Polarimetric Radar Cross Section Modeling of Tornadic Debris

Polarimetric Radar Cross Section Modeling of Tornadic Debris

 

Javier Lujan, Boon Leng Cheong, Caleb Fulton, and Robert Palmer

 

The recent implementation of dual polarization on the US WSR-88D radar network has brought polarimetric weather radar out of the realm of research and into operational status.  These polarimetric systems continue to improve the science of hydrometeor classification and data quality improvement, particularly when weather is in its most extreme.  Tornadic debris, however, often exhibits poorly-understood polarimetric and spectral characteristics on these systems.  For example, negative values of Z_DR have been observed, suggesting the possibility of common alignment within debris; this has yet to be confirmed theoretically or observationally.  More generally, the polarimetric signatures of tornadic debris likely contain information into the underlying centrifuging, wind speed, debris loading/lofting, and damage characteristics. 

To achieve a better understanding of these relationships, a complex radar signal simulator is being developed that couples a large eddy simulation (LES) model with the careful injection of an ensemble of candidate debris types and objects, each of which is subjected to the dynamics of simulated tornados.  To obtain reasonable and realistic polarimetric radar returns, it is necessary to carefully incorporate the polarimetric scattering characteristics of each debris object, taking polarization, rotation, orientation, frequency, geometry, and material properties into account.  To this end, a suite of electromagnetic support tools has been developed to provide this information for a variety of candidate debris types.  The overall process is depicted in the figure.  The radar simulator (SimRadar) computes the Euler rotation angles associated with the relative orientation (a and b) and polarimetric rotation (g) of each object, then interfaces through an RCS data lookup engine indexed according to debris type, and characteristics, and the orientation angles a and b.  The actual polarimetric scattering matrices S_act(a,b) in each object's local coordinate system are then carefully transformed to and from the radar location through a polarimetric basis transformation, with each object's scattering providing a contribution to the resulting I/Q streams. 

Three distinct approaches are used for generating libraries for S_act(a,b), depending on the debris type and purpose of each calculation; these approaches are summarized herein, and will be detailed in the paper. Derivations are used for the scattering characteristics of simple objects like spheres, cylinders, and flat plates by using electromagnetic theory. Small flat shingles, rods and sticks, leaves, etc. can all be approximated by combinations of thin flat sheets and cylinders using physical optics, especially for lossy materials. T-matrix approaches are used for oblate spheroids, approximating clods of dirt. 

 

1.      Second approach: Simulate in FEKO/HFSS

a.       Provides answers for more complex objects (e.g. Japanese rooftile, 2x4s, etc.)

b.      Used to validate theoretical returns and to understand when measurements of poorly known objects are needed.

 

c.       Done to add variety (e.g. complex branch shapes)

d.      Provide support for material properties that are used in (1) and (2)

 

To prove that the modeling of the object's scattering is correct, real measurements of the modeled objects will be acquired using a state of the art anechoic chamber to record and compare them to the modeled scattering. Once the validation of the model with the measurements are concluded the simple objects can be combined to make more complex shapes that could be present in the debris field like leaves and twigs. With the scattering properties of simple objects now defined and stored, the radar simulator can access this and populate the simulated space with debris to run simulations of flying debris.  The chaotic nature of tornadic debris makes its analysis very complicated, but with the radar simulator we can give insight into the dynamics and polarimetric scattering characteristics that still haven't been fully described.

 

It is hypothesized that the impact of debris on polarimetric scattering can be largely attributed to i) specular scattering off of a small number of large objects and ii) strong depolarization effects from a large collection of objects with one primary linear extent (e.g. twigs, stems, grass, and branches) – all of these can be well-approximated using these techniques.  In order to validate these calculations and to model more complex objects,

 

There are also limitations to discuss in the full paper, which can be mentioned here:

1.      Multiple scattering from flying debris is neglected as it adds an enormous amount of complexity for the calculations of the returns and simulations.

2.      Validation of our exact scenario or simulations using real data would prove impossible as controlled simulations will be run.

3.      Different coordinate transformation schemes are used in the radar simulator and in theoretical derivations because of the difference in difficulty when applying them accordingly.