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Mississippi River at Kaskaskia, Illinois, during the Great Flood of 1993

A 100-year flood, also called a 1% flood,[1] or High Probability in the UK,[2] is a flood event for a defined location at a level reached or exceeded once per hundred years, on average, but as there are many locations there are multiple independent 100-year floods within the same year. In the US, it is estimated on past records as having a 1 in 100 chance (1% probability) of being equaled or exceeded in any given year.[3][4]

The estimated boundaries of inundation in a 100-year or 1% flood are marked on flood maps.[5][2]

UK planning guidance defines Flood Zone 3a "High Probability" as Land having a 1% or greater annual probability of river flooding; or Land having a 0.5% or greater annual probability of sea.[2]

Maps, elevations and flow rates

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For coastal flooding and lake flooding, a 100-year flood is generally expressed as a water level elevation or depth, and includes a combination of tide, storm surge, and waves.[6]

For river systems, a 100-year flood can be expressed as a flow rate, from which the flood elevation is derived. The resulting area of inundation is referred to as the 100-year floodplain. Estimates of the 100-year flood flow rate and other streamflow statistics for any stream in the United States are available.[7] A 100-year storm may or may not cause a 100-year flood, because of rainfall timing and location variations among different drainage basins, and independent causes of floods, such as snow melt and ice dams.

In the UK, the Environment Agency publishes a comprehensive map of all areas at risk of a 100-year flood.[8] In the US, the Federal Emergency Management Agency publishes maps of the 100-year and 500-year floodplains.[5]

Maps of the riverine or coastal 100-year floodplain may figure importantly in building permits, environmental regulations, and flood insurance. These analyses generally represent 20th-century climate and may underestimate the effects of climate change.

Risk

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Observed intervals between floods at Passau, 1501–2013

A common misunderstanding is that a 100-year flood happens once in a 100-year period. On average one happens per 100 years, five per 500 years, ten per thousand years. Any average hides variations. In any particular 100 years at one spot, there is a 37% chance that no 100-year flood happens, 37% chance that exactly one happens, and 26% chance that two or more happen. On the Danube River at Passau, Germany, the actual intervals between 100-year floods during 1501 to 2013 ranged from 37 to 192 years.[9]

A related misunderstanding is that floods bigger than 100-year floods are too rare to be of concern. The 1% chance per year accumulates to 10% chance per decade, 26% chance during a 30-year mortgage,[10] and 55% chance during an 80-year human lifetime. It is common to refer to 100-year floods as floods with 1% chance per year. It is equally true to refer to them as floods with 10% chance per decade.

Over a large diverse area, such as a large country or the world, in an average year 1% of watersheds have 100-year floods or bigger, and 0.1% of watersheds have 1,000-year floods or bigger. There are more in wet years, fewer in dry years. Of 1.6 million kilometers of coastline in the world,[11] in an average year 1,600 kilometers have 1,000-year floods or bigger, more in stormy years, fewer in calmer years.

The US flood insurance program, starting in the 1960s, chose to foster rules in, and insure buildings in, 100-year floodplains, as "a fair balance between protecting the public and overly stringent regulation."[10] After the North Sea flood of 1953, the United Kingdom mapped 1,000-year floods and the Netherlands raised its flood defenses to protect against up to 10,000 year floods.[12] In 2017 the Netherlands designed some areas against million-year floods.[13] The American Society of Civil Engineers recommends designing some structures for up to 1,000-year floods,[14] while it recommends designing for up to 3,000-year winds.[15] Per century, any one area has a 63% chance of a 100-year flood or worse, 10% chance of a 1,000-year flood, 1% chance of a 10,000-year flood, and 0.01% chance of a million-year flood. As David van Dantzig, working on the government response to the 1953 flood, said, "One will surely be willing to spend a multiple of the amount that would be lost by a flood if the flood can thereby be prevented."[16]

Flood insurance

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Main article: Flood insurance

In the United States, the 100-year flood provides the risk basis for flood insurance rates. A regulatory flood or base flood is routinely established for river reaches through a science-based rule-making process targeted to a 100-year flood at the historical average recurrence interval. In addition to historical flood data, the process accounts for previously established regulatory values, the effects of flood-control reservoirs, and changes in land use in the watershed. Coastal flood hazards have been mapped by a similar approach that includes the relevant physical processes. Most areas where serious floods can occur in the United States have been mapped consistently in this manner. On average nationwide, those 100-year flood estimates are sufficient for the purposes of the National Flood Insurance Program (NFIP) and offer reasonable estimates of future flood risk, if the future is like the past.[9]: 24  Approximately 3% of the U.S. population lives in areas subject to the 1% annual chance coastal flood hazard.[17]

In theory, removing homes and businesses from areas that flood repeatedly can protect people and reduce insurance losses, but in practice it is difficult for people to retreat from established neighborhoods.[18]

Probability

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The probability Pe that one or more floods occurring during any period will exceed a given flood threshold can be expressed, using the binomial distribution, as

where T is the threshold mean recurrence interval[15] (e.g. 100-yr, 50-yr, 25-yr, and so forth), greater than 1. If T is in years, then n is the number of years in the period, and Pe is the chance per year, Annual Exceedance Probability.[19]

The formula can be understood as:

  • Chance per year of a T-year flood is 1/T for example 1/100 = 0.01
  • Chance per year of no such flood is 1 − 1/T for example 1 − 0.01 = 0.99
  • Chance that n independent years have no such flood, by multiplying, is (1 − 1/T)n for example 0.99100 = 0.366
  • Chance of at least one flood in n years is 1 − (1 − 1/T)n for example 1 − 0.99100 = 0.634 = 63.4%

The probability of exceedance Pe is also described as the natural, inherent, or hydrologic risk of failure.[20][21] However, the expected value of the number of 100-year floods occurring in any 100-year period is 1.

Ten-year floods have a 10% chance of occurring in any given year (Pe =0.10); 500-year floods have a 0.2% chance of occurring in any given year (Pe =0.002); etc. The percent chance of a T-year flood occurring in a single year is 100/T, where T is bigger than 1.

During this many years, chance of at least one storm of severity shown on left, or worse[15]
Storm with chance shown below, of being equaled or exceeded each year 1 year 10 years 30 years 50 years 80 years 100 years 200 years
1/100 1.0% 9.6% 26.0% 39.5% 55.2% 63.4% 86.6%
1/500 0.2% 2.0% 5.8% 9.5% 14.8% 18.1% 33.0%
1/1,000 0.1% 1.0% 3.0% 4.9% 7.7% 9.5% 18.1%
1/10,000 0.0% 0.10% 0.30% 0.50% 0.80% 1.00% 1.98%
1/1,000,000 0.0001% 0.001% 0.003% 0.005% 0.008% 0.010% 0.020%

The same formula above can give the chance of occurrence in less than a year. A 1-year flood is a 12-month flood, with a 1/12 chance each month, and the formula in months shows 65% chance each year.

The field of extreme value theory was created to model rare events such as 100-year floods for the purposes of civil engineering. This theory is most commonly applied to the maximum or minimum observed stream flows of a given river. In desert areas where there are only ephemeral washes, this method is applied to the maximum observed flow over a given period of time (24-hours, 6-hours, or 3-hours). The extreme value analysis only considers the most extreme event observed in a given year. So, between the large spring runoff and a heavy summer rain storm, whichever resulted in more runoff would be considered the extreme event, while the smaller event would be ignored in the analysis (even though both may have been capable of causing terrible flooding in their own right).

Statistical assumptions

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There are a number of assumptions that are made to complete the analysis that determines the 100-year flood. First, the extreme events observed in each year must be independent from year to year. In other words, the maximum river flow rate from 1984 cannot be found to be significantly correlated with the observed flow rate in 1985, which cannot be correlated with 1986, and so forth. The second assumption is that the observed extreme events must come from the same probability density function. The third assumption is that the probability distribution relates to the largest storm (rainfall or river flow rate measurement) that occurs in any one year. The fourth assumption is that the probability distribution function is stationary, meaning that the mean (average), standard deviation and maximum and minimum values are not increasing or decreasing over time. This concept is referred to as stationarity.[21][22]

The first assumption is often but not always valid and should be tested on a case-by-case basis. The second assumption is often valid if the extreme events are observed under similar climate conditions. For example, if the extreme events on record all come from late summer thunderstorms (as is the case in the southwest U.S.), or from snow pack melting (as is the case in north-central U.S.), then this assumption should be valid. If, however, there are some extreme events taken from thunder storms, others from snow pack melting, and others from hurricanes, then this assumption is most likely not valid. The third assumption is only a problem when trying to forecast a low, but maximum flow event (for example, an event smaller than a 2-year flood). Since this is not typically a goal in extreme analysis, or in civil engineering design, then the situation rarely presents itself.

The final assumption about stationarity is difficult to test from data for a single site because of the large uncertainties in even the longest flood records[9] (see next section). More broadly, substantial evidence of climate change strongly suggests that the probability distribution is also changing[23] and that managing flood risks in the future will become even more difficult.[24] The simplest implication of this is that most of the historical data represent 20th-century climate and might not be valid for extreme event analysis in the 21st century.

Probability uncertainty

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When these assumptions are violated, there is an unknown amount of uncertainty introduced into the reported value of what the 100-year flood means in terms of rainfall intensity, or flood depth. When all of the inputs are known, the uncertainty can be measured in the form of a confidence interval. For example, one might say there is a 95% chance that the 100-year flood is greater than X, but less than Y.[1]

Direct statistical analysis[22][25] to estimate the 100-year riverine flood is possible only at the relatively few locations where an annual series of maximum instantaneous flood discharges has been recorded. In the United States as of 2014, taxpayers have supported such records for at least 60 years at fewer than 2,600 locations, for at least 90 years at fewer than 500, and for at least 120 years at only 11.[26] For comparison, the total area of the nation is about 3,800,000 square miles (9,800,000 km2), so there are perhaps 3,000 stream reaches that drain watersheds of 1,000 square miles (2,600 km2) and 300,000 reaches that drain 10 square miles (26 km2). In urban areas, 100-year flood estimates are needed for watersheds as small as 1 square mile (2.6 km2). For reaches without sufficient data for direct analysis, 100-year flood estimates are derived from indirect statistical analysis of flood records at other locations in a hydrologically similar region or from other hydrologic models. Similarly for coastal floods, tide gauge data exist for only about 1,450 sites worldwide, of which only about 950 added information to the global data center between January 2010 and March 2016.[27]

High-water scale 1501–2002 at Passau, Germany, as of September 2012

Much longer records of flood elevations exist at a few locations around the world, such as the Danube River at Passau, Germany, but they must be evaluated carefully for accuracy and completeness before any statistical interpretation.

For an individual stream reach, the uncertainties in any analysis can be large, so 100-year flood estimates have large individual uncertainties for most stream reaches.[9]: 24  For the largest recorded flood at any specific location, or any potentially larger event, the recurrence interval always is poorly known.[9]: 20, 24  Spatial variability adds more uncertainty, because a flood peak observed at different locations on the same stream during the same event commonly represents a different recurrence interval at each location.[9]: 20  If an extreme storm drops enough rain on one branch of a river to cause a 100-year flood, but no rain falls over another branch, the flood wave downstream from their junction might have a recurrence interval of only 10 years. Conversely, a storm that produces a 25-year flood simultaneously in each branch might form a 100-year flood downstream. During a time of flooding, news accounts necessarily simplify the story by reporting the greatest damage and largest recurrence interval estimated at any location. The public can easily and incorrectly conclude that the recurrence interval applies to all stream reaches in the flood area.[9]: 7, 24 

Observed intervals between floods

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Peak elevations of 14 floods as early as 1501 on the Danube River at Passau, Germany, reveal great variability in the actual intervals between floods.[9]: 16–19  Flood events greater than the 50-year flood occurred at intervals of 4 to 192 years since 1501, and the 50-year flood of 2002 was followed only 11 years later by a 500-year flood. Only half of the intervals between 50- and 100-year floods were within 50 percent of the nominal average interval. Similarly, the intervals between 5-year floods during 1955 to 2007 ranged from 5 months to 16 years, and only half were within 2.5 to 7.5 years.

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

100-year flood

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A 100-year flood is a statistically defined flood event with a 1% annual exceedance probability, meaning it has a 1 in 100 chance of being equaled or exceeded in any given year based on analysis of historical data. This recurrence interval represents the long-term average frequency derived from empirical records of peak discharges at stream gages, rather than a of temporal spacing; such floods can occur consecutively or with irregular intervals due to the of annual probabilities. Hydrologists compute these estimates using statistical models fitted to observed data, often incorporating log-Pearson Type III distributions, with updates as new flood records refine the probability curves and can shift prior delineations. The concept underpins flood risk mapping, infrastructure design, and floodplain management , where the 1% annual chance flood serves as a benchmark for federal regulations like the , though it does not account for non-stationary trends in or land use that empirical data increasingly reveal. Common misconceptions arise from interpreting the term literally as a once-per-century event, but probabilistic implies a 26% chance of at least one occurrence over a 30-year period, highlighting the need for over deterministic expectations.

Definition and Conceptual Basis

Statistical Definition

The 100-year flood is statistically defined as the magnitude of a flood event—typically measured by peak discharge or —that has an annual exceedance probability (AEP) of 1%, equivalent to a 1 in 100 chance of being equaled or exceeded in any single year. This definition arises from flood frequency analysis, where historical records of maximum annual flood peaks at a gauging station are used to construct an empirical or fitted , identifying the flood quantile at the 0.01 exceedance level. The AEP framework emphasizes the independence of yearly events under the assumption of a stationary hydrological , though real-world non-stationarities like variability or land-use changes can affect estimates. In quantitative terms, if Q100Q_{100} denotes the 100-year flood discharge, it satisfies P(Q≥Q100)=0.01P(Q \geq Q_{100}) = 0.01 for the annual maximum flood QQ, often modeled via extreme value distributions. This threshold is not a fixed prediction but a probabilistic benchmark, with the probability of occurrence in a given year remaining constant at 1% regardless of prior floods—such that multiple 100-year floods could occur within a , as seen in clustered events due to atmospheric . For instance, the U.S. Geological Survey applies this definition in records spanning decades, where short datasets (e.g., fewer than 50 years) introduce higher uncertainty in Q100Q_{100} estimates compared to longer records. The 1% AEP standard was formalized in U.S. federal policy during the for flood risk mapping and infrastructure design, replacing earlier deterministic approaches with this probabilistic metric to account for variability in natural flood processes. Agencies like the USGS and NOAA compute these values using log-transformed to handle , ensuring the definition aligns with observed empirical frequencies over time. While robust for many rivers, the definition assumes —treating time averages as equivalent to ensemble averages—which may not hold in regions with regime shifts, necessitating periodic recalibration of estimates.

Return Period and Probability

The return period, or recurrence interval, of a flood event is the average expected time between occurrences of floods equal to or exceeding a specified magnitude, calculated as the reciprocal of the annual exceedance probability (AEP). For a 100-year , the return period is 100 years, indicating an AEP of 1%, or a 1 in 100 chance of the event occurring or being surpassed in any single year based on statistical analysis of historical peak flow data. This metric assumes a stationary hydrological where flood probabilities remain constant over time, derived from distributions fitted to long-term gage records. The AEP for a flood with return period T is given by p = 1/T, such that the probability remains independent across years under the model of rare, uncorrelated events. Thus, a 100-year (T = 100) has p = 0.01 annually, allowing for the possibility of multiple occurrences within a short span or extended absences, as each year resets the probabilistic assessment without regard to prior events. Empirical records confirm this, with instances of back-to-back "100-year" documented in various U.S. basins, underscoring that the describes long-term averages rather than deterministic cycles. Over multiple years, the cumulative probability of at least one exceedance compounds as 1 - (1 - p)^n, where n is the number of years. For a 100-year event over a 100-year span, this equates to roughly a 63% likelihood, highlighting how the descriptor can understate risks for planning horizons exceeding decades. Such calculations, rooted in , inform flood zoning and design standards but require robust data to mitigate estimation errors from short or non-stationary records.

Common Misconceptions

A prevalent misconception is that a "100-year " occurs precisely once every 100 years, implying a regular cycle. In reality, the designation refers to a magnitude with a 1% probability of being equaled or exceeded in any given year, based on statistical analysis of historical data, and events are independent across years, allowing multiple occurrences in short succession or long gaps, such as the Skagit River in Washington state reaching major flood levels and prompting Level 3 evacuations in its 100-year floodplain on December 10, 2025. Another common error holds that experiencing a 100-year flood grants immunity for the subsequent 99 years. This overlooks the annual independence of flood probabilities; the 1% risk persists each year regardless of prior events, akin to independent coin flips where heads (a ) can occur consecutively. The term is often misinterpreted as denoting the maximum possible flood or an absolute benchmark, whereas it represents an estimated from probabilistic modeling, subject to data limitations and potential revisions with new observations. For instance, regional analyses may reveal that "100-year" events occur more frequently than the label suggests in certain basins, such as an average of every 4.5 years for rivers draining into . Over longer periods, the cumulative risk is understated by focusing solely on the annual figure; a property in a 100-year floodplain faces approximately a 26% chance of flooding at least once in 30 years and nearly 64% over a century, highlighting the non-negligible exposure even in standard mortgage durations.

Historical Development

Origins in Flood Frequency Analysis

The concept of the return period, central to the 100-year flood designation, originated in the early amid efforts to apply statistical techniques to hydrological data for predicting flood magnitudes. Prior to systematic statistical analysis, flood estimation relied on empirical rational formulas, such as those proposed by Mulvany in 1851, which linked peak discharge to basin characteristics like area and rainfall intensity without probabilistic recurrence. However, the expansion of U.S. Geological Survey (USGS) stream gaging stations starting in the late provided annual peak discharge records, enabling probabilistic modeling of flood frequencies. W.G. Fuller pioneered modern flood frequency analysis in his 1914 USGS Water-Supply Paper 378, "Floods in the United States," where he first formalized the as the average interval between floods of a given magnitude, derived from ranked annual maxima at gauged sites. Fuller's approach involved plotting discharges against their rank order (using plotting positions like m/(n+1), where m is rank and n is record length) to construct frequency curves, allowing extrapolation to rare events such as those with 100-year s (1% annual exceedance probability). He analyzed data from over 150 stations, establishing regional formulas like Q_T = a * A^b / T^c, where Q_T is discharge for T, A is drainage area, and a, b, c are fitted coefficients, thus linking flood severity to probabilistic recurrence rather than deterministic maxima. This marked a shift from regional estimates to data-driven inference, though limited by short records (often under 30 years) and assumptions of stationarity. Early adoption built on Fuller's framework through refinements in plotting and distribution fitting. By the 1920s, hydrologists like (1927) advocated log-probability plots for linearizing frequency distributions, facilitating estimation of high s from limited data. These methods assumed floods followed an extreme value distribution, with independence between events, laying groundwork for later parametric models despite challenges like data scarcity and non-stationarities from land-use changes. Fuller's concept directly underpins the "100-year flood" as a benchmark for events with T=100 years, though it was not termed as such until later in practice.

Adoption in Engineering and Policy

The 100-year flood standard was formalized in flood policy through the National Flood Insurance Act of 1968, which established the (NFIP) under the Department of Housing and Urban Development, later transferred to FEMA in 1979. This program designated the 1% annual exceedance probability (AEP) flood—equivalent to the 100-year event—as the "base flood" for identifying Special Flood Hazard Areas (SFHAs), requiring flood insurance for federally backed mortgages in those zones and mandating local zoning regulations to restrict development. By 1973, NFIP mapping standards explicitly incorporated the 100-year to delineate hazard areas, influencing community participation and federal aid eligibility. In engineering practice, the standard gained traction earlier through agencies like the (TVA), which adopted the 100-year flood for designing dams and levees in the mid-20th century to balance cost against flood control efficacy. The U.S. Army Corps of Engineers integrated it into post-1936 Flood Control Act projects, using for structural works, though designs often incorporated safety factors beyond the probabilistic threshold. Professional bodies such as the (ASCE) endorsed the 100-year event as a benchmark for assessing vulnerability, applying it to systems, bridges, and urban drainage to quantify failure risks under rare events. Policy adoption extended to executive actions, including Executive Order 11988 (1977), which directed federal agencies to avoid supporting development in the 100-year unless no practicable alternatives existed, embedding the standard in environmental reviews and cost-benefit analyses. This framework has shaped billions in infrastructure investments, with NFIP-mapped floodplains covering over 12 million properties as of 2023, though critics note its static nature overlooks non-stationary risks from climate variability. In engineering codes, states and municipalities reference it for minimum elevation requirements, such as base flood elevation plus freeboard, to mitigate losses estimated at $8-10 billion annually from floods exceeding design levels.

Statistical Methodology

Probability Distributions Used

In flood frequency analysis for estimating 100-year floods, the Log-Pearson Type III (LPIII) distribution is the primary model recommended by the (USGS) for fitting annual maximum peaks. This three-parameter distribution applies after log-transforming flood magnitudes to address positive skewness, assuming the transformed values follow a Pearson Type III form characterized by location, scale, and shape parameters estimated via method of moments or other techniques outlined in USGS Bulletin 17C. The LPIII's flexibility in capturing the heavy-tailed nature of flood data has made it the standard for U.S. federal flood risk assessments since the 1970s, with parameters adjusted using regional skew coefficients to improve extrapolation beyond observed records. Alternative distributions include the Generalized Extreme Value (GEV) distribution, which encompasses Gumbel (Type I), Fréchet (Type II), and Weibull (Type III) as special cases and is theoretically derived for block maxima under extreme value theory, making it suitable for modeling rare flood events. The GEV is widely applied in international contexts and non-U.S. studies for its parsimony in parameter estimation via maximum likelihood or L-moments, often outperforming LPIII in goodness-of-fit for datasets with climatic non-stationarities. The Gumbel distribution, a two-parameter extreme value Type I model assuming exponential tails, was historically prevalent before LPIII adoption but is now used selectively for its simplicity in preliminary analyses or when data suggest lighter tails. Other candidates, such as the log-normal and Gamma distributions, are evaluated in comparative studies but less routinely adopted for regulatory 100-year flood quantiles due to poorer fits for high-return-period extrapolations in skewed hydrological series. Distribution selection typically involves statistical tests like Anderson-Darling or Kolmogorov-Smirnov for goodness-of-fit, with LPIII retained in U.S. practice for consistency in infrastructure design and floodplain mapping despite ongoing debates over its performance in non-stationary climates.

Estimation from Data

Flood frequency analysis estimates the magnitude of a 100-year flood by applying statistical methods to historical records of annual maximum instantaneous peak discharges collected at stream gaging stations. These records, typically spanning decades, form the annual maximum series (AMS), with a minimum of 10 years required for analysis, though longer records improve reliability. The U.S. Geological Survey's Bulletin 17C provides standardized guidelines, emphasizing the Expected Moments Algorithm (EMA) to derive unbiased estimates while accommodating censored observations, historical floods, and low outliers. Data preparation begins with screening for low outliers using the Multiple Grubbs-Beck test to identify potentially influential low floods (PILFs), which are censored to avoid skewing estimates of rare high floods. Historical data, such as high-water marks predating systematic gauging, are incorporated via perception thresholds defining lower and upper bounds for flood magnitudes during ungaged periods (e.g., flows exceeding 21,000 ft³/s for certain intervals). Peak flows are then log-transformed (base-10) to stabilize variance, and sample moments—mean (μ\mu), standard deviation (σ\sigma), and skewness (γ\gamma)—are computed, with EMA adjusting for interval-censored and applying bias (e.g., factors c2c_2 and c3c_3) per equations 7-1 through 7-5 in Bulletin 17C. For sites with short records, a regional skew coefficient, estimated via Bayesian , supplements station skew to constrain γ>−1.4\gamma > -1.4 and reduce uncertainty. The Log-Pearson Type III (LPIII) distribution is fitted using these moments, as it flexibly models the positively skewed, heavy-tailed nature of flood data. The 100-year flood magnitude Q100Q_{100} is then calculated as Qp=10(μ+Kγ,pσ)Q_p = 10^{(\mu + K_{\gamma,p} \sigma)}, where p=0.01p = 0.01 is the annual exceedance probability and Kγ,pK_{\gamma,p} is the frequency factor tabulated or computed for the LPIII based on γ\gamma and pp. Software such as PeakFQ implements these EMA-LPIII procedures, yielding point estimates (e.g., 22,480 ft³/s for a sample site) alongside confidence intervals derived from EMA variance (equation 7-21), often spanning 20-50% or more due to beyond observed maxima. This parametric approach assumes the LPIII adequately captures underlying flood-generating processes, but estimates for rare events like the 100-year flood rely on , amplifying sensitivity to high-magnitude observations and regional adjustments. Non-parametric alternatives, such as plotting positions (e.g., Weibull for ranking floods), provide bounds but are less common for formal design due to limited capability.

Uncertainty in Calculations

Uncertainty in estimating the magnitude of a 100-year flood arises primarily from sampling variability due to finite historical records, which limits the precision of statistical extrapolations to rare events with low annual exceedance probabilities. In flood frequency analysis, the Log-Pearson Type III distribution, as recommended in USGS guidelines, relies on estimating parameters (location, scale, and skew) from annual peak flow data, but short records—often less than 50 years—result in high variance for tail quantiles. For instance, measurement errors in peak flows, such as those from extrapolations in high-flow conditions, can exceed 25% and propagate into broader estimate errors. Confidence intervals provide a measure of this statistical uncertainty, typically computed using the Expected Moments Algorithm (EMA) that accounts for at-site data, regional information, and potential low outliers via tests like the Multiple Grubbs-Beck. The interval for a quantile X^q\hat{X}_q at the 100-year return period (AEP=0.01) follows X^q±z1−α/2Var(X^q)\hat{X}_q \pm z_{1-\alpha/2} \sqrt{\text{Var}(\hat{X}_q)}
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