Models in Irrigation andWater Management - Practices of Irrigation and On-farm Water Management - page 387

expressed in terms of the state variables, control variables, and parameters
of the system.
Dynamic system : A system that contains time as one of the variables. The
changes of parameters and variables and inter-relationship between them
occur through time.
Empirical result/solution : A result (or solution) that is based on an empirical
(data-driven) analysis.
Analytical solution : A mathematical solution to the objective that is based on
an analytical analysis. Analytical solutions are more general than numerical
results.
10.2.3.4 Sensitivity Analysis
Sensitivity analysis : Computer-based simulation models are used widely for
the investigation of complex physical systems. These models typically con-
tain parameters, and the numerical results can be highly sensitive to small
changes in the parameter values.
Sensitivity analysis is a tool for characterizing the uncertainty associated with a
model. It is the study of how variation (uncertainty) in the output of a mathemati-
cal model can be apportioned quantitatively, or qualitatively, to different sources of
variation in the input of a model. In models involving many input variables, sen-
sitivity analysis is an essential ingredient of model building and quality assurance.
Sensitivity analysis is performed by changing a particular variable or parameter,
while keeping all other variables or parameters constant, and observed how the out-
put is changed. This is an important method for checking the quality of a given
model, as well as a powerful tool for checking the robustness and reliability of its
analysis.
Sensitivity information is useful in two ways. First, sensitivity indicates the sim-
ulation error that results if an error was made when assuming the original parameter
values. Second, sensitivity indicates how changing a characteristic value can influ-
ence the simulation output or system comparisons. If a small change in a parameter
results in relatively large change (in percentage form) in its outcomes, the outcomes
are said to be sensitive to that parameter. The variable or parameter which is most
sensitive, very accurate data for that variable or parameter has to be determined, or
that the alternative has to be redesigned for low sensitivity.
Sensitivity analysis can be used to determine/ascertain:
1. The quality of model definition.
2. Factors that mostly contribute to the output variability.
3. The region in the space of input factors for which the model variation is
maximum.
4. Optimal- or instability-region(s) within the space of factors for use in a subse-
quent calibration study.
5. Interactions between factors.
6. How a given model output depends upon the input parameters.