# KDP estimation

### From Lrose Wiki

LROSE procedure to estimate [math]\displaystyle{ K_{DP} }[/math] from [math]\displaystyle{ \phi_{DP} }[/math]

## Contents

**Overview**

[math]\displaystyle{ K_{DP} }[/math] is estimated from the range derivative of [math]\displaystyle{ \phi_{DP} }[/math], which accumulates along a radar beam as it passes through a precipitating medium. Regions of higher [math]\displaystyle{ K_{DP} }[/math] correspond to regions of increased raindrop size and concentration. [math]\displaystyle{ \phi_{DP} }[/math] must be pre-processed so that [math]\displaystyle{ K_{DP} }[/math] is useful.

The LROSE method for estimating [math]\displaystyle{ K_{DP} }[/math] 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. [math]\displaystyle{ \phi_{DP} }[/math] measures the difference between these phase shifts. However, [math]\displaystyle{ \phi_{DP} }[/math] accumulates along the beam, which makes the field difficult to interpret. Calculating the range derivative of [math]\displaystyle{ \phi_{DP} }[/math] produces the [math]\displaystyle{ K_{DP} }[/math] field, which highlights areas of strong changes in [math]\displaystyle{ \phi_{DP} }[/math].

In order to ensure the KDP field is useful, pre-processing of the [math]\displaystyle{ \phi_{DP} }[/math] field is necessary. First, [math]\displaystyle{ \phi_{DP} }[/math] is a noisy field. We want the [math]\displaystyle{ K_{DP} }[/math] algorithm to identify regions of substantial change in [math]\displaystyle{ \phi_{DP} }[/math]. Second, although phase shifts in Rayleigh-scattering regimes are dominated by changes in the wave propagation speed, Mie-scattering regimes 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. Refer to Figure 3 of Stepanian et al. (2016) for a good visualization of Mie-scattering effects. Before [math]\displaystyle{ K_{DP} }[/math] is calculated, these two issues need to be accounted for.

**The primary objectives of the LROSE [math]\displaystyle{ K_{DP} }[/math] computation are: **

- smooth the [math]\displaystyle{ \phi_{DP} }[/math] profile
- remove local increases in [math]\displaystyle{ \phi_{DP} }[/math] caused by backscatter differential phase

**Algorithm**

(1) unfold [math]\displaystyle{ \phi_{DP} }[/math].

(2) apply a finite impulse response (FIR) filter to unfolded [math]\displaystyle{ \phi_{DP} }[/math], a specified number of times, to create 'smoothed [math]\displaystyle{ \phi_{DP} }[/math]'. This step is similar to Hubbert and Bringi (1995), but uses fewer iterations.

(3) for increasing range, identify peaks in 'smoothed [math]\displaystyle{ \phi_{DP} }[/math]' which are followed by a minimum. Remove these peaks, by trimming them down to the minimum that follows. We call the result the 'conditioned [math]\displaystyle{ \phi_{DP} }[/math]'. This step removes the local increases in [math]\displaystyle{ \phi_{DP} }[/math] due to backscatter differential phase.

(4) apply FIR filter to 'conditioned [math]\displaystyle{ \phi_{DP} }[/math]' a number of times, to provide further smoothing.

(5) Compute [math]\displaystyle{ K_{DP} }[/math] as the (slope of conditioned [math]\displaystyle{ \phi_{DP} }[/math] 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 [math]\displaystyle{ K_{DP} }[/math] 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 [math]\displaystyle{ \phi_{DP} }[/math] profile and broaden regions of higher [math]\displaystyle{ K_{DP} }[/math] to radar gates that are beyond the precipitation causing the phase shift. The self-consistency method attempts to identify regions where high [math]\displaystyle{ K_{DP} }[/math] is likely. The algorithm can estimate [math]\displaystyle{ K_{DP} }[/math] from Z and ZDR (this estimated [math]\displaystyle{ K_{DP} }[/math] will be incorrect and differ from observations). The synthetic [math]\displaystyle{ K_{DP} }[/math] is then compared to the measured [math]\displaystyle{ \phi_{DP} }[/math] 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