Full wave electromagnetic approach to the calculation of polarimetric variables for ensembles of rough and nonspheroidal hydrometeors

Full wave electromagnetic approach to the calculation of polarimetric variables for ensembles of rough and nonspheroidal hydrometeors Djordje Mirković*1,3,4, Dušan Zrnić2 and Alexander Ryzhkov1 1National Severe Storm Laboratory, University of Oklahoma CIMMS, Norman OK 2 National Severe Storm Laboratory, NOAA, Norman OK 3 School of Electrical and Computer Engineering, University of Oklahoma, Norman OK 4 School of Electrical Engineering, University of Belgrade, Serbia

1           Introduction

Hydrometeor scattering, until now, has been investigated using simple spheroidal models to represent most of the observed precipitation. These simple models provide satisfying interpretation of reflectivity values from most precipitation observed with the recently upgraded network of polarimetric WSR-88D radars. This upgrade has provided opportunities to   discern large hail, insects, or birds all of which can differ substantially from oblate or prolate bodies.  Thus, researchers are studying ways to quantitatively discriminate between different precipitation types on the basis of the measured differential reflectivity , backscattered differential phase , and correlation coefficient . Therefore, a new demand is set before the polarimetric variable modeling in order to facilitate all of the new capabilities offered. Available spheroidal based modeling procedures have proven to have difficulties quantitatively replicating observed low values of cross-correlation coefficient of wet snow in the melting layer and hail in severe storms, especially in cases when rough hail was observed on the ground.

The aforementioned difficulties of spheroidal models are inherent to the widely accepted T-Matrix method and similar techniques, as they solely rely on spheroidal geometry. Therefore, such approaches are unsuccessful despite the fact that they can account for a set of hydrometeor axis ratios and dielectric properties. In order to overcome these deficiencies as well as other limitations of the existing codes, new ensemble models need to include rough, spiky hail, as previous studies discovered that the low  values are related to the protuberances of the hail surface or to the spike-like protrusions. 2           Proposed approach

The proposed approach relies on using an electromagnetic (EM) solver that uses EM Method of Moments (MoM) software for modeling complex geometries of hydrometeors without any limitations inherent to T-Matrix and other approaches that can be part of larger ensembles. Alleviating T-Matrix limitations regarding the maximum axis ratio of 0.2 for oblate spheroid axis ratio and approximately 5 for prolate spheroids allows for wider variety of hydrometeor shapes as well as more complex ones. These complex geometries as shown in fig. 1 may have protuberances of different ratio of radius and distribution, axis ratio, coating (dry, “wet”(water coated) etc.) spikes etc.

Fig. 1 – Rough hail models of dry 40mm hailstone of axis ratio 0.6 with non-uniform distribution of protuberances up to 14% of radius (left), 80mm water coated (“wet”) hailstone with 0.6 axis ratio and uniform distribution of protuberances up to 10% of radius (right).

           Calculation of the polarimetric variables for scatterer ensembles in the proposed modeling approach is separated into three stages. The first stage is calculation of angle depended scattering coefficients for different types of scatterers (meteorological, biota, etc.) using the WIPL-D software. The WIPL-D software has demonstrated the capability of accurately modeling scattering of simple and complex objects without limitations existing in the currently used tools and can store this data in a scattering library. Creation of the overall scattering library allows limitless options regarding its content including any possible size shape axis ratio etc. of hydrometeors, biota and other scatterers of interest that can be used in ensemble polarimetric modeling.

                Second portion is the ensemble creation part for the purpose of gathering the hydrometeor ensemble with the required statistical properties regarding the size, shape, protrusion type and characteristics, and orientation of the every single hydrometeor particle in the ensemble. Every particle is averaged over the set of user defined orientation, allowing for the possibility of the orientation studies of large and giant hail. These, orientation averaged scattering coefficients, are then used for the calculation of the polarimetric variables.

Final stage of the simulation includes the calculation of the polarimetric variables including reflectivities  , the correlation coefficient , and the backscattered differential phase  for the required size, shape and roughness distribution. We are purposely differentiating this from the statistical properties used in the second part as the purpose of this distribution is to allow for studies of hail size distribution that later on could be extended to include other available parameters such as roughness etc. 3           Conclusion

The proposed modeling architecture proves to be useful in a variety of cases, as it assumes that ensembles are created off of the statistically independent objects. This therefore allows for the characterization of coupling between scatterers in the EM modeling while still treating them as independent statistical elements in the ensemble creation. Furthermore, as the ensemble creation topology is “unaware” of the objects, it allows for the ensembles of non-meteorological scatterers such as insects or birds, ipso facto providing a new tool for the research in this area.

To the best of our knowledge, this is the first application of WIPL-D, and one of the first attempts to use MoM for hydrometeor scattering. As well as the first approach developed on grounds to overcome limitations existing in the current modeling algorithms. We suggest specific topologies, orientations, sizes, distribution and EM properties for the sampled scatterers. Specifically we suggest models of giant hail resembling observations to replicate observations made by weather radars.