PROBABILISTIC FLOOD FORECAST: BOUNDS AND APPROXIMATIONS

Abstract

The probabilistic river stage forecast (PRSF) specifies a sequence of exceedance functions {n:n=1,...,N} such that n(hn)=P(Hn>hn), where Hn is the river stage at time instance tn, and P stands for probability. The probabilistic flood forecast (PFF) should specify a sequence of exceedance functions {Fn:n=1,...,N} such that Fn(h)=P(Zn>h), where Zn is the maximum river stage within time interval (t0,tn], practically Zn=max{H1,...,Hn}. In the absence of information about the stochastic dependence structure of the process {H1,...,HN}, the PFF cannot be derived from the PRSF. This article presents simple methods for calculating bounds on Fn and approximations to Fn using solely the marginal exceedance functions 1,...,n. The methods are illustrated with tutorial examples and a case study for a 1430km2 headwater basin wherein the PRSF is for a 72-h interval discretized into 6-h steps.