CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 51

= f ( w ,…, w )

1 n

A special case of the disaggregated pattern, which is referred to as the principal pattern by
Maskey et al. (2003a), occurs when the coefficients take the value 1 for one of the
subperiods, say j * , and zero for the rest, i.e.

(4.5)

Consequently, from Equations (4.2) and (4.5),

(4.6)

It should be noticed, however, that this principal pattern of temporal distribution does not
necessarily correspond to the extreme (upper bound or lower bound) values of the output.
Note that this methodology is based on the implicit assumption that the length of a
subperiod is larger than the correlation time of the input signal. If it is not the case, the
coefficients b j should not be generated independently from each other. The length of the
subperiod, however should not be too large, in which case the resulting signals will be
close to the average signals over the period. Note that methods exist, that allow signals to
be generated taking into account the signal correlation (Rodriguez-Iturbe and Eagleson,
1987; Mantoglou and Wilson, 1982). In the absence of any information about the
correlogram of the input signal, such methods cannot be used and the coefficients b j are
to be generated independently from each other. However, due to the requirement of
Equation (4.3), these coefficients cannot be fully independent. Various methods for the
generation of the disaggregation coefficients are discussed in Subsection 4.1.6.
Also note that the number of subperiods has a direct influence on the maximum possi-
ble intensity of the input (e.g. maximum rainfall intensity). This is because the maximum
possible intensity is obtained when the given value W for the period T is concentrated over one
subperiod, with an intensity nW/T . Too many subperiods not only increases the computa-
tional requirements (see Subsection 4.1.4 and 4.1.5 for the algorithms) but may also
lead to physically unfeasible results. Therefore, care must be taken in selecting the appro-
priate number of subperiods. A more rational solution to this problem may be achieved by
constraining the disaggregation using more catchment specific information on the rainfall
intensity and pattern. For example, relationships between the maximum intensity and the
duration of the rainfall can be derived. Analysis of historical rainfall patterns may lead to
the identification of several most probable rainfall patterns for various intensities for the region.