Space-time covariance: An effective tool to evaluate the simulated spatiotemporal patterns in land surface models

Space-time patterns of surface fluxes and states have direct implications for boundary layer growth, cloud development, phenology, and runoff generation, among other processes. Emerging field-scale resolving land surface models (the terrestrial component of Earth system models), such as HydroBlocks, aim to represent this complexity by modeling the water, energy, and biogeochemical cycles at meter-km spatial scales over continental extents. Although there have been significant advances in the representation of heterogeneity in land surface modeling over the past decade, there has yet to be a concerted effort to evaluate the realism of the simulated time-evolving field-scale spatial patterns; this, in part, is due to the challenge of how to interpret the space-time fields. Empirical space-time covariance presents a unique solution; it can robustly summarize the space-time structure of a given flux or state for a given area (e.g., watershed) via a simple 2D surface (e.g., Figure 1). In this presentation, we will demonstrate how space-time covariance provides an effective and efficient approach to facilitate evaluation of the simulated spatiotemporal patterns.

            As a proof of concept, the simulated spatiotemporal patterns of land surface temperature (LST) of a HydroBlocks model simulation over the central United States are evaluated using observations from satellite remote sensing (GOES-16/17). First, for each 0.25 arcdegree grid cell over the study domain, the empirical spatiotemporal covariance functions (ESTCFs) are assembled for HydroBlocks (simulation) on one side and GOES (observation) on another. For this case, each ESTCF is calculated from hourly data for clear-sky pixels during the summers of 2017-2022. The ESTCFs are then initially compared via simple metrics (e.g., RMSE). To ease understanding, a space-time parametric covariance function is then fit to each ESTCF; the comparison of the parameters (e.g., spatial correlation length) provides a richer understanding of the strengths and weaknesses of the model. The resulting analysis illustrates how space-time covariance can efficiently summarize the complex simulated spatiotemporal patterns and thus serve as a useful metric to both evaluate and inform model development to improve process representation.