Metrics to describe NWP scaling behavior of convective rainfall in mountainous regions: parameterization dependency, zero- value problem, and downscaling applications in the Southern Appalachians

Heavy rain events over mountainous terrain present a great challenge for forecasters and are responsible for mountain hazards including flashfloods, landslides and debris flows. Their prediction requires high spatial and temporal resolution and the resolved scales may be strongly influenced by scales unresolved by model or observations. Taking into consideration that the atmospheric fields can be extremely variable over wide ranges of spatial scales, with a scale ratio of 109-1010 between largest (planetary) and smallest (viscous dissipation) scale, but also that there are clear (statistical) regime-dependent scaling relationships among different scales, it is important that these are conserved for numerical modeling sub-grid parameterization and downscaling applications. Here we focus on two critical questions: i) how to handle the presence of large portions zero values associated with thresholding in rain and cloud fields; and ii) the ability of NWP parameterizations to capture and preserve known observed physical scaling relationships at resolved scales and among resolved and unresolved scales. The spatial scaling in observed reflectivity and surface precipitation fields in the Southern Appalachian region is compared against simulated fields generated with the widely used NWP model WRF. The results show that at low wavenumbers the scaling behavior is well represented by the simulations, including the deformations associated with large portions of zeros in the field. However, at the higher wavenumbers the model spectra decay faster than observations, indicating an excess of energy removal by the model's (explicit and implicit) dissipation mechanisms. This behavior is used to define the model's effective resolution, and the effect of the particular choice of physical options and parameterizations on scaling behavior on the range of scales resolved by the model is examined subsequently. The scaling in the initial conditions and the effect of the model spinup on the scaling properties is also explored. Finally, the knowledge on scaling behavior, obtained from observations and model, is used to perform a statistical fractal interpolation downscaling of surface rainfall fields, focusing on extreme rainfall applications.