Glossary

9.3 Statistical methods in flood frequency analysis

3 min read•july 22, 2024

Flood frequency analysis is a crucial tool in hydrology, helping us predict the likelihood and size of future floods. By applying statistical methods to historical flood data, we can estimate the probability of extreme events and design structures to withstand them.

This analysis uses probability distributions like Gumbel and Log-Pearson Type III to model flood patterns. By estimating flood quantiles and return periods, we can assess risks and plan for future events, though uncertainties in data and methods must be considered.

Flood Frequency Analysis

Importance of flood frequency analysis

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  • Crucial for hydrologic design and water resources management estimates magnitude and frequency of flood events
  • Enables design of hydraulic structures and flood protection measures (bridges, culverts, levees, dams)
  • Supports flood and management for insurance studies, floodplain mapping and zoning
  • Informs land use planning and development decisions in flood-prone areas (floodplains, coastal zones)

Application of probability distributions

  • Model frequency and magnitude of flood events using Gumbel (Extreme Value Type I) and Log-Pearson Type III distributions
  • assumes flood events are independent and identically distributed based on extreme value theory
    • Probability density function: f(x)=1αexp⁡[−x−βα−exp⁡(−x−βα)]f(x) = \frac{1}{\alpha} \exp\left[-\frac{x-\beta}{\alpha} - \exp\left(-\frac{x-\beta}{\alpha}\right)\right] (α\alpha: scale parameter, β\beta: location parameter)
  • commonly used in the US assumes logarithms of flood data follow Pearson Type III distribution
    • Requires estimation of mean, standard deviation, and skewness of log-transformed data
    • Probability density function: f(x)=1x∣β∣Γ(α)(ln⁡(x)−γβ)α−1exp⁡(−ln⁡(x)−γβ)f(x) = \frac{1}{x|\beta|\Gamma(\alpha)}\left(\frac{\ln(x)-\gamma}{\beta}\right)^{\alpha-1} \exp\left(-\frac{\ln(x)-\gamma}{\beta}\right) (α\alpha: shape parameter, β\beta: scale parameter, γ\gamma: location parameter)

Estimation of flood quantiles

  • Represent magnitude of flood events associated with specific probabilities or return periods
  • is average time interval between flood events of given magnitude or greater calculated as reciprocal of (AEP)
    • 100-year flood has AEP of 0.01 or 1%
  • Methods for estimating flood quantiles and return periods include:
    1. Graphical methods using probability plots (Gumbel, Log-Pearson Type III) and fitting straight line to data points
    2. Analytical methods like method of moments estimating distribution parameters using sample moments (mean, variance, skewness) and maximizing likelihood function
    3. Regional flood frequency analysis combining data from multiple sites in a region to improve reliability of estimates when site-specific data is limited or unavailable (pooled frequency analysis)

Uncertainties in frequency analysis

  • Arise from data quality and quantity issues (measurement errors, missing data, short record lengths, non-stationarity due to climate change and land use modifications)
  • Choice of probability distribution and parameter estimation methods may yield different results
  • Extrapolation beyond observed data range to estimate rare events (100-year or 500-year floods) involves increased uncertainty
  • Limitations include assuming future floods follow same statistical distribution as historical events, not explicitly considering physical processes driving floods (rainfall-runoff dynamics, hydraulic routing, river channel morphology), and relying on quality and representativeness of available flood data
  • Address uncertainties by using multiple probability distributions and parameter estimation methods, incorporating additional data sources (historical records, paleoflood evidence), applying regional flood frequency analysis, using physically-based hydrologic and hydraulic models to complement statistical approaches, and communicating uncertainties to decision-makers and stakeholders (risk communication)

Key Terms to Review (18)

Annual exceedance probability: Annual exceedance probability (AEP) is the likelihood of a flood event occurring in any given year, expressed as a percentage. It is used in flood frequency analysis to determine the probability of a certain magnitude of flood occurring within a specified time frame, helping to inform risk management and infrastructure design.
Exceedance Probability: Exceedance probability is the likelihood that a given variable, such as precipitation or river flow, will exceed a specified threshold within a defined time period. This concept is crucial for assessing risk and understanding the frequency of extreme events, helping in the planning and management of water resources. It is closely related to statistical analysis, allowing for the evaluation of historical data to predict future occurrences of significant events like floods or droughts.
Flood duration: Flood duration refers to the length of time that a flood event remains at or above a specified flood level within a given area. This measurement is crucial in understanding the impacts of flooding, as longer durations can lead to increased damage to property and ecosystems, while also influencing the design of flood control measures and infrastructure planning.
Flood magnitude: Flood magnitude refers to the size or severity of a flood event, typically measured in terms of discharge (volume of water flow) or its effects on the surrounding area. Understanding flood magnitude is crucial for assessing flood risk and implementing effective management strategies, as it provides insight into the frequency and intensity of flooding events over time.
Frequency analysis model: A frequency analysis model is a statistical tool used to estimate the likelihood of flood events based on historical data. This model helps to analyze the frequency and magnitude of floods, allowing hydrologists to predict future flood risks and inform water resource management decisions. By evaluating historical occurrences, the model provides insights into extreme weather patterns and their potential impacts on communities and ecosystems.
Gumbel Distribution: The Gumbel distribution is a probability distribution used to model the distribution of extreme values, specifically for predicting the maximum or minimum values in a dataset. This distribution is particularly relevant in hydrology for flood frequency analysis, helping to estimate the likelihood of extreme flood events based on historical data.
HEC-RAS: HEC-RAS (Hydrologic Engineering Center's River Analysis System) is a software used for modeling the hydraulics of water flow through rivers and channels. This powerful tool helps engineers and hydrologists perform one-dimensional steady and unsteady flow analyses, making it essential for understanding floodplain management, flood routing, and flood frequency analysis. Its ability to incorporate various hydraulic structures, terrain data, and flow conditions allows for detailed simulations crucial for effective water resource management.
L-moments: L-moments are a set of statistics used to describe the characteristics of a probability distribution, particularly in the context of hydrology and flood frequency analysis. They provide a robust alternative to conventional moments, like mean and variance, by offering better performance with small sample sizes and heavy-tailed distributions, which are common in hydrological data. L-moments focus on linear combinations of order statistics, making them particularly useful for estimating parameters of distribution functions relevant to extreme value analysis.
Log-pearson type iii distribution: The log-pearson type iii distribution is a statistical method used to model the distribution of flood peaks and low flow events, transforming data using a logarithmic scale to achieve a normal distribution. This approach is particularly useful in hydrology for estimating flood frequencies and analyzing low flow conditions by providing a reliable way to predict the occurrence and magnitude of extreme hydrological events.
Maximum likelihood estimation: Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution by maximizing a likelihood function. This technique is pivotal in flood frequency analysis, as it allows researchers to fit models to historical flood data, ensuring that the estimated parameters are those that make the observed data most probable. MLE helps in identifying the best-fitting distribution for analyzing flood events, which is essential for predicting future flood risks and managing water resources effectively.
Regression analysis: Regression analysis is a statistical method used to determine the relationship between a dependent variable and one or more independent variables. By estimating the strength and form of these relationships, it helps in making predictions, understanding data trends, and quantifying how variables impact each other. This technique is vital for modeling complex processes, such as estimating evapotranspiration rates in water balance calculations or analyzing flood frequency data.
Return Period: The return period is a statistical measure that estimates the average time interval between events of a certain intensity or magnitude, commonly used in the context of precipitation and flooding. This concept helps in understanding the likelihood of rare events occurring over a specified timeframe, and it plays a critical role in assessing flood risk and designing infrastructure. By analyzing historical data, the return period aids in predicting future occurrences, which is essential for effective water resource management and planning.
Risk assessment: Risk assessment is the process of identifying, evaluating, and prioritizing risks associated with potential hazards in order to minimize their impact on resources and human life. This method helps decision-makers understand vulnerabilities and allocate resources effectively, ensuring that strategies are in place to manage both floods and droughts, as well as adapt to changing water resource demands.
Risk ratio: The risk ratio is a statistical measure used to compare the likelihood of a specific outcome occurring in two different groups. It is commonly used in flood frequency analysis to assess the risk of flooding events by comparing the probability of occurrence between different time periods or locations. This measure helps to identify how much more or less likely an event is to happen in one group compared to another.
Stochastic model: A stochastic model is a mathematical representation that incorporates randomness and unpredictability in its processes, allowing for the modeling of systems affected by uncertain variables. This type of model is particularly useful in understanding and predicting phenomena in fields like hydrology, where factors such as rainfall and flood occurrences are inherently variable. By capturing the probabilistic nature of these elements, stochastic models enable better risk assessments and decision-making in flood frequency analysis.
SWMM: SWMM, or the Storm Water Management Model, is a computer program developed by the U.S. Environmental Protection Agency for simulating the quantity and quality of stormwater runoff in urban areas. It helps engineers and hydrologists analyze how stormwater interacts with the landscape and infrastructure, enabling effective flood management, water quality assessment, and urban planning. By utilizing SWMM, users can evaluate the impacts of different stormwater management practices on flooding and water pollution in a watershed.
Time Series Analysis: Time series analysis is a statistical technique used to analyze a sequence of data points collected over time. This method helps identify trends, seasonal patterns, and cyclical fluctuations, allowing researchers to make forecasts based on historical data. By understanding these temporal patterns, scientists can better assess changes in environmental variables and their implications for water balance calculations and flood frequency.
Vulnerability analysis: Vulnerability analysis is the systematic assessment of the susceptibility of a system or community to harm from various hazards, such as floods and droughts. This analysis helps identify weaknesses in infrastructure, preparedness, and response strategies, enabling stakeholders to prioritize resources and implement measures to mitigate risks associated with environmental changes. By understanding vulnerabilities, effective management strategies can be developed to improve resilience in both flood and drought scenarios.
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