APPLICATION: FLOOD FORECASTING MODEL FOR KLODZKO CATCHMENT (POLAND) - Modelling Uncertainty in Flood Forecasting Systems - page 92

1. Select a value of ! [0,1] (called an ! -cut level) for the MF of the input precipitation
(Fig. 5.5) of all subbasins.

2. For the selected &-cut, determine for all i =1,…, m the lower bound, and the

upper bound, (See Fig. 5.5)
.
3. Start the GA with following parameters (decision variables) and constraints:
Parameters for the input precipitation: where

for all i =1,…, m .
Parameters for the disaggregation coefficients: ( b 1,1 ,…, b 1, k ),…,( b m, 1 ,…, b m,k ) where
b i,j =[0, 1] for all i =1,…, m; j =1,…, k . The value of k depends on the type of the
methods used for the generation of disaggregation coefficients. Three different
methods for the generation of the disaggregation coefficients are presented in
Subsection 4.1.6. For methods 1 and 2, k = n !1, and for method 3, k = n .
4. The GA generates initial population (sets of parameter values).
5. Call an external program to adjust the disaggregation coefficients depending on
the type of the method for determining the coefficients.
6. The GA evaluates the initial population using the forecasting model as an external
program and a specified objective function (also called the fitness function in
GA terminology). The fitness functions used are

(5.15)

where Q is the forecast discharge (model output) given by Equation (5.14).
7. The GA continues with crossover, mutation etc. (Subsection 5.3.2), generation of new
population and re-evaluation of the fitness function until the termination criteria are met.

The output of the procedures 1 to 7 is either or depending
on the type of the fitness function used. The whole procedure needs to be repeated for as
many ! -cuts as are needed to produce a complete MF for the output. See Figure 5.8 for a
flowchart of this methodology combined with a conventional or normal GA.
In this methodology the number of parameters for the GA is given by

N p = m +( n !1) m
= nm

(5.16)

where N p is the number of parameters for the GA, m is the number of subbasins and n is
the number of subperiods.