Modification of the radiation-based Abtew reference evapotranspiration model under humid climate, Northeast India

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). ET₀ 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 ET₀ 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 ET₀ 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 ET₀ (Xing et al. 2008).

The FAO-56 Penman–Monteith (PM) model was determined to be the most appropriate alternative model for estimating evapotranspiration (ET₀) due to its proper and precise prediction of ET₀ when compared to the findings of other ET₀ estimation models (Pandey et al. 2017). ET₀ 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 ET₀ 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 ET₀ 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 ET₀ (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 ET₀ 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 ET₀ 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 ET₀ estimation.

There are various research studies in which the R_S have been analyzed and applied in ET₀ estimation (Teke & Bașak Yildirim 2014; Yao et al. 2014). Tabari et al. (2016) analyzed 11 R_S models and their impact on daily ET₀. 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 ET₀ on monthly, seasonal, and annual time scales in Serbia. The FAO-56 PM and adjusted Hargreaves were used for the estimation of ET₀. 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 ET₀ 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 ET₀ process in the region. At the same time, wind speed has just a little influence. Poddar et al. (2021) tested 12 ET₀ 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 ET₀ 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 ET₀ 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 ET₀ estimation by using seven temperature-based solar radiation models and evaluate the estimation accuracy of seven improved radiation-based Abtew models and selected ET₀ models at Dibrugarh, Northeast India.

The present study used different temperature-based solar radiation models to modify the Abtew model for ET₀ 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.

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).

In Equations (1)–(8), ET₀ 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), u₂ is the wind speed at 2 m height (m/s), u₁₀ 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).

In Equations (9)–(16), P_z is the atmospheric pressure at the site (kPa), P₀ 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).

Using meteorological variables from 1994 to 2016, the accuracy and performance of the models to estimate ET₀ were assessed using the following statistical indices.

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.

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_i signify the ET₀ values estimated by the FAO PM model and the examined models, respectively, and represent the corresponding mean ET₀ values; the subscript i refers to the ith value of the ET₀. Accuracy indices, including R², 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_i is the predicted value, O_i is the observed value, n is the number of observations, is the observed mean, and is the predicted mean.

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.

Table 1

Calibrated parameters of the seven selected solar radiation equations

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

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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 ET₀ 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).

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 (R²), 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.

The study's findings suggest that modified Abtew equations can be an effective and reliable method for estimating monthly ET₀ in the Dibrugarh region. The first-ranked A6 equation is a reliable and accurate method for estimating monthly ET₀ 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, R², 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 R² 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 R² 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 ET₀ 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 R² 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.

The Irmak model had the highest ET₀ 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 ET₀, and its conclusions are comparable to those of previous studies.

The results suggested that A6 had the most precise ET₀ 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 ET₀ 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 ET₀ 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 ET₀ 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 ET₀ 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 ET₀ models cannot accurately represent the changing mechanisms of ET₀, leading to ambiguity. Parameter localization is the fundamental method for reducing uncertainty and improving the computation accuracy of simple empirical models.

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 ET₀ models have been compared statistically using indices MAE, RMSE, SE, r, R², and D.

The main conclusions of this study are shown as follows:

• 1.

  For ET₀ estimation at the Dibrugarh site, the seven Abi models (R² = 0.69–0.79) were more accurate than the other selected ET₀ models (R² = 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 ET₀.

• 3.

  The improved Abtew (Abi) models outperformed the Mkk, SS, Ir, and MT models for ET₀ estimate in Dibrugarh.

• 4.

  Overall, the present investigation discovered that the Abi models outperformed the Mkk, SS, Ir, and MT models for ET₀ estimate in Northeast India (MT). It is strongly advised to use the A6, which needs air temperature as an input parameter, to estimate ET₀ in Northeast India.

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

The authors declare there is no conflict.