# Training Local Models from Reanalysis Data to Estimate Reference Evapotranspiration with Fewer Onsite Sensors, an Evaluation in West Africa

Jérémy Lavarenne, Audrey Brouillet

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Jérémy Lavarenne, Audrey Brouillet. Training Local Models from Reanalysis Data to Estimate Reference Evapotranspiration with Fewer Onsite Sensors, an Evaluation in West Africa. 2025. hal-04920988

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1 **Title**

2 Training local models from reanalysis data to estimate reference evapotranspiration with fewer

3 onsite sensors, an evaluation in West Africa

4 **Authorship**

5 Jérémy LAVARENNE¹,²,* (0000-0002-1954-4150), Audrey BROUILLET³ (0000-0001-9466-

6 0197)

7 ¹CIRAD, UMR TETIS, Montpellier, FR

8 ²TETIS, Univ Montpellier, AgroParisTech, CIRAD, CNRS, INRAE, Montpellier, FR

9 ³IRD, Espace Dev joint research unit, Maison de la Télédétection, 34000 Montpellier, FR

10 * corresponding author, jeremy.lavarenne@cirad.fr

11 **Abstract**

12 This study addresses the critical need for accurate reference evapotranspiration (ET0)

13 estimation in data-scarce environments such as West Africa, where rapid population growth

14 and climate change intensify water resource challenges. Traditionally, computing ET0 with the

15 FAO-56 Penman-Monteith method requires multiple meteorological inputs—such as solar

16 radiation, humidity, and wind speed—collected from costly, fully instrumented weather

17 stations. However, the availability and maintenance of such equipment can be prohibitive in

18 remote regions. To overcome these constraints, we explore the potential of machine learning

19 (ML), specifically XGBoost (XGB) models, trained on NASA Power climate reanalysis

20 datasets. Our approach relies on a limited subset of easily measured in situ variables—daily

21 minimum and maximum temperatures and rainfall—to estimate ET0. Departing from standard

22 ML practices that depend on short-term, site-specific data, we leverage the extensive historical
depth and broad spatial coverage of reanalysis products. We trained and validated twenty
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locally adapted XGB models using measurements from twenty diverse West African weather
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stations. Our results show that certain XGB model configurations, notably those incorporating
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temperature and rainfall data, can approximate ET0 estimates from the FAO-56 Penman-
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Monteith equation with median RMSE values frequently below 1 mm/day—levels comparable
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to commonly employed empirical formulas. This finding demonstrates that minimal on-site
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instrumentation, combined with ML and reanalysis data, can effectively support irrigation
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scheduling and enhance water-use efficiency under varying agro-ecological conditions. To
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foster broader implementation, we have released our XGB-ET0 code under the GPLv3 licence
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(https://github.com/SARRA-cropmodels/RF-ET0), enabling researchers and practitioners to
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locally train and deploy these models, thereby improving ET0 estimation and sustainable
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agricultural water management in resource-limited settings.
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Keywords

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• Evapotranspiration estimation

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• Machine learning

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• Precision irrigation

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• XGBoost models

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• Reanalysis datasets

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• FAO-56 Penman-Monteith

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• West Africa

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# 1. Introduction

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Accurately estimating actual evapotranspiration (ETa) is critical for optimizing irrigation
practices and promoting sustainable agricultural water management. This need is particularly
acute in West Africa, where growing population pressures and increasing variability in water
availability caused by climate change (Arnell and Lloyd-Hughes, 2014; Ayers et al., 2023; Brouillet and Sultan, 2023; Satgé et al., 2020) have intensified demands on limited water resources. Precision irrigation (PI), which tailors water inputs to compensate for ETa, offers a promising solution to reduce excessive irrigation, even in humid environments (Adeyemi et al., 2017; González Perea et al., 2018). Beyond irrigation scheduling, reliable ETa estimates play a pivotal role in understanding the water cycle, modeling water availability, and predicting changes in hydrological conditions. ETa is also a key input in process-based crop models, helping farmers anticipate the impact of different irrigation strategies on yields and overall water usage (Gu et al., 2020; Lopez-Jimenez et al., 2022; Pereira et al., 2020). Consequently, improving ETa estimation methods under data-scarce conditions is essential for both advancing scientific understanding and informing practical water management decisions in the region.

However, direct experimental methods for estimating ETa often require complex instrumentation, careful handling, and trained personnel, making them difficult to deploy and maintain (Li et al., 2009; Valayamkunnath et al., 2018). As a result, indirect ETa estimation methods have been developed, including several mathematical formulations based on meteorological variables (compiled in (McMahon et al., 2013)). Some of these methods rely on the concept of reference crop evapotranspiration (ET₀), which represents the amount of water lost to the atmosphere by a reference healthy, well-watered grass or alfalfa cover; this ET₀ is further modulated by a crop and growth stage-specific coefficient (crop coefficient, symbolised as Kc), to provide an estimate of actual evapotranspiration (noted ET₀). This ET₀, which represents the climate forcing component and is a widely used variable in crop water modelling and management, can be computed based on air temperature, solar radiation, relative humidity, and wind speed using the FAO-56 standardized Penman-Monteith equation (FAO-56-PM) (Richard G. Allen et al., 1998), the most widely-used procedure for estimating the ET₀ value.

However, obtaining all the meteorological variables required by the FAO-56-PM equation can be challenging. The cost, maintenance, and limited availability of fully
instrumented weather stations restrict the widespread calculation of ET₀, especially in developing countries (Djaman et al., 2016, 2015; Fisher and Pringle Iii, 2013; Valipour, 2015). To circumvent these constraints, a range of empirical ET₀ estimation models requiring fewer input variables has emerged (McMahon et al., 2013). While these simplified approaches can reduce the need for complex instrumentation, their accuracy varies markedly depending on local agroclimatic conditions (Djaman et al., 2015; Tabari and Talaee, 2011; Xystrakis and Matzarakis, 2011). Consequently, selecting and calibrating an appropriate empirical model for a given site remains a non-trivial, expert-dependent process that complicates routine ET₀ estimation and its integration into decision support services.

This study explores whether leveraging climate reanalysis datasets can help overcome these challenges. We hypothesize that machine learning (ML) models trained exclusively on local and extensive historical coverage of reanalysis data, and used to predict ET₀ from a limited set of weather variables (from only a few meteorological instruments) can achieve ET₀ estimation accuracy comparable to established empirical formulas. If confirmed, this approach could significantly simplify ET₀ estimation by reducing instrumentation requirements and expanding applicability in data-scarce contexts.

Recent ML advancements have shown promise for deriving agroclimatic indicators, including ET₀, from limited meteorological inputs. Such estimations have been performed using methods like support vector machines (SVM), random forests (RF), Gaussian process regression (GPR), and artificial neural networks (ANN) (Chia et al., 2020; Hebbalaguppae Krishnashetty et al., 2021). Yet, most existing ML-based ET₀ models rely on short-term, site-specific datasets, limiting their generalizability (see **Supplementary Table 1**). To our knowledge, no previous work has utilized global climate reanalysis products—datasets generated by assimilating historical weather station data into global circulation models—for training ET₀ estimation models. Such reanalysis datasets provide near-global coverage of past weather conditions at various resolutions (often down to 0.5 degrees), sub-daily time steps, and spanning multiple decades.
In this paper, we explicitly test the hypothesis that ML models, trained from reanalysis data using only a few simple on-site measurements (e.g., daily minimum and maximum temperatures and rainfall), can achieve ET₀ estimation accuracies on par with widely used empirical methods. By tapping into the historical depth and spatial consistency of the NASA Power reanalysis dataset, we aim to develop locally adapted models capable of capturing the long-term statistical relationships underlying ET₀-PM. Confirming this hypothesis would greatly simplify the ET₀ estimation process, providing a practical and precise tool for routine agricultural management and crop modelling in regions with sparse meteorological infrastructure.

Unlike previous approaches limited by geographically sparse or short-term training datasets, our method exploits the rich spatiotemporal coverage of reanalysis data to train and evaluate locally adapted ML models systematically. Furthermore, we examine the sensitivity of model performance to different subsets of input variables—a dimension rarely explored in the literature. To evaluate our methodology, we train local extreme gradient boosting (XGB) models (chosen for their robustness in regression tasks, e.g., as shown in hydrological studies such as (Niazkar et al., 2024)) using NASA Power data. We then compare the ET₀ estimates generated by these models—under various combinations of meteorological inputs—with ET₀ values derived from the FAO-56-PM approach using ground measurements from twenty weather stations spread across West Africa. We assess model performance both statistically and qualitatively and discuss the implications of our findings for local calibration. Finally, we present a Python software module called RF-ET₀, allowing researchers and practitioners to easily train and apply these XGB models anywhere in the world.
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# 2. Materials and methods

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## 2.1. General workflow

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The workflow for training, evaluating, and testing XGB models to estimate reference evapotranspiration (ET0) involved several key steps. First, ground truth ET0 values (ET0-PM-GT) were computed using the FAO-56 Penman-Monteith equation and daily meteorological data collected from weather stations. These included air temperature (TMIN, TMAX), wind speed, rainfall, relative humidity (HR), and solar radiation (IRRAD).

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To complement these observations, daily time series data for each site were retrieved from the NASA Power reanalysis dataset, spanning 1979–2020. Using the same FAO-56 Penman-Monteith equation, ET0 values (ET0-PM-RM) were computed from the reanalysis data to serve as the target for model training. The reanalysis dataset was split into a training subset (historical data up to one year before station observations) and a validation subset (the period immediately preceding the observations).

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XGBoost (XGB) models were trained locally for each site using combinations of meteorological variables derived from reanalysis data as input features (e.g., TMIN, TMAX, WIND, IRRAD), forming distinct model classes. Each model class represented the variable configurations measurable by different types of weather stations. Model training used default hyperparameters with 1000 boosting rounds for robust regression.

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Model performance was evaluated on the validation dataset by comparing predicted ET0 values against ET0-PM-RM, using root mean square error (RMSE) and the coefficient of determination (R²) as metrics. Finally, the trained models were tested against ground truth ET0 values (ET0-PM-GT) derived from station observations. Performance was assessed across agro-ecological zones to analyze variability and identify the most reliable variable combinations for different climatic conditions.

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## 2.2. In situ meteorological datasets

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For this study, we used the data from the archive of the AfricaRice weather station network (https://dataverse.harvard.edu/dataverse/Weather), providing a representative set of meteorological observations for West Africa, as the data provided from their agrometeorological stations is openly available, homogeneous, and quality controlled. We selected sites for which original metadata (coordinates and elevation) were provided, and containing all the necessary variables to compute ET₀ using the FAO-56 standardized Penman-Monteith equation: air temperature, rainfall, wind speed, vapour pressure, and global radiation. A total of twenty sites were retained for the study, (Figure 1, Table 1). spanning from 17°N, 18°W to 4°N, 18°E covering seven distinct agro-ecological zones as classified by the FAO Global Agro-ecological Zones V4, simplified (FAO and IIASA, 2021). Of these, seventeen sites fall within the "lowland tropics", further categorised into nine "humid", five "sub-humid", and three "semi-arid" zones; the remaining sites are distributed among "desert/arid climate", "land with severe soil/terrain constraints", and "land with ample irrigated soils" (Figure 2), ensuring a representative sample of the agro-ecological variability within West Africa, albeit with some underrepresentation of arid zones.

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The duration of these records varies depending on the station, and spans from March 19, 2012, to December 31, 2020. Table 2 describes dataset durations and periods considered for the analysis on each station. To establish a ground truth for reference evapotranspiration (ET₀-PM-GT), we utilised the FAO-56 standardized Penman-Monteith equation, implemented through the reference ET function in the Python Crop Simulation Environment (PCSE) package v.5.4.0 (de Wit, 2023).

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## 2.3. Climate reanalysis datasets

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To complement our in-situ data, we sourced daily weather data from the NASA Power API, which offers a comprehensive depiction of long-term meteorological conditions at a
173 regional scale. The data for our measurement sites was retrieved using the
174 NASA Power Weather Provider function of PCSE v.5.4.0. NASA Power provides a detailed
175 dataset including solar parameters from the GEWEX/SRB 3.0 and the CERES FlashFlux
176 versions 2 and 3 models, as well as meteorological parameters from the GMAO MERRA-2
177 and GEOS 5.12.4 FP-IT models on a granular 0.5° x 0.5° latitude/longitude grid. such as the
178 NASA Prediction of Worldwide Energy Resources (NASA Power) (Sparks, 2018; Zhang et al.,
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180 For our study, the dataset spanned from January 1st, 1984, to June 1st, 2022. It
181 included a range of daily meteorological variables crucial for our analysis: minimal temperature
182 (TMIN), maximal temperature (TMAX), average temperature (TEMP), rainfall (RAIN), average
183 wind speed (WIND), average vapour pressure (VAP), and global radiation (IRRAD). We
184 computed daily reference evapotranspiration values from reanalysis model (ET₀-PM-RM) from
185 these reanalysis model variables. This computation was done using the reference_ET function
186 from PCSE v.5.4.0, integrating station-specific elevation data from the AfricaRice dataset
187 metadata, instead of the broader 0.5° x 0.5° elevation averages typically provided by NASA
188 Power.

## 2.4. XGB model training and validation

190 In this study, XGBoost (XGB) models were trained and validated using daily weather
191 data from NASA Power for each of the twenty sites. We chose to work only with this family of
192 models as there are recognized as robust and adapted to a variety of tasks. Furthermore, we
193 wanted to focus on the comparison in the performance of models of the same nature, but
194 including an increasing number of predictor variables, rather than comparing different model
195 formalisms. To evaluate the feasibility and performance of this approach, in this work we will
196 train twenty local XGB models using data from NASA Power, as its API and companion tools
197 allow for very efficient requests. For each site, a data partitioning was done to split the data
198 into training and validation subsets. Specifically, the training dataset included NASA Power
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records until a year prior to the first on-site observations, while the days leading up to these
first observations formed the validation dataset. The in-situ observations themselves served
as the test set. The periods used for each site are detailed in **Table 2**.

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Our approach utilised eleven distinct combinations of daily variables from the NASA
Power reanalysis model, forming the basis for 11 XGB model classes (Table 3). The target
output for these models was the ET₀-PM-RM value. Model training was conducted using
XGBoost v1.6.2 (Chen and Guestrin, 2016) within a Python v3.9.6 environment. To optimise
performance, we increased the number of boost rounds to 1000 while keeping other
hyperparameters at their default settings.

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The performance of each XGB model was assessed through two key metrics: root mean squared error (RMSE) and coefficient of determination (R²). This evaluation involved comparing the XGB-estimated ET₀ values with the ET₀-PM-RM values from the validation set, allowing for a robust analysis of model precision and accuracy over the 20 locations.

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## 2.5. Comparison of the locally-trained neural network estimation models with other ET₀ estimation methods

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In this study, we benchmarked the performance of our locally-trained XGB models for
estimating ET₀ against traditional empirical methods described in **Table 4**. This comparison
was based on ET₀ calculations on test sets from in situ datasets (Table 2). We employed two
primary performance metrics for this analysis: the correlation coefficient and root mean square
error (RMSE). These metrics were applied to evaluate both our neural network approach and
the selected empirical formulas, with a focus on their accuracy in estimating ET₀-PM-GT
across the twenty study sites.

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To facilitate a comprehensive understanding of the results, we visualised the
performance comparisons using Taylor diagrams. This graphical representation allowed us to
simultaneously assess the correlation, standard deviation, and RMSE of the different methods.

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Additionally, we conducted a qualitative analysis to provide deeper insights into the strengths and limitations of each approach in various agro-climatic conditions.

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# 3. Results

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## 3.1. Training and validation of the XGB models

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In our study, an average of 10,000 records from NASA Power were utilised for each site to train the different XGB model classes presented in **Table 3**. Analysing the performance metrics against the validation sets (left-out training data from NASA Power), as detailed in **Table 5**, revealed distinct patterns in model efficacy. Notably, model class M11 emerged as the top performer, achieving a mean $R^2$ of 0.99 and a mean RMSE of just 0.09 mm. This superior performance aligns with our expectations, considering that M11's set of training variables - or features - closely mimics the variables used by the FAO56-PM-ET$_0$ formula. This suggests a high capability of XGB models to approximate the FAO56-PM-ET$_0$ method accurately.

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Model classes M9 and M10 also demonstrated strong results, with $R^2$ values around 0.95, but their RMSEs were higher, approximately 0.15 mm. Model class M7, while showing promising results with a mean $R^2$ of 0.87, exhibited variability across different sites. In contrast, the least effective models (M1-M4) recorded $R^2$ values around 0.62 and an RMSE of 0.68 mm, indicating a lower level of performance.

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These findings imply that the performance of ET$_0$-PM-RM estimation might vary with agro-ecological zones (AEZs) as the main driving factors of evapotranspiration are not identical in all environments. A notable observation was the underperformance of model class M7 in north-western sites, suggesting that adding more features could potentially enhance accuracy. Specifically, including the irradiance (IRRAD) feature in the models significantly improved ET$_0$ estimations by incorporating the radiative component, as evidenced by the improved validation metrics.

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## 3.2. Comparison of the trained XGB performance against empirical ET₀ estimation formulas from ground data

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Then, from the in-situ values of the test set, we calculated ET₀ using established empirical formulas (presented in **Table 4**), estimated ET₀ using our different XGB model classes, and compared these calculations with the ET₀ value computed using in situ weather measurements (ET₀-PM-GT) across the twenty sites (**Table 6**). The performance of each method was quantified using the root mean square error (RMSE) and correlation coefficient, with the results further illustrated in Taylor diagrams (representing correlation coefficient, RMSE and reference value in one plot) for a visual comparison (**Figure S1**).

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A qualitative analysis was performed from these Taylor diagrams, in which we consider as a suitable model a model in which the RMSE was below 1 mm, and that is inside the highest available and the least high available correlation coefficient quadrant. The models were then scored and ranked based on their adherence to these criteria at each site (Table 7). According to the data, XGB model class 11 was distinguished as the most accurate, followed by the Irmak-a model. Subsequent ranks were shared by Hargreaves, Irmak-c, Valiantzas-a, and XGB-M8 models, which displayed comparable performance.

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Notably, the Irmak-a model showed significant variability in RMSE across the sites, with a mean variability of 0.75, as opposed to 0.71 for M8 and 0.48 for M9. This variability is crucial as it affects the reliability and consistency of the model's performance in diverse climatic contexts, as represented by the various sites in West Africa.

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## 4. Discussion

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Our study contributes to the active research on machine learning (ML) methodologies for estimating ET₀ from a limited dataset of meteorological variables. In a field inclined towards the application of various ML approaches, we've selected XGB, and specifically extreme
gradient boosting (XGBoost) due to its proven robustness and established track record (Nielsen, 2016). Central to our discourse is the challenge of training data acquisition—a facet that, in our view, has not received due attention. The prevalent practice in the literature utilises weather data from a small number of locations over short time series to train models (see Supplementary Table 1 for a curated selection of studies on the topic). These models are then expected to extrapolate ET₀ estimations to larger, often regional scales, which risks significant extrapolation errors during application.

We propose a methodological pivot, employing a transversal ML approach that utilises local meteorological data from assimilation databases. This strategy has the distinct advantage of being deployable in areas devoid of ground weather data, offering uniform datasets that boast extensive historical records and spatial representativity—crucial for models that need to operate across varied geographic expanses. We harnessed the breadth of NASA Power's data, spanning a grid resolution of 0.5° x 0.5°, effectively training a model for every ~3000km² under West Africa's latitudes. However, we acknowledge that such a resolution may not fully encapsulate the microclimatic diversity within these regions, especially in areas with complex terrain. One solution to this limitation could involve debiasing reanalysis data using historical ground measurements, potentially through methods such as linear regression, prior to training the ML models (Chandler, William S., 2011).

Moreover, our approach stands to be further refined by incorporating data from sources with finer resolutions, such as the fifth generation of European ReAnalysis climate products (Copernicus ERA5) (Hersbach et al., 2020; Muñoz-Sabater et al., 2021). This would offer a more detailed 0.1° x 0.1° resolution and an extensive historical reach back to 1950—allowing the inclusion of rarer climatic events in our training set, however at a price of lengthier API calls thus overall computation time. Such granularity is anticipated to enhance the representativeness of training data and, consequently, the performance of ML models, although this hypothesis warrants additional research to quantify the influence of training data volume on model performance.
For example, the Hargreaves-Samani model (George H. Hargreaves and Zohrab A. Samani, 1985), the Schendel model (Schendel, U., 1967), and the Priestley-Taylor model (Priestley and Taylor, 1972) are based only on solar radiation and air temperature values; the Turc radiation-based model (Turc, L, 1961) uses temperature and relative humidity; the Makkink-based models (Allen, Richard, 2003; Hansen, 1984; Makkink, G.F., 1957) use radiation-related parameters. A thorough review of these methods can be found in (McMahon et al., 2013).

Aiming to serve practitioners with scant meteorological infrastructure, our study sought to validate the accuracy and precision of XGB-based ET₀ estimation models against the FAO-56 standardized PM equation. Our experiments scrutinised the impact of a limited set of input variables on ET₀ output quality. We also compared the ML-derived ET₀ estimates with those calculated from ground truth data across diverse West African climates, ensuring our models' efficacy relative to conventional methods.

The practicality of our approach is underscored by its minimal data requirements: a farm manager equipped with only a min/max thermometer and a rain funnel shall be able to use a locally trained model to estimate ET₀ with a level of precision and accuracy usually attainable by also having anemometer or hygrometer readings. Existing literature suggests different combinations of variables for efficient ET₀ estimation by models: (Granata, 2019) suggests mean temperature, mean relative humidity, and net solar radiation; wind and sunny hours as the strict minimum information for most locations according to (Shabani et al., 2020), and most empirical formulas need at least information about wind speed plus deficit pressure or solar radiation with air temperature. Meanwhile, our approach showed that it can yield models that perform relatively well, starting with only information about minimum, maximum, and average daily air temperature. With a dependency on a high number of devices to measure each variable needed, there is a greater risk in data gaps leading to impossibility to calculate ET₀; this issue of missing or incomplete meteorological data has been discussed in (Koudahe et al., 2018). Our finding suggests that practitioners may only need a quality
thermometer for reliable ET₀ estimation, simplifying an on-farm weather data acquisition
process that is already challenging in the region (Dinku, 2019). Stacking up variables will make
the estimations more reliable. Compared to other models that overestimate ET₀, our models
demonstrated better stability and less bias across various climates, although this observation
necessitates further validation with a broader dataset. The use of twenty weather stations
provides a solid foundation for our performance analysis, but a more expansive dataset would
enable a more comprehensive understanding of the models' applicability and robustness.

Most of these empiric models have been initially defined in a given climatic
environment and are less reliable or at least need recalibration when used in different climates.
In the context of climate change, with anticipated shifts in climatic zones (Cui et al., 2021), our
universally applicable method, supported by global assimilation data, could significantly aid in
ET₀ estimation efforts. Our XGB-ET₀ models, though in need of further validation, show
potential for at least equivalent performance compared to traditional empirical models, with
the added benefit of being more robust across different AEZs. This robustness is particularly
important in reducing bias risks, a common issue with empirical formulas lacking quality
assessment avenues.

To enable wider application and continued research, we have made our XGB-ET₀
code publicly available under the GPLv3 licence (doi: 10.5281/zenodo.10463369, repository
URL: https://github.com/SARRA-cropmodels/RF-ET0). This initiative allows researchers and
practitioners to conduct their own localised model training and ET₀ estimations, utilising the
model classes we've explored in this work.

## Conclusion

This research represents a significant stride in the application of machine learning for
agricultural water management, particularly within the challenging context of West Africa. The
study has successfully demonstrated the efficacy of XGB models in estimating
evapotranspiration (ET) using limited meteorological data. Our approach, which utilizes
extensive historical and spatial data from NASA Power's climate reanalysis datasets, marks a departure from traditional methods reliant on short-term, location-specific weather data. The ability of these models to accurately approximate ET estimations, as validated against ground measurements from diverse West African agro-ecological zones, underscores their potential in areas with limited meteorological infrastructure. This methodology not only simplifies the data requirements for ET estimation but also proves to be robust across various climatic conditions, enhancing its applicability for sustainable water management practices. The outcomes of this research contribute to the broader body of knowledge by showcasing the practicality of machine learning in agricultural contexts and underscore the importance of adopting innovative technologies in the face of climate change and resource constraints. The findings of this study hold significant implications for precision irrigation and water resource management, providing a sustainable and accessible solution to a region facing acute water-related challenges.

## Data Statement

All data, models, or code generated or used during the study are available in a repository or online in accordance with funder data retention policies. Data used for validation is available at the DOIs indicated in **Table 2**. Additionally, the climate reanalysis datasets utilized in this study, provided by NASA Power, are publicly accessible and can be retrieved for extended time series and various spatial resolutions through their API and data services. The XGB-ET₀ code developed for this study is publicly available under the GPLv3 licence, ensuring open access and facilitating further research and practical applications. The code can be accessed at the following repository URL: https://github.com/SARRA-cropmodels/RF-ET0 (doi:10.5281/zenodo.10463369).
377 Acknowledgements

378 The meteorological data were obtained from the NASA Langley Research Center

379 POWER Project funded through the NASA Earth Science Directorate Applied Science

380 Program. The authors would like to thank Vincent SIMONNEAUX and Michel LE PAGE

381 (CESBIO, Toulouse) and Gilles BELAUD (UMR G-EAU, Montpellier) for their contribution to

382 the early versions of this manuscript. Also, they would like to thank Dino IENCO and Roberto

383 INTERDONATO (UMR TETIS, Montpellier) for their feedback about the ML methodology.

384 Author contributions

385 • Jérémy LAVARENNE: Conceptualization, Methodology, Software, Formal Analysis,

386 Investigation, Writing - Original draft, Visualization, Supervision

387 • Audrey BROUILLET: Conceptualization, Methodology, Writing - Review and editing

388 Funding

389 This research did not receive any specific grant from funding agencies in the public,

390 commercial, or not-for-profit sectors.
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555 Figures

556 Figure 1

557 Map of Weather Measurement Sites and Agro-Ecological Zones

558 This color map of West Africa displays the geographic locations of the twenty weather
559 measurement sites used in the study, overlaid on a representation of global agro-ecological
560 zones as defined by the FAO and IIASA. Each site is indicated by a dot symbol. The color
561 legend for the agro-ecological zones (AEZ) is provided to differentiate between the zones.

<figure><img src="image_2.png" /></figure>

562

563 Figure 2

564 Surface Occupancy Histogram of AEZ

565 This histogram illustrates the distribution of surface occupancy percentages for the various
566 Agro-Ecological Zones (AEZ) within the study's geographic extent. Each bar represents the
567 proportion of an AEZ relative to the total area considered.
<figure><img src="image_3.png" /></figure>

568

569
This table enumerates the weather stations selected for the collection of daily in situ meteorological data. Detailed within are the geographical coordinates (latitude and longitude), altitude, country of location, data collection period, DOI for dataset reference, and the agro-ecological zones represented by each station.

<table><thead><tr><td>Station name</td><td>Station code</td><td>Latitude</td><td>Longitude</td><td>Altitude (m)</td><td>Country</td><td>Measurement start</td><td>Measurement end</td><td>Dataset DOI</td><td>Agro-ecological zone</td></tr></thead><tbody><tr><td>Glazoue</td><td>BEN3001</td><td>7.8800</td><td>2.2100</td><td>199</td><td>Benin</td><td>2012-07-05</td><td>2016-09-22</td><td>doi:10.7910/DVN/GVQYG</td><td>Tropics, lowland; sub-humid</td></tr><tr><td>AfricaRice_Calavi</td><td>BEN4001</td><td>6.4200</td><td>2.3300</td><td>41</td><td>Benin</td><td>2012-03-19</td><td>2018-01-08</td><td>doi:10.7910/DVN/WTIMYZ</td><td>Tropics, lowland; humid</td></tr><tr><td>Farakoba</td><td>BFA3001</td><td>10.5400</td><td>-4.7600</td><td>319</td><td>Burkina Faso</td><td>2013-06-21</td><td>2018-03-08</td><td>doi:10.7910/DVN/TQX3L9</td><td>Tropics, lowland; sub-humid</td></tr><tr><td>Gagnoa_HUB</td><td>CIV3001</td><td>6.1300</td><td>-5.9000</td><td>248</td><td>Ivory Coast</td><td>2015-07-25</td><td>2018-06-13</td><td>doi:10.7910/DVN/A6SGP3</td><td>Tropics, lowland; humid</td></tr><tr><td>Man</td><td>CIV3002</td><td>7.2800</td><td>-7.7000</td><td>376</td><td>Ivory Coast</td><td>2012-07-21</td><td>2019-05-31</td><td>doi:10.7910/DVN/DQXCJC</td><td>Tropics, lowland; humid</td></tr><tr><td>Mbe_Low</td><td>CIV4001</td><td>7.8744</td><td>-5.1138</td><td>273</td><td>Ivory Coast</td><td>2014-10-10</td><td>2020-12-12</td><td>doi:10.7910/DVN/</td><td>Tropics, lowland; humid</td></tr></tbody></table>
<table><tr><td>land</td><td></td><td></td><td></td><td>Coast</td><td>03</td><td>31</td><td>10/DVN/ HVKBPL</td><td>lowland; humid</td></tr><tr><td>Mbe_Upl and</td><td>CIV4002</td><td>7.8856</td><td>-5.1123</td><td>303</td><td>Ivory Coast</td><td>2014-10-10</td><td>2018-08-05</td><td>doi:10.79 10/DVN/2 C7XKY</td><td>Tropics, lowland; humid</td></tr><tr><td>Ndop</td><td>CMR300 1</td><td>5.9500</td><td>10.4400</td><td>1185</td><td>Cameroon</td><td>2012-08-03</td><td>2015-06-24</td><td>doi:10.79 10/DVN/Z SP7NQ</td><td>Land with severe soil/terrain limitations</td></tr><tr><td>Gimbi</td><td>COD300 1</td><td>-5.2200</td><td>13.2700</td><td>364</td><td>Democratic Rep. Congo</td><td>2013-08-03</td><td>2014-02-01</td><td>doi:10.79 10/DVN/I XPDM3</td><td>Tropics, highland; sub-humid</td></tr><tr><td>Kumasi</td><td>GHA3001</td><td>6.6700</td><td>-1.8100</td><td>236</td><td>Ghana</td><td>2012-06-23</td><td>2016-04-20</td><td>doi:10.79 10/DVN/ EUPQPZ</td><td>Tropics, lowland; humid</td></tr><tr><td>Navrongo</td><td>GHA3002</td><td>10.8400</td><td>-1.0900</td><td>173</td><td>Ghana</td><td>2013-05-14</td><td>2014-05-17</td><td>doi:10.79 10/DVN/ H5MX3J</td><td>Tropics, lowland; semi-arid</td></tr><tr><td>Kankan</td><td>GIN3001</td><td>10.5300</td><td>-9.3200</td><td>432</td><td>Guinea</td><td>2013-11-09</td><td>2016-03-16</td><td>doi:10.79 10/DVN/6 PHUPC</td><td>Tropics, lowland; sub-humid</td></tr><tr><td>Central_River</td><td>GMB300 1</td><td>13.5600</td><td>-14.8700</td><td>41</td><td>Gambia</td><td>2013-03-07</td><td>2020-03-02</td><td>10.7910/ DVN/ZLH PFP</td><td>Tropics, lowland; semi-arid</td></tr><tr><td>Cari</td><td>LBR3001</td><td>7.1000</td><td>-9.6500</td><td>273</td><td>Liberia</td><td>2015-10-08</td><td>2018-02-21</td><td>doi:10.79 10/DVN/ MJQVZO</td><td>Tropics, lowland; humid</td></tr></table>
<table><tr><td>Tillabery_ HUB</td><td>NER3001</td><td>14.3800</td><td>1.2200</td><td>234</td><td>Niger</td><td>2012-07-29</td><td>2015-07-03</td><td>doi:10.79 10/DVN/ Q6ZDBV</td><td>Tropics, lowland; semi-arid</td></tr><tr><td>Lafia</td><td>NGA3001</td><td>8.5600</td><td>8.5400</td><td>150</td><td>Nigeria</td><td>2012-08-09</td><td>2018-02-25</td><td>doi:10.79 10/DVN/8 ERRWL</td><td>Tropics, lowland; sub-humid</td></tr><tr><td>Fanaye</td><td>SEN3001</td><td>16.5300</td><td>-14.8000</td><td>11</td><td>Senegal</td><td>2013-02-06</td><td>2020-12-31</td><td>doi:10.79 10/DVN/9 HVYWP</td><td>Desert/Ar id climate</td></tr><tr><td>Ndiaye</td><td>SEN4001</td><td>16.2200</td><td>-16.2900</td><td>13</td><td>Senegal</td><td>2013-02-01</td><td>2019-12-14</td><td>doi:10.79 10/DVN/ HTLG35</td><td>Land with ample irrigated soils</td></tr><tr><td>Tormabu m</td><td>SLE3002</td><td>7.3900</td><td>-12.0100</td><td>9</td><td>Sierra Leone</td><td>2014-05-28</td><td>2016-05-01</td><td>doi:10.79 10/DVN/ VWGJHE</td><td>Tropics, lowland; sub-humid</td></tr><tr><td>Tandjile_ East</td><td>TCD3001</td><td>9.6600</td><td>16.7200</td><td>345</td><td>Chad</td><td>2013-06-07</td><td>2013-07-03</td><td>doi:10.79 10/DVN/ WKP6HR</td><td>Tropics, lowland; humid</td></tr><tr><td>Adeta</td><td>TGO3001</td><td>7.1700</td><td>0.7700</td><td>295</td><td>Togo</td><td>2013-04-04</td><td>2015-12-05</td><td>doi:10.79 10/DVN/0 SQFGQ</td><td>Tropics, lowland; humid</td></tr></table>
Table 2

Dataset Durations for Model Development

Summary of dataset lengths for ground weather observations, detailing the periods utilised for
the training, validation, and testing of XGB models.

<table><thead><tr><th rowspan="2">station code</th><th colspan="2">on-site observations interval</th><th colspan="3">subset duration (days)</th></tr><tr><th>start</th><th>end</th><th>train set</th><th>validation set</th><th>test set</th></tr></thead><tbody><tr><td>BEN3001</td><td>2012-07-05</td><td>2016-09-22</td><td>10048</td><td>365</td><td>1540</td></tr><tr><td>BEN4001</td><td>2012-03-19</td><td>2018-01-08</td><td>9940</td><td>365</td><td>2121</td></tr><tr><td>BFA3001</td><td>2013-06-21</td><td>2018-03-08</td><td>10399</td><td>365</td><td>1721</td></tr><tr><td>CIV3001</td><td>2015-06-25</td><td>2018-06-13</td><td>11133</td><td>365</td><td>1084</td></tr><tr><td>CIV3002</td><td>2012-07-21</td><td>2019-05-31</td><td>10064</td><td>365</td><td>2505</td></tr><tr><td>CIV4001</td><td>2014-10-03</td><td>2020-12-31</td><td>10868</td><td>365</td><td>2281</td></tr><tr><td>CIV4002</td><td>2014-10-10</td><td>2018-10-05</td><td>10875</td><td>365</td><td>1456</td></tr><tr><td>CMR3001</td><td>2012-08-03</td><td>2015-06-24</td><td>10077</td><td>365</td><td>1055</td></tr><tr><td>COD3001</td><td>2013-08-03</td><td>2014-02-01</td><td>10442</td><td>365</td><td>182</td></tr><tr><td>GHA3001</td><td>2012-06-23</td><td>2016-04-20</td><td>10036</td><td>365</td><td>1397</td></tr><tr><td>GHA3002</td><td>2013-05-14</td><td>2014-05-17</td><td>10361</td><td>365</td><td>368</td></tr><tr><td>GIN3001</td><td>2013-11-09</td><td>2016-03-16</td><td>10540</td><td>365</td><td>858</td></tr><tr><td>GMB3001</td><td>2013-03-07</td><td>2020-03-07</td><td>10293</td><td>365</td><td>2557</td></tr><tr><td>LBR3001</td><td>2015-10-08</td><td>2018-02-21</td><td>11238</td><td>365</td><td>867</td></tr><tr><td>NER3001</td><td>2012-01-01</td><td>2015-07-03</td><td>9862</td><td>365</td><td>1279</td></tr><tr><td>NGA3001</td><td>2012-01-01</td><td>2018-02-25</td><td>9862</td><td>365</td><td>2247</td></tr><tr><td>SEN3001</td><td>2013-01-01</td><td>2020-12-31</td><td>10228</td><td>365</td><td>2921</td></tr><tr><td>SEN4001</td><td>2013-02-01</td><td>2019-12-31</td><td>10259</td><td>365</td><td>2524</td></tr><tr><td>SLE3002</td><td>2014-01-01</td><td>2016-06-22</td><td>10593</td><td>365</td><td>903</td></tr><tr><td>TCD3001</td><td>2013-01-12</td><td>2013-07-03</td><td>10239</td><td>365</td><td>172</td></tr><tr><td>TGO3001</td><td>2013-01-01</td><td>2015-12-05</td><td>10228</td><td>365</td><td>1068</td></tr></tbody><tfoot><tr><td></td><td></td><td>average</td><td>10361</td><td></td><td>1481</td></tr></tfoot></table>

582
584 Training Features for XGB Model Classes

This table specifies the combinations of meteorological variables used to train the eleven distinct XGB model classes, with each variable corresponding to data typically collected by standard meteorological instruments. X indicates the correspondence between the set of variables and the minimum set of sensors needed to measure these variables on site

<table><thead><tr><th>model alias</th><th>Features used for training</th><th>maximum-<br>minimum<br>thermometer</th><th>temperature<br>data logger</th><th>rain gauge</th><th>anemome<br>ter</th><th>hygrom<br>eter</th><th>pyrano<br>meter</th></tr></thead><tbody><tr><td>M1</td><td>TMIN, TMAX</td><td>x</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>M2</td><td>TEMP, TMIN, TMAX</td><td></td><td>x</td><td></td><td></td><td></td><td></td></tr><tr><td>M3</td><td>TMIN, TMAX, RAIN</td><td>x</td><td></td><td>x</td><td></td><td></td><td></td></tr><tr><td>M4</td><td>TEMP, TMIN, TMAX, RAIN</td><td></td><td>x</td><td>x</td><td></td><td></td><td></td></tr><tr><td>M5</td><td>TEMP, TMIN, TMAX, RAIN, WIND</td><td></td><td>x</td><td>x</td><td>x</td><td></td><td></td></tr><tr><td>M6</td><td>TEMP, TMIN, TMAX, RAIN, VAP</td><td></td><td>x</td><td>x</td><td></td><td>x</td><td></td></tr><tr><td>M7</td><td>TEMP, TMIN, TMAX, RAIN, IRRAD</td><td></td><td>x</td><td>x</td><td></td><td></td><td>x</td></tr><tr><td>M8</td><td>TEMP, TMIN, TMAX, RAIN, WIND,<br>VAP</td><td></td><td>x</td><td>x</td><td>x</td><td>x</td><td></td></tr><tr><td>M9</td><td>TEMP, TMIN, TMAX, RAIN, WIND,<br>IRRAD</td><td></td><td>x</td><td>x</td><td>x</td><td></td><td>x</td></tr><tr><td>M10</td><td>TEMP, TMIN, TMAX, RAIN, VAP,<br>IRRAD</td><td></td><td>x</td><td>x</td><td></td><td>x</td><td>x</td></tr><tr><td>M11</td><td>TEMP, TMIN, TMAX, RAIN, WIND,<br>VAP, IRRAD</td><td></td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr></tbody></table>
591 **Empirical methods used for ET₀ estimations.**

592 ET₀ reference evapotranspiration (mm); u2 represents the wind speed measured at 2 m from
593 the ground (ms⁻¹); (es—ea) vapour saturation deficit (kPa); Ta is the average air temperature
594 (°C); Tmax—maximum temperature (°C); Tmin—minimum temperature (°C); Rs is the short
595 wavelength solar radiation (MJ m⁻²d⁻¹); φ represents the latitude of the station in radian
596 degree, and λ is the latent heat of vaporisation (MJ.m⁻²d⁻¹).

<table><thead><tr><th>Category</th><th>Reference</th><th>Formula</th></tr></thead><tbody><tr><td rowspan="5">Aerodynamic</td><td>Dalton (Dalton, J, 1802)</td><td>ET<sub>0</sub> = (0.3648 + 0.07223u2)(es - ea)</td></tr><tr><td>Trabert (Trabert, W, 1896)</td><td>ET<sub>0</sub> = 0.3075√u2(es - ea)</td></tr><tr><td>Penman (Penman, H. L., 1963)</td><td>ET<sub>0</sub> = 0.35(1 + 0.24u2)(es - ea)</td></tr><tr><td>Rohwer (Rohwer, Carl, 1931)</td><td>ET<sub>0</sub> = 0.44(1 + 0.27u2)(es - ea)</td></tr><tr><td>Mahringer (Mahringer, 1970)</td><td>ET<sub>0</sub> = 0.15072√3.6u2(es - ea)</td></tr><tr><td>Temperature</td><td>Hargreaves (George H. Hargreaves and Zohrab A. Samani, 1985)</td><td>ET<sub>0</sub> = 0.0135 × 0.408Rs(Ta + 17.8)</td></tr><tr><td rowspan="6">Radiation</td><td>Jensen & Haise (Jensen and Haise, 1963)</td><td>ET<sub>0</sub> = 0.025(Ta - 3)Rs</td></tr><tr><td>Abtew (Abtew, 1996)</td><td>ET<sub>0</sub> = 0.53 Rs / λ</td></tr><tr><td>Oudin (Oudin, Ludovic, 2004)</td><td>ET<sub>0</sub> = Rs × (Ta + 5) / 100</td></tr><tr><td>Irmak (a) (Irmak et al., 2003a, 2003b)</td><td>ET<sub>0</sub> = 0.149Rs + 0.079Ta - 0.611</td></tr><tr><td>Irmak (b) (Irmak et al., 2003a, 2003b)</td><td>ET<sub>0</sub> = 0.174Rs + 0.353Ta - 0.642</td></tr><tr><td>Irmak (c) (Irmak et al., 2003a, 2003b)</td><td>ET<sub>0</sub> = 0.156Rs - 0.0112Tmax + 0.0733Tmin - 0.478</td></tr></tbody></table>
<table><tr><td rowspan="3">Combinatory</td><td>Valiantzas (a) (Valiantzas, 2013)</td><td>ET<sub>0</sub> = (0.0393Rs × √Ta + 9.5) - 0.19Rs<sup>0.6</sup>φ<sup>0.15</sup> + 0.048(Ta + 20)(1 - <sup>Hr</sup>/<sub>100</sub>)u<sup>2.07</sup></td></tr><tr><td>Valiantzas (b) (Valiantzas, 2013)</td><td>ET<sub>0</sub> = (0.0393Rs × √Ta + 9.5) - 0.19Rs<sup>0.6</sup>φ<sup>0.15</sup> + 0.078(Ta + 20)(1 - <sup>Hr</sup>/<sub>100</sub>)</td></tr><tr><td>Valiantzas (c) (Valiantzas, 2013)</td><td>ET<sub>0</sub> = (0.0393Rs × √Ta + 9.5) - 0.19Rs<sup>0.6</sup>φ<sup>0.15</sup> + 0.0061(Ta + 20)(1.12Ta - Tmin - 2)<sup>0.7</sup></td></tr></table>
599

Table 5

600

Validation Metrics for XGB Models

601

This table provides the root mean square error (RMSE) and coefficient of determination (R2)

602

obtained from the validation sets used in the training of the eleven XGB model classes.
<table><thead><tr><th rowspan="2">station</th><th colspan="11">model class</th></tr><tr><th>M1</th><th>M2</th><th>M3</th><th>M4</th><th>M5</th><th>M6</th><th>M7</th><th>M8</th><th>M9</th><th>M10</th><th>M11</th></tr></thead><tbody><tr><td>BEN3001</td><td>0,43</td><td>0,43</td><td>0,42</td><td>0,42</td><td>0,42</td><td>0,41</td><td>0,20</td><td>0,41</td><td>0,15</td><td>0,16</td><td>0,06</td></tr><tr><td>BEN4001</td><td>0,50</td><td>0,48</td><td>0,47</td><td>0,47</td><td>0,47</td><td>0,46</td><td>0,14</td><td>0,47</td><td>0,12</td><td>0,12</td><td>0,06</td></tr><tr><td>BFA3001</td><td>0,77</td><td>0,78</td><td>0,74</td><td>0,76</td><td>0,49</td><td>0,68</td><td>0,61</td><td>0,48</td><td>0,29</td><td>0,51</td><td>0,10</td></tr><tr><td>CIV3001</td><td>0,41</td><td>0,41</td><td>0,40</td><td>0,41</td><td>0,40</td><td>0,42</td><td>0,13</td><td>0,41</td><td>0,10</td><td>0,10</td><td>0,06</td></tr><tr><td>CIV3002</td><td>0,38</td><td>0,38</td><td>0,38</td><td>0,38</td><td>0,37</td><td>0,38</td><td>0,15</td><td>0,37</td><td>0,12</td><td>0,12</td><td>0,07</td></tr><tr><td>CIV4001</td><td>0,55</td><td>0,56</td><td>0,55</td><td>0,56</td><td>0,50</td><td>0,53</td><td>0,35</td><td>0,48</td><td>0,25</td><td>0,32</td><td>0,09</td></tr><tr><td>CIV4002</td><td>0,55</td><td>0,56</td><td>0,55</td><td>0,56</td><td>0,50</td><td>0,53</td><td>0,35</td><td>0,48</td><td>0,25</td><td>0,32</td><td>0,09</td></tr><tr><td>CMR3001</td><td>0,41</td><td>0,42</td><td>0,39</td><td>0,39</td><td>0,40</td><td>0,37</td><td>0,12</td><td>0,38</td><td>0,12</td><td>0,09</td><td>0,05</td></tr><tr><td>COD3001</td><td>0,69</td><td>0,67</td><td>0,70</td><td>0,68</td><td>0,67</td><td>0,66</td><td>0,06</td><td>0,66</td><td>0,06</td><td>0,06</td><td>0,04</td></tr><tr><td>GHA3001</td><td>0,43</td><td>0,44</td><td>0,43</td><td>0,44</td><td>0,43</td><td>0,42</td><td>0,24</td><td>0,42</td><td>0,19</td><td>0,20</td><td>0,07</td></tr><tr><td>GHA3002</td><td>0,81</td><td>0,82</td><td>0,81</td><td>0,83</td><td>0,53</td><td>0,72</td><td>0,67</td><td>0,51</td><td>0,34</td><td>0,54</td><td>0,12</td></tr><tr><td>GIN3001</td><td>0,71</td><td>0,72</td><td>0,71</td><td>0,73</td><td>0,50</td><td>0,69</td><td>0,58</td><td>0,50</td><td>0,33</td><td>0,53</td><td>0,11</td></tr><tr><td>GMB3001</td><td>0,96</td><td>0,94</td><td>0,95</td><td>0,96</td><td>0,57</td><td>0,81</td><td>0,90</td><td>0,50</td><td>0,46</td><td>0,74</td><td>0,13</td></tr><tr><td>LBR3001</td><td>0,40</td><td>0,40</td><td>0,39</td><td>0,40</td><td>0,38</td><td>0,39</td><td>0,11</td><td>0,38</td><td>0,10</td><td>0,10</td><td>0,06</td></tr><tr><td>NER3001</td><td>1,14</td><td>1,14</td><td>1,13</td><td>1,14</td><td>0,57</td><td>0,98</td><td>1,09</td><td>0,50</td><td>0,48</td><td>0,95</td><td>0,16</td></tr><tr><td>NGA3001</td><td>0,75</td><td>0,75</td><td>0,76</td><td>0,76</td><td>0,53</td><td>0,63</td><td>0,66</td><td>0,50</td><td>0,34</td><td>0,43</td><td>0,12</td></tr><tr><td>SEN3001</td><td>1,44</td><td>1,45</td><td>1,43</td><td>1,45</td><td>0,61</td><td>1,22</td><td>1,33</td><td>0,48</td><td>0,53</td><td>1,09</td><td>0,19</td></tr><tr><td>SEN4001</td><td>1,09</td><td>1,08</td><td>1,07</td><td>1,06</td><td>0,63</td><td>0,90</td><td>1,03</td><td>0,45</td><td>0,62</td><td>0,75</td><td>0,19</td></tr><tr><td>SLE3002</td><td>0,55</td><td>0,55</td><td>0,54</td><td>0,55</td><td>0,53</td><td>0,55</td><td>0,10</td><td>0,54</td><td>0,09</td><td>0,09</td><td>0,06</td></tr><tr><td>TCD3001</td><td>0,97</td><td>0,95</td><td>0,98</td><td>0,97</td><td>0,53</td><td>0,79</td><td>0,83</td><td>0,53</td><td>0,31</td><td>0,63</td><td>0,11</td></tr><tr><td>TGO3001</td><td>0,43</td><td>0,43</td><td>0,43</td><td>0,43</td><td>0,43</td><td>0,42</td><td>0,18</td><td>0,42</td><td>0,14</td><td>0,17</td><td>0,07</td></tr><tr><td>mean</td><td>0,68</td><td>0,68</td><td>0,68</td><td>0,68</td><td>0,50</td><td>0,62</td><td>0,47</td><td>0,47</td><td>0,26</td><td>0,38</td><td>0,09</td></tr><tr><td>median</td><td>0,55</td><td>0,56</td><td>0,55</td><td>0,56</td><td>0,50</td><td>0,55</td><td>0,35</td><td>0,48</td><td>0,25</td><td>0,32</td><td>0,09</td></tr><tr><td>BEN3001</td><td>0,58</td><td>0,57</td><td>0,60</td><td>0,59</td><td>0,60</td><td>0,62</td><td>0,91</td><td>0,62</td><td>0,95</td><td>0,94</td><td>0,99</td></tr><tr><td>BEN4001</td><td>0,43</td><td>0,46</td><td>0,49</td><td>0,49</td><td>0,50</td><td>0,51</td><td>0,96</td><td>0,50</td><td>0,97</td><td>0,97</td><td>0,99</td></tr><tr><td>BFA3001</td><td>0,76</td><td>0,76</td><td>0,78</td><td>0,77</td><td>0,90</td><td>0,82</td><td>0,85</td><td>0,91</td><td>0,97</td><td>0,90</td><td>1,00</td></tr><tr><td>CIV3001</td><td>0,33</td><td>0,32</td><td>0,34</td><td>0,32</td><td>0,35</td><td>0,28</td><td>0,93</td><td>0,31</td><td>0,96</td><td>0,96</td><td>0,99</td></tr><tr><td>CIV3002</td><td>0,61</td><td>0,62</td><td>0,61</td><td>0,62</td><td>0,62</td><td>0,62</td><td>0,94</td><td>0,62</td><td>0,96</td><td>0,96</td><td>0,99</td></tr><tr><td>CIV4001</td><td>0,75</td><td>0,74</td><td>0,75</td><td>0,74</td><td>0,80</td><td>0,77</td><td>0,90</td><td>0,81</td><td>0,95</td><td>0,91</td><td>0,99</td></tr><tr><td>CIV4002</td><td>0,75</td><td>0,74</td><td>0,74</td><td>0,73</td><td>0,79</td><td>0,77</td><td>0,90</td><td>0,81</td><td>0,95</td><td>0,91</td><td>0,99</td></tr><tr><td>CMR3001</td><td>0,68</td><td>0,67</td><td>0,72</td><td>0,71</td><td>0,70</td><td>0,74</td><td>0,97</td><td>0,73</td><td>0,97</td><td>0,98</td><td>1,00</td></tr><tr><td>COD3001</td><td>0,11</td><td>0,15</td><td>0,09</td><td>0,14</td><td>0,16</td><td>0,18</td><td>0,99</td><td>0,19</td><td>0,99</td><td>0,99</td><td>1,00</td></tr><tr><td>GHA3001</td><td>0,72</td><td>0,71</td><td>0,72</td><td>0,71</td><td>0,72</td><td>0,73</td><td>0,91</td><td>0,73</td><td>0,95</td><td>0,94</td><td>0,99</td></tr><tr><td>GHA3002</td><td>0,78</td><td>0,77</td><td>0,78</td><td>0,77</td><td>0,91</td><td>0,83</td><td>0,85</td><td>0,91</td><td>0,96</td><td>0,90</td><td>1,00</td></tr><tr><td>GIN3001</td><td>0,82</td><td>0,82</td><td>0,82</td><td>0,81</td><td>0,91</td><td>0,83</td><td>0,88</td><td>0,91</td><td>0,96</td><td>0,90</td><td>1,00</td></tr><tr><td>GMB3001</td><td>0,81</td><td>0,82</td><td>0,81</td><td>0,81</td><td>0,93</td><td>0,86</td><td>0,83</td><td>0,95</td><td>0,96</td><td>0,89</td><td>1,00</td></tr><tr><td>LBR3001</td><td>0,42</td><td>0,42</td><td>0,44</td><td>0,42</td><td>0,47</td><td>0,44</td><td>0,96</td><td>0,48</td><td>0,97</td><td>0,96</td><td>0,99</td></tr><tr><td>NER3001</td><td>0,57</td><td>0,57</td><td>0,58</td><td>0,57</td><td>0,89</td><td>0,68</td><td>0,61</td><td>0,92</td><td>0,92</td><td>0,70</td><td>0,99</td></tr><tr><td>NGA3001</td><td>0,82</td><td>0,82</td><td>0,82</td><td>0,82</td><td>0,91</td><td>0,88</td><td>0,87</td><td>0,92</td><td>0,96</td><td>0,94</td><td>1,00</td></tr><tr><td>SEN3001</td><td>0,55</td><td>0,54</td><td>0,55</td><td>0,54</td><td>0,92</td><td>0,67</td><td>0,61</td><td>0,95</td><td>0,94</td><td>0,74</td><td>0,99</td></tr><tr><td>SEN4001</td><td>0,59</td><td>0,59</td><td>0,60</td><td>0,61</td><td>0,86</td><td>0,72</td><td>0,64</td><td>0,93</td><td>0,86</td><td>0,80</td><td>0,99</td></tr><tr><td>SLE3002</td><td>0,54</td><td>0,54</td><td>0,55</td><td>0,54</td><td>0,57</td><td>0,54</td><td>0,99</td><td>0,56</td><td>0,99</td><td>0,99</td><td>0,99</td></tr><tr><td>TCD3001</td><td>0,74</td><td>0,75</td><td>0,73</td><td>0,74</td><td>0,92</td><td>0,83</td><td>0,81</td><td>0,92</td><td>0,97</td><td>0,89</td><td>1,00</td></tr><tr><td>TGO3001</td><td>0,65</td><td>0,65</td><td>0,65</td><td>0,64</td><td>0,65</td><td>0,66</td><td>0,94</td><td>0,66</td><td>0,96</td><td>0,95</td><td>0,99</td></tr><tr><td>mean</td><td>0,62</td><td>0,62</td><td>0,63</td><td>0,62</td><td>0,72</td><td>0,66</td><td>0,87</td><td>0,73</td><td>0,96</td><td>0,91</td><td>0,99</td></tr><tr><td>median</td><td>0,65</td><td>0,65</td><td>0,65</td><td>0,64</td><td>0,79</td><td>0,72</td><td>0,90</td><td>0,81</td><td>0,96</td><td>0,94</td><td>0,99</td></tr></tbody></table>
605 Table 6

606 Performance Comparison of XGB and Empirical ET0 Formulas

607 This table presents the average metrics from the comparison between XGB model estimations

608 and those calculated using empirical ET₀ formulas against the standard ET₀-PM-GT values.

609 Metrics include RMSE and R² values for each model and formula.
<table><thead><tr><th rowspan="2">station</th><th colspan="14">model class</th><th colspan="14">empirical methods</th></tr><tr><th>M1</th><th>M2</th><th>M3</th><th>M4</th><th>M5</th><th>M6</th><th>M7</th><th>M8</th><th>M9</th><th>M10</th><th>M11</th><th>ahew</th><th>dalton</th><th>hargreaves</th><th>irmak-a</th><th>irmak-b</th><th>irmak-c</th><th>jensen-haise</th><th>mahringer</th><th>oudin</th><th>penman</th><th>rohwer</th><th>trabert</th><th>vallantzas-a</th><th>vallantzas-b</th><th>vallantzas-c</th></tr></thead><tbody><tr><td>BEN3001</td><td>1.16</td><td>1.17</td><td>1.25</td><td>1.25</td><td>1.20</td><td>1.09</td><td>1.49</td><td>0.95</td><td>1.51</td><td>0.93</td><td>0.84</td><td>1.81</td><td>4.90</td><td>1.65</td><td>1.68</td><td>3.16</td><td>2.10</td><td>4.43</td><td>4.63</td><td>1.08</td><td>4.69</td><td>4.80</td><td>4.96</td><td>1.76</td><td>1.70</td><td>1.61</td></tr><tr><td>BEN4001</td><td>1.52</td><td>1.48</td><td>1.61</td><td>1.54</td><td>1.20</td><td>1.04</td><td>1.68</td><td>1.16</td><td>1.16</td><td>1.23</td><td>1.80</td><td>5.14</td><td>1.66</td><td>1.62</td><td>2.13</td><td>1.39</td><td>1.52</td><td>5.11</td><td>1.37</td><td>1.54</td><td>5.19</td><td>5.13</td><td>5.13</td><td>1.94</td><td>1.93</td><td>1.75</td></tr><tr><td>BFA3001</td><td>2.08</td><td>2.05</td><td>2.33</td><td>2.26</td><td>1.21</td><td>4.27</td><td>2.02</td><td>2.08</td><td>1.10</td><td>3.59</td><td>0.99</td><td>0.81</td><td>4.06</td><td>0.79</td><td>0.65</td><td>1.97</td><td>1.16</td><td>6.27</td><td>4.17</td><td>1.54</td><td>4.06</td><td>3.97</td><td>4.15</td><td>0.78</td><td>0.97</td><td>0.80</td></tr><tr><td>CIV3001</td><td>0.59</td><td>0.61</td><td>0.61</td><td>0.64</td><td>0.58</td><td>0.66</td><td>0.83</td><td>0.49</td><td>0.85</td><td>0.78</td><td>0.70</td><td>0.97</td><td>4.07</td><td>0.92</td><td>0.78</td><td>2.21</td><td>5.16</td><td>4.17</td><td>1.14</td><td>4.07</td><td>3.99</td><td>4.15</td><td>1.12</td><td>0.88</td><td>0.89</td><td>0.89</td></tr><tr><td>CIV3002</td><td>0.55</td><td>0.55</td><td>0.58</td><td>0.55</td><td>0.53</td><td>0.81</td><td>0.61</td><td>0.80</td><td>0.61</td><td>0.44</td><td>0.45</td><td>0.82</td><td>3.60</td><td>0.80</td><td>0.52</td><td>1.99</td><td>1.04</td><td>4.34</td><td>3.71</td><td>0.94</td><td>3.60</td><td>3.53</td><td>3.69</td><td>0.92</td><td>0.81</td><td>0.72</td></tr><tr><td>CIV4001</td><td>1.31</td><td>1.31</td><td>1.27</td><td>1.17</td><td>2.21</td><td>1.39</td><td>1.45</td><td>1.42</td><td>1.63</td><td>0.81</td><td>1.60</td><td>4.49</td><td>1.56</td><td>1.44</td><td>2.84</td><td>1.36</td><td>4.00</td><td>4.55</td><td>1.17</td><td>4.49</td><td>4.40</td><td>4.56</td><td>1.67</td><td>1.57</td><td>1.49</td></tr><tr><td>CIV4002</td><td>0.91</td><td>0.92</td><td>0.93</td><td>0.91</td><td>0.82</td><td>2.38</td><td>0.99</td><td>1.55</td><td>1.05</td><td>1.93</td><td>0.63</td><td>1.18</td><td>4.30</td><td>1.10</td><td>1.01</td><td>1.52</td><td>5.08</td><td>4.35</td><td>1.13</td><td>4.30</td><td>4.22</td><td>4.39</td><td>1.24</td><td>1.15</td><td>1.05</td></tr><tr><td>CMF3001</td><td>0.66</td><td>0.65</td><td>0.65</td><td>0.59</td><td>0.56</td><td>0.79</td><td>0.72</td><td>0.69</td><td>0.76</td><td>0.46</td><td>0.51</td><td>0.88</td><td>4.26</td><td>1.11</td><td>1.10</td><td>2.23</td><td>3.19</td><td>4.32</td><td>0.69</td><td>4.26</td><td>4.18</td><td>4.33</td><td>1.08</td><td>0.91</td><td>0.94</td></tr><tr><td>CCD3001</td><td>2.03</td><td>2.06</td><td>2.09</td><td>2.12</td><td>2.19</td><td>2.54</td><td>2.62</td><td>2.42</td><td>2.68</td><td>2.77</td><td>2.82</td><td>2.33</td><td>4.66</td><td>2.44</td><td>2.04</td><td>3.46</td><td>2.46</td><td>2.53</td><td>4.67</td><td>2.02</td><td>4.66</td><td>4.59</td><td>4.70</td><td>2.42</td><td>2.42</td><td>2.32</td></tr><tr><td>GHA3001</td><td>1.26</td><td>1.23</td><td>1.26</td><td>1.17</td><td>0.93</td><td>2.36</td><td>0.89</td><td>1.86</td><td>0.74</td><td>1.89</td><td>0.86</td><td>0.57</td><td>3.38</td><td>0.60</td><td>0.44</td><td>1.65</td><td>0.72</td><td>5.18</td><td>3.53</td><td>1.27</td><td>3.38</td><td>3.31</td><td>3.49</td><td>0.71</td><td>0.68</td><td>0.63</td></tr><tr><td>GHA3002</td><td>1.63</td><td>1.61</td><td>1.62</td><td>1.60</td><td>1.22</td><td>3.57</td><td>1.63</td><td>1.47</td><td>1.24</td><td>3.24</td><td>0.70</td><td>1.60</td><td>5.33</td><td>1.34</td><td>1.54</td><td>3.05</td><td>2.11</td><td>7.12</td><td>5.35</td><td>1.54</td><td>4.52</td><td>5.17</td><td>5.43</td><td>1.16</td><td>1.28</td><td>1.36</td></tr><tr><td>GIN3001</td><td>1.41</td><td>1.43</td><td>1.44</td><td>1.44</td><td>1.01</td><td>2.89</td><td>1.28</td><td>1.58</td><td>0.98</td><td>2.30</td><td>0.57</td><td>1.36</td><td>4.71</td><td>1.24</td><td>1.26</td><td>2.69</td><td>1.90</td><td>5.25</td><td>4.77</td><td>1.10</td><td>4.71</td><td>4.61</td><td>4.79</td><td>1.11</td><td>1.04</td><td>1.12</td></tr><tr><td>PMSE (mm)</td><td>2.16</td><td>2.07</td><td>2.10</td><td>2.03</td><td>1.53</td><td>3.62</td><td>2.00</td><td>1.82</td><td>1.49</td><td>3.59</td><td>1.07</td><td>2.60</td><td>6.62</td><td>2.20</td><td>2.65</td><td>4.06</td><td>3.25</td><td>7.35</td><td>6.54</td><td>1.83</td><td>6.62</td><td>6.49</td><td>6.68</td><td>1.53</td><td>1.95</td><td>2.22</td></tr><tr><td>GMF3001</td><td>1.01</td><td>1.03</td><td>1.01</td><td>1.03</td><td>0.98</td><td>0.70</td><td>1.41</td><td>0.64</td><td>1.40</td><td>0.77</td><td>0.95</td><td>1.48</td><td>4.77</td><td>1.43</td><td>1.33</td><td>2.82</td><td>1.80</td><td>4.32</td><td>4.79</td><td>1.02</td><td>4.77</td><td>4.72</td><td>4.80</td><td>1.28</td><td>1.60</td><td>1.43</td></tr><tr><td>LEB3001</td><td>1.24</td><td>2.11</td><td>2.22</td><td>2.07</td><td>1.14</td><td>2.74</td><td>2.10</td><td>1.20</td><td>1.01</td><td>2.43</td><td>0.65</td><td>1.96</td><td>6.26</td><td>1.83</td><td>2.10</td><td>3.43</td><td>2.67</td><td>8.16</td><td>6.23</td><td>2.13</td><td>6.25</td><td>6.16</td><td>6.31</td><td>1.16</td><td>1.54</td><td>1.85</td></tr><tr><td>NGA3001</td><td>2.03</td><td>2.10</td><td>2.04</td><td>2.15</td><td>1.58</td><td>5.14</td><td>1.69</td><td>3.07</td><td>1.18</td><td>4.46</td><td>1.67</td><td>1.25</td><td>4.04</td><td>1.11</td><td>0.87</td><td>2.40</td><td>1.41</td><td>5.38</td><td>4.15</td><td>1.31</td><td>4.04</td><td>3.95</td><td>4.13</td><td>1.01</td><td>1.05</td><td>0.99</td></tr><tr><td>SEN3001</td><td>3.33</td><td>3.24</td><td>3.27</td><td>3.17</td><td>1.59</td><td>4.32</td><td>2.65</td><td>2.02</td><td>1.33</td><td>3.69</td><td>1.15</td><td>2.54</td><td>6.03</td><td>2.27</td><td>2.49</td><td>3.86</td><td>3.14</td><td>6.25</td><td>5.98</td><td>1.88</td><td>6.02</td><td>5.90</td><td>6.10</td><td>1.65</td><td>1.96</td><td>2.18</td></tr><tr><td>SEN4001</td><td>2.61</td><td>2.61</td><td>2.54</td><td>2.53</td><td>2.18</td><td>2.34</td><td>2.40</td><td>2.17</td><td>2.04</td><td>3.43</td><td>1.62</td><td>2.63</td><td>6.48</td><td>2.56</td><td>2.87</td><td>4.03</td><td>3.34</td><td>5.76</td><td>6.38</td><td>2.08</td><td>6.47</td><td>6.35</td><td>6.54</td><td>2.08</td><td>2.44</td><td>2.64</td></tr><tr><td>SLE3002</td><td>0.68</td><td>0.64</td><td>0.69</td><td>0.64</td><td>0.66</td><td>0.69</td><td>1.19</td><td>0.66</td><td>1.21</td><td>1.01</td><td>1.03</td><td>1.57</td><td>4.11</td><td>1.43</td><td>1.05</td><td>2.72</td><td>1.57</td><td>3.51</td><td>4.16</td><td>0.98</td><td>4.11</td><td>4.07</td><td>4.15</td><td>1.14</td><td>1.52</td><td>1.30</td></tr><tr><td>TCD3001</td><td>2.07</td><td>2.07</td><td>1.88</td><td>1.90</td><td>1.39</td><td>1.84</td><td>1.90</td><td>0.33</td><td>1.46</td><td>1.57</td><td>0.90</td><td>2.72</td><td>6.69</td><td>2.42</td><td>2.72</td><td>3.28</td><td>6.12</td><td>6.68</td><td>1.63</td><td>6.68</td><td>6.54</td><td>6.75</td><td>2.18</td><td>2.31</td><td>2.49</td></tr><tr><td>TGC3001</td><td>0.89</td><td>0.87</td><td>0.88</td><td>0.82</td><td>0.75</td><td>1.68</td><td>0.75</td><td>1.29</td><td>0.76</td><td>1.28</td><td>0.71</td><td>0.77</td><td>3.76</td><td>0.81</td><td>0.67</td><td>1.75</td><td>0.90</td><td>5.80</td><td>3.88</td><td>1.52</td><td>3.76</td><td>3.68</td><td>3.95</td><td>0.80</td><td>0.81</td><td>0.80</td></tr><tr><td>mean</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td><td>1.61</td></tr><tr><td>median</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td><td>1.41</td></tr><tr><td>BEN3001</td><td>0.43</td><td>0.44</td><td>0.41</td><td>0.42</td><td>0.50</td><td>0.48</td><td>0.56</td><td>0.57</td><td>0.65</td><td>0.62</td><td>0.76</td><td>0.58</td><td>0.60</td><td>0.62</td><td>0.62</td><td>0.58</td><td>0.66</td><td>0.63</td><td>0.88</td><td>0.62</td><td>0.62</td><td>0.64</td><td>0.76</td><td>0.63</td><td>0.44</td><td>0.95</td></tr><tr><td>BEN4001</td><td>0.03</td><td>0.10</td><td>0.04</td><td>0.11</td><td>0.28</td><td>0.20</td><td>0.43</td><td>0.45</td><td>0.51</td><td>0.49</td><td>0.65</td><td>0.56</td><td>-0.20</td><td>0.56</td><td>0.55</td><td>0.56</td><td>0.59</td><td>0.55</td><td>-0.12</td><td>0.56</td><td>-0.19</td><td>-0.19</td><td>-0.17</td><td>0.53</td><td>0.39</td><td>0.50</td></tr><tr><td>BFA3001</td><td>0.24</td><td>0.24</td><td>0.38</td><td>0.39</td><td>0.50</td><td>0.52</td><td>0.61</td><td>0.61</td><td>0.69</td><td>0.69</td><td>0.75</td><td>0.52</td><td>0.48</td><td>0.56</td><td>0.57</td><td>0.53</td><td>0.52</td><td>0.67</td><td>0.70</td><td>0.70</td><td>0.65</td><td>0.33</td><td>0.34</td><td>0.54</td><td>0.71</td><td>0.58</td></tr><tr><td>CIV3001</td><td>0.53</td><td>0.54</td><td>0.52</td><td>0.54</td><td>0.66</td><td>0.65</td><td>0.58</td><td>0.69</td><td>0.69</td><td>0.60</td><td>0.75</td><td>0.52</td><td>0.48</td><td>0.56</td><td>0.57</td><td>0.53</td><td>0.57</td><td>0.59</td><td>0.85</td><td>0.58</td><td>0.50</td><td>0.52</td><td>0.71</td><td>0.62</td><td>0.53</td><td>0.54</td></tr><tr><td>CIV3002</td><td>0.60</td><td>0.59</td><td>0.59</td><td>0.66</td><td>0.61</td><td>0.78</td><td>0.66</td><td>0.85</td><td>0.81</td><td>0.88</td><td>0.71</td><td>0.68</td><td>0.75</td><td>0.78</td><td>0.72</td><td>0.74</td><td>0.77</td><td>0.81</td><td>0.76</td><td>0.69</td><td>0.70</td><td>0.76</td><td>0.78</td><td>0.66</td><td>0.75</td><td>0.75</td></tr><tr><td>CIV4001</td><td>0.13</td><td>0.15</td><td>0.13</td><td>0.19</td><td>0.35</td><td>0.25</td><td>0.35</td><td>0.53</td><td>0.51</td><td>0.47</td><td>0.68</td><td>0.50</td><td>0.27</td><td>0.55</td><td>0.57</td><td>0.51</td><td>0.61</td><td>0.53</td><td>0.85</td><td>0.57</td><td>0.31</td><td>0.34</td><td>0.64</td><td>0.61</td><td>0.44</td><td>0.48</td></tr><tr><td>CIV4002</td><td>0.44</td><td>0.45</td><td>0.44</td><td>0.47</td><td>0.54</td><td>0.57</td><td>0.54</td><td>0.67</td><td>0.59</td><td>0.63</td><td>0.74</td><td>0.54</td><td>0.55</td><td>0.60</td><td>0.52</td><td>0.55</td><td>0.63</td><td>0.64</td><td>0.89</td><td>0.62</td><td>0.57</td><td>0.59</td><td>0.78</td><td>0.65</td><td>0.52</td><td>0.57</td></tr><tr><td>CMF3001</td><td>0.66</td><td>0.69</td><td>0.64</td><td>0.71</td><td>0.73</td><td>0.80</td><td>0.78</td><td>0.84</td><td>0.82</td><td>0.84</td><td>0.90</td><td>0.69</td><td>0.68</td><td>0.75</td><td>0.76</td><td>0.69</td><td>0.66</td><td>0.80</td><td>0.90</td><td>0.78</td><td>0.70</td><td>0.71</td><td>0.81</td><td>0.84</td><td>0.77</td><td>0.78</td></tr><tr><td>CCD3001</td><td>0.17</td><td>0.18</td><td>0.08</td><td>0.07</td><td>0.17</td><td>0.27</td><td>0.61</td><td>0.23</td><td>0.61</td><td>0.62</td><td>0.61</td><td>0.60</td><td>0.59</td><td>0.60</td><td>0.61</td><td>0.60</td><td>0.59</td><td>0.60</td><td>0.79</td><td>0.60</td><td>0.61</td><td>0.62</td><td>0.69</td><td>0.67</td><td>0.62</td><td>0.62</td></tr><tr><td>GHA3001</td><td>0.17</td><td>0.18</td><td>0.16</td><td>0.19</td><td>0.29</td><td>0.28</td><td>0.51</td><td>0.41</td><td>0.80</td><td>0.64</td><td>0.89</td><td>0.77</td><td>0.40</td><td>0.77</td><td>0.77</td><td>0.77</td><td>0.79</td><td>0.77</td><td>0.77</td><td>0.87</td><td>0.77</td><td>0.42</td><td>0.75</td><td>0.81</td><td>0.70</td><td>0.72</td></tr><tr><td>GHA3002</td><td>0.22</td><td>0.23</td><td>0.28</td><td>0.29</td><td>0.46</td><td>0.52</td><td>0.37</td><td>0.62</td><td>0.54</td><td>0.57</td><td>0.83</td><td>0.44</td><td>0.53</td><td>0.53</td><td>0.53</td><td>0.44</td><td>0.95</td><td>0.58</td><td>0.81</td><td>0.55</td><td>0.56</td><td>0.57</td><td>0.68</td><td>0.67</td><td>0.50</td><td>0.48</td></tr><tr><td>GIN3001</td><td>0.26</td><td>0.26</td><td>0.31</td><td>0.33</td><td>0.43</td><td>0.49</td><td>0.38</td><td>0.60</td><td>0.54</td><td>0.58</td><td>0.84</td><td>0.38</td><td>0.54</td><td>0.52</td><td>0.55</td><td>0.39</td><td>0.53</td><td>0.59</td><td>0.68</td><td>0.52</td><td>0.54</td><td>0.58</td><td>0.68</td><td>0.50</td><td>0.50</td><td>0.45</td></tr><tr><td>LEB3001</td><td>0.30</td><td>0.31</td><td>0.28</td><td>0.23</td><td>0.38</td><td>0.33</td><td>0.47</td><td>0.44</td><td>0.53</td><td>0.52</td><td>0.84</td><td>0.47</td><td>0.33</td><td>0.50</td><td>0.50</td><td>0.47</td><td>0.54</td><td>0.52</td><td>0.47</td><td>0.52</td><td>0.47</td><td>0.33</td><td>0.34</td><td>0.38</td><td>0.31</td><td>0.08</td></tr><tr><td>NEF3001</td><td>-0.08</td><td>-0.17</td><td>-0.04</td><td>0.64</td><td>0.03</td><td>0.03</td><td>0.83</td><td>0.70</td><td>0.47</td><td>0.70</td><td>0.10</td><td>0.90</td><td>0.02</td><td>-0.03</td><td>0.03</td><td>0.02</td><td>0.13</td><td>0.03</td><td>0.55</td><td>0.03</td><td>0.01</td><td>0.03</td><td>0.18</td><td>0.62</td><td>0.18</td><td>-0.06</td></tr><tr><td>NGA3001</td><td>0.33</td><td>0.29</td><td>0.33</td><td>0.32</td><td>0.34</td><td>0.48</td><td>0.40</td><td>0.47</td><td>0.47</td><td>0.60</td><td>0.61</td><td>0.68</td><td>0.44</td><td>0.35</td><td>0.50</td><td>0.54</td><td>0.44</td><td>0.51</td><td>0.54</td><td>0.61</td><td>0.52</td><td>0.36</td><td>0.37</td><td>0.48</td><td>0.68</td><td>0.51</td><td>0.50</td></tr><tr><td>SLE3002</td><td>0.40</td><td>0.43</td><td>0.41</td><td>0.46</td><td>0.42</td><td>0.48</td><td>0.41</td><td>0.67</td><td>0.61</td><td>0.61</td><td>0.73</td><td>0.45</td><td>0.15</td><td>0.50</td><td>0.54</td><td>0.48</td><td>0.54</td><td>0.34</td><td>0.15</td><td>0.16</td><td>0.23</td><td>0.23</td><td>0.52</td><td>0.52</td><td>0.29</td><td>0.53</td><td>0.53</td></tr><tr><td>TCD3001</td><td>0.72</td><td>0.69</td><td>0.64</td><td>0.59</td><td>0.96</td><td>0.59</td><td>0.60</td><td>0.96</td><td>0.59</td><td>0.90</td><td>0.55</td><td>0.83</td><td>0.56</td><td>0.56</td><td>0.55</td><td>0.53</td><td>0.57</td><td>0.95</td><td>0.57</td><td>0.84</td><td>0.85</td><td>0.88</td><td>0.73</td><td>0.63</td><td>0.58</td><td>0.58</td></tr><tr><td>TGC3001</td><td>0.32</td><td>0.34</td><td>0.29</td><td>0.36</td><td>0.42</td><td>0.38</td><td>0.55</td><td>0.60</td><td>0.63</td><td>0.63</td><td>0.58</td><td>0.61</td><td>0.59</td><td>0.59</td><td>0.59</td><td>0.59</td><td>0.59</td><td>0.59</td><td>0.91</td><td>0.59</td><td>0.63</td><td>0.65</td><td>0.85</td><td>0.70</td><td>0.60</td><td>0.60</td><td>0.58</td></tr><tr><td>mean</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td><td>0.37</td></tr><tr><td>median</td><td>0.39</td><td>0.29</td><td>0.39</td><td>0.39</td><td>0.46</td><td>0.49</td><td>0.59</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td><td>0.60</td></tr></tbody></table>
611 Table 7

612 Taylor Diagram Analysis

613 Summary of the qualitative analysis based on Taylor diagrams for model performance across

614 the 20 study sites.

615
# Supplementary figures

## Figure S1

### Taylor diagrams for comparison of our approach versus empirical methods

<figure><img src="image_4.png" /><figcaption>S1(a) Taylor diagram for station BEN3001</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>S1(c) Taylor diagram for station BFA3001</figcaption></figure>

<figure><img src="image_6.png" /></figure>
<figure><img src="image_7.png" /><figcaption>S1(e) Taylor diagram for station CIV3002</figcaption></figure>

<figure><img src="image_8.png" /></figure>
<figure><img src="image_9.png" /><figcaption>S1(g) Taylor diagram for station CIV4002</figcaption></figure>

<figure><img src="image_10.png" /></figure>
<figure><img src="image_11.png" /><figcaption>S1(i) Taylor diagram for station COD3001</figcaption></figure>

<figure><img src="image_12.png" /></figure>
<figure><img src="image_13.png" /><figcaption>S1(k) Taylor diagram for station GHA3002</figcaption></figure>

<figure><img src="image_14.png" /></figure>
<figure><img src="image_15.png" /><figcaption>S1(m) Taylor diagram for station GMB3001</figcaption></figure>

<figure><img src="image_16.png" /></figure>
<figure><img src="image_17.png" /><figcaption>S1(o) Taylor diagram for station NER3001</figcaption></figure>

<figure><img src="image_18.png" /></figure>
<figure><img src="image_19.png" /><figcaption>S1(q) Taylor diagram for station SEN3001</figcaption></figure>

<figure><img src="image_20.png" /></figure>
<figure><img src="image_21.png" /><figcaption>S1(s) Taylor diagram for station SLE3002</figcaption></figure>

<figure><img src="image_22.png" /></figure>
<figure><img src="image_23.png" /><figcaption>S1(u) Taylor diagram for station TGO3001</figcaption></figure>

<figure><img src="image_24.png" /></figure>
<figure><img src="image_25.png" /><figcaption>S1(v) Symbol legend for plotted models</figcaption></figure>
# Supplementary Tables

## Supplementary Table 1

### Summary of Selected Literature on Machine Learning Applications for ET0 Estimation

This table presents a curated selection of recent studies that compare and utilise machine learning methods to estimate reference evapotranspiration (ET0). The literature compilation was achieved through a search for "machine learning ET0 estimation" in Google Scholar for the years 2016-2021. The table collates the most pertinent studies identified in the initial pages of search results, with additional relevant papers supplemented by the authors' further reading.

<table><thead><tr><td>Reference</td><td>Compared machine learning models</td><td>Origin and type of data</td><td>Climate</td><td>Location</td></tr></thead><tbody><tr><td>(Feng et al., 2016)</td><td>extreme learning machine (ELM), neural networks optimized by genetic algorithm (GANN), wavelet neural networks (WNN)</td><td>13 weather stations, 1994-2013 period, daily data</td><td>warm humid</td><td>Central Sichuan, China</td></tr><tr><td>(Gocic et al., 2016)</td><td>ELM</td><td>2 weather stations, 1980-2010 period, daily data</td><td>ND</td><td>Serbia</td></tr><tr><td>(Kisi, 2016)</td><td>least square support vector regression (LSSVR), multivariate adaptive regression splines (MARS), M5Tree</td><td>2 weather stations, 1982-2006 period, monthly data</td><td>mediterranean</td><td>Western Turkey</td></tr><tr><td>(Patil and Deka, 2016)</td><td>ELM, artificial neural networks (ANN), least square support vector machine (LSSVM)</td><td>2 weather stations, 1970-2010 period, weekly data</td><td>arid</td><td>Rajasthan, India</td></tr></tbody></table>
<table><tr><td>(Yassin et al., 2016)</td><td>ANN, gene expression programming (GEP)</td><td>19 weather stations, 1980-2010 period, daily data</td><td>arid</td><td>Saudi Arabia</td></tr><tr><td>(Yin et al., 2017)</td><td>Genetic algorithm support vector machine (GA-SVM), ANN</td><td>1 weather station, 2009-2010 period, daily data</td><td>temperate</td><td>Qilian Mountains, NW China</td></tr><tr><td>(Antonopoulos and Antonopoulos, 2017)</td><td>ANN</td><td>1 weather station, 2009-2013 period, daily data</td><td>mediterranean</td><td>Greece</td></tr><tr><td>(Feng et al., 2017a)</td><td>random forest (RF), generalized regression neural network (GRNN)</td><td>2 weather stations, 2009-2014 period, daily data</td><td>warm humid</td><td>Sichuan, SW China</td></tr><tr><td>(Feng et al., 2017b)</td><td>ELM, GRNN</td><td>6 weather stations, 1961-2014 period, daily data</td><td>warm humid</td><td>Sichuan, SW China</td></tr><tr><td>(Karimi et al., 2017)</td><td>GEP, support vector machine (SVM)</td><td>8 weather stations, 1997-2006 period, daily data</td><td>humid</td><td>South Korea</td></tr><tr><td>(Mehdizadeh et al., 2017)</td><td>GEP, polynomial SVM, radial basis function SVM, MARS</td><td>44 weather stations, 1951-2010 period, monthly data</td><td>arid</td><td>Iran</td></tr><tr><td>(Pandey et al., 2017)</td><td>evolutionary regression (ER), ANN, multi-nonlinear regression (MNLR), SVM</td><td>2 weather stations, 2008-2012 period, daily data</td><td>ND</td><td>Arunacha Pradesh, India</td></tr><tr><td>(Fan et al., 2018)</td><td>RF, M5Tree, gradient boosting decision tree (GBDT), extreme gradient boosting/XGBoost</td><td>8 weather stations, 1961-2010 period, daily data</td><td>various</td><td>China</td></tr></table>
<table><tr><td></td><td>(XGB), SVM, ELM</td><td></td><td></td><td></td></tr><tr><td>(Keshtegar et al., 2018)</td><td>adaptive neuro-fuzzy inference system (ANFIS), M5Tree, ANN</td><td>3 weather stations, 20 year data (period unknown), daily data</td><td>cold arid</td><td>Central Anatolia, Turkey</td></tr><tr><td>(Kisi and Alizamir, 2018)</td><td>wavelet extreme learning machine (WELM), WNN, ANN, online sequential ELM (OS-ELM)</td><td>2 weather stations, 1985-2005 period, daily data</td><td>semi arid</td><td>Central Anatolia, Iran</td></tr><tr><td>(Mehdizadeh, 2018)</td><td>MARS, GEP with lagged ET0</td><td>6 weather stations, 2000-2014 period, daily data</td><td>semi arid, arid, hyper arid</td><td>Iran</td></tr><tr><td>(Zhang et al., 2018)</td><td>SVM, ANN, ANFIS</td><td>9 weather stations, MODIS remote sensing data, 2010-2013 period, daily data</td><td>ND</td><td>Hexi corridor, NW China</td></tr><tr><td>(Ehteram et al., 2019)</td><td>SVM with cuckoo algorithm (SVM-CA), gaussian process regression (GPR), M5Tree, ANFIS</td><td>1 weather station, 1990-2016 period, daily data</td><td>humid</td><td>Himalaya, India</td></tr><tr><td>(Ferreira et al., 2019)</td><td>ANN, SVM</td><td>203 weather stations, 2001-2015 period, daily data</td><td>various</td><td>Brazil</td></tr><tr><td>(Granata, 2019)</td><td>M5Tree, bagging, RF, support vector regression (SVR)</td><td>1 weather station, 2000-2004 period, daily data</td><td>subtropical humid</td><td>Florida, USA</td></tr><tr><td>(Huang et al., 2019)</td><td>gradient boosting with categorical features support/CatBoost (CAT),</td><td>5 weather stations, 2001-2015 period,</td><td>humid</td><td>southern China</td></tr></table>
<table><tr><td></td><td>RF, SVM</td><td>daily data</td><td></td><td></td></tr><tr><td>(Mosavi and Edalatifar, 2019)</td><td>ANFIS, particle swarm optimization (PSO), principal component analysis (PCA)</td><td>2 weather stations, 1981-2011 period, monthly data</td><td>arid</td><td>Iran</td></tr><tr><td>(Nourani et al., 2019)</td><td>feed forward ANN, ANFIS, SVR</td><td>14 weather stations, 1987-2018 period, monthly data</td><td>various</td><td>Turkey, Cyprus, Iran, Iraq, Lybia</td></tr><tr><td>(Reis et al., 2019)</td><td>ANN, ELM, multiple linear regression (MLR)</td><td>5 weather stations, 1996-2016 period, daily data</td><td>warm tropical, dry winter</td><td>Verde Grande Basin, Brazil</td></tr><tr><td>(Wu and Fan 2019)</td><td>multi-layer perceptron (MLP), GRNN, ANFIS, SVM, kernel-based nonlinear extension of Arps decline (KNEA), M5Tree, XGB, MARS</td><td>14 weather stations, 2001-2015 period, daily data</td><td>various</td><td>China</td></tr><tr><td>(Wu et al., 2019)</td><td>ANN, RF, GBDT, XGB, MARS, SVM, ELM, KNEA</td><td>11 weather stations, 2011-2015 period, daily data</td><td>subtropical humid</td><td>Jiangxi province, China</td></tr><tr><td>(Zhang et al. 2019)</td><td>SVM</td><td>5 weather stations, 1990-2014 period, daily data</td><td>ND</td><td>Shaangxi, China</td></tr><tr><td>(Ashrafzadeh et al., 2020)</td><td>seasonal autoregressive integrated moving average (SARIMA), SVM</td><td>4 weather stations, 1993-2014 period, daily data</td><td>ND</td><td>Northern Iran</td></tr><tr><td>(Chia et al., 2020)</td><td>SVM</td><td>4 weather stations 2014-2018 period, daily data</td><td>tropical</td><td>west coast Malaysia</td></tr><tr><td>(Dos Santos</td><td>cubist regression, ANN, SVM,</td><td>23 weather stations,</td><td>various</td><td>MATOPIBA,</td></tr></table>
<table><tr><td>Farias et al., 2020)</td><td>MLR</td><td>2000-2016 period, daily data</td><td></td><td>Brasil</td></tr><tr><td>(Hossein Kazemi et al., 2020)</td><td>GEP</td><td>7 weather stations, 2008-2017 period, daily data</td><td>arid</td><td>Iran</td></tr><tr><td>(Kim et al., 2020)</td><td>RF</td><td>9 weather stations + MODIS remote sensing data + numerical weather prediction data, 2013-2019 period, daily data</td><td>ND</td><td>South Korea</td></tr><tr><td>(Mohammadi and Mehdizadeh, 2020)</td><td>SVR with whale optimization algorithm (WOA)</td><td>3 weather stations, 2000-2014 period, daily data</td><td>semi arid, arid, hyper arid</td><td>Iran</td></tr><tr><td>(Wu et al., 2020)</td><td>Adaptive boosting (ADA), GBDT, XGB, light gradient boosting decision machine (LGB), CAT</td><td>10 weather stations, 1997-2016 period, daily data</td><td>temperate, subtropical and tropical</td><td>eastern monsoon zone, China</td></tr><tr><td>(Yu et al., 2020)</td><td>ANN, SVR, ELM</td><td>1 weather station, 2005-2017 period, daily data</td><td>semiarid, arid</td><td>Xinjiang Uygur, China</td></tr><tr><td>(Zhang et al., 2020)</td><td>CAT, GRNN, RF</td><td>15 weather stations, 1996-2015 period, daily data</td><td>arid, semi-arid</td><td>northern China</td></tr><tr><td>(Adnan et al., 2020)</td><td>ANN, MARS, M5Tree</td><td>2 weather stations, 1968-2015 period, daily data</td><td>mediterranean</td><td>southern Turkey</td></tr></table>
<table><tr><td>(Ayaz et al., 2021)</td><td>LSTM, GBDT, RF, SVR</td><td>2 weather stations, 1965-2015 period, daily data</td><td>hot semi arid, west coast marine climate</td><td>Hyderabad, India, Waipara, New Zealand</td></tr><tr><td>(Bellido-Jiménez et al., 2021)</td><td>MLP, ELM, GRNN, SVM, RF, XGB</td><td>5 weather stations, 2000-2018 period, daily data</td><td>semi arid</td><td>Andalusia, Spain</td></tr><tr><td>(Chia et al., 2021a)</td><td>MLP, SVM, ANFIS, bootstrap aggregating, Bayesian model averaging (BMA), ELM</td><td>4 weather stations, undetermined period, daily data</td><td>ND</td><td>peninsular Malaysia</td></tr><tr><td>(Chia et al., 2021b)</td><td>ELM-PSO hybrid, ELM-moth-flame optimization (MFO) hybrid, ELM-WOA hybrid</td><td>3 weather stations, 2014-2018 period, daily data</td><td>tropical</td><td>Eastern Malaysia</td></tr><tr><td>(Rashid Niaghi et al., 2021)</td><td>GEP, SVM, MLR, RF</td><td>6 weather stations, 2003-2016 period, daily data</td><td>continental</td><td>North Dakota and Minnesota, USA</td></tr><tr><td>(Sattari et al., 2021)</td><td>GPR, SVR, Broyden Fletcher Goldfarb Shanno ANN, LSTM</td><td>1993-2018 period, monthly regional measurements</td><td>arid, semi-arid</td><td>Turkey</td></tr><tr><td>(Wu et al., 2021)</td><td>ELM coupled with K-means clustering and firefly algorithms, ANFIS, RF, M5Tree</td><td>26 weather stations, 1966-2015 period, monthly data</td><td>ND</td><td>Poyang Lake basin, Southern China</td></tr><tr><td>(Yan et al., 2021)</td><td>XGB-WOA</td><td>8 weather stations, 1966-2015 period, daily data</td><td>arid, humid</td><td>China</td></tr></table>
References for supplementary materials

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