Leveraging unsupervised learning for optimizing the number of sub-grid tiles for land surface modeling over the Contiguous United States
Authors: Torres-Rojas Laura , Vergopolan Noemi , Herman Jonathan D. , Chaney Nathaniel W. 
Published: March 2021

&lt;p&gt;The representation of land surface&amp;#8217;s sub-grid heterogeneity in Earth System models remains a persistent challenge. The evolution of grid-cell partitioning techniques has evolved from user-defined equally sized tiles (Chen et al., 1997) to structural partition techniques based on vegetation or soil spatial distribution (Melton &amp; Arora, 2014), and finally, to advanced clustering techniques, based on the concept of Hydrological Response Units (HRU) (Chaney et al., 2018). These sub-grid tiling schemes for Land Surface Models (LSM) have emerged as efficient and effective options to represent sub-grid heterogeneity. However, such approaches rely on an arbitrarily-defined number of tiles per macroscale grid cell with no assurance of a robust representation of heterogeneity. To address this challenge, we introduce a physically coherent approach that uses a Random Forest Model (RFM) to precompute the optimal tile configuration per macro-grid cell. An RFM is trained on a set of environmental covariates, their spatial organization features over the modeling domain (i.e., correlation lengths), and hydrological target-variables errors of several model outputs.&lt;/p&gt;&lt;p&gt;We assemble and run the HydroBlocks LSM for 100 tiles&amp;#8217; configurations for 100 domains of 0.5x0.5-degree resolution in the Contiguous United States (CONUS). The tiles&amp;#8217; configuration is defined by two clustering algorithm parameters and one height discretization one. From this parameter combination, 10,000 simulations emerged. For each simulation, we compiled the spatial standard deviation of specific hydrological target-variables and evaluated the tiles&amp;#8217; configuration convergence by comparing various multi-objective optimization methodologies to determine the optimal compromise solutions on each study domain. Preliminary results show that as the number of tiles increases, the hydrological fluxes and states converge toward stable conditions. With the optimal parameter combination set for each domain and information on the environmental characteristics, an RFM is trained to predict the optimal cluster configuration. Using this approach, we demonstrate how a reduced-order model can effectively compute a priori the appropriate tile complexity based solely on environmental characteristics.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Chaney, N. W. el al. (2018). Harnessing big data to rethink land heterogeneity in Earth system models. Hydrology and Earth System Sciences, 22(6), 3311&amp;#8211;3330. https://doi.org/10.5194/hess-22-3311-2018&lt;/p&gt;&lt;p&gt;Chen, T. H. et al. (1997). Cabauw experimental results from the Project for Intercomparison of Land-Surface Parameterization Schemes. Journal of Climate, 10(6), 1194&amp;#8211;1215. https://doi.org/10.1175/1520-0442(1997)010&lt;1194:CERFTP&gt;2.0.CO;2&lt;/p&gt;&lt;p&gt;Melton, J. R., &amp; Arora, V. K. (2014). Sub-grid scale representation of vegetation in global land surface schemes: implications for estimation of the terrestrial carbon sink. Biogeosciences, 11, 1021&amp;#8211;1036. https://doi.org/10.5194/bg-11-1021-2014&lt;/p&gt;