Comparative study of various reference evapotranspiration models under different agroclimatic zones Open Access

The following symbols are used in this paper:

a

function of I used in the Thornthwaite method

c

adjustment factor to compensate for the effect of day and night weather conditions

C

adjustment factor, which depends on the mean humidity and daytime wind conditions

C'

adjustment factor, which depends on minimum relative humidity, sunshine hours, and daytime wind estimates

d

correction factor depends on latitude and month

ET_o

reference evapotranspiration (mm/day)

e_a

actual vapor pressure (kPa)

(e_a − e_d)

difference between saturation vapor pressure at mean air temperature and mean actual vapor pressure of air (mb)

e_s

saturation vapor pressure (kPa)

G

soil heat flux density (MJ/(m²day))

I

annual thermal index, i.e., the sum of monthly indices I

N

photoperiod for a given day

p

mean daily percentage of total annual daytime hours obtained for a given month and latitude (%)

RH

average relative humidity (%)

R_a

extraterrestrial solar radiation (MJ/(m²day))

R_n

net radiation at crop surface (MJ/(m²day))

R′_n

net radiation at crop surface (mm/day)

R_s

incoming solar radiation (MJ/(m²day))

R′_s

incoming solar radiation (mm/day)

T

mean air temperature at 2 m height (°C)

T_dew

monthly mean temperature at dew point (°C)

T_max

maximum temperatures of air (°C)

T_min

minimum temperatures of air (°C)

U

wind speed at 2 m (km/day)

u

wind speed at 2 m (m/s)

W

a psychrometric weighting function depends on temperature and altitude

β

Priestley–Taylor coefficient

γ

psychrometric constant (kPa/°C)

Δ

slope of vapor pressure versus temperature curve at mean temperature (kPa/°C)

Evapotranspiration is an essential aspect of the water cycle (Song et al. 2018). An exact assessment of ET_o is required for the proper execution of irrigation scheduling and agricultural yield modeling in hilly areas (Almorox & Hontoria 2004; Rahimi Khoob 2008; Singh & Pawar 2011; Song et al. 2018; Kumar et al. 2020; Kumar et al. 2022). Water availability is not usually the key concern for irrigation in hilly places; however, the process of conveying water and effectively irrigating fields becomes challenging and expensive due to various factors, i.e., the diverse topography, steep slopes, and rugged terrains (Singh & Thakur 2018). These physical characteristics need expensive technical solutions and infrastructure to ensure effective water distribution, making irrigation in mountainous places more expensive than in flat areas. The Food and Agriculture Organization of the United Nations (FAO) has recommended the FAO-56PM combination equation as the standard method for estimating ET_o. However, a significant drawback of the FAO-56PM equation is its reliance on extensive weather data such as temperature, wind speed, air humidity, and solar radiation, which may not always be accessible in many locations. This issue is particularly prominent in developing countries, where reliable weather datasets containing radiation, relative humidity, and wind speed information are limited (Trajkovic & Kolakovic 2009).

The weighing lysimeter is the approach for determining precise ET_o (Xu & Chen 2005). However, because there is a scarcity of lysimeter data and extensive weather data required for FAO-56PM in hilly areas, alternative approaches have been established (Bashir et al. 2023). Numerous original and modified methods for calculating ET_o have been proposed, which can be categorized based on their data requirements:

• (1) Combination methods (Allen et al. 1998; Song et al. 2018; Ghasemi-Saadatabadi et al. 2024),

• (2) Radiation methods (Djaman et al. 2015; Hasani & Shahid 2024; Raja et al. 2024), and

• (3) Temperature methods (Xu & Singh 2001; Oudin et al. 2005; Hasani & Shahid 2024; Raja et al. 2024).

Several studies have shown that the FAO-56PM method is the best in a variety of climatic conditions (Kashyap & Panda 2001; Irmak et al. 2003; Itenfisu et al. 2003; Cai et al. 2007) and is considered the standard method for calculating ET_o (Allen et al. 1998). The FAO-56PM is commonly employed by researchers to estimate ET_o (Alexandris et al. 2006); though this is a combination method, it is limited in its daily or regular usage due to the lack of meteorological data at most of the locations. This justifies using radiation and/or temperature-based ET_o approaches instead of the FAO-56PM method (Poddar et al. 2021). Various researchers have evaluated the efficacy of ET_o approaches across a variety of climatic conditions, as represented in Table 1.

The present study was carried out in Himachal Pradesh, a state located in the Western Himalayas in the northern part of India. In hilly regions like Himachal Pradesh, data availability is a significant challenge. The state has a limited number of weather stations, and their maintenance is often inadequate. Consequently, acquiring reliable observed data becomes a difficult task. Therefore, the present study utilizes a blend of observed and gridded data, necessitated by the unavailability of all required accessible observed data. The primary objective of this study is to assess the effectiveness of nine different evapotranspiration (ET_o) models, specifically with the FAO-56PM method, in four distinct agroclimatic zones (Jithendran & Bhat 2000; Dev et al. 2022) within Himachal Pradesh. The evaluation of ET_o in different agroclimatic zones is crucial as each zone exhibits unique ET_o requirements. The main objectives of the study are:

• i Estimation of ET_o employing various models for different agroclimatic zones.

• ii Performance evaluation of various ET_o models and establishing the best alternative ET_o method for different agroclimatic zones of Himachal Pradesh.

Agroclimatic zones (Jithendran & Bhat 2000):

• Zone I: Subtropical sub-mountainous low hills (up to 1,100 m)

• Zone II: Sub-humid mid hills (1,100 < 2,000 m)

• Zone III: Wet temperate high hills (2,000 < 3,000 m)

• Zone IV: Dry temperate high hills (>3,000 m)

The monthly meteorological data, including maximum temperature, minimum temperature, mean temperature, and wind speed, were provided by the hydrology cell, State Data Center (Mandi). Sunlight duration and relative humidity were obtained from the NASA power system (Data Access Viewer) (https://power.larc.nasa.gov/data-access-viewer/) for the period of 10 years (2011–2021). The meteorological data modeled by MERRA2 (Modern-Era Retrospective analysis for Research and Application) having a resolution of 0.5° × 0.625° and solar radiation data modeled by CERES (Clouds and Earth's Radiant Energy System) and FLASHFlux (Fast Longwave and Shortwave flux) having a resolution of 1° × 1° is used in this study. The integrity and quality check of different data used in the study was carried out in accordance with Allen et al. (1998).

Nine ET_o models (Table 2) are selected for the study purpose, which is further divided into three methods, i.e., combination (CPEN, MPEN) methods, radiation (24RAD, P-T, T-C, MAK) methods, and temperature (H-S, B-C, and T-W) methods. The analysis employs these methods across all 12 locations within four agroclimatic zones of Himachal Pradesh, with the paper focusing on presenting results from four specific locations (Table 3). They are chosen to represent the diversity and broader regional context within the agroclimatic zone. These nine ET_o methods are validated with the standard FAO-56PM method using RMSE, R², PE, and scatter index (SI) to determine the best ET_o model.

Table 2

Methods of reference evapotranspiration (ET_o) used

Classification .	Method .	Abbreviations .	Parameters used .	Equations .	References .
Combination-type methods	FAO-56 Penman–Monteith	FAO-56PM	Solar radiation, temperature, wind speed, humidity		Allen et al. (1998)
	FAO-24 corrected Penman	CPEN	Solar radiation, temperature, wind speed, humidity		Doorenbon & Pruitt (1977)
	Modified Penman	MPEN	Solar radiation, temperature, wind speed, humidity		Burman & Pochop (1994)
Radiation-type methods	FAO-24 Radiation	24RAD	Solar radiation, temperature		Doorenbon & Pruitt (1977)
	Priestley–Taylor	P-T	Solar radiation, temperature		Priestley & Taylor (1972)
	Turc	T-C	Solar radiation, temperature, humidity	⁠; for RH < 50% ⁠; for RH 50%	Turc (1961)
	Makkink	MAK	Solar radiation, temperature		Makkink (1957)
Temperature-type methods	FAO-56 Hargreaves–Samani	H-S	Temperature, solar radiation		Hargreaves & Samani (1985)
	FAO-24 Blaney–Criddle	B-C	Temperature		Doorenbon & Pruitt (1977)
	Thornthwaite	T-W	Temperature	⁠;	Thornthwaite (1948)

Classification .	Method .	Abbreviations .	Parameters used .	Equations .	References .
Combination-type methods	FAO-56 Penman–Monteith	FAO-56PM	Solar radiation, temperature, wind speed, humidity		Allen et al. (1998)
	FAO-24 corrected Penman	CPEN	Solar radiation, temperature, wind speed, humidity		Doorenbon & Pruitt (1977)
	Modified Penman	MPEN	Solar radiation, temperature, wind speed, humidity		Burman & Pochop (1994)
Radiation-type methods	FAO-24 Radiation	24RAD	Solar radiation, temperature		Doorenbon & Pruitt (1977)
	Priestley–Taylor	P-T	Solar radiation, temperature		Priestley & Taylor (1972)
	Turc	T-C	Solar radiation, temperature, humidity	⁠; for RH < 50% ⁠; for RH 50%	Turc (1961)
	Makkink	MAK	Solar radiation, temperature		Makkink (1957)
Temperature-type methods	FAO-56 Hargreaves–Samani	H-S	Temperature, solar radiation		Hargreaves & Samani (1985)
	FAO-24 Blaney–Criddle	B-C	Temperature		Doorenbon & Pruitt (1977)
	Thornthwaite	T-W	Temperature	⁠;	Thornthwaite (1948)

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In this study, the efficacy of the nine most commonly used ET_o models for humid Himalayan regions is evaluated with FAO-56PM as a standard reference method (ASCE-EWRI 2005). The primary goal of the study is to discover the most suitable approach that yields ET_o values that are nearest to those obtained by the FAO-56PM model for the agroclimatic zones of the study region.

To estimate ET_o values, combination-type methods depend upon a vast variety of input climatic parameters. These methods are well-known for producing reliable ET_o predictions (Poddar et al. 2021). This study uses the FAO-56PM approach as the standard for evaluating alternative methods. The other approach in this category is FAO-24 corrected Penman (CPEN) (Doorenbon & Pruitt 1977) and modified Penman (MPEN) (Burman & Pochop 1994). The performance of these methods is evaluated as an alternative method. The FAO-56 guidelines are used to compute relevant parameters such as the psychometric constant, net radiation, and the slope of the saturation vapor pressure curve, and the soil heat flow is considered to be zero (Allen et al. 1998; Poddar et al. 2021).

The current study considers four radiation-based models: FAO-24 Radiation (24RAD) (Doorenbon & Pruitt 1977), Priestley–Taylor (P-T) (Priestley & Taylor 1972), Turc (T-C) (Priestley & Taylor 1972; Xu & Singh 2001), and Makkink (MAK) (Jacobs & De Bruin 1998). These methods estimate ET_o using solar radiation and other climate data. However, the accuracy and reliability of these approaches are heavily reliant on radiation data from the study area (Poddar et al. 2021).

Temperature-based approaches have been seen as feasible substitutions to combination-type methods owing to the availability of temperature readings (maximum, minimum, and mean temperature) at practically all sites. Hargreaves–Samani (H-S) (Hargreaves & Samani 1985), Blaney–Criddle (B-C) (Doorenbon & Pruitt 1977), and Thornwaite (T-W) (Thornthwaite 1948) temperature-based methodologies are employed for evaluation in this work (Poddar et al. 2021).

Sensitivity analysis of the best-performing model in each zone (P-T and H-S) was conducted in order to evaluate the effect of changes in parameters on ET_o estimate. In this study, T and R climatic parameters were selected and varied at ±5, 10, 15, and 20% by changing one parameter at a time while keeping other parameters constant and were compared with the generated outputs (Sharma et al. 2024a, b). Over a 10-year period, the monthly ET_o value change is averaged. To keep the sensitivity within a specific linear range, the parameters are adjusted within a range of ±20% (Poddar et al. 2021; Sharma et al. 2024a, b).

Among the combination methods, i.e., MPEN and CPEN, ET_o estimations using the CPEN approach are comparable to FAO-56PM ET_o predictions for all four agroclimatic zones. Figures 2(a), 3(a), 4(a), and 5(a) depict a qualitative comparison of monthly ET_o values derived for all four zones using the CPEN, MPEN, and FAO-56PM methods. Supplementary Tables S2–S5 contain error statistics for all four agroclimatic zones. A significant connection exists between ET_o values computed by CPEN, MPEN, and FAO-56PM methods, as indicated by higher R² values ranging from 0.86 to 0.99 and low error statistics (Supplementary Tables S2–S5). The CPEN and MPEN methods’ reliable results might be due to the fact that the parameter requirements for both these methods are almost similar to FAO-56PM. Therefore, CPEN and MPEN were not selected as alternatives to the FAO-56PM technique for the same reason.

Figures 2(b), 3(b), 4(b), and 5(b) depict the comparison of monthly mean daily ET_o values derived using the FAO-56PM method and radiation-based approaches. Supplementary Tables S2–S5 display the error statistics of radiation-based approaches using FAO-56PM.

For zone I, subtropical mountain and low hills ET_o estimations derived by the P-T technique agreed well with the FAO-56PM ET_o estimates, showing low error statistics (RMSE = 0.63 mm/day). The FAO-56PM ET_o data, when compared to the 24RAD approach, produced the underestimation (RMSE = 1.62 mm/day), while the MAK method offered the most underestimation (RMSE = 3.58 mm/day). Tabari (2010) found that the MAK model provided the worst estimates in all climates except cold humid conditions while testing ET_o values in four Iranian climates. ET_o value obtained by T-C provides the overestimated results. In this zone, the next-ranked approach is 24RAD (Table 4), having PE (22.55%) better than the MAK and T-C method. Poddar et al. (2021) found that among the radiation methods used, 24RAD performed best for sub-humid and subtropical locations.

For zone II, sub-humid mid hills, the results are similar to zone I, the T-C approach overestimates (RMSE = 2.22 mm/day) the ET_o values, while the 24RAD and MAK methods underestimate the FAO-56PM results.

For zone III, wet temperate (humid) high hills ET_o values obtained by the T-C method show excellent agreement with those obtained by the FAO-56PM method, with low error statistics. Trajkovic & Kolakovic (2009) concluded that the T-C equation provides the most accurate computation in all humid places and is the most adaptable to local climatic circumstances.

Comparatively, the MAK method yields the worst results when compared to other radiation approaches. Tabari (2010) found that the MAK model provided the worst estimates in all climates except cold humid conditions while testing ET_o values in four Iranian climates. P-T overestimates ET_o values in zone III, whereas 24RAD underestimates the ET_o. Tabari (2010) claims that the P-T model used for the humid climate study overestimated the ET_o value determined by FAO-56PM.

For zone IV, dry temperate high hills (cold) among all radiation approaches, the T-C method produces the most acceptable results. According to the findings of Tabari (2010), the T-C and MAK models are the most accurate methods for determining ET_o in environments with cold and dry conditions. MAK and 24RAD also provide very close ET_o values relative to FAO-56PM, while P-T underestimates the ET_o values for zone IV.

Figures 2(c), 3(c), 4(c), and 5(c) display the plots depicting the comparison of monthly mean daily ET_o values obtained from the FAO-56PM approach against temperature-based methods. Among the temperature methods, the H-S method demonstrates the superior performance in the study area across all four agroclimatic zones. The H-S equation, as proposed by Hargreaves & Samani (1985) and further supported by Almorox et al. (2015), has been found to be highly effective in dry, semi-arid, temperate, cold, and polar locations worldwide.

However, the performance of the T-W method is particularly poor in zone III, as depicted in Figure 4(c). Thornthwaite's techniques, initially introduced in 1948, generally yield the least accurate estimates across various climatic conditions, as mentioned by Almorox et al. (2015). In contrast, the H-S method has been proposed by Nandagiri & Kovoor (2006) as a suitable alternative to the FAO-56PM method specifically for sub-humid environments like Bangalore in India. Furthermore, Allen et al. (1998) and Hargreaves & Allen (2003) have suggested the H-S approach as a viable substitute for the FAO-56PM method across all agroclimatic zones.

Zone IV, which is characterized by a cold climate where temperatures fall below 0 °C during winters, it is observed that several methods underestimate ET_o during this season owing to their zero outputs when the temperature drops below 0 °C (Song et al. 2018). Consequently, the zero values of ET_o in Figure 9 can be attributed to the winter season in this zone. It is important to consider this limitation when applying temperature-based methods in cold climates with freezing temperatures during specific periods.

In P-T and H-S models, the radiation parameter is found to be more sensitive than temperature, which aligns with the outcomes reported by Abraham & Mohan (2023) for all climates.

In order to identify suitable ET_o methods for different agroclimatic zones in the study area, the FAO-56PM method and nine other ET_o methods were evaluated using the monthly mean of daily ET_o values. Sensitivity analysis is also done to better understand the parameter variation. The study area encompassed four zones: zone I (subtropical sub-mountainous low hills), zone II (sub-humid mid hills), zone III (wet temperate high hills), and zone IV (dry temperate high hills). Based on the statistical error analysis, the following observations were made:

• 1. Among the radiation methods, the P-T method demonstrated strong performance for subtropical low hills (RMSE = 0.63, R² = 0.93, PE = 2.48, SI = 0.10) and sub-humid mid hills (RMSE = 0.69, R² = 0.90, PE = 1.55, SI = 0.11).

• 2. The T-C method overestimated ET_o values compared with the FAO-56PM method in zone I and zone II (subtropical and sub-humid).

• 3. The 24RAD and MAK methods, which underestimated ET_o values, are not recommended for subtropical low hills and sub-humid mid hills.

• 4. The T-C method yielded satisfactory results in zone III (humid) (RMSE = 0.71, R² = 0.89, PE = 10.20, SI = 0.15) and zone IV (RMSE = 1.17, R² = 0.90, PE = 13.99, SI = 0.34), among the radiation methods.

• 5. Results from the temperature method indicated that the H-S method outperformed the B-C approach in all agroclimatic zones.

• 6. The T-W approach exhibited the least reliable performance across all agroclimatic zones in the study area.

Based on the findings, it was established that the P-T and H-S methods can be employed to calculate ET_o in subtropical low hills and sub-humid mid hills, depending on the data. Similarly, for zones III and IV, the T-C and H-S methods performed better and can be used to estimate ET_o, taking into account the data availability. The assumption of the constant coefficients in the T-C and H-S techniques, which may not apply to all the regions, is the limitation of the study, as it may introduce bias in the ET_o estimation.

I would like to express my sincere gratitude to my Professor Dr Vijay Shankar and research scholar Mr Abhishek Sharma for their invaluable guidance, encouragement, and support throughout the course of my research.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.