Can the Comparative Use of Multiple Z-R Relationships during Similar Precipitation Events Lead to Improved WSR-88D Rainfall Estimates?

Mark A. Rose and Timothy W. Troutman
NWSO Nashville, TN

ABSTRACT

Because of consistent precipitation underestimation following the passage of several low-topped, heavy precipitation events during the late summer and fall of 1995 across middle Tennessee, approval was obtained from the WSR-88D Operational Support Facility to change the Z-R relationship from the standard Z=300R1.4 to the experimental Z=250R1.2. It was hoped that changing the algorithm would improve precipitation estimates. In early winter, the precipitation algorithm was reset to the original relationship.

Twenty stratiform precipitation events were analyzed at NWSO Nashville, TN between November 28, 1995 and February 28, 1996, ten using each Z-R relationship. The data gathered were analyzed using several methods, and conclusions were then made. Although the average rainfall per station for each event did fall within the average precipitation estimate range using each algorithm, when the experimental algorithm was used, the average observed rainfall was toward the low end of the range. Conversely, when the standard algorithm was used, the average observed rainfall was closer to the high end. But whereas both algorithms overall accurately estimated precipitation, when the cases were analyzed individually, it was discovered that the experimental algorithm allowed for accurate rainfall estimates more often than when the standard algorithm was used.

The primary conclusion made was that since the experimental algorithm did not conclusively improve precipitation estimates, the standard Z-R relationship should continue to be used, although it is important that forecasters identify situations and time periods when correction factors need to be employed. Further comparative studies made during periods if and when the WSR-88D makes consistent questionable rainfall estimates should be conducted in order to properly assess several items, including: 1) what correction factors, if any, should be used and when they should be used, 2) whether the standard algorithm itself is sufficiently reliable during the entire year to warrant its use, and 3) what alternative Z-R relationships, if any, would allow the WSR-88D to estimate precipitation more accurately during certain times of the year.

1. Introduction

The methodology for this study is rather simple. In each of the twenty cases analyzed (See Appendices I and II.), six rain gage sites were used. (At the six sites, eight-inch rain gages are used.) The twenty-four hour (1200 UTC to 1200 UTC) observed rainfall amounts for each station were collected and averaged, and the twenty-four hour WSR-88D precipitation estimate ranges during the same time were determined for each rain gage site and also averaged. The results were then compared in order to determine the estimation errors (if any) incurred by the WSR-88D. Finally, the averages for the ten cases using each algorithm were compiled in order to determine which had performed most accurately.

The purpose of this study is twofold: 1) to establish an improved fall-winter algorithm that can be used during non-convective precipitation events, and 2) to establish a methodology for conducting longer-term studies.

2. Experimental/Standard Z-R Relationship Investigations and Comparisons

During the late fall and early winter, a precipitation algorithm using an experimental Z-R relationship, Z=250R1.2 (as determined by the WSR-88D Operational Support Facility), was implemented in the WSR-88D at NWSO Nashville, TN. Ten subsequent rainfall events were analyzed in which WSR-88D storm total precipitation estimates were compared to observed amounts.

Collectively, the WSR-88D performed quite well in these cases. Since the WSR-88D estimates precipitation as a range between two values, the average range of the precipitation estimates is given. In these cases, the average observed rainfall per station for each event was 0.32 inches, whereas the average range given by the WSR-88D was 0.25-0.49 inches. (See table 1.) Following the tenth precipitation event, the algorithm was changed to the standard Z-R relationship, where Z=300R1.4. Subsequently, an additional ten cases using this relationship were analyzed and compared using the same methodology.

Table 1. Storm total precipitation estimates vs. observed amounts using Z=250R1.2
Storm Total Precipitation Estimates vs. Observed Amounts Using Z=250R1.2
Rain Gage Site Observed Rainfall per Event (inches) WSR-88D Estimated Rainfall per Event Discrepancy
Celina 0.28 0.13-0.40 0
Lewisburg 0.38 0.41-0.67 +0.03
Monterey 0.30 0.19-0.38 0
Murfreesboro 0.23 0.13-0.37 0
Waverly 0.30 0.34-0.58 +0.04
Waynesboro 0.42 0.29-0.56 0

During the investigation using the standard Z-R relationship it was noted that the WSR-88D gave reasonably good estimates again. In these ten cases, the average observed rainfall per station for each event was 0.32 inches. The average range given by the WSR-88D was 0.17-0.39 inches. (See Table 2.) Thus, the average observed rainfall in these cases fell once again within the average range given by the WSR-88D, although toward the high end, whereas in the first ten cases, the average observed rainfall was nearer the low end of the average range given by the WSR-88D.

Table 2. Storm total precipitation estimates vs. observed amounts using standard algorithm
Storm Total Precipitation Estimates vs. Observed Amounts Using Z=300R1.4
Rain Gage Site Observed Rainfall per Event (inches) WSR-88D Estimated Rainfall per Event Discrepancy
Celina 0.40 0.17-0.42 0
Lewisburg 0.34 0.45-0.72 +0.11
Monterey 0.48 0.10-0.34 -0.14
Murfreesboro 0.21 0.07-0.30 0
Waverly 0.37 0.13-0.31 -0.06
Waynesboro 0.10 0.10-0.27 0

Although this analysis is in itself inconclusive when trying to determine the optimal precipitation algorithm, when each algorithm is analyzed case-by-case, the experimental Z-R relationship is shown to have been the better. (See Table 3.) It is interesting that whereas the average rainfall per station for each event was equal for the ten cases in which each algorithm was employed, the corresponding WSR-88D rainfall estimate range shifted somewhat lower when the standard Z-R relationship was employed.

Using six stations in each of ten events, a total of sixty individual cases is available for each relationship. When the experimental algorithm was used, the observed rainfall fell within the estimated range given by the WSR-88D in nearly half of all cases (29), or 48%. Conversely, when the standard algorithm was employed, the WSR-88D gave accurate estimates in approximately one-third of all cases (21), or 35%. Therefore, it is concluded that because the experimental Z-R relationship allowed for a significantly higher frequency of accurate rainfall estimates than the standard, it was the better relationship of the two.

Table 3. Experimental/standard Z-R relationship comparison
Experimental/Standard Z-R Relationship Comparison
Z-R Relationship Observed Rainfall per Station for Each Event (inches) WSR-88D Estimated Rainfall per Site for Each Event Percentage of Cases in which Rainfall Estimates were Accurate
Experimental 0.32 0.25-0.49 48
Standard 0.32 0.17-0.39 35

3. Storm Total Precipitation Estimate Advantages and Disadvantages

The WSR-88D storm total precipitation estimates examined in these twenty cases incurred the normal precipitation estimate advantages and disadvantages. The advantages of radar estimates are that aerial distribution is continuous, and if all the radars are operational, coverage is nearly one hundred percent. Also, the use of bin analyses vice the standard rainfall estimate depictions allow for precipitation estimates at specific locations to be viewed as a single value rather than as a range.

Disadvantages of radar estimates include that they are not ground based, precipitation may be missed between volume scans, and quality control of the estimates using ground truth is required. Also, the existence of a bright band may cause the overestimation of precipitation, since melting snowflakes appear as oversized raindrops.

4. Conclusion

Two cases were presented in which different Z-R relationships were compared using observed and estimated precipitation amounts for six stations across middle Tennessee. Based on the findings, an experimental Z-R relationship improved precipitation estimates.

Although it is difficult to assign a "correct" Z-R relationship to the precipitation estimate algorithm, by using such cases as presented, it is possible to determine an approximate relationship for obtaining optimal estimates. Here, it is apparent that the Z-R relationship Z=250R1.2 was the better in the cases presented for estimating precipitation amounts using the WSR-88D, although the improvement exhibited is not necessarily sufficient to warrant the replacement of the standard Z-R relationship. Conversely, forecasters should recognize those times when correction factors must be used to adjust precipitation estimates in order to improve their accuracy.

Acknowledgements

The authors thank Scott Sharp, Meteorologist, Henry Steigerwaldt, SOO, and Michael Murphy, Hydrologist, NWSO Nashville, TN, for their reviews of this paper. Also, special thanks go to Jessica Thomale, Meteorologist, Algorithm Section, WSR-88D Operational Support Facility, for painstakingly gathering WSR-88D data for use in this paper.

Appendix I.

Summary of Surface Synoptic and 500 mb Conditions Associated with Each Precipitation Event
Event Date Surface Pattern 500 mb Pattern
1 28 Nov 1995 cold frontal passage strong shortwave to the west
2 04 Dec 1995 cold frontal passage shortwave
3 09 Dec 1995 cold frontal passage shortwave
4 13 Dec 1995 stationary front to the north weak shortwave
5 16 Dec 1995 cold frontal passage weak shortwave
6 18 Dec 1995 warm frontal passage ridge
7 19 Dec 1995 approaching cold front low height center to the west
8 20 Dec 1995 cold frontal passage strong shortwave
9 31 Dec 1995 approaching warm front weak ridge
10 01 Jan 1996 inverted trough weak ridge
11 02 Jan 1996 approaching warm front approaching strong shortwave
12 06 Jan 1996 stationary front weak ridge
13 21 Jan 1996 weak trough strong shortwave
14 24 Jan 1996 cold frontal passage strong shortwave
15 27 Jan 1996 cold frontal passage strong shortwave
16 02 Feb 1996 approaching cold front shortwave to the west
17 08 Feb 1996 frontogenesis to the west weak shortwave
18 09 Feb 1996 cold frontal passage shortwave
19 16 Feb 1996 trough strong shortwave
20 28 Feb 1996 cold frontal passage weak shortwave

Appendix II.

Case-by-Case Analysis of Z-R Relationship Study:Observed Rainfall (in inches) vs. WSR-88D Estimated Rainfall Range
Part A. Experimental Algorithm
  Celina Lewisburg Monterey Murfreesboro Waverly Waynesboro
Case Date Obs Est Obs Est Obs Est Obs Est Obs Est Obs Est
1 112895 .24 .01-.3 0 .01-.3 .05 0 0 .01-.3 0 0 .07 .01-.3
2 120495 .38 .01-.3 .26 .01-.3 .56 .01-.3 .25 .01-.3 0.25 .01-.3 0 .01-.3
3 120995 .16 .01-.3 .50 .31-.6 .11 .01-.3 .24 .31-.6 0.15 .31-.6 0 .31-.6
4 121395 .06 0 0 0 .01 0 .04 0 0 0 0 0
5 121695 .44 .31-.6 .64 1.51-2 .38 .31-.6 .54 .31-.6 0.41 .31-.6 .65 .61-1
6 121895 .40 .31-.6 .65 .61-1 .30 .01-.3 0 .01-.3 1.13 .61-1 1.10 1-1.5
7 121995 .46 .01-.3 1.00 .61-1 .67 .01-.3 .65 .01-.3 .32 .01-.3 .58 .31-.6
8 122095 .26 .01-.3 0 0 .29 0 .11 .01-.3 0 0 .06 0
9 123195 0 .01-.3 0 0 .14 0 .08 0 0 .61-1 1.10 .01-.3
10 010196 .36 .61-1 .74 1-1.5 .50 1.51-2 .38 .61-1 .73 1.51-2 .63 .61-1
Part B. Standard Algorithm
  Celina Lewisburg Monterey Murfreesboro Waverly Waynesboro
Case Date Obs Est Obs Est Obs Est Obs Est Obs Est Obs Est
11 010296 .69 .31-.6 .97 1.51-2 .50 .31-.6 0 .31-.6 .59 .31-.6 .05 .01-.3
12 010696 .30 .01-.3 .47 .31-.6 .34 .01-.3 0 .01-.3 .16 .01-.3 .05 .01-.3
13 012196 0 0 0 .01-.3 0 0 0 .01-.3 0 0 0 0
14 012496 .79 .31-.6 .65 .31-.6 1.17 .61-1 .56 .01-.3 1.38 .61-1 0 .31-.6
15 012796 0 .01-.3 .51 .01-.3 .45 .01-.3 .31 .01-.3 0.47 .01-.3 0 .31-.6
16 020296 .60 .01-.3 0 2-2.5 .49 .01-.3 .34 .01-.3 .04 .01-.3 0 .01-.3
17 020896 .32 .01-.3 .02 0 .49 .01-.3 .07 .01-.3 .15 0 0 0
18 020996 .15 .01-.3 0 .01-.3 .50 .01-.3 0 0 0 0 0 0
19 021696 0 0 .14 0 .06 0 .20 0 .27 0 0 0
20 022896 1.11 1-1.5 .66 .31-.6 .83 .01-.3 .66 .31-.6 .64 .31-.6 .85 .31-.6

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