Recent development in physically-based upscaling of snow process modeling for time-dependent sub-grid variability
Abstract
It is well-recognized that seasonal snow plays an important role in land surface modeling while the sub-grid variability of snow tends to be ignored. This presentation will explore the Fokker-Planck Equation (FPE) method, one of the most promising modeling approaches for stochastic system modeling. The model concept was mainly tested by the high-resolution snow surveys by airborne Lidar over two mountainous regions in southwestern Wyoming, Snowy Range and Laramie Range. We analyzed the snow depth distributions in 284 sub-areas (1km x 1km) using the geospatial statistics including variogram, and probability density function (PDF). While spatial variability of snow depth is highly dependent on land cover type at the 1 km scale, PDFs of snow depth within the sub-areas found to be Gaussian distributions if sufficient snow presents. Snow redistribution and snowmelt made them non-Gaussian distributions as no-snow areas increase. These analyses were useful to characterize the sub-grid variability of snow depth and to select the factors that need to be considered in large scale snow modeling. Accordingly, the FPE model was formulated to model sub-grid variability for snow process from the point-scale process-based governing equations. This FPE describes the evolution of the PDF of snow depth within a finite area. We chose snow depth as a random state variable while snow redistribution and snowmelt rate as the sources of stochasticity. The time-space covariances of snowmelt rate were externally evaluated by an independent distributed snow model for proof of the concept, and the ones of snow redistribution were estimated from the topography and wind. The FPE model was applied to the No-name experimental watershed in Snowy Range, where one weather and snow monitoring system situates. It was shown that the point-observed snow depth fell within the simulated envelope (within one sigma) during most of the two-year study period. The simulated PDFs of snow depth within the study area were comparable to the observed PDFs of snow depth by GPR and Lidar. Despite a number of unexplored challenges of the relatively new stochastic modeling method, with an additional diffusivity of the PDF, the proposed FPE model is capable to express the sub-grid variability of snow depth based on the process-based knowledge.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.C43C..05O
- Keywords:
-
- 0736 Snow;
- CRYOSPHERE;
- 0740 Snowmelt;
- CRYOSPHERE;
- 0798 Modeling;
- CRYOSPHERE