# Predictive Modelling of Reference Evapotranspiration Using Machine Learning Models Coupled with Grey Wolf Optimizer

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## Abstract

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_{0}) values, which is considered a standard method. Hence, predicting ET

_{0}is vital in allocating and managing available resources. In this study, different machine learning (ML) algorithms, namely random forests (RF), extreme gradient boosting (XGB), and light gradient boosting (LGB), were optimized using the naturally inspired grey wolf optimizer (GWO) viz. GWORF, GWOXGB, and GWOLGB. The daily meteorological data of 10 locations falling under humid and sub-humid regions of India for different cross-validation stages were employed, using eighteen input scenarios. Besides, different empirical models were also compared with the ML models. The hybrid ML models were found superior in accurately predicting at all the stations than the conventional and empirical models. The reduction in the root mean square error (RMSE) from 0.919 to 0.812 mm/day in the humid region and 1.253 mm/day to 1.154 mm/day in the sub-humid region was seen in the least accurate model using the hyperparameter tuning. The RF models have improved their accuracies substantially using the GWO optimizer than LGB and XGB models.

## 1. Introduction

_{0}) is a reliable and standard practice. ET

_{0}is a parameter that could be employed for all the regions based on the local climatic parameters [3]. The estimation of models is classified as (a) fully physically-based combination models that employ mass and energy conservation principles; (b) semi-physically based models that consider either mass or energy conservation; and (3) black-box models that are empirical in nature [4,5]. Many researchers have formulated empirical and semi-empirical methods to estimate the ET

_{0,}like mass transfer based [6,7,8], radiation based [9,10,11,12,13,14], temperature based [15,16,17], and combination based [18,19]. Some empirical equations might require extensive agro-meteorological data, which are unavailable for every region. Therefore, there is a scope for models with less data requirement [20].

_{0}is a phenomenon that depends on various meteorological parameters that give rise to a complex non-linear problem. Henceforth, machine learning (ML) models have been extensively used in their estimation which could solve these complex problems [21]. The previous studies available have been discussed below. Various data-driven algorithms like random forests (RF) [22,23,24,25,26,27], gradient boosting decision tree (GBDT), extreme gradient boosting (XGB) [24,27,28], light gradient boosting (LGB) [27,29,30,31], etc. have been employed for ET

_{0}estimation. Most of the research did not confine to a single algorithm. However, a comparison is made either with different machine learning techniques or empirical models. Shiri et al. [22] evaluated 12 different machine learning algorithms like multivariate adaptive regression spline (MARS), boosted regression tree (BT), random forest (RF), model tree (MT), support vector machine (SVM), etc., with other optimizers for stations in Iran using 12-year meteorological data. They have compared two input scenarios, i.e., radiation and temperature based. A study in Brazil [32] used the machine learning models like RF, XGB, artificial neural network (ANN), and convolutional neural network (CNN) models for daily and hourly ET

_{0}estimates. Zhou et al. [27] have used the agro-meteorological data from twelve stations in China for ET

_{0}prediction. They have tested the algorithms like extremely randomized trees, RF, and GBDT, and gradient boosting models like XGB, LGB, and gradient boosting with categorical features support (CatBoost), factorization machine-based neural network model (DeepFM), and SVM. They have concluded that the CatBoost and LGB models outperformed the other models, followed by XGB and GBDT.

_{0}models in New Mexico, United States of America, using extreme learning machine (ELM), genetic programming (GP), RF, and SVM for different climates, was done by [33]. The results of their study indicated that the models performed in the order of SVM > ELM > RF > GP. Another study used 14 stations in different climates, i.e., arid desert, semi-arid steppe, semi-humid cold-temperate, semi-humid warm temperate, humid subtropical, and humid tropical regions in China for ET

_{0}prediction [30]. They have evaluated multi-layer perceptron (MLP), generalized neural network (GRNN) and adaptive neuro-fuzzy inference system (ANFIS), SVM, kernel-based non-linear extension of arps decline (KNEA), M5 model tree (M5Tree), XGB and MARS models and suggested the use of SVM over other models. Wu et al. [34] compared the basic models like RF, SVM, MLP, and K-Nearest Neighbor (KNN) regression and their stacked and blended ensemble models using data from five stations in China.

_{0}modelling. These research findings have revealed an improvement in accuracy over conventional ML models. Yan et al. [35] evaluated the performance of hybrid XGB coupled with whale optimization algorithm (WOA) for ET

_{0}modelling at humid and arid stations in China. They concluded that hybrid models had improved the accuracies in both local and external data scenarios. Grey wolf optimizer (GWO) has been employed with ANN by [36] for modelling purposes in Iran. The results were compared with least square support vector regression (LS-SVR) and conventional ANN. They found that the hybrid models were superior in their prediction. Dong et al. [37] attempted to use four types of bio-inspired optimizers with the kernel-based non-linear extension of arps decline (KNEA) model for 51 stations in China. The optimizers they employed were the grasshopper optimization algorithm (GOA), GWO, particle swarm optimization algorithm (PSO), and salp swarm algorithm (SSA). They reported that the GWO-optimized KNEA performed better than other models.

_{0}using state-of-the-art machine learning models like RF, XGB, and LGB for humid and sub-humid climates of India; (2) to couple these models with a heuristic GWO technique for finding any improvement in the efficiency and (3) to compare various empirical models with the ML models in the study area.

## 2. Materials and Methods

#### 2.1. Study Area and Data Collection

#### 2.2. ET_{0} Estimaton Using FAO-56 Penman-Monteith and Empirical Equations

_{0}. They found that the FAO 56 Penman-Monteith can be used in all locations. Hence, the standardised equation of reference evapotranspiration is used as the target variable in the modelling stages. The equation for predicting ET

_{0}by FAO 56 Penman-Monteith is given below. The machine learning models were compared with different empirical equations. The estimation of ET

_{0}using different empirical equations using the formulae as described in Table 2.

#### 2.3. Description of Machine Learning Models and Optimizer

#### 2.3.1. Random Forest (RF)

#### 2.3.2. Extreme Gradient Boosting Model (XGB)

#### 2.3.3. Light Gradient Boosting Model (LGB)

#### 2.3.4. Grey Wolf Optimizer (GWO)

#### 2.4. ET_{0} Estimaton Using ML and Hybrid ML

#### 2.4.1. Input Scenarios

_{0}. The inputs consisted of maximum air temperature (T

_{max}, °C), minimum air temperature (T

_{min}, °C), mean relative humidity (RH, %), wind speed at 2 m height (u

_{2}, m/s), number of sunshine hours (n, hours), solar radiation (R

_{n}, MJ/m

^{2}day) and extra-terrestrial radiation (R

_{a}, MJ/m

^{2}day).

_{0}calculated from the FAO-56 Penman-Monteith equation. The statistical indicators of the inputs and output at various stations are presented in Figure S1. The time series graphs of ET

_{0}from some stations of the study on a daily basis from 2001 to 2020 were shown in Figure S2 (Supplementary Materials).

#### 2.4.2. Model Development

_{norm}is the normalised value of the input, x

_{0}is the actual value of the input that is being normalised, and x

_{max}and x

_{min}are the maximum and minimum values of all the inputs.

#### 2.4.3. Hyper Parameter Tuning in Hybrid ML

#### 2.5. Model Performance Indicators

^{2}), mean absolute error (MAE) [27], and agreement index (d) [59]. The formulae for these indicators are described in Table 6.

#### Global Performance Indicator (GPI)

^{2}, MAE, d, were normalized between 0 and 1 using Equation (22), and the value of GPI for a model is found using Equation (23). Higher values of GPI would give the best model compared to other models [60,61].

_{j}is the normalized statistical index, S

_{j}is the original statistical index, min(S) is the minimum value in that statistical index, and max(S) is the maximum value in that statistical index.

_{i}is the value of the Global Performance Indicator for model i, S

_{j}is the median value of the statistical indicator j, S

_{ij}is the value of the statistical indicator j for model i, α

_{j}is a constant with a value of −1 for R

^{2}, d and 1 for MAE, RMSE. The ranking based on the GPI value was also done.

## 3. Results

#### 3.1. Comparison of the Empirical Models in Estimating ET_{0}

#### 3.2. Comparison of Various Input Combinations in Conventional ML Models

#### 3.2.1. Best-Performing Models in ML

^{2}value has improved with higher inputs, and LGB models were more accurate than other models. A substantial increase in the accuracy and reduced errors was observed in model indices 8 and 9 across all the stations. The ranking of the eighteen best models (six models in each ML) at humid locations based on the GPI is shown in Table 9. The results indicated that the models that used the most inputs (Index 17 and 18) were superior with higher GPI. The LGB17 and LGB18 performed best in Palampur and Thrissur, whereas the XGB17 was the best at Jorhat and Mohanpur. It was observed that the XGB8 and LGB8, which used wind speed and solar radiation data, performed better in all the stations except Palampur, where the LGB7, RF7, and XGB7 gave accurate estimates. Overall, the performance of RF was found to be inferior to both XGB and LGB. The lowest error (RMSE = 0.096 mm/day) was found using XGB17 at Mohanpur station and, the highest R

^{2}value (0.994) was observed at Palampur and Thrissur for LGB18 and at Mohanpur for LGB17.

^{2}= 0.995), whereas the least RMSE (0.094 mm/day) was recorded at Ranichauri for LGB17.

#### 3.2.2. Least-Performing Models in ML

_{0}. The RF models had the lowest GPI values compared to other models’ counterparts at most stations, indicating their higher errors. It was observed that the LGB models performed better than other ML models using the same input combinations. The error was found to be highest (RMSE = 0.919 mm/day) at Thrissur using RF1, whereas the least R

^{2}(0.371) was seen at Jorhat for RF1. The model combination that used extra-terrestrial radiation, i.e., model indices 10 and 11, did not yield accurate results.

^{2}(0.631) was reported at Samastipur with the same set of ML model.

#### 3.3. Empirical Models v/s Conventional ML Models

#### 3.4. Comparison of Various Input Combinations in GWO Hybrid ML Models

#### 3.4.1. Best-Performing Models in Hybrid ML

^{2}of 0.997.

^{2}was found to be the highest (0.997) at Jabalpur for both GWOLGB18 and GWOLGB17. The overall performance of the hybrid models is in the order of GWOXGB > GWOLGB > GWORF at most stations.

#### 3.4.2. Least Performing Models in Hybrid ML

^{2}(0.478) was observed at Jorhat stations with the same model combination.

^{2}was found to be the least at Samastipur station, with a value of 0.693. The RF models have got the advantage of improving their efficiency by the hyperparameter tuning by GWO than the XGB and LGB models.

#### 3.5. Best-Performing Models across Conventional and Hybrid MLs

^{2}at different locations in the humid region are shown in Figure 4 and Figure 5, respectively. The results indicate that the hybrid models outperformed their conventional ML counterparts in most of the combinations. The models that used the six inputs were the superior, followed by the models with indices 7, 8, 9, 16, and 12. The accuracy of the XGB and LGB models was higher than RF models at almost all stations. The use of solar radiation could be attributed to the excellent performance of models 7, 8, and 9 than the other models that have employed more inputs.

^{2}at different locations in the humid region are shown in Figure 6 and Figure 7, respectively. The observed results at the sub-humid locations were in good resonance with that of the humid locations. The models with indices 17, 18, and 16 were also predicting with greater accuracy at these locations. The solar radiation data used in models 7, 8, and 9 were also ranked best in comparison. The application of GWO has improved the accuracy of the ML models in all the combinations at all stations. The higher GPI values were observed in LGB and XGB when compared with the RF models using a similar set of inputs.

#### 3.6. Least-Performing Models across Conventional and Hybrid MLs

## 4. Discussion

_{0}. The comparison between the conventional ML models based on the performance indicators showed that the XGB and LGB models showed similar accuracies. [30] have also indicated that both of these models exhibited the same model efficacy. The boosting methods were to be a potential tool for humid regions according to [65]. RF models were found to be less accurate than the other boosting models, as reported in [24,29].

## 5. Conclusions

_{0}modelling capabilities of tree-based ML like RF, XGB, and LGB in addition to the GWO-optimized tree-based ML for ten locations in humid and sub-humid regions across India. The daily data from 2001 to 2020 of agro-meteorological parameters like maximum temperature, minimum temperature, wind speed, relative humidity, number of sunshine hours, solar radiation and extra-terrestrial radiation were employed for modelling purposes. The FAO-56 Penman-Monteith was used as the target value. Different input combinations were tested at all the stations using a cross-validation strategy. The comparison of the empirical equations was also made for the ML that used the same input combinations. The ranking of the models based on GPI value for comparison at each level was considered. The conclusions that could be drawn from the study are below.

- The LGB and XGB models outperformed the RF models, while all the ML models were found to be more accurate than empirical models.
- Among the empirical methods investigated in the study, the Turc model was determined to have the greatest performance with higher GPI values.
- Solar radiation was adjudged to be an important parameter that could improve the prediction capability.
- The GWO hybrid ML models had the highest prediction efficiencies at all the locations, with RF models improving considerably well.
- The study consolidated the fact that the use of optimizers would substantially reduce the modelling error.
- Further studies could be done using cross-station data and other optimizers to improve the accuracy.

## Supplementary Materials

_{0}(mm/day) at humid (Jorhat, Thrissur) and sub-humid (Raipur, Samastipur) stations; Table S1. Performance indicators of empirical models at humid stations; Table S2. Performance indicators of empirical models at sub-humid stations; Table S3. Performance indicators of conventional ML models at Jorhat; Table S4. Performance indicators of conventional ML models at Mohanpur; Table S5. Performance indicators of conventional ML models at Palampur; Table S6. Performance indicators of conventional ML models at Thrissur; Table S7. Performance indicators of conventional ML models at Faizabad; Table S8. Performance indicators of conventional ML models at Jabalpur; Table S9. Performance indicators of conventional ML models at Raipur; Table S10. Performance indicators of conventional ML models at Ranchi; Table S11. Performance indicators of conventional ML models at Ranichauri; Table S12. Performance indicators of conventional ML models at Samastipur; Table S13. Best hyper parameters in RF models at humid stations; Table S14. Best hyper parameters in XGB models at humid stations; Table S15. Best hyper parameters in LGB models at humid stations; Table S16. Best hyper parameters in RF models at sub-humid stations; Table S17. Best hyper parameters in XGB models at sub-humid stations; Table S18. Best hyper parameters in LGB models at sub-humid stations; Table S19. Performance indicators of hybrid ML models at Jorhat; Table S20. Performance indicators of hybrid ML models at Mohanpur; Table S21. Performance indicators of hybrid ML models at Palampur; Table S22. Performance indicators of hybrid ML models at Thrissur; Table S23. Performance indicators of hybrid ML models at Faizabad; Table S24. Performance indicators of hybrid ML models at Jabalpur; Table S25. Performance indicators of hybrid ML models at Raipur; Table S26. Performance indicators of hybrid ML models at Ranchi; Table S27. Performance indicators of hybrid ML models at Ranichauri; Table S28. Performance indicators of hybrid ML models at Samastipur.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Schematic diagram of GWO optimizers (Source: [56]).

**Figure 4.**RMSE (mm/day) at humid locations of all ML models at (

**a**) Jorhat, and Mohanpur; (

**b**) Palampur, and Thrissur.

**Figure 5.**R

^{2}values at humid locations of all ML models at (

**a**) Jorhat, and Mohanpur; (

**b**) Palampur, and Thrissur.

**Figure 6.**RMSE (mm/day) at sub-humid locations of all ML models at (

**a**) Faizabad, and Jabalpur; (

**b**) Raipur, and Ranchi; (

**c**) Ranichauri, and Samastipur.

**Figure 7.**R

^{2}values at sub-humid locations of all ML models at (

**a**) Faizabad, and Jabalpur; (

**b**) Raipur, and Ranchi; (

**c**) Ranichauri, and Samastipur.

S. No. | State | Station | Code | AER | Latitude (N) | Longitude (E) | Altitude (m) |
---|---|---|---|---|---|---|---|

1 | Assam | Jorhat | JHT | Humid | 26°45′ | 94°12′ | 116 |

2 | West Bengal | Mohanpur | MHP | Humid | 21°50′ | 87°15′ | 17 |

3 | Himachal Pradesh | Palampur | PLP | Humid | 32°07′ | 76°32′ | 1220 |

4 | Kerala | Thrissur | TRS | Humid | 10°31′ | 76°13′ | 28 |

5 | Uttar Pradesh | Faizabad | FZB | Sub-humid | 26°46′ | 82°08′ | 97 |

6 | Madhya Pradesh | Jabalpur | JBP | Sub-humid | 23°11′ | 79°59′ | 412 |

7 | Chattisgarh | Raipur | RPR | Sub-humid | 21°15′ | 81°37′ | 290 |

8 | Jharkhand | Ranchi | RNI | Sub-humid | 23°20′ | 85°18′ | 651 |

9 | Uttarakhand | Ranichauri | RCH | Sub-humid | 30°19′ | 78°24′ | 1800 |

10 | Bihar | Samastipur | SMP | Sub-humid | 25°59′ | 85°40′ | 51 |

Method | Symbol and Equations | Reference | |
---|---|---|---|

Target for the Models | |||

FAO-56 Penman-Monteith | ${\mathrm{ET}}_{\mathrm{PM}}=\frac{0.408\u2206\left({R}_{n}-G\right)+\gamma \frac{900}{{T}_{mean}+273}{u}_{2}\left({e}_{s}-{e}_{a}\right)}{\u2206+\gamma \left(1+0.34{u}_{2}\right)}$ | (1) | [40] |

Mass Transfer based | |||

Albrecht (ALB) | ET_{ALB} = $F\left({e}_{s}-{e}_{a}\right)$ where $F=0.4if{u}_{2}\ge 1m/sandF=0.1005+0.297{u}_{2},if{u}_{2}1m/s$ | (2) | [6] |

Mahringer (MAH) | ${\mathrm{ET}}_{\mathrm{MAH}}=0.15072\sqrt{3.6{u}_{2}}\left({e}_{s}-{e}_{a}\right),$ where$\left({e}_{s}-{e}_{a}\right)inhPa$ | (3) | [7] |

Penman (PEN) | ${\mathrm{ET}}_{\mathrm{PEN}}=0.35\left(1+\frac{0.98}{100{u}_{2}}\right)\left({e}_{s}-{e}_{a}\right),$ where$\left({e}_{s}-{e}_{a}\right)inmmHgand{u}_{2}inmilesperday$ | (4) | [8,41] |

Radiation based | |||

Jensen-Haise (JH) | ${\mathrm{ET}}_{\mathrm{JH}}=\left(\frac{{R}_{s}}{\lambda}\right)\left(0.025{T}_{mean}+0.08\right)$ | (5) | [11,42] |

Makkink (MAK) | ${\mathrm{ET}}_{\mathrm{MAK}}=0.61\left(\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\gamma}\right)\left(\frac{{R}_{s}}{\lambda}\right)-0.12$ | (6) | [43] |

McGuinness-Bordne (MGB) | ${\mathrm{ET}}_{\mathrm{MGB}}=\left(\frac{{R}_{a}}{\lambda \rho}\right)\left(\frac{{T}_{mean}+5}{68}\right)$ | (7) | [12] |

Priestly-Taylor (PT) | ${\mathrm{ET}}_{\mathrm{PT}}=1.26\left(\frac{\mathsf{\Delta}}{\mathsf{\Delta}+\gamma}\right)\left(\frac{{R}_{n}}{\lambda}\right)$ | (8) | [13] |

Turc (TUR) | $\begin{array}{c}{\mathrm{ET}}_{\mathrm{TUR}}=0.013\left(\frac{{T}_{mean}}{{T}_{mean}+15}\right)(23.8846{R}_{s}+50),forRH50\%\mathrm{=}0.013\left(\frac{{T}_{mean}}{{T}_{mean}+15}\right)(23.8846{R}_{s}+\\ 50)(1+\frac{50-RH}{70}),forRH50\%\end{array}$ | (9) | [14] |

Temperature based | |||

Hargreaves-Samani (HS) | ${\mathrm{ET}}_{\mathrm{H}-\mathrm{S}}=0.0026\sqrt{{T}_{max}-{T}_{min}}\left({T}_{mean}+17.8\right)\left(0.408{R}_{a}\right)$ | (10) | [16] |

Hargreaves-Samani 1 (HS1) | ${\mathrm{ET}}_{\mathrm{HS}1}=0.0030{({T}_{max}-{T}_{min})}^{0.4}\left({T}_{mean}+20\right)\left(0.408{R}_{a}\right)$ | (11) | [17] |

Hargreaves-Samani 2 (HS2) | ${\mathrm{ET}}_{\mathrm{HS}2}=0.0025\sqrt{{T}_{max}-{T}_{min}}\left({T}_{mean}+16.8\right)\left(0.408{R}_{a}\right)$ | (12) | [17] |

Thorththwaite (Modified) (THO) | ${\mathrm{ET}}_{\mathrm{THO}}=0.533\frac{N}{12}{\left(\frac{10{T}_{mean}}{33.617}\right)}^{1.033}$ | (13) | [44] |

Combination based | |||

Copais (COP) | $\begin{array}{c}{\mathrm{ET}}_{\mathrm{COP}}=0.057+0.277\left(-0.0033+0.00812{T}_{mean}+0.101{R}_{s}+0.00584{R}_{s}{T}_{mean}\right)+\\ 0.643\left(0.6416-0.00784RH+0.372{R}_{s}-0.00364RH\right)+0.0124(0.6416-0.00784RH+\\ 0.372{R}_{s}-0.00364RH)\left(-0.0033+0.00812{T}_{mean}+0.101{R}_{s}+0.00584{R}_{s}{T}_{mean}\right)\end{array}$ | (14) | [18] |

Valiantzas 1 (VA1) | ET_{VA1} = $0.0393{R}_{s}\sqrt{{T}_{mean}+9.5}-0.19{R}_{s}{}^{0.6}{\phi}^{0.15}+0.078\left({T}_{mean}+20\right)\left(1-\frac{RH}{100}\right)$ | (15) | [19] |

Valiantzas 2 (VA2) | ET_{VA2} = $0.0393{R}_{s}\sqrt{{T}_{mean}+9.5}-0.19{R}_{s}{}^{0.6}{\phi}^{0.15}+0.0061\left({T}_{mean}+20\right){\left(1.12{T}_{mean}-{T}_{min}-2\right)}^{0.7}$ | (16) | [19] |

_{n}is the net radiation at the crop surface in MJ/ m

^{2}day, G is the soil heat flux density in MJ/ m

^{2}day, γ is the psychrometric constant in kPa/°C, e

_{s}is the saturation vapour pressure, kPa; e

_{a}is the actual vapour pressure, kPa; u

_{2}is the wind speed at 2 m above the ground surface, m/s; T

_{mean}is the mean daily air temperature,°C; R

_{n}is the net solar radiation, MJ/m

^{2}day; R

_{s}is the incident shortwave solar radiation flux, MJ/m

^{2}/day; R

_{a}is the extra-terrestrial solar radiation, MJ/m

^{2}day; T

_{max}is the maximum daily air temperature, °C; T

_{min}is the minimum daily air temperature, °C; N is the maximum possible duration, hrs; RH is the mean daily relative humidity, %; and φ is latitude, Radians.

Model Index | Input Combinations | Model Index | Input Combinations |
---|---|---|---|

1 | T_{max}, T_{min} | 10 | T_{max}, T_{min}, RH, R_{a} |

2 | T_{max}, T_{min}, RH | 11 | T_{max}, T_{min}, U_{2}, R_{a} |

3 | T_{max}, T_{min}, U_{2} | 12 | T_{max}, T_{min}, n, R_{a} |

4 | T_{max}, T_{min}, n | 13 | T_{max}, T_{min}, RH, U_{2} |

5 | T_{max}, T_{min}, R_{s} | 14 | T_{max}, T_{min}, RH, n |

6 | T_{max}, T_{min}, R_{a} | 15 | T_{max}, T_{min}, U_{2}, n |

7 | T_{max}, T_{min}, RH, R_{s} | 16 | T_{max}, T_{min}, RH, U_{2}, n |

8 | T_{max}, T_{min}, U_{2}, R_{s} | 17 | T_{max}, T_{min}, RH, U_{2}, n, R_{s} |

9 | T_{max}, T_{min}, n, R_{s} | 18 | T_{max}, T_{min}, RH, U_{2}, n, R_{a} |

Cross-Validation | Training | Testing |
---|---|---|

V1 | 2005–2020 | 2001–2004 |

V2 | 2001–2004 and 2009–2020 | 2005–2008 |

V3 | 2001–2008 and 2013–2020 | 2009–2012 |

V4 | 2001–2012 and 2017–2020 | 2013–2016 |

V5 | 2001–2016 | 2017–2020 |

Model | Parameter | Default Value | Hyperparameter Range for Tuning |
---|---|---|---|

RF | n_estimators | 100 | Range of 10 to 500, increment by 10 |

min_samples_leaf | 1 | Range of 1 to 6, increment by 2 | |

max_depth | None | Range of 2 to 20, increment by 2 and None | |

XGB | n_estimators | 100 | Range of 10 to 500, increment by 10 |

learning_rate | 0.3 | [0.05, 0.1, 0.15, 0.3] | |

max_depth | 6 | Range of 2 to 20, increment by 2 and None | |

LGB | n_estimators | 100 | Range of 10 to 500, increment by 10 |

learning_rate | 0.3 | [0.05, 0.1, 0.15, 0.3] | |

max_depth | 6 | Range of 2 to 20, increment by 2 and None |

Indicator | Code | Formula | |
---|---|---|---|

Root mean square error | RMSE | $\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left({O}_{i}-{P}_{i}\right)}^{2}}{N}}$ | (18) |

Coefficient of determination | R^{2} | ${\left(\frac{{{\displaystyle \sum}}_{i=1}^{N}\left\{\left({O}_{i}-{\overline{O}}_{i}\right)\left({P}_{i}-{P}_{i}\right)\right\}}{\sqrt{{{\displaystyle \sum}}_{i=1}^{N}{\left({O}_{i}-{O}_{i}\right)}^{2}{{\displaystyle \sum}}_{i=1}^{N}{\left({P}_{i}-{\overline{P}}_{i}\right)}^{2}}}\right)}^{2}$ | (19) |

Mean absolute error | MAE | $\frac{{{\displaystyle \sum}}_{i=1}^{N}\left|\left({P}_{i}-{O}_{i}\right)\right|}{N}$ | (20) |

Agreement index | d | $1-\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left({P}_{i}-{O}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{N}{\left(|{P}_{i}-{\overline{O}}_{i}|+|{O}_{i}-{\overline{O}}_{i}|\right)}^{2}}$ | (21) |

_{i}and P

_{i}are the actual ET

_{0}by FAO 56 Penman-Monteith and predicted values of the models, respectively.

Jorhat | Mohanpur | Palampur | Thrissur | |||||
---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

1 | TUR | 1.467 | MAK | 1.521 | TUR | 1.423 | TUR | 1.439 |

2 | PT | 1.390 | TUR | 1.508 | VA2 | 1.292 | VA2 | 1.305 |

3 | MAK | 1.276 | PT | 1.330 | JH | 0.863 | PT | 0.818 |

4 | VA2 | 1.216 | VA2 | 1.027 | HS | 0.783 | MAK | 0.769 |

5 | JH | 0.550 | VA1 | 0.813 | PT | 0.721 | PEN | 0.372 |

6 | VA1 | 0.484 | HS | 0.361 | HS2 | 0.663 | JH | 0.154 |

7 | HS | −0.265 | HS2 | 0.082 | MAK | 0.613 | ALB | 0.034 |

8 | ALB | −0.302 | HS1 | 0.052 | HS1 | 0.467 | HS | 0.028 |

9 | COP | −0.370 | THO | 0.032 | THO | −0.233 | MAH | −0.084 |

10 | HS2 | −0.488 | JH | −0.092 | MAH | −0.516 | HS2 | −0.111 |

11 | HS1 | −0.552 | COP | −0.812 | PEN | −0.517 | COP | −0.171 |

12 | THO | −0.579 | ALB | −1.033 | ALB | −0.586 | HS1 | −0.351 |

13 | PEN | −0.782 | PEN | −1.173 | COP | −1.071 | VA1 | −0.727 |

14 | MAH | −0.807 | MAH | −1.687 | MGB | −1.323 | THO | −0.917 |

15 | MGB | −2.238 | MGB | −1.927 | VA1 | −2.577 | MGB | −2.559 |

Faizabad | Jabalpur | Raipur | Ranchi | Ranichauri | Samastipur | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

1 | TUR | 1.037 | TUR | 1.234 | TUR | 1.117 | TUR | 1.587 | VA2 | 1.487 | TUR | 1.037 |

2 | JH | 0.882 | VA2 | 1.014 | VA2 | 0.969 | PT | 1.510 | TUR | 1.468 | JH | 0.882 |

3 | VA2 | 0.840 | PT | 0.887 | HS | 0.894 | VA2 | 1.294 | MAK | 1.258 | VA2 | 0.840 |

4 | HS | 0.642 | HS | 0.686 | PT | 0.784 | MAK | 1.122 | JH | 1.048 | HS | 0.642 |

5 | HS1 | 0.520 | JH | 0.646 | HS1 | 0.722 | JH | 0.347 | PT | 0.932 | HS1 | 0.520 |

6 | PT | 0.517 | HS1 | 0.487 | HS2 | 0.705 | HS | 0.311 | HS | 0.875 | PT | 0.517 |

7 | HS2 | 0.500 | THO | 0.444 | JH | 0.556 | THO | 0.262 | HS2 | 0.762 | HS2 | 0.500 |

8 | THO | 0.390 | HS2 | 0.440 | THO | 0.414 | HS1 | −0.059 | HS1 | 0.544 | THO | 0.390 |

9 | COP | 0.119 | MAK | 0.377 | MAK | 0.171 | HS2 | −0.065 | THO | −0.279 | COP | 0.119 |

10 | PEN | 0.050 | PEN | −0.150 | PEN | −0.131 | ALB | −0.643 | ALB | −1.032 | PEN | 0.050 |

11 | MAK | −0.007 | COP | −0.554 | COP | −0.386 | PEN | −0.661 | MGB | −1.038 | MAK | −0.007 |

12 | MGB | −0.737 | MAH | −0.883 | MAH | −1.053 | MAH | −0.729 | MAH | −1.230 | MGB | −0.737 |

13 | MAH | −1.148 | MGB | −1.016 | MGB | −1.106 | VA1 | −0.744 | VA1 | −1.552 | MAH | −1.148 |

14 | ALB | −1.212 | ALB | −1.501 | ALB | −1.523 | COP | −1.493 | COP | −1.567 | ALB | −1.212 |

15 | VA1 | −2.392 | VA1 | −2.110 | VA1 | −2.131 | MGB | −2.041 | PEN | −1.675 | VA1 | −2.392 |

Jorhat | Mohanpur | Palampur | Thrissur | |||||
---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

1 | XGB17 | 1.889 | XGB17 | 1.941 | LGB18 | 1.952 | LGB18 | 1.199 |

2 | XGB18 | 1.753 | LGB17 | 1.939 | LGB17 | 1.893 | LGB17 | 1.187 |

3 | LGB17 | 1.717 | LGB18 | 1.721 | XGB18 | 1.777 | XGB17 | 1.159 |

4 | LGB18 | 1.716 | XGB18 | 1.691 | XGB17 | 1.755 | XGB18 | 1.118 |

5 | RF17 | 0.795 | RF17 | 1.424 | RF18 | 1.658 | RF17 | 0.911 |

6 | XGB8 | 0.748 | RF18 | 1.286 | RF17 | 1.501 | RF18 | 0.769 |

7 | LGB8 | 0.721 | LGB8 | 0.853 | LGB7 | −0.063 | LGB16 | 0.224 |

8 | RF18 | 0.582 | XGB8 | 0.702 | RF7 | −0.146 | LGB8 | 0.130 |

9 | RF8 | 0.309 | RF9 | 0.607 | XGB7 | −0.258 | XGB16 | 0.077 |

10 | RF9 | 0.304 | RF8 | 0.598 | LGB16 | −0.337 | XGB8 | 0.067 |

11 | LGB12 | −0.699 | LGB9 | −1.208 | RF16 | −0.527 | RF16 | −0.008 |

12 | LGB9 | −0.726 | LGB12 | −1.369 | XGB16 | −0.628 | RF8 | −0.010 |

13 | RF12 | −1.040 | RF12 | −1.439 | LGB8 | −1.070 | RF9 | −0.017 |

14 | XGB9 | −1.231 | LGB7 | −1.546 | RF8 | −1.191 | LGB15 | −0.413 |

15 | XGB12 | −1.321 | XGB9 | −1.619 | RF9 | −1.212 | RF15 | −0.536 |

16 | LGB7 | −1.633 | RF7 | −1.712 | XGB8 | −1.373 | XGB15 | −0.558 |

17 | RF7 | −1.806 | XGB12 | −1.815 | LGB12 | −1.684 | LGB7 | −2.499 |

18 | XGB7 | −2.079 | XGB7 | −2.053 | XGB12 | −2.048 | XGB7 | −2.801 |

Faizabad | Jabalpur | Raipur | Ranchi | Ranichauri | Samastipur | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

1 | LGB17 | 1.752 | LGB18 | 1.265 | LGB18 | 1.265 | LGB17 | 1.637 | LGB17 | 2.374 | LGB17 | 1.908 |

2 | LGB18 | 1.682 | LGB17 | 1.222 | LGB17 | 1.248 | XGB17 | 1.593 | LGB18 | 2.303 | LGB18 | 1.821 |

3 | XGB17 | 1.630 | XGB18 | 1.138 | XGB18 | 1.197 | LGB18 | 1.566 | XGB17 | 2.207 | XGB17 | 1.761 |

4 | XGB18 | 1.561 | XGB17 | 1.137 | XGB17 | 1.191 | XGB18 | 1.546 | XGB18 | 2.034 | XGB18 | 1.583 |

5 | RF17 | 1.373 | RF17 | 0.993 | RF17 | 1.036 | RF17 | 1.147 | RF18 | 1.693 | RF17 | 1.397 |

6 | RF18 | 1.321 | RF18 | 0.965 | RF18 | 0.973 | RF18 | 1.065 | RF17 | 1.531 | RF18 | 1.041 |

7 | LGB16 | 0.162 | LGB16 | 0.347 | LGB16 | 0.473 | LGB8 | 0.463 | LGB7 | 0.216 | LGB8 | 0.282 |

8 | XGB16 | −0.027 | XGB16 | 0.195 | XGB16 | 0.323 | RF8 | 0.321 | RF7 | −0.005 | RF9 | 0.135 |

9 | LGB8 | −0.125 | RF16 | 0.112 | RF16 | 0.247 | RF9 | 0.304 | XGB7 | −0.071 | RF8 | 0.128 |

10 | RF9 | −0.156 | LGB8 | 0.079 | LGB8 | −0.070 | XGB8 | 0.281 | LGB9 | −1.159 | XGB8 | 0.037 |

11 | RF8 | −0.195 | RF8 | 0.016 | RF9 | −0.131 | LGB16 | −0.394 | LGB8 | −1.164 | LGB16 | −0.586 |

12 | RF16 | −0.289 | RF9 | 0.015 | RF8 | −0.140 | XGB16 | −0.601 | LGB12 | −1.237 | RF16 | −0.746 |

13 | XGB8 | −0.298 | XGB8 | −0.076 | XGB8 | −0.193 | RF16 | −0.749 | RF9 | −1.358 | XGB16 | −0.888 |

14 | LGB15 | −1.194 | LGB15 | −0.608 | LGB15 | −0.607 | LGB15 | −1.136 | RF8 | −1.388 | LGB7 | −1.211 |

15 | XGB15 | −1.460 | RF15 | −0.769 | RF15 | −0.771 | RF15 | −1.357 | RF12 | −1.416 | RF7 | −1.354 |

16 | RF15 | −1.520 | XGB15 | −0.845 | XGB15 | −0.851 | XGB15 | −1.361 | XGB9 | −1.459 | XGB7 | −1.502 |

17 | LGB13 | −1.970 | LGB13 | −2.450 | LGB13 | −2.455 | LGB12 | −1.962 | XGB8 | −1.474 | LGB15 | −1.713 |

18 | XGB13 | −2.248 | XGB13 | −2.735 | XGB13 | −2.735 | XGB12 | −2.363 | XGB12 | −1.626 | XGB12 | −2.092 |

Jorhat | Mohanpur | Palampur | Thrissur | |||||
---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

54 | RF1 | −2.139 | RF1 | −2.503 | RF1 | −2.748 | RF1 | −2.429 |

53 | XGB1 | −1.541 | XGB1 | −1.401 | XGB1 | −2.185 | XGB1 | −1.862 |

52 | LGB1 | −1.099 | RF2 | −1.098 | LGB1 | −1.766 | LGB1 | −1.542 |

51 | RF3 | −0.885 | XGB2 | −0.907 | RF3 | −0.781 | RF6 | −1.450 |

50 | XGB3 | −0.743 | LGB1 | −0.789 | XGB3 | −0.390 | XGB6 | −1.296 |

49 | XGB6 | −0.458 | RF3 | −0.404 | RF6 | −0.249 | LGB6 | −1.054 |

48 | LGB3 | −0.405 | LGB2 | −0.208 | XGB6 | −0.071 | RF2 | −0.006 |

47 | RF6 | −0.403 | XGB3 | −0.142 | LGB3 | −0.042 | XGB2 | 0.111 |

46 | XGB11 | −0.036 | RF6 | 0.032 | LGB6 | 0.410 | XGB10 | 0.332 |

45 | RF11 | −0.028 | XGB6 | 0.117 | RF4 | 0.497 | LGB2 | 0.334 |

44 | LGB6 | 0.029 | XGB13 | 0.513 | RF2 | 0.607 | RF10 | 0.362 |

43 | LGB11 | 0.198 | LGB3 | 0.533 | XGB4 | 0.704 | LGB10 | 0.569 |

42 | RF2 | 0.649 | RF13 | 0.728 | XGB11 | 0.733 | RF3 | 1.111 |

41 | XGB2 | 0.682 | LGB6 | 0.813 | XGB2 | 0.807 | XGB3 | 1.130 |

40 | LGB2 | 1.076 | XGB10 | 0.884 | RF11 | 0.976 | LGB3 | 1.335 |

39 | XGB10 | 1.532 | RF10 | 1.141 | LGB4 | 1.110 | XGB13 | 1.372 |

38 | RF10 | 1.709 | LGB13 | 1.192 | LGB11 | 1.190 | RF5 | 1.413 |

37 | LGB10 | 1.861 | LGB10 | 1.497 | LGB2 | 1.197 | LGB5 | 1.571 |

Faizabad | Jabalpur | Raipur | Ranchi | Ranichauri | Samastipur | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

54 | RF1 | −2.377 | RF1 | −2.344 | RF1 | −2.271 | RF1 | −2.028 | RF1 | −2.560 | RF1 | −2.505 |

53 | XGB1 | −1.815 | XGB1 | −1.787 | XGB1 | −1.686 | XGB2 | −1.328 | XGB1 | −1.774 | XGB1 | −1.999 |

52 | LGB1 | −0.991 | LGB1 | −1.128 | LGB1 | −0.998 | RF2 | −1.215 | LGB1 | −1.307 | LGB1 | −1.514 |

51 | XGB2 | −0.618 | XGB2 | −1.103 | XGB2 | −0.758 | XGB1 | −1.164 | RF3 | −1.065 | RF6 | −0.654 |

50 | RF2 | −0.471 | RF2 | −0.919 | RF2 | −0.629 | LGB2 | −0.549 | XGB3 | −1.047 | XGB6 | −0.624 |

49 | RF6 | −0.439 | XGB6 | −0.504 | XGB6 | −0.544 | LGB1 | −0.509 | LGB3 | −0.596 | XGB2 | −0.315 |

48 | XGB4 | −0.407 | LGB2 | −0.475 | RF6 | −0.524 | XGB10 | −0.480 | XGB2 | −0.131 | RF2 | −0.202 |

47 | XGB6 | −0.388 | RF6 | −0.283 | LGB2 | −0.302 | XGB6 | −0.419 | RF2 | −0.075 | LGB6 | −0.161 |

46 | RF4 | −0.171 | LGB6 | 0.106 | XGB10 | −0.096 | RF6 | −0.268 | LGB2 | 0.287 | XGB3 | 0.053 |

45 | LGB2 | −0.021 | XGB10 | 0.132 | LGB6 | 0.072 | RF10 | −0.097 | XGB6 | 0.497 | LGB2 | 0.172 |

44 | LGB6 | 0.068 | RF10 | 0.479 | RF10 | 0.333 | LGB10 | 0.354 | RF6 | 0.560 | RF3 | 0.224 |

43 | LGB4 | 0.357 | LGB10 | 0.601 | XGB4 | 0.449 | LGB6 | 0.419 | XGB13 | 0.641 | LGB3 | 0.523 |

42 | XGB14 | 0.792 | XGB4 | 0.842 | LGB10 | 0.615 | XGB3 | 0.629 | RF13 | 0.790 | XGB11 | 0.790 |

41 | RF14 | 1.069 | RF4 | 0.912 | RF4 | 0.713 | RF3 | 0.677 | LGB6 | 0.843 | RF11 | 1.055 |

40 | XGB10 | 1.185 | LGB4 | 1.255 | LGB4 | 1.088 | XGB13 | 1.228 | LGB13 | 1.026 | XGB10 | 1.115 |

39 | LGB14 | 1.263 | XGB3 | 1.277 | XGB5 | 1.178 | LGB3 | 1.306 | XGB11 | 1.104 | LGB11 | 1.232 |

38 | RF5 | 1.339 | RF3 | 1.285 | RF5 | 1.632 | RF13 | 1.473 | RF11 | 1.366 | RF10 | 1.316 |

37 | LGB10 | 1.623 | LGB14 | 1.656 | LGB14 | 1.729 | LGB13 | 1.972 | LGB11 | 1.440 | LGB10 | 1.495 |

Jorhat | Mohanpur | Palampur | Thrissur | ||||||
---|---|---|---|---|---|---|---|---|---|

Inputs used | RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

T_{max}, T_{min}, RH, U_{2} | 1 | LGB13 | 1.708 | LGB13 | 1.696 | LGB13 | 1.908 | LGB13 | 1.802 |

2 | RF13 | 1.576 | RF13 | 1.639 | RF13 | 1.844 | RF13 | 1.690 | |

3 | XGB13 | 1.561 | XGB13 | 1.612 | XGB13 | 1.808 | XGB13 | 1.639 | |

4 | ALB | −0.988 | ALB | −1.315 | MAH | −1.786 | PEN | −1.195 | |

5 | PEN | −1.823 | PEN | −1.501 | PEN | −1.849 | ALB | −1.842 | |

6 | MAH | −2.034 | MAH | −2.132 | ALB | −1.925 | MAH | −2.093 | |

T_{max}, T_{min}, R_{s} | 1 | LGB5 | 0.824 | LGB5 | 0.982 | LGB5 | 1.037 | LGB5 | 0.942 |

2 | RF5 | 0.792 | RF5 | 0.974 | XGB5 | 0.990 | RF5 | 0.907 | |

3 | XGB5 | 0.786 | XGB5 | 0.966 | RF5 | 0.975 | XGB5 | 0.902 | |

4 | PT | 0.560 | MAK | 0.501 | JH | 0.178 | PT | 0.337 | |

5 | MAK | 0.410 | PT | 0.435 | PT | −0.001 | MAK | 0.293 | |

6 | JH | −0.246 | JH | −0.870 | MAK | −0.216 | JH | −0.323 | |

7 | MGB | −3.126 | MGB | −2.988 | MGB | −2.963 | MGB | −3.058 | |

T_{max}, T_{min}, R_{a} | 1 | LGB6 | 2.110 | LGB6 | 1.864 | LGB6 | 1.306 | LGB6 | 1.678 |

2 | RF6 | 1.483 | XGB6 | 1.660 | XGB6 | 1.071 | XGB6 | 1.525 | |

3 | XGB6 | 1.369 | RF6 | 1.635 | RF6 | 0.984 | RF6 | 1.436 | |

4 | HS | −0.676 | HS | −0.685 | HS | 0.352 | HS | −0.212 | |

5 | HS1 | −1.245 | HS2 | −1.400 | HS2 | −0.163 | HS2 | −0.746 | |

6 | HS2 | −1.328 | HS1 | −1.416 | HS1 | −0.856 | HS1 | −1.398 | |

7 | THO | −1.713 | THO | −1.657 | THO | −2.694 | THO | −2.282 | |

T_{max}, T_{min}, RH, R_{s} | 1 | LGB7 | 1.272 | LGB7 | 1.219 | LGB7 | 1.177 | LGB7 | 1.235 |

2 | RF7 | 1.230 | RF7 | 1.206 | RF7 | 1.168 | RF7 | 1.227 | |

3 | XGB7 | 1.162 | XGB7 | 1.180 | XGB7 | 1.156 | XGB7 | 1.199 | |

4 | TUR | 0.731 | TUR | 0.361 | TUR | 0.880 | TUR | 0.854 | |

5 | VA2 | 0.177 | VA2 | −0.368 | VA2 | 0.760 | VA2 | 0.638 | |

6 | VA1 | −1.113 | VA1 | −0.455 | COP | −1.439 | COP | −1.656 | |

7 | COP | −2.728 | COP | −2.781 | VA1 | −2.823 | VA1 | −2.643 |

Faizabad | Jabalpur | Raipur | Ranchi | Ranichauri | Samastipur | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Inputs used | RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

T_{max}, T_{min}, RH, U_{2} | 1 | LGB13 | 1.535 | LGB13 | 1.502 | LGB13 | 1.523 | LGB13 | 1.860 | LGB13 | 1.763 | LGB13 | 1.425 |

2 | RF13 | 1.517 | RF13 | 1.465 | RF13 | 1.498 | RF13 | 1.746 | RF13 | 1.705 | RF13 | 1.404 | |

3 | XGB13 | 1.507 | XGB13 | 1.458 | XGB13 | 1.487 | XGB13 | 1.690 | XGB13 | 1.668 | XGB13 | 1.317 | |

4 | PEN | −0.909 | PEN | −0.982 | PEN | −0.970 | PEN | −1.665 | ALB | −1.308 | PEN | −0.827 | |

5 | MAH | −1.687 | MAH | −1.336 | MAH | −1.433 | ALB | −1.720 | MAH | −1.590 | MAH | −1.464 | |

6 | ALB | −1.962 | ALB | −2.107 | ALB | −2.104 | MAH | −1.910 | PEN | −2.237 | ALB | −1.854 | |

T_{max}, T_{min}, R_{s} | 1 | LGB5 | 1.303 | LGB5 | 1.210 | LGB5 | 1.280 | LGB5 | 0.960 | LGB5 | 0.913 | LGB5 | 1.536 |

2 | RF5 | 1.211 | RF5 | 1.175 | RF5 | 1.253 | RF5 | 0.924 | RF5 | 0.882 | RF5 | 1.496 | |

3 | XGB5 | 1.196 | XGB5 | 1.156 | XGB5 | 1.189 | XGB5 | 0.918 | XGB5 | 0.881 | XGB5 | 1.490 | |

4 | JH | 0.465 | PT | 0.064 | PT | 0.002 | PT | 0.582 | MAK | 0.424 | JH | −0.090 | |

5 | PT | −0.483 | JH | −0.131 | JH | −0.141 | MAK | 0.159 | JH | 0.058 | PT | −0.749 | |

6 | MAK | −1.162 | MAK | −0.684 | MAK | −0.862 | JH | −0.503 | PT | −0.071 | MAK | −1.365 | |

7 | MGB | −2.530 | MGB | −2.790 | MGB | −2.720 | MGB | −3.040 | MGB | −3.087 | MGB | −2.318 | |

T_{max}, T_{min}, R_{a} | 1 | LGB6 | 1.866 | LGB6 | 1.741 | LGB6 | 1.716 | LGB6 | 1.517 | LGB6 | 1.138 | LGB6 | 1.917 |

2 | XGB6 | 1.615 | RF6 | 1.613 | RF6 | 1.531 | RF6 | 1.280 | RF6 | 0.992 | XGB6 | 1.559 | |

3 | RF6 | 1.593 | XGB6 | 1.539 | XGB6 | 1.523 | XGB6 | 1.226 | XGB6 | 0.960 | RF6 | 1.535 | |

4 | HS | −0.667 | HS | −0.636 | HS | −0.367 | HS | −0.514 | HS | 0.522 | HS | −0.772 | |

5 | HS1 | −1.265 | THO | −1.342 | HS1 | −1.161 | THO | −0.632 | HS2 | 0.036 | HS1 | −1.147 | |

6 | HS2 | −1.365 | HS1 | −1.386 | HS2 | −1.201 | HS1 | −1.429 | HS1 | −0.785 | HS2 | −1.246 | |

7 | THO | −1.777 | HS2 | −1.530 | THO | −2.040 | HS2 | −1.448 | THO | −2.862 | THO | −1.845 | |

T_{max}, T_{min}, RH, R_{s} | 1 | LGB7 | 0.946 | LGB7 | 1.071 | RF7 | 1.063 | LGB7 | 1.156 | LGB7 | 0.979 | LGB7 | 1.141 |

2 | RF7 | 0.938 | RF7 | 1.063 | LGB7 | 1.061 | RF7 | 1.132 | RF7 | 0.966 | RF7 | 1.131 | |

3 | XGB7 | 0.875 | XGB7 | 1.039 | XGB7 | 1.021 | XGB7 | 1.103 | XGB7 | 0.962 | XGB7 | 1.120 | |

4 | TUR | 0.477 | TUR | 0.675 | TUR | 0.544 | TUR | 0.724 | VA2 | 0.794 | TUR | 0.143 | |

5 | VA2 | 0.275 | VA2 | 0.436 | VA2 | 0.387 | VA2 | 0.441 | TUR | 0.776 | VA2 | −0.028 | |

6 | COP | −0.457 | COP | −1.354 | COP | −1.139 | VA1 | −1.982 | COP | −2.163 | COP | −0.648 | |

7 | VA1 | −3.054 | VA1 | −2.929 | VA1 | −2.937 | COP | −2.574 | VA1 | −2.312 | VA1 | −2.859 |

Jorhat | Mohanpur | Palampur | Thrissur | |||||
---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

1 | GWOXGB17 | 2.175 | GWOXGB17 | 2.176 | GWOXGB18 | 2.078 | GWOXGB18 | 1.376 |

2 | GWOXGB18 | 2.134 | GWOXGB18 | 2.072 | GWOLGB18 | 2.078 | GWOLGB18 | 1.360 |

3 | GWOLGB18 | 1.843 | GWOLGB17 | 2.052 | GWOXGB17 | 2.038 | GWOXGB17 | 1.287 |

4 | GWOLGB17 | 1.747 | GWOLGB18 | 1.798 | GWOLGB17 | 2.030 | GWOLGB17 | 1.271 |

5 | GWOXGB8 | 0.854 | GWORF17 | 1.209 | GWORF18 | 1.621 | GWORF17 | 0.820 |

6 | GWORF17 | 0.530 | GWORF18 | 1.079 | GWORF17 | 1.466 | GWORF18 | 0.687 |

7 | GWOLGB8 | 0.469 | GWOXGB8 | 0.812 | GWOXGB7 | −0.197 | GWOLGB16 | 0.220 |

8 | GWORF18 | 0.313 | GWOLGB8 | 0.731 | GWOLGB7 | −0.207 | GWOXGB16 | 0.183 |

9 | GWORF8 | 0.041 | GWORF8 | 0.421 | GWORF7 | −0.252 | GWOLGB8 | 0.101 |

10 | GWORF9 | −0.167 | GWORF9 | 0.357 | GWOLGB16 | −0.457 | GWOXGB8 | 0.059 |

11 | GWOLGB12 | −0.835 | GWOLGB9 | −1.312 | GWOXGB16 | −0.468 | GWORF16 | −0.103 |

12 | GWOLGB9 | −0.886 | GWOXGB9 | −1.368 | GWORF16 | −0.705 | GWORF8 | −0.123 |

13 | GWOXGB9 | −0.912 | GWOLGB12 | −1.496 | GWOLGB8 | −1.258 | GWORF9 | −0.203 |

14 | GWORF12 | −0.971 | GWORF12 | −1.599 | GWORF8 | −1.295 | GWOXGB15 | −0.513 |

15 | GWOXGB12 | −0.983 | GWOLGB7 | −1.673 | GWORF9 | −1.318 | GWOLGB15 | −0.538 |

16 | GWOLGB7 | −1.765 | GWOXGB12 | −1.726 | GWOXGB8 | −1.372 | GWORF15 | −0.650 |

17 | GWOXGB7 | −1.782 | GWOXGB7 | −1.749 | GWOLGB12 | −1.861 | GWOLGB7 | −2.610 |

18 | GWORF7 | −1.807 | GWORF7 | −1.786 | GWOXGB12 | −1.922 | GWOXGB7 | −2.624 |

Faizabad | Jabalpur | Raipur | Ranchi | Ranichauri | Samastipur | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

1 | GWOXGB17 | 1.865 | GWOLGB18 | 1.366 | GWOXGB17 | 1.412 | GWOXGB18 | 1.856 | GWOLGB17 | 2.504 | GWOXGB17 | 1.985 |

2 | GWOXGB18 | 1.855 | GWOXGB18 | 1.361 | GWOXGB18 | 1.384 | GWOXGB17 | 1.847 | GWOXGB17 | 2.486 | GWOLGB17 | 1.982 |

3 | GWOLGB17 | 1.826 | GWOLGB17 | 1.360 | GWOLGB17 | 1.332 | GWOLGB17 | 1.747 | GWOLGB18 | 2.476 | GWOXGB18 | 1.883 |

4 | GWOLGB18 | 1.759 | GWOXGB17 | 1.350 | GWOLGB18 | 1.310 | GWOLGB18 | 1.696 | GWOXGB18 | 2.439 | GWOLGB18 | 1.868 |

5 | GWORF17 | 1.207 | GWORF17 | 0.900 | GWORF17 | 0.929 | GWORF17 | 0.996 | GWORF18 | 1.547 | GWORF17 | 1.286 |

6 | GWORF18 | 1.160 | GWORF18 | 0.877 | GWORF18 | 0.866 | GWORF18 | 0.947 | GWORF17 | 1.393 | GWORF18 | 0.985 |

7 | GWOLGB16 | 0.215 | GWOLGB16 | 0.378 | GWOXGB16 | 0.519 | GWOXGB8 | 0.348 | GWOLGB7 | 0.060 | GWOLGB8 | 0.186 |

8 | GWOXGB16 | 0.176 | GWOXGB16 | 0.358 | GWOLGB16 | 0.483 | GWOLGB8 | 0.321 | GWOXGB7 | 0.054 | GWOXGB8 | 0.122 |

9 | GWOXGB8 | −0.214 | GWORF16 | 0.007 | GWORF16 | 0.149 | GWORF8 | 0.166 | GWORF7 | −0.176 | GWORF8 | 0.011 |

10 | GWOLGB8 | −0.255 | GWOXGB8 | −0.009 | GWOLGB8 | −0.113 | GWORF9 | 0.063 | GWOLGB8 | −1.359 | GWORF9 | 0.004 |

11 | GWORF8 | −0.359 | GWOLGB8 | −0.013 | GWOXGB8 | −0.142 | GWOXGB16 | −0.338 | GWOXGB8 | −1.365 | GWOLGB16 | −0.653 |

12 | GWORF9 | −0.376 | GWORF8 | −0.092 | GWORF8 | −0.259 | GWOLGB16 | −0.423 | GWOLGB9 | −1.369 | GWOXGB16 | −0.762 |

13 | GWORF16 | −0.447 | GWORF9 | −0.201 | GWORF9 | −0.363 | GWORF16 | −0.904 | GWOLGB12 | −1.399 | GWORF16 | −0.894 |

14 | GWOXGB15 | −1.269 | GWOXGB15 | −0.724 | GWOXGB15 | −0.730 | GWOXGB15 | −1.253 | GWOXGB9 | −1.422 | GWOXGB7 | −1.330 |

15 | GWOLGB15 | −1.325 | GWOLGB15 | −0.764 | GWOLGB15 | −0.762 | GWOLGB15 | −1.304 | GWOXGB12 | −1.455 | GWOLGB7 | −1.357 |

16 | GWORF15 | −1.679 | GWORF15 | −0.898 | GWORF15 | −0.903 | GWORF15 | −1.488 | GWORF9 | −1.457 | GWORF7 | −1.475 |

17 | GWOXGB13 | −2.011 | GWOLGB13 | −2.625 | GWOXGB13 | −2.522 | GWOLGB12 | −2.131 | GWORF12 | −1.464 | GWOLGB15 | −1.837 |

18 | GWOLGB13 | −2.128 | GWOXGB13 | −2.630 | GWOLGB13 | −2.588 | GWOXGB12 | −2.144 | GWORF8 | −1.496 | GWOXGB9 | −2.001 |

Jorhat | Mohanpur | Palampur | Thrissur | |||||
---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

54 | GWORF1 | −1.832 | GWOXGB1 | −2.195 | GWOXGB1 | −2.715 | GWOXGB1 | −2.220 |

53 | GWOLGB1 | −1.798 | GWOLGB1 | −2.163 | GWOLGB1 | −2.690 | GWORF1 | −2.217 |

52 | GWOXGB1 | −1.789 | GWORF1 | −2.158 | GWORF1 | −2.666 | GWOLGB1 | −2.183 |

51 | GWOLGB3 | −0.965 | GWORF2 | −1.330 | GWOXGB3 | −0.542 | GWORF6 | −1.687 |

50 | GWORF3 | −0.944 | GWOLGB2 | −1.314 | GWOLGB3 | −0.523 | GWOLGB6 | −1.648 |

49 | GWOXGB3 | −0.802 | GWOXGB2 | −1.142 | GWORF3 | −0.513 | GWOXGB6 | −1.584 |

48 | GWORF6 | −0.413 | GWORF3 | −0.257 | GWORF6 | −0.002 | GWORF2 | 0.139 |

47 | GWOXGB6 | −0.361 | GWOXGB3 | 0.095 | GWOXGB6 | 0.044 | GWOLGB2 | 0.172 |

46 | GWOLGB6 | −0.339 | GWOLGB3 | 0.159 | GWOLGB6 | 0.131 | GWOXGB2 | 0.180 |

45 | GWORF11 | −0.271 | GWORF6 | 0.487 | GWORF4 | 0.922 | GWORF10 | 0.422 |

44 | GWOLGB11 | −0.189 | GWOLGB6 | 0.576 | GWOXGB4 | 0.924 | GWOLGB10 | 0.475 |

43 | GWOXGB11 | 0.065 | GWOXGB6 | 0.600 | GWOXGB11 | 0.953 | GWOXGB10 | 0.490 |

42 | GWORF2 | 1.016 | GWORF13 | 0.955 | GWOLGB4 | 0.957 | GWORF3 | 1.447 |

41 | GWOLGB2 | 1.072 | GWOLGB13 | 1.301 | GWORF11 | 1.066 | GWOLGB3 | 1.495 |

40 | GWOXGB2 | 1.139 | GWOXGB13 | 1.362 | GWOLGB11 | 1.070 | GWOXGB3 | 1.503 |

39 | GWORF10 | 2.119 | GWORF10 | 1.560 | GWORF2 | 1.108 | GWORF11 | 1.711 |

38 | GWOLGB10 | 2.134 | GWOLGB10 | 1.679 | GWOXGB2 | 1.234 | GWOXGB13 | 1.727 |

37 | GWOXGB10 | 2.157 | GWOXGB11 | 1.786 | GWOLGB2 | 1.241 | GWOLGB13 | 1.777 |

Faizabad | Jabalpur | Raipur | Ranchi | Ranichauri | Samastipur | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

54 | GWOXGB1 | −2.067 | GWOXGB1 | −2.069 | GWOXGB1 | −2.052 | GWOXGB2 | −1.696 | GWOLGB1 | −2.296 | GWOLGB1 | −2.328 |

53 | GWOLGB1 | −2.059 | GWORF1 | −2.025 | GWOLGB1 | −2.029 | GWOLGB2 | −1.618 | GWORF1 | −2.272 | GWORF1 | −2.322 |

52 | GWORF1 | −1.942 | GWOLGB1 | −2.018 | GWORF1 | −1.977 | GWORF2 | −1.599 | GWOXGB1 | −2.257 | GWOXGB1 | −2.276 |

51 | GWORF6 | −0.563 | GWORF2 | −1.151 | GWOXGB2 | −0.901 | GWOXGB1 | −1.542 | GWORF3 | −1.348 | GWORF6 | −0.666 |

50 | GWOLGB2 | −0.460 | GWOXGB2 | −1.084 | GWORF2 | −0.900 | GWORF1 | −1.535 | GWOLGB3 | −1.296 | GWOLGB6 | −0.583 |

49 | GWOLGB6 | −0.404 | GWOLGB2 | −1.063 | GWOLGB2 | −0.853 | GWOLGB1 | −1.535 | GWOXGB3 | −1.218 | GWOXGB6 | −0.552 |

48 | GWOXGB2 | −0.402 | GWOXGB6 | −0.375 | GWOLGB6 | −0.579 | GWORF10 | −0.354 | GWORF2 | 0.031 | GWOXGB2 | −0.230 |

47 | GWOXGB6 | −0.373 | GWORF6 | −0.300 | GWOXGB6 | −0.548 | GWORF6 | −0.304 | GWOXGB2 | 0.032 | GWORF2 | −0.195 |

46 | GWORF2 | −0.252 | GWOLGB6 | −0.273 | GWORF6 | −0.514 | GWOXGB10 | −0.148 | GWOLGB2 | 0.046 | GWOLGB2 | −0.165 |

45 | GWORF4 | −0.238 | GWOXGB10 | 0.356 | GWOXGB10 | 0.422 | GWOLGB10 | −0.106 | GWORF6 | 0.776 | GWOXGB3 | 0.321 |

44 | GWOXGB4 | −0.143 | GWORF10 | 0.462 | GWORF10 | 0.429 | GWOXGB6 | −0.023 | GWOLGB6 | 0.790 | GWOLGB3 | 0.337 |

43 | GWOLGB4 | −0.139 | GWOLGB10 | 0.503 | GWOLGB10 | 0.534 | GWOLGB6 | 0.035 | GWOXGB6 | 0.799 | GWORF3 | 0.368 |

42 | GWOXGB14 | 1.105 | GWORF4 | 1.126 | GWORF4 | 1.036 | GWORF3 | 1.161 | GWORF13 | 0.956 | GWORF11 | 1.073 |

41 | GWOLGB14 | 1.180 | GWOXGB4 | 1.265 | GWOLGB4 | 1.083 | GWOXGB3 | 1.365 | GWOLGB13 | 1.136 | GWOXGB11 | 1.127 |

40 | GWORF14 | 1.239 | GWOLGB4 | 1.286 | GWOXGB4 | 1.108 | GWOLGB3 | 1.404 | GWOXGB13 | 1.143 | GWOLGB11 | 1.240 |

39 | GWOXGB10 | 1.791 | GWORF14 | 1.757 | GWOXGB14 | 1.904 | GWORF13 | 1.959 | GWORF11 | 1.640 | GWORF10 | 1.534 |

38 | GWORF5 | 1.817 | GWOXGB14 | 1.782 | GWORF14 | 1.915 | GWOXGB13 | 2.237 | GWOXGB11 | 1.645 | GWOLGB10 | 1.651 |

37 | GWOLGB10 | 1.909 | GWOLGB3 | 1.823 | GWOLGB14 | 1.922 | GWOLGB13 | 2.299 | GWOLGB11 | 1.692 | GWOXGB10 | 1.665 |

Jorhat | Mohanpur | Palampur | Thrissur | |||||
---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

1 | GWOXGB17 | 2.031 | GWOXGB17 | 2.077 | GWOXGB18 | 1.953 | GWOXGB18 | 1.302 |

2 | GWOXGB18 | 1.995 | GWOXGB18 | 1.982 | GWOLGB18 | 1.953 | GWOLGB18 | 1.288 |

3 | GWOLGB18 | 1.740 | GWOLGB17 | 1.964 | GWOXGB17 | 1.916 | GWOXGB17 | 1.222 |

4 | GWOLGB17 | 1.656 | GWOLGB18 | 1.732 | GWOLGB17 | 1.909 | GWOLGB17 | 1.207 |

5 | XGB17 | 1.538 | XGB17 | 1.635 | LGB18 | 1.810 | LGB18 | 1.062 |

6 | XGB18 | 1.419 | LGB17 | 1.633 | LGB17 | 1.754 | LGB17 | 1.051 |

7 | LGB17 | 1.388 | LGB18 | 1.439 | XGB18 | 1.642 | XGB17 | 1.025 |

8 | LGB18 | 1.388 | XGB18 | 1.413 | XGB17 | 1.621 | XGB18 | 0.987 |

9 | GWOXGB8 | 0.869 | GWORF17 | 1.193 | GWORF18 | 1.537 | GWORF17 | 0.799 |

10 | GWORF17 | 0.589 | RF17 | 1.176 | RF18 | 1.528 | RF17 | 0.793 |

11 | RF17 | 0.579 | GWORF18 | 1.075 | GWORF17 | 1.395 | GWORF18 | 0.679 |

12 | GWOLGB8 | 0.533 | RF18 | 1.054 | RF17 | 1.376 | RF18 | 0.661 |

13 | XGB8 | 0.533 | GWOXGB8 | 0.829 | GWOXGB7 | −0.110 | GWOLGB16 | 0.252 |

14 | LGB8 | 0.510 | GWOLGB8 | 0.755 | GWOLGB7 | −0.119 | GWOXGB16 | 0.220 |

15 | GWORF18 | 0.399 | LGB8 | 0.673 | LGB7 | −0.129 | LGB16 | 0.152 |

16 | RF18 | 0.392 | XGB8 | 0.540 | GWORF7 | −0.159 | GWOLGB8 | 0.150 |

17 | GWORF8 | 0.159 | GWORF8 | 0.473 | RF7 | −0.210 | GWOXGB8 | 0.112 |

18 | RF8 | 0.148 | RF9 | 0.454 | XGB7 | −0.318 | LGB8 | 0.063 |

19 | RF9 | 0.144 | RF8 | 0.445 | GWOLGB16 | −0.348 | XGB16 | 0.015 |

20 | GWORF9 | −0.023 | GWORF9 | 0.414 | GWOXGB16 | −0.358 | XGB8 | 0.005 |

21 | GWOLGB12 | −0.607 | GWOLGB9 | −1.103 | LGB16 | −0.393 | GWORF16 | −0.037 |

22 | GWOLGB9 | −0.652 | GWOXGB9 | −1.154 | GWORF16 | −0.571 | GWORF8 | −0.050 |

23 | GWOXGB9 | −0.675 | LGB9 | −1.169 | RF16 | −0.577 | RF16 | −0.065 |

24 | GWORF12 | −0.726 | GWOLGB12 | −1.270 | XGB16 | −0.673 | RF8 | −0.069 |

25 | GWOXGB12 | −0.736 | LGB12 | −1.313 | GWOLGB8 | −1.068 | RF9 | −0.075 |

26 | LGB12 | −0.739 | GWORF12 | −1.363 | GWORF8 | −1.101 | GWORF9 | −0.123 |

27 | LGB9 | −0.762 | RF12 | −1.376 | LGB8 | −1.102 | GWOXGB15 | −0.407 |

28 | RF12 | −1.040 | GWOLGB7 | −1.433 | GWORF9 | −1.122 | GWOLGB15 | −0.430 |

29 | XGB9 | −1.208 | LGB7 | −1.469 | GWOXGB8 | −1.171 | LGB15 | −0.445 |

30 | XGB12 | −1.288 | GWOXGB12 | −1.478 | RF8 | −1.218 | GWORF15 | −0.529 |

31 | GWOLGB7 | −1.422 | GWOXGB7 | −1.501 | RF9 | −1.238 | RF15 | −0.561 |

32 | GWOXGB7 | −1.436 | GWORF7 | −1.535 | XGB8 | −1.394 | XGB15 | −0.581 |

33 | GWORF7 | −1.458 | XGB9 | −1.537 | GWOLGB12 | −1.611 | GWOLGB7 | −2.275 |

34 | LGB7 | −1.564 | RF7 | −1.617 | GWOXGB12 | −1.665 | GWOXGB7 | −2.288 |

35 | RF7 | −1.717 | XGB12 | −1.712 | LGB12 | −1.694 | LGB7 | −2.413 |

36 | XGB7 | −1.958 | XGB7 | −1.923 | XGB12 | −2.047 | XGB7 | −2.698 |

**Table 20.**Ranking of the best-performing models in conventional and hybrid MLs at sub-humid stations.

Faizabad | Jabalpur | Raipur | Ranchi | Ranichauri | Samastipur | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

1 | GWOXGB17 | 1.810 | GWOLGB18 | 1.315 | GWOXGB17 | 1.368 | GWOXGB18 | 1.739 | GWOLGB17 | 2.383 | GWOXGB17 | 1.944 |

2 | GWOXGB18 | 1.801 | GWOXGB18 | 1.311 | GWOXGB18 | 1.343 | GWOXGB17 | 1.731 | GWOXGB17 | 2.366 | GWOLGB17 | 1.941 |

3 | GWOLGB17 | 1.774 | GWOLGB17 | 1.310 | GWOLGB17 | 1.295 | GWOLGB17 | 1.642 | GWOLGB18 | 2.357 | GWOXGB18 | 1.847 |

4 | GWOLGB18 | 1.711 | GWOXGB17 | 1.301 | GWOLGB18 | 1.273 | GWOLGB18 | 1.595 | GWOXGB18 | 2.323 | GWOLGB18 | 1.834 |

5 | LGB17 | 1.556 | LGB18 | 1.146 | LGB18 | 1.120 | LGB17 | 1.434 | LGB17 | 2.136 | LGB17 | 1.726 |

6 | LGB18 | 1.491 | LGB17 | 1.104 | LGB17 | 1.105 | XGB17 | 1.394 | LGB18 | 2.069 | LGB18 | 1.644 |

7 | XGB17 | 1.443 | XGB18 | 1.025 | XGB18 | 1.056 | LGB18 | 1.369 | XGB17 | 1.980 | XGB17 | 1.588 |

8 | XGB18 | 1.378 | XGB17 | 1.023 | XGB17 | 1.052 | XGB18 | 1.352 | XGB18 | 1.818 | XGB18 | 1.421 |

9 | RF17 | 1.203 | GWORF17 | 0.887 | GWORF17 | 0.921 | RF17 | 0.985 | GWORF18 | 1.505 | GWORF17 | 1.284 |

10 | GWORF17 | 1.199 | RF17 | 0.887 | RF17 | 0.907 | GWORF17 | 0.964 | RF18 | 1.499 | RF17 | 1.245 |

11 | GWORF18 | 1.155 | GWORF18 | 0.866 | GWORF18 | 0.863 | GWORF18 | 0.921 | GWORF17 | 1.364 | GWORF18 | 1.002 |

12 | RF18 | 1.155 | RF18 | 0.860 | RF18 | 0.849 | RF18 | 0.910 | RF17 | 1.347 | RF18 | 0.909 |

13 | GWOLGB16 | 0.278 | GWOLGB16 | 0.406 | GWOXGB16 | 0.540 | GWOXGB8 | 0.382 | GWOLGB7 | 0.144 | GWOLGB8 | 0.247 |

14 | GWOXGB16 | 0.241 | GWOXGB16 | 0.388 | GWOLGB16 | 0.507 | GWOLGB8 | 0.358 | GWOXGB7 | 0.139 | LGB8 | 0.194 |

15 | LGB16 | 0.073 | LGB16 | 0.270 | LGB16 | 0.381 | LGB8 | 0.357 | LGB7 | 0.114 | GWOXGB8 | 0.187 |

16 | XGB16 | −0.103 | XGB16 | 0.125 | XGB16 | 0.241 | RF8 | 0.226 | GWORF7 | −0.071 | GWORF8 | 0.083 |

17 | GWOXGB8 | −0.119 | GWORF16 | 0.066 | GWORF16 | 0.199 | GWORF8 | 0.219 | RF7 | −0.094 | GWORF9 | 0.077 |

18 | GWOLGB8 | −0.157 | GWOXGB8 | 0.053 | RF16 | 0.169 | RF9 | 0.210 | XGB7 | −0.156 | RF9 | 0.055 |

19 | LGB8 | −0.196 | GWOLGB8 | 0.050 | GWOLGB8 | −0.042 | XGB8 | 0.189 | GWOLGB8 | −1.152 | RF8 | 0.048 |

20 | RF9 | −0.225 | RF16 | 0.045 | GWOXGB8 | −0.069 | GWORF9 | 0.127 | GWOXGB8 | −1.158 | XGB8 | −0.038 |

21 | GWORF8 | −0.253 | LGB8 | 0.014 | LGB8 | −0.128 | GWOXGB16 | −0.234 | GWOLGB9 | −1.161 | GWOLGB16 | −0.541 |

22 | RF8 | −0.262 | GWORF8 | −0.022 | GWORF8 | −0.175 | GWOLGB16 | −0.310 | LGB9 | −1.178 | LGB16 | −0.627 |

23 | GWORF9 | −0.269 | RF8 | −0.047 | RF9 | −0.185 | LGB16 | −0.432 | LGB8 | −1.183 | GWOXGB16 | −0.642 |

24 | GWORF16 | −0.335 | RF9 | −0.047 | RF8 | −0.193 | XGB16 | −0.624 | GWOLGB12 | −1.189 | GWORF16 | −0.767 |

25 | RF16 | −0.348 | GWORF9 | −0.121 | XGB8 | −0.243 | GWORF16 | −0.741 | GWOXGB9 | −1.210 | RF16 | −0.779 |

26 | XGB8 | −0.358 | XGB8 | −0.135 | GWORF9 | −0.272 | RF16 | −0.760 | GWOXGB12 | −1.240 | XGB16 | −0.913 |

27 | GWOXGB15 | −1.096 | GWOXGB15 | −0.602 | GWOXGB15 | −0.612 | GWOXGB15 | −1.053 | GWORF9 | −1.242 | GWOXGB7 | −1.176 |

28 | GWOLGB15 | −1.148 | GWOLGB15 | −0.638 | LGB15 | −0.631 | GWOLGB15 | −1.098 | GWORF12 | −1.248 | GWOLGB7 | −1.201 |

29 | LGB15 | −1.196 | LGB15 | −0.644 | GWOLGB15 | −0.642 | LGB15 | −1.118 | LGB12 | −1.252 | LGB7 | −1.219 |

30 | XGB15 | −1.445 | GWORF15 | −0.760 | GWORF15 | −0.771 | GWORF15 | −1.263 | GWORF8 | −1.277 | GWORF7 | −1.312 |

31 | GWORF15 | −1.476 | RF15 | −0.798 | RF15 | −0.785 | RF15 | −1.323 | RF9 | −1.366 | RF7 | −1.355 |

32 | RF15 | −1.501 | XGB15 | −0.871 | XGB15 | −0.860 | XGB15 | −1.326 | RF8 | −1.393 | XGB7 | −1.495 |

33 | GWOXGB13 | −1.783 | GWOLGB13 | −2.335 | GWOXGB13 | −2.261 | GWOLGB12 | −1.831 | RF12 | −1.420 | GWOLGB15 | −1.653 |

34 | GWOLGB13 | −1.891 | GWOXGB13 | −2.340 | GWOLGB13 | −2.322 | GWOXGB12 | −1.843 | XGB9 | −1.461 | LGB15 | −1.695 |

35 | LGB13 | −1.923 | LGB13 | −2.411 | LGB13 | −2.368 | LGB12 | −1.888 | XGB8 | −1.475 | GWOXGB9 | −1.805 |

36 | XGB13 | −2.183 | XGB13 | −2.684 | XGB13 | −2.632 | XGB12 | −2.261 | XGB12 | −1.617 | XGB12 | −2.054 |

Jorhat | Mohanpur | Palampur | Thrissur | |||||
---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

108 | RF1 | −2.443 | RF1 | −2.685 | RF1 | −2.858 | RF1 | −2.488 |

107 | XGB1 | −1.829 | XGB1 | −1.645 | XGB1 | −2.313 | XGB1 | −1.934 |

106 | LGB1 | −1.374 | RF2 | −1.357 | LGB1 | −1.909 | LGB1 | −1.620 |

105 | GWORF1 | −1.158 | XGB2 | −1.176 | GWOXGB1 | −1.811 | GWOXGB1 | −1.543 |

104 | RF3 | −1.150 | LGB1 | −1.066 | GWOLGB1 | −1.793 | GWORF1 | −1.541 |

103 | GWOLGB1 | −1.134 | GWOXGB1 | −0.891 | GWORF1 | −1.774 | RF6 | −1.530 |

102 | GWOXGB1 | −1.128 | GWOLGB1 | −0.875 | RF3 | −0.956 | GWOLGB1 | −1.515 |

101 | XGB3 | −1.001 | GWORF1 | −0.871 | XGB3 | −0.578 | XGB6 | −1.380 |

100 | XGB6 | −0.703 | RF3 | −0.703 | RF6 | −0.439 | LGB6 | −1.144 |

99 | LGB3 | −0.655 | LGB2 | −0.517 | XGB6 | −0.266 | GWORF6 | −1.143 |

98 | RF6 | −0.644 | XGB3 | −0.455 | LGB3 | −0.242 | GWOLGB6 | −1.114 |

97 | GWOLGB3 | −0.504 | GWORF2 | −0.413 | GWOXGB3 | −0.202 | GWOXGB6 | −1.066 |

96 | GWORF3 | −0.488 | GWOLGB2 | −0.405 | GWOLGB3 | −0.188 | RF2 | −0.120 |

95 | GWOXGB3 | −0.379 | GWOXGB2 | −0.310 | GWORF3 | −0.180 | XGB2 | −0.006 |

94 | XGB11 | −0.264 | RF6 | −0.292 | LGB6 | 0.198 | XGB10 | 0.210 |

93 | RF11 | −0.259 | XGB6 | −0.212 | GWORF6 | 0.201 | LGB2 | 0.211 |

92 | LGB6 | −0.200 | XGB13 | 0.163 | GWOXGB6 | 0.235 | GWORF2 | 0.221 |

91 | GWORF6 | −0.078 | GWORF3 | 0.180 | RF4 | 0.281 | RF10 | 0.239 |

90 | GWOXGB6 | −0.040 | LGB3 | 0.182 | GWOLGB6 | 0.299 | GWOLGB2 | 0.246 |

89 | LGB11 | −0.025 | RF13 | 0.367 | RF2 | 0.386 | GWOXGB2 | 0.252 |

88 | GWOLGB6 | −0.024 | GWOXGB3 | 0.374 | XGB4 | 0.481 | GWORF10 | 0.431 |

87 | GWORF11 | 0.028 | GWOLGB3 | 0.409 | XGB11 | 0.511 | LGB10 | 0.442 |

86 | GWOLGB11 | 0.090 | LGB6 | 0.446 | XGB2 | 0.580 | GWOLGB10 | 0.470 |

85 | GWOXGB11 | 0.284 | XGB10 | 0.513 | RF11 | 0.744 | GWOXGB10 | 0.481 |

84 | RF2 | 0.450 | GWORF6 | 0.593 | LGB4 | 0.873 | RF3 | 0.971 |

83 | XGB2 | 0.484 | GWOLGB6 | 0.640 | GWORF4 | 0.882 | XGB3 | 0.989 |

82 | LGB2 | 0.888 | GWOXGB6 | 0.653 | GWOXGB4 | 0.883 | LGB3 | 1.189 |

81 | GWORF2 | 1.004 | RF10 | 0.756 | GWOXGB11 | 0.906 | GWORF3 | 1.192 |

80 | GWOLGB2 | 1.045 | LGB13 | 0.804 | GWOLGB4 | 0.908 | XGB13 | 1.226 |

79 | GWOXGB2 | 1.097 | GWORF13 | 0.848 | LGB11 | 0.952 | GWOLGB3 | 1.228 |

78 | XGB10 | 1.359 | GWOLGB13 | 1.038 | LGB2 | 0.957 | GWOXGB3 | 1.234 |

77 | RF10 | 1.540 | GWOXGB13 | 1.071 | GWORF11 | 0.990 | RF5 | 1.269 |

76 | LGB10 | 1.695 | LGB10 | 1.092 | GWOLGB11 | 0.993 | GWORF11 | 1.387 |

75 | GWORF10 | 1.826 | GWORF10 | 1.183 | GWORF2 | 1.019 | GWOXGB13 | 1.398 |

74 | GWOLGB10 | 1.837 | GWOLGB10 | 1.250 | GWOXGB2 | 1.113 | LGB5 | 1.423 |

73 | GWOXGB10 | 1.854 | GWOXGB11 | 1.312 | GWOLGB2 | 1.118 | GWOLGB13 | 1.435 |

**Table 22.**Ranking of the least-performing models in conventional and hybrid MLs at sub-humid stations.

Faizabad | Jabalpur | Raipur | Ranchi | Ranichauri | Samastipur | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RANK | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI | MODEL | GPI |

108 | RF1 | −2.488 | RF1 | −2.511 | RF1 | −2.473 | RF1 | −2.276 | RF1 | −2.703 | RF1 | −2.620 |

107 | XGB1 | −1.954 | XGB1 | −1.969 | XGB1 | −1.909 | XGB2 | −1.606 | XGB1 | −1.931 | XGB1 | −2.127 |

106 | LGB1 | −1.173 | LGB1 | −1.330 | LGB1 | −1.246 | RF2 | −1.498 | LGB1 | −1.471 | LGB1 | −1.656 |

105 | GWOXGB1 | −1.140 | XGB2 | −1.304 | GWOXGB1 | −1.036 | XGB1 | −1.449 | GWOLGB1 | −1.322 | GWOLGB1 | −1.492 |

104 | GWOLGB1 | −1.135 | RF2 | −1.126 | GWOLGB1 | −1.020 | LGB2 | −0.861 | GWORF1 | −1.305 | GWORF1 | −1.487 |

103 | GWORF1 | −1.058 | GWOXGB1 | −1.119 | XGB2 | −1.013 | LGB1 | −0.823 | GWOXGB1 | −1.295 | GWOXGB1 | −1.454 |

102 | XGB2 | −0.819 | GWORF1 | −1.090 | GWORF1 | −0.986 | XGB10 | −0.793 | RF3 | −1.233 | RF6 | −0.818 |

101 | RF2 | −0.679 | GWOLGB1 | −1.086 | RF2 | −0.889 | XGB6 | −0.735 | XGB3 | −1.215 | XGB6 | −0.789 |

100 | RF6 | −0.648 | XGB6 | −0.719 | XGB6 | −0.806 | GWOXGB2 | −0.690 | LGB3 | −0.772 | XGB2 | −0.488 |

99 | XGB4 | −0.618 | LGB2 | −0.695 | RF6 | −0.787 | GWOLGB2 | −0.643 | GWORF3 | −0.698 | RF2 | −0.379 |

98 | XGB6 | −0.599 | GWORF2 | −0.520 | LGB2 | −0.574 | GWORF2 | −0.631 | GWOLGB3 | −0.665 | LGB6 | −0.339 |

97 | RF4 | −0.394 | RF6 | −0.504 | XGB10 | −0.372 | GWOXGB1 | −0.597 | GWOXGB3 | −0.614 | GWORF6 | −0.293 |

96 | LGB2 | −0.253 | GWOXGB2 | −0.477 | GWOXGB2 | −0.297 | GWOLGB1 | −0.593 | XGB2 | −0.313 | GWOLGB6 | −0.234 |

95 | LGB6 | −0.167 | GWOLGB2 | −0.463 | GWORF2 | −0.296 | GWORF1 | −0.593 | RF2 | −0.258 | GWOXGB6 | −0.212 |

94 | GWORF6 | −0.139 | LGB6 | −0.127 | GWOLGB2 | −0.266 | RF6 | −0.591 | LGB2 | 0.098 | XGB3 | −0.131 |

93 | GWOLGB2 | −0.075 | XGB10 | −0.100 | LGB6 | −0.212 | RF10 | −0.427 | GWOXGB2 | 0.203 | LGB2 | −0.016 |

92 | GWOXGB2 | −0.036 | GWOXGB6 | −0.009 | GWOLGB6 | −0.088 | LGB10 | 0.005 | GWORF2 | 0.203 | GWOXGB2 | 0.015 |

91 | GWOLGB6 | −0.034 | GWORF6 | 0.040 | GWOXGB6 | −0.068 | LGB6 | 0.066 | GWOLGB2 | 0.213 | RF3 | 0.035 |

90 | GWOXGB6 | −0.014 | GWOLGB6 | 0.057 | GWORF6 | −0.044 | GWORF10 | 0.121 | XGB6 | 0.304 | GWORF2 | 0.040 |

89 | GWORF2 | 0.063 | RF10 | 0.236 | RF10 | 0.040 | GWORF6 | 0.151 | RF6 | 0.366 | GWOLGB2 | 0.062 |

88 | GWORF4 | 0.074 | LGB10 | 0.354 | XGB4 | 0.152 | GWOXGB10 | 0.246 | XGB13 | 0.445 | LGB3 | 0.326 |

87 | LGB4 | 0.106 | GWOXGB10 | 0.468 | LGB10 | 0.313 | XGB3 | 0.267 | RF13 | 0.592 | GWOXGB3 | 0.412 |

86 | GWOXGB4 | 0.137 | GWORF10 | 0.536 | RF4 | 0.405 | GWOLGB10 | 0.271 | LGB6 | 0.645 | GWOLGB3 | 0.423 |

85 | GWOLGB4 | 0.139 | GWOLGB10 | 0.563 | GWOXGB10 | 0.556 | RF3 | 0.313 | GWORF6 | 0.696 | GWORF3 | 0.446 |

84 | XGB14 | 0.520 | XGB4 | 0.585 | GWORF10 | 0.559 | GWOXGB6 | 0.321 | GWOLGB6 | 0.706 | XGB11 | 0.586 |

83 | RF14 | 0.783 | RF4 | 0.652 | GWOLGB10 | 0.626 | GWOLGB6 | 0.356 | GWOXGB6 | 0.711 | RF11 | 0.844 |

82 | XGB10 | 0.893 | GWORF4 | 0.964 | LGB4 | 0.767 | XGB13 | 0.840 | GWORF13 | 0.810 | XGB10 | 0.903 |

81 | LGB14 | 0.967 | LGB4 | 0.986 | XGB5 | 0.857 | LGB3 | 0.915 | LGB13 | 0.825 | GWORF11 | 0.954 |

80 | GWOXGB14 | 0.967 | XGB3 | 1.006 | GWORF4 | 0.942 | GWORF3 | 1.036 | XGB11 | 0.902 | GWOXGB11 | 0.993 |

79 | GWOLGB14 | 1.017 | RF3 | 1.014 | GWOLGB4 | 0.972 | RF13 | 1.075 | GWOLGB13 | 0.927 | LGB11 | 1.016 |

78 | RF5 | 1.039 | GWOXGB4 | 1.055 | GWOXGB4 | 0.986 | GWOXGB3 | 1.159 | GWOXGB13 | 0.932 | GWOLGB11 | 1.074 |

77 | GWORF14 | 1.054 | GWOLGB4 | 1.068 | RF5 | 1.293 | GWOLGB3 | 1.183 | RF11 | 1.159 | RF10 | 1.098 |

76 | LGB10 | 1.309 | LGB14 | 1.377 | LGB14 | 1.387 | GWORF13 | 1.519 | LGB11 | 1.232 | LGB10 | 1.271 |

75 | GWOXGB10 | 1.420 | GWORF14 | 1.378 | GWOXGB14 | 1.504 | LGB13 | 1.552 | GWORF11 | 1.263 | GWORF10 | 1.287 |

74 | GWORF5 | 1.439 | GWOXGB14 | 1.394 | GWORF14 | 1.511 | GWOXGB13 | 1.687 | GWOXGB11 | 1.266 | GWOLGB10 | 1.370 |

73 | GWOLGB10 | 1.497 | GWOLGB3 | 1.417 | GWOLGB14 | 1.514 | GWOLGB13 | 1.724 | GWOLGB11 | 1.297 | GWOXGB10 | 1.380 |

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## Share and Cite

**MDPI and ACS Style**

Heramb, P.; Ramana Rao, K.V.; Subeesh, A.; Srivastava, A. Predictive Modelling of Reference Evapotranspiration Using Machine Learning Models Coupled with Grey Wolf Optimizer. *Water* **2023**, *15*, 856.
https://doi.org/10.3390/w15050856

**AMA Style**

Heramb P, Ramana Rao KV, Subeesh A, Srivastava A. Predictive Modelling of Reference Evapotranspiration Using Machine Learning Models Coupled with Grey Wolf Optimizer. *Water*. 2023; 15(5):856.
https://doi.org/10.3390/w15050856

**Chicago/Turabian Style**

Heramb, Pangam, K. V. Ramana Rao, A. Subeesh, and Ankur Srivastava. 2023. "Predictive Modelling of Reference Evapotranspiration Using Machine Learning Models Coupled with Grey Wolf Optimizer" *Water* 15, no. 5: 856.
https://doi.org/10.3390/w15050856