfactory outputs for ET

_{o}estimation. Also, LSTM-ANN recommends a hybrid approach for ET

_{o}estimation. The estimation of ET

_{o}has been predicted by Wang et al. [59] through the utilization of a combination of time granulation computing techniques and gradient boosting decision tree (GBDT) with Bayesian optimization (BO). Subsequently, GBDT is deployed to anticipate evapotranspiration, while BO determines the optimum hyperparameter values from the pared-down granules. The study’s findings align with current research, indicating that the GB algorithm substantiates the sufficiency of ET prediction. The effectiveness of various types of ML algorithms, including tree-based, neural network-based, multifunction-based algorithms, and a combination of ML and physical models, have been investigated in predicting hydrological variables (ET

_{o}, river discharge, precipitation, monitoring droughts) and their related factors [60,61,62,63,64,65,66,67,68,69,70,71,72,73,74]. Wang et al. [59] analyzed temperature data from several different climatic stations located in Pakistan [60]. The TB model produced outperforming results (R

^{2}and NSE = 1.00, MAE and RMSE = 0.26 and 0.37) when an input combination based only on temperatures (T

_{max}and T

_{min}) was used. The study’s outputs support the current study in terms of tree-based algorithms showing high performance in ET

_{o}model estimation. However, ET

_{o}estimation established only with the maximum and minimum temperatures does not overlap in delivering the highest performance.

_{mean}, RH

_{mean}, and Sh were critical indicators of ET

_{0}in our study. The study’s findings supported the assertion made by [75] that increased air moisture content causes relative humidity to have greater impacts in wet locations; as a result, when the aridity index increases, air moisture content is constrained, and its effects are less. Temperature and relative humidity were discovered to be the most important predictors of ET

_{o}in a study conducted by Estévez et al. [76]. Eslamian et al. [77] investigated the effect of weather parameters on ET

_{o}estimation in Esfahan province. The study concluded that T

_{min}, Sh, and RH

_{mean}found effective parameters on ET

_{o}estimation in this region. Similarly, it was observed by [45] that climatic variables related to RH

_{mean}significantly influenced the ML modeling of ET

_{o}. Including RH

_{mean}in ML models increased performance by up to 24%. These earlier observations support our finding in the selection of the best input combination.

_{o}values. ET

_{o}is underrated with more training data, but it is overestimated with less training data. The use of ML models requires a sufficient amount of input data for good calibration. Therefore, in order to test the efficacy of the ML models, the current study evaluated ML models using various set of climatic variables. The data requirements for ET

_{o}estimation using the PMF and ML models are displayed in Table 4. The PMF may be observed in Table 4 to depend on numerous characteristics that are difficult to obtain, especially in the Sindh and Balochistan areas (underdeveloped provinces of Pakistan). As an alternative to the PMF approach, ML models use fewer parameters that yield ET

_{o}-value approaches to the PMF which aid in crop scheduling and irrigation planning. In Table 4, the parameters required for ET

_{o}estimates are denoted by “▀▀”, while “X” denotes that they were not employed in the corresponding method. Sabino and Souza [78] indicated that changes in solar radiation, relative humidity, and wind speed are the main driving forces that impact the ET

_{o}. In addition, RHmean and Ws have higher sensitivity indices during the dry season, which is also affirmed in our study area as it is arid in nature.

## 6. Conclusions

_{o}values at the Jacobabad, Sindh, Pakistan station. It also aims to analyze the effect of various model input combinations on the ET

_{o}prediction. Model performances were evaluated according to Smith chart heatmap, radar chart, and bullet chart results. As a result of the analysis, M2 (RH

_{mean}, Sh), M3 (RH

_{mean}, Sh, Ws), M4 (RH

_{mean}, Ws), M8 (T

_{max}, T

_{min}, RH

_{mean}, Sh), M9 (T

_{mean}, RH

_{mean}, Sh), M15 (T

_{mean}, RH

_{mean}), and M16 (T

_{mean}, Sh) model combinations exhibited lower levels of prediction success compared with the remaining model combinations. When evaluating model performances based on statistical criteria, the most suitable model combination is M12 (T

_{mean}, RH

_{mean}, Ws). In general, satisfactory results have been obtained in the models where WS and T values are used together as inputs for ET

_{o}estimation. The RBFFNN model, which exhibits the most precise estimation results, demonstrates RMSE values of 0.30 during the training phase and 0.22 during the testing phase, according to the findings. In addition, during training and testing, the MAE values for this model are 0.15 and 0.17, respectively. The R

^{2}and NSE value analysis revealed that they were 0.98 and 0.99 in the training and testing phases, respectively. The conducted analyses have provided empirical evidence indicating that the ID3 model demonstrates relatively inferior performance in comparison with alternative models.

#### Limitations, Suggested Improvements, and Future Directions

_{o}ML models can only be used in the research area and only with the available meteorological data. Therefore, it is required to design comparable or innovative ML models using less or similar meteorological data to examine how well the established ML models function in various places. In addition, the present study’s suggested ET

_{o}model must be calibrated and appropriately trained before being used in other locations. Furthermore, ML does not have physical processes, and the user is just aware of the input and the anticipated output of the model. Therefore, developing an appropriate ML model is complex without understanding functional criteria. Because the dataset was divided at random, over-fitting and under-fitting issues may arise during the ML model’s training and calibration.

_{o}models using EM and ELM that consider a more comprehensive range of climate types (from humid to desert) and, if applicable, the impacts of climate change. Since extensive and trustworthy data on ET

_{o}modeling is necessary for successfully planning, managing, and controlling water resource systems, gap-in-filling strategies must be actively pursued. Regional models are critical because they develop local models in regions with little data. Crop water needs (CWRs) may be used to manage crucial data about ground and surface water resource planning and management, regional water use analysis, water allocation, water consumption, and water rights. Water resource planning for seasonal variation (summer, winter, autumn, and spring) can benefit from estimating ET

_{o}in different months for determining CWRs. While this study focused on arid climates, future research should include other climate types to examine climatic variability in greater depth.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Map indicating the location of Jacobabad District (highlighted in red) within the Sindh province of Pakistan.

**Figure 2.**(

**a**) Monthly variations in climatic and ET

_{o}variables obtained from JMO, RMC, Karachi. (

**b**) Interannual variations in climatic and ET

_{o}variables obtained from JMO, RMC, Karachi.

**Figure 10.**The identification of the best AI model for the implementation of a radar chart (MAE, RMSE, and MBE unit: mm/day).

**Figure 11.**The determination of the best AI model through the use of a Smith graph (MAE, RMSE, and MBE unit: mm/day).

**Figure 12.**Comparison of ET

_{o}estimated with RBFNN using M12 input combination (best model) and standardized PMF.

**Figure 13.**Temporal variation in ET

_{o}estimated with RBFNN and PMF from 1986 to 2016 in training and testing phases.

**Table 1.**Summary of 30 years (1987–2016) of climatic data obtained from Jacobabad weather station installed by the RMC.

Variables | T_{min} | T_{max} | RH_{mean} | Ws | Sh |
---|---|---|---|---|---|

°C | °C | % | m/s | h | |

Mean | 20.33 | 34.23 | 38.10 | 1.29 | 7.79 |

Standard Error | 0.42 | 0.38 | 0.63 | 0.04 | 0.03 |

Median | 21.50 | 35.90 | 37.00 | 1.24 | 7.70 |

Mode | 29.10 | 25.70 | 33.00 | 1.11 | 7.30 |

Standard Deviation | 7.96 | 7.23 | 11.88 | 0.67 | 0.59 |

Sample Variance | 63.35 | 52.25 | 141.21 | 0.45 | 0.35 |

Kurtosis | −1.39 | −1.10 | −0.52 | −0.40 | −1.65 |

Skewness | −0.30 | −0.21 | 0.22 | 0.28 | 0.10 |

Range | 25.80 | 27.20 | 62.00 | 3.15 | 1.60 |

Minimum | 5.20 | 20.10 | 11.00 | 0.00 | 7.00 |

Maximum | 31.00 | 47.30 | 73.00 | 3.15 | 8.60 |

Sum | 7318.30 | 12,322.20 | 13,717.00 | 465.89 | 2805.00 |

Count | 360.00 | 360.00 | 360.00 | 360.00 | 360.00 |

Decision-Based ML Algorithm | Parametric Variables | ||
---|---|---|---|

Tree Numbers | Splitter | Node Size | |

Iterative Dichotomizer (ID3) | 12 | 22 | 04 |

Gradient Boosting (GB) | 14 | 26 | 06 |

Random Forest (RF) | 18 | 29 | 08 |

Input Combination | Symbol |
---|---|

T_{min}, T_{max}, RH_{mean}, Ws, Sh | M1 |

RH_{mean}, Sh | M2 |

RH_{mean}, Sh, Ws | M3 |

RH_{mean}, Ws | M4 |

T_{max},T_{min}, Sh, Ws | M5 |

T_{max}, RH_{mean}, Sh, Ws | M6 |

T_{max}, RH_{mean}, Ws | M7 |

T_{max}, T_{min}, RH_{mean}, Sh | M8 |

T_{mean}, RH_{mean}, Sh | M9 |

T_{min}, RH_{mean}, Ws | M10 |

T_{min}, RH_{mean}, Sh, Ws | M11 |

T_{mean}, RH_{mean}, Ws | M12 |

T_{max}, T_{min}, RH_{mean}, Ws | M13 |

T_{mean}, RH_{mean}, N, Ws | M14 |

T_{mean}, RH_{mean} | M15 |

T_{mean}, Sh | M16 |

T_{mean}, Ws | M17 |

_{min}, minimum temperature; T

_{max}, maximum temperature; RH

_{mean}, mean relative humidity; Ws, wind speed; Sh, sunshine hours.

Chosen Method | Climatic Variables | Aerodynamic Factors | |||||||
---|---|---|---|---|---|---|---|---|---|

T_{min} | T_{max} | T_{mean} | RH_{min} | RH_{max} | RH_{mean} | Ws | Sh | R_{n}, e_{s}, e_{a}, e_{min}, e _{max}, Δ, G, and Ɣ | |

PMF | ▀▀ | ▀▀ | ▀▀ | ▀▀ | ▀▀ | ▀▀ | ▀▀ | ▀▀ | ▀▀ |

ML models | X | X | ▀▀ | X | X | ▀▀ | ▀▀ | X | X |

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**MDPI and ACS Style**

Raza, A.; Fahmeed, R.; Syed, N.R.; Katipoğlu, O.M.; Zubair, M.; Alshehri, F.; Elbeltagi, A.
Performance Evaluation of Five Machine Learning Algorithms for Estimating Reference Evapotranspiration in an Arid Climate. *Water* **2023**, *15*, 3822.
https://doi.org/10.3390/w15213822

**AMA Style**

Raza A, Fahmeed R, Syed NR, Katipoğlu OM, Zubair M, Alshehri F, Elbeltagi A.
Performance Evaluation of Five Machine Learning Algorithms for Estimating Reference Evapotranspiration in an Arid Climate. *Water*. 2023; 15(21):3822.
https://doi.org/10.3390/w15213822

**Chicago/Turabian Style**

Raza, Ali, Romana Fahmeed, Neyha Rubab Syed, Okan Mert Katipoğlu, Muhammad Zubair, Fahad Alshehri, and Ahmed Elbeltagi.
2023. "Performance Evaluation of Five Machine Learning Algorithms for Estimating Reference Evapotranspiration in an Arid Climate" *Water* 15, no. 21: 3822.
https://doi.org/10.3390/w15213822