Skip to Main Content
The flood forecasting model was established with single and multi-objective functions to calibrate the model parameters and simulate the flood process. Seven flood forecasting schemes were put forward with three single objective functions and their combination in different ways. The specific description of each scheme is listed in Table 2. In order to compare the performance of single and multi-objective functions, the averages of the absolute evaluation values of the overall 30 flood events are listed in Table 3, and their variations are presented in Figure 3. The results are discussed in the following subsections.
Table 2

Specific description of each objective function scheme

SchemeObjective functionDescription
F1(θ) Volume error of the flood events 
F2(θ) Root mean square error of the flood events 
Fp(θ) Peak flow error of the flood events 
F1(θ)F2(θ) Combination of volume error and root mean square error of the flood events 
F1(θ)Fp(θ) Combination of volume error and peak flow error of the flood events 
F2(θ)Fp(θ) Combination of root mean square error and peak flow error of the flood events 
F1(θ)F2(θ)Fp(θ) Combination of volume error, root mean square error and peak flow error of the flood events 
SchemeObjective functionDescription
F1(θ) Volume error of the flood events 
F2(θ) Root mean square error of the flood events 
Fp(θ) Peak flow error of the flood events 
F1(θ)F2(θ) Combination of volume error and root mean square error of the flood events 
F1(θ)Fp(θ) Combination of volume error and peak flow error of the flood events 
F2(θ)Fp(θ) Combination of root mean square error and peak flow error of the flood events 
F1(θ)F2(θ)Fp(θ) Combination of volume error, root mean square error and peak flow error of the flood events 
Table 3

The performance measures of the 30 flood events with different objective functions

SchemeRE (%)NSEQre (%)ΔT (h)
4.67 0.8386 19.32 2.03 
6.98 0.8892 10.87 1.63 
24.79 0.4217 6.54 5.8 
5.8 0.8793 12.76 1.4 
7.06 0.4368 7.11 7.07 
7.93 0.8894 6.8 1.4 
7.29 0.8923 6.75 1.4 
SchemeRE (%)NSEQre (%)ΔT (h)
4.67 0.8386 19.32 2.03 
6.98 0.8892 10.87 1.63 
24.79 0.4217 6.54 5.8 
5.8 0.8793 12.76 1.4 
7.06 0.4368 7.11 7.07 
7.93 0.8894 6.8 1.4 
7.29 0.8923 6.75 1.4 
Figure 3

Box plots of different evaluation indexes of 30 simulated flood event processes with different objective functions: (a) relative error of water volume; (b) Nash-Sutcliffe coefficient; (c) relative error of peak flow; (d) time lag of peak flow.

Figure 3

Box plots of different evaluation indexes of 30 simulated flood event processes with different objective functions: (a) relative error of water volume; (b) Nash-Sutcliffe coefficient; (c) relative error of peak flow; (d) time lag of peak flow.

Close Modal

or Create an Account

Close Modal
Close Modal