A reduced-order modeling approach to represent subgrid-scale hydrological dynamics for land-surface simulations: application in a polygonal tundra landscape

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 the molecular scale (pore-scale O₂ consumption) to tens of kilometers (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 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 developed four different methods and applied them 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 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 2 validation years not used in training the ROM. We also demonstrate 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 data set with relatively good accuracy (< 1.7% relative error), thereby allowing for the possibility of applying these ROMs across a much larger landscape. By coupling the ROMs constructed at different scales together hierarchically, this method has the potential to efficiently increase the resolution of land models for coupled climate simulations to spatial scales consistent with mechanistic physical process representation.