## Abstract

This study aimed to improve the Abtew model for reference evapotranspiration (ET_{0}) calculation in Northeast India using seven temperature-based solar radiation models. The temperature-based models require only air temperature as input data, which can be easily measured in most locations worldwide. The performance of the improved Abtew models (A1-A7), along with the Stephen Stewart model (SS), the Irmak model (Ir), and the modified Turc model (MT), was evaluated under the climatic conditions of Dibrugarh, Northeast India, using statistical indices such as mean absolute error (MAE), root mean square error (RMSE), standard error (SE), coefficient of correlation (r), coefficient of determination (R^{2}), and index of agreement (D). The results showed that the seven improved Abtew models (RMSE = 0.40–0.53 mm/day; D = 0.81–0.93) outperformed the four physical models (RMSE = 0.43–2.77 mm/day; D = 0.49–0.91) for the ET_{0} estimate at Dibrugarh. The statistical analysis identified that the A6 model ranked highest for Dibrugarh. This study highlights the significant improvement in ET_{0} estimation accuracy by utilizing temperature-based solar radiation models in the Abtew model. Therefore, we strongly recommend using the A6 model to estimate ET_{0}, which requires only temperature data as input, for estimating ET_{0} under the climatic conditions of Dibrugarh, Northeast India.

## HIGHLIGHTS

In this study, seven temperature-based solar radiation models were adopted to improve the Abtew model for ET

_{0}estimation in humid climate.Modified Abtew using Bristow–Campbell equation ranked best for the study region.

In general, the seven improved Abtew models were more accurate than the others selected ET

_{0}models.

## INTRODUCTION

In hydrology and irrigation, evapotranspiration and evaporation and transpiration are synonymous. Among the fundamental components of the hydrological cycle, evaporation is responsible for water loss from rivers, lakes, and reservoirs. Under changing climatic conditions, irrigation scheduling based on accurate evapotranspiration estimation is needed across regional climatic conditions (Wang & Liang 2008). ET_{0} significantly impacts hydrology, climatology, vegetation, energy segmentation at the land mass across the season and interannual variability (Goroshi *et al.* 2017). Under changing climate scenarios, the ET_{0} estimation accuracy is crucial not only for analyzing the impact of global climate change, environmental issues, and water resource appraisal but also for irrigation scheduling, flood drought assessment, and improving water resource utilization for agriculture (Zhang *et al.* 2015; Fan *et al.* 2016). Field-based measurement of ET_{0} using lysimeters is considered an accurate and efficient approach; however, their practical application is challenging compared to the meteorological data-based estimation at weather stations (Pandey *et al.* 2014; Tabari *et al.* 2016). In practice, climate data from a weather station are frequently utilized to estimate ET_{0} (Xing *et al.* 2008).

The FAO-56 Penman–Monteith (PM) model was determined to be the most appropriate alternative model for estimating evapotranspiration (ET_{0}) due to its proper and precise prediction of ET_{0} when compared to the findings of other ET_{0} estimation models (Pandey *et al.* 2017). ET_{0} methods can be categorized based on their assumptions and input data as temperature data-based, radiation data-based, pan-evaporation data-based, mass transfer-based, and combination-based (Feng *et al.* 2016; Liu *et al.* 2017). Consequently, it is vital to determine the simplest model or model modification that satisfies the primary criteria for ET_{0} estimation under any climatic situation without requiring the collection of a significantly larger dataset. In this study, the FAO-56 PM reference model is compared with various ET_{0} estimation models, including the Abtew model (1996), Hargreaves and Samani model (1982), Modified Turc equation (1996), Makkink model (1957), Stephens-Stewart model (1963), Allen model (1997), Annandale model (2002), Chen model (2004), El-Sebail model (2009), Bristow–Campbell (1984) model, and Goodin model (1999) at Dibrugarh, Northeast India.

Literature implies that temperature and solar radiation factors are the most critical parameters for determining ET_{0} (Samani 2000), and they are frequently utilized in radiation-based simple equations. Numerous studies have demonstrated the advantages of radiation-based techniques over temperature-based ones (Lu *et al.* 2005; Gebhart *et al.* 2013). The Abtew model is one of the most straightforward radiation-based models, resulting in reasonable estimations of ET_{0} in numerous global investigations (Djaman *et al.* 2017; Bourletsikas *et al.* 2018).

Solar radiation (*R*_{S}) is one of the essential parameters for calculating the ET_{0} using the FAO-56 PM method (Trajkovic & Kolakovic 2009). The values of *R*_{S} can be determined using empirical equations. Solar radiation can be accurately estimated using common meteorological factors like cloud cover, sunshine duration, air temperature, and relative humidity (Zhang *et al.* 2018). The studied region has only one solar measurement site, including measured data on sunshine duration. Generally, the most frequently used models worldwide are sunshine-based because of their accuracy and best results compared with other models like Bristow–Campbell (B-C) and Hargreaves–Samani. Usually, sunshine data are not available in many places, which restricts ET_{0} estimation.

There are various research studies in which the *R*_{S} have been analyzed and applied in ET_{0} estimation (Teke & Bașak Yildirim 2014; Yao *et al.* 2014). Tabari *et al.* (2016) analyzed 11 *R*_{S} models and their impact on daily ET_{0}. The Allen model (1997) generally gave the best *R*_{S} values in semi-arid and arid climates. The Samani (2000) and El-Sebail *et al*. (2009) models had the most remarkable improvements after calibration in an arid climate. Gocic & Trajkovic (2014) analyzed the trends of ET_{0} on monthly, seasonal, and annual time scales in Serbia. The FAO-56 PM and adjusted Hargreaves were used for the estimation of ET_{0}. Significantly increasing trends characterized approximately 70% of observed stations.

Previous research in India (Pandey *et al.* 2016; Poddar *et al.* 2021) indicated that radiation-based models were more accurate than temperature-based ones. The computation of ET_{0} involves air temperature and solar radiation data; hence, the preceding model's calculation techniques are relatively simple (Zhang *et al.* 2018). In Northeast India, Pandey *et al.* (2016) tested the applicability of six temperature-based and ten radiation-based models against the FAO-56 PM model and identified that the Irmak model performed well. The improved performance of radiation-based models generally confirms that severe temperature and radiation are the major drivers behind the ET_{0} process in the region. At the same time, wind speed has just a little influence. Poddar *et al.* (2021) tested 12 ET_{0} models in sub-humid sub-tropical regions of India's western Himalayan agroclimatic zone. The researchers concluded that solar radiation, followed by maximum temperature and relative humidity, is the most sensitive metric for estimating ET_{0} in the study area environment. Nandagiri & Kovoor (2006) evaluated seven models throughout India's climatic conditions, concluding that radiation-based models performed better in humid areas. Tomar (2015) investigated multiple ET_{0} estimates in sub-humid regions of India and discovered that FAO24-Radiation outperformed other models. Considering the above, a study was conducted with the following objectives: To improve the Abtew model for ET_{0} estimation by using seven temperature-based solar radiation models and evaluate the estimation accuracy of seven improved radiation-based Abtew models and selected ET_{0} models at Dibrugarh, Northeast India.

The present study used different temperature-based solar radiation models to modify the Abtew model for ET_{0} estimation under humid climates. Improvement in the Abtew model using temperature-based solar radiation models is an attractive and viable option for this study site and impacts local evaluation with the FAO-56 PM reference model.

## MATERIALS AND METHODS

### Study area and data collection

The Brahmaputra River runs through the district's northwestern boundary. The single tributary in the district that flows into the Brahmaputra is the burdening tributary, which divides the region from east to west. It runs through Naharkatia in the east, Khowang in the middle, and forms the border between Dibrugarh and Sivasagar districts in the west. The Dibrugarh district is an almost plain area in Assam.

The entire area is level, with a modest incline from the East Arunachal hills to the west. The district's soil is mainly fertile alluvial soil, with varying quantities of sand and clay. The meteorological data for the research area was obtained from the India Meteorological Department (IMD).

### Calculation of reference evapotranspiration (ET_{0})

#### FAO-56 PM model

*et al.*(1998) recommended methods and procedures followed while calculating all the necessary variables for estimating ET

_{0}. The and were computed using data on

*u*

_{10}and sunshine duration as follows (Feng

*et al.*2017):

#### Abtew model

#### Makkink model (Mkk)

#### Stephens-Stewart model (SS)

#### Irmak model (Ir)

*et al.*(2003) proposed the Irmak model (Zhang

*et al.*2018):

#### Modified Turc model (MT)

_{0}depending on solar radiation and maximum air temperature. The original Turc equation used average air temperature. However, the maximum air temperature was employed here since it showed a stronger association with evapotranspiration in humid climates than the average air temperature.

In Equations (1)–(8), ET_{0} is the reference evapotranspiration (mm/day), *R*_{n} is the net radiation (MJ/m² day), *G* is the soil heat ﬂux density (MJ/m² day), *T* is the mean air temperature (°C), is the maximum air temperature (°C), *e*_{s} is the saturation vapor pressure (kPa), *e*_{a} is the actual vapor pressure (kPa), Δ is the slope of the saturation vapor pressure function (kPa/°C), is the psychometric constant (kPa/°C), *u*_{2} is the wind speed at 2 m height (m/s), *u*_{10} is the measured wind speed at 10 m height (m/s), *z* is the height of measurement, *R*_{S} is the solar radiation (MJ/m² day), *n* is the sunshine duration (h), *N* is the maximum possible duration of sunshine or day–light hours (h), *R*_{a} is the extraterrestrial radiation (MJ/m day), and *a* and *b* are constant with a value of 0.25 and 0.50 recommended by Allen *et al.* (1998).

### Solar radiation estimation based on temperature input

#### Allen model

*et al.*2018):

#### Annandale model

*et al.*(2002) developed a model based on the Hargreaves–Samani model, considering the effects of lower height and atmospheric thickness on

*R*

_{S}(Zhang

*et al.*2018):

#### Hargreaves model

*R*

_{a}) as input (Zhang

*et al.*2018):

#### Chen model

*et al.*(2004) recommended a model to estimate solar radiation based on temperature difference and extraterrestrial radiation as input (Zhang

*et al.*2018):

#### El-Sebail model

*et al.*(2009) recommended a model to estimate solar radiation based on mean temperature and relative humidity as input (Zhang

*et al.*2018):

#### B-C model

#### Goodin model

*et al.*(1999) improved the B-C model by including an

*R*

_{a}term that serves as a scaling factor, allowing the temperature term difference to tolerate a broader range of

*R*

_{S}values (Zhang

*et al.*2018):

In Equations (9)–(16), *P _{z}* is the atmospheric pressure at the site (kPa),

*P*

_{0}is the atmospheric pressure at sea level (kPa),

*K*

_{r}and

*K*

_{ra}are empirical coefficients, and

*Z*is the altitude of the site (km). An empirical coefficient RH is the relative humidity (%), and

*a*,

*b*, and

*c*are empirical coefficients. (°C).

### Performance evaluation of models

Using meteorological variables from 1994 to 2016, the accuracy and performance of the models to estimate ET_{0} were assessed using the following statistical indices.

#### Different accuracy statistical indices applied

##### Coefficient of determination (*R*²)

##### Coefficient of correlation (*r*)

*D* (Index of agreement)

When the accuracy indices mentioned above are close to 1, it indicates a strong correlation between the observed and predicted values. Conversely, when the indices are close to 0, it suggests poor performance.

#### Different error statistical indices applied

##### RMSE (root-mean-square error)

##### MAE (mean absolute error)

##### Standard error ()

When the error indices mentioned above are close to 0, it indicates a strong correlation between the observed and predicted values. Conversely, when the indices are close to 1, it suggests poor performance.

In Equations (17)–(22), *X _{i}* and

*Y*signify the ET

_{i}_{0}values estimated by the FAO PM model and the examined models, respectively, and represent the corresponding mean ET

_{0}values; the subscript

*i*refers to the

*i*th value of the ET

_{0}. Accuracy indices, including

*R*²,

*r*, and

*d*, indicate how closely a model matches observed values, with higher values indicating better model performance. RMSE, MAE, and are in mm/day, with values ranging from 0 (perfect fit) to 1 (worst fit);

*P*is the predicted value,

_{i}*O*is the observed value,

_{i}*n*is the number of observations, is the observed mean, and is the predicted mean.

## RESULTS

### Calibration of selected radiation equations

The parameters of the seven improved radiation models are presented in Table 1. For A1, A2, and A3, the calibration is done using regression analysis, whereas the remaining equation calibration coefficients are estimated using nonlinear regression analysis. The coefficients and the modified Abtew equations for respective solar radiation models are presented in Table 1 and are further used to estimate the evapotranspiration values using the Abtew model.

Model Abb. . | Radiation-based equations . | Equations . | Calibrated coefficient of different equations . | ||
---|---|---|---|---|---|

a
. | b
. | c
. | |||

A1 | Allen equation | ||||

Modified Abtew using Allen equation | |||||

A2 | Annandale equation | 0.1481 | 2.7 × 10^{−5} | ||

Modified Abtew using Annandale equation | |||||

A3 | Hargreaves equation | 0.179 | |||

Modified Abtew using Hargreaves equation | |||||

A4 | Chen equation | 0.2148 | 0.0162 | ||

Modified Abtew using Chen equation | |||||

A5 | El-Sebail equation | 1.0057 | − 0.0059 | − 0.0055 | |

Modified Abtew using El-Sebail equation | |||||

A6 | Bristow–Campbell equation | 44.798 | 0.0034 | 0.488 | |

Modified Abtew using Bristow–Campbell equation | |||||

A7 | Goodin equation | 0.54 | 9.44 | 0.85 | |

Modified Abtew using Goodin equation |

Model Abb. . | Radiation-based equations . | Equations . | Calibrated coefficient of different equations . | ||
---|---|---|---|---|---|

a
. | b
. | c
. | |||

A1 | Allen equation | ||||

Modified Abtew using Allen equation | |||||

A2 | Annandale equation | 0.1481 | 2.7 × 10^{−5} | ||

Modified Abtew using Annandale equation | |||||

A3 | Hargreaves equation | 0.179 | |||

Modified Abtew using Hargreaves equation | |||||

A4 | Chen equation | 0.2148 | 0.0162 | ||

Modified Abtew using Chen equation | |||||

A5 | El-Sebail equation | 1.0057 | − 0.0059 | − 0.0055 | |

Modified Abtew using El-Sebail equation | |||||

A6 | Bristow–Campbell equation | 44.798 | 0.0034 | 0.488 | |

Modified Abtew using Bristow–Campbell equation | |||||

A7 | Goodin equation | 0.54 | 9.44 | 0.85 | |

Modified Abtew using Goodin equation |

### Performance of modified Abtew models and selected evapotranspiration models

Table 2 provides a detailed statistical analysis of the selected equations, including Makkink (Mkk), Stephens-Stewart equation (SS), Irmak (Ir), and Modified Turc (MT). To assess the performance of different models, the evapotranspiration series generated by each equation is compared to the original evapotranspiration values generated by the FAO-56 PM model.

A comprehensive analysis of the statistical performance of the predicted evapotranspiration series generated by Mkk, SS, Ir, and MT equations are provided in Table 2. The table presents two statistical indices categories: error and accuracy. The error indices measure the difference between the observed ET_{0} values and the predicted values generated by the respective equations. These indices include mean absolute error (MAE), root-mean-square error (RMSE), and standard error (SE).

. | Error estimation (mm/day) . | Accuracy estimation . | ||||||
---|---|---|---|---|---|---|---|---|

Equation . | Mean . | MAE . | RMSE . | SE . | r
. | R^{2}
. | D
. | Rank . |

A1 | 3.2490 | 0.3546 | 0.4431 | 0.2500 | 0.8750 | 0.7650 | 0.9028 | 5 |

A2 | 3.2357 | 0.3540 | 0.4414 | 0.2500 | 0.8750 | 0.7650 | 0.9123 | 2 |

A3 | 3.2394 | 0.3542 | 0.4418 | 0.2510 | 0.8750 | 0.7650 | 0.9122 | 3 |

A4 | 3.2824 | 0.3547 | 0.4381 | 0.2610 | 0.8827 | 0.7790 | 0.8879 | 4 |

A5 | 3.3067 | 0.3908 | 0.4420 | 0.2950 | 0.8325 | 0.7930 | 0.8695 | 7 |

A6 | 3.2820 | 0.3526 | 0.4028 | 0.2480 | 0.8814 | 0.7760 | 0.9340 | 1 |

A7 | 3.2672 | 0.4222 | 0.5315 | 0.1760 | 0.8937 | 0.7580 | 0.8188 | 8 |

Mkk | 2.72 | 0.3209 | 0.4336 | 0.3700 | 0.8435 | 0.7115 | 0.8915 | 9 |

SS | 3.1787 | 0.659 | 0.774 | 0.358 | 0.865 | 0.748 | 0.790 | 10 |

Ir | 3.314 | 0.2897 | 0.4174 | 0.3400 | 0.8704 | 0.7500 | 0.9170 | 6 |

MT | 0.49 | 2.66 | 2.77 | 1.8 | 0.869 | 0.75 | 0.497 | 11 |

. | Error estimation (mm/day) . | Accuracy estimation . | ||||||
---|---|---|---|---|---|---|---|---|

Equation . | Mean . | MAE . | RMSE . | SE . | r
. | R^{2}
. | D
. | Rank . |

A1 | 3.2490 | 0.3546 | 0.4431 | 0.2500 | 0.8750 | 0.7650 | 0.9028 | 5 |

A2 | 3.2357 | 0.3540 | 0.4414 | 0.2500 | 0.8750 | 0.7650 | 0.9123 | 2 |

A3 | 3.2394 | 0.3542 | 0.4418 | 0.2510 | 0.8750 | 0.7650 | 0.9122 | 3 |

A4 | 3.2824 | 0.3547 | 0.4381 | 0.2610 | 0.8827 | 0.7790 | 0.8879 | 4 |

A5 | 3.3067 | 0.3908 | 0.4420 | 0.2950 | 0.8325 | 0.7930 | 0.8695 | 7 |

A6 | 3.2820 | 0.3526 | 0.4028 | 0.2480 | 0.8814 | 0.7760 | 0.9340 | 1 |

A7 | 3.2672 | 0.4222 | 0.5315 | 0.1760 | 0.8937 | 0.7580 | 0.8188 | 8 |

Mkk | 2.72 | 0.3209 | 0.4336 | 0.3700 | 0.8435 | 0.7115 | 0.8915 | 9 |

SS | 3.1787 | 0.659 | 0.774 | 0.358 | 0.865 | 0.748 | 0.790 | 10 |

Ir | 3.314 | 0.2897 | 0.4174 | 0.3400 | 0.8704 | 0.7500 | 0.9170 | 6 |

MT | 0.49 | 2.66 | 2.77 | 1.8 | 0.869 | 0.75 | 0.497 | 11 |

The accuracy indices, however, measure the reliability and precision of the predicted values generated by each equation. These indices include correlation coefficient (*r*), coefficient of determination (*R*²), and Willmott's index of agreement (*D*) by analyzing both the error and accuracy indices. Table 2 provides a holistic assessment of the predictive power of each equation, helping researchers and practitioners choose the most reliable and accurate equation for their specific needs.

_{0}than the four selected physical models. Among the Abtew models, the A6 equation, which is a modified version of the Bristow–Campbell-based Abtew equation, exhibited the highest accuracy for Dibrugarh with a mean of 3.267 (mm/day) compared to the mean FAO 56 PM of 3.157 (mm/day), MAE of 0.3526 (mm/day), RMSE of 0.4428 (mm/day),

*r*of 0.88, and SE of 0.2480 (mm/day). Additionally, the index of agreement

*D*was found to be 0.88, while

*R*² was 0.77. The relationship between the original and predicted series is visually presented in Figure 2.

*r*of 0.875, SE of 0.2500 (mm/day), and index of agreement

*D*of 0.8823. The ranking statistics are very close to the best rank model (A6). The

*R*² of 0.7650 of A2 is similar to A6. The relationship between the original and predicted series is visually presented in Figure 3.

_{0}in the Dibrugarh region. The third-best equation was found to be A3, which is a modified Abtew equation using the Hargreaves method, with a mean of 3.2394 (mm/day), MAE of 0.3542 (mm/day), RMSE of 0.4418 (mm/day),

*r*of 0.87, SE of 0.2510 (mm/day), index of agreement

*D*of 0.87 (same as the previous equation), and

*R*² of 0.7650. The relationship between the original and predicted series is visually presented in Figure 4.

*r*of 0.88, SE of 0.2510 (mm/day), index of agreement

*D*of 0.88 (same as the previous equation), and

*R*² of 0.7790. The relationship between the original and predicted series is visually presented in Figure 5.

*r*of 0.88, SE of 0.2500 (mm/day), index of agreement

*D*of 0.88 (same as the previous equations), and

*R*² of 0.76. The relationship between the original and predicted series is visually presented in Figure 6.

The study's findings suggest that modified Abtew equations can be an effective and reliable method for estimating monthly ET_{0} in the Dibrugarh region. The first-ranked A6 equation is a reliable and accurate method for estimating monthly ET_{0} for the study region. The results of this study provide valuable insights for researchers and practitioners working on water resources management and agricultural planning in the region.

Table 2 provides the study's findings to estimate the error and accuracy of various equations. Table 2 presents several performance metrics for each equation, including mean, MAE, RMSE, SE, *r*, R^{2}, and the Durbin-Watson statistic (*D*).

The equations were evaluated based on their average error and accuracy estimation. The A5 and A7 models had similar error statistics, but there was a notable difference in their *D* index. As a result, the A5 model was assigned the 7th rank (Table 2). Based on Table 2, Equation A6 has the highest accuracy estimation (ranked 1) with the lowest MAE, RMSE, and SE values compared to other equations. The A2, A3, and A4 equations have high-accuracy estimations with similar MAE, RMSE, and SE values. Equation Mkk has the highest error estimation, the highest MAE, RMSE, and SE values, and the lowest *r* and *R*^{2} values. Details of equations A1, A5, and A7 performance can be seen in Table 2.

Equation MT which is the Modified Turc equation with mean as 0.49 (mm/day) and MAE as 2.66 (mm/day), RMSE as 2.77 (mm/day), and SE as 1.8 (mm/day), index of agreement *D* is found as 0.497, and *R*^{2} as 0.75. The highest MAE, RMSE, and SE values indicate that it has the highest error among all equations. However, it has a low accuracy estimation with the lowest rank (ranked 11).

The best equation among four selected physical models for monthly estimation ET_{0} is found as Ir with mean as 3.314 (mm/day) and MAE as 0.2897 (mm/day), RMSE as 0.417(mm/day), and SE as 0.340 (mm/day), index of agreement *D* is found as 0.9170, and *R*^{2} as 0.750 (Table 2).

In summary, Table 2 comprehensively compares different equations based on their error and accuracy estimation, which can help select the most appropriate equation for a particular application.

## DISCUSSION

The Irmak model had the highest ET_{0} performance among the four physical models assessed in this study. The Irmak model is based on temperature and radiation input data, which are the key factors influencing ET_{0}, and its conclusions are comparable to those of previous studies.

The results suggested that A6 had the most precise ET_{0} estimation in Northeast India, followed by A2, A3, A4, and A1. The M6 was the enhanced Abtew model based on the Bristow–Campbell radiation model. Using data regarding air temperature, the Bristow–Campbell model estimated *R*_{S}. Pandey & Pandey (2020) examined the sensitivity of ET_{0} in Northeast India. They discovered that the minimum temperature was the most sensitive variable, followed by a sunshine hour (relative sensitivity of 0.77 and 0.66, respectively). According to Djaman *et al.* (2017), the Abtew ET_{0} equation, which utilizes solar radiation and maximum temperature, was found to have the best performance compared to other methods across all three climatic zones in Mali. Bourletsikas *et al.* (2018) evaluated 24 different reference evapotranspiration equations in a grass-covered ground in a Mediterranean forest environment in Greece and reported among the radiation-based models, and their analysis found that the Abtew model demonstrated the most robust performance. All the above-cited studies confirm that the Abtew model showed good performance under different climatic conditions across the globe.

In contrast, the wind speed had the most negligible effect; there was no improvement in model performance when wind speed was added as an input parameter. A2, A3, A4, and A1 also demonstrated an excellent performance for ET_{0} estimation in Northeast India, while A6 inclusion of the minimum temperature effect was the primary factor in its superior accuracy.

The Bristow–Campbell, Goodin, and Chen models were used to calibrate four ET_{0} models that can accurately estimate *R*_{S} based on temperature differences using exponential and logarithmic functions. The Allen, Annandale, and Hargreaves models were used with simple monomial expressions to increase the estimation precision of A5, A1, and A6 relative to A2 and A6. In addition, the seven enhanced Abtew models (A1–A7) were more precise than the four chosen physical models. As a result of the single input parameter, most basic empirical ET_{0} models cannot accurately represent the changing mechanisms of ET_{0}, leading to ambiguity. Parameter localization is the fundamental method for reducing uncertainty and improving the computation accuracy of simple empirical models.

## CONCLUSIONS

The calibrated solar radiation equations estimate the evapotranspiration using Abtew (A1–A7) models. In the present study, seven temperature-based solar radiation models were locally calibrated under climatic conditions for Dibrugarh, Assam, to improve the performance of the Abtew model (A1–A7). These modified Abtew models, along with the Mkk, SS, Ir, and MT models, are compared statistically against original FAO-56 PM evapotranspiration values on monthly average data for 23 years data. The performances of all the modified equations (A1–A7) and other selected ET_{0} models have been compared statistically using indices MAE, RMSE, SE, *r*, *R*², and *D*.

The main conclusions of this study are shown as follows:

- 1.
For ET

_{0}estimation at the Dibrugarh site, the seven Abi models (*R*^{2}= 0.69–0.79) were more accurate than the other selected ET_{0}models (*R*^{2}= 0.71–0.75). - 2.
The A6, A2, A3, A4, and A1 models outperformed the others. The A6 model performed best at the Dibrugarh station and was thus suggested for estimating ET

_{0}. - 3.
The improved Abtew (Abi) models outperformed the Mkk, SS, Ir, and MT models for ET

_{0}estimate in Dibrugarh. - 4.
Overall, the present investigation discovered that the Abi models outperformed the Mkk, SS, Ir, and MT models for ET

_{0}estimate in Northeast India (MT). It is strongly advised to use the A6, which needs air temperature as an input parameter, to estimate ET_{0}in Northeast India.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

*Journal of irrigation and drainage engineering*

**132**(3), 238–249.