Observations of Specific Differential Phase, KDP Chris Collier Acknowledgements: Lindsay Bennett, Alan Blyth and David Dufton

Specific Differential Phase (KDP) ɸ DP, differential phase, is the difference in phase between the horizontally- and vertically- polarized pulses at a given range along the propagation path. 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 occurring. This derivative is called the specific differential phase, or KDP. There is a phase shift on both the outbound trip and the return trip. KDP= ½ ∂ΦDP/∂r (degrees/km) Factor of ½ accounts for two-way propagation. KDP based QPE is very appealing, because of the enhanced KDP value at X band (compared to C and S band) and the insensitivity to absolute calibration errors. KDP based QPE is less sensitive to the path attenuation, drop size distribution (DSD), and radar calibration errors. KDP is proportional to the product of liquid water content and mass-weighted mean axis ratio. KDP can be non-zero even in the presence of small drops. X C S

Derivation of KDP Filtering of PhiDP data is essential to obtain suitable input for further dual-polarisation algorithms. The interative finite impulse (FIR) filter of Hubbert and Bringi (1995) is used. KDP is derived by a least-squares regression of PhiDP over several range gates. The exact number of range gates depends upon the range resolution used.

Removing ground clutter and insects KDP minimizes ground clutter and insects at 0921 on 6 August.

Measuring rainfall using KDP Otherwise use Z : R relationship with a and b set to 200 and 1.6 as per the Marshall-Palmer relation.

Example of rainfall measurement (Dufton et al, 2014) Pre-processing – attenuation correction Raw reflectivity volume scan data was first re-processed using Rainbow’s included dual polarization attenuation correction routine. The correction was undertaken using the ZPHI routine based on the work of Hitschfeld and Bordan (1954), which uses filtered PhiDP to constrain the total path attenuation for each ray before correcting for along path attenuation using the algorithms detailed by Gematronik (2007). Hitschfeld and Bordan (1954Gematronik (2007 Location of observation sites used in this study, including 50m DTM map of the Inny catchment. Grid co-ordinates are UK national grid in metres.

KDP and DBR fields IOP 12 Line of deep convection 5 August 2013

Comparison of X and C-band estimates of rainfall Comparison of ground observations and radar data for the COPE period, where each cross represents a single 15 minute observation at one of the 20 gauging stations. On the left is the comparison for X-Band data, with fitted linear regression (green line). On the right is the comparison for the Network data from the same period, with a fitted linear regression (red line).

Negative values of KDP occurring above positive values IOP The left hand panel shows the distribution of ZDR at 1218 on 5 August 2013, whereas the right hand panel (KDP deg/km) shows a vertical cut along the line convection. Note that negative values of KDP occur above positive values at about 5.5 km altitude. It was suggested by Metcalf (1995) and others that this occurs when hydrometeors have become oriented such that their long axes are approximately in the vertical direction. Ice crystals may assume this vertical orientation when they are subjected to a suitably strong electric field.

Indicating rainfall process from ZDR and KDP KDP is dependent not only on the shape of the target particles, but on their concentration. For example, low ZDR values, say around dB with elsewhere ZDR values approaching say 3 dB indicate that the drops having the larger ZDR values are larger in size than the drops having the lower ZDR values. However where the smaller values of ZDR occur (small drops) there may be higher KDP values, it is because the concentration of the drops is higher. The reason for this is the type of process by which the drops are formed. The drops are most likely formed via a warm rain process, whereas if the opposite is true a cold rain process is involved.

ZDR columns and positive values of KDP occurring next to smaller values of ZDR IOPs 10 and 11

Further work Further work on rainfall amount and flow estimation in the Inny catchment for IOP 12 and others. Using ZDR and KDP to study rainfall processes concentrating on IOP 10 – 12. Comparison of Z, ZDR, ΦDP and KDP with other measurements.