Tools › Civil and Geotechnical › Hydraulics › Flood Frequency Analysis › Example
Flood frequency of the Moose River at Victory, Vermont: log-Pearson Type III by Bulletin 17C with a weighted skew (appendix 10, example 1)
| Tool | Flood Frequency Analysis |
| Source | England, J. F., Jr., Cohn, T. A., Faber, B. A., Stedinger, J. R., Thomas, W. O., Jr., Veilleux, A. G., Kiang, J. E., and Mason, R. R., Jr. (2018). Guidelines for Determining Flood Flow Frequency, Bulletin 17C, ver. 1.1. Techniques and Methods, Book 4, Chapter B5, U.S. Geological Survey, Reston, VA. Appendix 10, systematic record example, pp. 105-110 (tables 10-2 to 10-5, figures 10-2 and 10-3). |
| Level | Professional |
Problem
USGS station 01134500, Moose River at Victory, Vermont, has 68 annual peaks from 1947 to 2014 (1,160 to 4,940 ft³/s), all known, with no historical information. Fit the log-Pearson Type III distribution by Bulletin 17C: screen for potentially influential low floods with the Multiple Grubbs-Beck test, weight the station skew with the regional skew 0.44 (mean square error 0.078), and find the flows at annual exceedance probabilities from 10 % to 0.2 %.
Inputs to Enter
- 68 annual peaks of Bulletin 17C table 10-2 (water years 1947 to 2014), ft³/s; no perception thresholds (every year fully observed)
- Method Bulletin 17C; low floods by the Multiple Grubbs-Beck test; skew weighted with the regional skew 0.44, MSE 0.078
- Weibull plotting positions, 95 % confidence, design life 50 years
Answers
- Multiple Grubbs-Beck test: smallest p(k; n) = 0.26 over the 34 tested peaks, no low flood (book: 0 peaks below the PILF threshold)
- Moments of log Q: mean 3.3286, standard deviation 0.1403 (book 3.3286, 0.1403); station skew 0.3966 with MSE 0.1012 (book 0.397, 0.101 on figure 10-3)
- Weighted skew = (0.078 · 0.3966 + 0.1012 · 0.44)/(0.078 + 0.1012) = 0.4211 (book 0.421)
- 1 % flood with the weighted skew: K = 2.6303 (Wilson-Hilferty 2.6323), log Q = 3.3286 + 2.6303 · 0.1403 = 3.6976, Q = 4,985 ft³/s; 10 %, 4 %, 2 %, 0.5 %, 0.2 %: 3,262, 3,920, 4,440, 5,560, 6,374 ft³/s
- With the station skew only (Skew = Station skew only): 3,261, 3,911, 4,422, 4,957, 5,519, 6,313 ft³/s, which are the six flows of the book's table 10-5 to every digit
- Risk that the 1 % flood is exceeded in 50 years: 1 − 0.99⁵⁰ = 0.395
Notes
The tool's default inputs are this record; press Submit. The bulletin's text says table 10-5 was computed with the weighted skew 0.421, but its six flows are reproduced exactly by the station skew 0.397 and not by 0.421; the tool follows the text, so its default 1 % flood is 4,985 ft³/s against the table's 4,957 (0.6 % higher). The confidence limits differ from the book's: the tool prints first-order limits (3,956 to 6,281 ft³/s at 1 %, 95 %) where PeakFQ prints the adjusted limits of equations 7-33 and 7-34 (4,131 to 7,735 ft³/s), which the tool does not compute. Examples 2, 3, 5 and 6 of the same appendix and examples 1 to 4 of Bulletin 17B appendix 12 load from the Record dropdown and are reproduced by test_flood_frequency.php.