Geoscience Reference
In-Depth Information
added a rainstorm profile component to the Eagleson model based on the statistics of observed cumulative
rainstorm profiles normalised to a unit duration and unit rainstorm volume. This was later adapted by
Cameron
et al.
(1999) to use a database of observed normalised profiles from 10 000 real storms, classified
by different duration classes. When a new storm profile is required, a normalised profile is chosen
randomly from the database. An interesting variation on this technique of using normalised profiles that
will produce rainfall intensities with fractal characteristics has been suggested by Puente (1997). Another
way of using actual storm data in flood frequency analysis is to use the random transposition of real storms
recorded in a region over a catchment of interest (Franchini
et al.
, 1996). Finally a number of rainstorm
models have been proposed based on pulse or cell models, where the time series of generated rainfalls
is based on the superposition of pulses of randomly chosen intensity and duration by analogy with the
growth and decay of cells in real rainfall systems. Thus rainstorms are not generated directly but arise
as periods of superimposed cells separated by dry periods. The Bartlett-Lewis (Onof
et al.
, 1996) and
Neyman-Scott (Cowpertwait
et al.
, 1996a, 1996b) models are of this type while Blazkova and Beven
(1997, 2004, 2009) have used mixed distributions of high intensity and low intensity events. Such models
require a significant number of parameters, especially when the model is fitted to individual months of
the year. This type of model has been included in the UKCP09 weather generator for future climate
scenarios (see Section 8.9).
One interesting feature of driving flood frequency models by stochastic rainstorm generators is that the
period of simulation is not restricted to the lengths of historical records. In fact, when checking against
actual flood frequency data for limited observation periods, the length of the record should be taken
into account since there will be an important realisation effect for the extremes in these limited periods
(Beven, 1987; Blazkova and Beven, 1997, 2004). The historical data is, in fact, only one realisation of all
the possible sequences of events and resulting flood extremes that could have occurred for a period of the
length of the observations. That realisation might be subject to significant variability in the occurrences
of floods (see the example of Blazkova and Beven (2009) in Section 8.5), particularly where climate
is subject to el Nino oscillations (Kiem
et al.
, 2003). Thus, finding a model that is consistent with the
observed frequencies for such a period will depend not only on the model parameters but also on the
particular realisation of inputs.
Actually this is also an issue for models driven by observed rainfalls. Although potentially a model
might be able to represent any changes in the hydrological response of a catchment under more extreme
conditions, there is no guarantee that a model calibrated by a prior parameter estimation or by calibration
against a period of observed discharges will, in fact, produce accurate simulations for extreme flood peaks
(Fontaine, 1995). Lamb (1999), for example, has shown how the PDM model, calibrated over a two-year
continuous simulation period, can reproduce the magnitudes of the largest observed flood peaks when
driven by a longer period of observed rainfall data, but not necessarily from the same events that produce
the recorded peaks.
Running much longer periods of stochastic inputs to a model can also have another interesting effect.
Since the distributions that are used in a stochastic rainfall model are often assumed to be standard
statistical distributions with infinite tails some very, very large events might be generated. They will occur
with low probability, but under the infinite tail assumption there is always a small but finite probability
of very large events occurring. Such events might be inconsistent with the potential meteorological
conditions at the site (sometimes expressed in terms of a “probable maximum precipitation” (PMP),
although this is a value that is always difficult to define for a site). However, such events might also
be much higher than anything that has been observed in a region. The infinite tail assumption is not,
however, a necessary assumption. Cameron
et al.
(2001) showed how it could be changed within the
Barlett-Lewis rainfall generator to reflect the upper envelope of observed rainfalls for given durations
in the UK. Verhoest
et al.
(2010) suggest that stochastic rainfall models should be evaluated not only in
terms of reproducing point rainfall statistics, but also in terms of reproducing flood statistics allowing for
the dynamics of antecedent conditions in the periods between rainstorms.
