Example 7 illustrates the computation of a peak flow frequency curve using EMA and Bulletin 17C procedures when a low outlier threshold and confidence limits are specified by the user. The data for this example comes from the USGS gage 06412500 Rapid Creek above Canyon Lake near Rapid City, South Dakota. Pactola Dam, which is located upstream of this stream gage, controls approximately 321 sq mi. As such, regulation effects were removed from the period of record. The annual maximum series for this example contains 90 peaks beginning in 1878 and ending in 2009. Information pertaining to 27 events not contained within the systematic record were sourced from a USGS report (Harden, O'Connor, Driscoll, & Stamm, 2011). Within this record, the June 1972 flood is by far the largest observed event. In fact, the June 1972 flood event is nearly 2.5 times larger than the next largest historical flood event and approximately 12 times larger than the next largest systematic (i.e. gaged) flood event at this location (Schwarz, Hughes, Hansen, Petersen, & Kelly, 1975). The annual maximum series is plotted in Figure 1 and tabulated in Table 1.

Figure 1. Rapid Creek above Canyon Lake near Rapid City, SD Annual Peak Flow Record.
Table 1. Rapid Creek above Canyon Lake near Rapid City, SD Annual Peak Flow Record.

Date

Flow (cfs)

1878

7060

1883

7900

1905

2350

1906

922

1907

12200

1915

654

1916

217

1917

287

1920

7540

1929

870

1930

213

1931

170

1932

747

1933

1690

1934

128

1935

479

1936

110

1937

92

1938

94

1939

68

1940

268

1941

592

1942

448

1943

882

1944

254

1945

359

1946

943

23 Jun 1947

950

22 Jun 1948

245

15 Aug 1949

290

15 Apr 1950

209

15 Jun 1951

77

23 May 1952

2600

16 Jun 1953

152

12 Aug 1954

140

29 Jul 1955

326

29 May 1956

203

14 Jul 1957

595

30 May 1958

131

30 Jun 1959

169

16 Jul 1960

135

01 Jul 1961

111

13 Jul 1962

1700

06 Jun 1963

827

11 Jun 1964

735

19 May 1965

2380

22 Mar 1966

174

15 Jun 1967

726

04 Oct 1967

123

20 May 1969

246

14 Jun 1970

1150

26 Apr 1971

353

09 Jun 1972

31200

09 May 1973

196

22 Aug 1974

476

07 Jun 1975

253

15 Jun 1976

1220

08 May 1977

216

21 May 1978

498

17 Jun 1979

200

16 Jul 1980

87

13 Jul 1981

96

22 Jul 1982

384

11 May 1983

303

15 Jun 1984

229

15 Jul 1985

87

04 Jun 1986

142

29 May 1987

115

03 Aug 1988

80

12 Jul 1989

64

07 Jul 1990

108

11 May 1991

487

21 May 1992

64

20 Jun 1993

1000

29 Apr 1994

227

09 Jun 1995

1020

01 Jun 1996

823

02 Jun 1997

1090

24 Jun 1998

1490

16 Jun 1999

698

20 May 2000

264

15 Jul 2001

131

06 Jul 2002

159

21 Jun 2003

243

01 Jul 2004

67

10 Jul 2005

61

07 Aug 2006

104

17 Aug 2007

177

24 May 2008

1000

26 Apr 2009

277

A Bulletin 17 Analysis using EMA and Bulletin 17C procedures has been developed for this example. To open the analysis, either double-click on the analysis labeled "B17C Example 7" from the Study Explorer or from the Analysis menu select open, then select "B17C Example 7" from the list of available analyses. When "B17C Example 7" is selected, the Bulletin 17 analysis editor will appear as shown in Figure 2. As shown, the Skew option was set to use the Station Skew and the default confidence limits were modified to 0.025 and 0.975 to produce a 95% confidence interval.

Figure 2. Bulletin 17 Analysis General Tab for B17C Example 7.
A low outlier threshold of 100 cfs was specified on the Options tab, as shown in Figure 3. This low outlier threshold was selected to censor more information than the default Grubbs-Beck critical value. When using this option, careful attention should be paid to the selection of the specified low outlier threshold as the resultant parameter estimation can be heavily impacted.


The EMA Data tab for this example is shown in Figure 4. This example uses an annual maximum series consisting of systematic and historical data with several missing periods. The missing periods span 1879 – 1882, 1884 – 1904, 1908 – 1914, 1918 – 1919, and 1921 – 1928. Since 17C EMA requires a non zero – inf perception threshold for all periods of missing data, a total of four perception thresholds are required. In this example, the June 1878 event can be used to inform the perception threshold for the missing periods of annual peak flow data. The use of a perception threshold of 7050 – inf for this period implies that had a flood event occurred with a peak flow greater than 7050 cfs, someone would have measured and recorded it. This value was chosen because historical events of this magnitude were in fact recorded. Once all four perception thresholds have been entered as shown in Figure 4, click the Apply Thresholds button to assign the complementary flow ranges for the periods of missing data.

Figure 4. Bulletin 17 Analysis EMA Data Tab for B17C Example 7.
Once all of the General and EMA Data tab settings are set or selected, the user can press the Compute button to perform the analysis. Once the computations have been completed, a message window will open stating Compute Complete. Close this window and then select the Tabular Results tab. The analysis window should resemble Figure 5.

Figure 5. Bulletin 17 Analysis Tabular Results Tab for B17C Example 7.
In addition to the tabular results, a graphical plot of the computed frequency curves can be obtained by pressing the Plot Curve button at the bottom of the analysis window. The Log Pearson Type III distribution fit using EMA to the input annual maximum flow data set, the 2.5% and 97.5% confidence limits, and the computed plotting positions are shown in Figure 6.

Figure 6. Plotted Frequency Curves for B17C Example 7.
As shown in Figure 7, twelve values less than the defined low outlier threshold of 100 cfs were identified. These annual peak flows were then recoded to have a flow interval of zero – 100. The perception thresholds for the years in which an annual peak flow was recorded were also adjusted to correspond with the defined low outlier threshold. Consequently, these perception thresholds were changed from zero – inf to 100 – inf, as shown in Figure 8.

Figure 7. Report File for B17C Example 7 showing censored low outliers.

Figure 8. Report File for B17C Example 7 showing recoded perception thresholds.