KDP estimation

LROSE procedure to estimate KDP from PHIDP

Overview

KDP is estimated from the range derivative of PHIDP, which accumulates along a radar beam as it passes through a precipitating medium. Regions of higher KDP correspond to regions of increased raindrop size and concentration. PHIDP must be pre-processed so that KDP is useful.

The LROSE method for estimating KDP is based on an updated version of the technique developed by Hubbert and Bringi (1995).

Background and Objectives

As a radar beam propagates through a precipitating medium, the electromagnetic wave slows down resulting in a phase shift. In radar volumes where the hydrometeors are not spherical, the phase shifts of the horizontal and vertical pulses are different. PHIDP measures the difference between these phase shifts. However, PHIDP accumulates along the beam, which makes the field difficult to interpret. Calculating the range derivative of PHIDP produces the KDP field, which highlights areas of strong changes in PHIDP.

In order to ensure the KDP field is useful, pre-processing of the PHIDP field is necessary. First, PHIDP is a noisy field. We want to ensure the KDP algorithm identifies regions of substantial change in PHIDP. Second, although phase shifts in Rayleigh-scattering regimes are dominated by changes in the wave propagation speed, Mie-scattering regimes will induce a additional phase shift component related to backscatter differential phase (or phase shift on backscatter). That is, where nonspherical hydrometeors are large compared to the radar wavelength, constructive and destructive interference in the backscattered signal due to resonance can produce local phase shifts that aren't directly related to the liquid water content slowing down the radar beam. Figure 3 of Stepanian et al. (2016) offers a good visualization of Mie-scattering effects. Before KDP is calculated, these two issues need to be accounted for.

The primary objectives of the LROSE KDP computation are:

• smooth the PHIDP profile
• remove local increases in PHIDP caused by backscatter differential phase

Algorithm

(1) unfold PHIDP.

(2) apply a finite impulse response (FIR) filter to unfolded PHIDP, a specified number of times, to create 'smoothed PHIDP'. This step is similar to Hubbert and Bringi (1995), but uses fewer iterations.

(3) for increasing range, identify peaks in 'smoothed PHIDP' which are followed by a minimum. Remove these peaks, by trimming them down to the minimum that follows. We call the result the 'conditioned PHIDP'. This step removes the local increases in PHIDP due to backscatter differential phase.

(4) apply FIR filter to 'conditioned PHIDP' a number of times, to provide further smoothing.

(5) Compute KDP as the (slope of conditioned PHIDP in range) / 2.0.

Notes

For these steps, the user can modify the FIR length and the number of iterations in steps 2 and 4. The number of gates used to calculate KDP are reflectivity-dependent, where the number of gates decreases from 8 to 4 to 2 where reflectivities surpass thresholds of 20 and 35 dBZ.

Self-consistency

One drawback of this method is that it can over-smooth the PHIDP profile and broaden regions of higher KDP to radar gates that are beyond the precipitation causing the phase shift. The self-consistency method attempts to identify regions where high KDP is likely. The algorithm can estimate KDP from Z and ZDR (this estimated KDP will be incorrect and differ from observations). The synthetic KDP is then compared to the measured PHIDP change and is then scaled to match the observed values.

References

Hubbert, J. and V.N. Bringi, 1995: An Iterative Filtering Technique for the Analysis of Copolar Differential Phase and Dual-Frequency Radar Measurements. J. Atmos. Oceanic Technol., 12, 643–648. Link Stepanian, P. M., K. G. Horton, V. M. Melnikov, D. S. Zrnić, and S. A. Gauthreaux Jr., 2016: Dual-polarization radar products for biological applications. Ecosphere, 7, e01539. Link