Flood Frequency Analysis in Context of Climate Change or with Mixed Populations

Abstract

The thesis addresses two challenges in flood frequency analysis (FFA). The first is how to analyze annual maximum series (AMS) with maxima from two or more distinct processes (e.g. rainfall and snowmelt). The second is how one might incorporate climate change trends into flood risk models. The mixed-population flood-risk estimators considered include a joint model that includes correlation between rainfall and snowmelt events, a mixture model that treats the two as independent, and an AMS model. The mixture estimator is simple and the most efficient when the complete series of both events are available and the log-cross-correlation is 0.5 or less. When the rainfall distribution dominants the large flood risk, using just the rainfall flood distribution works well. We explore a Kirby-estimator and an Expected Moments Algorithm (EMA) for situations when only the AMS is available. Kirby used the conditional distributions for snowmelt and for rainfall given they are the annual maximum for their year. EMA employs a censored sampling paradigm to represent each data series. EMA generally performs better than the Kirby estimator. A fundamental assumption of FFA is that flood series are stationary. This thesis evaluates FFA methods that might be used when flood records have trends due to climate change. We consider six estimators. The “Stationary” estimator retains the time-invariance assumption and employs the AMS. Possible methods with time-varying parameters are represented by 3 estimators: Trend_0 uses the true trends in the AMS mean and variance; Trend_1 estimates the trend in the mean of the log-AMS; Trend_2 estimates trends in both the mean and the variance of the log-AMS. “30-year record” is the “Stationary” estimator using only the most recent 30 years of data. “Safety factor” increases or decreases the 100-year flood estimator by a prescribed percentage. With modest trends (≤ ±0.25% per year), the stationary estimator works well for short records (n=40), but is inferior to Trend_1 with larger trends. With longer records (n=100), Trend_1 performs well for most cases except when the trend in both the mean and variance was ±1%, when Trend_2 is a good alternative. FFA in a dynamic world is a challenge.