Predicting reference evapotranspiration in semi-arid-region by regression- based machine learning methods using limited climatic inputs

doi:10.21203/rs.3.rs-2600302/v1

Accurately estimation of evapotranspiration is very essential for water resources planning and management projects. In this study, different regression-based machine learning techniques including support vector machine (SVM), random forest (RF), Bagged trees algorithm (BaT) and Boosting trees algorithm (BoT) were adopted in order to model daily reference evapotranspiration (ET₀) for semi-arid region. Five stations in Hemren catchment basin located at the North-East part of Iraq were selected as case study. Several climatic parameters including solar radiation (SR), wind speed (Us), relative humidity (RH), and maximum and minimum air temperatures (Tmax and Tmin) of 35 years (1979–2014) period were used as inputs to the models. Assessment of the methods with various input combinations indicated that the RF method especially with Tmax, Tmin, Tmean & SR inputs provided the best accuracy in estimating daily ET₀ in all stations. It was followed by the BaT and BoT methods while the SVM had the worst accuracy. In some cases, 1st input scenario (Tmax, Tmin, Tmean, SR, WS and RH) provided slightly better accuracy than the 2nd input scenario (Tmax, Tmin, Tmean & SR).

Evapotranspiration

Machine learning

Prediction

Climatic inputs

Hemren catchment

Evapotranspiration is an important factor in hydrological cycle and it is used in water resources management for irrigation (Trezza 2006; Calera et al. 2017; French et al. 2018), in drought estimation and monitoring (Velpuri et al. 2013; Senay et al. 2015; Anderson et al. 2016; Su et al. 2016), and in estimation of crop production (Doorenbos et al. 1980; Khan et al. 2019). Evapotranspiration (ET) could be defined as the amount of water that is transferred from the earth surface to the atmosphere and it plays a significant role in the world ecosystem that is related to water, energy and carbon cycles (Sellers et al. 1997; Trenberth et al. 2007; Wang and Dickinson 2012). ET is affected by different factors including precipitation, temperature, relative humidity, wind speed and solar radiation (Granata 2019). In addition, there is a common consent that the terrestrial ET around the world has been changed as a result of climate change and human activity in the last decades (Jung et al. 2010; Douville et al. 2012; Zeng et al. 2012, 2014; Mueller et al. 2013; Al-Janabi et al. 2019). Therefore, in order to calculate the terrestrial ET, it is necessary to recognize the roles of water management, hydrological cycle and impact of climate change (Kustas and Anderson 2009; Petropoulos et al. 2016; Fisher et al. 2017; He et al. 2020b).

Reference evapotranspiration (ET₀) can be estimated using different methods and approaches including statistical or empirical methods, remote sensing methods and physical model-based methods (Jung et al. 2010). In the first method, the ET₀ is estimate using flux tower observations (Wang et al. 2010; Jung et al. 2011; Xu et al. 2018) while in the second method, the ET₀ is calculated using the integration of remote sensing data with the experimental observations (Wang and Liang 2008; Jia et al. 2009; Zhu et al. 2017; Zhao et al. 2020), surface energy balance equation (Miralles et al. 2011; Ma et al. 2018), Penman–Monteith or Priestley–Taylor equation (Bateni et al. 2013b; Yao et al. 2015; Zhang et al. 2016), and data assimilation methods (Bateni et al. 2013a; Xu et al. 2014; Carrera et al. 2015; Lu et al. 2017; He et al. 2018, 2019, 2020a). In the third method, the ET₀ is estimated using physical model alone or integrated it with data simulation algorithms (Xu et al. 2011; Long et al. 2014; Xia et al. 2019; Zhang et al. 2020). Although several studies have used these methods globally, but the daily estimation of the ET₀ using these methods came with some uncertainty (Kalma et al. 2008). Relative variation between the observed and estimated values was found to range from 14–44% (Velpuri et al. 2013; Yao et al. 2013; Anapalli et al. 2016). On the other hand, lysimeters provide more precise measurement of ET values and many researchers estimated the ET by employing the measurements of lysimeters (Stanhill 2005; Liu et al. 2017). Unfortunately, use of lysimeters has some drawbacks such as the cost of installation and maintenance environmental impacts. Additionally, the restricted amount of lysimeters is impeded the observation of ET at specific locations (Chen et al. 2012). Based on above, the development of new adequate methods to estimate the reference evapotranspiration (ET₀) with more accurate and low cost is important and necessary.

In the last decades, use of machine learning (ML) has received more attention in the field of water resources management and specifically for ET₀ estimation around the world. ML was applied to estimate the parameters of hydrology (Ebtehaj et al. 2021; Yaseen et al. 2021; Malik et al. 2021; Sihag et al. 2021b; Sammen et al. 2021; Hashim et al. 2022), hydraulic (Sammen et al. 2020; Sihag et al. 2021a; Alomari et al. 2023) and water quality by many researchers (Yaseen et al. 2021; Ehteram et al. 2021; Abba et al. 2021). Several previous researches have reported the capability of ML techniques in estimating ET₀ (Yang et al. 2006). Ladlani et al. (Ladlani et al. 2012) presented a comparative study using two ML techniques, namely, RBF and GRNN in addition to empirical methods for ET₀ estimation in Algeria. They concluded that the GRNN is better than the RBF for ET₀ estimation. Wen et al. (Wen et al. 2015) developed a support vector machine (SVM) model for ET₀ estimation using limited climatic data. They used different parameters such as maximum and minimum temperature, wind speed and solar radiation with several input combinations. The results acknowledged that the SVM is useful to be used for ET₀ estimation with acceptable accuracy. Vassilis and Athanasios (Antonopoulos and Antonopoulos 2017) compared artificial neural network (ANN) with the empirical approaches to estimate the ET₀ using the daily meterological data. They used two types of ANN with three empirical approaches that include Priestley-Taylor, Makkink, Hargreaves and mass transfer.

Muhammad Adnan et al. (Adnan et al. 2017) used different machine learning techniques for ET₀ estimation with more actual and precise limited meteorological variables. Their results generalized the relation between the various meteorological parameters. Moreover, the performance of ten ML techniques were evaluated by (Carter and Liang 2019). They used three statistical indices which include RMSE, R² and bias to evaluate the modeling results. Atilla and Sevim (Atilla Özgür and Yamaç 2020) developed the deep neural network (DNN) model for ET₀ estimation using four meteorological stations in Turkey. In their study, the results of DNN were compared with results of ANN. The study revealed that the output of DNN was more accurate compared to ANN. Wu et al. (Wu et al. 2019) evaluated eight ML techniques to estimate the ET₀ using temperature data only. Additionally, they compared their results with Hargreaves–Samani equation (a temperature-based equation). They concluded that the accuracy of the developed models was varied with various scenarios. Wu et al. (Wu et al. 2020) developed five machine learning models to predict daily ET₀ across ten meteorological stations in China. Results of comparison showed that the CAT model outperformed the other models.

In this research, 35 models were constructed with different climate variables and evaluated by employing four regression-based ML techniques, namely, Random Forest (RF), Support Vector Machine (SVM), Bagged trees algorithm (BaT) and Boosting trees algorithm (BoT). The daily climate data during the period 1979–2014 were collected from the study area and used for models’ development. To the best of the authors’ knowledge, these regression-based ML methods have not been previously compared in estimating ET₀ in semi-arid region.

2.1 Support Vector Machine

Support Vector Machine is a widely used technique that applied in many real-world applications (Bárcenas et al. 2022). The theoretical basis for classification method of SVM is similar to that for Support Vector Regression (SVR), with slight changes. The general structure of the SVR model is presented in Fig. 1.

The application of SVM aims to minimize error and increase the limit of tolerance by taking into consideration that the portion of error is tolerated. Moreover, SVM identifies the function (x) to be in the flattest form, about to be a linear function (Fig. 2). In the figure, w and b represent the dot products in x, while ℇ represents the maximum deviation value from the observed target values. The ξ, and ξ^* represent the slack variables which are ≥ 0, C represents a constant that has an effect on the function of flatness and tolerated variations. From the figure, errors less than ε can be ignored, while the effect of deviations is considered.

2.2 Decision Trees

Decision tree learning is a supervised learning approach that used to solve both classification and regression problems. The model is able to forecast the target value based on independent inputs. In a decision tree each decision node in the tree represents a test on some input variables. Some techniques were used in this study, often called ensemble methods, which is consists of more than one decision tree as shown in Figs. 3 and 4. As indicated by (Friedman 2002; Elith et al. 2008) Boosted tree model incorporates important advantages of tree-based methods and has an unique features. Its performance is based on an ensemble for training new samples. Ada-Boost is the typical model of Decision Tree which is suited the regression-type. Another type of decision trees is Bootstrap aggregated (also known as bagged). It is an early ensemble method, which has numerous trees designed to improve the stability and accuracy of models. The random forest regression can be considered as a specified type of the Bootstrap model. Figure 4 shows that the algorithms are different for the way regression trees are built.

In each stage, the system has two subdivisions as unconnected segments to reduce the quared deviation values, as follows:

$$R\left(t\right)=\frac{1}{N \left(t\right)}\sum _{i\in t}{(yi-ym\left(t\right))}^{2}$$

2

Where N (t) represents the number of sample groups in (t), yi is the value taken by target variables in i unit, while ym equals the average of target variable in (t).

2.3 Evaluation of Models Performance

The most important step in using machine learning models is to evaluate the accuracy of the models. Performance evaluation of the four soft computing models was conducted based on regression analysis using four statistical indices, namely, mean absolute error (MAE), root mean square error (RMSE), mean square error (MSE) and coefficient of determination (R²).

Hemren Basin, a large catchment area located in the north-eastern of Iraq within Diyala governorate, extends between (33° 53΄ 13.00˝ to 35° 25΄ 41.61˝ Northern latitude) and (44° 30΄ 47.68˝ to 45° 48΄ 39.59˝ Eastern longitude) inside Iraqi land, and it is located about (120 km) in the northeastern of Baghdad capital city in Iraq (Fig. 5).

The catchment area of Diyala River is at the east border of Iraq towards Iran. The north part of it (within Iran) is mostly mountainous character, with about 3000 m heights. The relief of study area is characterized with topographic difference, their elevation ranges vary from 225 to 900 m above M.S.L. Therefore, the area is divided into three main regions. The length of Diyala River within the catchment area is about 150 km, with average gradient of 1 m per kilometer. While ALwand river, which is the main tributary on the left side of Diyala River, has a gradient of 2 m /km. It drains an area of (3974 km²), and after eliminating the part of Iranian land, area will become (1974 km²). Narin River, which is the largest tributary on the right side, has a small gradient with a catchment area of (2344 km²), and empties into the Diyala River near Hemren Mountain. Moreover, the downstream part of the catchment area, located between Derbendi Khan and Hemren, has lower altitudes and gradients. Different meteorological stations were used in the catchment area. Table 1 shows the statistical properties of the meteorological stations used in this study.

In the present study, the capability of four regression-based machine learning methods, SVM, RF, BoT and BaT were investigated for ET₀ estimation. Several input scenarios including T_max, T_min, T_mean, SR, WS & RH climatic variables were used as model inputs and data in daily scale were collected from five stations, Qarah-Tapah, Mandali, Kalar, Iran-Iraq Border and Adhim stations, Iraq. Utilized input scenarios for daily ET₀ estimation are presented in Table 2. Scenario M1 uses full variables as inputs while M7 has only two variables T_mean& SR.

Table 3 sums up the performance metrics of the employed methods in estimating daily ET₀ of Qarah-Tapah Station. RF method has the R², MSE, RMSE and MAE ranges from 0.86 (RF-5) to 1 (RF-1), from 0.05 (RF-2) to 0.414 (RF-5), from 0.074 (RF-2) to 0.643 (RF-5) and from 0.055 (RF-2) to 0.487 (RF-5), respectively while the ranges of the corresponding metrics for SVM are from 0.87 (SVM-5) to 0.97, from 0.077 (SVM-1) to 0.367 (SVM-5), from 0.28 (SVM-1) to 0.606 (SVM-5) and from 0.23 (SVM-1) to 0.488 (SVM-5), for BoT and BaT, the ranges are from 0.90 (BoT-5) to 0.99, from 0.029 to 0.297 (BoT-5), from 0.172 to 0.545 (BoT-5), from 0.135 to 0.439 (BoT-5) and from 0.90 (BaT-5) to 1 (BaT-2), from 0.008 (BaT-2) to 0.297 (BaT-5), from 0.091 (BaT-2) to 0.545 (BaT-5), from 0.052 (BaT-2) to 0.428 (BaT-5), respectively. It is evident from the metrics’ ranges; the RF method is generally more successful in estimating daily ET₀ of Qarah-Tapah Station. According to the RF method, there is a small difference between the 1^st and 2^nd scenarios and the 2^nd one produces the best accuracy. The other methods behave differently, for example, 1^st and 2^nd input combinations provide same accuracy for the BoT method. M1 scenario has slightly better accuracy than the M2 for the SVM method while the 1^st scenario performs worse compared to latter and for the BaT. This difference can be explained by the different working principles of the four methods implemented. The best estimates belong to the RF method and it is followed by the BaT methods while the SVM generally produces the worst ET₀ estimates.

Table 4 reports the test performances of the RF, SVM, BoT and BaT methods in estimating ET₀ of Mandali Station. Here also the RF-2 model has the lowest MSE (0.024), RMSE (0.156) and MAE (0.059) followed by the RF-1 and BaT-2 models. SVM produces the worst estimates similar to the previous station. The models’ ranks from the best to worst are RF-2 > RF-1 > RF-3 > RF-7 > RF-4 > RF-6 > RF-5; SVM-1 > SVM-2 > SVM-3 > SVM-7 > SVM-4 > SVM-6 > SVM-5; BoT-1 > BoT-2 > BoT-3 > BoT-7 > BoT-4 > BoT-6 > BoT-5 and BaT-2 > BaT-1 > BaT-7 > BaT-4 > BaT-3 > BaT-6 > BaT-5. From this, we can say that 1^st or 2^nd input scenarios inlcuding T_max, T_min, T_mean, SR, WS & RH and T_max, T_min, T_mean & SR variables generally provide the best estimates while the 5^th scenario involving RH, WS & T_max gives the worst ET₀ estimates. The main reason of this might be the fact that the SR input is very effective on ET₀ and not involved in this combination (5^th) and involving WS parameter may worsen the estimation accuracy. Adding some input variables may negatively affect the variance and cause worse model accuracy in machine learning modeling. Here, adding WS might deteriorate the model performance as this can be observed from the 1^st and 2^nd input cases.

Test performances of the implemented four methods in estimating ET_o of Kalar Station are reported in Table 5. Parallel to the Qarah-Tapah and Mandali stations, RF-2 model provides the best performance with the lowest MSE (0.022), RMSE (0.148) and MAE (0.056) and the highest R² (0.998) followed by the RF-1 and BaT-2 models. In this station, the BaT and BoT are ranked 2^nd and 3^rd places while the SVM was the least accurate model. The ranks of the models with respect to different input scenarios are RF-2 > RF-1 > RF-3 > RF-7 > RF-4 > RF-6 > RF-5; SVM-1 > SVM-2 > SVM-3 > SVM-7 > SVM-4 > SVM-6 > SVM-5; BoT-2 > BoT-1 > BoT-3 > BoT-7 > BoT-4 > BoT-6 > BoT-5 and BaT-2 > BaT-1 > BaT-7 > BaT-4 > BaT-3 > BaT-6 > BaT-5. Here also clearly seen that the 1^st and 2^nd scenarios produce the best estimates whereas the 5^th scenario has the worst results.

Table 6 gives the performance metrics of the four methods in the test period of Iraq-Iran Border Station. In this station also the RF-2 is ranked in the 1^st place by providing the lowest MSE (0.020), RMSE (0.143) and MAE (0.055) and the highest R² (0.998) followed by the RF-1 and BaT-2 models. Here also the BoT and BaT also perform superior to the SVM method. The accuracy ranks of the implemented models are RF-2 > RF-1 > RF-3 > RF-7 > RF-4 > RF-6 > RF-5; SVM-1 > SVM-2 > SVM-3 > SVM-7 > SVM-4 > SVM-6 > SVM-5; BoT-1 > BoT-2 > BoT-3 > BoT-7 > BoT-4 > BoT-6 > BoT-5 and BaT-2 > BaT-1 > BaT-7 > BaT-4 > BaT-3 > BaT-6 > BaT-5. Here also the 5^th scenario provides the worst results while the 1^st and 2^nd input scenarios have the best ET_o estimates. The performance measures of the RF, SVM, BoT and BaT methods in estimation of Adhim Station are presented in Table 7. Here also the RF-2 model has the lowest MSE (0.006), RMSE (0.078) and MAE (0.058) followed by the RF-1 and BaT-2 models. SVM generally produces the worst estimates while the BaT and BoT methods follow the RF in accuracy for estimating daily ET_o. The models has the accuracy ranks are RF-2 > RF-1 > RF-3 > RF-7 > RF-4 > RF-6 > RF-5; SVM-1 > SVM-2 > SVM-3 > SVM-7 > SVM-4 > SVM-6 > SVM-5; BoT-1 > BoT-2 > BoT-3 > BoT-7 > BoT-4 > BoT-6 > BoT-5 and BaT-2 > BaT-4 > BaT-1 > BaT-7 > BaT-3 > BaT-6 > BaT-5. Here also the models including the 1^st and/or 2^nd scenarios perform the best while the models with 5^th combination has the worst results in all methods. In this station, the BoT-1 has better accuracy than the BoT-2, however, this difference is marginal.

Overall, the RF method especially with the T_max, T_min, T_mean & SR inputs provides the best accuracy in estimating daily ET_o of all stations. Its accuracy is followed by the BaT and BoT methods while the SVM has the worst accuracy. In most of the cases, 2^nd input scenario provides the best accuracy in estimating daily ET₀. It is also worth to say that the 7^th input scenario having only T_mean and SR inputs perform superior to the 4^th, 5^th and 6^th input scenarios.

Figures 6 and 7 illustrate the time variation and scatter plots of the best model (RF-2) estimates. It is clear from Figure 1 that the ET_o estimates by the RF-2 are closely following the observed values. As clearly seen from Figure 2 that the fit line of the RF-2 overlaps the ideal line (1:1 line) and it has high correlation for all stations. All these results highly recommend the RF method in estimating daily ET₀.

By this study, the applicability of four different regression-based machine learning methods in estimating ET₀ was investigated. Climatic data from five stations located in semi-arid region of Iraq was used as inputs to the models. According to the comparison statistics (R², MSE, RMSE and MAE) and graphical inspection, the random forest model offered the best ET₀ estimates in all stations while the SVM provided the accuracy. Employing various combinations of climatic inputs revealed that the models with Tmax, Tmin, Tmean & SR inputs produced the best estimations. The best random forest model with Tmax, Tmin, Tmean & SR improved the estimation accuracy of corresponding SVM, BoT and BaT models by 94%, 83% and 38% for Qarah-Tapah, by 68%, 50% and 8% for Mandali, by 73%, 49% and 8% for Kalar, by 72%, 51% and 9% for Iran-Iraq Border and by 93%, 81% and 73% for Adhim with respect to RMSE in the test period, respectively. The outcomes of the study recommend the random forest in estimating ET₀ in semi-arid region. The study used data from one region and more data can be used to assess the regression-based machine learning methods in future studies. The regression-based methods considered in this study may be compared with more complex machine learning methods.

Authors' contributions

Conceptualization: Saad Sh. Sammen, Ahmed Al-Janabi, Ozgur Kisi and Ahmed Elbeltagi; Data creation: Ozgur Kisi and Saad Sh. Sammen; Formal analysis: Ozgur Kisi and Saad Sh. Sammen; Investigation: Ozgur Kisi, Ahmed Al-Janabi; Methodology: Saad Sh. Sammen, Ahmed Al-Janabi and Ahmed Elbeltagi; Software: Saad Sh. Sammen and Ozgur Kisi; Validation: Saad Sh. Sammen and Ozgur Kisi; Writing – original draft: Ozgur Kisi, Ahmed Al-Janabi and Saad Sh. Sammen; Writing – review & editing, all authors.

Funding:

This research received no external funding.

Competing Interests:

The authors declare that they have no competing interests.

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Table 1 Details of some meteorological stations used in this study

Station Name	Station Location		Temperature (ºC)		Relative Humidity (%)		Solar Radiation (MJ/m²)		Wind Speed (m/sec)
Station Name	Lon.	Lat.	Max.	Min.	Max.	Min.	Max.	Min.	Max.	Min.
Mandali	45.31	33.88	51.18	-8.76	96	3.2	32.2	0.81	12.7	0.7
Kalar	45.31	34.50	50.31	-4.69	98	3.5	32.65	0.3	10.25	0.72
Iraq - Iran Borders	45.63	34.19	48.82	-11.67	96.6	3.62	33.28	0.56	11.13	0.63
Adhim	44.68	34.18	52.23	-3.45	99	3.7	32.05	0.3	10.82	0.66

Table 2 Different input combination used for daily ET_o estimation at study stations

Code	Inputs	Technique
Code	Inputs	RF	SVM	BoT	BaT
M1	T_max, T_min, T_mean, SR, WS & RH	×	×	×	×
M2	T_max, T_min, T_mean & SR	×	×	×	×
M3	T_mean, SR & WS	×	×	×	×
M4	SR, WS, RH & T_min	×	×	×	×
M5	RH, WS & T_max	×	×	×	×
M6	T_max, RH & T_min	×	×	×	×
M7	T_mean& SR	×	×	×	×

Table 3 The effectiveness of the applied models in daily ET_o estimation at Qarah-Tapah station during testing period

Model	ML algorithm	Performance metric
Model	ML algorithm	R²	MSE (mm/month)²	RMSE (mm/month)	MAE (mm/month)
M1	RF-1	1.00	0.006	0.077	0.061
	SVM-1	0.97	0.077	0.280	0.230
	BoT-1	0.99	0.029	0.172	0.135
	BaT-1	0.99	0.019	0.141	0.085
M2	RF-2	0.998	0.005	0.074	0.055
	SVM-2	0.97	0.086	0.293	0.239
	BoT-2	0.99	0.029	0.172	0.135
	BaT-2	1.00	0.008	0.091	0.052
M3	RF-3	0.99	0.029	0.170	0.125
	SVM-3	0.97	0.089	0.299	0.241
	BoT-3	0.98	0.044	0.211	0.161
	BaT-3	0.98	0.053	0.229	0.163
M4	RF-4	0.99	0.043	0.208	0.149
	SVM-4	0.96	0.105	0.325	0.258
	BoT-4	0.98	0.054	0.232	0.174
	BaT-4	0.99	0.029	0.171	0.122
M5	RF-5	0.86	0.414	0.643	0.487
	SVM-5	0.87	0.367	0.606	0.488
	BoT-5	0.90	0.297	0.545	0.439
	BaT-5	0.90	0.297	0.545	0.428
M6	RF-6	0.90	0.288	0.536	0.395
	SVM-6	0.91	0.267	0.516	0.421
	BoT-6	0.92	0.241	0.490	0.398
	BaT-6	0.92	0.229	0.478	0.372
M7	RF-7	0.99	0.031	0.176	0.129
	SVM-7	0.97	0.092	0.303	0.245
	BoT-7	0.98	0.045	0.212	0.161
	BaT-7	0.99	0.026	0.162	0.119

Table 4 The effectiveness of the applied models in daily ET_o estimation at Mandali station during testing period

Model	ML algorithm	Performance metric
Model	ML algorithm	R²	MSE (mm/month)²	RMSE (mm/month)	MAE (mm/month)
M1	RF-1	0.99	0.025	0.157	0.067
	SVM-1	0.98	0.065	0.255	0.206
	BoT-1	0.98	0.048	0.220	0.146
	BaT-1	0.99	0.036	0.189	0.090
M2	RF-2	0.998	0.024	0.156	0.059
	SVM-2	0.97	0.075	0.274	0.223
	BoT-2	0.98	0.048	0.220	0.146
	BaT-2	0.99	0.026	0.161	0.066
M3	RF-3	0.98	0.056	0.237	0.150
	SVM-3	0.97	0.088	0.296	0.237
	BoT-3	0.98	0.069	0.263	0.180
	BaT-3	0.97	0.077	0.278	0.181
M4	RF-4	0.97	0.074	0.272	0.176
	SVM-4	0.96	0.109	0.330	0.262
	BoT-4	0.97	0.080	0.283	0.195
	BaT-4	0.98	0.055	0.236	0.147
M5	RF-5	0.85	0.425	0.652	0.492
	SVM-5	0.87	0.360	0.600	0.481
	BoT-5	0.89	0.310	0.556	0.442
	BaT-5	0.89	0.309	0.556	0.431
M6	RF-6	0.89	0.316	0.562	0.414
	SVM-6	0.90	0.263	0.513	0.418
	BoT-6	0.91	0.259	0.509	0.406
	BaT-6	0.91	0.250	0.500	0.385
M7	RF-7	0.98	0.063	0.251	0.162
	SVM-7	0.97	0.093	0.304	0.244
	BoT-7	0.97	0.071	0.266	0.182
	BaT-7	0.98	0.054	0.234	0.148

Table 5 The effectiveness of the applied models in daily ET_o estimation at Kalar station during testing period

Model	ML algorithm	Performance metric
Model	ML algorithm	R²	MSE (mm/month)²	RMSE (mm/month)	MAE (mm/month)
M1	RF-1	0.99	0.022	0.149	0.062
	SVM-1	0.97	0.071	0.268	0.216
	BoT-1	0.98	0.044	0.210	0.138
	BaT-1	0.99	0.034	0.186	0.087
M2	RF-2	0.998	0.022	0.148	0.056
	SVM-2	0.97	0.080	0.284	0.231
	BoT-2	0.98	0.043	0.209	0.137
	BaT-2	0.99	0.024	0.155	0.060
M3	RF-3	0.98	0.046	0.215	0.132
	SVM-3	0.97	0.087	0.029	0.238
	BoT-3	0.98	0.058	0.242	0.162
	BaT-3	0.98	0.069	0.263	0.169
M4	RF-4	0.98	0.061	0.248	0.157
	SVM-4	0.96	0.104	0.322	0.257
	BoT-4	0.97	0.069	0.263	0.178
	BaT-4	0.98	0.047	0.217	0.131
M5	RF-5	0.85	0.412	0.641	0.484
	SVM-5	0.88	0.343	0.586	0.476
	BoT-5	0.89	0.302	0.549	0.439
	BaT-5	0.89	0.300	0.548	0.429
M6	RF-6	0.90	0.288	0.536	0.390
	SVM-6	0.91	0.243	0.493	0.403
	BoT-6	0.91	0.244	0.494	0.395
	BaT-6	0.91	0.230	0.480	0.368
M7	RF-7	0.98	0.047	0.217	0.134
	SVM-7	0.97	0.089	0.299	0.242
	BoT-7	0.98	0.058	0.242	0.163
	BaT-7	0.98	0.042	0.206	0.124

Table 6 The effectiveness of the applied models in daily ET_o estimation at Iraq-Iran Borders during testing period

Model	ML algorithm	Performance metric
Model	ML algorithm	R²	MSE (mm/month)²	RMSE (mm/month)	MAE (mm/month)
M1	RF-1	0.99	0.021	0.145	0.062
	SVM-1	0.97	0.064	0.253	0.204
	BoT-1	0.98	0.041	0.203	0.133
	BaT-1	0.99	0.032	0.178	0.084
M2	RF-2	0.998	0.020	0.143	0.055
	SVM-2	0.97	0.071	0.266	0.216
	BoT-2	0.98	0.041	0.203	0.133
	BaT-2	0.99	0.022	0.151	0.059
M3	RF-3	0.98	0.042	0.205	0.125
	SVM-3	0.97	0.078	0.279	0.225
	BoT-3	0.98	0.055	0.237	0.157
	BaT-3	0.98	0.060	0.246	0.156
M4	RF-4	0.98	0.058	0.241	0.154
	SVM-4	0.96	0.093	0.306	0.242
	BoT-4	0.97	0.067	0.259	0.175
	BaT-4	0.98	0.045	0.213	0.130
M5	RF-5	0.84	0.401	0.633	0.478
	SVM-5	0.87	0.329	0.574	0.466
	BoT-5	0.88	0.287	0.536	0.427
	BaT-5	0.88	0.286	0.534	0.418
M6	RF-6	0.89	0.264	0.514	0.375
	SVM-6	0.91	0.230	0.480	0.390
	BoT-6	0.91	0.228	0.477	0.383
	BaT-6	0.91	0.217	0.466	0.358
M7	RF-7	0.98	0.045	0.213	0.132
	SVM-7	0.97	0.080	0.283	0.228
	BoT-7	0.98	0.056	0.237	0.158
	BaT-7	0.98	0.041	0.202	0.121

Table 7 The effectiveness of the applied models in daily ET_o estimation at Adhim station during testing period

Model	ML algorithm	Performance metric
Model	ML algorithm	R²	MSE (mm/month)²	RMSE (mm/month)	MAE (mm/month)
M1	RF-1	1.00	0.006	0.082	0.061
	SVM-1	0.97	0.075	0.275	0.222
	BoT-1	0.99	0.031	0.178	0.140
	BaT-1	0.99	0.033	0.184	0.093
M2	RF-2	0.998	0.006	0.078	0.058
	SVM-2	0.97	0.082	0.287	0.234
	BoT-2	0.99	0.032	0.179	0.140
	BaT-2	0.99	0.022	0.148	0.059
M3	RF-3	0.99	0.034	0.185	0.134
	SVM-3	0.97	0.086	0.294	0.234
	BoT-3	0.98	0.053	0.231	0.173
	BaT-3	0.98	0.068	0.261	0.173
M4	RF-4	0.98	0.047	0.218	0.156
	SVM-4	0.97	0.103	0.321	0.253
	BoT-4	0.98	0.058	0.241	0.182
	BaT-4	0.99	0.031	0.177	0.127
M5	RF-5	0.86	0.405	0.636	0.481
	SVM-5	0.88	0.367	0.606	0.485
	BoT-5	0.90	0.296	0.544	0.434
	BaT-5	0.90	0.292	0.541	0.422
M6	RF-6	0.89	0.319	0.565	0.415
	SVM-6	0.90	0.301	0.548	0.443
	BoT-6	0.91	0.253	0.503	0.404
	BaT-6	0.92	0.243	0.493	0.381
M7	RF-7	0.98	0.044	0.211	0.152
	SVM-7	0.97	0.090	0.300	0.239
	BoT-7	0.98	0.057	0.239	0.178
	BaT-7	0.98	0.491	0.221	0.143

No competing interests reported.

Predicting reference evapotranspiration in semi-arid-region by regression- based machine learning methods using limited climatic inputs

Status:

Version 1

Abstract

Figures

1. Introduction

2. Machine Learning Models

2.1 Support Vector Machine

2.2 Decision Trees

2.3 Evaluation of Models Performance

3. Description Of Study Area

4. Results And Discussion

5. Conclusion

Declarations

References

Tables

Additional Declarations

Status:

Version 1