Dynamic Flood Modelling: Combining Hurst and Gumbel's Approach

Abstract

When 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 some a financial model, which does not consider only annual maxima but 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.