Assimilation of Simulated Polarimetric Radar Data for a Convective Storm Using the Ensemble Kalman Filter. Part I: Observation Operators for Reflectivity and Polarimetric Variables

Abstract

A radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed. This simulator serves as a test bed for developing and testing forward observation operators of polarimetric radar variables that are needed when directly assimilating these variables into storm-scale numerical weather prediction (NWP) models, using either variational or ensemble-based assimilation methods. The simulator takes as input the results of high-resolution NWP model simulations with ice microphysics and produces simulated polarimetric radar data that may also contain simulated errors. It is developed based on calculations of electromagnetic wave propagation and scattering at the S band of wavelength 10.7 cm in a hydrometeor-containing atmosphere. The T-matrix method is used for the scattering calculation of raindrops and the Rayleigh scattering approximation is applied to snow and hail particles. The polarimetric variables are expressed as functions of the hydrometeor mixing ratios as well as their corresponding drop size distribution parameters and densities. The presence of wet snow and wet hail in the melting layer is accounted for by using a new, relatively simple melting model that defines the water fraction in the melting snow or hail. The effect of varying density due to the melting snow or hail is also included. Vertical cross sections and profiles of the polarimetric variables for a simulated mature multicellular squall-line system and a supercell storm show that polarimetric signatures of the bright band in the stratiform region and those associated with deep convection are well captured by the simulator.

A Balloonborne Particle Size, Imaging, and Velocity Probe for in Situ Microphysical Measurements

“…Several of the observed particles in the PSD are well within the Mie regime of the radar and thus this approach provided too large of an oversimplification. Instead, a T-matrix approach was used (Vivekanandan et al, 1991, Zhang et al, 2001, Jung et al, 2008, Cao et al, 2010, Jung et al, 2010. The T-matrix calculations provide the scattering amplitude at a given radar wavelength for particles of rain, hail, graupel, or snow types for various assumed bulk densities.…”

Low-Level ZDR Signatures in Supercell Forward Flanks: The Role of Size Sorting and Melting of Hail

“…In that case, these bins are simply transferred back to the corresponding bins in the rain distribution; this procedure is done to ensure the emulator treats this portion of the wet graupel and hail spectrum as rain. Thus, our diagnostic water fraction approach differs from that of Jung et al (2008) and JXZ10 by allowing F w,i to vary in a physically consistent manner across the graupel and hail size distributions, instead of assuming a constant F w applied to each bin. The above-mentioned procedure is likewise applied to the large-hail distribution if it is active.…”

A Variational Approach for Retrieving Raindrop Size Distribution from Polarimetric Radar Measurements in the Presence of Attenuation

“…(5), it is expensive to directly compute the transpose of linearized operator H, which is a matrix of partial derivatives of H. In general, an adjoint method is applied to compute H T efficiently without storing the full matrix. The forward operator that can be functionally represented in terms of physical parameters (e.g., Jung et al 2008) facilitates the development of adjoint code (Errico, 1997). In this study, the calculation of radar variables [in Eqs.…”