Flood Frequency Analysis Through Time

Hydrologic monitoring instruments installed in a river to collect flow and water level data

Flood frequency analysis (FFA) is a core element of water resource engineering and critical for floodplain management, infrastructure design, risk assessment and more. Over the last 35 years, methodologies to perform FFA have evolved significantly, adapting to changing environmental conditions, new data sources, improved computational capabilities, statistical innovations, and a better understanding of hydrological processes.

As engineers, we know that flood frequency analysis has traditionally relied on historical streamflow records. The process typically involved fitting probability distributions to annual maximum flood series using graphical techniques to estimate flood quantiles, with the assumption that flood events were predominantly stationary and independent. Current non-stationary conditions, combined with a better understanding of hydrologic system dynamics and other sources of variability, often require modified strategies. This article gives a general overview of how FFA methodology has changed over the years.

Developing best practices in flood frequency analysis

Some form of the Pearson system, currently known as the Log-Pearson Type III distribution (LP3), has been in use since the 1940s. The LP3 method generally involves calculating the mean, standard deviation, and skew coefficient of the logarithms of annual peak flows to estimate flood magnitudes for various return periods. The U.S. Water Resources Council adopted this methodology in federal guidelines for FFA and flood design with publication of Guidelines for Determining Flood Flow Frequency (or Bulletin 17) in 1976. In the decades that followed, LP3 would form the baseline from which to do further research and build on existing methodology; the integration of generalized skew, low-outlier tests, and paleoflood evidence to fill out the record on extreme floods represent examples of subsequent adaptations. These guidelines were incorporated into federal guidance through the release of Bulletin 17B in 1982.

Index flood methods were also developed in the 1980s and 1990s, which assumed that the frequency distribution of floods at different sites within a largely uniform region could be scaled with a site-specific index flood (typically the mean annual flood). This method was used frequently in regions with limited data at individual sites. These developments coincided with emergence of Bayesian methodology, which is a form of inferential analysis that builds on estimated probability by integrating new data as they become available.

Additional statistical techniques were introduced in the 1990s and 2000s with the Expected Moments algorithm (EMA), maximum likelihood estimation, potentially influential low floods, and L-moments methodology for parameter estimation of probability distributions. These methods allowed for more robust and efficient estimation of flood quantiles and were published in federal Bulletin 17C guidelines, released in 2018.

Methodologies to address regional variability in flood frequency analysis through large sample simulations became more standardized in later years. Generalized extreme value, Gumbel distribution and LP3 have been tested in different hydroclimatic regions with the pooling of data from multiple sites to improve estimation accuracy.

As applications and objectives evolved, Bayesian inference techniques continue to be used in current flood frequency analyses. These methods allow for the incorporation of prior knowledge, parameter uncertainty quantification, and the combination of multiple data sources, including historical and paleoflood information. Recognition that flood events can result from different meteorological mechanisms (e.g., snowmelt, rainfall, hurricanes) has led to the development of mixed population distribution models. These approaches separate flood series into distinct groups and analyze them separately before combining results.

Advances in computational capacity and uncertainty

Given advances in computational power, continuous hydrologic simulation models representative of multiple scenarios are being used to generate long synthetic streamflow series. These can be analyzed to derive flood frequency estimates, particularly useful for assessing the joint probability of flood characteristics.

A growing awareness of the need to quantify and communicate uncertainties in flood frequency estimates has focused attention on parameter uncertainty, sampling uncertainty, and model structural uncertainty. Accordingly, instead of relying on a single best-fit distribution, current practices often involve considering multiple probability distributions and weighting their results based on their fit to the observed data. Parameters are structured to vary with time, climate or different land use covariates.

In conclusion, flood frequency analysis has evolved from relatively simple, stationary approaches to advanced methodologies that account for non-stationarity, regional influences, and multiple data sources. Current best practices emphasize the importance of uncertainty quantification, the integration of diverse data types, and the consideration of spatial variability and changing environmental conditions. As climate change continues to modify hydrological regimes, the field of flood frequency analysis will likely see further innovations. Reliable assessment of flood risk to ensure suitable project and infrastructure design is increasingly important in the years ahead.