KOUN Case Study 18-20 October 2002: Heavy rain in southern Oklahoma Author: Kevin Scharfenberg, CIMMS/OU Last Updated: 1 November 2002

Introduction

Radar rainfall accumulation algorithms, such as those employed by the WSR-88D network, relate reflectivity (Z) to rainfall rate (R). Unfortunately, the Z/R relationship is not constant, but depends on drop size distribution. Since drop size distributions cannot be directly measured by radar, the Z/R relationship used is typically an estimate, subject to error. For KOUN, the traditional WSR-88D Z/R relationship of Z = 300 R^1.4 is used.

In addition, rainfall accumulation estimation using a Z algorithm is subject to contamination from hail, radar miscalibration, anomalous propagation, ground clutter, and partial beam blockage. These factors may cause significant overestimation or underestimation of actual rainfall totals.

Polarimetric radars are capable of measuring the difference in propagation constants between horizontally- and vertically- polarized radar pulses over a given range, called the specific differential phase (K_DP). K_DP is directly related to the number concentration of rain drops in the radar volume, meaning there is a direct relationship between K_DP and rain rate.

Rainfall accumulation estimation using a K_DP algorithm is immune to contamination from hail, radar miscalibration, anomalous propagation, ground clutter, and partial beam blockage.

A heavy rainfall event in southern Oklahoma, between 100 and 200 km from the National Severe Storms Laboratory's polarimetric radar (KOUN), occurred between 18 and 20 October 2002. Polarimetric radar data were collected throughout the event without interruption. Rainfall accumulation estimation algorithms were run on the data in real time, and made available to forecasters at the Norman NWS WFO.

Reflectivity (Z) Rainfall Estimation Algorithm

A Z algorithm, corresponding to the Z/R algorithm employed by the WSR-88D, was run as KOUN operated during the 18-20 October 2002 rain event. The estimated storm total precipitation by the Z algorithm, with Oklahoma Mesonet rainfall totals overlaid, is shown in Figure 1 below. The Z algorithm showed a significant overestimation of rainfall totals over much of southern Oklahoma. Several regions of partial beam blockage are also apparent. In these radials, rainfall estimates are reduced below surrounding values because attenuation of the radar radiation has reduced reflectivity values. Reduction of rainfall accumulation estimates due to partial beam blockage is a typical problem for many WSR-88Ds.

A verification chart can be constructed that shows how the algorithm estimation compares to corresponding Oklahoma Mesonet rainfall accumulation reports. This image shows how such verification charts are produced. Mesonet rainfall reports are plotted in the Y direction, while the corresponding radar algorithm estimation is plotted in the X direction. In this example, a Mesonet report of 1.00" total rainfall corresponds to a hypothetical radar algorithm estimate of 3.00". A linear least squares (L.L.S.) "best fit" line can be fitted to the data. If the algorithm estimates match the Mesonet reports exactly, the algorithm's "best fit" line will lie exactly over the "perfect" line. Data points to the left of the "perfect" line represent algorithm underestimates of Mesonet reports, while data points to the right represent algorithm overestimates.

For this event, the verification chart, shown in Figure 2 below, reveals the Z algorithm overestimated the reported rainfall for 24 of the 29 Mesonet reports. The algorithm overestimates became more severe for higher Mesonet rainfall totals.

Specific Differential Phase (KDP) Rainfall Estimation Algorithm

The estimated storm total precipitation by the K_DP algorithm, with Oklahoma Mesonet rainfall totals overlaid, is also shown in Figure 1. This algorithm output a much more reasonable estimation of rainfall totals. Note also that the partial beam blockage problems apparent in the Z estimation image are not present in the K_DP image. The corresponding verification chart, shown in Figure 2, reveals the algorithm matched the Mesonet reports quite well for most observations.

Z Algorithm QPE	KDP Algorithm QPE
Algorithm estimate (in.)

Figure 1: Output of the Z and K_DP QPE algorithms from the KOUN polarimetric radar, and mesonet rainfall total reports, for a 48 period on 18-20 October 2002. Click images for more detail.

Z Algorithm Verification Chart

KDP Algorithm Verification Chart

Figure 2: Verification charts for the Z and K_DP QPE algorithms. Click images for more detail.

Conclusions

A total of four rainfall estimation algorithms are run in real time during KOUN operation. In addition to the Z and K_DP algorithms previously discussed, output from an algorithm using both K_DP and Z_DR (differential reflectivity) data, and an algorithm using both Z and Z_DR data were examined. A composite verification chart compares the "best fit" lines for the output of all four algorithms. Table 1 summarizes the error statistics for all four algorithms.

It is clear that for this case, the algorithms using K_DP data significantly outperformed the algorithms using Z data, particularly in regions of heavy rainfall. In addition, while the Z algorithm showed a bias toward overestimation, the K_DP algorithm showed no consistent bias. Finally, while partial beam blockage hindered the Z algorithm, little corresponding beam blockage was noted in the K_DP algorithm output.

NWS WFO Norman forecasters were able to use these data in real time to determine that traditional Z/R algorithms were significantly overestimating rainfall accumulation near the Red River. "The (K_DP) data matched the Mesonet so well it wasn't necessary to make any significant subjective adjustments, unlike the Z/R products which significantly overestimated amounts," said NWS Norman meteorologist David Andra, who was on duty during the afternoon of 19 October. "I had greater confidence that flooding was not a serious problem."

Table 1: Summary Statistics
Algorithm	Mean Absolute Error	Root Mean Squared Error
Z	1.18"	1.99
Z-ZDR	1.29"	2.20
ZDR-KDP	-0.21"	0.63
KDP	-0.26"	0.61

Related Links

• National Severe Storms Laboratory (NSSL)
• Oklahoma Mesonet
• JPOLE: Joint POLarimetric Experiment
• NSSL Polarimetric Radar Page
• Hondl, K.D., 2002: Current and planned activities for the Warning Decision Support System - Integrated Information (WDSS-II). Preprints, 21st conference on severe local storms, San Antonio, TX, American Meteorological Society, 146-148.
• Zrnic, D.S., A. Ryzhkov, 1996: Advantages of Rain Measurements Using Specific Differential Phase. Journal of Atmospheric and Oceanic Technology, 13, 454-464.

Acknowledgements

This case study would not have been possible without the dedicated work of the scientists who maintain, operate, and collect data from KOUN radar. Thank you!