Ensemble Machine Learning Outperforms Empirical Equations for the Ground Heat Flux Estimation with Remote Sensing Data

Estimating evapotranspiration at the field scale is a major component of sustainable water management. Due to the difficulty to assess some major unknowns of the water cycle at that scale, including irrigation amounts, evapotranspiration is often computed as the residual of the instantaneous surface energy budget. One of the Surface Energy Balance components with the largest uncertainties in their quantification over bare soils and sparse vegetation areas is the ground heat flux (G). Over the last decades, the estimation of G with remote sensing (RS) data has been mainly achieved with empirical equations, on the basis of the G and net radiation (Rn) ratio, G/Rn. The G/Rn empirical equations generally require vegetation data (Type I empirical equations), in combination with surface temperature (Ts) and albedo (Type II empirical equations). In this article, we aim to evaluate the estimation of G with RS data. Here, we compared eight G/Rn empirical equations against two types of machine learning (ML) methods: an ensemble ML type, the Random Forest (RF), and the Neural Networks (NN). The comparison of each method was evaluated using a wide range of climate and land cover datasets, including data from Eddy-Covariance towers that extend along the mid-latitude areas that encompass the European and African continents. Our results have shown evidence that the driver of G in bare soils and sparse vegetation areas (Fraction of Vegetation, Fv ≤ 0.25) is Ts, instead of vegetation greenness indexes. On the other hand, the accuracy in the estimation of G with Rn, Ts or Fv decreases in densely vegetated areas (Fv ≥ 0.50). There are no significant differences between the most accurate Type I and II empirical equations. For bare soils and sparse vegetation areas the empirical equation which combines the Leaf Area Index (LAI) and Ts (E7) estimates G best. In densely vegetated areas, an exponential empirical equation based on Fv (E4), shows the best performance. However, ML better estimates G than the empirical equations, independently of the Fv ranges. An RF model with Rn, LAI and Ts as predictor variables shows the best accuracy and performance metrics, outperforming the NN model