h 0, v 0
The horizontally polarized pulse will, therefore, be affected by more water than the vertically polarized pulse. Since electromagnetic waves travel more slowly through water than through air, the horizontally polarized wave will travel more slowly through the field of raindrops than will the vertically polarized pulse. This is a two way process -- the backscattered radiation, horizontally polarized, will travel more slowly back to the radar than the vertically-polarized backscatter.
DP, or differential phase, is simply the difference in phase between the horizontally- and vertically- polarized pulses at a given range along the propagation path. Naturally, differential phase will increase with range from the radar, so we can take the range derivative to determine where along the propagation path phase changes are ocurring. This derivative is called the specific differential phase, or KDP. Note the "2" in the denominator appears because there is a phase shift on both the outbound trip and the return trip.
For meteorological echoes, KDP typically ranges from -1°km-1 to 6°km-1
It is important to note that KDP is insensitive to isotropic (spherical) scatterers.. For example, when encountering tumbling hailstones, both the horizontally- and vertically- polarized radar pulses will slow down. Because these hydrometeors are nearly spherical, however, both pulses should change phase at approximately the same rate, so DP and KDP should not change. For this reason, KDP is very helpful in rainfall accumulation estimation, because the amount of rain in a rain-hail mixture can be directly estimated.
Another advantage of using KDP for rainfall accumulation estimation is the fact that KDP is immune to the reduction in reflectivity factor caused by partial beam blockage. The differential phase will shift at the same rate no matter the reflectivity factor, as long as some signal can make it to the scatterers and back.