Addressing Weather Data Gaps in Reference Crop Evapotranspiration Estimation: A Case Study in Guinea-Bissau, West Africa

Abstract

Crop water use (ET_c) is typically estimated as the product of crop evapotranspiration (ET_o) and a crop coefficient (K_c). However, the estimation of ET_o requires various meteorological data, which are often unavailable or of poor quality, particularly in countries such as Guinea-Bissau, where the maintenance of weather stations is frequently inadequate. The present study aimed to assess alternative approaches, as outlined in the revised FAO56 guidelines, for estimating ET_o when only temperature data is available. These included the use of various predictors for the missing climatic variables, referred to as the Penman–Monteith temperature (PMT) approach. New approaches were developed, with a particular focus on optimizing the predictors at the cluster level. Furthermore, different gridded weather datasets (AgERA5 and MERRA-2 reanalysis) were evaluated for ET_o estimation to overcome the lack of ground-truth data and upscale ET_o estimates from point to regional and national levels, thereby supporting water management decision-making. The results demonstrate that the PMT is generally accurate, with RMSE not exceeding 26% of the average daily ET_o. With regard to shortwave radiation, using the temperature difference as a predictor in combination with cluster-focused multiple linear regression equations for estimating the radiation adjustment coefficient (k_Rs) yielded accurate results. ET_o estimates derived using raw (uncorrected) reanalysis data exhibit considerable bias and high RMSE (1.07–1.57 mm d⁻¹), indicating the need for bias correction. Various correction methods were tested, with the simple bias correction delivering the best overall performance, reducing RMSE to 0.99 mm d⁻¹ and 1.05 mm d⁻¹ for AgERA5 and MERRA-2, respectively, and achieving a normalized RMSE of about 22%. After implementing bias correction, the AgERA5 was found to be superior to the MERRA-2 for all the studied sites. Furthermore, the PMT outperformed the bias-corrected reanalysis in estimating ET_o. It was concluded that PMT-ET_o can be recommended for further application in countries with limited access to ground-truth meteorological data, as it requires only basic technical skills. It can also be used alongside reanalysis data, which demands more advanced expertise, particularly for data retrieval and processing.

1. Introduction

An accurate estimation of the reference crop evapotranspiration (ET_o) is critical for agricultural water resources planning and management [1,2,3]. ET_o quantifies the natural loss of water to the atmosphere, incorporating an approximation that accounts for both evaporation and transpiration from a reference surface [1,2]. The FAO-PM ET_o was parametrized for a hypothetical reference crop with specific characteristics in terms of height (0.12 m), albedo that reflects 23% and absorbs 77% of the incoming radiation under standard conditions, and a fixed surface resistance of 70 s m⁻¹ [1]. ET_o is essential for estimating crop water use (ET_c) as it represents the climatic demand conditions. Crop ET is commonly estimated using the FAO approach, which involves multiplying ET_o by a crop coefficient (K_c). The latter considers the differences in characteristics of the crop under study relative to the reference crop. Therefore, it enables the quantification of water use by any agroecosystem, landscape, wetland, or riparian ecosystem [4]. Under water or salinity stress, crop ET decreases [1,5,6,7].

The FAO-PM ET_o requires data on several weather variables, including maximum and minimum temperature, shortwave or net radiation, relative humidity or dew point temperature, and wind speed. The FAO 56 guidelines [1], which have recently been revised [2], describe alternative approaches for estimating missing weather variables data, namely when using temperature data only (FAO-PMT), making these tools particularly valuable in regions with insufficient weather stations or low maintenance capabilities [1,2]. To improve the accuracy of the ET_{o PMT} estimates, the calibration of the predictors may be performed for local conditions [8,9,10,11] or, alternatively, simplifications to the method can be adopted [2,12]. The accuracy of the PMT approach has been demonstrated in several studies conducted across Africa [13,14,15,16,17], although in many of these cases, adequate observed weather datasets were not available for a consolidated assessment of alternative approaches. Another commonly used approach that uses temperature data only for ET_o estimation is the Hargreaves–Samani (HS) equation, earlier developed for the Senegal River Basin [18] and later commonly used [12,19,20,21]. The ET_o estimates with HS can also be used with the FAO K_c-ET_o approach despite the need for adjustments.

Various heuristic approaches have also been used to estimate ET_o with minimal data availability, with machine learning (ML) algorithms being among the most widely used. However, as discussed by Pereira et al. [3], these approaches do not use the fundamental physics underlying the FAO-PM ET_o equation, which is considered relevant when selecting alternative approaches to calculate ET_o when weather datasets are incomplete. These algorithms leverage training data to model variables for specific regions or sites [22]. However, they have limited applicability as they are generally not transferable and are only effective for the sites for which they were developed. Examples of these approaches include support vector machines (SVMs) and random forest (RF), which are renowned for their accuracy in predictions using limited input data [23,24].

Alternative sources of weather data are those based on observational data with different spatial and temporal resolutions and different available weather variables. Examples include the Climate Research Unit Time Series (CRU) [25] and WorldClim for the globe [26], E-OBS for Europe [27], PRISM climate data for the USA [28], Iberia01 [29] for the Iberian Peninsula, or those provided by [30] for Brazil. For given weather variables, such as shortwave radiation, satellite data can be obtained, e.g., data provided by the geostationary Meteosat Second Generation (MSG) system, which includes the Satellite Application Facility for Land Surface Analysis (LSA-SAF) [31,32,33].

Other sources of weather data include reanalysis gridded data obtained by integrating observations from various sources, including ground-based weather stations, ocean buoys, ships, aircraft, and satellite sensors [34,35]. This integration is carried out by modeling and data assimilation systems, which provide accurate and continuous estimates of climate and meteorological variables [36,37]. Their temporal resolution can be hourly, daily, or monthly. The spatial resolution varies, depending on the data source. One of the most widely used sources is the ERA5 reanalysis, made available by the European Centre for Medium-Range Weather Forecasts (ECMWF) [36,38]. The AgERA5 dataset, which focuses on agriculture, is derived from this dataset. This dataset provides hourly data with a spatial resolution of 0.1° [39,40]. Another often-used reanalysis dataset is MERRA-2 version 2, an atmospheric reanalysis developed by NASA (National Aeronautics and Space Administration). MERRA-2 provides a reanalysis of global climatic and weather information [41]. Another reanalysis-based dataset is that provided by the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP/NCAR) [42]. Reanalysis data have been used in several studies to estimate ET_o and assess its spatial distribution [40,43,44,45,46]. One of the key advantages of using reanalysis data is that they provide all the weather variables required to calculate ET_o without any gaps [47,48]. However, many studies have found that these gridded datasets require bias corrections, such as additive bias correction [32,49], simple regional bias correction [50,51], and Kalman filtering for temperature modeling [52], as well as adequate downscaling methods [53], to improve their quality.

The above-cited studies emphasize the critical importance of bias correction, particularly in regions lacking baseline meteorological information, such as many tropical areas [36], including part of Africa. This is the case of Guinea-Bissau (GB), located in West Africa, with an economy based primarily on agriculture. GB has limited economic resources, which has led to a decline in government investment in meteorological and agricultural information after independence. Although long-term weather records exist at three sites in the country (Bissau, Bafata, and Bolama), they are incomplete due to the loss of documents during the civil war (1998–1999), poor resources for digitizing the data and maintaining the weather stations, and a lack of financial resources for purchasing new sensors [54,55]. However, these sites only cover a small part of the country as they exclude the most important agricultural areas, regions in the north affected by drought, humid zones in the south, and the archipelago of Bijagós [56,57,58]. This hinders the spatial quantification of ET_o across the country, particularly in agricultural water management studies [59,60], and highlights the need for easy-to-use approaches to cope with reduced weather datasets.

Therefore, the main objective of this study is to evaluate different approaches for estimating FAO-PM ET_o using only temperature data (PMT). In addition, the study aims to assess the accuracy of AgERA5 and MERRA-2 reanalysis weather datasets to support the scaling of ET_o estimates from field level to regional and national levels. This is the first study of its kind conducted in Guinea-Bissau, and its novelty lies in the combined use of ground-truth meteorological observations and reanalysis datasets. The methodologies developed will be made accessible to GB technical staff, who have diverse skills levels, namely relative to the use modeling tools aimed at improving water management in mangrove rice cultivation. Furthermore, the results of the current study are expected to enhance water resource management across different spatial scales and may contribute to improved water governance, particularly under conditions of climate variability and freshwater increasing scarcity.

2. Materials and Methods

2.1. Climate

The study was conducted in GB, West Africa (Figure 1). The study sites were located mainly in the coastal region (Figure 1), where, according to the Köppen–Geiger classification [61,62], the climate is of equatorial savannah with dry winter (Aw) but with different life zones as per the Holdridge classification [63,64]. The aridity index (AI, Table S2 in Supplemental Material), as defined by [65], is the ratio of the long-term mean annual precipitation (P, mm) [66] to the mean annual climatic evaporation index (CEI_TH, mm). The northern part of GB is classified as moist sub-humid (AI ≈ 0.7), while the south of the country has AI > 1.0.

2.2. Data

2.2.1. Ground-Truth Weather Data

Automatic weather stations were installed over well-watered grass at various locations across the country (

Table 1. Geographic coordinates, elevation, and data recording periods of the weather stations in Guinea-Bissau.

Region	Weather Station	Latitude (°N)	Longitude (°W)	Elevation (m)	Start of Data Collection	End of Data Collection	Number of 30 min Records
South	Cafine	11.214919	−15.174659	6.0	8 April 2021	1 June 2024	45,563
	Quebil	11.270221	−15.236727	8.4	10 March 2021	30 May 2024	16,378
	Buba	11.587290	−14.998417	10.9	22 August 2021	30 May 2024	45,193
Central	Malafu	12.014828	−15.020001	24.9	10 April 2021	30 May 2024	48,388
	Enchugal	12.046918	−15.436894	16.6	11 April 2021	29 May 2024	43,768
	Bissora	12.220728	−15.444387	15.1	11 January 2022	3 June 2024	41,951
	Cacheu	12.258014	−16.157159	21.2	12 January 2022	11 June 2024	42,280
North	S. Domingos	12.414232	−16.182400	12.5	12 April 2021	4 June 2024	45,132
	Djobel	12.280922	−16.392913	10.0	12 July 2022	5 June 2024	49,978
	Elalab	12.246547	−16.443420	10.8	12 April 2021	4 June 2024	45,176
Island	Bubaque	11.299951	−15.831088	29.8	9 January 2022	31 December 2023	34,634

, Figure 1), situated in open areas, away from trees and buildings. The ATMOS 41 weather stations (Meter Environment Products, Pullman, WA, USA) were mounted on metal poles at a height of two meters above ground level, oriented northward according to the installation guidelines. Data were recorded every 30 min using ZL6 data loggers (Meter Group, Pullman, WA, USA). The stations were regularly maintained to ensure data quality, including the removal of Saharan dirt and dust, inspection of battery levels, and cleaning of the solar panels on the data loggers, typically every two months or whenever malfunctions were detected. Detailed information on weather station locations (Figure 1) and data collection periods is provided in Table 1.

This study was carried out using the daily weather data recorded at each weather station. Thirty-minute measurements were processed to obtain daily values of maximum and minimum temperature (T_max, T_min, °C), maximum and minimum relative humidity (RH_max, RH_min, %), wind speed at 2 m height (u₂, m s⁻¹), and short wave solar radiation (R_s, MJ m⁻¹). In line with common practices in several meteorological services, the RH measured at 9 a.m. (RH₉) was taken to represent the mean daily conditions (RH_mean). Rainfall (mm) data at 30 min intervals (mm) were also available from all weather stations.

2.2.2. Reanalysis Weather Data

Reanalysis datasets were obtained from two sources: the European Center for Medium-Range Weather Forecasts (ECMWF), platform AgrERA5, part of the Copernicus project [67], and the Global Modeling and Assimilation Office (GMAO), platform MERRA-2.

AgERA5 is a daily reanalysis dataset provided by ECMWF, available from 1979 to the present, with a focus on providing data for agricultural and agroecological studies [68,69]. It is provided at a spatial resolution of 0.1° × 0.1° (approximately 11 km × 11 km) [67] and is derived by forcing hourly ECMWF ERA5 data at the surface level. AgERA5 includes a wide range of atmospheric and surface variables. For this study, the following variables were downloaded from the Copernicus Climate Change Service (C3S) Climate Data Store (CDS) website: R_s (J m⁻² d⁻¹), T_min and T_max (K), dew point temperature (T_dew, K), RH₉ (%), and wind speed measured at 10 m height (u₁₀, m s⁻¹).

MERRA also has a version tailored for agricultural studies, known as (AgMERRA). However, this dataset was not used in the present study due to its limited temporal coverage (1980–2010) [70,71]. Instead, the more recent product MERRA-2, developed by NASA to replace the original MERRA using a fixed assimilation system [41], was used, as it spans from 1980 to the present. MERRA-2 provides daily weather data at a spatial resolution of 0.5° × 0.625° [72,73]. All variables required for the calculation of FAO-PM ET_o were downloaded: T_min (K), T_max (K), T_dew (K), RH₉ (%), u₁₀ (m s⁻¹), R_s (J m⁻² d⁻¹), and vapor pressure (hPa). The appropriate conversion of units was therefore performed on both datasets, with the wind speed at 10 m adjusted to 2 m in accordance with the recommendation of FAO 56 [1]. Further details on the data assimilation system and performance metrics for AgrERA5 are reported by [74] and for MERRA-2 by [75].

The datasets were accessed using a script written in Python version 3.11 [76]. The MERRA-2 reanalysis data featured fewer grid centroids (36) compared to the AgERA5 (356), due to differences in spatial resolution between the two datasets. Both datasets were organized to cover the same period as the observed weather data, from January 2021 to May 2024 (Table 1). The Euclidean distance (straight line between two points) was calculated between each grid centroid and the weather station locations [77]. A filtering process was applied, and each grid centroid was classified based on its proximity to the weather stations. Following other approaches in the literature, the nearest grid point to each station was selected for use in this study [32,78,79,80]. Although other methods exist, e.g., multiple linear regression [49] or triangle-based bi-linear interpolation method [81], these approaches have not been shown to outperform the simpler and widely adopted method of using the nearest grid point to the targeted station.

2.3. Computation of the FAO-Penman Monteith ET_o

The FAO Penman–Monteith equation is the most widely used method in agriculture for estimating the reference crop evapotranspiration (PM-ET_o) [1,2]. It allows for an accurate determination of the climatic demand conditions as it integrates various meteorological variables. The daily ET_o is estimated as follows:

$${\mathrm{E}\mathrm{T}}_{\mathrm{o}}={\displaystyle \frac{0.408 \Delta \left({\mathrm{R}}_{\mathrm{n}}-\mathrm{G}\right)+\mathsf{\gamma }\frac{900}{\mathrm{T}+273}{\mathrm{u}}_2({\mathrm{e}}_{\mathrm{s}}-{\mathrm{e}}_{\mathrm{a}})}{\Delta +\mathsf{\gamma } (1+0.34{\mathrm{u}}_2)}}$$

(1)

where $\Delta$ is the slope vapor pressure curve (kPa °C⁻¹); 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), which is negligible at daily steps; T is the air temperature at 2 m height (°C); u₂ is the wind speed at 2 m height (m s⁻¹); e_s is the saturation vapor pressure (kPa); e_a is the actual vapor pressure (kPa); e_s − e_a is the vapor pressure deficit (kPa); and γ is the psychrometric constant (kPa °C⁻¹).

The net radiation at the crop surface (R_n, MJ m⁻² d⁻¹) is calculated as the difference between the net shortwave radiation (R_ns, MJ m⁻² d⁻¹) and the net longwave radiation (R_nl, MJ m⁻² d⁻¹), where R_ns is calculated as (1 − α) R_s, assuming an albedo (α) value of 0.23 for the green grass reference crop, and R_nl is calculated as follows:

$${\mathrm{R}}_{\mathrm{n}\mathrm{l}}=\mathsf{\sigma }\left[{\displaystyle \frac{{\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}},{\mathrm{K}}^4+{\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}},{\mathrm{K}}^4}{2}}\right]\left(0.34-0.14\sqrt{{\mathrm{e}}_{\mathrm{a}}}\right)\left(1.35{\displaystyle \frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{s}\mathrm{o}}}}-0.35\right)$$

(2)

where $\mathsf{\sigma }$ is the Stefan–Boltzmann constant (4.903 × 10⁻⁹ MJ K⁻⁴ d⁻¹), and T_max and T_min are the daily maximum and minimum temperatures (K), respectively. The mean e_s for a day is calculated as the average of the vapor pressure at the maximum and minimum temperature, while e_a is estimated from the RH_max and RH_min as follows:

$${\mathrm{e}}_{\mathrm{a}}={\displaystyle \frac{{\mathrm{e}}^{\mathrm{o}}\left({\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right)\frac{{\mathrm{R}\mathrm{H}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{100}+{\mathrm{e}}^{\mathrm{o}}\left({\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)\frac{{\mathrm{R}\mathrm{H}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{100}}{2}}$$

(3)

where e^o (T_min) (kPa) and e^o (T_max) (kPa) are the saturation vapor pressure at the daily minimum and maximum air temperature, respectively, and RH_max (%) and RH_min (%) are the maximum and minimum relative humidity, respectively.

The wind speed data (u₂, m s⁻¹) at the standard height of two meters above the ground level is obtained from that measured at height z (m) through the following logarithmic transformation:

$${\mathrm{u}}_2={\mathrm{u}}_{\mathrm{z}}{\displaystyle \frac{4.87}{\mathrm{l}\mathrm{n}\left(67.8 \mathrm{z}-5.42\right)}}$$

(4)

where u_Z is the wind speed measured at z meters above the ground surface (m s⁻¹), and z is the height of the measurement above the ground surface (m).

2.4. Calculation of ET_o Using Only Temperature Data (FAO-PMT)

Several approaches were used to estimate T_dew, u₂, and R_s to overcome missing data or data with poor quality. The predictors and the combination of approaches used in the current study are detailed in Figure 2. For e_a computation, and therefore the prediction of T_dew, the first approach used was straightforward and assumed T_min as the best predictor for T_dew [1,2]. A second approach used either T_min (for moist sub-humid sites), or the T_mean − a_D (for humid sites) with a_D = 2, both depending on the location aridity index (AI) [2,32,82]. Therefore, the first step was to calculate the already mentioned AI for each location. The third approach consisted of the numerical optimization of the value of a_D by minimizing the root mean squared error (RMSE) using the “L-BFGS-B” algorithm (See Supplementary Material S1). To overcome the missing u₂ data, two predictors were used, the average local or regional (u_{2 avg}) or the world average value (u_{2 def} = 2 m s⁻¹) [1,2].

The shortwave radiation was estimated using the following equation [83]:

$${\mathrm{R}}_{\mathrm{s}}={\mathrm{k}}_{\mathrm{R}\mathrm{s}} {({\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}})}^{0.5} {\mathrm{R}}_{\mathrm{a}}$$

(5)

where k_Rs is the empirical adjustment coefficient (°C^−0.5), T_max and T_min are the maximum and minimum air temperature (°C), and R_a is the extraterrestrial radiation (MJ m⁻² d⁻¹).

The estimation of k_Rs was carried out using three different approaches (Figure 2). The first two were based on the use of pre-established multiple linear regression (MLR) equations derived from long-term data collected from 555 weather stations across the Mediterranean. These MLR equations were derived by testing the average daily temperature difference (TD_avg), the daily average local or regional wind speed (u_{2 avg}), and the daily average relative humidity (RH_avg) as predictors of k_Rs using a set of goodness-of-fit indicators, as detailed by Paredes et al. [12]. Therefore, one MLR global application across all climate types (global), and the other tailored to specific climate conditions (climate-focused), based on the AI [2,12,84] as follows:

$$\mathbf{Global} \mathbf{equation} \mathbf{(}\mathbf{all} \mathbf{climate} \mathbf{types}\mathbf{)} {\mathrm{k}}_{\mathrm{R}\mathrm{s}}=0.365-0.0099 {\mathrm{T}\mathrm{D}}_{\mathrm{a}\mathrm{v}\mathrm{g}}+0.0194 {\mathrm{u}}_{2\mathrm{a}\mathrm{v}\mathrm{g}}-0.0017 {\mathrm{R}\mathrm{H}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$$

(6)

Climate focused equations:

$$\mathrm{Humid} \mathrm{climates} (\mathrm{AI} > 1.0) {\mathrm{k}}_{\mathrm{R}\mathrm{s}}=0.519-0.0104 {\mathrm{T}\mathrm{D}}_{\mathrm{a}\mathrm{v}\mathrm{g}}+0.0188 {\mathrm{u}}_{2\mathrm{a}\mathrm{v}\mathrm{g}}-0.0035 {\mathrm{R}\mathrm{H}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$$

(7a)

$$\mathrm{Moist} \mathrm{locations} (0.50 \le \mathrm{AI} < 1.00) {\mathrm{k}}_{\mathrm{R}\mathrm{s}}=0.396-0.0105 {\mathrm{T}\mathrm{D}}_{\mathrm{a}\mathrm{v}\mathrm{g}}+0.0186 {\mathrm{u}}_{2\mathrm{a}\mathrm{v}\mathrm{g}}-0.0021 {\mathrm{R}\mathrm{H}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$$

(7b)

where TD_avg is the average daily temperature difference T_max − T_min, u_{2 avg} is the daily average local or regional wind speed, and RH_avg is the daily average relative humidity, all computed using a long-term dataset.

The third approach was developed to improve k_Rs estimates and, consequently, the ET_{o PMT} estimates. New adjusted MLR equations were derived at the cluster level (cluster-focused) using the same k_Rs predictors as in the previous approaches (TD _avg, HR_avg, u_{2 avg}). The optimization was performed using the “L-BFGS-B” algorithm with the aim of minimizing the root mean square error (RMSE) between the ET_o and the ET_{o PMT} (see Supplementary Material S1). Therefore, k_Rs was considered a cluster-specific constant of proportionality, derived through MLR using long-term mean values of the referred predictors. Due to the relatively short weather dataset (<20 years), it was divided into calibration and validation subsets, comprising 70% and 30% of the data, respectively.

All the approaches were applied at two levels: individually at each site and across groups of sites as defined by the cluster analysis (Section 2.5).

2.5. Data Quality Assurance and Quality Checking (QAQC)

All the weather datasets used in this study were subjected to prior quality assurance and control procedures to ensure consistency, integrity, and quality for ET_o calculations. This step is mandatory to avoid error propagation into ET_o calculations. To this end, a custom script was developed to analyze data behavior through visual diagnostic tools, including Q-Q plots and normal probability plots (qqnorm), to identify data patterns and trends. Given the tropical location of the study, outliers were removed by applying a threshold of 3.5 times the interquartile range (IQR) below the first quartile (Q1) and above the third quartile (Q3) [85,86]. This procedure aimed to exclude extreme values likely resulting from measurement errors that could significantly bias the analysis. Subsequently, the datasets were tested for mean homogeneity, trend, and variance homogeneity tests, following established statistical procedures [2,87,88,89].

Wind speed data were specifically examined for prolonged periods of nearly constant and low values (≤0.5 m s⁻¹), which may indicate anemometer malfunction or a numerical ‘offset’ in the sensor calibration.

Shortwave radiation data (R_s, MJ m⁻² d⁻¹) were evaluated following the procedure recommended by [87,90]. The R_s values were compared with estimated clear-sky solar radiation (R_so, MJ m⁻² d⁻¹) for each location, with R_so calculated as follows [1,2]:

$${\mathrm{R}}_{\mathrm{s}\mathrm{o}}={\mathrm{R}}_{\mathrm{a}}(0.75+(2\times {10}^{-5} \mathrm{z}\left)\right)$$

(8)

where R_a is the extraterrestrial radiation (MJ m⁻² d⁻¹), and z is the weather station altitude (m) (Table 1). R_a calculation method is detailed in [1].

The R_s/R_so ratio was calculated as the highest recorded observation within each 15-day period. This ratio was then used to adjust the remaining R_s observations by dividing each observed R_s by the ratio calculated for the highest record in that period. This procedure was systematically applied across the entire dataset for each weather station. All calculations and analyses were carried out using R statistical software version 2025.05.1 +513 [91]. This tool performs functions similar to those of the agweather-qaqc software [92].

Relative humidity values were plotted against air temperature throughout the day to check for inverse behavior. RH_max values were inspected to determine whether they approached saturation or were no more than 3–5% higher in the early morning or during rain events, indicating the need to recalibrate the sensors. In addition, RH records were evaluated for consistency on rainy days, when RH values should typically exceed 95%.

A rigorous data filtering process was applied, retaining only those dates with complete records for all variables required for ET_o estimation (Equation (1)). This ensured homogeneity across all sites. Once homogenized, the data were subjected to the Shapiro–Wilk test to assess the normality of distributions for subsequent analyses. To identify relationships between sites, a comparative analysis of climatic variables was performed using the non-parametric Kruskal–Wallis test [93,94], followed by pairwise comparisons using the Bonferroni method using a significance level of 0.01 (α = 0.01 indicates a 1% maximum probability of committing a Type I error across all comparisons when performing multiple statistical tests). This approach provided a robust evaluation of whether significant differences existed among sites. The same data filtering process was applied for the cluster analysis, ensuring that only data common to all sites were used. The sites were then normalized and grouped, and a distance matrix was calculated. A dendrogram based on site altitude guided the selection of site groups [95]. The optimal number of clusters was determined using the Elbow method, which suggested K = 5 (K represents the number of clusters into which the data was divided), indicating that the data naturally grouped into five distinct clusters [96,97]. Hierarchical clustering then identified the four final site groups.

2.6. Bias Correction of Reanalysis-Based ET_o Estimates

To improve the accuracy of ET_o estimates derived from reanalysis data (ET_{o rean}) at both individual sites and cluster levels and to support the subsequent application of gridded data for regional ET_o estimation [59,60,98,99], four correction methods were implemented. Rather than adjusting the underlying meteorological variables used in the calculation of ET_o, these correction techniques were applied directly to the reanalysis-based ET_o estimates [49]. The correction methods included linear model (LM) adjustment, slope correction, robust linear modeling, and simple bias correction. Each correction was applied at both the individual site level and across groups of sites defined by the cluster analysis. Further details on each correction method are provided below:

(A)

The adjusted linear model correction (ALM_c) involved fitting a linear regression between ET_{o rean} ($\mathrm{y}$) and ET_{o obs} ($\mathrm{X}$) as follows:

$$\mathrm{y}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1·\mathrm{X}+\mathsf{\epsilon }$$

(9)

where β₀ is the regression intercept, β₁ is the slope, and $\mathsf{\epsilon }$ represents the random error term [100].

The resulting intercept and slope values were then used to adjust the ET_o for each site. The ET_{o rean} values were corrected for both systematic bias and scale error [89] by subtracting the intercept and dividing by the slope.

(B)

The slope correction (S_c) method involved fitting a simple linear regression (LM) model between the ET_{o rean} and ET_{o obs} values, with the intercept of 0 (${\mathsf{\beta }}_0=0$). Once the model was fitted, the slope was calculated and applied as a correction factor. Each ET_{o rean} value was adjusted by dividing it by the estimated slope (ET_o/slope = ET_{o rean_adjusted}) [100]. This correction was applied individually to each site and aimed to compensate for systematic bias identified in the relationship between reanalysis and observed data.

(C)

The robust linear model correction (RLM_c) followed a similar principle to the slope correction but employed a robust linear regression instead of the ordinary least squares method. Unlike standard linear regression, which minimizes the sum of squared residuals, RLM_c minimizes a loss function that is less sensitive to large deviations [100,101]. In this study, the Huber M-estimator was used, implemented through the ‘rlm’ function in the R software version 2025.05.1 +513. Fitting was carried out using integrated weighted least squares (IWLS). The Huber function addresses a convex optimization problem and provides parameter estimates that are more robust in the presence of outliers. As with the slope correction, the new ${\mathsf{\beta }}_1^{\mathrm{r}\mathrm{l}\mathrm{m}}$ (means the updated or robust slope coefficient obtained from this Huber-based fitting procedure) was used to fit ET_{o rean}, reducing the influence of extreme values on the correction process, which are common in tropical regions. Therefore, the corrected ET_{o rean} is estimated as follows:

$${\mathrm{E}\mathrm{T}}_{\mathrm{o} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{n} \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}={\displaystyle \frac{{\mathrm{E}\mathrm{T}}_{\mathrm{o} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{n}}}{{\mathsf{\beta }}_{1 \mathrm{r}\mathrm{l}\mathrm{m}}}}$$

(10)

(D)

A simplified bias correction was applied to adjust ET_{o rean} at different sites. The simplified BIAS correction (BIAS_c) was calculated as follows:

$$\mathrm{B}\mathrm{I}\mathrm{A}\mathrm{S}\mathrm{c}={\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{E}\mathrm{T}}_{\mathrm{o} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{n},\mathrm{i}}-{\mathrm{E}\mathrm{T}}_{\mathrm{o} \mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}\right)$$

(11)

where n is the number of observations per site, ${\mathrm{E}\mathrm{T}}_{\mathrm{o} \mathrm{r}\mathrm{e}\mathrm{a}\mathrm{n},\mathrm{i}}$ represents the reanalysis values for the i-th observation, and ${\mathrm{E}\mathrm{T}}_{\mathrm{o} \mathrm{o}\mathrm{b}\mathrm{s},\mathrm{i}}$ is the corresponding observed value. The new estimated ET_{o rean_corrBIAS} was calculated by subtracting BIAS_c from each daily ET_{o rean} value. This correction aimed to eliminate systematic deviations inherent to the original estimates.

2.7. Accuracy Assessment

To assess the accuracy of the tested approaches, a set of goodness-of-fit indicators [3,32] was employed to compare the observed (O_i = ET_{o obs}) and estimated (P_i = ET_{o PMT} or ET_{o REAN}) values. The regression coefficient (b₀) of a forced-to-the-origin (FTO) linear regression was used to assess the proportionality between the estimated and observed ET_o values. A value of _b0 close to 1.0 indicates that the estimated and observed ET_o values are statistically similar. A b₀ < 1 suggests underestimation, while a b₀ > 1 suggests overestimation. The coefficient of determination (R²) from an ordinary least squares (OLS) linear regression was used to assess the degree of dispersion of the O_i and P_i pairs along the regression line. R² represents the proportion of variance in the observed data that is explained by the estimation approach. Values of R² approaching 1 indicate a strong linear relationship between the observed and predicted values and hence a better model fit. To quantify estimation errors, the root mean square error (RMSE) was calculated, providing an overall measure of the differences between O_i and P_i. Additionally, the normalized root mean square error (NRMSE, %) was calculated as the RMSE divided by the mean of the observations ($\overline{O}$). Lower RMSE and/or NRMSE values indicate greater estimation accuracy. Two further indicators were used to assess the systematic bias of the estimates, the BIAS and the percentage bias (PBIAS, %). BIAS was calculated as the average difference between the observed and predicted values, while PBIAS was obtained by dividing BIAS by the sum of the O_i. The positive values of BIAS and PBIAS indicate a tendency toward overestimation, whereas negative values indicate underestimation. Values close to zero suggest lower systematic bias in the model’s predictions [89]. All goodness-of-fit indicators were calculated using R statistical software [91].

2.8. Spatial Variability of ET_O in Guinea-Bissau

As Figure 1 clearly shows, there are few weather stations in the country, most of which are in western Guinea-Bissau. Furthermore, the distribution of stations varies greatly between regions. Following a thorough evaluation of the two reanalysis datasets, the one demonstrating superior performance was selected to estimate ET_o at all gridded centroids across the country, to overcome this lack of data.

Initially, ET_o was calculated using the raw reanalysis data. These values were subsequently corrected using the most appropriate method identified in the study, with adjustments applied to each centroid based on its proximity to the most influential weather station. The mean annual cumulative ET_o for the period 2021–2023 was then estimated and mapped using ordinary kriging. Spatial autocorrelation analysis was conducted using the Global Moran’s I statistic, together with Z-score and p-value calculations for the annual ET_o (Table S8), following a methodology similar to that used for soil salinity mapping by [99]. All special analyses were carried out using ArcMap 10.8.2 and the Geostatistical Analyst (GS+) tool. In addition, RStudio version 2025.05.1 +513 was used to compute the goodness-of-fit indicators for the interpolated maps.

3. Results and Discussion

3.1. QAQC Assessment

The results of the tests for mean homogeneity, trend, and variance homogeneity of the ground-truth data relative to T_max and T_min, RH, and u₂ are shown in

Table 2. Statistical tests applied—mean homogeneity (Mann–Kendall test), trend analysis (Wilcoxon rank-sum test), and variance homogeneity (Levene’s test)—for weather variables used in for calculation of the ET_o in Guinea-Bissau.

Variable	Mann–Kendall Test		Wilcoxon Rank Test		Levene’s Test
	Z-Value	p-Value	Rank–W	p-Value	F-Value	p-Value
RHAvg	0.09	0.47	124.70	0.43	1.56	0.27
RHMax	1.22	0.25	96.30	0.27	3.51	0.30
RHMin	0.07	0.55	141.10	0.52	3.14	0.34
Tavg	1.02	0.44	97.40	0.37	0.58	0.54
Tmax	1.57	0.21	77.05	0.14	1.39	0.47
Tmin	−0.07	0.56	133.90	0.62	1.17	0.44
Wind speed	1.64	0.11	68.10	0.07	2.94	0.23

. The results of the Mann–Kendall test showed that none of the variables exhibited statistically significant trends, as the z-values were close to zero and the p-values were greater than 0.05. The Wilcoxon rank-sum test was then used to compare the central tendencies of the data from different locations. All variables yielded p-values above the 0.05 significance threshold, indicating that there were no significant differences in median values between the locations being compared. The analysis of the equality of variances across different locations (Levene’s test) showed that all p-values exceeded 0.05, suggesting homoscedasticity (equal variances) across the dataset. Overall, the results of the statistical tests demonstrate that the analyzed meteorological variables are stable over time and comparable between locations. They also show that the variables exhibit consistent variability and are unaffected by outliers or measurement errors at all sites. Therefore, they can be used to estimate ET_o.

Additionally, R_s was checked and corrected as necessary, and examples of this correction are presented in Figure 3. These examples demonstrate the need for R_s correction due to inadequate pyranometer sensor calibration.

3.2. Meteorological Characteristics of the Studied Sites

A high variability in the different weather variables used for the calculation of ET_o was observed among the different sites in GB (

Table 3. Weather characterization of various locations in Guinea-Bissau based on the mean daily maximum (T_max), minimum (T_min), and average temperature difference (TD_avg); maximum (RH_max), minimum (RH_min), and average (RH_avg) relative humidity; and average wind speed (u_{2 avg}) for the period 2021–2023.

Site	Tmin	Tmax	TDavg	RHmax	RHmin	RHavg	u2 avg
	°C	°C	°C	%	%	%	m s−1
Cafine	22.9 b	31.7 d	9.5 bc	99.1 a	68.9 a	78.8 a	1.3 c
Malafu	21.5 f	33.3 bc	13.3 ab	98.6 b	62.2 bc	75.2 b	0.8 f
Djobel	22.5 bcd	32.7 c	10.8 b	98.8 b	59.8 cd	77.7 a	2.1 a
Enchugal	21.8 de	33.1 bc	12.1 ab	93.7 c	57.8 de	70.5 c	0.9 e
Buba	22.6 cde	33.3 ab	12.1 ab	99.2 ab	55.8 e	75.0 b	1.6 c
Elalab	22.6 bc	31.9 d	10.5 b	92.9 cd	56.1 e	71.3 c	1.7 b
Cacheu	21.5 ef	33.4 ab	13.2 a	92.7 d	55.5 e	70.1 c	1.1 d
Bubaque	24.3 a	30.8 e	6.8 c	92.3 d	67.5 ab	76.8 ab	0.8 f
Bissora	20.3 f	34.2 a	14.8 a	89.4 e	49.9 f	67.3 c	0.7 g
S. Domingo	19.8 f	33.7 a	13.9 a	94.8 c	49.3 f	71.9 c	0.8 f
Quebil	22.2 cd	33.2 ab	11.0 b	88.7 e	40.4 g	64.6 d	0.8 f
Shp_wilk	<0.01	<0.01	<0.01	<0.01	<0.01	< 0.01	<0.01
n	492	492	492	492	492	492	492
α	<0.01	<0.01	<0.01	<0.01	<0.01	<0.01	<0.01

Note: means followed by the same letter do not represent significant differences; n = number of common days for all sites compared. α = Bonferroni test with an α = 0.01 using Kruskal–Wallis test. Shp_wilk = Shapiro–Wilk test.

). The sites with the significantly (α = 0.01) highest temperatures were Bissora, Cacheu, and Buba. The sites with the lowest temperatures were Bissora, Cacheu, and Malafu. The results indicate that Bissora and Cacheu have the highest thermal amplitude among the studied locations, while Bubaque has the lowest thermal amplitude significantly (α = 0.01). This trend was similar when the average daily temperature difference (TD) was analyzed. From one perspective, the site with the significantly (α = 0.01) highest RH value was Cafine, which was the most humid site in the country. On the other hand, Bissora had significantly lower RH values (RH_min: 49.9% and RH_avg: 67.3%; α = 0.01) and was therefore considered the least humid site compared to the others. Buba presented contrasting humidity conditions. Djobel was the windiest location (u_{2 avg} = 2.1 m s⁻¹), while Bissora was the least windy location (u_{2 avg} = 0.7 m s⁻¹), both with significant differences (α = 0.01) relative to the other sites.

The dendrogram generated by the cluster analysis identified three distinct groups based on the accumulated precipitation and ET_o at each site (Figure 4). These groups were formed according to their position in the dendrogram and the geographical proximity of the sites. The first cluster included Buba and Cafine; the second included Malafu, Cacheu, and Enchugal; and the third included Elalab, Djobel, and S. Domingos. These clusters represent the southern, central, and northern regions, respectively. As mentioned above, Bissora presented contrasting weather conditions and did not fit into any cluster within the analysis. Its inland-like location resulted in distinct weather characteristics. Bubaque was also not included in the cluster analysis as it is located on an island. Quebil was excluded from the cluster analysis due to a lack of observations relating to sensor malfunction problems, which began in mid-2022. However, it was included in the ET_o estimates using the available weather data.

In Guinea-Bissau, there is considerable climatic variability between different sites, and this study demonstrated sensitivity in identifying moist sub-humid and humid areas, regions with greater thermal amplitude, and sites with variable wind patterns (Table 2). Tropical climates are variable because they are frequently influenced by tropical storms [102,103]. These regions typically experience two well-defined seasons, namely the rainy season and the dry season, but with high interannual variability [104]. Subsistence agriculture is highly dependent on the behavior of the rainy season, particularly for the Mangrove Swamp Rice production in the country [59,105,106]. However, this seasonality is becoming increasingly unpredictable, with global warming exacerbating variability, particularly in rainfall distribution patterns and intensity [107,108]. As a result, these areas are becoming increasingly vulnerable, making sustainable agricultural production more challenging [98,109]. Appropriate management of water resources is therefore necessary.

3.3. FAO-PM ET_o Using Temperature Data Only

As previously stated, one of the new approaches for humid climates consisted of optimizing the a_D value used in the prediction of T_dew from T_mean. The results showed that a_D values ranged from 2.5 °C to 5.0 °C, depending on the location, with an average a_D of 4.8 °C when used alongside with u_{2 avg}. When the u_{2 def} was used instead, the optimized a_D values ranged from 1.5 to 5.0 °C, with an average of 4.5 °C. These results are consistent with those reported by [110] for humid climates in China, with a_D values of 5.14 ± 1.33 °C. Similarly, ref. [11] reported a_D values ranging from 1.5 °C to 4 °C for the humid oceanic islands of the Azores, Portugal.

The new cluster-focused MLR equations, which were derived from observed weather datasets by minimizing RMSE, are presented in

Table 4. Cluster-focused optimized predictive multi-linear regression equations for estimating k_Rs values and respective values.

Cluster		Predictive Equations	kRs	Minimized RMSE (°C−0.5)	Equation
1	Cafine, Buba, Quebil	${\mathrm{k}}_{\mathrm{R}\mathrm{s}}=0.410097-0.009323 {\mathrm{T}\mathrm{D}}_{\mathrm{a}\mathrm{v}\mathrm{g}}+0.021961 {{\mathrm{u}}_2}_{\mathrm{a}\mathrm{v}\mathrm{g}}-0.001902 {\mathrm{R}\mathrm{H}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$	0.196	7.9 × 10−7	(12)
2	Enchugal, Cacheu, Malafu	${\mathrm{k}}_{\mathrm{R}\mathrm{s}}=0.415814-0.009169 {\mathrm{T}\mathrm{D}}_{\mathrm{a}\mathrm{v}\mathrm{g}}+0.022404 {{\mathrm{u}}_2}_{\mathrm{a}\mathrm{v}\mathrm{g}}-0.001868 {\mathrm{R}\mathrm{H}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$	0.183	1.1 × 10−6	(13)
3	Djobel, Elalab, S. Domingo	${\mathrm{k}}_{\mathrm{R}\mathrm{s}}=0.409351-0.009369 {\mathrm{T}\mathrm{D}}_{\mathrm{a}\mathrm{v}\mathrm{g}}+0.021829 {{\mathrm{u}}_2}_{\mathrm{a}\mathrm{v}\mathrm{g}}-0.001911 {\mathrm{R}\mathrm{H}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$	0.208	5.6 × 10−7	(14)
-	Bissora	${\mathrm{k}}_{\mathrm{R}\mathrm{s}}=0.418652-0.009110 {\mathrm{T}\mathrm{D}}_{\mathrm{a}\mathrm{v}\mathrm{g}}+0.022572 {{\mathrm{u}}_2}_{\mathrm{a}\mathrm{v}\mathrm{g}}-0.001855 {\mathrm{R}\mathrm{H}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$	0.174	9.4 × 10−7	(15)
-	Bubaque	${\mathrm{k}}_{\mathrm{R}\mathrm{s}}=0.416080-0.009035 {\mathrm{T}\mathrm{D}}_{\mathrm{a}\mathrm{v}\mathrm{g}}+0.022784 {{\mathrm{u}}_2}_{\mathrm{a}\mathrm{v}\mathrm{g}}-0.001840 {\mathrm{R}\mathrm{H}}_{\mathrm{a}\mathrm{v}\mathrm{g}}$	0.232	2.9 × 10−6	(16)

k_Rs—shortwave radiation empirical adjustment coefficient (°C^−0.5); TD_avg—long-term average temperature difference, i.e., (T_max − T_min); u_{2 avg}—long-term average local wind speed (m s⁻¹) measured at 2 m height; RH_avg—long-term average relative humidity.

. The statistical indicators related to the test and validation datasets are presented in Table S3 of the Supplemental Material. All the considered variables (TD_avg, u_{2 avg}, and HR_avg) contribute differently to the estimation of k_Rs but play complementary roles. As with the global (Equation (6)) and climate-focused MLR equations (Equations (7a) and (7b)), and in line with the findings of [84], TD_avg has a negative regression coefficient associated with the loss of long-wave radiation when TD_avg is high. The impact of u_{2 avg} on k_Rs values is positive and may be related to the transport of air moisture masses in windy conditions, leading to a clearer atmosphere. The impact of RH_avg on the k_Rs value is negative, representing the influence of cloudiness and air moisture. This is consistent with previous findings in other parts of the world [2,10,11,84]. It should be noted that the cluster-focused MLR regression to the origin presents a small range of 0.409–0.416, while the regression coefficients are relatively similar among the clusters (Table 4). The other two locations, which were not within the three clusters, present slightly different regression coefficients. Table 4 shows the k_Rs values estimated for each cluster.

The goodness-of-fit indicators for the different approaches tested for estimating ET_o using ground-truth temperature and u₂ data, i.e., the FAO-PMT ET_o approach, are shown in

Table 5. Goodness-of-fit indicators used to compare PM-ET_o with ET_{o PMT} when using T_min or T_mean as a predictor of T_dew, when k_Rs was calibrated for each site, when computed with the global Equation (6) or with the climate-focused Equations (7a) and (7b), and when using the default or the average local u₂ value, for the eleven sites of Guinea-Bissau.

Climate	Predictors			Goodness-of-Fit Indicators
	Tdew	kRs	u2	b0	R2	RMSE (mm d−1)	NRMSE (%)	BIAS	PBIAS (%)
Moist sub-humid	Tmin	Global	Default	0.93 abc	0.96 a	1.00 ab	20.59 ab	−0.28 bc	−5.83 abc
			Avg	0.82 ab	0.97 a	1.13 ab	23.62 ab	−0.78 a	−16.40 ab
		Climate	Default	0.90 abc	0.96 a	1.04 ab	21.5 ab	−0.42 abc	−8.4 abc
			Avg	0.79 a	0.97 a	1.24 a	25.73 a	−0.91 ab	−19.17 a
		Optm	Default	1.07 c	0.97 a	1.08 ab	22.53 ab	0.43 c	9.28 c
			Avg	0.98 bc	0.98 a	0.80 b	16.49 b	−0.01 bc	−0.33 bc
Humid	Tmin	Global	Default	0.92 abcde	0.97 a	0.87 abcde	18.61 abcde	−0.36 abcde	−6.78 abcde
			Avg	0.82 abc	0.98 ab	1.03 abc	22.01 abc	−0.76 abc	−16.22 abc
		Climate	Default	0.97 bcde	0.97 ab	0.86 abcde	18.32 abcde	−0.06 bcde	−1.22 bcde
			Avg	0.88 abcde	0.98 ab	0.87 abcde	18.63 abcde	−0.48 abcde	−10.22 abcde
		Optm	Default	1.07 e	0.97 ab	0.91 abcde	19.31 abcde	0.38 e	8.12 e
			Avg	0.98 cde	0.98 ab	0.68 de	14.60 de	−0.01 cde	−0.21 cde
	Tmean-2	Global	Default	0.86 ab	0.98 ab	1.12 ab	23.82 ab	−0.86 ab	−18.33 ab
			Avg	0.78 a	0.98 ab	1.20 a	25.43 a	−0.97 a	−20.68 a
		Climate	Default	0.86 abcd	0.98 ab	0.95 abcde	21.11 abcde	−0.57 abcd	−12.15 abcd
			Avg	0.85 abcd	0.98 ab	0.99 abcde	21.14 abcde	−0.66 abcd	−14.03 abcd
		Optm	Default	0.97 bcde	0.98 ab	0.72 bcde	15.42 bcde	−0.09 bcde	−1.83 bcde
			Avg	0.96 abcde	0.98 ab	0.71 cde	15.10 cde	−0.14 abcde	−2.95 abcde
	Tmean-aD (aD opt)	Global	Default	0.91 abcde	0.98 ab	1.02 abcde	16.64 abcd	−0.33 abcde	−6.91 abcde
			Avg	0.82 abcd	0.98 ab	1.02 abcd	21.72 abcde	−0.75 abcd	−15.91 abcd
		Climate	Default	0.95 abcde	0.98 ab	0.72 abcde	15.31 cde	−0.15 abcde	−3.10 abcde
			Avg	0.91 abcde	0.98 ab	0.78 cde	16.63 abcde	−0.33 abcde	−6.91 abcde
		Optm	Default	0.99 de	0.98 ab	0.70 cde	14.90 cde	0.03 de	0.57 de
			Avg	0.99 cde	0.98 b	0.67 e	14.33 e	0.02 cde	0.47 de

T_dew—dew point temperature; k_Rs—shortwave radiation empirical adjustment coefficient; u₂—wind speed at 2 m height; Global—global multiple linear regression (Equation (6)); Climate—climate-focused multiple linear regression (Equations (7a) or (7b)); Optm—cluster-focused multi-linear regression (Equations (12)–(16)); Notes: means followed by the same letter are not significantly different (α < 0.05) according to the Kruskal–Wallis test; The most effective approach is highlighted in grey, while bold numbers indicate the least error in estimates.

, and the ranges of each indicator are presented in Table S4. It was found that the climate type of the site influenced the results. For the moist sub-humid locations, i.e., those sites located in the north of GB, the best predictor for k_Rs was, as expected, the value derived from the optimized LMR value (Table 5); for u₂, the best predictor was the regional/local average u₂ (u_{2 avg}) value. This combination resulted in no tendency to over- or underestimation of ET_o (b₀ = 0.98) and yielded acceptable errors in estimates, with RMSE of 0.80 mm d⁻¹ and NRMSE of 16.5%. However, small and no significant differences in estimates were found when u_{2 def} was used as a predictor, with RMSE of 1.08 mm d⁻¹ and NRMSE of 22.5%.

The second-best approach was to use either the global (Equation (6)) or the climate-focused MLR (Equations (7a) and (7b)) to estimate k_Rs in combination with the u_{2 def}. For this set of sites, there was no significant difference (p < 0.05) between using the climate-focused equations and using the global MLR, with RMSE of 1.04 mm d⁻¹ and 1.00 mm d⁻¹, and NRMSE of 21.5% and 20.5%, respectively (Table 5). The results also showed that using u_{2 avg} did not improve predictions of k_Rs when either global or climate-focused MLR equations were used. This is because it led to an increase in RMSE and NRMSE, which was not only statistically significant but also resulted in a large underestimation of ET_o, with b₀ values decreasing to 0.82 and 0.79 when the global and climate-focused MLR equations were used, respectively.

The results for the humid sites (Table 5) showed that, similarly to the moist sub-humid sites, the best predictor was the one resulting from the optimized MLR combined with the u_{2 avg}. However, there was no significant difference (p < 0.05) in the RMSE values using the tested T_dew predictors, i.e., T_min or the adjusted T_mean with either a_D = 2 or calibrated a_D value, with RMSE of 0.68 mm d⁻¹, 0.71 mm d⁻¹, and 0.67 mm d⁻¹, respectively. When analyzing the results in terms of NRMSE, using the adjusted a_D value led to statistically different values, but there were few improvements in the results: NRMSE was 14.3%, compared to 14.6% with T_min and 15.1% with T_mean-2. There were also few differences in the other goodness-of-fit indicators, except for b₀, which showed a clear tendency toward underestimation when u_{2 avg} was used with either the global or the climate-focused MLR. These results showed that optimizing the predictors leads to very good results, but this approach is only possible when a good dataset is available, hence uncommonly. Moreover, for the optimization approach (L-BFGS-B) applied in all the studied sites (Supplementary S1), there was a general tendency for slight underestimation when using u_2avg, distinguishing these results from other studies that relied on trial-and-error calibration of the T_dew and R_s predictors [9,12,82].

The global LMR and the u_{2 deaf} results showed the advantage of optimizing the a_D value when using T_mean-a_D as T_dew predictor in relation to the use of the a_D = 2 °C, as the latter led to a clear underestimation of ET_o (b₀ = 0.88) and higher RMSE (0.89 mm d⁻¹ vs. 0.71 mm d⁻¹). The use of T_min as the T_dew predictor also revealed good results, with an RMSE of 0.83 mm d⁻¹. Overall, the results for the humid climates showed a limited advantage in adjusting the T_mean as a T_dew predictor, when combined with the use of the global or climate-focused equations using the u₂ default value, with NRMSE ranging from 16.6% to 23.8% and 15.3% to 21.1%, respectively.

The results of using the climate-focused LMR equations showed that these had an advantage over the global equation, but it was not statistically significant (α > 0.05). This advantage resulted from a decrease in the underestimation, as well as in the RMSE and NRMSE. In such cases, it is beneficial to use T_mean rather than T_min as the T_dew predictor considering that there are lower errors in the ET_o estimates. As with the global LMR, there was a slight advantage in adjusting the a_D value. However, the improvements were not significant, and therefore, the T_min should be used as a predictor of T_dew in humid climates, with these findings agreeing with those of FAO56rev [2].

Selected examples of comparison results between ET_{o PMT} and PM-ET_o when the analysis focused at the cluster level are shown in Figure 5 and Table S5. Examples also include the locations that were excluded from, the clusters Bissora (moist sub-humid) and Bubaque (humid). The scatter plots in Figure 5 demonstrate the strong correlation between ET_{o PMT} using u_{2 def} and the various MLR equations, as well as PM-ET_o. The plots show that ET_{o PMT} slightly underestimates PM-ET_o in Clusters 1 and 2, as well as in Bissora, when either the global or climate-focused equations are used to predict k_Rs. Furthermore, using the cluster-focused equations did not offer any advantages in these locations as the RMSEs were higher. Conversely, Cluster 3 and Bubaque show high underestimation when using the same predictors for k_Rs estimation, demonstrating the advantage of using cluster-focused equations in this case.

Table S5 provides the results of the goodness-of-fit indicators for all approaches when the analysis was performed at the cluster level. The results showed, as in the previous analysis, that the best approach was to optimize the predictors of T_dew and k_Rs (i.e., a_D and cluster-focused MLR). Therefore, the results are discussed with a focus on the previous simplified approaches.

The first cluster included only locations with humid climates, and the results showed that using T_min relative to T_mean-2 as a predictor of T_dew was advantageous. Additionally, there was a clear advantage from using the climate-focused MLR alongside u_{2 def}. For the second cluster, which included both humid and moist sub-humid locations, the results showed that the best approach was to use T_dew predictors according to the AI, along with the climate-focused MLR equations and u_{2 def}. The use of u_{2 avg} yielded a higher RMSE and a stronger tendency to underestimate ET_o. The third cluster comprised only moist sub-humid locations and showed the poorest results in terms of errors of all the clusters. In this case, the second-best approach was to use u_{2 def} alongside either the global or climate-focused MLR, as there were no significant differences. For Bissora (moist sub-humid), the second-best approach was to use the climate-focused equation with u_{2 def}, while for Bubaque, despite being classified as humid, T_min was a better predictor of T_dew, with u_{2 def} being the best predictor over u_{2 avg}.

As mentioned previously, the cluster-focused optimized MLR equations using numerical models outperformed the global and climate-focused MLR equations for the set of sites, whether considering individual sites or clusters (Figure 6). Some sites exhibited similar RMSE values when using the climate-focused MLR and the global equation. However, the box-and-whiskers plot revealed variations where the metrics overlapped, indicating that while these standard approaches may be effective for certain sites, they are not suitable for most of them (Figure 6). The metrics indicate that the best adjustments for estimating ET_o using temperature alone were achieved by applying either T_dew = T_min or T_dew = T_mean − a_D criterion with optimized a_D, u_{2 def}, and using the cluster-focused MLR to estimate k_Rs for each site or group of sites. The results for T_min showed a wider spread of RMSE values (Figure 6), possibly because humid and moist sub-humid sites were considered together. In contrast, for the other two predictors using T_mean, the spread was smaller, because only humid sites were considered.

The results of the current study when using any of the MLR equations were within the range of those reported for several sites in Africa, such as the study performed by [13] in Tanzania and Kenya when using the PMT approach with u_{2 avg} and the default predictors of T_dew and R_s (RMSE ranging 0.64 mm d⁻¹ to 1.09 mm d⁻¹). A study performed in Côte d’Ivoire [15] reported RMSE ranging from 0.43 mm d⁻¹ to 0.89 mm d⁻¹ when using PMT with the default values for the different predictors [1]. A study performed at several sites in Ghana [16], reported RMSE values ranging from 0.58 to 1.11 mm d⁻¹ when using PMT, while RMSE decreased when using artificial neural networks (ANNs) and gene expression programming (GEP) to 0.53–0.84 mm d⁻¹ and 0.51–0.79 mm d⁻¹, respectively. The study performed in humid climates of Uganda by [14] tested several approaches to cope with missing data and reported that the PMT with default values for the predictors of k_Rs and T_dew and u_{2 avg} outperformed the other approaches with an RMSE ranging from 0.69 mm d⁻¹ to 1.34 mm d⁻¹. Better results were reported in a study applied to Burkina Faso with an RMSE 0.53 mm d⁻¹ and a tendency to overestimate ET_o (PBIAS = 6%) when the PMT approach was used, optimizing the R_s and T_dew predictors and using the u_2avg value [17]. The globally applied study by [10] reported an RMSE of 0.63 mm d⁻¹ for Aw of climates as in GB when using the default predictors for T_dew and u₂ and calibrated or default k_Rs values. In the current study, using the same approach, RMSE was 0.79 mm d⁻¹ and 0.85 mm d⁻¹ for humid and moist sub-humid sites, respectively. Trajkovic et al. [111] reported a wide range of RMSE for several humid locations in Hungary, ranging from 0.10 mm d⁻¹ to 0.81 mm d⁻¹ when using the default k_Rs and T_dew predictors values with u_{2 avg}. Other studies such as those by [9,82] for sub-humid and humid climates in the Mediterranean basin and in Iran, respectively, also reported better results when calibrating k_Rs, u_{2 avg}, and using the different T_dew predictors. Furthermore, the results of the current study when using the LMR equations with the PMT approach are in line with those reported in [12] for humid and moist sub-humid climates.

Enhancing the accuracy of ET_o estimation can be challenging, particularly when analyzing sites with high climate variability and limited weather data availability. The FAO-PMT ET_o approach, which uses global and climate-focused MLR equations, showed good accuracy, particularly when considering each site individually, demonstrating that there is no significant advantage in developing cluster-focused MLR equations or optimizing a_D. However, when performing the analysis at the cluster level, there was a consistent trend toward improved performance with this optimization, despite the robustness of the approach needing to be further tested using a wider set of weather data. Overall, due to the simplicity of the approach, the use of the global and/or climate-focused LMRs as predictors of k_Rs is advocated despite their tendency to underestimate ET_o, in combination with the u_{2 default} when it leads to less underestimation. Furthermore, these approaches demonstrated their potential as valuable tools for improving water use efficiency in the absence of accurate data, as they can serve as a baseline for estimating water and salt balances using different models [7,59,60,112]. Future applications of the method would benefit from enhanced ground observation networks, particularly in data-scarce regions like central and eastern GB, to strengthen calibration and reduce potential uncertainties.

3.4. ET_o Estimation Using Different Reanalysis Datasets

Analysis of wind speed data from AgERA5 (u_{2 ERA5}) and MERRA-2 (u_{2 MERRA}) revealed significant discrepancies with u₂ observations (results not shown), as reported in previous studies assessing reanalysis data [46,49]. This led to ET_o estimation using reanalysis data that excluded this variable. Two approaches were then used: one replaced u_{2 ERA5} and u_{2 MERRA} with the u_{2 def} value, while the other used the u_{2 avg} value. The results show that the estimation of ET_o using raw AgERA5 reanalysis data (ET_{o ERA5}) exhibited significant variability compared to the ET_o values calculated from ground-truth (observed, ET_{o OBS}) data (Figure 7 and Figure S7), particularly when the default u₂ was used in the ET_{o ERA5} estimations.

Using raw (uncorrected) reanalysis data with u_{2 avg} to estimate ET_o yielded a wide range of regression coefficients b₀ (0.90–1.18) (Table S6) and PBIAS (−7.72–21.14) (Figure 7), but most sites did not show an under- or overestimation tendency (b₀ near 1.0 and PBIAS near 0%) (Figure S7). When u_{2 def} was used, however, the b₀ and PBIAS values varied in a wider range, with two groups of sites, one with an underestimation tendency (b₀ < 0.90, PBIAS) and the other with an overestimation tendency (b₀ > 1.10, PBIAS). In both approaches, R² was generally above 0.95, showing that ET_{o ERA5} was able to explain most of the ET_{o OBS} variance. When analyzing the errors due to using u_{2 avg}, the RMSE ranged from 0.84 to 1.48 mm d⁻¹. This value decreased slightly when u_{2 def} was used instead (RMSE from 0.80 to 1.46 mm d⁻¹), corresponding to NRMSE ranging from 17.9% to 31.9% and 17.9% to 31.8%, respectively.

After applying different bias correction methods to the ET_{o ERA5} data, the results showed a general decrease in the RMSE values and, as expected, in PBIAS and BIAS (Figure 7) and as well as in b₀ (Table S6). The analysis of the BIAS and PBIAS metrics revealed that BIAS_c and ALM_c effectively removed the under- and overestimation of the ET_{o ERA5} data. However, the ALM_c ability to explain the variability in the data was lower than that of the other bias correction methods, suggesting lower predictive performance. This is evident in the decrease in R² from 0.96 to 0.90 and 0.92 when using u_{2 avg} or u_{2 def}, respectively (Table S6). Although ALM_c removed the bias of the reanalysis data, it failed to reduce the estimation errors.

Analyzing the set of goodness-of-fit indicators (Figure 7 and Table S6), it was found that the different bias correction methods exhibited further differences in accuracy, with the simple BIAS_c method performing the best. The average RMSE values were very similar for BIAS_c (1.05 mm d⁻¹ or 0.99 mm d⁻¹ when using u_{2 avg} and u_{2 def}, respectively), RLM_c (1.04 mm d⁻¹ or 0.97 mm d⁻¹), and S_c (1.04 mm d⁻¹ or 0.98 mm d⁻¹). This small difference in NRMSE indicated that these bias correction methods were not significantly different (α <0.05). Similarly, the mean NRMSE values were 22.0%, 21.7%, and 21.7%, respectively (Table S6). For ALMc, the bias correction was successfully applied; however, the RMSE was higher (>1.3 mm d⁻¹) than that of the other correction methods in both AgERA5 and MERRA-2, indicating lower accuracy. Using the u_{2 def} value resulted in slightly higher accuracy for all bias correction methods, but this was not statistically significant (NS). Overall, the BIAS_c was the simplest and most effective, leading to significant differences (α = 0.05) compared to using raw data. This makes it a practical option for calculating ET_o using AgERA5 and MERRA-2 data with either u_{2 avg} or u_{2 def}.

Using raw MERRA-2 data to estimate ET_o (ET_{o MERRA}) produced greater variability, a marked underestimation (Figure 7), and less precision (Table S6). Comparing the two datasets (Figure 7), the superiority of using raw AgERA5 becomes evident, i.e., the results indicate that MERRA-2 underperforms compared to AgERA5. Similar results were reported by [78] for the estimation of annual ET_o in Greece. The differences in performance between the reanalysis datasets may be due to the coarser resolution of the MERRA-2 dataset, which makes it difficult to adequately capture climate variability within GB. When u_{2 avg} and u_{2 def} were used, the latter performed slightly better but did not reach statistical significance.

The results show that, for operational use, the ET_{o MERRA} needs to be bias-corrected (see Figure 7). As with ET_{o ERA5}, the results also highlight that ALM_c and BIAS_c were the only methods that effectively removed the bias. The RMSE was 1.57 mm d⁻¹ when raw data were used, and it decreased to 1.38 mm d⁻¹ with the ALMc method and to 1.01 mm d⁻¹ with the BIASc method. As with the AgERA5 data, ALMc’s ability to explain the variability in the data was lower than that of the other bias correction methods, showing a smaller reduction in RMSE (see Table S6). BIAS_c was the best bias correction method, as it improved all accuracy indicators.

The results of the current study using raw reanalysis data are comparable to those reported in the literature. Tiruye et al. [113] reported a tendency for overestimation when using ERA5-Land for the Tana Basin in Ethiopia, which has a subtropical climate, with RMSE ranging from 0.54 mm d⁻¹ to 1.82 mm d⁻¹. Lopez-Guerrero et al. [114] reported RMSE values ranging from 0.49 mm d⁻¹ to 0.88 mm d⁻¹ for Egypt, Morocco, and Tunisia. Nouri et al. [43] reported an NRMSE ranging from 11% to 20% for ET_o estimates on a monthly timescale for the humid sites of Iran. Various studies have been carried out for Italy and Portugal. For example, [80] reported an NRMSE ranging from 15% to 47% when using two ERA5 products, depending on the time scale. Other studies carried out in Italy using ERA5-Land datasets reported a tendency toward underestimation and generally lower RMSE; for instance, Pelosi et al. [51] reported an RMSE ranging from 0.44 to 1.04 mm d⁻¹, with NRMSE values lower than 14%, and [115] reported RMSE ranging from 0.42 to 1.26 mm d⁻¹. Paredes et al. [49] reported better results using ERA-Interim for mainland Portugal, with RMSE > 0.75 mm d⁻¹ for most sites, combined with a tendency of underestimation. After simple bias correction, the RMSE decreased to a range of 0.50–0.75 mm d⁻¹ for most sites [49].

There are few studies in the literature that have used MERRA-2 to estimate ET_o. The results of the current study are comparable with those reported by [43], with lower NRMSE values ranging from 10 to 20% at humid sites in Iran.

Overall, the results of the analysis of the gridded datasets emphasize the need for bias correction to enhance the accuracy of ET_o estimates derived from reanalysis products in data-scarce regions. Furthermore, a comparison of the results from AgERA5 and MERRA-2 (Figure 7, Table S6) with the FAO-PMT approach (Section 3.2, Table 5) shows that the latter performs better and therefore can be used to estimate ET_o when temperature data is available.

The results of the current study suggest that AgERA5 data could be used with caution for estimating ET_o, particularly when the observed weather data are unavailable. Further caution is needed, particularly for studying climate variability and change, as previously reported [107,108,116]. To allow for a more thorough evaluation of the gridded dataset’s accuracy, it is advisable to continue collecting meteorological data over a longer period and across different regions. The method can be adapted to other regions but local ground data are key for improving accuracy. Further long-term studies are encouraged, particularly in areas with limited station coverage, where expanding or recovering weather observations could reduce uncertainties.

3.5. ET_o Mapping

Figure 8 shows the spatial variability of the mean annual ET_{o ERA5} in the country after applying the best bias correction method (BIAS_c). The results show that the spatial distribution of the annual ET_o presents strong spatial coherence and continuity (Table S8). The fitted exponential variogram with a nugget of 10 mm, sill of 17.8 km, and an extensive range of 240.3 km indicates a well-structured spatial dependence on the regional scale. Autocorrelation results support this, with a Global Moran’s I of 0.84, a Z-score of 20.71, and p < 0.001, confirming significant spatial clustering of ET_o values. The model achieved excellent annual accuracy, with errors less than 2.5% of the observed NRMSE mean and minimal bias (BIAS = 0.14, negligible PBIAS). These values indicate both high precision and negligible systematic errors in the estimation. The high R² (0.87) and Spearman correlation (ρ = 0.94) further validate the model’s reliability across spatial domains.

In practice, the ET_o map is consistent with the observed patterns in the country, where southern areas have higher temperatures and ET_o, while some inland locations have lower ET_o values. This reflects the typical variability observed in tropical regions, where climatic and topographic conditions contribute to significant spatial differences in ET_o. The results of this study highlight the value of gridded climate datasets such as AgERA5, after appropriate bias correction, for regional-scale agroclimatic applications. For regions of Guinea-Bissau where ground-based meteorological data are sparse, corrected satellite-derived ET_o maps can provide important support for water management planning, drought monitoring, and sustainable agricultural management. However, it is advisable to collect more observational data to further support the findings of the current study.

4. Conclusions

The approach developed in this study is an important tool for Guinea-Bissau (GB), where limited government investment in sensors hinders the rapid acquisition of accurate meteorological data. The findings of the present study underscore that the PMT approach yielded more accurate ET_o estimates than either of the reanalysis products, even after its bias correction. However, in the absence of observed temperature data, AgERA5 data could be used as an alternative source, although caution is advised due to known biases and uncertainties associated with ET_o estimation from this reanalysis product. When using the PMT approach, it can be concluded that T_min is an adequate predictor of T_dew in both moist sub-humid and humid climates. Therefore, there is no need to use corrected T_mean to predict T_dew, as this does not significantly affect ET_o estimates. Furthermore, the u₂ default value of 2 m s⁻¹ was found to be the best predictor when coupled with either the global or the climate-focused equations for estimating ET_o. The newly proposed cluster-focused equations improve the accuracy of ET_o compared to the global or climate-focused equations but require further validation for GB. More broadly, this study demonstrates the suitability of the user-friendly approaches outlined in FAO56rev, particularly in regions where access to comprehensive weather information is limited.

The study provides a robust framework for enhancing agricultural practices and fostering resilience in areas grappling with climatic and environmental challenges. In the case of GB specifically, the approximate datasets and tools provided by the developed approaches could greatly benefit organizations working to improve the country’s social and food security, such as international cooperation projects and GB’s development ministries.

However, the approach explored in this study could be further enhanced by expanding the ground-truth database to include more years of observations. It is important to test the global and climate-focused equations with more data from tropical countries, especially those with high rainfall and climate variability. This is particularly relevant for regions between 0° and 20° N latitude, which experience the greatest climate variability and have not been the focus of previous studies. Overall, it is essential to refine the tools further to improve the estimation of ET_o in regions where investment in specialized equipment is low. Nevertheless, this work provides a foundation for calculating water and salt balances in MSR production in Guinea-Bissau and other West African countries where this system exists.