Conditional Frequency Analysis of Autocorrelated Lake Levels

Abstract

In contrast to annual peak river flows, annual maximum lake levels often possess significant autocorrelation. The presence of autocorrelation in the time series of annual lake floods can be exploited to generate conditional estimates of near-term flood risk that are more accurate than estimates from traditional frequency analysis. Lake flooding is visualized as the joint occurrence of a time-dependent lakewide static water level and an independent local storm surge. Data from three gauges on Lake Erie show that the static water level behaves as a normal AR(1) process and the storm surge is normally distributed. Conditional trajectories of annual maximum water levels, obtained from the convolution of the static level and storm surge, are computed along 20-year time horizons for various initial conditions. Results show that traditional frequency analysis overestimates the risk of near-term flooding when static levels are low, and it underestimates the risk of near-term flooding when static levels are high. Knowledge of the near-term conditional distribution of annual maximum lake levels can be helpful in developing more-effective shoreline management plans.