CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 54

(4.11)

6. Use the ( i =1,…, m; j =1,…, n ) as inputs to the model (Equation (4.10)).

produces an output

This

7. Repeat Steps 4 to 6 s times. This means that for every value of the input generated
in Step 3, s disaggregated sets of inputs are generated. This produces s outputs.
8. Repeat Steps 3 to 7 r times. This produces s $ r outputs. From the s $ r outputs
determine the minimum and maximum of the outputs. The minimum and maximum
values correspond to the lower bound and upper bound of the outputs, respectively, i.e.

(4.12)

The values of s and r are primarily governed by the size of the search space for the
determination of minimum and maximum values of the outputs. The search space in this
example is the function of m and n . Obviously, more subbasins and subperiods means
more possible combinations of input sets. Different types of algorithms for the
determination of the minimum and maximum values may deal differently for the values
of s and r, such as using stopping criteria. In this study, genetic algorithms are used for
the determination of the optima and are presented in Section 5.3.

9. Repeat Steps 2 to 8 for as many ! -cuts as are needed to produce a complete
MF for the output.

4.1.5 Algorithm for the Monte Carlo approach
For the probabilistic assessment of uncertainty, the methodology can be used in the
framework of the Monte Carlo simulation (see Subsection 3.1.1). Assuming that the
uncertainties in the accumulated sums W i are represented by PDFs (Fig. 4.2a), the
algorithm used for the methodology is the following:

1. Generate randomly a value W i,(r) based on its PDF (see Subsection 3.1.1)
for all i =1,…, m . This value corresponds to the accumulated sum over the period
T, i.e. W i in Equation (4.1).
2. Generate coefficients b i,j,(s) between 0 and 1 ( i =1,…, m, j =1,…, n ) using one
of the methods described in Subsection 4.1.6.
3. Use the value W i,(r) generated in step 1 and the coefficients b i,j,(s) generated in
Step 2 in Equation (4.8) to redistribute the quantity over the subperiods, i.e.