FFA is extrapolation

Flood frequency analysis estimates the magnitude of rare floods from a limited record of annual peak flows, called an annual maximum series (AMS). A common method is to fit a probability distribution to the observed annual maximum flow series and in general extrapolate beyond the observed range of flow.

No measured record is long enough to show the full distribution of possible floods. The estimate is therefore sensitive to record length, sampling variability, measurement uncertainty, and the assumption that processes driving flood runoff are stationary.

Explore estimation uncertainty

Use the input controls below (slider) to select a Water Survey of Canada station. Set the number of Monte Carlo simulations and the uncertainty range you assume on the estimated daily flow: the smaller value represents the error assumed on the smallest observed flow, the larger value represents the error assumed on the largest observed flow, and errors between the minimum and maximum are linearly interpolated. This flow-dependent scaling approximates heteroscedastic uncertainty, where larger flows can have greater measurement uncertainty. More explicitly, for each peak $Q$ in the AMS, a unique error is sampled uniformly from $[−e(Q),+e(Q)]$ in each Monte Carlo simulation:

$$Q_\text{sim} = Q \times \mathbb{U} (1 - e, 1 + e)$$

The shaded bands in the main flood frequency plot show the 90% confidence interval (light green) and and the middle third (blue) percentiles of the simulated fits. These intervals show how the selected measurement-error model propagates through the fitted flood-frequency curve. They do not include all sources of hydrologic or model uncertainty.

The distribution of simulated return period flows is shown against the deterministic LPIII fit in the plot above (right). The purpose is to show the range of possible fits that can result from the assumed measurement uncertainty. For the default configuration, the distribution shows that for a given range of uncertainty in the individual values making up the annual maximum flow series, the Log-Pearson III best fit value can vary substantially.

Disclaimer

The explorer presented here is a tool for demonstrating sensitivity to just one assumption that is often assumed deterministic, that is how return period flows can change according to an assumed uncertainty model. The information presented here does not replace a formal flood-frequency study or a review of station history, data quality, regional information, and non-stationarity.