Discovering new Influences on Dispersive Heat Fluxes over Heterogeneous Surfaces with Machine Learning

To better understand and quantify the dynamics of surface thermal heterogeneities and their effect on energy transport in form of dispersive fluxes within the atmospheric boundary layer, we investigate the significance and applicability of the heterogeneity parameter after Margairaz et al. (2020). We aim to overcome this non-dimensional scaling quantity, since it depends on parameters such as the heterogeneity length, scale, and temperature amplitude, which are originally determined for checker-board-type surfaces but may be less suited to describe the complexity of real-world surface structures. To address this goal, we train separate artificial neural networks (ANNs) to predict dispersive sensible and latent heat fluxes for a randomized quadratically shaped heterogeneity distribution, as well as for datasets from the CHEESEHEAD19 campaign representing a real-world complex surface heterogeneity with a broad spectrum of patch sizes and gradual changes in surface characteristics. To investigate the role of the different input variables, we train various ANNs receiving different combinations of variables and compute feature importance weightings afterwards. We scrutinize the role of traditional input variables such as the heterogeneity parameter, temperature or humidity gradients, boundary layer height, and atmospheric stability measures. Further, we consider the incorporation of raw input features, such as horizontal and vertical wind speed, temperatures, and humidities. Finally, we incorporate spatial temperature maps, which we pre-process with a convolutional ANN. We make three core observations. First, the incorporation of raw input features beyond traditional variables improves both the dispersive sensible and latent heat flux diagnosis, suggesting room for improvement in the input variable selection and combination. Second, the inclusion of the spatial temperature map is more meaningful for dispersive latent than for sensible heat flux diagnosis. Third, the heterogeneity parameter after Margairaz et al. (2020) is informative for synthetic randomized quadratically shaped surfaces, but not for real-world complex surface heterogeneity environments, in which case the spatial temperature map processed by a convolutional ANN is most valuable. The results imply that the role of the compressed spatial temperature map should be explored further. We ultimately aim to extract an equation from the neural network characterizing heterogeneous surfaces. Furthermore, the incorporation of the other identified useful raw input features – ideally in form of an equation – needs to be assessed in further depth.