Geospatial Foundation Models for Mapping Daily Reference Evapotranspiration in Africa

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Abstract
Timely and accurate estimations of reference evapotranspiration (ETo) are critical for effective water resource management and resilient agriculture planning in data-limited, climate-heterogeneous regions such as Africa. Here, we propose a physics-guided two-stage surrogate modeling framework to enable real-time estimation of daily ETo over Africa using satellite-derived surface solar radiation (Rs) and the TabPFN foundation model. First, a hybrid CNN-Windowed-Attention U-Net architecture was developed and trained using the spectral angle mapper loss to harmonize data from the MODIS Terra and Aqua sensors, thereby improving spatial coverage across Africa. Next, to capture radiative transfer processes, we build a surrogate model emulating MCD18A1.062 Rs from top-of-the-atmosphere reflectance and conditioning variables. Then, ETo was estimated in two ways: a physics-guided approach using surrogate Rs and a direct, end-to-end, data-driven approach. The framework was also evaluated against the widely adopted empirical methods, namely Priestley–Taylor, Makkink, Hargreaves–Samani, and Abtew, calibrated, in turn, against the FAO-56 Penman-Monteith as a reference. For Rs, results demonstrate that the surrogate model accurately reproduces Rs variability, with an RMSE of 2.03 MJ.m⁻².day⁻¹. For ETo, TabPFN improves from an RMSE of 0.93 mm.day⁻¹ in the end-to-end approach to 0.79 mm.day⁻¹ in the two-stage approach, outperforming both classical machine learning models and empirical formulations. Furthermore, continental and regional evaluations across nine IPCC climate regions show improved generalization of TabPFN across diverse hydroclimatic regimes, with RMSE values ranging from 0.26 to 0.91 mm.day⁻¹. In contrast, although they require difficult-to-obtain variables, empirical models exhibit systematic errors and limited adaptability to regional variability, with RMSE ranging from 0.49 to 2.94 mm.day⁻¹. With no reliance on costly ground measurements and being fully based on remotely sensed data, this framework can support timely estimation of irrigation water needs across Africa.

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