Dynamic flood modeling: combining Hurst and Gumbel's approach

Abstract

SUMMARYWhen working on river floods-annual river levels maxima-, two approaches are usually considered: one inspired from Emil Gumbel where annual maxima are supposed to be i.i.d. and distributed according to Gumbel's distribution, and one inspired from Edwin Hurst where annual maxima are strongly dependent, and exhibit long range memory. This paper tries to solve this apparent paradox by deriving a dynamic model inspired from financial models, which does not take into account annual maxima only but also threshold exceedances. It studies the implications of such a paradox in terms of return period-a notion valid as long as the data are i.i.d-and of extremal events.

Floods in future climates: a review

“…From the other perspective, long‐term persistence has been associated with climate variations. Recently, Charpentier and Sibai () considered combining the Gumbel () iid approach and Hurst long‐term memory in flood analysis. These approaches seek to directly incorporate long‐term persistence in the analysis.…”