CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 55

w i,j(r),(s) = W i,(r) b i,j,(s) (4.13)

4. Use the w i,j,(r),(s) ( i =1,…, m; j =1,…, n ) as inputs to the model (Equation (4.10)).
This produces an output y (r),(s) .
5. Repeat Steps 2 to 4 s times. This produces s outputs for a set of W i,(r) generated in
Step 1.
6. Repeat Steps 1 to 5 r times. This produces s $ r outputs. Determine the frequency
distribution and other statistical properties of the output from the r $ s sets of
inputs-outputs. The values of r and s depend on the values of n and m, the
degree of non-linearity and the level of details required for the output distribution.

4.1.6 Generation of the pattern (disaggregation) coefficients

In this methodology, the generation of the disaggregation coefficient (b j ) needs further
elaboration. When the number of subperiods (n) for disaggregation is more than 1, and
since the summation of the coefficients must be 1, b j cannot be generated as fully
independent random variables. Therefore, the way the coefficients are generated may
influence the results. The following methods are identified:

1. By rejection
2. By symmetry
3. By normalization

The first method, by rejection, implies that the first n !1 coefficients are randomly
generated independently. The sum of the generated coefficients is then checked to see if it
exceeds 1. If this is true, the whole set is rejected and a new set is generated until the
sum remains equal to or less than 1. The n th coefficient is then calculated using
Equation (4.14). The implementation of this method is presented in Procedure (1).

(4.14)

Procedure (1): PatternCoef by Rejection
begin
sum←A (A>1) ;
while (sum<1) do
begin
generate b 1 ,…, b n !1 randomly;
sum ← b 1 +…+ b n !1 ;