A confidence interval refers to a range of values that likely contains a population parameters, such as discharge. It provides a means for reporting the level of uncertainty and reliability of an estimate.
Figure 1.1.1a displays the maximum annual flow on the American River at Fair Oaks from 1905-1948 ranked by exceedance probability. An LP3 distribution fitted to the data is shown in a blue solid line, with 95% confidence intervals shown by the red dashed lines. The exceedance probability is given on the bottom x-axis, while the return interval is given on the top x-axis.
Figure 1.1.1a. Log Pearson Type III distribution fitted to gauge data available at the time of Folsom Dam construction
Folsom dam was designed to attenuate a 200 year design flood, or a flood with a 0.5% chance of exceedance in any given year. From Figure 1.1.1a, approximately what discharge magnitude corresponds to a 200 year flood based on the fitted LP3?
At the time of Folsom's construction, the USACE had just over 40 year of gauged flow data from which to extrapolate the size of a 200 year flood. An additional data point in the historical record came from the estimated flow of the 1862 flood. With an estimated 3 day average discharge of 265,000 cfs, the 1862 flood is considered one of the largest floods to hit the region after European settlement in California. As an engineer planning for Folsom Dam in 1948, think about how you might incorporate the estimated magnitude of the 1862 storm into your design considerations.
What exceedence probability would you assign to the 1862 storm?