HEC-FIA uses the Monte Carlo algorithm to incorporate uncertainty in HEC-FIA calculations. Incorporating parameters that consider uncertainty allows for the evaluation of consequences, yielding results that span the range of possible outcomes for a modeled event. Furthermore, policy requires all calculations that contribute to a benefit-to-cost ratio for USACE projects, be evaluated with a risk-based analysis (ER-1105-2-101, 2017).
Therefore, to evaluate risk and uncertainty, HEC-FIA uses a mathematical model to describe the relationship between the range of all input parameters (e.g., depth-damage relationship, time-percent mobilization relationship, etc.) and the output parameters (e.g., flood damage, life loss, etc.) that HEC-FIA produces. Using this approach, each input parameter can be expressed as a continuous distribution and input parameter values for each Monte Carlo simulation are selected using randomly drawn numbers. The mathematical model then selects samples from that randomly described set of input parameters. This process is repeated to provide a set of deterministic results, with each result in that set arising from the randomly sampled input parameters.
The set of deterministic results from the Monte Carlo simulation can then be analyzed as an empirical distribution of possible outcomes. Summary statistics that describe the range of possibilities, such as the central tendency (i.e., probability-weighted average of all possible outcomes) can be computed using the outputs of the Monte Carlo analysis. This mathematical modeling process is generally referred to as a Monte Carlo application (simulation). This chapter discusses the inputs required for an HEC-FIA Monte Carlo simulation, the computational procedures, and the outputs produced from the computations.