Using Unsupervised Learning to Determine the Optimal Number of Sub-Grid Tiles in Land Surface Models over the Contiguous United States

Abstract:

An effective, and yet efficient, representation of sub-grid heterogeneity over the land surface in Earth system models remains a persistent challenge. To address this issue, over the past decades, Land Surface Models (LSM) have adopted increasingly complex tiling schemes, including approaches that divide each macroscale grid cell into clusters that statistically represent the sub-grid heterogeneity. However, choosing the optimal number of tiles remains mostly an arbitrary decision that does not ensure the sub-grid heterogeneity is adequately described. To address this persistent challenge, we introduce a physically consistent scheme that uses a Random Forest Model (RFM) to precompute the optimal tile configuration from a set of environmental covariates and target error values in model outputs. This approach is an upgrade from the subjective selection of tiles’ configuration, and it confirms that the procedures used in current tiling schemes need to be refined further.

We assembled and run the HydroBlocks LSM for 64 configurations, over 50 domains of 0.5x0.5-degree resolution in the Contiguous United States (CONUS). The sites compose a geographically distributed set, with varied topographic and climatological characteristics. The tiles’ configuration was defined by two clustering parameters and one height discretization parameter. From these simulations, the spatial standard deviation of specific target fluxes and states were used to evaluate the configurations’ convergence and to fit a RFM to predict the optimal configuration. Our results show that: 1) a reduced-order model effectively reproduces a highly heterogeneous model setup with a significantly lower computational expense; 2) as the number of tiles increases, the fluxes and states converge toward stable conditions; 3) the parameters that drive the large and small scale heterogeneity in the tiling are mostly influenced by the target error values; 4) height binning, which ensures hydrological connectivity between tiles, is mainly defined by climatological and topographic variability; 5) the overall performance for the RFM is satisfactory; however, the accuracy for individual configuration parameters must be improved. The emerging approach provides a path forward to precompute robust tile configuration for use within Earth system models.