Sensitivity

If no analytical analysis is possible, we have to turn to numerical methods. The numerical solution of the model requires all parameters to take on certain values and as a result is dependent on parameters that have been specified. These include coefficients, or constants, initial conditions, forcing function, and control parameters. Some parameters do not matter much. We can vary them quite significantly, but will not see any large changes in the model dynamics. However, other parameters may have a very significant effect on the model performance. Even small changes in their values result in dramatically different solutions.

Analyzing model performance under various conditions is called 'sensitivity analysis'. If we start modifying a parameter and keep rerunning the model, instead of a single trajectory, we will be generating a bunch of trajectories (Figure 1). Similarly we can start changing the initial conditions or even some of the formalizations in the process descriptions. By comparing the model output we get an idea of the most essential parameters or factors in the model. We will also get a better feeling of the role of individual parameters and processes in how the model output is formed, what parameters affect what variables, and in which ranges the parameters may be allowed to vary. This is very important because in contrast to an analytical solution, where we could find an equation relating model output to the input parameters, with numerical models we do not have any other way to learn what is the connection between the various parameters and the model output, except than rerunning the model.

Eventually when we get sufficient confidence in the model performance and collect evidence of the model being actually adequate to the system that it represents, we can further sensitivity analysis to the point where we make conclusions about the sensitivity of the original system to certain processes and factors. It will be then those processes that should get the most attention in experimental research and which may become important management tools if we intend to modify the system behavior to match certain criteria.

A full sensitivity analysis of a model is a difficult task, since changing parameters one by one and in combinations may produce entirely different results. But even a partial analysis that will look at some parameters is certainly better than nothing. It will also be of great help for the next step of model analysis, which is calibration.

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