The depolarization produced by randomly oriented scatterers can be shown to
depend only on the sphericity parameter g (Scott, 1999; Krehbiel and
Scott, 1999), where
Figure 11 shows how g varies with ZDR and . The top graph shows that g is a maximum when the particles are spherical (ZDR= 0 dB) and decreases as the particles depart from sphericity; hence the term sphericity parameter for g. The bottom graph shows how g is related to to for different values of ZDR. For positive, 0 < g< 1. g is unity only in the limiting case when ZDR and are unity. The dashed line in the upper right quadrant of the graph indicates when the two quantities are equal; g is greater or less than depending on ZDR and the particular value of .
An interesting situation occurs if were to ever reverse sign. The terms in the denominator of (34) would then tend to cancel and g would become large and negative. It turns out that this would cause the polarization state to suddenly switch from the top to the bottom half of the Poincaré sphere (or vice versa) and be near the circular polarization pole (Krehbiel and Scott, 1999). Such a sign reversal would occur if . Since is the phase difference of backscattered Hand V signals if the aligned particles were aligned, such a situation would arise only at higher order resonances in the Mie scattering regime or when the particles are highly elongated. Such an effect, if it occurs in nature, would provide a strong signature of randomly oriented particles.