Reliability of parameter estimation in respirometric models

When modelling a biochemical system, the fact that model parameters cannot be estimated exactly stimulates the definition of tests for checking unreliable estimates and design better experiments. The method applied in this paper is a further development from Marsili-Libelli et al. [2003. Confidence regions of estimated parameters for ecological systems. Ecol. Model. 165, 127–146.] and is based on the confidence regions computed with the Fisher or the Hessian matrix. It detects the influence of the curvature, representing the distortion of the model response due to its nonlinear structure. If the test is passed then the estimation can be considered reliable, in the sense that the optimisation search has reached a point on the error surface where the effect of nonlinearities is negligible. The test is used here for an assessment of respirometric model calibration, i.e. checking the experimental design and estimation reliability, with an application to real-life data in the ASM context. Only dissolved oxygen measurements have been considered, because this is a very popular experimental set-up in wastewater modelling. The estimation of a two-step nitrification model using batch respirometric data is considered, showing that the initial amount of ammonium-N and the number of data play a crucial role in obtaining reliable estimates. From this basic application other results are derived, such as the estimation of the combined yield factor and of the second step parameters, based on a modified kinetics and a specific nitrite experiment. Finally, guidelines for designing reliable experiments are provided.