Electromagnetic Scattering by Oscillating Rain Drops
of Asymmetric Shapes
Nada J. Sekeljic, Ana B. Manic, Elene Chobanyan, Merhala Thurai, V. N. Bringi, Branislav M. Notaros
Electrical and Computer Engineering Colorado State University
Fort Collins, CO, USA
inadasek@engr.colostate.edu, manic.ana@gmail.com, elene.chobanyan@gmail.com, merhala@engr.colostate.edu,
bringi@engr.colostate.edu, notaros@engr.colostate.edu
Abstract—Computational electromagnetic analysis of scatting
by oscillating rain drops with asymmetric shapes is presented.
Mixed-mode oscillations of drops are attributed to sustained
drop collisions in events having a highly organized line
convection embedded within a larger rain system. The
scattering matrix and differential reflectivity of drops are
dependent on the particular oscillation modes and different
time instants within the oscillation cycle. The results also
demonstrate the superiority of the higher order method of
moments over the conventional discrete dipole approximation
method in oscillating rain drop analysis.
I. INTRODUCTION
Rain drop shapes and their oscillation modes are important
factors affecting earth-space propagation, both in terms of
co-polar attenuation and the induced cross-polarization. The
“most probable” shapes of rain drops conform to those
arising from the axisymmetric (2,0) mode. However, recent
studies using two collocated 2D-video disdrometer (2DVD)
instruments and a C-band polarimetric radar have clearly
shown that in events having a highly organized line
convection embedded within a larger rain system, mixed-
mode oscillations could be inferred within the line, which in
turn is attributed to sustained drop collisions [1]. Inferences
made from the 2DVD camera data showed that a substantial
fraction of drops were undergoing asymmetric mode
oscillations (i.e., their images did not possess a rotational
axis of symmetry), while the radar data showed much higher
than expected differential attenuation within the line.
Hence, it is important to be able to numerically predict
electromagnetic (EM) scattering properties of such
oscillating rain drops with asymmetric shapes. It is then
possible to perform more detailed calculations with
superposition of modes with different oscillation amplitudes
and phases, which can be tied in with radar measurements
over a 2DVD site.
This paper presents analysis of EM scatting of rain drops in
mixed mode oscillations by means of a numerical technique
based on the method of moments (MoM) in the surface
integral equation (SIE) formulation [2], which enables
accurate and efficient scattering matrix calculations of
asymmetric hydrometeors of electrically large sizes.
II. RAIN DROP OSCILLATION MODES
According to [3], oscillation of rain drops can be
characterized via different (n, m) modes and described in a
spherical coordinate system as
) cos( ) ( ) sin( ) , , (
, 0 ,
m P t A r t r
m n m n
, (1)
where r
0
=D/2 is the “mean” radius of the drop, A is the
oscillation amplitude, and P
n,m
(θ) are Legendre polynomials.
Recently, techniques based on the time-variation of the
apparent axis ratio and other image characteristics such as
circumscribed box and projected area have been developed
to identify the three distinct fundamental modes: (i) the
axisymmetric (spherical harmonic n = 2, m = 0) mode, (ii)
the transverse (2,1) mode, and (iii) the horizontal (2,2)
mode. For these modes, Legendre polynomial functions are
) 2 , 2 ( ) , ( sin 3
) 1 , 2 ( ) , ( sin cos 3
) 0 , 2 ( ) , ( ) 1 cos 3 ( 5 . 0
) (
2
2
,
m n
m n
m n
P
m n
. (2)
Fig. 1 depicts the three fundamental modes at two different
times within the oscillation cycle.
Figure 1. Three fundamental rain oscillation modes, for two
phases of the oscillation cycle.
1572 978-1-4799-3540-6/14/$31.00 ©2014 IEEE AP-S 2014