Non-parametric frequency analysis of extreme values for integrated disaster management considering probable maximum events

Abstract:

This paper describes a non-parametric frequency analysis method for hydrological extreme-value samples with a size larger than 100, verifying the estimation accuracy with a computer intensive statistics (CIS) resampling such as the bootstrap. Probable maximum values are also incorporated into the analysis for extreme events larger than a design level of flood control.

Traditional parametric frequency analysis methods of extreme values include the following steps: Step 1: Collecting and checking extreme-value data; Step 2: Enumerating probability distributions that would be fitted well to the data; Step 3: Parameter estimation; Step 4: Testing goodness of fit; Step 5: Checking the variability of quantile (T-year event) estimates by the jackknife resampling method; and Step_6: Selection of the best distribution (final model). The non-parametric method (NPM) proposed here can skip Steps 2, 3, 4 and 6.

Comparing traditional parameter methods (PM) with the NPM, this paper shows that PM often underestimates 100-year quantiles for annual maximum rainfall samples with records of more than 100 years. Overestimation examples are also demonstrated. The bootstrap resampling can do bias correction for the NPM and can also give the estimation accuracy as the bootstrap standard error. This NPM has advantages to avoid various difficulties in above-mentioned steps in the traditional PM.

Probable maximum events are also incorporated into the NPM as an upper bound of the hydrological variable. Probable maximum precipitation (PMP) and probable maximum flood (PMF) can be a new parameter value combined with the NPM. An idea how to incorporate these values into frequency analysis is proposed for better management of disasters that exceed the design level. The idea stimulates more integrated approach by geoscientists and statisticians as well as encourages practitioners to consider the worst cases of disasters in their disaster management planning and practices.