Objectives

Flood frequency studies relate the magnitude of discharge, stage, or volume to the probability of occurrence or exceedance. The resulting flood-frequency functions provide information required for:

  • Evaluating the economic benefits of flood risk management projects, as described in the Flood Risk Management (FRM) Studies.
  • Sizing and designing water-control measures if a target exceedance level or reliability is specified.
  • Establishing reservoir operation criteria and reporting performance success.
  • Establishing floodplain management regulations.
  • Developing requirements for regulating local land use.

Authority and Procedural Guidance

USACE flood frequency studies are authorized generally by:

  • The Flood Control Act of 1936. This is the general authority under which the USACE is involved in control of floods (and associated damage reduction) on navigable waters or their tributaries.
  • Section 206 of the Flood Control Act of 1960. This authorizes the USACE to provide information, technical planning assistance, and guidance in describing flood hazards and in planning for wise use of floodplains.
  • Executive Order 11988. This directed USACE to take action to reduce the hazards and risk associated with floods.

The following USACE guidance is particularly relevant to the conduct of flood frequency studies:

  • ER 1110-2-1450 (USACE, 1994) describes the scope and general requirements for flood frequency studies.
  • EM 1110-2-1415 (USACE, 1993) describes the procedure and computational guidelines for flood frequency studies. The procedures generally follow Bulletin 17B (IACWD, 1982) recommendations. Bulletin 17B has since been superseded by Bulletin 17C (England et al., 2019), which introduced the Expected Moments Algorithm so that interval and censored data can be used, a generalized approach to identifying low outliers, and an improved method for computing confidence intervals.
  • EM 1110-2-1417 (USACE, 1994) describes methods and general guidance for evaluating flood-runoff characteristics. Procedures for development of frequency-based estimates are included.
  • EM 1110-2-1619 (USACE, 2025) describes how the uncertainty in a flow-frequency function is characterized and carried into risk assessment. Chapter 3 covers discharge-frequency uncertainty, including effective record length.
  • ECB 2026-1 (USACE, 2026) requires an assessment of long-term hydrometeorological conditions for studies that rely on flow-frequency or stage-frequency relationships, which assume stationarity. The bulletin expires 9 January 2028.

Study Procedures

To meet the objectives of a flood frequency study, peak flows, stages, and volumes for specified annual exceedance probabilities (also known as quantiles) are required. The flow and stage frequency curves are often used for flood-damage calculations, as discussed in the Flood Risk Management (FRM) Studies. The volumes are often used for sizing flood control structures such as detention ponds. The values may be required for:

  • Current development, without-project conditions.
  • Future development, without-project conditions.
  • Current development, with-project conditions.
  • Future development, with-project conditions.

Here, the terms current and future are used to refer to watershed conditions existing at the time of the study and at some point later in time, respectively. The terms without- and with-project refer to the state of the watershed and channels if no action is taken and if a proposed action is taken, respectively. For example, the with-project condition might refer to construction of a proposed detention in the watershed, while the without-project condition refers to the absence of this detention. The without-project, future condition, therefore, is the project area's most likely future condition if no action is taken to resolve whatever problem is addressed by the study.

Frequency functions for current development, without-project conditions can be developed through statistical analysis of observations of flow, stage, or volume. As noted above, ER 1110-2-1450 (USACE, 1994) and EM 1110-2-1415 (USACE, 1993) present procedures for such analysis, and the HEC-SSP software implements them. Current versions of HEC-SSP apply Bulletin 17C.

The USGS (Sauer, 1983; Jennings, 1994) and others have performed regional flood-frequency studies for undeveloped and various levels of urbanizing watersheds. Current regional regression equations are delivered through the USGS StreamStats application. If the physical characteristics of the study watershed fall within the range of data used in the regional study, the regional relationships may be used to estimate flow frequencies for existing and future land use conditions.

As a general rule, annual maximum flow-frequency functions estimated from statistical analysis of long records of annual maximum flow are the most reliable frequency functions. However, long records of data are seldom available. Even if a long record was available, the watershed conditions may have changed dramatically due to urbanization or other non-stationary processes, or no large events may have occurred during the period of record. Therefore, an accurate flow-frequency function may not be derived from the historical data alone  A calibrated watershed model with precipitation events of known frequency is often used to develop a flow-frequency function and to compare with other estimates. The calibration of the model is typically based on available historical events of similar frequencies.

Furthermore, with-project condition frequency functions must be developed without statistical analysis. Gage records do not exist for these future, with-project watershed conditions. A commonly used method for this relies on application of a watershed model, such as HEC-HMS, with the so-called design storm assumption. Pilgrim (1975) describe this assumption as follows:

...in the normal approach to design flood estimation, the intention is to estimate the flood of a selected frequency from a design rainfall of the same frequency... The basic premise [ of this approach ] is that if median or average values of all other parameters are used, the frequency of the derived flood should be approximately equal to the frequency of the design rainfall.

This is the assumption of annual exceedance probability (AEP) neutrality: the AEP of the computed peak flow is taken to be the AEP of the design rainfall (a 1 percent AEP rainfall is assumed to produce the 1 percent AEP flow). The assumption is convenient and is standard practice for design and regulation, but it remains an assumption. The HEC-HMS Technical Reference Manual notes that when historical gage records are examined, the depths for every duration within a real storm rarely share a single exceedance probability. Antecedent conditions, storm pattern, and storm area also affect the resulting peak. Computed curves should therefore be compared with independent estimates (described later in this chapter) before one is adopted.

The following steps are taken to develop a frequency function with this procedure:

1. Develop a rainfall-runoff-routing model that reflects the characteristics of a watershed and channels for the case of interest: current or future, without- or with-project condition. The current, without-project model should be calibrated to observed data if available, or verified using regional equations or flow estimates. Where possible, calibrate to observed events whose magnitude is similar to the frequencies of interest. Parameters fitted only to frequent, small events may not represent watershed response during the rarer events that govern the upper end of the frequency curve.

2. Collect precipitation data, conduct statistical analyses, and define depths of known frequency for the watershed. The results of the statistical analysis may be presented as an Intensity-Duration-Frequency (IDF) function or DDF function, as a set of isohyetal maps, or as a set of equations that define depths for specified durations and frequencies. From these, storm hyetographs can be developed.

In many cases, this work has been done by NWS or by a local government agency. For example, NOAA Atlas 14 presents precipitation-frequency estimates for a range of durations and annual exceedance probabilities and now covers most of the United States in twelve volumes. The estimates are published through the NOAA Precipitation Frequency Data Server. Where Atlas 14 coverage does not yet exist, NOAA Atlas 2 (NOAA, 1973) remains the current source, and the earlier NWS publications TP-40 (NOAA, 1961), TP-49 (NOAA, 1964), and HYDRO-35 (NOAA, 1977) underlie annual-partial conversion factors and area-reduction curves still offered in HEC-HMS. NOAA Atlas 15 is in development and will replace Atlas 14. Volume 1 will account for observed temporal trends and Volume 2 will provide estimates projected through 2100. For the contiguous United States, preliminary estimates for peer review are expected in September 2026 and published estimates in 2027.

3. For a selected frequency, use the IDF or DDF information to define a precipitation hyetograph, then use the rainfall-runoff-routing model to compute peak flow, stage, or volume. Assign the frequency (AEP) of the precipitation to the peak flow, stage, or volume, following the design-storm assumption described above.

4. Repeat the process for a range of frequency events.

5. Assemble the results to yield a complete frequency function.

6. Use sensitivity analysis to determine the most important parameters if further adjustment of the frequency curve is needed.

7. Compare these storm frequency hydrologic model results with other methods (e.g., if available, flow statistics and regional regression equations) to determine the best estimate of the current, without-project flow-frequency curve.

Two HEC-HMS precipitation methods build the events of Step 3. The Frequency Storm method assembles a balanced, or nested, hyetograph in which the depths for every duration within the storm share the same exceedance probability. Storm-type options cover NOAA Atlas 14 and the older TP-40/TP-49/Atlas 2 data, and an annual-partial conversion is available. The Hypothetical Storm method is more data-driven. The analyst supplies the temporal pattern (derived from historical storms, or taken from the NOAA Atlas 14 temporal patterns published with the precipitation-frequency estimates), along with the storm area and spatial distribution. This method can be used directly with precipitation-frequency products.

Precipitation-frequency products such as NOAA Atlas 14 report depths for a point, so an area (depth-area) reduction should normally be applied. The exceptions are very small study areas and depths to which reduction factors have already been applied. HEC-HMS can apply the TP-40/TP-49 curves, user-specified factors, or a parametric function. The TP-40/TP-49 curves should not be applied to study areas larger than about 400 square miles, where the curves become asymptotic. Site- or region-specific area-reduction factors entered as user-specified values are preferred. The storm area should equal the drainage area at the location where the flow estimate is needed, and a watershed with several evaluation locations requires a separate storm for each.

The Frequency Analysis compute type, available beginning with HEC-HMS version 4.10, combines the events of Steps 3 and 4 into a single compute and assembles the flow-frequency function of Step 5 at a selected element. Beginning with version 4.14, the computed curve can be compared directly with an observed frequency curve, such as a Bulletin 17C analysis from HEC-SSP. The Uncertainty Analysis compute type supports the sensitivity analysis of Step 6 by sampling storm and basin parameters.

Such application is the subject of the case study that follows.