Nonstationary or Stationary Frequency Analysis? (Invited Presentation)

There is increasing attention to the development of a myriad of complex methods for nonstationary frequency analysis (NFA) of floods, droughts and other hydrometeorological processes. A common assumption in NFA, questioned here, is that more accurate estimates of design event quantiles result when more realistic, complex and sophisticated models are employed. By considering the mean annual flood (or other hydrologic event), general conditions are derived when the sample mean (SM) is a more efficient (lower mean square error, MSE) estimator than a regression estimate of the mean (RM) under nonstationary conditions. Naturally under stationary conditions SM is always preferred over RM, yet under nonstationary conditions SM only has lower MSE than RM when the attained significance level p, associated with the regression is above about 17%, raising questions about the use of typical significance level thresholds for NFA. We introduce an optimal fractional mean estimator, FM*, which is simply the SM of the most recent period of record nf*, where f* is the optimal fraction of the full sample n, which leads to minimum MSE among all possible values of f. Interestingly, FM* is generally preferred over RM for attained significance levels in excess of about 0.05. Given the considerable attention and uncertainty surrounding potential nonstationary conditions, we demonstrate that approaches which exploit some optimal recent subset of the period of record may be more attractive than many of the more complex nonstationary approaches commonly advocated.