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Francesca Raffaele, Rita Nogherotto, Adriano Fantini
ICTP, Trieste, Italy
Validation and change for
CA2D hydraulic model
Based on Maione et al., 2003
(over nine domains)
The RP is a common measure of probability used for extreme events: it represents the probability of the event happening any given year. For example:
The SDH is the curve giving the "typical" flood event discharge (Q) as a function of time (t), for any given Return Period (RP):
There are two components to the SDH (at a given RP):
The FDF is the curve maximising the flood event discharge (Q) averaged over a duration (D) around the peak, so that for a given event:
Notice that, by definition, for an idealised event with Return Period RP, the peak flood discharge is:
From Maione, 2003
The shape of the SDH is dictated by the peak-duration ratio , which is the ratio of the time before the peak and the total duration (D) of the averaging window.
The smaller the , the more skewed the hydrograph will be towards steeper (flatter) rising (falling) limbs of the hydrograph.
Also notice that:
Following Maione et al. (2003), we assume that the reduction ratio ( ), which is the ratio of the FDF and the peak flood discharge is constant for any Return Period (RP), so that:
Which is a reasonable assumption also according to NERC (1975): the shape of the hydrograph, given by this ratio, does NOT depend on the RP!
Moreover, following Alfieri et al. (2014), we assume that the hydrograph is symmetric, that is to say that:
Set the flood peak as t=0, and split the left and right limb of the SDH as follows:
Only for the falling limb, differentiate the previous equation with respect to D:
Once we know the reduction ratio and the FDF, we can then calculate the SDH!
But remember that we set the reduction ratio to one half, so that:
We assume (Maione, 2003):
Where θ only depends on the (known!) drained area; a function for it is conveniently obtained by Maione based on observed data. We are only missing !
Possible approach: fitting an extreme value distribution, such as a Gumbel distribution (Maione, 2003; Alfieri, 2015) to the distribution of yearly maxima:
we use the available years of data (up to 30) to estimate the peak discharge for any RP, thus extrapolating data for higher Return Periods!