Degree of Polarization: Theory and Applications for weather radar at hybrid mode

Abstract

In this work, fully polarimetric data from POLDIRAD (DLR C-band research weather radar) are used to evaluate the degree of polarization of weather radar targets. The degree of polarization can be derived from Wolf’s coherency matrix and, for a given incoherent target, is dependent on the transmit polarization state. However, thanks to unitary transformations, fully polarimetric data allow the retrieval of the degree of polarization corresponding to any desired transmit state. The concept of depolarization response, indicated with p(χ , ψ), is introduced to illustrate this dependency, and computed depolarization response graphs are shown for canonical incoherent scatterers. Canonical incoherent scatterers are constructed as discrete sums of clouds of canonical (coherent) scatterers and are used to illustrate the behaviour of the degree of polarization at different transmit states for both anisotropic and isotropic weather targets. The degree of polarization is then compared with the copolar correlation coefficient, a variable already in use in radar meteorology, in order to assess whether it brings complementary information or not. When rain is illuminated, if the transmit state lies on the circular/slant circle of the Poincare sphere, (the great circle passing through the poles and +/- 45 linear polarization) we experimentally and theoretically show that the degree of polarization performance is very similar to the copolar correlation coefficient and, indeed, the capability of carrying complementary information to the set of variables normally available to dual-pol radars at hybrid is limited. However, exploration of fully polarimetric weather radar data reveal that these variables can differ. Experimental data are shown and possible physical mechanisms explaining these unexpected differences are discussed. Besides cloud microphysics research, the results might be relevant also for operational purposes because planned weather radars are supposed to operate at hybrid mode. Together with the copolar correlation coefficient, the degree of polarization at circular/slant send is naturally available to these radars and the use of the latter might bring additional information essentially at zero cost. For a sound evaluation of the utility of the degree of polarization at circular/slant send, it must not be forgotten that the copolar correlation coefficient measured by hybrid radars differs from the copolar correlation coefficient measured at alternate H/V mode. Since the copolar correlation coefficient used in the present work is collected at alternate H/V transmit mode, further research is needed for a more precise assessment of the potential to bring complementary information.