Estimating Non-stationary Flood Risk in a Changing Climate

Abstract:

Flood risk is usually described by a probability distribution for annual maximum streamflow which is assumed not to change with time. Federal, state and local governments in the United States are demanding guidance on flood frequency estimates that account for climate change. If a trend exists in peak flow series, ignoring it could result in large quantile estimator bias, while trying to estimate a trend will increase the flood quantile estimator’s variance. Thus the issue is, what bias-variance tradeoff should we accept?

This paper discusses approaches to flood frequency analysis (FFA) when flood series have trends. GCMs describe how annual runoff might vary over sub-continental scales, but this information is nearly useless for FFA in small watersheds. A LP3 Monte Carlo analysis and a re-sampling study of 100-year flood estimation (25- and 50-year projections) compares the performance of five methods:

1. FFA as prescribed in national guidelines (Bulletin 17B), assumes the flood series is stationary and follows a log-Pearson type III (LP3) distribution;
2. Fitting a LP3 distribution with time-varying parameters that include future trends in mean and perhaps variance, where slopes are assumed known;
3. Fitting a LP3 distribution with time-varying parameters that capture future trends in mean and perhaps variance, where slopes are estimated from annual peak flow series;
4. Employing only the most recent 30 years of flood records to fit a LP3 distribution;
5. Applying a safety factor to the 100-year flood estimator (e.g. 25% increase).

The 100-year flood estimator of method 2 has the smallest log-space mean squared error, though it is unlikely that the true trend would be known. Method 3 is only recommended over method 1 for large trends (≥ 0.5% per year). The 100-year flood estimators of method 1, 4, and 5 often have poor accuracy. Clearly, flood risk assessment will be a challenge in an uncertain world.