July 1995


A Comparison of NEXRAD Precipitation Estimates to Real-Time Data


Jonathan P. Racy
Monique L. Kopsky



Wording of text throughout the paper.
The data on the graphic reading for Figures 3 and 5.



A Comparison of NEXRAD Precipitation Estimates to Real-Time Data

Jonathan P. Racy and Monique L. Kopsky
National Weather Service Office
Fort Wayne, Indiana




A brief study was conducted to compare WSR-88D precipitation estimates with real-time data. The study was done during September to December 1993.

A four-month case study was conducted to compare the Indianapolis National Weather Service Forecast Office (NWSFO) WSR-88D precipitation estimates with real-time data. The real-time data consisted of rainfall reports from the Fort Wayne Flood Alert System (FWFAS) across northeast Indiana and northwest Ohio. This data was then compared with precipitation estimates from Indianapolis' WSR-88D. Seven cases were obtained that included three cumuliform events, one mixed stratiform/cumuliform event, and three stratiform events. The results of the comparisons for each type of event are detailed in what follows. Also discussed are how radar characteristics, atmospheric conditions, and the distance from the radar to the target affected the WSR-88D precipitation estimates. To conclude, a discussion is presented on the future of the project and desired goals.


Three main systems were used for obtaining the data needed in this project: the Indianapolis NWSFO WSR-88D, FWFAS, and cooperative observer rainfall reports, including the official NWSO Fort Wayne's rain guage.

The WSR-88D utilized the One-Hour Precipitation, Three-Hour Precipitation, and Storm Total Precipitation products. A variety of map backgrounds were used to depict precipitation totals.

Eleven tipping-bucket rain guages linked to a battery powered radio transmitter characterized FWFAS. These guages were scattered across northeast Indiana and northwest Ohio (Figure 1). For the 0.04 inches of water, or its water equivalent, the measuring "bucket" tips to initiate a radio message. This message consists of the precipitation report and where the guage is located. Further description of the FWFAS can be found in Shipe et al. (1985). In addition, data was extracted from the official rain guage at NWSO Fort Wayne.

Finally, use was made of amateur radio reports. Amateur radio operators have access to NWS rain guages and report 24-hour rainfall daily at 1200 UTC. This data is then transmitted to NWSO's via the Automation of Field Operation and Services (AFOS).

The data for this study was collected for four months, from September to December 1993. A summary of the various types of storm scenarios and the exact dates in which they were collected is in Table 1.

Figure 1. Map of the FWFAS gage locations in Northeast Indiana and Extreme Northwest Ohio.


Events collected from September to December 1993.
(The asterisk denotes events highlighted in this paper.)
Cumuliform* September 2, 3 Showers and Thunderstorms
Cumuliform October 16 Showers and Thunderstorms
Cumuliform October 17 Low-topped Convection
*Mixed Cumuliform/
September 25 Showers going into rain
Stratiform* November 3 Light rain
Stratiform December 3, 4 Light rain

As each scenario unfolded, data was continuously collected and archived by the FWFAS system and the Indianapolis WSR-88D. Since the FWFAS and WSR-88D allow the user to request data for a specific period, it was quite simple to obtain identical time frames for comparison.

The data collection process was straightforward. Before a significant precipitation event, a member of the Fort Wayne office would notify the Indianapolis staff and request that the WSR-88D precipitation estimates be archived during an event.

When the precipitation event had ended, we began to collect data from several different sources. First, we retrieved the precipitation data collected by the FWFAS. We then examined the data and determined the period in which we wanted to compare WSR-88D precipitation estimates to the real-time data. A hard copy was then sent to us in the mail. Additionally, the official NWSO Fort Wayne rain gauge charts were copied, and used for comparison. Occasionally, we also used 24-hour precipitation reports from the cooperative observer network as another source of data.


As stated previously, the precipitation products that the WSR-88D provides are presented as one-hour, three-hour and storm total estimates, all part of the Precipitation Process System (PPS). This section discusses the steps that the WSR-88D follows to generaste the precipitation output.

Initially, the WSR-88D performs a "Hybrid Scan", which involves measuring the reflectivity from four elevation angles. These are 0.5, 1.5, 2.5 and 3.5 degrees. The sources of error in this data collection process are numerous. Therefore, the algorithm does extensive tests and corrections on the data.

A quality control check of the reflectivity data is done. In a city or within hilly terrain, the radar beam can be blocked partially or completely. Therefore, to compensate the WSR-88D computes a correction. If over 60 percent of a bin (a three-dimensional sampling of the atmosphere via the radar) is blocked, then that bin is considered "totally blocked". This blockage problem occurs often in the lowest tilt of the Hybrid Scan (i.e., 0.5 degrees). If the blockage is caused by too much ground clutter at a certain level, then that tilt is simply excluded from the Hybrid Scan.

The next step is the conversion of the reflectivity into a rainfall rate estimate using the Z-R relationship. The following equations were taken from Ahnert et al. (1983).


Z = 300*R1.4

"Z" represents the equivalent reflectivity and "R" represents the rainfall rate. The Z-R coefficient used frequently is "300". However, this coefficient is adjusted according to the precipitation type and/or season. It can vary from 140 for drizzle to 84,000 for hail.

The WSR-88D then averages two adjacent 1 degree by 1 kilometer radar bins along the same radial out to 230 km to come up with values for the 1 degree by 2 kilometer average precipitation rate scan. This value is then converted to the nearest 0.5 dBR through the following equation:

1 dBR = 1- log [R/(1 mm/hr)].

A time continuity test is then conducted on the processed data. Each new precipitation scan is compared to the last good scan for continuity. The radar checks for any sudden or unreasonable echo development or dissipation. If any strange anomalies are found, the scan is rejected and a new scan begins.

As the radar beam travels further and further from the radar, the area of each horizontal bin increases. Thus, the averaging of precipitation rates is done over increasingly larger areas at further distances. This radar characteristic is called "the range effect", and is innate in all radars. Theoretically, the WSR-88D has a correction equation for this problem. However, most WSR-88D's currently perform under the assumption that the Hybrid Scan is accurate enough and therefore do not use the range effect correction.

The range effect correction is executed through the following equation:


R1(mm/hr) = a[R(mm/hr) b*r c].

"R1" represents the corrected rainfall rate and " R" is the original rainfall rate. The range is signified by "r", while the coefficients that have to be derived for the individual radar are "a", "b", and "c". The derivation of these coefficients entails extensive research of each radar site.

After each new scan is processed, hourly precipitation accumulations are recomputed and updated using the new scan. This data is then used in the generation of the one-hour and the three-hour precipitation estimates and is also used to update the storm total product. However, problems arise when more than ten minutes have passed without the processing of a new scan. Reasons for this lapse of time could possibly be due to system malfunction or temporary system shutdown. When this occurs, the hourly accumulation product is not generated due to lack of time continuity. This will affect the one-hour and the three-hour products, but not the storm total estimates.

A final correction involves comparison of the WSR-88D estimated precipitation values to real-time data. In the future, the WSR-88D will compare its estimates to hourly precipitation measured in rain guages and then attempt to correct any errors. However, there are several problems with comparing these two types of data.

The only step remaining is the actual generation of the visual product. The polar coordinates used by the radar are converted to a gridded format to produce the maps. This is achieved by using two different methods. First, the method of conversion is 2 kilometers by 2 kilometers grids. This gives the one-hour, the three-hour and the storm total maps. These maps are color graphics using 16 different colors to show intensity. The pixel resolution is 640 by 512. The user can choose from several map backgrounds, recenter the product, zoom into an area, and produce a time lapse display. The second type of conversion is 4 kilometers by 4 kilometers grids. This map is used mainly by the River Forecast Centers (RFC) and by water management specialists (Rohrbach 1994).


In comparing the data, this paper will be limited to discussing one case in each of the three types of events, as shown in Table 1. Some extremely interesting features occurred during each case. All conclusions are preliminary.

Figure 2 shows WSR-88D precipitation estimates for the September 2 and 3 event. This is a three-hour precipitation estimate (TSP). Plotted on the photograph are some corresponding FWFAS rainfall data.

Figure 2. Three-hour precipitation total ending at 2019 UTC, 2 September 1993, from the WSR-88D located in Indianapolis, Indiana. This example is cumuliform in nature.

Here, the WSR-88D depicted the precipitation well, showing the greatest accumulated precipitation in a corridor extending from southwest to northeast across Allen County. Notice, however, that the precipitation estimate is displaced to the west when comparing with the rain guages. The 1.5 inch radar estimated amounts were located mainly in eastern Huntington County, while Smith Field, in northwestern Allen County, reported 1.54 inches. Elsewhere, the radar estimates are representative of actual rainfall amounts.

As Rolinski (1992) described, it is difficult to make any fine detailed comparisons between the precipitation estimates and actual measurements because of the resolution levels associated with the precipitation products. Each data level is incremented every 0.5 inches.

Late September offered an intriguing episode which was captured by the WSR-88D. Figures 3 and 4 show storm total precipitation estimates. Figure 3 includes the precipitation for the first half of the event while Figure 4 depicts the total storm precipitation.

Figure 3. Storm total precipitation ending at 1815 UTC, 25 September 1993, from the WSR-88D site in Indianapolis, Indiana. Precipitation is convective in nature.

Figure 4. Same as in Figure 3 except total is for period ending at 0235 UTC 26 September 1993. This includes totals found in Figure 3. Mostly stratiform rain is depicted here.

A cold front was moving east through the northern sections of Indiana, resulting in scattered convection during the late morning and early afternoon of September 25. Although coverage of the showers was sparse and amounts were light, the WSR-88D did very well with precipitation amounts in Figure 3. Notice the guage located along the Ohio border with a higher amount and the corresponding gradient in precipitation estimate of the WSR-88D just to its south.

The cold front became stationary that afternoon along Interstate-70, at the bottom of the photograph. That evening, warm air flowing north from the Gulf of Mexico was forced isentropically over the cooler air over northern Indiana resulting in a significant overrunning pattern. Consequently, a large shield of light rain evolved with tops around 10,000 feet. Notice, in Figure 4 the precipitation estimates show a significant error when compared with real-time data. Even at the guage, located south along the Indiana-Ohio border, one-inch amounts were common with WSR-88D estimating less than one inch. Meanwhile, convection along and south of the front in central Indiana and southwest Ohio, showed up very well with greater than or equal to one inch amount. The most probable cause of the underestimated precipitation in the last half of the day is due to the height of the radar beam. This issue will be discussed during the next section.

Stratiform precipitation events are the most difficult for the WSR-88D precipitation algorithm. Again, the main problem was that stratiform events tended to have low altitude echo tops and thus, the radar beam often "overshot" the precipitation beyond a certain distance. The result was that the precipitation algorithm would underestimate rainfall amounts.

Figure 5, depicting storm total precipitation, is a classic example of what can result when the radar beam overshoots stratiform precipitation. Notice that many reporting stations had over 0.10 inches, while the estimation from the WSR-88D showed that no precipitation had fallen. In Table 2, the manually coded weather radar observations from the WSR-74C, located in Fort Wayne, are presented. According to the observations, echo tops during the event were under 10,000 feet.

Figure 5. Storm total precipitation ending at 1202 UTC, 3 November 1993, from the WSR-88D in Indianapolis, Indiana. The precipitation is stratiform in nature.


Excerpts from the MF7-60's for the WSR-74C located in Fort Wayne, Indiana.
The stratiform event was on November 3, 1993.

  |FWA 0545 AREA 6R-/NC 357/55 169/70 100W A2315 MT U90
  ^JL1 KL111 KL11111 ML1111 NL1111 OM111=

  |FWA 0643 AREA 6R-/NC 42/60 215/60 90W A2320 MT U100
  ^JM11 KL1111 LL1111 MK111111 NL1111 OM11=

  |FWA 0737 AREA 6R-/NC 314/140 129/70 100W A2320 MT U100
  ^JM11 KL1111 LL1111 ML11111 NL11111 ON1=

  |FWA 1037 AREA 6R-/NC 73/55 192/45 70W A2520 MT U80
  ^KN11 LN111 MM1111 NN11 ON1=


Figure 6 shows a polar coordinate grid from the Indianapolis WSR-88D, centered over northeast Indiana and northwest Ohio. This grid depicts the height of the radar beam given standard atmospheric conditions. As shown, the radar beam is located 10,000 feet above the ground at 80 nautical miles from the radar antenna.

Figure 6. Map of polar coordinates from the WSR-88D in Indianapolis, Indiana. This is used to denote the height of the radar beam under standard atmospheric conditions.

Figure 7 gives a graphical view of the range-radar beam altitude for different elevation angles. Table 3 explains the height of a radar beam above the ground given a certain distance. According to Batton (1973), the height above the ground is found by the following formula:

H = 1/2*[(S^2)/R(p)]

where "H" represents the height of the radar beam above the ground, R(p) represents 4/3 the radius of the Earth, and "S" is equal to the horizontal distance from the radar antenna. The values are assuming the radar beam is pointed horizontally at zero degree elevation. From Figure 5, it can be seen that the radar was unable to detect any precipitation beyond 80 nautical miles, correlating well with the findings shown in Figures 6 and 7.

Figure 7. The Range-Radar Beam Altitude Nomogram from FMH-11.


The following is a list of radar beam heights above the ground given a certain horizontal distance from the radar antenna. *This assumes that radar beam is at 0 degrees elevation and pointed horizontally.


H = 1/2*((s^2)/r>(p))

The variable "H" is the altitude of a radar beam above the ground neglecting index of refraction; "s" is the horizontal distance from the radar antenna and r(p) is approximately 1.3 times the Earth's radius.


s(miles)s(feet)r(p)(feet) *H(feet)
0 0 20850671.36 0
25 132000 20850671.36 321.406363653
50 264000 20850671.36 1285.62545461
75 396000 20850671.36 2892.65727288
100 528000 20850671.36 5142.50181845
125 660000 20850671.36 8035.15909132
150 792000 20850671.36 11570.6290915

The underestimation of rainfall can be quite alarming, especially during a prolonged stratiform event when flooding is involved, like that shown in Figure 8. Notice the amateur radio reports received in southern Indiana. The WSR-88D radar beam was overshooting echo tops and therefore severely underestimating the precipitation estimates. As additional WSR-88D's are installed, overlapping fields of view and mosaicking precipitation estimates should alleviate these affects.

Figure 8. Same as in Figure 5, except for period ending at 1122 UTC 4 December 1993. The event included flooding rains over southern Indiana.


There are several factors that limit the accuracy of precipitation estimation by the WSR-88D. Some of these include improper coefficients in the algorithm equations, radar characteristics, atmospheric conditions, and distance from the radar.

The greatest limitation of these algorithms lies within the use of the Z-R relation. The Z-R relations vary from location-to-location, season-to-season, and even day-to-day. For instance, in the mixed stratiform/cumuliform event presented earlier, the initial precipitation was in showers with pockets of heavier rain. Later, the precipitation evolved into a stratiform and more widespread less intense rain. Clearly, one Z-R relationship is not representative of this type of event nor of the entire surveillance area. The WSR-88D was designed to compensate for these problems by using an area-wide bias, but as Rasmussen et al. (1989) state, this area-wide bias does not keep up with the evolution of the precipitation regime. Other factors that make the Z-R relationship biased include: ground clutter, anomalous propagation, partial beam filling, wet radomes, and incorrect hardware calibrations. Further studies will need to be completed for each radar site to allow the adjustment of the coefficients that go into the Z-R equation.

Besides the Z-R relationship, a range effect correction has to be added to the algorithm. The range effect has been found correlated with echo intensity (or precipitation rate) and is more prominent in shallow precipitation situations. Currently, by using the hybrid scan, the radar assumes that the range effect correction is not needed. This is because the range effect correction equation requires three coefficients that must be determined based on data from each radar site. The coefficients vary seasonally, and are determined based on local storm climatology, terrain, and range effect studies conducted at the radar site. Because WSR-88D's have not been in operation for a very long time, sufficient data has not been collected to determine these site-specific coefficients.

Besides the discrepancies that arise through the Z-R relationship, another problem lies with comparing WSR-88D estimations with real-time rain guages. The WSR-88D instantaneously samples a volume of the atmosphere several thousands of feet above the ground. The surface projection is over one square-mile and measurements are reported every 5 to 10 minutes. Rain guage data, on the other hand, is continuous as precipitation falls. The area is less than one square-foot. Consequently, "point" measurements may not represent the radar "volume" measurements. Similarly, the rain rates observed instantaneously by the radar in any given measurement bin may not show intervals between observations. These sampling-related discrepancies are very important to procedures that adjust radar estimates to match guage data.

The path of the radar beam through the atmosphere obviously has an impact on the accuracy of precipitation estimation. Presented earlier were classic examples as the radar beam propagated over the precipitation tops. As already mentioned, for a standard atmosphere, the WSR-88D radar beam from Indianapolis is at approximately 10,000 feet above ground level at 80 nautical miles. However, the condition of the atmosphere can have a large affect on the path of the beam by causing superrefraction or subrefraction. With super-refraction the radar beam travels a path curved more than that of a beam in a standard atmosphere. Often, the superrefraction is so great that the beam is bent to the earth's surface. These ground echoes result in an overestimation of accumulated precipitation. On the other hand, subrefraction causes the radar beam to travel a path less curved than a beam in a standard atmosphere that can then result in underestimation.


The purpose of this study was to give an overview of how the Indianapolis WSR-88D precipitation algorithm handled different types of precipitation events during four months (September to December 1993). While the results are preliminary, it was generally found that the precipitation algorithm was most accurate at longer ranges when estimating cumuliform precipitation. That may be true since most cumuliform precipitation is usually associated with higher cloud tops. Therefore, the radar beam can intersect the droplets even at a long range. Stratiform precipitation, on the other hand, showed a significantly reduced estimation accuracy at longer ranges as the radar beam propagated over the lower clouds.

Further studies are pending to address the range effect problem. However, we need to first decide how to handle the "comparison problem". This refers to the effectiveness of comparing a volume measurement from the radar to a point measurement given by the precipitation guages. Once these methods are established with a sufficient sample, the next step would be to derive the three coefficients used in the range effect correction equation. This would effectively calibrate the precipitation algorithm of the Indianapolis WSR-88D, and could possibly aid in the calibration of other surrounding radars.

Although there are still errors lurking in the algorithms, the WSR-88D has come a long way during the past several years. As testing continues to improve on the accuracy of the WSR-88D precipitation products and algorithms, the radar will one day provide highly accurate precipitation estimates and will ultimately have a greater impact on saving lives and property.


The authors thank the staff of the NWSFO Indianapolis for their patience and help, especially Steve Haines and Mike Sabones. Thanks also to the staff at NWSO in Fort Wayne for their help in collecting the data. We would also like to thank Russ Marshall, Official-in-Charge of NWSO Fort Wayne, and John Curran, Meteorologist-in-Charge of NWSFO Indianapolis, for allowing us to conduct this project. Thanks also to Mark Walton, Service Hydrologist at the NWSFO Detroit, Michigan, for his expertise, and Al Shipe, Service Hydrologist at NWSFO Indianapolis, for his help in getting hydrological data. Many thanks to Steve Goss from the NWSO Nashville for the reviewing of the manuscript.


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Batton, L.J., 1973: Propagation of Electromagnetic Waves. Radar Observation of the Atmosphere. The University of Chicago Press, 18-23.

DOC/NOAA/OFC MSSR, 1988: Federal Meteorological Handbook No. 11 (Interim Version One), Part B, 1990. Doppler Radar Theory and Meteorology. Doppler Radar Meteorological Observations, Government Printing Office (GSA), 171pp.

Rasmussen, E.N., J.K. Smith, J.F. Pratte, and R.C. Lipschutz, 1989: Real-Time Precipitation Accumulation Estimation Using the NCAR CP-2 Doppler Radar. Preprints, 24th Conference on Radar Meteorology, Tallahassee, FL, AMS (Boston), 236-239.

Rolinski, T., 1992: Precipitation Estimate at Long Ranges Using WSR-88D. Postprints, Third Conference on Heavy Precipitation Workshop, Pittsburgh, PA, AMS (Boston), 261-266pp.

Rohrbach, J., 1994: Measurement of Precipitation Using the WSR-88D. Penn State University (Thesis), 9 pp.

Shipe, A., E.C. Yess, III, and R.D. Marshall, 1985: Performance of Flood Alert System at Ft. Wayne, Indiana. Preprints, Sixth Hydrometeorology Conference, Indianapolis, IN, AMS (Boston), 190-192.


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