The development of a nonhydrostatic model and a numerical study of flash flooding in the Ohio Valley.

摘要

This dissertation consists of two parts. In the first part, a nonhydrostatic model has been developed. The use of the semi-implicit scheme has relaxed the constraint of an exceedingly small time step. However, an Elliptic Partial Differential Equation (EPDE) of pressure perturbation is generated after applying the implicit scheme to high frequency waves. For high resolution nonhydrostatic models, a huge sparse matrix of the EPDEs has to be solved. We apply the Multigrid solver, coded by Adams (1998) at NCAR, to solve these EPDEs and to address the performance and efficiency of the Multigrid method.; The Flexible Hybrid Coordinate (FHC) is introduced in the nonhydrostatic model to overcome a constant vertical space interval required in the Multigrid solver. The FHC includes base and deviation functions. FHC is named due to its flexibility as well as its similar features to the (modified) hybrid coordinate after choosing a proper deviation function.; A thermal bubble (Robert 1993), the linear mountain waves (Queney 1948), and a downslope windstorm (Lilly and Klemp 1979) are examined. The model results are in good agreement with the analytical solution and other numerical simulations, and the applied Multigrid solver is very efficient.; In the second part, the Purdue Mesoscale Model (PMM), the new developed nonhydrostatic model, ECMWF analysis, NCDC precipitation data, and NCEP observational data are applied to study two flash floods in the Ohio Valley. Five experiments are performed, and the Ertel's potential vorticity, frontogenesis, stability indexes, and moisture budgets are calculated to identify the major processes of these two flash floods.; The PMM reasonably simulates both flooding cases in terms of synoptic scale features, precipitation amounts, and orientations of precipitation bands. Several similarities and discrepancies between these two cases are summarized. The sensitivity tests show that the Appalachian Mountains can influence the maximum rainfall location. The modification of the soil moisture also affects the precipitation results. The heavy precipitation amount in the 1997 case is significantly improved in fine-gird simulations. The moisture budget analysis shows that the convergence term plays the most important role in the moisture supply to the flood-producing thunderstorms.