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Critical Examination of Area Reduction Factors
Article in Journal of Hydrologic Engineering · June 2013
DOI: 10.1061/(ASCE)HE.1943-5584.0000855
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Critical Examination of Area Reduction Factors
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Daniel B. Wright, Ph.D., M.ASCE 1; James A. Smith, Ph.D. 2; and Mary Lynn Baeck, Ph.D. 3
Abstract: Area reduction factors (ARFs), which are used to convert estimates of extreme point rainfall to estimates of extreme area-averaged
rainfall, are central to conventional flood risk assessment. Errors in the estimation of ARFs can result in large errors in subsequent estimates of
design rainfall and discharge. This paper presents a critical examination of commonly used ARFs, particularly those from the U.S. Weather
Bureau TP-29, demonstrating that they do not adequately represent the true properties of extreme rainfall. This lack of representativeness is
due mainly to formulations that mix rainfall observations from different storms and different storm types. Storm catalogs developed from a
10-year high-resolution radar rainfall data are used set to estimate storm-centered ARFs for Charlotte, North Carolina. Storms are classified as
either tropical or nontropical to demonstrate that storm type strongly influences spatial rainfall structure. While there appears to be some
relationship between ARF structure and areal rain rate, basin-specific ARFs for the five largest storms from 2001 to 2010 in Little Sugar Creek
in Charlotte do not show any systematic deviation from the larger population of storms. Given the challenges presented in this paper as well as
other difficulties associated with ARF estimation, the authors suggest that research and practice should shift toward more robust methods,
such as stochastic storm transposition, that incorporate realistic representations of the spatial and temporal structure and variability of extreme
rainfall and its interactions with watershed surface, subsurface, and drainage network properties into flood risk estimation. DOI: 10.1061/
(ASCE)HE.1943-5584.0000855. © 2014 American Society of Civil Engineers.
Author keywords: Radar rainfall; Area reduction factors; Extreme rainfall; Flood risk estimation; Urban hydrology.
Introduction
Area reduction factors (ARFs; also known as depth-area relationships) are used to convert point rainfall estimates to area-averaged
estimates and are central to conventional flood risk estimation in ungauged watersheds. Misspecification of ARFs can result in major
errors in estimates of the intensity of areal rainfall and in the development of design storms, which in turn can have important impacts on
subsequent flood risk estimates. In this study, the authors argue that
insufficient attention has been given to commonly used ARFs and
the formulations used to estimate them. The results demonstrate that
there are large discrepancies between commonly used ARFs and the
true properties of extreme rainfall in the study region. These discrepancies imply overestimation of flood risk and overdesign of infrastructure. Moreover, the authors show that there is considerable
variability in the spatial structure of extreme rainfall, particularly
between tropical cyclones and organized thunderstorm systems, that
is not considered in conventional ARF estimates. To the authors’
knowledge, no widely used ARF source or academic study attempts
to quantify the impact that this variability has on ARF estimates.
1
Disaster Risk Management Analyst, Latin America and Caribbean Region Disaster Risk Management and Urban Development Unit, World
Bank, 1818 H St. NW, Washington, DC 20433; formerly, Doctoral Candidate, Dept. of Civil and Environmental Engineering, Princeton Univ.,
E-209A Engineering Quad, Princeton, NJ 08544 (corresponding author).
E-mail: danielb.wright@gmail.com
2
Chair and Professor, Dept. of Civil and Environmental Engineering,
Princeton Univ., E-209A Engineering Quad, Princeton, NJ 08544.
3
Hydrometeorology Programmer, Dept. of Civil and Environmental
Engineering, Princeton Univ., E-209A Engineering Quad, Princeton, NJ
08544.
Note. This manuscript was submitted on February 17, 2013; approved
on May 30, 2013; published online on June 3, 2013. Discussion period
open until September 1, 2014; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Hydrologic Engineering, Vol. 19, No. 4, April 1, 2014. © ASCE, ISSN 1084-0699/2014/
4-769-776/$25.00.
Areal rainfall estimates are sensitive to the ARF value that is
chosen. As an illustration, the National Oceanic and Atmospheric
Adminstration (NOAA) Atlas 14 (Bonnin et al. 2004) 6-h, 100-year
intensity-frequency duration (IDF) estimate for Charlotte, North
Carolina, is 139 mm (23.2 mm h−1 ) with 90% confidence intervals
ranging from 124 to 151 mm (20.7 to 25.2 mm h−1 ). The U.S.
Weather Bureau TP-29 (U.S. Weather Bureau 1958) 6-h,
100-km2 ARF estimate is 0.96, resulting in an areal estimate of
133 mm (22.2 mm h−1 ) with 90% confidence levels ranging from
119 to 145 mm (19.8 to 24.2 mm h−1 ). If, hypothetically, the
ARF is in fact 20% lower (0.77) than the TP-29 value, the resulting
100-km2 areal accumulation estimate is 107.0 mm (17.8 mm h−1 ).
This lower areal estimate is approximately equal to the NOAA
Atlas 14 6-h, 25-year rainfall estimate using TP-29 ARFs and is
far lower than the confidence bound of the 6-h, 100-year estimate.
The authors present evidence that conventional ARFs, such as those
from TP-29, may be overestimated by a magnitude comparable to
that given in this hypothetical example. Several other ARF
studies have also suggested that conventional ARF estimates
may be too high (Asquith and Famiglietti 2000; Lombardo
et al. 2006).
ARFs fall into two broad classes. The first—and more commonly
used—are termed fixed-area or geographically fixed ARFs, which
are computed by dividing an extreme value of area-averaged rainfall
by an extreme-point rainfall value of the same duration that is typical
for that area. Fixed-area ARFs are commonly used in engineering
practice due to their ease of calculation and application. The most
commonly used ARFs in the United States for watersheds less than
approximately 1,000 km2, from TP-29 (discussed further in the
following section) are fixed-area, as are those used in the United
Kingdom [Natural Environment Research Council (NERC) 1975].
Storm-centered ARFs, as their name implies, are calculated
for particular storms by dividing an observed area-averaged accumulation by the maximum observed point accumulation from
that storm (Huff 1995). Storm-centered ARFs are often used to
develop estimates of probable maximum precipitation (PMP)
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(Hansen 1987). Storm-centered approaches are rarely used outside
of PMP, partly because they are inextricably linked to storm type
and due to complications resulting from multicell storms (Svensson
and Jones 2010; Omolayo 1993).
Despite the challenges associated with the application of
storm-centered ARFs, they can still serve as a reality check to
examine the validity of their fixed-area counterparts. Flooding
is not the result of idealized design storms but rather of highly
complex meteorological systems, and ARFs should represent
at least basic properties of observed storm structure and variability. This study shows that commonly used ARFs in fact fail this
reality check, with important implications for flood risk estimation. This failure is rooted in the way in which conventional ARF
estimates are formulated, including a disregard for important rainfall characteristics such as storm type or season (Willems 2000;
Allen and DeGaetano 2005a; Durrans 2010). Different storm
types are characterized by very different spatial and temporal
structures that interact with complex land surface, subsurface,
and drainage network properties to produce flooding (Wright et al.
2013a, b). Urban flood risk in the eastern United States, for example, comprises floods produced by tropical storms and by
warm-season organized thunderstorm systems (Smith et al.
2005, 2011; Ntelekos et al. 2007). Storms in Charlotte, North
Carolina, are classified as tropical or nontropical to show that
storm-centered ARFs can vary dramatically by storm type.
A number of studies have pointed to a dependence of ARFs on
rainfall return period (Sivapalan and Bloeschl 1998; Asquith and
Famiglietti 2000; Allen and DeGaetano 2005a; Veneziano and
Langousis 2005). In at least some of these studies, however, the
dependence on return period may be an artifact of the chosen estimation method. This is discussed further in the following section.
In this paper, the authors examine storm-centered ARFs from a
sample of five extreme storms for Little Sugar Creek, Charlotte,
North Carolina, and compare them to storm-centered ARFs from
a larger population of storms to determine whether ARFs from
more extreme (i.e., longer return period) storms are different
from those of less extreme storms.
Review of Standard ARF Methods
This section includes a critical examination of the formulation of
TP-29 ARFs. The focus is on TP-29 because it is the most widely
used source of ARFs in the United States and has often served as a
point of comparison in the literature. NERC ARFs are estimated
from similar procedures. Several methods available in the literature
address some of the criticisms made in this paper, although most
methods share some common limitations. More detailed reviews of
the ARF literature can be found in Svensson and Jones (2010) and
Durrans (2010).
The TP-29 ARF for duration t and area A is defined as follows:
Pn
1
0
j¼1 Rj ðt; AÞ
n
ARFðt; AÞTP29 ¼ 1 Pn 1 Pk
j¼1 ½k
i¼1 Rij ðtÞ
n
where Rj0 ðt; AÞ = maximum areal rainfall of duration t over a circle
of area A for year j; Rij ðtÞ = maximum point rainfall of duration t
for year j at station i; k = number of rain gauges enclosed by area A;
and n = gauge record length in years.
A principal weakness of this method is that it does not stipulate
that the rainfall values Rj0 ðt; AÞ and Rij ðtÞ be from the same storm
event. In fact, it is very likely that as A increases, Rij ðtÞ and Rj0 ðt; AÞ
will be produced by separate storms of different types and perhaps
occurring in different seasons. This is particularly true for urban
areas such as those in the eastern United States, where the storm
and flood climatologies are a mixture of tropical cyclones and
organized thunderstorm systems, which can vary dramatically in
the spatial and temporal scales at which they produce extreme rainfall and flooding (Wright et al. 2013b). If Rij ðtÞ and Rj0 ðt; AÞ are
indeed drawn from different storms under the TP-29 procedure,
the resulting ARF must be greater than if they were drawn from
the same storm because it implies that Rj0 ðt; AÞ is larger than the
area-averaged rainfall produced by the storm that produced
Rij ðtÞ. The annual maxima-centered approach taken by Asquith
and Famiglietti (2000) requires that Rij ðtÞ and Rj0 ðt; AÞ be concurrent, and they estimate 24-h ARFs that are lower than TP-29 estimates for three cities in Texas (see Wright et al. 2012a) for similar
conclusions using the same technique for subdaily durations in
Charlotte, North Carolina.
TP-29 states that its ARF estimates are not dependent on storm
magnitude. Several studies, however, have produced ARF estimates that are dependent on return period (Sivapalan and Bloeschl
1998; Asquith and Famiglietti 2000; Allen and DeGaetano 2005a;
Veneziano and Langousis 2005). Reported dependencies of ARFs
on return period may be real but can also be explained by their
formulations. For example, Asquith and Famiglietti (2000) report
that ARF magnitude declines with increasing return period in their
annual maxima-centered approach, which is based on the ratio
of annual maximum point rainfall and concurrent areal rainfall.
Svensson and Jones (2010) point out, however, that one would
expect to see a return period dependency using this approach
because annual maximum point rainfall is often the result of spatially small convective systems that do not tend to produce areal
rates of correspondingly high return periods. More generally, if
areal rainfall exhibits greater increases with increasing return
period than does point rainfall, then ARFs should exhibit a dependence on return period. It is not clear from a hydrometeorological
perspective why this should be true, and it is not supported by
long-return period estimates of areal rainfall presented in Wright
et al. (2013b).
The TP-29 method for estimating ARFs has been described as a
ratio of averages (NERC 1977) and, as such, no estimate of the
variability of the ARF ratio can be computed without employing
a bootstrapping approach. Other methods in the literature may lend
themselves more readily to uncertainty quantification, but the authors are not familiar with any studies that quantify the uncertainties associated with presented ARF estimates.
The TP-29 method states that ARFs obtained using its methodology do not vary by region of the United States. This claim has
been challenged by Omolayo (1993), Asquith and Famiglietti
(2000), Allen and DeGaetano (2005a), and Myers and Zehr (1980).
The authors do not address these concerns in this study.
Study Area, Data, and Methods
The study region is centered on the Charlotte, North Carolina,
metropolitan area (Fig. 1). Charlotte, is an ideal setting for flood
hydrology research due to the data resources and the variety
of flood-producing hydrometeorological processes (Smith et al.
2002; Turner-Gillespie et al. 2003; Villarini et al. 2010; Wright
et al. 2013c).
Storm-centered ARFs were derived from a 10-year
(2001–2010), high-resolution (15-min, 1-km2 ), bias-corrected
radar rainfall data set developed with the Hydro-NEXRAD system (Krajewski et al. 2011; Smith et al. 2012; Wright et al. 2012b)
using reflectivity observations from the National Weather Service
Greer (radar code KGSP) Weather Surveillance Radar 1988
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(a)
(b)
Fig. 1. Study region: (a) KGSP 200-km radar range umbrella with state boundaries, regional topography, and the Charlotte, North Carolina,
metropolitan boundary (topography from the USGS National Elevation data set); (b) Charlotte, North Carolina, metropolitan area with CRN rain
gauges, the four study watersheds, and their corresponding USGS stream gauges; the background map shows the percentage of impervious cover
(impervious cover from the National Land Cover Dataset)
Doppler (WSR-88D, Greer, South Carolina). The data set has been
extensively validated (Wright et al. 2013c) and used for rainfall and
flood frequency analysis (Wright et al. 2013a, b). While most ARF
estimation methods use rain gauge observations, a growing number
have used radar reflectivity or radar rainfall estimates (Durrans et al.
2002; Allen and DeGaetano 2005b; Lombardo et al. 2006). In this
paper, mean-field bias correction of the 10-year radar rainfall data
set is done at the daily scale using 71 rain gauges from the Charlotte
Raingauge Network (CRN) (Wright et al. 2013c). Radar and rain
gauge data are also available for the remnants of Hurricane Danny,
which caused catastrophic flooding in much of the Charlotte, area
on July 23–24, 1997 [refer to Villarini et al. (2010) for an in-depth
examination of the July 1997 event].
The storm-centered ARFs (henceforth denoted ARFSC ) examined in this study are derived using the following procedure:
1. A t-hour storm catalog is created by identifying the time
periods of the 50 largest t-hour rainfall accumulations from
the radar rainfall data set occurring within a square 3,600 km2
search domain centered on Charlotte. The authors develop two
storm catalogs for each duration. The first is based on the 50
largest t-hour single pixel rainfall accumulations. The second
is based on the 50 largest t-hour rainfall accumulations of the
size and shape of the watershed of Little Sugar Creek at Archdale, Charlotte, North Carolina (110 km2 ). The procedure
used to develop the storm catalogs is the same as that used
in Wright et al. (2013b).
2. For each storm in the storm catalog, the largest single-pixel
t-hour rainfall accumulation within the 3,600 km2 domain
is identified.
3. For each storm, the largest adjacent t-hour pixel rainfall accumulation is identified, the average accumulation for the two
pixels is computed, and the ratio of the two-pixel area-average
rainfall to the maximum single-pixel rainfall is calculated. This
ratio is then the t-hour ARFSC for that storm for the area of two
radar pixels (approximately 2 km2 ). The process is repeated
by finding the next-largest adjacent t-hour pixel accumulation,
computing the three-pixel areal average, and computing the
resulting ARFSC for the area covered by three radar pixels.
This process of successively identifying the next-largest adjacent t-hour pixel rainfall accumulation and calculating the corresponding average areal accumulation and associated ARFSC
is repeated until a threshold area is reached [in this study,
1; 036 km2 (400 mi2 ), the largest area over which ARFTP29
are reported]. The ARFSC computed using this procedure need
not decrease monotonically with area because two or more radar pixels of intense rainfall may be separated by intervening
radar pixels with lower rainfall accumulations.
Each storm is classified as either tropical or nontropical. Tropical cyclone rainfall is identified using the hurricane database
(HURDAT) from NOAA’s National Hurricane Center (Jarvinen
et al. 1984; Neumann et al. 1993) as any rainfall occurring 12 h
before to 12 h after a HURDAT storm track passes within 500 km
of Charlotte, [refer to Hart and Evans (2001), Villarini and Smith
(2010), and Kunkel et al. (2010) for similar classification criteria
for tropical rainfall].
Results
ARFSC is computed from 1, 3, 6, and 12-h duration storm catalogs based on the 50 largest single-pixel rainfall accumulations
(Fig. 2). For all durations, the ARFSC are below the ARFTP29 .
For long durations, several ARFSC approach the ARFTP29 value,
including one 12-h storm for which the ARFSC roughly matches
the ARFTP29 value for areas larger than approximately 300 km2.
Longer-duration ARFSC are closer to the ARFTP29 because storms
(particularly tropical storms) that produce high long-duration point
accumulations tend to also produce high long-duration areal
accumulations, whereas storms that produce high short-duration
point accumulations (usually organized thunderstorms) do not
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1.00
0.75
0.50
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ARF (-)
0.25
1h
0.00
3h
1.00
0.75
0.50
0.25
6h
0.00
0
12 h
250
500
750
1000
0
250
500
750
1000
Area (km2)
TP-29
mean all storms
mean nontropical
mean tropical
individual nontropical
individual tropical
Fig. 2. The ARFSC for 50 storms at 1, 3, 6, and 12-h timescales; storms were selected based on the 50 largest single-pixel bias-corrected radar rainfall
accumulations
necessarily produce high short-duration accumulations over larger
areas. For all durations, the mean ARFSC for tropical storms is
larger than the mean ARFSC for nontropical storms. Both the mean
tropical and mean nontropical ARFSC are significantly less than the
ARFTP29 value for all areas and all durations. There is a greater
tendency toward multicell storm structure for longer-duration
storms based on the number of ARFSC that do not monotonically
decrease with area.
ARFSC is also computed from 1-h, 3-h, 6-h, and 12-h duration
storm catalogs based on the 50 largest basin-averaged rainfall accumulations of the size and shape of Little Sugar Creek at Archdale, to demonstrate the impacts of storm selection criteria on
subsequent ARFSC estimation (Fig. 3). Some differences can be
seen in individual ARFSC between Figs. 2 and 3. For all time scales,
the mean ARFSC decays more rapidly with area for the storms selected with respect to the size and shape of Little Sugar Creek, than
for the storms selected based on single radar pixel accumulations
(for example, the 12-h mean ARFSC for all storms in Fig. 3 decays
to approximately 0.35 at 1,000 km2 compared with approximately
0.42 in Fig. 2). This is because the storms selected with respect to
the size and shape of Little Sugar Creek, tend to be characterized by
higher sustained rain rates over larger areas rather than high point
rain rates.
The mean and standard deviation of ARFSC is computed from
the 1, 3, 6, and 12-h storm catalogs based on the 50 largest basinaveraged rainfall accumulations of the size and shape of Little
Sugar Creek at Archdale, for four areas: 7, 30, 48, and 110 km2
(Table 1). These areas correspond to the areas of the four subwatersheds shown in Fig. 1. There are relatively few tropical storms
from which to compute statistics (for example, 8 out of 50 storms
are classified as tropical for all durations). The mean (standard
deviation) ARFSC for all durations decreases (increases) monotonically with increasing area. The mean ARFSC increases with duration for the larger three areas but is relatively constant for the
smallest area (7 km2 ). The ARFTP29 is greater than the mean plus
at least one standard deviation of the ARFSC for all durations and
areas regardless of storm type. The 1-h duration ARFTP29 at
110 km2 is larger than the mean plus three standard deviations
of the ARFSC of the same size and duration for nontropical storms.
The dependence of ARFSC on rainfall magnitude is assessed by
examining the estimated parameters of a nonlinear least-squares
regression of the form
β
ARFðtÞSC ¼ eðA=αÞ
The scale parameter α controls the limit of the decay of
ARFðtÞSC as A → ∞, while the shape parameter β controls the rate
of decay of ARFðtÞSC . A higher (lower) value of α indicates a
higher (lower) ARFðtÞSC value as A → ∞, while a higher (lower)
value of β indicates a slower (faster) decay. The authors plot α and
β against the peak 100 km2 rainfall accumulation (Fig. 4) for each
of the 50 storms in the 1-h and 12-h duration storm catalogs created
with respect to the size and shape of Little Sugar Creek. There is no
systematic relationship between β and 100 km2 rainfall accumulation, nor between β and storm type for either duration. There is,
however, a systematic relationship between α and 100 km2 rainfall
accumulation. This relationship is stronger for 1-h storms than for
12-h storms. Values of α are generally greater for tropical storms
than for nontropical storms. Results are similar for 3-h and
6-h storm catalogs and for storm catalogs based on the largest
single-pixel rainfall accumulations (results not shown). In contrast,
there is no systematic relationship between α or β and peak singlepixel rainfall accumulation for 1-h, 3-h, 6-h, and 12-h durations
(results not shown), pointing to a stronger relationship between
100 km2 rainfall accumulations and accumulations over larger
areas than between single-pixel rainfall accumulations and accumulations over larger areas.
Basin-specific ARFSC is also computed for five storms for four
subwatersheds of Little Sugar Creek, ranging in size from 6.8 to
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ARF (-)
0.25
1h
0.00
3h
1.00
0.75
0.50
0.25
6h
0.00
0
12 h
250
500
TP-29
mean all storms
750
1000
0
250
Area (km2)
mean nontropical
mean tropical
500
750
1000
individual nontropical
individual tropical
Fig. 3. The ARFSC for 50 storms at 1-h, 3-h, 6-h, and 12-h timescales; storms were selected based on the 50 largest bias-corrected radar rainfall
accumulations of the size and shape of Little Sugar Creek at Archdale, Charlotte (110 km2 )
Table 1. TP-29 ARFs and the Mean and Standard Deviation of ARFSC for
Four Areas Corresponding to the Areas of the Four Subwatersheds
Area (km2 )
1-h duration
ARFTP29
μARFtropical
SC
σARFtropical
SC
μARFnontropical
SC
σARFnontropical
SC
3-h duration
ARFTP29
μARFtropical
SC
σARFtropical
SC
μARFnontropical
SC
σARFnontropical
SC
6-h duration
ARFTP29
μARFtropical
SC
σARFtropical
SC
μARFnontropical
SC
σARFnontropical
SC
12-h duration
ARFTP29
μARFtropical
SC
σARFtropical
SC
μARFnontropical
SC
σARFnontropical
110
48
30
7
0.88
0.60
0.18
0.43
0.13
0.96
0.70
0.15
0.60
0.13
0.94
0.76
0.14
0.69
0.12
1.00
0.86
0.06
0.85
0.08
0.92
0.72
0.12
0.49
0.17
0.97
0.82
0.08
0.63
0.17
0.96
0.86
0.07
0.70
0.15
1.00
0.91
0.06
0.84
0.11
0.94
0.70
0.14
0.56
0.20
0.97
0.79
0.10
0.67
0.17
0.98
0.82
0.08
0.73
0.14
1.00
0.90
0.05
0.85
0.08
0.96
0.68
0.16
0.62
0.19
0.98
0.76
0.12
0.71
0.16
0.99
0.80
0.09
0.76
0.14
1.00
0.90
0.04
0.86
0.09
SC
Note: For each duration, statistics for ARFtropical
are estimated from eight
SC
are estimated from 42 events.
events, whereas statistics for ARFnontropical
SC
110 km2 . The four subwatersheds are defined by U.S. Geological
Survey (USGS) stream gauges (refer to Fig. 1). The five storms
correspond to the five largest USGS annual peak discharge observations at Little Sugar Creek at Archdale for which contemporaneous radar rainfall records are available. These storms are used
to illustrate the role of spatial variability of rainfall in flood
generation and to examine whether ARFSC for extreme floodproducing storms are different from other, less intense storms.
For each event, the authors compute basin ARFSC for each of
the four study watersheds illustrated in Fig. 1. A summary of
the peak single-pixel and basin-averaged 12-h duration rainfall,
associated ARFSC , and peak discharge for four Little Sugar Creek
subwatersheds is shown in Table 2.
The two largest flood peaks (385 and 382 m3 =s) at Little Sugar
Creek at Archdale, (110 km2 ) were the product of tropical storms
Hurricane Danny (July 23–24, 1997) and Tropical Storm Fay
(August 27, 2008), respectively. These two storms were characterized by high maximum 12-h rainfall accumulations and were relatively spatially uniform over Little Sugar Creek, as shown by the
high-basin ARFSC in Table 2. The June 7–8, 2003 nontropical
storm produced nearly as high a flood peak (379 m3 =s) but lower
maximum 12-h accumulations and basin ARFSC than the tropical
storms. The two remaining nontropical storms (August 30–31,
2006, and May 5–6, 2009) produced lower rainfall accumulations,
lower basin ARFSC , and lower flood peaks at Archdale (310 and
314 m3 =s, respectively). The basin ARFSC for Briar Creek are
higher than for the smaller Little Sugar Creek at Medical Center
for all five storms, suggesting an important role of rainfall organization and subsequent runoff production in Briar Creek on flood
response downstream at Archdale. This observation is supported
by the modeling results presented in Wright et al. (2013a).
A comparison of 12-h basin ARFSC in Table 2 to the mean
ARFSC in Table 1 does not reveal any systematic differences between 12-h basin ARFSC corresponding to storms causing flooding
at Archdale and the 12-h ARFSC from the population of 50 storms
over the region. Basin ARFSC for Little Sugar Creek at Archdale
and Briar Creek are higher for Hurricane Danny (July 23, 1997) and
Tropical Storm Fay (August 27, 2008) than for the mean tropical
ARFSC . Basin ARFSC for Little Hope Creek and Little Sugar
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Fig. 4. Estimates of the shape (α) and scale (β) parameters of nonlinear least-squares regressions of ARFSC on rainfall area for 50 1-h and 12-h storms
plotted against peak 100 km2 rainfall accumulations of the same duration for the same storms
Table 2. Measured Peak Discharge, Maximum 12-h Point Radar Rainfall, Maximum Contemporaneous Basin-Averaged Radar Rainfall, and Corresponding
Basin ARFSC for the Five Storms That Produced the Five Largest Peak Discharges at Little Sugar Creek at Archdale
Watershed
Hurricane Danny (July 23–24, 1997)
Little Sugar Creek at Archdale
Briar Creek above Colony
Little Sugar Creek at Medical Center
Little Hope Creek at Seneca
Nontropical (June 7–8, 2003)
Little Sugar Creek at Archdale
Briar Creek above Colony
Little Sugar Creek at Medical Center
Little Hope Creek at Seneca
Nontropical (August 30–31, 2006)
Little Sugar Creek at Archdale
Briar Creek above Colony
Little Sugar Creek at Medical Center
Little Hope Creek at Seneca
Tropical Storm Fay (August 27, 2008)
Little Sugar Creek at Archdale
Briar Creek above Colony
Little Sugar Creek at Medical Center
Little Hope Creek at Seneca
Nontropical (May 5–6, 2009)
Little Sugar Creek at Archdale
Briar Creek above Colony
Little Sugar Creek at Medical Center
Little Hope Creek at Seneca
a
Peak discharge (m3 =s)
Maximum point rainfall (mm)
Basin-averaged rainfall (mm)
ARFSC (-)
385a
161a
150a
48
220
220
205
187
180
196
175
173
0.82
0.89
0.85
0.92
379
153
125
73a
86
86
77
76
60
66
48
69
0.70
0.77
0.63
0.91
310
65
108
59
149
104
146
146
84
74
90
132
0.57
0.71
0.61
0.90
382
100
110
35
162
162
160
116
128
141
121
104
0.79
0.87
0.76
0.89
314
85
109
48
126
126
112
126
72
79
50
100
0.57
0.63
0.45
0.79
Largest officially recorded flood peak for gauge station.
Creek at Medical Center for Hurricane Danny are higher than the
tropical mean but basin ARFSC for Fay are lower. For the June 7–8,
2003, storm, Little Sugar Creek at Archdale and Briar Creek have
above-average basin ARFSC , whereas the other two storms have
below-average ARFSC . Little Sugar Creek at Medical Center has
above-average basin ARFs for all three nontropical storms, whereas
Little Hope Creek is above average for June 7–8, 2003, and August
30–31, 2006, and below average for May 5–6, 2009.
All storms show significant variation in inter-event and intraevent variability in the spatial structure of maximum 12-h rainfall
(Fig. 5). Rainfall accumulation maps for all five storms show
southwest-to-northeast structure, typical of rainfall systems in the
774 / JOURNAL OF HYDROLOGIC ENGINEERING © ASCE / APRIL 2014
J. Hydrol. Eng. 2014.19:769-776.
60
0
16
30
200
45
180
60
75
120
100
80
7-8 Jun 2003
Nontropical
30-31 Aug 2006
Nontropical
40
150
20
135
40
120
0
10
105
80
90
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23 Jul 1997
Hurricane Danny
0
12
0
0
14
60
27 Aug 2008
Trop Storm Fay
5-6 May 2009
Nontropical
Fig. 5. Maps of peak 12-h bias-corrected radar rainfall accumulations for five storms; contour labels are in mm
region (Weisman 1990a, b; Murphy and Konrad 2005). Urban
modification of rainfall may also contribute to observed spatial
gradients (Wright et al. 2012b, 2013c).
Discussion and Conclusions
ARFs are central to conventional flood risk estimation in ungauged
watersheds, and errors in their estimation can result in major errors
in flood risk estimates. This study presents a critical examination of
commonly used ARFs, suggesting that these ARFs are not
representative of the true properties of extreme rainfall. This lack
of representativeness is due mainly to formulations that mix rainfall
observations from different storms and different storm types. These
errors can lead to overestimation of flood risk and overdesign of
infrastructure. The authors show that storm-centered ARFs in Charlotte, North Carolina, vary substantially and that storm type plays a
central role in this variability. Rainfall from tropical storms tends to
be spatially larger and of longer duration than rainfall from organized thunder storm systems; thus, tropical storm ARFs decay less
rapidly with increasing area. While there does appear to be some
relationship between ARF structure and areal rain rate (but not
maximum point rain rate), basin ARFs for the five largest storms
from 2001–2010 in Little Sugar Creek in Charlotte do not show any
systematic deviation from population statistics across a range of
spatial scales. This contrasts with studies that show a relationship
between ARFs and rainfall return period.
The radar-estimated ARFSC presented in this paper provides
one direction for improving ARF estimates, principally because
they capture a wide range of storm behavior and can be readily
used to characterize rainfall spatial variability. This variability
could then be incorporated into design storms and flood risk
estimates. This study illustrates, however, that there are
fundamental challenges with ARF estimation and application,
not limited to the criteria used for storm selection, treatment
of different storm types, and the role that watershed characteristics play in flood response. The impacts of additional design
storm assumptions, such as spatially uniform and temporally
uniform or idealized rainfall structure, on flood risk estimates
are poorly understood (Wright et al. 2013a, b). Further problems
include transferring ARFs to different regions, to areas with
variable topography, and to areas where urban modification of
rainfall is nonnegligible.
Given the challenges and uncertainties highlighted in this paper,
the authors suggest that, rather than update ARF estimates using
new data, research and practice should instead shift toward more
robust flood risk estimation techniques. In particular, stochastic
storm transposition (Foufoula-Georgiou 1989; Fontaine and Potter
1989; Wilson and Foufoula-Georgiou 1990; Franchini et al. 1996)
coupled with radar rainfall observations represent an important step
forward in flood risk estimation that incorporates the full observed
spatial and temporal variability of extreme rainfall and its interactions with watershed surface, subsurface, and drainage network
properties while avoiding many of the assumptions involved in
ARF estimation and design storm development (Wright et al.
2013a, b).
Acknowledgments
This paper was partially funded by the Willis Research Network,
the NOAA Cooperative Institute for Climate Sciences (Grant
NOAA CICS NA08OAR4320752), the Dept. of the Interior under
the USGS (Award G11AP20215), and the National Science
Foundation (Grant CBET-1058027). The authors acknowledge
the helpful comments of the three anonymous reviewers.
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References
Allen, R. J., and DeGaetano, A. T. (2005a). “Areal reduction factors for two
eastern United States regions with high rain-gauge density.” J. Hydrol.
Eng., 10.1061/(ASCE)1084-0699(2005)10:4(327), 327–335.
Allen, R. J., and DeGaetano, A. T. (2005b). “Considerations for the use of
radar-derived precipitation estimates in determining return intervals for
extreme areal precipitation amounts.” J. Hydrol., 315(1–4), 203–219.
Asquith, W. H., and Famiglietti, J. S. (2000). “Precipitation areal-reduction
factor estimation using an annual-maxima centered approach.”
J. Hydrol., 230(1–2), 55–69.
Bonnin, G. M., Martin, D., Lin, B., Parzybok, T., and Riley, D. (2004).
“NOAA atlas 14: Precipitation-frequency atlas of the United States.”
Vol. 2, National Oceanic and Atmospheric Administration, 71.
Durrans, S. R. (2010). “Intensity-duration-frequency curves.” Rainfall:
State of the science, geophysical monograph series, F. Y. Testik
and M. Gebremichael, eds., Vol. 191, American Geophysical Union,
Washington, DC, 159–169.
Durrans, S. R., Julian, L. T., and Yekta, M. (2002). “Estimation of deptharea relationships using radar-rainfall data.” J. Hydrol. Eng., 10.1061/
(ASCE)1084-0699(2002)7:5(356), 356–367.
Fontaine, T. A., and Potter, K. W. (1989). “Estimating exceedance probabilities of extreme floods.” J. Hydraul. Eng., 10.1061/(ASCE)07339429(1989)115:11(1562), 1562–1574.
Foufoula-Georgiou, E. (1989). “A probabilistic storm transposition approach for estimating exceedance probabilities of extreme precipitation
depths.” Water Resour. Res., 25(5), 799–815.
Franchini, M., Helmlinger, K. R., Foufoula-Georgiou, E., and Todini, E.
(1996). “Stochastic storm transposition coupled with rainfall-runoff
modeling for estimation of exceedance probabilities of design floods.”
J. Hydrol., 175(1–4), 511–532.
Hansen, E. M. (1987). “Probable maximum precipitation for design floods
in the United States.” J. Hydrol., 96(1–4), 267–278.
Hart, R. E., and Evans, J. L. (2001). “A climatology of the extratropical
transition of Atlantic tropical cyclones.” J. Clim., 14(4), 546–564.
Huff, F. A. (1995). “Characteristics and contributing causes of an abnormal
frequency of flood-producing rainstorms at Chicago.” J. Am. Water
Resour. Assoc., 31(4), 703–714.
Jarvinen, B. R., Neumann, C. J., and Davis, M. A. S. (1984). “A
tropical cyclone data tape for the North Atlantic basin, 1886–1983:
Contents, limitations, and uses.” NOAA Technical Memorandum
NWS NHC Rep. No. 22, National Hurricane Center, Coral Cables, FL.
Krajewski, W. F., et al. (2011). “Towards better utilization of NEXRAD
data in hydrology: An overview of Hydro-NEXRAD.” J. Hydroinf.,
13(2), 255–266.
Kunkel, K. E., Easterling, D. R., Kristovich, D. A. R., Gleason, B.,
Stoecker, L., and Smith, R. (2010). “Recent increases in U.S. heavy
precipitation associated with tropical cyclones.” Geophys. Res. Lett.,
37(L24706).
Lombardo, F., Napolitano, F., and Russo, F. (2006). “On the use of radar
reflectivity for estimation of the areal reduction factor.” Nat. Hazard
Earth Sys., 6, 377–386.
Murphy, M. S., and Konrad, C. E. (2005). “Spatial and temporal patterns of
thunderstorm events that produce cloud-to-ground lightning in the
interior southeastern United States.” Mon. Weather Rev., 133(6),
1417–1430.
Myers, V. A., and Zehr, R. M. (1980). “A methodology for point to area
ratios.” NOAA Tech. Rep. NWS 24, National Weather Service, Silver
Springs, MD.
Natural Environment Research Council. (1975). Flood studies report,
Vol. II, London, U.K.
Natural Environment Research Council. (1977). “The area reduction factor
in rainfall frequency estimation.” Flood Studies Supplementary
Rep. No. 1, London, U.K.
Neumann, C. J., Jarvinen, B. R., McAdie, C. J., and Elms, J. D. (1993).
“Tropical cyclones of the North Atlantic Ocean, 1871-1992.” NOAA
Historical Climatological Series 6-2, National Climatic Data Center,
Asheville, NC.
Ntelekos, A. A., Smith, J. A., and Krajewski, W. F. (2007). “Climatological
analyses of thunderstorms and flash floods in the Baltimore metropolitan region.” J. Hydrometeor., 8(1), 88–101.
Omolayo, A. (1993). “On the transposition of areal reduction factors for
rainfall frequency estimation.” J. Hydrol., 145(1–2), 191–205.
Sivapalan, M., and Bloeschl, G. (1998). “Transformation of point rainfall
to areal rainfall: Intensity-duration-frequency curves.” J. Hydrol.,
204(1–4), 150–167.
Smith, J. A., Baeck, M. L., Meierdiercks, K. L., Nelson, P. A., Miller, A. J.,
and Holland, E. J. (2005). “Field studies of the storm event hydrologic
response in an urbanizing watershed.” Water Resour. Res., 41(10),
W10413.
Smith, J. A., Baeck, M. L., Morrison, J. E., Sturdevant-Rees, P.,
Turner-Gillespie, D. F., and Bates, P. D. (2002). “The regional
hydrology of extreme floods in an urbanizing drainage basin.” J. Hydrometeor., 3(3), 267–282.
Smith, J. A., Baeck, M. L., Villarini, G., Welty, C., Miller, A. J., and
Krajewski, W. F. (2012). “Analyses of a long-term high-resolution radar
rainfall data set for the Baltimore metropolitan region.” Water Resour.
Res., 48(4), W04504.
Smith, J. A., Villarini, G., and Baeck, M. L. (2011). “Mixture distributions
and the hydroclimatology of extreme rainfall and flooding in the eastern
United States.” J. Hydrometeor., 12(2), 294–309.
Svensson, C., and Jones, D. (2010). “Review of methods for deriving areal
reduction factors.” J. Flood Risk Manage., 3(3), 232–245.
Turner-Gillespie, D. F., Smith, J. A., and Bates, P. D. (2003). “Attenuating
reaches and the regional flood response of an urbanizing drainage
basin.” Adv. Water Resour., 26(6), 673–684.
U.S. Weather Bureau. (1958). “Rainfall intensity-frequency regime,
Part 2—Southeastern United States.” Technical Paper No. 29, U.S.
Dept. of Commerce, Washington, DC.
Veneziano, D., and Langousis, A. (2005). “The areal reduction factor:
A multifractal analysis.” Water Resour. Res., 41(7), W07008.
Villarini, G., and Smith, J. A. (2010). “Flood peak distributions for the
eastern United States.” Water Resour. Res., 46(6), W06504.
Villarini, G., Smith, J. A., Baeck, M. L., Sturdevant-Rees, P., and
Krajewski, W. F. (2010). “Radar analyses of extreme rainfall and flooding in urban drainage basins.” J. Hydrol., 381(3–4), 266–286.
Weisman, R. A. (1990a). “An observational study of warm season southern
Appalachian lee troughs. Part I: Boundary layer circulation.” Mon.
Weather Rev., 118(4), 950.
Weisman, R. A. (1990b). “An observational study of warm season southern
Appalachian lee troughs. Part II: Thunderstorm genesis zones.” Mon.
Weather Rev., 118(10), 2020.
Willems, P. (2000). “Compound intensity/duration/frequency-relationships
of extreme precipitation for two seasons and two storm types.”
J. Hydrol., 233(1–4), 189–205.
Wilson, L. L., and Foufoula-Georgiou, E. (1990). “Regional rainfall
frequency analysis via stochastic storm transposition.” J. Hydraul.
Eng., 10.1061/(ASCE)0733-9429(1990)116:7(859), 859–880.
Wright, D. B., Smith, J. A., and Baeck, M. L. (2013a). “Estimating flood
frequency using radar rainfall fields and stochastic storm transposition.”
Water Resour. Res.. .
Wright, D., Smith, J. A., Villarini, G., and Baeck, M. L. (2012a).
“Applications of radar-based rainfall estimates for urban flood studies.”
Pragmatic modeling of urban water systems, Monograph 21, W. James,
ed., CHI, Guelph, ON, 85–110.
Wright, D. B., Smith, J. A., Villarini, G., and Baeck, M. L. (2012b).
“The hydroclimatology of flash flooding in Atlanta.” Water Resour.
Res., 48(4), W04524.
Wright, D. B., Smith, J. A., Villarini, G., and Baeck, M. L. (2013b).
“Estimating the frequency of extreme rainfall using weather radar
and stochastic storm transposition.” J. Hydrol., 488, 150–165.
Wright, D. B., Smith, J. A., Villarini, G., and Baeck, M. L. (2013c). “Longterm high-resolution radar rainfall fields for urban hydrology.” J. Am.
Water Resour. Assoc., 1–22.
776 / JOURNAL OF HYDROLOGIC ENGINEERING © ASCE / APRIL 2014
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