Dissertation Information

Title: Comparing Finite-Difference and Continuous Galerkin Numerical Methods for Snowfall Prediction in Complex Terrain

Program: Computing Ph.D. Computational Math Science and Engineering emphasis

Advisor: Dr. Michal Kopera

Committee Members: Dr. H. P. Marshalls, Dr. Lejo Flores, Dr. Simone Marras

Abstract: Forecasting snowfall in complex terrain poses an important challenge for numerical weather prediction models, as the interplay among topography, atmospheric dynamics, and cloud microphysics leads to significant uncertainties in predictions, with serious societal consequences, including disruptions to infrastructure, transportation, and public safety.

This proposal seeks to investigate the impact of parametric uncertainties, numerical discretization errors, and boundary layer turbulence on inaccuracies in orographic snowfall forecasts through three methodologies: Conduct a sensitivity analysis of 24 WRF simulations for the February 2023 snowfall event in Portland, Oregon, by varying initial and boundary conditions (CFSRv2, ERA5, GFS) and microphysics schemes (Thompson, WSM6, WDM6, WSM7, Morrison, Milbrandt, NSSL, Goddard) to assess their relative impacts.  Isolate the effects of numerical discretization through two idealized two-dimensional test cases—a moist cold thermal bubble and flow over a Gaussian bell-shaped mountain using identical microphysics (WSM6 in WRF; SAM in JExpresso) to allow direct comparisons between finite-difference methods in WRF and high-order continuous Galerkin (CG) spectral element methods in JExpresso.  Conduct three-dimensional large eddy simulations (approximately 40 m resolution) of the atmospheric boundary layer over flat terrain and a 1 km Alpine ridge utilizing JExpresso to accurately capture explicit turbulence, mountain wave breaking, and surface drag.

Together, these three components of my dissertation establish a comprehensive framework for analyzing the sources of error in mountain snowfall forecasts. This comprehensive approach would enhance atmospheric modeling by integrating real-world sensitivity analyses, idealized benchmarks, and high-resolution large eddy simulations to inform the implementation of next-generation numerical techniques for more accurate winter storm forecasting.