UC Santa Barbara

The importance of the Gumbel probability distribution for the description of extreme hydrologic events is examined in this article. The key findings of this work are: (1) an iterative method of least squares was developed and found to be well-suited for the efficient fitting of the two-parameter Gumbel distribution to hydrologic extremes; (2) negative truncation is necessary to adequately describe hydrologic minima (non-negative) data, while the standard Gumbel distribution for maxima is well-suited for modeling extreme (large) hydrologic events; (3) the distribution function of the sum of two independent Gumbel variables, of importance in hydrology, has been derived and successfully applied to spring flow data. Several examples that involve the modeling of hydrologic extremes are presented and analyzed.