Sensitivity analysis of neural networks to input variation is an important research area as it goes some way to addressing the criticisms of their black-box behaviour. Such analysis of RBFNs for hydrological modelling has previously been limited to exploring perturbations to both inputs and connecting weights. In this paper, the backward chaining rule that has been used for sensitivity analysis of MLPs, is applied to RBFNs and it is shown how such analysis can provide insight into physical relationships. A trigonometric example is first presented to show the effectiveness and accuracy of this approach for first order derivatives alongside a comparison of the results with an equivalent MLP. The paper presents a real-world application in the modelling of river stage shows the importance of such approaches helping to justify and select such models.
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