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Prediction of pollution in water flow is a very important task. To this end, it is imperative to be able to define the uncertainty in a model prediction. This is the purpose of sensitivity analysis whose role is to identify what uncertainty in the model outputs is attributable to the model inputs (parameters in this case). Traditionally, this is achieved by running the model perturbed by many random samples in the parameter space to determine their impact on the model outputs. It provides information on how much of the output variance is controlled by each parameter of the inputs.

On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems