Specific Differential Phase (KDP) Primer

Specific Differential Phase (KDP): The difference between propagation constants for horizontally- and vertically- polarized radar pulses over a given range.
DP(r2) - DP(r1)
KDP
---------------------------
    [°km-1]
2 (r2 - r1)
DP h - v    [°]

h    0,     v    0


where:
h is the phase of the horizontally-polarized pulse at a given point in the propagation path,
v is the phase of the vertically-polarized pulse at the same point in the propagation path,
and:
r1 and r2 refer to measurements at range 1 and range 2 from the radar [km], where r1 < r2

To understand the above equations, consider two consecutive radar pulses that travel the same propagation path. The first pulse is horizontally polarized, the second is vertically polarized. Along the propagation path is a uniform field of falling raindrops. As discussed earlier, falling raindrops are oblate, so the electric field will encounter more water content in the horizontal direction than in the vertical.

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

  • Values of KDP greater than zero indicate that DP has increased over the range of interest (r2-r1). Since h and v are always 0, that means the phase of the horizontally-polarized pulse has gotten larger more rapidly than the phase of the vertically-polarized pulse. In other words, the horizontally-polarized pulse has slowed down more than the vertically-polarized pulse over the given range. This means there is more hydrometeor content in the horizontal plane, e.g., oblate hydrometeors.
  • Likewise, values of KDP below zero indicate vertically oriented hydrometeors are present in the range of interest.
  • Values of KDP near zero indicate nearly isotropic (spherical) hydrometeors are present.

    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.

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