On the asymptotic behavior of flood peak distributions – theoretical results

Abstract. This paper presents some analytical results and numerical illustrations on the asymptotic properties of flood peak distributions obtained through derived flood frequency approaches. It confirms and extends the results of previous works: i.e. the shape of the flood peak distributions are asymptotically controlled by the rainfall statistical properties, given limited and reasonable assumptions concerning the rainfall-runoff process. This previous result is partial so far: only two types of rainfall intensity distributions have been considered (extreme value distributions of types I and II), and the impact of the rainfall spatial heterogeneity has not been studied. From a practical point of view, it provides a general framework for analysis of the outcomes of previous works based on derived flood frequency approaches and leads to some proposals for the estimation of very large return-period flood quantiles. This paper, focussed on asymptotic distribution properties, does not propose any new approach for the extrapolation of flood frequency distribution to estimate intermediate return period flood quantiles. Nevertheless, the large distance between frequent flood peak values and the asymptotic values as well as the simulations conducted in this paper help quantifying the ill condition of the problem of flood frequency distribution extrapolation: it illustrates how large the range of possibilities for the shapes of flood peak distributions is.