Background
A copula is a mathematical function that describes the dependence among two or more random variables independently of their individual probability distributions (marginal distributions). By separating the dependence structure from the marginals, copulas provide a flexible framework for modeling multivariate relationships.
Compound flooding occurs when multiple flood drivers, such as heavy rainfall, storm surge, and fluvial flooding, occur simultaneously. In these situations, the frequency relationship of a response variable that depends on two or more contributing variables must be quantified. Historically, USACE studies have relied on the total probability method, commonly referred to as coincident frequency analysis, to evaluate joint probability. This approach is documented in Engineer Manual (EM) 1110-2-1415, Hydrologic Frequency Analysis (1993), and EM 1110-2-1413, Hydrologic Analysis of Interior Areas. However, copulas offer numerous advantanges, documented here, over coincident frequency analysis as a statistical approach to compound flood scenarios.
Neptune Implementation
HEC-Neptune provides a Copula Analysis for characterizing joint probability between two dependent variables. It can be applied to combinations of flow, stage, precipitation, wind, surge, or other variables where dependence between the variables is relevant to the response of interest.
The analysis requires:
- Paired events for the two variables. The analyst must define a physically appropriate event extraction and pairing procedure, including the time window used to identify near-coincident events.
- Marginal probability distributions for each variable. HEC-Neptune fits distributions separately to the selected samples for the conditioning or extremal variable and the associated variable.
The program provides the following options:
- A dependence model. HEC-Neptune fits multiple copula families to the paired events and provides the Akaike Information Criterion value for each. In addition, probability-isoline plots are provided to support selection of a copula that reasonably represents the observed dependence, including its behavior for extreme events.
- Joint probability frequency ordinates. The analyst specifies the annual exceedance probabilities for which joint probability isolines and design points are needed.
HEC-Neptune computes joint probability isolines and identifies design point combinations associated with the specified joint annual exceedance probabilities. These combinations can be evaluated in the response model to develop or inform a response surface, evaluate critical loading combinations, and support selection of design events for the applicable flooding mechanism. A hydrologic or hydraulic response model. The selected design-point combinations must be entered into an external model, typically HEC-HMS, HEC-RAS, or an equivalent model, to estimate the response variable of interest.
