Environment

 

Precipitation Frequency

 

Precipitation Frequency in the Southeastern Wisconsin Region

 

NOAA Atlas 14, Precipitation-Frequency Atlas of the United States, Volume 8, Version 2.0: Midwestern States (Colorado, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Oklahoma, South Dakota, Wisconsin), published in 2013, presents the most-current precipitation depth-duration-frequency information for the State of Wisconsin and the seven-county Southeastern Wisconsin Region. The Wisconsin portion of the NOAA study that produced Atlas 14 was funded by the Wisconsin Departments of Natural Resources (WDNR) and Transportation (WisDOT) and SEWRPC. The Atlas 14, volume 8, version 2.0 report can be accessed at: http://www.nws.noaa.gov/oh/hdsc/PF_documents/Atlas14_Volume8.pdf

The information in Atlas 14 supersedes that in SEWRPC Technical Report No. 40, and the Commission staff recommends that Atlas 14 precipitation data be used in stormwater and floodland management applications. The SEWRPC storm time distribution issued on March 30, 2006, is still recommended by SEWRPC for use in stormwater and floodland management applications, including regulatory floodplain mapping studies, in the Southeastern Wisconsin Region.

Atlas 14 precipitation-frequency data for durations from 5 minutes to 60 days and frequencies of one through 1,000 years is provided in tabular and graphical formats and as geographic information system(GIS)-compatible ASCII grids on the NOAA Hydrometeorological Design Studies Center Precipitation Frequency Data Server (PFDS) at: http://hdsc.nws.noaa.gov/hdsc/pfds/ Generalized maps of the data are also provided, but NOAA recommends use of the PFDS point-and-click interface or the GIS-compatible ASCII grids to obtain precipitation values for analysis purposes.

The SEWRPC staff has coordinated with the United States Department of Agriculture Natural Resources Conservation Service (NRCS), WDNR, and WisDOT regarding the application of Atlas 14 in Wisconsin. Precipitation depths developed by NRCS for each county in the Southeastern Wisconsin Region for durations ranging from 5 minutes to 60 days, and for recurrence intervals from one year through 1,000 years can be found here. NRCS has also developed new 24-hour storm time distributions consistent with the Atlas 14 precipitation information. That information can be found here. WDNR has indicated that the NRCS time distribution applicable to the Southeastern Wisconsin Region or the 2006 SEWRPC distribution set forth below in Table 1 and Figure 1 will be acceptable for studies to delineate regulatory one-percent-annual-probability (100-year recurrence interval) floodplain boundaries. A description of the procedure used to develop the SEWRPC distribution can be found here.

The SEWRPC recommended rainfall distribution was developed for a range of storm durations and depths, up to, and including, 48 hours.  Therefore, unlike the 24-hour NRCS distributions, the SEWRPC distribution is not characteristic of a single duration. It is recommended that the SEWRPC distribution be applied with the Atlas 14 precipitation information to develop design storms for a range of durations and the storm, or storms, producing the highest peak flow(s) be used for analysis purposes.

A joint NRCS/SEWRPC presentation on Atlas 14 provides summary information on the development and application of Atlas 14 precipitation frequency information.

 

Intensity-Duration-Frequency Equations

 

In response to considerable interest expressed by counties and municipalities in the Region, the SEWRPC staff developed county-specific intensity-duration-frequency (IDF) equations utilizing NOAA Atlas 14 precipitation depth-duration-frequency information. The IDF equations developed are empirical formulas representing the relationship between maximum precipitation intensity, precipitation duration, and frequency. While the NOAA Atlas 14 depth-frequency information is developed for total precipitation depths characteristic of discrete durations (e.g., five minutes, ten minutes, 15 minutes), the IDF equations developed by the SEWRPC staff enable the computation of a rainfall intensity of a given frequency for any duration from 5 minutes through 24 hours. This would be useful to municipalities and consultants using spreadsheets, or other automated approaches, to apply the Rational method to develop peak flows for storm sewer design.

The IDF equations were developed by SEWRPC individually for Kenosha, Milwaukee, Ozaukee, Racine, Walworth, Washington, and Waukesha Counties in a manner consistent with the NRCS specification of representative 24-hour precipitation depth-duration-frequency information for each Wisconsin county (see previous section). That is, the representative location within each county in the Region that was selected by NRCS for determination of 24-hour precipitation depths was used by the SEWRPC staff for determination of precipitation depths for other durations.

Several commonly-used functions are found in the hydrology literature, including both linear and nonlinear regressions.  For this particular study, IDF equations developed using non-linear regression were found to provide the best fit to the IDF dataset in Southeastern Wisconsin for recurrence intervals of 1 year to 100 years and durations from 5 minutes through 24 hours. The equation expressed in the following form was utilized (Chow et al., 1988):

 

where i is the rainfall intensity (inches/hour); t is the duration (minutes); a, b, and k are constant parameters. The constant parameters were determined using the statistical method of least squares by minimizing the Root Mean Square Error. The final IDF equations for each of the seven counties can be found here.

References
Chow, V.T., Maidment, D.R. & Mays, L.W. (1988). Applied Hydrology, Mc-Graw-Hill

 

                                             Table 1

               SEWRPC RECOMMENDED RAINFALL DISTRIBUTION

 

Percent
of Total Storm Time

Cumulative Percent of
Total Storm Rain

0
0.0
5
2.7
10
4.8
15
6.9
20
9.5
25
13.2
30
18.9
35
28.5
40
42.2
45
56.6
50
68.4
55
76.5
60
81.6
65
85.2
70
88.0
75
90.3
80
92.2
85
94.0
90
95.8
95
97.7
100
100.0

Source: SEWRPC

 

 

Characterization of the June 2008 and July 2010 Heavy Rains in the Southeastern Wisconsin Region

 

The probabilities of the heavy rains of June 2008 and July 2010 for various durations from one-hour through 10 days were characterized using information from the NOAA Atlas 14, Volume 8, Version 2.0 Precipitation Frequency Data Server as set forth in Tables 2 and 3. Rainfall patterns for the  storms of June 2008 and July 2010 are provided here.

 

Rainfall Patterns for Storms of August 1986, June 1997, and August 1998

 

Map 1, Rainfall Pattern Over Southeastern Wisconsin 24-Hour Period on August 6, 1986

Map 2, Rainfall Pattern Over Southeastern Wisconsin 26-Hour Storm on June 20-21, 1997

Map 3, Rainfall Pattern Over Southeastern Wisconsin 24-Hour Period on August 6, 1998

 

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Southeastern Wisconsin Regional Planning Commission

 

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P.O. Box 1607
Waukesha, WI 53187-1607

 

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Phone: (262) 547-6721
Fax: (262) 547-1103
E-mail: sewrpc@sewrpc.org