2

Common Understanding of PMP

The Great Flood of March 1913 devastated cities along the Miami River of Ohio and resulted in more than 600 fatalities across Ohio, Indiana, and other states—a total eclipsed in the United States only by the Johnstown, Pennsylvania, Flood of 1889. The origins of PMP can be traced to the March 1913 flood through the scientific ideas that were subsequently formulated to characterize flood hazards and the engineering tools developed to protect the Miami River basin. PMP has provided a rational foundation for design of high-hazard structures and assessing the safety of these structures, but the core methods (Figure 2-1) remain grounded in scientific ideas from the early 20th century.

DEFINITION

PMP is currently defined in the United States as:

Theoretically, the greatest depth of precipitation for a given duration that is physically possible over a given size storm area at a particular geographical location at a certain time of year (AMS, 2022; Hansen et al., 1982).

Many countries around the world have adopted PMP as a design standard for high-hazard structures; the World Meteorological Organization (WMO) definition of PMP is:

The greatest depth of precipitation for a given duration meteorologically possible for a design watershed or a given storm area at a particular location at a particular time of year, with no allowance made for long-term climatic trends (WMO, 2009).

The notion that rainfall and floods are bounded and that engineering design for high-hazard structures should revolve around assessments of the largest possible flood evolved rapidly through the development of flood control plans for the Miami River

(Miami Conservancy District, 1916; Morgan, 1917). The preeminent hydrologist of the era, Robert Horton, argued for the existence of upper bounds of rainfall, based on both statistical arguments and physical reasoning (Horton, 1919, 1948a). The notion that a physical upper bound exists has remained implicit in the concept of PMP through its definitions and estimation methodologies since its earliest conception (see additional discussion in Chapters 4, 5, and Appendix B).

Also explicit in the WMO definition, and implicit in others (Appendix B), is the notion of stationarity—that PMP values are only associated with the current climate state. The WMO definition acknowledges the challenge of climate change, but current practice typically neglects consideration of climate change.

FUNDAMENTAL COMPONENTS OF PMP

Major Components: Storm Catalog and Storm Transposition

Tasked with estimating the largest rainfall accumulations possible over the Miami River basin, the Miami Conservancy District developed a storm catalog, consisting of extreme rainfall accumulations from around the United States, and a method called storm transposition, which specifies procedures for taking storms that occurred in other locations and placing them over the Miami River watershed. These two ingredients remain the cornerstone of PMP estimation in 2024.

Spurred by the rapid acceleration of dam building in the United States during the 1930s, interest in meteorological assessments of “maximum possible precipitation” (Showalter and Solot, 1942) led the U.S. Army Corps of Engineers (USACE) to adopt the Miami Conservancy District storm catalog and implement a program for updating it (USACE, 1973; see also England et al., 2020). USACE advanced meteorological studies through a joint research program with the U.S. Weather Bureau (USWB) (Hathaway, 1944). Collaboration between the two agencies was facilitated through the creation in 1937 of the Hydrometeorology Section of the USWB, which was “invested with the responsibility of determining limiting rates of precipitation” (Showalter and Solot, 1942). This group, with changing names over time, played a central role in the development and implementation of PMP procedures during the federal dam building era from the 1930s to the 1980s (e.g., Hansen, 1987). In 1970 the USWB was renamed the National Weather Service (NWS) and became a component of the National Oceanic and Atmospheric Administration (NOAA).

Rainfall analyses for PMP storm catalogs are often based on observations from non-standard rain gauges obtained from bucket surveys conducted following major storms. These observations include the U.S. and world record rainfall accumulations of 305 mm in 42 minutes on 22 June 1947 at Holt, Missouri (Lott, 1954; WMO, 2009), 560 mm in 2.75 hours on 31 May 1935 at D’Hanis, Texas (Dalrymple, 1939; WMO, 2009), and 780 mm in 4.5 hours on 18–19 July 1942 near Smethport, Pennsylvania (Eisenlohr, 1952; WMO, 2009). In a bucket survey, a container left outside can be a potential rain gauge; rainfall accumulation is computed as the ratio of the volume of water in the container to the cross-sectional area of the opening. A cattle trough was the

difference is the sampling of rainfall extremes. Bucket surveys provide rainfall observations by “going to the storm”; precipitation frequency studies rely on storms going to the gauges. The sparse distribution of rain gauges with long records needed for precipitation frequency studies introduces obstacles for assessment of rainfall extremes (see Foufoula-Georgiou, 1989b, for discussion of the sampling problem for extreme rainfall). For sub-daily time scales, the network of long-term rain gauge records is exceedingly sparse in many regions and not suitable for monitoring rainfall from extreme convective storms that control PMP estimation (see, e.g., Giordano and Fritsch, 1991).

PMP estimates require rainfall observations that are both temporally and spatially resolved. NOAA precipitation frequency studies use rain gauge observations to develop point assessments of rainfall extremes. Bucket surveys are well suited to provide spatial analyses of rainfall extremes, as detailed above, and radar rainfall estimates have been integrated into recent PMP studies, providing a key resource for developing spatially and temporally resolved rainfall analyses. The density of climatological rain gauge networks, especially for sub-daily time scales, limits the ability to spatially resolve rainfall extremes, except for the small number of dense rain gauge networks, typically located in urban settings.

The focus of PMP on the most extreme events over a wide range of time (1 to 72 hours) and space (1 to 20,000 mi²) scales has dictated that PMP estimation rely on rainfall analyses derived from non-standard observations, like those obtained in bucket surveys. Unlike rain gauge datasets used for precipitation frequency analysis, storm catalog data do not, however, provide systematic observations over time. The nature and completeness of storm data vary significantly over the period represented in the catalog (England et al., 2020).

Moisture Maximization

Recognizing that observed storms could potentially be larger given optimal atmospheric conditions, USWB grounded its approach to determining physical limits to precipitation in the atmospheric water balance (Bernard, 1944; Showalter and Solot, 1942). The atmospheric water balance relates precipitation to three terms: evaporation from the surface to the atmosphere, time changes in precipitable water (the column-integrated amount of water vapor in the atmosphere), and convergence of water vapor. For extreme rainfall, the atmospheric water balance simplifies to the following: precipitation equals convergence of water vapor. The enduring difficulty with determining bounds on rainfall has centered on convergence of the wind field, which has been “notoriously elusive” (Myers, 1967).

The solution adopted by USWB meteorologists for PMP was “to use storm precipitation itself as the effective measure of convergence” of the wind field (Myers, 1967). The approach adopts the cornerstone of Miami Conservancy District analyses—the transposition of storms from a storm catalog. To determine limiting rates of precipitation, an additional step, moisture maximization, was added. This step scales observed rainfall for a storm catalog event by the ratio of the maximum precipitable water for the location to the observed precipitable water from the storm. These PMP methods are

USES AND USERS OF PMP

The use of PMP expanded rapidly in the 1940s based on a consensus among federal, state, and local agencies and various professional meteorological and engineering societies about the need for an engineering standard with which to design dams to avoid potential failure due to extreme precipitation events and their associated flood flows. Although the period of major dam building has passed, the need for accurate, uniform, and transparent PMP estimates continues. Today, the primary users of PMP are federal, state, and local government agencies and private-sector owners of dams and nuclear facilities, as well as their consultants and contractors who are engaged in the review, evaluation, rehabilitation, and regulation of these facilities and who must demonstrate compliance with safety regulations.

Importance of PMP for Dam Safety

Since the 1940s, many federal and state dam safety programs have utilized PMP in dam design and construction (Billington et al., 2005) and to assess the safety of existing high- and significant-hazard dams (FEMA, 2012, 2013). Modern PMP estimates are important in understanding and assessing the potential for failure of existing critical infrastructure and in developing new infrastructure. PMP estimates are critical inputs for estimating the design floods for spillways. A design flood is defined as “the maximum flood hydrograph or a range of flood hydrographs for a given AEP, used in the design of a dam and its appurtenant structures, particularly for sizing the dam, spillway, and outlet works” (USBR, 2013). Design floods are used in the rehabilitation, modernization, and new construction of dams (examples of these applications to dam rehabilitation and new construction are provided in Box 2-2), which provide enhanced water supply, flood protection, hydropower, recreation, and other benefits at tens of thousands of locations across the United States.

Extreme Storm Rainfall, Dam Failures, and Fatalities

Despite excellent safety records for the vast majority of dam owners and regulators, some notable extreme storm rainfall events have led to overtopping, dam failure, and fatalities. The Association of State Dam Safety Officials (ASDSO) provides numerous case histories across the United States on floods and dam failures from extreme rainfall (ASDSO, 2023). These events are then used to estimate PMP and revise PMP estimates. A few examples that illustrate the ongoing importance of collecting and synthesizing extreme rainfall data and revising PMP (and precipitation frequency) estimates include:

• The record 6–8 June 1964 rainfall in northern Montana resulted in two dam failures that caused 19 fatalities; this event defines PMP for much of the Rocky Mountain region in HMR 55A (Hansen et al., 1988).
• The 9 June 1972 record rainfall in Rapid City, South Dakota, led to the failure of Canyon Lake Dam and 238 fatalities.

• The 20 July 1977 rainfall in Johnstown, Pennsylvania, of about 11.8 inches in 8 hours resulted in the overtopping failure of Laurel Run Dam with 40 fatalities.
• The 23–24 September 1983 Prescott, Arizona, storm caused extensive property damage and breaching of small dams. The maximum 6-hour rainfall accumulations at 100 km² spatial scale was 1.14 times larger than the General Storm PMP (Leverson, 1986).
• The 14 March 2006 heavy rainfall in Kauai, Hawaii, led to the Ka Loko dam failure and caused 7 fatalities.

nearby cities of Boulder and Lafayette. The project (currently under construction) will raise the height of the existing dam by 131 feet, which will more than triple Gross Reservoir’s capacity from approximately 42,000 acre-feet to 119,000 acre-feet.

Chimney Hollow Dam, Colorado

Chimney Hollow Dam is currently under construction and will be one of the first asphalt core rockfill dams in the United States. It will be 350 feet tall and 3,700 feet long, spanning the Chimney Hollow valley west of Loveland, Colorado. When built, the reservoir will store 90,000 acre-feet of water for nine municipalities, two water districts, and a power provider.

• Record July 2010 rainfall and flooding in Iowa led to the failure of Lake Delhi Dam.

Events in 2015 and 2016 in the Carolinas illustrate the need to modernize the storm catalog, PMP estimates, and precipitation frequency estimates. The historic 1–5 October 2015 rainfall and flooding across South Carolina resulted in 50 dam failures in that state (FEMA, 2016). During this event, point rainfall depths at many locations exceeded 20 inches in 3 days (Figure 2-4) and exceeded the NOAA Atlas 14 10^-3 AEP depth for the

2-day through 7-day durations (FEMA, 2016). The 50 dam failures, including Old Mill Pond (Figure 2-5), were located across the state, with most on small watersheds less than 30 mi². One year later, Hurricane Matthew resulted in the failure of 12 state-regulated dams in North Carolina and 20 in South Carolina (FEMA, 2017). Rainfall totals again were extreme, exceeding the 10^-3 24-hour AEP depth on 9 October 2016.

Many of the events described above are not included in current extreme rainfall guidelines. For example, NOAA Atlas 14 input data ended in 2000 and PMP in the Carolinas is set by HMR 51, published in 1978. PMP estimates in the Carolinas could change significantly with the consideration of Hurricanes Floyd (1999), Fran (1996), Matthew (2016), and Florence (2018) (Caldwell et al., 2011; M. Liu et al., 2022).

Regulators and Dam Safety Criteria

A dam safety regulator is a governmental or regulatory authority responsible for overseeing and enforcing dam safety regulations and guidelines within a specific region or state. Their primary role is to ensure that dams are designed, constructed, operated, and maintained in a manner that minimizes the risk of failure and protects public safety, property, and the environment. This protection includes the ability of dams to successfully pass extreme floods without failure or misoperation (FEMA, 2013). The criteria used for flood control design are based principally on dam size and hazard classification. Size classification is derived from dam height and/or reservoir storage volume. Hazard classifications are high, significant, and low, where high hazard indicates the probable loss of human life caused by dam failure or misoperation, and significant hazard indicates nonfatal impacts including economic loss, environmental damage, or

disruption of lifeline facilities (FEMA, 2004). The methods used to assess dam safety may include prescriptive inflow design floods based on PMP or its derivative Probable Maximum Flood (PMF), site-specific PMP studies, incremental consequence analysis, and risk-informed flood hazard analysis (FEMA, 2013, 2015).

PMP usage and application vary among state regulators, as reviewed in FEMA (2012). In assessing high-hazard dams, many states use full PMP estimates, some states use PMP fractions, and others (WA, CO, CA) use precipitation frequency estimates. FEMA has discouraged the use of PMP fractions (FEMA, 2013). To assess significant-hazard dams, states use either PMP fractions or precipitation frequency estimates. In some cases, different safety criteria (usually more stringent) are used for new dams as compared to existing dams. Federal agencies have broadly moved to risk-informed flood-hazard analysis (see below); PMP/PMF estimates are used when potential dam modifications are considered to reduce risk.

Conclusion 2-1: Both PMP and extreme precipitation frequency estimates are important for dam safety, and national updates are needed.

NOAA Atlas 15 will provide national updates to precipitation frequency estimates, including the effects of climate change. These updated estimates will not provide rainfall frequency products at AEPs needed for Risk-Informed Decision Making (RIDM; see Boxes 2-1 and 2-3) and do not address high-hazard infrastructure. The model-based PMP estimates that form a central component of modernized PMP (Chapter 5) can provide the information needed for risk-informed dam safety programs over the entire United States (as detailed below).

Overview of High-hazard Dam Characteristics

Out of the 91,750 dams in the National Inventory of Dams (NID), 16,564 (about 18%) dams are classified as high hazard. The number of high-hazard dams has increased by about 18 percent from 13,990 in NRC (2012) and about 52 percent from 10,856 in FEMA (2012). This increase may be due to updated data, reclassification, and possibly a sign of “hazard creep” (Schoolmeesters, 2023) resulting from urbanization (NASEM, 2019). Hazard reclassification is frequently necessary when new development occurs downstream of a previously classified low- and/or significant-hazard dam, creating the potential for loss of life.

The locations of high-hazard dams in the United States are shown in Figure 2-6. High-hazard dams are concentrated in the eastern United States. Texas, Missouri, and North Carolina have more than 1,000 each. California, Pennsylvania, South Carolina, and Georgia have more than 500 each. Drainage areas for high-hazard dams extend from 0.1 mi² to about 20,000 mi² (discussed below in subsection on Spatial and Temporal Scales for PMP Estimates). Nearly 82 percent of high-hazard dams are classified as earthen embankment dams, a dam type particularly susceptible to overtopping failure (USACE, 2019b). A program to provide consistent and reliable PMP estimates across the United States would be useful for understanding and potentially mitigating hazards at many of these locations.

The vast majority of high-hazard dams are owned by either private entities (44 percent) or local governments (32 percent). Local government owners include cities, towns, counties, and/or their associated public work departments. The federal government, state governments, tribal governments, and public utilities comprise the remainder. Consequently, more than three quarters of dams are regulated by states. Self-regulating federal dam owners include USACE (and Department of Defense agencies), Tennessee Valley Authority (TVA), USBR (and Department of Interior Bureaus), International Boundary and Water Commission, and several other federal agencies. Privately owned hydropower and mine tailings dams are regulated by FERC and the Mine Safety and Health Administration, respectively. Additional details on dams and NID are provided in Appendix C.

Importance of PMP for Nuclear Power Plant Safety

There are currently 53 operating nuclear reactors and two planned reactors in the United States, based on data from the U.S. Energy Information Administration. Reactor locations are shown in Figure 2-7. Nuclear facilities must be resilient to both

pluvial flooding driven by localized PMP-magnitude precipitation events and to fluvial inundation arising from flooding from nearby rivers or coasts. Thus, PMP estimates for U.S. nuclear reactors are needed for drainage areas ranging from 1 mi² (for localized flooding) to about 1,112,293 mi² for riverine flooding on the lower Mississippi River.

The drainage areas at reactor sites are generally much larger than for high-hazard dams because most are located along major rivers or lakes. For reactor sites, the median drainage area is 3,325 mi² and the mean drainage area is 88,591 mi². Given this diversity in drainage areas and locations concentrated along major lakes, coastlines, and other large water bodies (Figure 2-7), site-specific PMP estimates are warranted.

As in the case of dam safety, requirements for hydrologic screening and analysis of nuclear facilities are undergoing an evolution from use of prescriptive performance criteria based on PMP and PMF estimates to performance criteria based on RIDM processes. This evolution has been broadly supported. The American Nuclear Society (ANS, 2019) in its revision to ANSI/ANS 2.8 rescinded the use of PMP and PMF as a design flood standard and replaced it with a probabilistic flood hazard evaluation. Relevant excerpts from the ANSI document are as follows.

“This standard differs from its predecessor in the following areas:

• The applicability of the standard extends to all nuclear facilities, not just power reactors.
• Probabilistic assessment: This standard replaces the prescriptive “probable maximum” approach for establishing design flood hazards with a probabilistic approach for analyzing the frequency and magnitude of flood hazards. Thus, this standard focuses on the performance of a probabilistic flood hazard assessment and development of site probabilistic hazard frequency curves. An integral part of this process is the treatment of uncertainty.”

The Nuclear Regulatory Commission utilizes PMP in performing safety assessments of licensed and operating nuclear reactors, and in evaluating and reviewing new reactor applications (Kanney, 2023). Extensive reviews of potential flooding at reactors were undertaken using existing PMP estimates after the 2011 Fukushima tsunami nuclear disaster. This disaster spurred reanalysis of all potential failure modes and vulnerabilities, especially those related to flooding. In general, insights from probabilistic risk assessment (PRA) are considered with other engineering information. PMP augments RIDM (see below) and enhances conservatism.

The Evolution of PMP Use and Risk-Informed Decision Making

In both the dam safety and nuclear facilities arenas, the use of PMP has evolved, somewhat independently, at the federal and state levels. For dams, federal agencies have increasingly adopted RIDM concepts as the basis for safety reviews and assessments; some state dam safety agencies are also pursuing risk-based approaches. Box 2-3 provides an overview of RIDM. For nuclear facilities, the Nuclear Regulatory Commission and industry are using RIDM techniques. Instead of basing an investment

decision or corrective action on whether a facility meets a design standard such as PMP, RIDM requires the use of a broad range of probabilistic estimates of initiating events (floods), structural response(s), and associated consequences (e.g., damages, service interruptions, deaths) to develop a comprehensive risk estimate for each facility and for all facilities in a portfolio. Thus, where PMP was once used as the primary, sometimes sole, design and safety standard among the federal agencies, it is increasingly one (very important) metric that supplements the use of risk estimates.

The current PMP estimation process cannot provide AEP estimates or quantitative assessments of uncertainty. The resulting dichotomy between the direct use of PMP estimates to assess dam performance at project overflow and risk analyses requiring AEP estimates is currently bridged only by using the PMP and PMF estimates as informal guides with which to assess the reasonableness of the AEP-based flood hazard curves.

The proposed model-based approach to PMP estimation (Chapter 5) provides a path for risk-based methods to be applied to dam safety across the United States.

Conclusion 2-2: Many practitioners are using or moving toward RIDM processes. Current PMP estimates, and arbitrary fractions of them, do not include AEP estimates or uncertainty characterizations, making them less useful for RIDM.

SPATIAL AND TEMPORAL SCALES FOR PMP ESTIMATES

The most important and relevant applications that use PMP are for high-hazard dams and nuclear reactors. The relevant spatial areas for these applications are drainage areas (watersheds), detailed below and in Appendix C, which typically range from 1 mi² to larger than 10,000 mi², and very small areas (about 1 mi²) directly over reactor sites.

Drainage Areas

PMP estimates are applied as area estimates over specific drainage areas (e.g., Hansen et al., 1982) to estimate PMF. Thus, drainage area summary statistics are useful for inferring the relevant spatial and temporal scales of PMP needed for watershed applications. Figure 2-9 shows empirical cumulative distribution functions (ECDFs) of drainage areas for high-hazard dams in the United States by owner type. Similar ECDF results are obtained for significant-hazard dams (see Appendix C). The median drainage area for all high-hazard dams is about 8 mi². Local government dams are located on the smallest watersheds (median of 4 mi²) and federally owned dams on the largest (median of 200 mi²). The median drainage area of most state-owned dams is about 10 mi². About 98 percent of drainage areas are smaller than 10,000 mi², suggesting that the largest storm area (10,000 mi²) provided in generalized PMP estimates (HMR 49, 55A, 57, 59) is adequate (see also summary Table C-1 in NRC, 1985).

Conclusion 2-3: The concentration of high-hazard dams in small watersheds points to the particular importance of PMP estimates for short durations and small areas, as noted in NRC (1994).

Dam safety regulations used by states have historically considered dam height and reservoir storage as factors in hazard classification of dams and selection of rainfalls and floods for spillway design/assessments (FEMA, 2012). Drainage area distributions for four classes of dam heights and three hazard classifications are shown in Appendix C. Although the distributions and median statistics differ significantly, the range of drainage areas does not. The range of drainage areas covered by any new PMP estimation process should be similarly broad, especially for high- and significant-hazard dams.

Areal Extent of PMP Studies

Development of PMP estimates is based on generalized, regional, and site-specific studies (England et al., 2020). Generalized PMP studies cover large regions of the United States; regional studies focus on states or major river basins; and site-specific studies provide PMP estimates for the hazard region of a specific structure (dam or nuclear power plant). The spatial scale for generalized and regional PMP studies ranges from 1 to 20,000 mi² and the temporal scale from 1 to 72 hours.

The 1982 generalized PMP study for the eastern United States (HMR 52; Hansen et al., 1982) distinguished between “storm PMP” (defined as PMP computed over an arbitrary area of a given size) and “basin PMP” (defined as the PMP computed over a particular river basin of a given shape and areal extent) and introduced procedures for estimating basin PMP from storm PMP. Conventional PMP procedures provide estimates of storm PMP, although basin PMP is needed for computing PMF. Methods for converting storm PMP to basin PMP require additional information on the spatial and temporal structure of rainfall, which are assumed to vary with PMP type.

Storm Sizes Relevant to PMP Estimates

Two broad storm classifications are often used by PMP practitioners: a general storm and a local storm (WMO, 1986). A general storm is defined as “a storm event which produces precipitation over areas in excess of around 1,300 km² (500 mi²) and durations longer than 6 hours and is associated with a major synoptic weather feature” (WMO, 2009). A local storm is defined in WMO (2009) as “a storm event that occurs over a small area in a short time period. Precipitation rarely exceeds 6 hours in duration and the area covered by precipitation is less than around 1,300 km². Frequently, local storms will last only 1 or 2 hours and precipitation will occur over area sizes up to 500 km². Precipitation in local storms will be isolated from general-storm rainfall.”

Two storm rainfall examples highlight the vastly different spatial and temporal scales for events that contribute to PMP estimation and that are applied to dams and nuclear facilities. The 6–12 May 1943 storm rainfall was a broad-scale, large-area general storm centered in Oklahoma (Figure 2-10a). This 144-hour event is a “controlling storm” (one that is used to estimate PMP for several area sizes and durations) in HMR 51 and is within 50 percent of PMP for numerous larger area sizes (5,000 to 20,000 mi²) and durations (Riedel and Schreiner, 1980). This storm was used in the design of Keystone Dam on the Arkansas River near Tulsa (Figure 2-10b) and numerous other

dams in the central United States; the watershed area is larger than 74,000 mi² with an estimated contributing storm area (that area that generates flood runoff) over the lower watershed area of 24,000 mi². This figure illustrates a partial-area case, where the storm area is much less than the watershed area, and the storm area is the critical input. Less than 2 percent of high-hazard dams are on watersheds that exceed 20,000 mi² (such as this one), thus there is lack of need for PMP estimates at scales larger than this.

In contrast, the 31 July 1976 extreme rainstorm and flood in the Big Thompson canyon in Colorado is a prototypical local storm characterized by its small area (Figure 2-11a) and short duration (4 hours), exceeding 12 inches over 0.2 mi² (Figure 2-11b) (Hansen et al., 1988), with most of the observations from bucket surveys (Miller et al., 1978). This storm was utilized to estimate local-storm PMP in the generalized PMP report HMR 55A (Hansen et al., 1988) and in the Colorado-New Mexico statewide study (AWA, 2018). Local storms such as this one are critical for estimating PMP and locally intense precipitation (LIP) at 1 mi² scales for nuclear reactors (Figure 2-12). LIP is defined as the 1-hour, 2.56-km² (1-mi²) PMP at the location of the site (Prasad et al., 2011), but it is sometimes estimated using the 6-hour, 10-mi² PMP rainfall depth (DeNeale et al., 2021).

PMP AND PROBABLE MAXIMUM FLOODS

For flood hydrologists and engineers conducting safety assessments and designing critical infrastructure, PMP is just the start of the process. PMP serves as a critical input to estimate PMF, which is the operative flood metric against which many high-hazard dams and nuclear facilities are generally designed and with which their vulnerability and safety are continually assessed using RIDM. Failure of a dam to competently pass the simulated PMF event or of a nuclear facility to survive simulated PMF inundation without damage indicates the need for potential safety enhancements to the structure, such as extending upward the elevation of a dam crest or lowering the normal operating level of the reservoir.

The PMP analysis provides the spatial and temporal rainfall inputs that drive the rainfall-runoff simulation process to estimate maximum peak flows, flood hydrograph shapes, total runoff volumes, and maximum reservoir and river stage levels that govern dam and facility designs and assessments. The modern hydrologic models used to simulate extreme floods and PMFs are spatially explicit, with inputs and computations on a 1 kilometer or smaller (250 meter) grid. Examples of modern hydrologic models for watershed flood applications at these scales are the two-dimensional runoff, erosion, and export (TREX) model (England et al., 2007); the gridded surface-subsurface hydrological analysis (GSSHA) model (Sharif et al., 2010); the Hydrologic Engineering Center hydrologic modeling system (HEC-HMS) two-dimensional model (URL: https://www.hec.usace.army.mil/software/hec-hms/); the watershed environmental hydrology hydroclimate model (WEHY-HCM) (Trinh et al., 2022a); and the national water model (NWM) (Cosgrove et al., 2024). These models require, or at least greatly benefit from, spatiotemporally distributed rainfall information in ways that earlier models did not. Key PMP and atmospheric variables to estimate extreme floods and PMF are described in Box 2-4.

In addition to the PMP rainfall, the PMF simulation requires estimates of (1) infiltration (loss) rates, (2) antecedent storms and soil moisture conditions within the watershed, (3) the nature, extent, and condition of vegetation that may intercept and slow the flow of runoff into streams, (4) the level of receiving streams and reservoirs that convey or temporally hold flood waters before they reach the location of the dam or nuclear facility, and (5) potential sequences of successive storms for large watersheds. Snowpack depth, distribution, and conditions are contributors in the northern portion of the United States. Finally, the PMF analysis requires the analyst to input operational rule curves of the dams or nuclear facilities at and upstream of the design site. Rule curves represent plans that describe how dam and nuclear facility operators are expected to respond to evolving flood conditions.

Different PMP rainfall distributions, either spatial or temporal, different antecedent soil moisture conditions, reservoir and river water levels prior to the PMF event, and different operational rules can each result in vastly different PMF estimates (Salas et al., 2014). Often, statistical distributions representing the likelihood of multiple possible combinations of each input are sampled in a generalized sensitivity analysis to identify a set of risk-informed design flood flows (e.g., Hall et al., 2018). The practicing community recognizes various sampling strategies, some of which can be used to assess the impacts of climate change on flood flows (e.g., Bahls and Holman, 2014).

Federal agencies have developed RIDM and design procedures that include sensitivity studies of the PMP and PMF, recognizing that PMF is not a single (deterministic) number, but an estimate with uncertainty (Salas et al., 2014). The USBR design standard for spillways provides procedures to account for uncertainties in flood estimates through scenarios and sensitivity analyses, with provisions for changes in hydrology and climate change (USBR, 2013). The USACE PMF estimation and inflow design flood procedures have evolved to include sensitivity analyses and to provide ranges on PMF hydrographs and reservoir elevations, with “recommended” PMF and “upper” PMF estimates (e.g., Sasaki and Margo, 2021.) These procedures can be improved to utilize PMP uncertainty estimates and ensembles through RIDM (Box 2-3) and include climate resilience (ASCE, 2018).

One aspect of PMF analysis is that, unlike PMP analysis, it can be informed by flood data based on pre-instrumental, even prehistoric flood events. Floods, past and present, leave various geological and biological markers that can be used to infer the magnitude (peak flow) of those events. Paleoflood techniques may involve exposure and dating of rock or soil terraces and strata deposited by past floods on adjoining floodplains, identification and dating of highwater marks and slackwater deposits in nearby caves, biological markers such as tree scars, and stable geologic features and soils that are used to estimate limits on floods (Figure 2-14). These paleoflood markers and non-exceedance bounds can be used with well-established hydraulic models to estimate past flood flows, often resulting in estimates of multiple floods occurring at the same site and spanning hundreds or thousands of years. Such flood evidence, together with radiocarbon and tree ring data can extend flood records back thousands of years in time and permit development of an “observed” flood record that can greatly augment the extreme flood record. These data can serve as an independent reference with which to judge and improve PMF estimates based on PMP simulations alone. Paleoflood data are being used by USBR (Swain et al., 2006), USACE (2020), and numerous other federal and state agencies (TVA, Colorado Division of Water Resources) in RIDM for dam safety. The U.S. Geological Survey, in cooperation with the Nuclear Regulatory Commission, has demonstrated the applicability of paleoflood and record-extension techniques to better characterize flood-inundation risks at nuclear facilitates (Harden et al., 2021; O’Connor, 2014).