Methodology for Obtaining ET_o Data for Climate Change Studies: Quality Analysis and Calibration of the Hargreaves–Samani Equation

Abstract

Reference evapotranspiration (ET_o) is an important part of the water cycle, essential for climate studies, water resource management, and agricultural planning. However, accurate estimation of ET_o is challenging when meteorological data are insufficient or of low quality. Furthermore, in climate change studies where large amounts of data need to be managed, it is important to minimize the complexity of the ET_o calculation. This study presents a comprehensive approach that integrates data quality analysis with two calibration methods—annual and cluster-based—to improve ET_o estimates based solely on temperature data from a set of weather stations (WS). First, the quality and integrity of meteorological data from several WS were analyzed to reduce uncertainty. Second, the Hargreaves–Samani equation (HS) is site calibrated using two approaches: (a) annual calibration, where the radiation coefficient (k_Rs) is adjusted using a data set covering the entire year; (b) cluster-based calibration, where independent radiation coefficients are adjusted for clusters of years and months. The methodology was evaluated for the Alentejo region in Southern Portugal, using data from 1996 to 2023. When using the original HS equation with a k_Rs = 0.17 °C^−0.5, ET_o was estimated with errors from 14.9% to 22.9% with bias ranging from −9.0% to 8.8%. The annual calibration resulted in k_Rs values between 0.157 and 0.165 °C^−0.5 with estimation errors between 13.3% and 20.6% and bias ranging from −1.5% to 1.0% across the different weather stations. Calibration based on clusters of months and years produced unclear results. Dry season months showed better results using cluster-based calibration, while wet season months performed poorly regardless of the calibration approach. The results highlight the importance of meteorological data quality and site-specific calibration for refining temperature-based ET_o estimation methods, and for the region studied, the gains do not justify the increased complexity of the cluster-based approach.

1. Introduction

Addressing the challenges posed by climate change (CC) to agriculture is crucial, particularly to understand the impacts on irrigation demands [1,2,3,4]. Accurate evapotranspiration (ET) estimates are becoming increasingly important when dealing with water scarcity, particularly where water resources are decreasing and demand is increasing [5,6]. Efforts to adapt to the potential effects of CC on agricultural productivity require improved information, particularly on crop evapotranspiration (ET_c). Depending on data availability and study objectives, there are different approaches to measure or estimate ET at different scales [7,8,9,10,11,12,13]. The predominant method for estimating ET_c is the K_c-ET_o approach, which combines the reference evapotranspiration (ET_o) with a crop coefficient (K_c). Therefore, accuracy in estimating ET_o is crucial [5,6,14,15]. There are several methods for estimating ET_o, with the FAO56 Penman–Monteith (ET_o-PM) equation being the standard as it accurately accounts for a wide range of meteorological variables and provides consistent values across regions and climates [6,12,16,17,18,19]. The ET_o-PM requires data on maximum and minimum air temperatures (T_max, T_min), relative humidity, shortwave solar radiation (R_s), and wind speed at 2 m height (u₂) [5,6]. However, challenges arise when working with large datasets or when data sets are unavailable, insufficient, or of questionable quality [6,19,20,21,22]. Therefore, assessing the quality of the observed data before computing ET_o is crucial as it is influenced by the considered variable, location, observation practices, temporal changes, sensor malfunctions, and lack of maintenance [23,24].

Reanalysis datasets have been used to estimate ET_o at locations with insufficient spatial coverage or without long time series measurements [25,26]. However, these datasets are subject to errors due to artificial trends and interpolation methods, and their reliability varies depending on climatic variables, locations, and time scales [27,28,29,30]. Therefore, this type of data may introduce uncertainty when estimating ET_o. In response to challenges due to poor quality and/or missing data, alternative approaches have been proposed, such as simplified ET_o formulas that require fewer climate variables. Temperature-based ET_o equations such as the Hargreaves–Samani equation [31] (ET_o-HS) are viable alternatives in areas with scarce or uncertain data quality [6,19,22]. Almorox et al. [23] and Paredes et al. [6] highlight its superior performance in different climates. However, the empirical development of the ET_o-HS equation limits its applicability in humid regions [32].

Another issue when estimating ET_o for climate change studies is the large amount of data that needs to be managed, especially when dealing with an ensemble of climate projections that integrate different models, scenarios, and time periods, each with numerous grids and in different formats [33,34,35]. Therefore, it is important to minimize the complexity of the ET_o calculation [36,37]. The challenge is increased by the need for careful bias correction to ensure accuracy when interpreting complex climate data [38,39,40,41]. Although the focus is on calculating ET_o, the methodology used must strike a balance between simplicity and accuracy. The HS equation requires careful calibration because it relies on model coefficients that are closely linked to local climate conditions and topographic characteristics. Calibration against ET_o-PM using high-quality data can minimize systematic errors and ensure accuracy [42]. Various studies have proposed calibration methods, including regional adjustments of the Hargreaves–Samani coefficient (k_Rs) [19,21,22,32,43,44,45,46,47]. The original HS equation has a coefficient of 0.023, introduced by Hargreaves and Samani [31], associated with a constant k_Rs of 0.17 °C^−0.5. However, various studies show that k_Rs should not be constant because it is affected by climate variables such as precipitation, wind speed, and relative humidity [6,19,21,32,48,49,50]. Calibrated versions of the Hargreaves–Samani equation have been developed and extensively compared with ET_o-PM, including its modified versions [51,52,53].

Some studies focus on local calibration to improve ET_o estimates from daily data [43,44,45,53,54,55,56]. Others have suggested other approaches to achieve better performance [57]. Recent advances show the potential of artificial intelligence to increase the precision of ET_o estimates using HS [17,36,57,58,59,60,61,62,63,64], with machine learning emerging as a good alternative to calibrate HS equations. Another approach is based on cluster analysis, a data mining technique that looks for patterns, relationships, correlations, and anomalies in large data sets to extract useful information [65]. It provides valuable insights into the influence of seasonal and spatial patterns of meteorological variables on the performance of ET_o estimation methods [66,67,68,69,70]. In addition, the interannual variability should be considered by ET_o estimation methods. The clustering process divides a large data set into smaller groups, where data in the same cluster have common characteristics while data in different clusters have heterogeneity [62,63,65,67].

The overall objective of this study is to develop a methodology to produce robust ET_o data for climate change studies based solely on temperature data. Specifically, this study aims to: (a) analyze the data quality of the main weather stations in the studied region; (b) perform the annual calibration of the Hargreaves–Samani equation for the entire year; (c) perform independent calibrations based on annual and monthly clusters; (d) evaluate the accuracy of the calibrated HS method using the different calibration approaches and estimate the respective error.

2. Materials and Methods

2.1. Study Area and Meteorological Data

This study was conducted in the Évora district (7393 km²) in the Alentejo region, Southern Portugal (Figure 1). The coordinates, elevations, and measurement periods of the weather stations (WS) are listed in

Table 1. Coordinates, elevation, and measurement periods of the weather stations.

Weather Station	Code	Latitude (N)	Longitude (W)	Elevation (m)	Measured Period	Source
Évora	EV	38.54	7.89	247.5	Jan/1996–Mai/2023	IPMA
Divor	DV	38.74	7.94	246.0	Sep/2001–Ago/2023	COTR
Maranhão	MR	39.00	8.00	94.0	Jan/2005–Apr/2021	WUASV
Montargil	M	39.05	8.17	92.0	Jan/2005–Apr/2021	WUASV
Viana do Alentejo	VA	38.36	8.12	138.0	Jan/2007–April/2023	COTR

IPMA—Portuguese Institute of the Sea and Atmosphere; COTR—Centre for Irrigation Technology; WUASV—Water Users Association of the Sorraia Valley.

, and their location is shown in Figure 1. Daily data were collected for several meteorological variables, including maximum and minimum air temperature (T_max, T_min), relative humidity (RH_max, RH_min), wind speed (u₂), and solar radiation (R_s), and their distributions were analyzed for all WS. Due to the unavailability of large datasets, only the weather stations Évora, Divor, Maranhão, Montargil, and Viana do Alentejo were considered.

According to the Köppen–Geiger classification [71], the region has a Csa climate, which corresponds to a semi-arid Mediterranean climate with a hot and dry season in summer and mild temperatures associated with an annual precipitation concentrated in winter (Figure 2). Between 1971 and 2000, annual precipitation in Évora WS averaged 598 ± 189 mm.

2.2. Data Quality Analysis

A data homogeneity analysis was performed for all weather stations to evaluate the quality of the meteorological data sets. As suggested by Allen et al. [5,72], shifts in properties can be attributed to various factors, such as changes in instrumentation, observation practices, or changes in site environmental conditions. The mean homogeneity test proposed by Rosa et al. [73] was used to study the evolution of the means over time. This test provides insights into the temporal evolution of the annual mean of the variables T_max, T_min, RH_max, RH_min, u_2, and R_s, through their partial means ($\overline{y}$_j). Assuming a normal distribution for the original annual series, the standard error of the mean was estimated. The confidence interval $\overline{y}$_j for a (1 − α) % confidence level was determined using either the t-Student variable (t) or the standardized normal variable (Z), depending on the sample size (Nj) (Equation (1)) [74,75,76,77].

$$\overline{y}\mp \left\{\begin{array}{c}{t}_{1-{\displaystyle \frac{\alpha }{2}}, N-1}{\displaystyle \frac{{\sigma }_y}{\sqrt{N_j}}} IF N<30\\ Z_{1-{\displaystyle \frac{\alpha }{2}}, N-1}{\displaystyle \frac{{\sigma }_y}{\sqrt{N_j}}} IF N\ge 30 \end{array}\right.$$

(1)

where $\overline{y}$ is the mean of the data period; t is the t-student variable; z is the standardized normality; α is the significance level; j is the year; ${\sigma }_y$ is the standard error of the mean, and N is the number of years. If a value of $\overline{y}$_j exceeds the confidence band, the homogeneity of the mean and thus the series is rejected for the chosen significance level. However, if the values of $\overline{y}$_j lie within the confidence band, the evolution of the mean over time is considered homogeneous. In addition, the integrity of the solar radiation data is verified using clear-sky comparisons to ensure data quality and reliability, as well as the accuracy and consistency of weather data. This method compares the measured solar radiation with values calculated under clear-sky conditions. In this case, changes in local environmental conditions affecting the measurements were the main cause of data bias, which was detected by visual inspection. The correct periods with bias in the measured solar radiation were determined by applying a multiplicative factor [72]. Wind speed, relative humidity, and temperature data were evaluated to check for outliers such as negative wind speed and minimum temperature above maximum temperature. Statistical tests and methods are used, such as the Mann–Kendall test for trend analysis to detect monotonic changes over time [73,74] and the Shapiro–Wilk test to assess data normality [78]. A flowchart showing the data quality analysis is presented in Figure 3.

2.3. Evapotranspiration Equations

The FAO Penman–Monteith reference evapotranspiration given by Equation (2) is defined as the evapotranspiration rate of a hypothetical reference crop with an assumed crop height h = 0.12 m, a daily canopy resistance r_s = 70 s m⁻¹, and an albedo of 0.23. It closely resembles the evapotranspiration of an extensive surface of green grass of uniform height, actively growing, completely shading the ground, and not short of water [5].

$${ET}_{o-PM}={\displaystyle \frac{0.408∆(R_n-G)+\gamma \frac{900}{T_{mean}+273}{u}_2(e_s-e_a)}{∆+\gamma (1+0.34u_2)}}$$

(2)

where R_n is the net radiation at the crop surface (MJ m⁻² d⁻¹), G is the soil heat flux density (MJ m⁻² d⁻¹), T_mean is the mean daily air temperature measured at 2 m height (°C) is computed from maximum and minimum air temperature (°C), u₂ is the wind speed at 2 m height (m s⁻¹), Δ is the slope of vapor pressure curve (kPa °C⁻¹), γ is the psychometric constant (kPa°C⁻¹); and e_s − e_a is the vapor pressure deficit (kPa) computed from the saturation vapor pressure (Equation (2.b)) and the actual vapor pressure (Equation (2.c)) as follows:

$${e^O}_{\left(\mathrm{T}\right)}=0.6108\times {exp}^{\left[{\displaystyle \frac{17.27\times \mathrm{T}}{\mathrm{T}+237.3}}\right]}$$

(2.a)

$$e_s={\displaystyle \frac{\left[{e^O}_{\left(T_{max}\right)}+{e^O}_{\left(T_{min}\right)}\right]}{2}}$$

(2.b)

where e_s is saturation vapor pressure (kPa), and T (T_max, T_min, or T_dew) refer to daily minimum and maximum air temperature or dew point temperature (°C).

$$e_a={\displaystyle \frac{\left[{e^O}_{\left(T_{min}\right)}\frac{{RH}_{max}}{100}+{e^O}_{\left(T_{max}\right)}\frac{{RH}_{min}}{100}\right]}{2}}$$

(2.c)

where e_a is the actual vapor pressure (kPa), T (T_max, T_min, or T_dew) is the daily minimum and maximum air temperature or dew point temperature (°C), and RH_max, RH_min is the relative humidity (%).

For reduced data sets, the FAO Penman–Monteith temperature approach (ET_o−PMT) is used. It consists of a combination of approaches to estimate ET_o−PMT: (a) the dew point temperature (Td_ew) from T_min or from mean temperature (T_mean) is used to calculate e_a in humid climates when relative humidity or psychrometric data are missing (Equation (2.a)); (b) the short-wave incoming radiation (R_s) from the temperature difference; and (c) the wind speed (u₂) from regional standard or average values. The Hargreaves–Samani equation, an empirical temperature-based approach first proposed in [14] and later revised in [31], is written as:

$${ET}_o=K_{ET}·R_a{\left(T_D\right)}^{0.5}·\left(T_C-17.8\right)$$

(3)

where ET_o−HS is the reference evapotranspiration (mm d⁻¹), (TD = T_max − T_min) is the maximum minus minimum temperature, T_C is the mean temperatures (°C), and K_ET, commonly written as Hargreaves coefficient (K_ET = CHS = (0.0135 k_Rs)/λ) [19]. The final equation is written as.

$${ET}_{o-HS}=0.0135K_{RS}{\displaystyle \frac{Ra}{\mathsf{\lambda }}}{\left(T_{max}-T_{min}\right)}^{0.5}\left(T_{mean}+17.8\right)$$

(4)

where ET_o−HS is the reference evapotranspiration (mm d⁻¹), T_max, T_min, and T_mean are the daily maximum, minimum, and mean temperatures (°C), λ is the latent heat of vaporization (2.45 MJ kg⁻¹), k_Rs is the empirical radiation adjustment coefficient (°C^−0.5), R_a is the extraterrestrial radiation (MJ m⁻² d⁻¹), 0.0135 is a unit conversion factor and 17.8 is an empirical factor related to temperature units.

2.4. Approaches for Hargreaves–Samani Calibration and Validation

The HS equation requires careful calibration as it relies on the empirical coefficient k_Rs, which is closely linked to local climate conditions and topographical characteristics. Originally, Hargreaves–Samani (1985) suggested calibrating k_Rs using solar radiation measurements. However, in the present study, the k_Rs is adjusted to minimize the differences between the ET_o calculated by the HS equation and the ET_o calculated by the FAO–PM equation. Calibration with ET_o−PM allows the k_RS coefficient to account for local environmental factors such as wind speed and relative humidity that HS might overlook.

Two approaches were used to determine the adjusted k_Rs coefficient: (a) annual calibration of the Hargreaves–Samani equation for the entire year; and (b) independent calibrations for annual and monthly clusters of meteorological data. For both approaches, 70% of the years with the full meteorological data set were selected for calibration, and the remaining years were used for validation. This ensures the accuracy and reliability of the results and reduces bias, allowing adjustment to a variety of temporal patterns within the data set. The k_Rs fitting was performed using the Microsoft Excel Solver tool, which uses the nonlinear optimization algorithm called Generalized Reduced Gradient (GRG), using 17 °C^−0.5 as the initial value as suggested by Hargreaves–Samani [31].

2.4.1. Annual Calibration of the Hargreaves–Samani Equation for the Entire Year

Annual calibration of the radiation adjustment coefficient for the Hargreaves–Samani (HS) equation was conducted using a dataset covering the entire year (Figure 4). The entire dataset was divided into years for calibration and validation to capture wet and dry seasonal variations.

2.4.2. Independent Calibrations for Annual and Monthly Clusters of Meteorological Data

Cluster analysis provides valuable insights into the influence of seasonal patterns of meteorological variables on the performance of ET_o estimation methods [60,66,79]. In this study, cluster analysis was used to improve the calibration of the Hargreaves–Samani equation for the Évora region by examining the effects of clustering meteorological data using annual and monthly similarities. First normality tests were performed on the climate variables using Shapiro–Wilk test [78]. The K-Means algorithm [67,69,80,81] was then used to identify clusters of months or years with similar correlations between meteorological variables, which were used to calculate ET_o–PM.

The results of the K-Means algorithm depend on the initial selection of centers, which must be carefully selected to minimize deviations (see

Table A3. List of annual clusters for each station.

Divor		Maranhão		Montargil		Viana de Alentejo
Year	Cluster	Year	Cluster	Year	Cluster	Year	Cluster
2003	1	2006	1	2007	1	2008	1
2004	1	2007	1	2008	1	2010	1
2006	1	2010	1	2010	1	2011	1
2007	1	2011	1	2012	1	2012	1
2008	1	2012	1	2013	1	2013	1
2009	1	2013	1	2014	1	2014	1
2010	1	2014	1	2016	1	2016	1
2011	1	2016	1	2018	1	2018	1
2012	1	2018	1	2019	1	2020	1
2013	1	2019	1	2020	1	2007	2
2014	1	2020	1	2005	2	2009	2
2016	1	2005	2	2006	2	2015	2
2018	1	2009	2	2009	2	2017	2
2019	1	2015	2	2011	2	2019	2
2020	1	2017	2	2015	2	2021	2
2005	2			2017	2	2022	2
2015	2					2023	2
2017	2
2021	2
2022	2

). To determine the positive impact of dividing the data into groups of months or years, the optimal number of clusters was evaluated using the within-cluster sum of squares method (elbow method) and the silhouette score [66,81]. Starting from the elbow method, the optimal number of clusters was determined by observing the decreases in the total sum of squares within the cluster as the number of clusters increased and selecting the optimal number as the rate decreased, thereby forming an “elbow”. In the next step, the K-Means algorithm performs the partition of the months and years by the number of clusters defined by the elbow method. The final step of cluster analysis was to use the silhouette method to measure how similar an object is to its own cluster compared to other clusters. The silhouette score has values ranging from −1 (incorrect clustering) to 1 (well defined), validating consistency within clusters. The K-Means algorithm sets a threshold; years above the threshold are associated with a dry cluster, while years below are associated with a wet cluster. The same applies to dry and wet months (Figure 5).

The calibration process was performed considering the cluster groups for each WS to minimize biases and account for the climatic variability of the region (Figure 5). This approach improves the robustness of the calibrated HS equation for application in studies of the impacts of climate change on water availability, irrigation demand, and the design of irrigation systems and distribution networks.

2.5. Goodness-of-Fit and Evaluation Criteria for Hargreaves–Samani Calibration and Validation

The goodness-of-fit between the ET_o estimated by the HS equation (ET_o–HS) and the ET_o obtained from the FAO PM equation (ET_o–PM) was evaluated using statistical indicators commonly used in previous studies [6,16,56,60]. The regression coefficient (b₁), which represents the slope of a linear regression forced through the origin (b₁), was used to evaluate the equality between ET_o–HS and ET_o–PM. The aim was to achieve a target value of b₁ = 1.0, where b₁ < 1.0 indicates that ET_o–HS underestimates ET_o–PM and b₁ > 1.0 indicates an overestimation. The coefficient of determination (R²) between ET_o–HS and ET_o–PM, with a perfect match (R² = 1.0) means that 100% of ET_o–PM is explained by ET_o–HS. The root mean square error (RMSE mm d⁻¹) and its normalization, NRMSE, indicate the estimation error between ET_o–PM and ET_o–HS. Thus, a smaller RMSE indicates a higher accuracy of predictions. The percentage bias (PBAIS) is the systematic error between ET_o–HS and ET_o–PM, indicating the average tendency of the ET_o–HS values to be larger or smaller than the ET_o–PM values. Modeling efficiency (EF) measures the relative magnitude of the mean square error relative to the observed data variance. According to Nash & Sutcliffe [82], the EF range is between −∞ and 1, and an EF close to 1.0 indicates better model performance (for further details, see Appendix A 

Table A1. Goodness-of-fit and evaluation criteria for Hargreaves–Samani calibration and validation.

Indicators	Equation
Regression coefficient	$b_0={\displaystyle \frac{{\sum }_{i=1}^n{ET}_{o-PM}{ET}_{o-HS}}{{{(ET}_{o-PM})}^2}}$	(A3)
Coefficient of determination	$R^2={\left\{{\displaystyle \frac{{\sum }_{i=1}^n{(ET}_{o-PM}-\overline{{ET}_{o-PM}}\left)\right({ET}_{o-HS}-\overline{{ET}_{o-HS}})}{{\left[{\sum }_{i=1}^n{({ET}_{o-PM}-\overline{{ET}_{o-PM}})}^2\right]}^{0.5}{\left[{({ET}_{o-HS}-\overline{{ET}_{o-HS}})}^2\right]}^{0.5}}}\right\}}^2$	(A4)
Root mean square error	$RMSE={\left[{\displaystyle \frac{{\sum }_{i=1}^n{{(ET}_{o-PM}-{ ET}_{o-HS})}^2}{n}}\right]}^{0.5}$	(A5)
Root mean square error normalized.	$NRMSE={\displaystyle \frac{RMSE}{\overline{{ET}_{o-PM}}}}\times 100\%$	(A6)
Percent bias	$PBIAS={\displaystyle \frac{{\sum }_{i=1}^n{ ET}_{o-HS}-{ET}_{o-PM}}{\overline{{ET}_{o-PM}}}}\times 100\%$	(A7)
Efficiency	$EF=1-{\displaystyle \frac{{{\sum }_{i=1}^n{(ET}_{o-PM}-{ET}_{o-HS})}^2}{{{\sum }_{i=1}^n{(ET}_{o-PM}-\overline{{ET}_{o-PM}})}^2}}$	(A8)

ET_o−HS—Hargreaves–Samani reference evapotranspiration ET_o−PM—FAO Penman–Monteith reference evapotranspiration; b₁—regression forced to the origin; R²—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error, PBIAS—percent bias, EF—Nash–Sutcliffe efficiency.

).

3. Results and Discussion

3.1. Data Quality Results

The distribution of the primary weather variables relevant to our study is shown in Figure 6. The variables T_max, T_min, and RH_min have a similar distribution for all stations, while there were some differences for RH_max, u₂, and R_s. For RH_max, the average value is similar, but the extreme values show some variability. The u₂ values show an average value of about 2 m s⁻¹ for the DV, MR, MT, and VA stations, while for the EV it is close to 3.5 m s⁻¹. The same applies to R_s, with the DV, MR, MT, and VA stations averaging 15 MJ m⁻² d⁻¹ and the EV station averaging 18 MJ m⁻² d⁻¹. Except for EV (located in the city), the remaining WS are in agricultural areas, with MR and MT being closer to each other and 3 km from a reservoir. Because they are at a low elevation, the recorded wind speed is lower and presents fewer extreme values than the remaining stations.

Regarding Évora WS, 61% of daily solar radiation data are missing. For relative humidity and wind speed, the percentage of missing values is 36.5% and 18%, respectively. Since those values are above the 10% threshold recommended by the WMO [83], this weather station was not considered for this study. In addition to these gaps, inconsistencies in the measured solar radiation data were observed. The measured values were compared with the calculated solar radiation under a clear-sky between 1997 and 2023. From 1999 to 2004, the radiation data were plausible; in the remaining years, the high values from April to August indicate a miscalibration of the sensor. There were no measurements from 2012 to 2020. Although data correction is possible in some situations, it was assumed that the existing data was insufficient. Therefore, the Évora WS station was excluded from this study as a complete data set is crucial for cluster-based HS calibration. When analyzing the solar radiation data, the DV showed low Rs values between April and August, which may be due to miscalibration, sensor degradation, or dust accumulation. Thus, measured solar radiation was adjusted using the methodology proposed by Allen et al. [72] as referred to in Section 2.2. The results are shown in Figure 7. The results of the Mann–Kendall trend and Shapiro–Wilk tests performed on the monthly and annual data of the DV MR, MT, and VA weather stations are shown in

Table A2. Results of the Shapiro–Wilk normality test and the Mann–Kendall trend test.

Weather Station	Variable	Shapiro–Wilk Normality Test				Mann–Kendall Test
		Year		Month		Year		Month
		Statistics	p-Value	Statistics	p-Value	Statistics	p-Value	Statistics	p-Value
DV	Tmax	0.92496	0.1235	0.90771	0.1994	0.2	0.22997	0.212	0.37269
	Tmin	0.91286	0.07227	0.90859	0.2046	0.274	0.09799	0.333	0.14986
	RHmax	0.95318	0.4179	0.88265	0.09477	0.0632	0.72118	−0.152	0.53713
	RHmin	0.94245	0.2666	0.93314	0.4146	−0.253	0.12729	−0.121	0.63122
	u2	0.87161	0.01254 *	0.91965	0.283	−0.4	0.01496 *	−0.273	0.24372
	RS	0.92463	0.1217	0.98225	0.9911	0.295	0.07435	−0.0303	0.94533
MR	Tmax	0.91255	0.1482	0.91477	0.2455	0.162	0.42848	0.242	0.30367
	Tmin	96612	0.797	0.90634	0.1914	−0.333	0.09246	0.333	0.14986
	RHmax	0.91751	0.1765	0.87927	0.08578	0.0476	0.84309	−0.152	0.53713
	RHmin	0.97625	0.9374	0.93001	0.3802	0.333	0.09246	−0.182	0.45067
	u2	0.93438	0.3169	0.96313	0.8274	0.295	0.13765	−0.333	0.14986
	RS	0.84487	0.0147 *	0.96313	0.8274	0.181	0.37305	−0.0303	0.94533
MT	Tmax	0.94985	0.4873	0.91558	0.2514	−0.15	0.44404	0.242	0.30367
	Tmin	0.91588	0.1448	0.90718	0.1963	0.15	0.44404	0.333	0.14986
	RHmax	0.85999	0.9809	0.92343	0.3157	0.167	0.39231	−0.152	0.53713
	RHmin	0.98262	0.9809	0.93963	0.4933	0.433	0.02167 *	−0.152	0.53713
	u2	0.84487	0.0147 *	0.96485	0.8502	0.5	0.07956	−0.0909	0.7317
	RS	0.84854	0.01297 *	0.91458	0.2441	−0.717	0.01754 *	−0.0303	0.94533
VA	Tmax	0.94415	0.3707	0.90709	0.1958	0.382	0.03566	0.242	0.30367
	Tmin	0.954	0.5227	0.89777	0.1484	0.353	0.05286	0.333	0.14986
	RHmax	0.93691	0.2833	0.91468	0.2449	0.0294	0.90165	−0.212	0.37269
	RHmin	0.97357	0.8773	0.93296	0.4126	0.0588	0.77308	−0.152	0.53713
	u2	0.98642	0.9936	0.90735	0.1973	−0.397	0.02902 *	0.152	0.53713
	RS	0.96041	0.6393	0.9255	0.3349	−0.0735	0.71084	−0.0303	0.94533

DV—Divor; MR—Maranhão; MT—Montargil; VA—Viana do Alentejo; T_max—maximum temperature; T_min—minimum temperature; RH_max—maximum relative humidity; RH_min—minimum relative humidity; u₂—average wind speed; R_s—solar radiation; p-values—α < 0.05; * α < 0.01.

.

At a significance level of α of 0.05, most variables were normally distributed, except annual u₂ in DV and MT and R_s in MR and MT. Most of the data also showed a trend with a significance level of 0.05, except for the variables u₂ in DV and VA, R_s, and RH_min in MT.

The temporal evolution of climate variables critical to understanding regional climate patterns (T_max, T_min, RH_max, RH_min, u₂, and R_s) is presented in Supplementary Materials (Figures S3 and S4). For the EV weather station, the T_min time series showed inhomogeneity at the significance level of 0.05. On the other hand, the time series of all variables for weather stations DV, MR, MT, and VA showed homogeneity at the significance level of 0.05.

The Pearson correlation coefficient between the monthly meteorological variables used to calculate ET_o–_PM for each weather station and the monthly ET_o–PM is presented in Figure 8. This analysis shows the importance of different weather variables in ET_o. The maximum and minimum temperature and the range between them (T_range) showed a high influence in ET_o in the dry months (spring and summer), with T_max having the highest values. The temperature range indicates that a higher diurnal temperature range increases ET_o during dry months. Relative humidity showed an opposite influence on ET_o throughout the year, particularly Rh_min, indicating that lower humidity levels significantly increase ET_o. Wind speed has a moderate contribution, particularly in summer and winter. Solar radiation has the highest influence on ET_o. The strong influence of solar radiation highlights its central role in the energy available for both evaporation and transpiration processes.

These results suggest that temperature, humidity, wind speed, and solar radiation interact in different ways over the seasons to modulate ET_o, with solar radiation and temperature being the dominant factors. For ET_o–PM, net radiation (Rₙ) and vapor pressure deficit (e_s − e_a) are usually the dominant factors, while for ET_o–HS, the temperature range (T_max − T_min) is the most important factor, with extraterrestrial radiation adding a seasonal influence.

3.2. Calibration of the Hargreaves–Samani Equation

The performance of the original Hargreaves–Samani equation (k_Rs = 0.17 °C^−0.5) before calibration is shown in

Table 2. Original Hargreaves–Samani reference evapotranspiration vs. FAO Penman–Monteith reference evapotranspiration: mean, standard deviation, and goodness-of-fit indicators of the reference evapotranspiration estimation.

Weather Station	N	Initial kRS	Mean and SD (mm d−1)		b1	R2	RMSE	NRMSE	PBIAS	EF
		(°C−0.5)	ETo–HS	ETo–PM			(mm d−1)	(%)	(%)
DV	7690	0.17	3.45 (±2.1)	3.77 (±2.2)	1.06	0.89	0.82	22.99	−9.00	0.86
MR	5987		3.44 (±2.1)	3.74 (±2.2)	1.07	0.96	0.59	16.23	8.80	0.93
MT	5621		3.55 (± 2.2)	3.72 (±2.2)	1.03	0.95	0.56	14.90	4.91	0.94
VA	6445		3.55 (±2.2)	3.62 (±2.1)	1.00	0.93	0.62	16.94	−1.96	0.93

N—number of days; Mean and SD—mean and standard deviation; b₁—slope of a linear regression forced to the origin; R²—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error, PBIAS—percent bias, EF—Nash-Sutcliffe Efficiency; DV—Divor; MR—Maranhão; MT—Montargil; VA—Viana do Alentejo weather stations.

. The original HS tended to overestimate _ETo–PM for most weather stations in this study, except for VA, which also had lower PBAIS. The calibration goal was to minimize the differences between ET_o–HS and ET_o–PM results by adjusting the empirical HS radiation coefficient, k_Rs. Different approaches were used to calibrate the HS equation: (a) perform annual calibration of the equation for the entire year; (b) perform independent calibrations based on annual and monthly clusters (Figure 9). Figure 10 and Figure 11 present the scatter plots for the calibration and validation phases of the HS equation for the Évora region

3.2.1. Annual Calibration

Annually calibrated k_Rs values are presented in

Table 3. Calibration Hargreaves–Samani equation using the annual approach: mean, standard deviation, and goodness-of-fit indicators of the reference evapotranspiration estimation.

Weather Station	Process	N	Adjusted kRS	Mean and SD (mm d−1)		b1	R2	RMSE	NRMSE	PBIAS	EF
			(°C−0.5)	ETo–HS	ETo–PM			(mm d−1)	(%)	(%)
DV	Calibration	5108	0.159	3.55 (±2.2)	3.54 (±2.1)	0.97	0.97	0.71	19.82	0.09	0.90
	Validation	2582		3.51 (±2.2)	3.56 (±2.1)	0.99	0.97	0.73	20.59	−1.51	0.90
MR	Calibration	4383	0.157	3.54 (±2.1)	3.52 (±2.1)	0.99	0.99	0.47	13.30	0.47	0.95
	Validation	1604		3.37 (±2.0)	3.39 (±2.0)	0.99	0.99	0.47	13.80	0.65	0.95
MT	Calibration	4526	0.163	3.62 (±2.2)	3.62 (±2.2)	0.99	0.99	0.46	12.79	0.03	0.96
	Validation	1095		3.45 (±2.1)	3.48 (±2.0)	1.01	0.99	0.45	13.32	1.00	0.96
VA	Calibration	4500	0.165	3.52 (±2.8)	3.53 (±2.1)	0.98	0.98	0.59	16.80	−0.30	0.93
	Validation	1945		3.51 (±2.2)	3.50 (±2.0)	0.97	0.98	0.59	16.80	0.51	0.92

N—number of days; Mean and SD—mean and standard deviation; b₁—slope of a linear regression forced to the origin; R₂—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error, PBIAS—percent bias, EF—Nash–Sutcliffe Efficiency; DV—Divor; MR—Maranhão; MT—Montargil; VA—Viana do Alentejo weather stations.

, with values typically lower than the original k_Rs. All weather stations show high R² values (0.97–0.99), indicating strong correlations between ET_o–HS and ET_o–PM (Figure 10a and Figure 11a). The RMSE values are relatively low (0.45–0.73 mm d⁻¹), with MT having the lowest values (0.46 mm d⁻¹ and 0.45 mm d⁻¹ for calibration and validation, respectively). Annual calibration minimized the error by approximately 0.10 mm d⁻¹. The PBIAS values were generally lower for all stations, indicating low bias in the ET_o–HS estimates. The exception is DV, where the validation has a PBIAS of −1.51%, indicating a slight underestimation. Annual calibration reduced bias by approximately 6% compared to the original calibration of HS. The EF values are high for all stations (0.90–0.96), with values close to 1, indicating excellent ET_o–HS estimation accuracy. The DV weather station has a relatively higher RMSE (0.71–0.73 mm d⁻¹) compared to other stations, while the MT station has a relatively lower RMSE (0.46–0.45 mm d⁻¹) and NRMSE (12.79–13.32%), indicating the most accurate adjustment. The validation results support the robustness and reliability of the calibration. Although the accuracy changed slightly, the annual adjusted k_Rs were similar for most stations analyzed.

The results of the goodness-of-fit indicators are consistent with those in the literature [6,22,32]. For example, Paredes et al. [6] reported an average RMSE of 0.60 ± 0.15 mm d⁻¹ for the HS calibration for different climates. Moratiel et al. [18] present similar results for the Duero basin (0.69 mm d⁻¹), while Rodrigues and Braga [57] found higher values (0.83 mm d⁻¹) for the Alentejo region. Similarly, in Iran, Raziei and Pereira [32] found that the HS model performed well with RMSE values generally below 0.70 mm d⁻¹ across most locations. The model’s performance in the windy and humid Azorean climate, as reported by Paredes et al. [19], showed RMSE values ranging from 0.47 to 0.86 mm d⁻¹, with satisfactory accuracy. This suggests that in regions where the effects of wind are minimal, the HS model can reliably estimate ET_o with relatively low error rates. Conversely, in more arid and semiarid regions, the performance of the HS model deteriorates. Ren et al. [84] reported RMSE values ranging from 0.65 to 1.15 mm d⁻¹ in arid areas of Inner Mongolia. Under extreme conditions, the accuracy of the model further decreases, as Zhu et al. [85] found in their evaluation of 838 weather stations in China, particularly the HS model, which neglects relative humidity and wind speed. The limitations of the HS model become particularly evident during the dry season in the São Francisco River Basin, Brazil, as reported by Althoff [66], where lower correlations between meteorological variables and ET_o reduce the effectiveness of the model. Additionally, the high variability in wind speed within certain sub-regions further diminishes the model’s accuracy.

Despite offering a good performance for the HS equation, the annual calibration overlooks the seasonal and interannual variability of the ET_o estimate. To address this, a cluster-based approach was chosen. This method grouped the data into clusters based on annual and monthly variations, with a particular focus on wet and dry periods.

3.2.2. Calibration of the Hargreaves–Samani Equation by Clusters of Years and Months

(a) Cluster analysis

The K-Means algorithm defined the optimal number of clusters into which the studied months and years are divided. Therefore, with the same number of clusters (k = 2) for the annual and monthly data, the total sum of squares for monthly data decreases considerably across different temporal groupings, particularly highlighting seasonal and annual variations (Figure 9). The analysis showed that grouping by months produced better results than by years, as indicated by the higher average silhouette coefficient for monthly data (0.44) compared to annual data (0.34). This suggests that monthly clusters provided more coherent and separated groups and optimized the partitioning of meteorological data. Furthermore, the total within-cluster sum of squares decreased significantly for monthly data, reinforcing the notion that seasonal variations are crucial for improving model calibration.

The clusters created for monthly data aligned well with seasonal patterns, dividing the year into a wet season (clusters 11 and 21) and the dry season from May to September (clusters 12 and 22). This clustering coincides with periods of different evapotranspiration demands, especially since irrigation requirements are primarily relevant during the dry season. This reinforces the potential benefit of calibrating the Hargreaves–Samani equation for the wet and dry seasons, as suggested by Zanetti et al. [86], Aguilar and Polo [87], and Althoff et al. [66]. The results for the annual clusters can be found in the Appendix A (Table A3).

(b) Cluster-based calibration

The cluster-based calibration using year and month clusters focused on four groups: years below the threshold (11 and 12), years above the threshold (21 and 22), wet months (11 and 21), and dry months (12 and 22). Most clusters had high R² values (0.94–0.99), indicating strong correlations between ET_o–HS and ET_o–PM (Figure 10b and Figure 11b). However, the accuracy varied depending on the cluster and weather station. For instance, the MR weather station consistently showed the lowest RMSE (0.32 mm d⁻¹) and NRMSE (9.2%).

On the other DV, the weather station experienced high errors in certain clusters (e.g., cluster 21 with NRMSE of 27.46%) and biases (e.g., cluster 11 with PBIAS of −3.06%) during validation. The MT weather station shows consistently high performance, although minor declines were observed in some clusters during validation. In contrast, VA shows moderate performance, with certain clusters experiencing declines in validation (cluster 11 with NRMSE of 24.7% and PBIAS of 4.87%) (

Table 4. Calibration Hargreaves–Samani equation using the independent cluster approach: mean, standard deviation, and goodness-of-fit indicators of the reference evapotranspiration estimation.

	Cluster		N	kRS	Mean and SD (mm d−1)		b1	R2	RMSE	NRMSE	PBIAS	EF
				(°C−0.5)	ETo–HS	ETo–PM			(mm d−1)	(%)	(%)
DV	11	Cal.	2122	0.151	1.95 (±1.0)	1.94 (±0.9)	0.96	0.96	0.45	23.25	0.57	0.81
		Val.	1058		2.05 (±1.1)	2.03 (±1.1)	0.96	0.96	0.46	22.61	0.89	0.84
	12	Cal.	1526	0.162	5.66 (±1.4)	5.6 (±1.4)	0.97	0.97	0.91	16.11	1.10	0.58
		Val.	795		5.42 (±1.5)	5.42 (±1.3)	0.97	0.97	0.90	16.68	−0.01	0.64
	21	Cal.	636	0.156	2.16 (±1.2)	2.13 (±1.1)	0.96	0.96	0.50	23.07	1.24	0.82
		Val.	423		1.85 (±1.0)	2.01 (±0.9)	1.02	0.94	0.53	27.46	−3.06	0.78
	22	Cal.	459	0.165	5.92 (±1.5)	5.84 (±1.5)	0.97	0.97	0.93	15.81	1.27	0.59
		Val.	306		5.45 (±1.6)	5.95 (±1.5)	1.07	0.97	0.99	16.96	−1.79	0.64
MR	11	Cal.	2031	0.152	1.97 (±1.0)	1.98 (±1.0)	1.00	0.98	0.35	17.7	0.59	0.89
		Val.	424		1.91 (±0.9)	2.04 (±1.1)	0.96	0.98	0.32	16.9	1.64	0.90
	12	Cal.	1400	0.156	5.39 (±1.3)	5.40 (±1.3)	0.99	0.99	0.54	9.9	0.52	0.83
		Val.	306		5.44 (±1.3)	5.27 (±1.5)	1.03	0.99	0.50	9.2	1.43	0.85
	21	Cal.	636	0.155	2.18 (±1.1)	2.16 (±1.2)	0.98	0.98	0.34	15.4	0.13	0.92
		Val.	212		2.05 (±1.1)	2.03 (±1.0)	0.99	0.98	0.32	15.7	0.52	0.92
	22	Cal.	459	0.161	5.70 (±1.3)	5.89 (±1.3)	0.99	0.99	0.55	9.6	0.12	0.81
		Val.	153		5.84 (±1.3)	5.82 (±1.4)	0.99	0.99	0.57	9.8	0.38	0.81
MT	11	Cal.	1819	0.161	2.03 (±1.1)	2.04 (±1.0)	0.98	0.98	0.35	17.28	−0.21	0.89
		Val.	424		2.11 (±1.1)	2.05 (±1.0)	0.98	0.97	0.38	18.46	2.86	0.89
	12	Cal.	1247	0.164	5.73 (±1.4)	5.72 (±1.4)	0.99	0.99	0.52	9.22	0.19	0.87
		Val.	306		5.36 (±1.3)	5.46 (±1.2)	1.01	0.99	0.52	9.84	−1.97	0.84
	21	Cal.	848	0.168	2.28 (±1.2)	2.28 (±1.2	0.98	0.98	0.36	15.91	−0.02	0.92
		Val.	424		2.21 (±1.3)	2.25 (±1.2)	1.03	0.98	0.37	16.87	1.93	0.92
	22	Cal.	612	0.169	6.08 (±1.4)	6.05 (±1.3)	0.99	0.99	0.56	9.29	0.47	0.83
		Val.	306		5.92 (±1.1)	5.91 (±1.3)	1.04	0.99	0.58	9.94	−0.25	0.70
VA	11	Cal.	1395	0.159	1.92 (±1.0)	1.92 (±0.9)	0.96	0.96	0.42	21.9	−0.10	0.83
		Val.	424		2.07 (±1.1)	1.93 (±1.0)	0.89	0.96	0.51	24.7	4.87	0.79
	12	Cal.	918	0.163	5.56 (±1.5)	5.55 (±1.4)	0.98	0.98	0.75	13.5	0.32	0.75
		Val.	306		5.35 (±1.5)	5.36 (±1.3)	0.98	0.98	0.72	13.5	−0.06	0.77
	21	Cal.	1269	0.168	2.18 (±1.5)	2.19 (±1.0)	0.96	0.96	0.47	21.5	−0.36	0.84
		Val.	423		2.20 (±1.3)	2.25 (±1.0)	0.99	0.98	0.40	18.1	2.02	0.91
	22	Cal.	918	0.169	5.57 (±1.5)	5.75 (±1.3)	0.98	0.98	0.74	12.8	0.37	0.74
		Val.	306		5.96 (±1.5)	6.09 (±1.3)	1.01	0.99	0.76	12.7	2.26	0.73

N—number of days; Mean and SD—mean and standard deviation; b₁—slope of a linear regression forced to the origin; R²—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error, PBIAS—percent bias, EF—Nash–Sutcliffe Efficiency. DV—Divor; MR—Maranhão; MT—Montargil; VA—Viana do Alentejo weather station; Cal—calibration and Val—validation.

).

Considering annual clusters

In the context of climate change studies, capturing long-term trends and variability in climate patterns is critical. The analysis focused on two sets of clusters (Table 4): clusters representing years below the threshold (11 and 12) and clusters representing years above the threshold (21 and 22) (Figure 10b and Figure 11b).

When analyzing the results, it showed that years below the threshold performed well during calibration, particularly for wet months, with annual clusters with RMSE values ranging from 0.35 to 0.45 mm d⁻¹, and NRMSE from 17.28% to 23.25%. During validation, values were similar, except for the VA weather station, which had a higher PBIAS value (4.87%), indicating a slight bias. For dry months (cluster 12), the RMSE was slightly higher (0.52 to 0.91 mm d⁻¹), but the NRMSE values were still within acceptable ranges (9.2% to 16.11%) and the EF was slightly 08.58 to 0.87.

Years above the threshold, cluster 21 (years above threshold × wet months) showed strong calibration performance with RMSE from 0.34 to 0.51 mm d⁻¹, and NRMSE from 15.4 to 23.07%. However, during the dry season, cluster 22 (years above threshold × dry months) showed slightly higher errors with RMSE from 0.55 to 0.93 mm d⁻¹. Nonetheless, the NRMSE values were lower for dry months (9.29% to 15.81%) compared to wet months, indicating relatively lower normalized errors during periods of higher ET_o.

Considering monthly clusters:

The analysis of the monthly clusters showed better performance during dry month clusters 12 and 22 (Table 4), with lower NRMSE values (varying between 9.2 and 16.96% for calibration), suggesting lower ET_o−HS estimation errors with little influence of the annual clusters. The higher ET_o values during the dry months naturally lead to higher RMSE values compared to the wet months, but when normalized, the NRMSE values were lower, which suggests that the model was able to capture the higher evapotranspiration rates more effectively in drier conditions. The results also suggest that the model was more reliable for some weather stations, such as MR, than for others, like DV, underscoring the importance of localized calibration.

These results suggest better performance for dry-month clusters, which is consistent with the results of Moratiel et al. [18]. However, these authors also present acceptable results for annual calibration (RMSE < 0.69 mm d⁻¹) despite poorer performance in winter. These results are also coherent with the work of Teixeira et al. [88], in which they showed that the relative error of the Hargreaves–Samani method for the Alentejo region decreased significantly to about 12% in the summer. Similar conclusions were reached by Shahidian et al. [44], for two different regions, California and Bolivia, where they showed that the annual correlations between Hargreaves–Samani and Penman–Monteith are not the most correct method to perform calibration because this correlation tends to increase in the dry season compared to the wet season, resulting in significant variation in model performance for these two periods.

Rodrigues and Braga [56] calibrated the HS equation for the irrigation season and presented an RMSE of 0.88 mm d⁻¹. In addition to the previous work [56] that focused on k_Rs calibration specifically for irrigation periods, the present study uses calibration approaches across all months and meteorological conditions (dry and wet seasons). This is important as it allows the application of HS for the entire cropping pattern, which includes winter crops (e.g., fodder crops and wheat). Furthermore, it is also intended to include inter-annual climate variability in this study to assess whether the calibrated k_Rs accurately reproduce ET_o for dry and wet years, which is very relevant for climate change studies. This broader scope increases the applicability of the methodology to other climates. Another contribution of our study that was not considered in the study [56] is the quality and consistency of meteorological data across the stations, which may affect the model results.

An accuracy improvement was expected when data were clustered by years and months, compared to annual calibration. Wet season clusters performed only slightly (1%) or even worse (5% below the annual calibration), while dry season clusters also performed slightly better (up to 3%) (Figure 12). The performance of the HS equation is often reported in the literature. For humid conditions, some studies [53,89,90] showed that the HS equation performs poorly, as observed in the present study, while other studies reported favorable results for humid conditions [22,32,53,84,89,90].

Note that solar radiation and relative humidity have a stronger correlation with ET_o in spring (Figure 8), and these variables are not considered in the HS equation. This could explain the worse performance of HS during wet season clusters. The maximum RMSE improvement for the cluster approach over the annual approach was 0.13 mm d⁻¹. According to Althoff [66], calibration of the HS equation for specific climatic periods or regions can improve its accuracy. However, this does not guarantee that predictions will be considerably better for every period or region. They found that minimal improvement was achieved by cluster calibration in tropical regions including the Cerrado, Caatinga, and Atlantic Forest with semi-arid to humid subtropical climates. Additionally, they suggested that calibration results using annual k_Rs provided good results, consistent with our observations that seasonal cluster-based calibration provided minimal improvements compared to simpler methods (annual k_Rs). The annual calibration approach reduces the error and bias of ET_o−HS estimates for all weather stations compared to the original HS equation. However, further refinement using cluster-based calibration, which accounts for annual and monthly patterns in the meteorological variables, produced unclear results. While for dry season clusters results showed small improvements compared to the annual approach, the gains do not justify the increased complexity of the cluster-based approach.

4. Conclusions

This study proposed a methodology to enhance reference evapotranspiration estimates using only temperature data by integrating data quality analysis and calibration of the Hargreaves–Samani (HS) equation. The methodology was evaluated for the Alentejo region in Southern Portugal. The results indicated that a thorough assessment of meteorological data quality is essential for minimizing uncertainty and improving model performance. When using the original HS equation with a k_Rs = 0.17 °C^−0.5, ET_o was estimated with errors from 14.9% to 22.9% with bias ranging from −9.0% to 8.8%. The annual calibration gave k_Rs values between 0.157 and 0.165 °C^−0.5 with estimation errors between 13.3% and 20.6% and bias ranging from−1.5% to 1.0% across the multiple weather stations. Annual calibration of the HS equation showed significant improvements over the original model, reducing bias and estimation errors across multiple weather stations. However, the cluster-based calibration approach, which considered seasonal and interannual variations, yielded mixed results. While dry season clusters achieved better accuracy, wet season clusters performed inconsistently, making the added complexity of this approach less justifiable. Therefore, this study recommends annual calibration for temperature-based ET_o estimation in regions with similar climatic characteristics and for climate change studies.

The results highlight the importance of site-specific calibration for refining temperature-based ET_o estimation methods. Furthermore, for the region studied, the gains do not seem to justify the increased complexity of the cluster-based approach. Selecting appropriate calibration strategies that are based on local climate conditions and data availability is important to provide a valuable framework for future climate change and water resources studies. Future research should focus on reducing uncertainties in crop evapotranspiration estimates for climate change scenarios, supported by reliable ET_o estimations. In addition, it is fundamental to ensure the quality of weather data.