A reduced order modeling approach to represent subgrid-scale hydrological dynamics for regional- and climate-scale land-surface simulations: application in a polygonal tundra landscape
Abstract. Existing land surface models (LSMs) describe physical and biological processes that occur over a wide range of spatial and temporal scales. For example, biogeochemical and hydrological processes responsible for carbon (CO2, CH4) exchanges with the atmosphere range from molecular scale (pore-scale O2 consumption) to tens of kilometer scale (vegetation distribution, river networks). Additionally, many processes within LSMs are nonlinearly coupled (e.g., methane production and soil moisture dynamics), and therefore simple linear upscaling techniques can result in large prediction error. In this paper we applied a particular reduced-order modeling (ROM) technique known as "Proper Orthogonal Decomposition mapping method" that reconstructs temporally-resolved fine-resolution solutions based on coarse-resolution solutions. We applied this technique to four study sites in a polygonal tundra landscape near Barrow, Alaska. Coupled surface-subsurface isothermal simulations were performed for summer months (June–September) at fine (0.25 m) and coarse (8 m) horizontal resolutions. We used simulation results from three summer seasons (1998–2000) to build ROMs of the 4-D soil moisture field for the four study sites individually (single-site) and aggregated (multi-site). The results indicate that the ROM produced a significant computational speedup (> 103) with very small relative approximation error (< 0.1%) for two validation years not used in training the ROM. We also demonstrated that our approach: (1) efficiently corrects for coarse-resolution model bias and (2) can be used for polygonal tundra sites not included in the training dataset with relatively good accuracy (< 1.5% relative error), thereby allowing for the possibility of applying these ROMs across a much larger landscape. This method has the potential to efficiently increase the resolution of land models for coupled climate simulations, allowing LSMs to be used at spatial scales consistent with mechanistic physical process representation.