radar rainfall uncertainties

8/8/2019 Radar Rainfall Uncertainties

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AFFILIATIONS:KrajewsKiIIHR-Hydroscience & Engineering,

The University of Iowa, Iowa City, Iowa; Villariniand smithDepartment of Civi and Environmenta Engineering, Princeton

University, Princeton, New Jersey

CORRESPONDING AUTHOR: Witod F. Krajewski, IIHR-

Hydroscience & Engineering, The University of Iowa, Iowa City,

IA 52242

E-mai: [email protected]

The abstract for this article can be found in this issue, following the

table of contents.

DOI:10.1175/2009BAMS2747.1

In fina form 7 September 2009

2010 American Meteoroogica Society

Now is good time to ssess thee decdes of pogess since Jim Wilson nd Ed Bndes

smmized the opetionl cpbility of d to povide qntittive infll estimteswith potentil pplictions to hydology.

The purpose of this article is to honor Jim Wilson

and Ed Brandes for their seminal paper (Wilson

and Brandes 1979), Radar measurement of

rainfallA summary. The work has been frequently

cited [163 times according to the Institute for Scientific

Information (ISI) Web of Knowledge as of 7 June

2009], and it was a comprehensive attempt to summa-

rize the capabilities of weather radar to provide quan-titative estimates of precipitation, which inspired a

generation of radar hydrometeorologists in the United

States and elsewhere. They discussed the numerous

sources of uncertainties associated with radar-based

rainfall estimates, including calibration, attenuation,

bright band, anomalous propagation, beam blockage,

ground clutter and spurious returns, random errors,

and variability in the relation between reflectivity

Zand rainfall rate R (ZR relations). The authors

also addressed the possible impact of the errors in

rain gauge measurements of rainfall and sampling

uncertainties (errors resulting from the approxima-

tion of an areal estimate using a point measurement).

In particular, based on contemporary research (e.g.,

Huff 1970; Woodley et al. 1975) concerning the spatialsampling error, Wilson and Brandes (1979) reported

that it decreases with increasing area size, increasing

time period, increasing gage density, and increasing

rainfall amount. Based on more recent research, we

have developed quantitative models that reflect how

the spatial sampling errors decrease with increasing

temporal and decreasing spatial scales, rain gauge

network density, and rainfall amount (e.g., Ciach and

Krajewski 1999; Zhang et al. 2007; Villarini et al. 2008;

Villarini and Krajewski 2008).

These uncertainties notwithstanding, Wilsonand Brandes foresaw the operational utility of radar-

rainfall estimation and promoted its use in flash flood

forecasting, noting that radar can be of lifesaving

usefulness by alerting forecasters to the potential for

flash f looding.

In this article, rather than trying to review the

(sizable) literature of the different methods of radar-

rainfall estimation and their accompanying sources

of uncertainties, our goal is to answer the question,

How much better can we do now versus what was

done 30 yr ago? To answer this question, we replicate,

RADAR-RAINFAll UNCERTAINTIESWhee e We fte Thity Yes of Effot?

by witold F. KrajewsKi, Gabriele Villarini, and james a. smith

87JaNuarY 2010aMErICaN METEOrOLOGICaL SOCIETY |


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to the highest degree possible, the analysis docu-

mented in Wilson and Brandes (1979) and report the

results. Acknowledging considerable technological

progress in electronics, computing, and communica-

tion, the basics of weather radar remain unchanged.

Because our focus is on recent operational data in

the United States, we do not assess polarimetric

radar performance (e.g., Zrni 1996; Petersen et al.1999; Zrni and Ryzhkov 1999; Doviak et al. 2000;

Bringi and Chandrasekar 2001; Brandes et al. 2002,

2004). We limit our analysis to a similar number of

warm-season storms that were analyzed by Wilson

and Brandes (1979) and stay with the performance

statistics they used.

This paper is organized as follows. In the next

section, we describe the data and the setup used for

the analysis. In the Results section, we present the

results of this study, and in the last section, we sum-

marize our main points and conclude the paper.

SETUP AND DATA. Wilson and Brandes study

(1979) represented the operational weather radar

technology of the 1970s and 1980s. In 1971, the U.S.

National Weather Service (NWS) began the Digitized

Radar Experiment (D/RADEX) to improve the opera-

tional use of radar data through computer processing.

The early stages of D/RADEX involved four sites:

Kansas City, Missouri, established in August 1971;

Oklahoma City, Oklahoma, (October 1971); Forth

Worth, Texas (December 1971); and Monett, Missouri

(February 1972). Several useful hydrometeoro-logical products were developed under the program,

including echo tops, vertically integrated liquid water

content, severe weather probability, storm structure,

and rainfall accumulation. In 1983, the system was

upgraded to quasi-operational status and renamed the

Radar Data Processor, version II (RADAP II). As of

1991, the RADAP II network consisted of 12 sites. Six

of these sites cover a major portion of the Arkansas

River basin in the central part of the United States.

The RADAP II system was designed as a prototype

of the Next Generation Weather Radar (NEXRAD)system of modern Doppler radars (Heiss et al. 1990;

Crum and Alberty 1993; Klazura and Imy 1993) and

served in that role until it ceased operation in 1992.

The RADAP II system used two types of radar:

Weather Surveillance Radar-1957 (WSR-57) and

Weather Surveillance Radar-1974 S band (WSR-74S).

Both share the same basic characteristics of a 2.2

beam width and a 10-cm wavelength (S band). The

RADAP II sites collected base-level and tilt-sequence

(volumetric) observations of reflectivity every

1012 min. These observations were built from input

scans of data processed into 180 radials covering 360

of azimuth under the radar umbrella. The radials

were centered on even azimuths, covered a range from

10 to 126 nautical miles, and contained a data value

for each nautical mile of range. The data values were

given in 16 (015) categories of radar reflectivity.

In the early 1990s, WSR-57 and WSR-74S radars

were replaced by the NEXRAD network of WeatherSurveil lance Radar-1988 Doppler (WSR-88D) radars

(e.g., Crum and Alberty 1993; Crum et al. 1998). The

first operational WSR-88D was installed in fall of

1990 in Norman, Oklahoma, while the last one was

installed in the summer of 1997 in North Webster,

Indiana. WSR-88D is an S-band radar with Doppler

capability. WSR-88D has a narrower 0.95 beamwidth

and collects base-level and tilt-sequence (volumetric)

observations of reflectivity every 56 or 1012 min,

depending on the scanning strategy (e.g., Klazura

and Imy 1993). Apart from the base data products

(reflectivity, mean radial velocity, and spectrum

width), WSR-88D radars use many different algo-

rithms to convert the base data into several hydro-

meteorological products (Klazura and Imy 1993). In

particular, rainfall estimates are generated through

the Precipitation Processing System (PPS; Fulton et al.

1998). PPS is a suit of algorithms with more than 40

adaptable parameters. Five subalgorithms comprise

the PPS: reflectivity preprocessing, rain-rate conver-

sion, rainfall accumulation, gaugeradar adjustment,

and rainfall product generation. Over the years, the

PPS has undergone frequent, albeit rather minor,improvements. It has now evolved into a mature and

robust algorithm that provides the nation with crucial

precipitation data. The rainfall products generated by

the PPS include the Digital Precipitation Array (DPA),

3-h total, Digital Hybrid Reflectivity, and storm total.

In the summer of 2008, WSR-88D radars began col-

lecting data in the so-called superresolution, that is, at

0.5 in azimuth and 250 m in range. However, the PPS

does not utilize this new capability, largely because

of the arrival of dual polarization [dual-polarization

rain-rate products will be available on a 250 m 1polar grid (Istok et al. 2009)].

Wilson and Brandes (1979) used radar-rainfall

estimates from the National Severe Storms Labora-

tory (NSSL) WSR-57 radar located close to Oklahoma

City. The radar was operated with a sampling interval

of 5 min. To convert reflectivity into rainfall rate,

the authors used the MarshallPalmer ZR relation

[Z= 200 R1.6 (Marshall and Palmer 1948; Marshall

et al. 1955)]. The radar data were complemented with

measurements from rain gauges located between 45

and 100 km from the radar site. Wilson and Brandes

88 JaNuarY 2010|


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(1979) compared radar and rain gauge data for

14 Oklahoma storms with durations ranging from

2 to 12 h from April to June 1974, plus a storm in

April 1975.

We mimic the analysis of Wilson and Brandes

(1979) as closely as possible. Our analysis is based

on 20 Oklahoma storms selected from a 6-yr period

from January 1998 to December 2003. The radardata came from the Oklahoma City WSR-88D radar

(KTLX). We processed level II data through the Build

4 (newer versions are currently available) of the Open

Radar Product Generator (ORPG) version of the PPS

software system used by the NWS and generated

DPAs. This product represents hourly accumulation

maps averaged over the Hydrologic Rainfall Analysis

Project (HRAP) grid [approximately 4 4 km 2

pixels (e.g., Reed and Maidment 1999)]. We used

the NEXRAD ZR relation [Z= 300 R1.4; see Fulton

et al. (1998)] to convert reflectivity into rainfall rate.

By using the ORPG, we assured consistency in data

processing for all storms.

Our radar-rainfall estimates are complemented

by concurrent and collocated rain gauge measure-

ments from the Oklahoma Mesonet (e.g., Brock et al.

1995) and U.S. Department of Agriculture (USDA)

Agricultural Research Service (ARS) Micronet (e.g.,

Allen and Naney 1991). As shown in Fig. 1, the former

consists of more than 110 weather stations distributed

almost uniformly across the state of Oklahoma, with

an intergauge distance of about 50 km; the Micronet is

a much denser network that consists of 42 rain gaugeslocated between 70 and 100 km from the Oklahoma

City radar site with an intergauge distance of about

5 km. Similarly to Wilson and Brandes (1979), we

include in our analysis only those gauges that are

located between 45 and 100 km.

While we made every effort to reproduce Wilson

and Brandes analysis (1979) as closely as possible

based on the information reported in their paper (see

in particular the Results in their paper), there are

some obvious differences between the two studies.

First, the radar technology is different. Our radardata come from the WSR-88D radar (e.g., Crum

and Alberty 1993; Klazura and Imy 1993), which is

much more sensitive and has a larger antenna than

the WSR-57 radar used by Wilson and Brandes.

Even though both of these radars operate at S band,

WSR-57 has 2.2 beamwidth, while WSR-88D has

0.95 beamwidth. This means that at 100-km range

from the radar, the WSR-57 provides ref lectivity over

pixels that are about 2 km 2 km (1 nm), while the re-

flectivity data available for the WSR-88D correspond

to about 1 km 1 km pixels. Wilson and Brandes

(1979) analyzed their rainfall estimates in polar

coordinates with 2 1 km resolution (E. Brandes

2009, personal communication). In our case, the

radar-rainfall estimates were averaged over the HRAP

grid. Even though this presumably implies a factor of

4 ratio in the spatial resolution between the two stud-

ies, we do not think that this significantly impacts our

comparisons, because we are working with rainfall

storm totals. The representativeness of rain gauge

data with respect to both resolutions can be assessed

(not included) based on the information collected at

the Piconet rain gauge network at the Oklahoma City

Airport and reported by Ciach and Krajewski (2006).

Another difference is the ZR relationship used inthe two studies: the default ZR relation for WSR-57

was MarshallPalmer (Z= 200 R1.6), while we used

the NEXRAD ZR (Z= 300 R1.4), which is the most

common ZR relationship used operationally. This

difference in the ZR relationship might impact the

results because there is some evidence (e.g., Villarini

2008; Villarini and Krajewski 2010) that Marshall

Palmer ZR leads to higher errors in radar-rainfall

estimates for a midwestern climate. We did not repro-

cess the data with the MarshallPalmer ZR relation

because it would necessitate use of the ORPG, whichis exceedingly tedious and cumbersome.

As we mentioned before, we selected 20 storms for

our study. We defined the beginning of a storm as

the point at which 1-h rainfall accumulation larger

than zero was first detected by any of the rain gauges

within 45 and 100 km from the radar; we defined

the conclusion of the event as the time at which a

prolonged zero-rainfall period began. Wilson and

Brandes (1979) did not offer their definition of a

storm, but we were able to determine that [s]torm

periods began comfortably before any gauge used for

Fig. 1. Map with the location of the rain gauges and

radar site.



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comparison experienced rain and ended well after

rain stopped at the last site affected. Events with rain

already in progress were not selected to avoid errors

associated with gauge timing (E. Brandes 2009, per-

sonal communication). Thus, even though the details

of the definition of a storm in these two studies might

differ, we do not believe that this aspect would signif i-

cantly influence our comparison of the results.

RESULTS. In Table 1, we summarize the results of

our analysis for the 20 storms considered in this study.

We tried to include only events that occurred between

April and October (the only exception were events

1 and 3) to avoid problems associated with rainfall

measurements by radar and rain gauges during the

winter months (e.g., Smith et al. 1996; Germann et al.

2006; Ciach et al. 2007). This is in agreement with

Table 2 in Wilson and Brandes (1979), where they only

included events that occurred in AprilJune.

A larger number of rain gauges were available for

this study. With the exception of event 6, in which

only 44 rain gauges were working for the entire storm,

we used at least 53 rain gauges for each event. On

average, Wilson and Brandes (1979) used measure-

ments from 16 rain gauges, with a minimum of 5 and

a maximum of 22. Comparing the storm durations

between the two studies, it is evident that our events

lasted longer than those in Wilson and Brandes

(1979). In this study, we have events with durations

ranging from 6 to 52 h (on average, they lasted ap-

proximately 21 h). The events selected by Wilson andBrandes (1979) were much shorter, ranging from 2

to 12 h, with an average duration of less than 6 h.

Moreover, the rain gauge averages (G-

) for our storms

tend to be higher than those in Wilson and Brandes

(1979). It is possible that these differences are due to

the contrasting definition of storm between the

two studies.

In column 8 in Table 1, we report the results for

the same quantities as those in Table 2 in Wilson and

Brandes (1979). In particular, representing with Giand

Ri the storm total rainfall accumulation values for theith rain gauge measurement and the corresponding

radar-rainfall estimate, we write

(1)

(2)

(3)

relative dispersion about E[G/R]

(4)

average difference (5)

average difference (storm bias removed)

(6)

where Nis the number of gauges available during a

particular event and [G/R] is the standard deviation

of the ratios between rain gauge measurements G and

radar-rainfall estimates R.

The column with the ratio between rain gauge and

radar accumulations (column 8) reports values ranging

from 0.58 (overestimation by the radar compared tothe rain gauges) to 1.66 (underestimation by the radar

compared to the rain gauges). Wilson and Brandes

(1979) found values ranging from 0.41 to 2.41, with a

more extreme underestimation and overestimation by

the radar compared to the rain gauges. When averag-

ing the results from the 20 selected storms, we obtain a

value of 0.99 compared to a value of 1.04 from Wilson

and Brandes (1979). Therefore, in general we have an

overall improvement in terms of the average gauge

radar ratios (with a value closer to 1 for WSR-88D), but

the statistical significance of the difference is difficultto establish within the scope of this study.

Column 9 summarizes the values of the coefficient

of variation of the gaugeradar ratios. Based on our

analysis, we obtain values ranging from about 15%

to 45%, with an average value of 25.5%. Even in this

case, we observe an overall improvement compared

to the results presented in Wilson and Brandes (1979):

their results ranged from 10% to 46%, with an average

value of 30%. Therefore, we have an overall improve-

ment on the order of 17% compared to the results

published 30 yr ago.

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We obtain an even larger improvement when

comparing the average differences between radar

and rain gauges (column 10). Overall, we observe

an average difference of 41.7% between radar and

rain gauges (48.9% considering only events lasting

15 h), with values ranging from about 15% to 91%.

These values are smaller than those reported in

Wilson and Brandes (1979); on average, the differ-

ence between radar and rain gauges was 63%, with

values ranging from 30% to 160%. Therefore, in this

case, we observe a reduction in the average differ-

ences between radar and rain gauges on the order

of 33% with respect to the data analyzed by Wilson

and Brandes (1979).

Table 1. Summary of the comparisons between radar and rain gauges for the 20 selected storms.

EventDate

(begin)Date (end)

Number

of gauges

Duration

(h)

G

(mm)

R

(mm)E[G/R]

Relative

dispersion

about

E[G/R] (%)

Avg

diff

%

Avg diff

(E[G/R

removed)

%

10100 UTC

4 Jan 1998

1500 UTC

4 Jan199854 15 60.57 45.98 1.33 15.02 23.57 11.89

21100 UTC

26 Apr 1998

1700 UTC

27 Apr 199853 31 61.40 44.82 1.39 20.57 27.18 16.35

32200 UTC

11 Mar 1999

0000 UTC

13 Mar 199956 27 42.15 32.49 1.38 20.55 32.29 19.93

40100 UTC

14 Apr 1999

1400 UTC

14 Apr 199956 14 28.37 18.74 1.48 17.15 30.40 14.86

50200 UTC

10 May 1999

1100 UTC

10 May 199955 10 31.17 31.21 1.04 23.28 15.94 17.24

60200 UTC

30 Oct 1999

2300 UTC

31 Oct 199944 46 55.31 52.33 1.10 23.17 16.54 17.38

70900 UTC

28 Jun 2000

1900 UTC

28 Jun 200055 11 28.34 29.16 0.97 17.42 14.93 14.38

80800 UTC

22 Ju 2000

1700 UTC

22 Ju 200053 10 21.46 27.33 0.81 36.54 41.29 25.09

91800 UTC

4 May 2001

1400 UTC

5 Mar 200156 21 32.67 41.83 0.78 18.74 32.92 13.79

100200 UTC

28 May 2001

1100 UTC

28 May 200154 10 31.10 40.99 0.80 27.63 39.80 24.32

111200 UTC

12 Apr 2002

2300 UTC

12 Apr 200255 12 19.56 38.30 0.58 33.84 91.37 24.33

122100 UTC

4 Jun 2002

1600 UTC

5 Jun 200254 20 42.45 68.58 0.62 18.61 68.06 15.23

131500 UTC

13 Jun 2002

2000 UTC

13 Jun 2002

55 6 18.87 29.12 0.65 21.32 61.24 17.87

140800 UTC

27 Aug 2002

1500 UTC

27 Apr 200254 8 21.78 32.89 0.65 30.53 72.64 31.13

151300 UTC

8 Sep 2002

1800 UTC

9 Sep 200255 30 40.20 24.80 1.66 34.12 37.32 32.98

160000 UTC

19 Sep 2002

1400 UTC

19 Sep 200254 15 27.68 44.15 0.63 25.47 69.04 22.25

170900 UTC

8 Oct 2002

2100 UTC

9 Oct 200256 37 61.69 47.66 1.26 17.23 24.52 15.03

181100 UTC

4 Jun 2003

2100 UTC

5 Jun 200354 35 45.58 53.34 0.90 45.48 34.41 26.01

190900 UTC

9 Aug 2003

1700 UTC

9 Aug 200355 9 23.46 28.66 0.71 39.06 77.30 44.72

202000 UTC

29 Aug 2003

2300 UTC

31 Aug 200355 52 64.80 67.55 0.96 24.72 23.23 21.98

Average 20 cases: 0.99 25.5 41.7 21.3



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Finally, we recalculated the average differences

after correcting for the storm bias (column 11). The

average differences between radar and rain gauges

decreased, with values ranging from 11.9% to 44.7%,

and with an average value of 21.3% (26.1% when

considering only events lasting 15 h). The results

in Wilson and Brandes (1979) were closer to these,

with values ranging from 8% to 42%, and on averageequal to 24%.

DISCUSSION AND CONCLUSIONS. This

short paper was written to acknowledge Wilson and

Brandes for their benchmark paper (Wilson and

Brandes 1979). Their study can be considered one

of the first in which uncertainties in radar-rainfall

estimates were quantitatively summarized and

discussed. Despite considerable uncertainties in

radar-rainfall estimates revealed by the study, they

foresaw the tremendous potential of using radar in

hydrology. Now, it is hard to even imagine the absence

of radar-rainfall maps in our everyday personal and

professional activities.

Thirty years after their paper was published,

we sought to answer the following question: How

much better can we do now? Our analysis confirms

that we can do significantly better. We found an

overall reduction in the average differences between

radar and rain gauges on the order of 33%; we also

found a reduction in the coefficient of variation of

the expected value of the ratios between rain gauge

measurements and radar estimates on the order of17%, and much of this improvement can be associ-

ated with the improved radar hardware and software

(e.g., smaller beam width). These numbers should

be interpreted in a qualitative sense rather than as

a new benchmark. There are several other studies

documented in the literature that have evaluated vari-

ous aspects of the current technology performance

(e.g., Smith et al. 1996; Baeck and Smith 1998; Young

et al. 1999; Brandes et al. 1999; Westrick et al. 1999;

Seo et al. 2000; Ciach et al. 2007) and cumulatively

provided a much more comprehensive assessment.Efforts continue to improve operational quantita-

tive precipitation estimation (QPE) products (e.g.,

Vasiloff et al. 2007), likely resulting in better results

than those indicated by our simple analysis. In the

future, it is expected that radar-rainfall uncertainties

will be reduced even more with the use of polari-

metric radars (e.g., Zrni 1996; Petersen et al. 1999;

Zrni and Ryzhkov 1999; Bringi and Chandrasekar

2001; Brandes et al. 2002, 2004), and we hope that in

30 yr there will be a similar study reporting further

progress.

Benchmarking performance of observing systems

is a critical element necessary for continued progress.

How can you argue that you could do better if you do

not know how well you can do? We take this oppor-

tunity to call for a more systematic approach to our

(hydrologic) communitys efforts to monitor its own

progress. Preserving data and legacy software would

allow long-term reanalysis similar to what has beendone in the area of numerical weather prediction mod-

eling (e.g., Kalney et al. 1996). Developing adequate

performance measures and evaluation technologies

should be an integral part of the approach. While

going back in time would be unfeasible, all-digital

archives of the present and future should facilitate

reanalysis and closer monitoring of the progress.

While trying to reduce uncertainties in radar-

rainfall estimates, we should also focus on finding

ways to account for various error sources. In

particular, we think that empirically supported

modeling of the total radar-rainfall uncertainties

warrants future investigations and studies. In the

literature, few studies present results about the im-

pact of the total uncertainties; however, in the vast

majority of the cases, these models are based on as-

sumptions and educated guesses.

One key factor in solving the persistent problem

of radar-rainfall uncertainties is the availability of

dense rain gauge networks that could provide valu-

able information for modeling these uncertainties.

Consequently, networks should be located in different

parts of the United States that are characterized bydifferent topography and climatic conditions. While

meteorological networks in the United States are

abundant (e.g., National Research Council 2009),

only a few meet the requirements for the density and

quality required to support radar-rainfall uncertainty

studies.

Despite over 30 yr of effort, the comprehensive

characterization of uncertainty of radar-rainfall

estimation has not been achieved. We hope that

ensemble forecasting (e.g., Schaake et al. 2007)

both in meteorology and hydrology will lead to anintensification of effort, because error covariance

is needed (e.g., Berenguer and Zawadzki 2008) to

improve forecasting ability. The celebrated study by

Wilson and Brandes (1979) will remain a cornerstone

of this effort.

ACKNOWLEDGMENTS.We appreciate the useful

comments and clarifications provided by both Jim Wilson

and Ed Brandes. Partial support for the first author was

provided by the Rose and Joseph Summers Endowment.

The second author was supported by NASA Headquarters

92 JaNuarY 2010|


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under the Earth Science Fellowship Grant NNX06AF23H

while he was a graduate student at The University of Iowa.

The authors also acknowledge discussions over the years

with Grzegorz Ciach, Dominique Creutin, Dong-Jun Seo,

and Dave Kitzmiller, among many others.

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