# Flood Frequency Analysis

Flood frequency analysis of annual peak flow data collected at a stream gage provides an estimate of flood frequency in terms of P-percent annual exceedance probability (AEP) at that specific location. The use of percent AEP conveys the probability of a flood of a given magnitude being equaled or exceeded for any given year. For example, a 1-percent AEP indicates that a particular flow magnitude has a 0.01 probability, or a 1% chance, of being equaled or exceeded in any given year. In previous USGS flood frequency reports, a T-year recurrence interval was used to describe the flood frequency. The use of a recurrence interval terminology, for example 100-year recurrence interval, is discouraged because it can be misleading. T-year reoccurrence may imply that there is a set time interval between particular magnitude floods when in reality floods are random processes that are best understood using probabilistic terms. For reference purposes, the following table describes the T-year recurrence intervals with corresponding P-percent AEP for flood-frequency flow estimates (Gotvald and others, 2009).

T-year recurrence interval (years) |
P-percent annual exceedance probability (percent) |
---|---|

2 | 50 |

5 | 20 |

10 | 10 |

25 | 4 |

50 | 2 |

100 | 1 |

200 | 0.5 |

500 | 0.2 |

Flood-frequency estimates at stream gages are computed by fitting a known statistical distribution to the series of annual peak flows. For these analyses, flood frequency was estimated according to methods established in Bulletin 17B of the Hydrology subcommittee on Water Data (1982) using the Expected Moments Algorithm (EMA) (Cohn and others, 1997) with the multiple Grubbs-Beck test. For sites with systematic annual peak discharge for complete period of record, no outliers, and no historical information, the EMA method calculates identical mean log, standard deviation log, and station skew as the Log Pearson III (LP3) method described in Bulletin 17B. However, EMA can also incorporate censored and individual peak data not used in the LP3 method. Censored data may be expressed in terms of discharge perception thresholds, bounded discharges, or low outliers. During historical periods outside the period of systematic data collection, perception thresholds are defined from anecdotal data that provide some information about the range of peak flows that would have been observed. Bounded discharges, interval data for specific events with some knowledge of the range values that the peak falls in, are used to characterize any missing data during periods of systematic data collection or during periods of interruption when the gage was not active. Low outliers are peak flow values collected during the period of systematic data collection that are significantly smaller than other recorded values, such as zero flow during a drought year. EMA also makes use of the Grubbs-Beck test to identify low outliers so they do not have a large influence on the fitting larger flows with lower AEPs of the flood frequency estimate. The multiple Grubbs-Beck test (Cohn et al., 2013), utilized in this analysis, provides a consistent standard for identifying multiple potential influential low flows and provides protection from lack-of-fit due to unimportant but potentially influential low flows. Estimates of uncertainty are provided at the 95-percent confidence interval. The confidence interval is a range of values over which the true value of the estimated flow occurs within the stated probability. For example, the 95-percent confidence interval for an estimated flow value means that the probability that the true flow value lies within the interval is 95 percent.

A weighted adjustment to the skew value was made using station and regional skew according to Bulletin 17B techniques. Best available regional skews were published in Hardison, 1974. Gages affected by urbanization or downstream of dams were not adjusted and use station skew.

A minimum of 10 years of systematic record are required for the flood frequency analysis to be run. The methods described are not applicable to sites where flows are appreciably altered by regulation or where unusual events have substantially altered the flow regime.

References Cited

Cohn, T.A., Lane, W.L. and Baier, W.G., 1997, An Algorithm for computing moments-based flood quantile estimates when historical information is available: Water Resources Research, v.33, no. 9, p.2089-2096.

Cohn, T.A., England, J.F., Berenbrock, C.E., Mason, R.R., Stedinger, J. R. , and Lamontagne, J.R., 2013, A generalized Grubbs-Beck test statistic for detecting multiple potentially influential low outliers in a flood series: Water Resources Research, v. 49, no. 8, p. 5047-5058.

Gotvald, A.J., Feaster, T.D., and Weaver, J.C., 2009, Magnitude and frequency of rural floods in the Southeastern United States, 2006-Volume 1, Georgia: U.S. Geological Survey Scientific Investigations Report 2009-5043, 120 p.

Hardison, C.H., 1974, Generalized skew coefficients of annual floods in the United States and their application: Water Resources Research, v. 10, no. 5, p. 745-752.

Interagency Committee on Water Data, 1982, Guidelines for Determining Flood Flow Frequency: Hydrologic Subcommittee Bulletin, 28 p., 14 app., 1pl.