A Stochastic Model for Flood Analysis

Abstract

A stochastic •nodel, based on the recent developments in the theory of extreme values, is presented to describe and analyze excessive streamflows. The model is a particular stochastic process x(t) defined as the maximum term among a random number of random observations in an interval of time [0, t]. Since the number of hydrograph peaks in [0, t] that exceed a certain level Xo and the magnitudes of these peaks are random variables, the foregoing tnodel seems to conform well to the flood phenomenon. The passage time T(x) of the process x(t) relevant to the risk evaluation in the design of hydraulic structures is also considered. The results obtained are applied on the 72-year record of the Susquehanna River at Wilkes-Barre, Pennsylvania. Theoretical and observed results agree reasonably well.

Defining high-flow seasons using temporal streamflow patterns from a global model

“…The first and most common is the annual-maximum (AM) method, which samples the largest streamflow in each year. The second method is the peaks-over-threshold (POT) method (Smith, 1984(Smith, , 1987Todorovic and Zelenhasic, 1970), in which all distinct, independent dominant peak flows greater than a fixed threshold are counted. In contrast to the AM method, POT can capture multiple large independent floods within a single year, including the annual maximum flow, but may not capture the annual maximum flow in years in which streamflow is less than the pre-defined threshold; this threshold can either be defined based on a specific average number of floods or a specific mean exceedance level over the entire period (Cunderlik et al, 2004a;Institute of Hydrology, 1999;Lang et al, 1999).…”

Statistics of extremes and estimation of extreme rainfall: I. Theoretical investigation / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: I. Recherche théorique

“…If n is not constant, but rather can be regarded as a realization of a Poisson distributed random variable with mean ν, then the distribution of X becomes (e.g. Todorovic & Zelenhasic, 1970;Rossi et al, 1984):…”

An analysis of flood levee reliability

“…The e n s u i n g f a i l u r e u s u a l l y l e a d s t o l a r g e i n f l o w s o f w a t e r i n t o t h e p r o t e c t e d a r e a s and t o t h e undermining o f t h e l e v e e ' s f o u n d a t i o n ; 4 ) Wave a c t i o n : h i g h f l o o d l e v e l s g i v e r i s e t o wave a c t i o n which s c o u r s t h e t o p o f t h e l e v e e . Such s c o u r i n g r e d u c e s l e v e e s t r e n g t h and c a u s e s p r e m a t u r e f a i l u r e .…”

“…It is assumed that the occurrence of independent events larger than Qb can be described by a Poisson process (the time between events being exponentially distributed), with ,an average annual arrival rate v. It is also assumed that the probability density function for the flows larger than Qb can be represented by a shifted exponential distribution of the form f (q lq 2 Qb) = a exp (-a21 (10 where This distribution is a fairly general form, since the upper tails of many distributions may be represented as being exponential. This proposed model has been used for extreme flood discharges by Shane and Lynn [31,Todorovic and Zelenharic [4], and Wood [51 .…”