Error in the frequency analysis of flood data from a single site

Abstract

Three experiments investigate the source, magnitude and measurement of errors in the frequency analysis of flood data from a single site. The results refute the objectivity claimed for flood frequency analysis and for decisions based on this information. A subjective approach to probability and decision-making is demonstrated.

A simulation experiment shows that bootstrap and jackknife statistics can be used to estimate quantile sampling errors for flood-like distributions. In a second experiment, daily mean discharge records from five New Zealand rivers are used to compare the merits of standard engineering models for the flood frequency analysis of annual maximum, partial duration and time series data. A third experiment, on one of New Zealand's best flood records (the Waimakariri River at Old Highway Bridge), identifies the source and magnitude of errors in the frequency analysis of the annual maximum series. For this data set, estimates of a design discharge for the 0.01 annual exceedance probability are a subjective choice from within a very wide interval (at least [missing equation]).

The conclusion from these experiments is that any estimate of a design discharge or a future exceedance probability is not objective because of error in measurements, parameter estimates and model assumptions. Any design discharge or future exceedance probability is a statement of opinion rather than an impersonal measure of some unobservable truth. Arguments are given to support the use of subjective probability, as it forces a person to coherently state their opinion, their uncertainty in opinion, and changes to both uncertainty and opinion in the light of new information. It is shown that if a person views past and future events as exchangeable, the distribution of exceedances expresses their opinion about the probability of future exceedances of an observed discharge.

Flood frequency analysis is part of making floodplain decisions. Subjective utility theory is a framework for detailed and subjective decision-making, and it should be used if the decision-maker finds its axioms compelling. An example demonstrates and addresses the problems that may arise in applying subjective utility theory to floodplain decisions. The example shows that with a subjective view of probability, it is both possible and practical to make sensible decisions.