Practical identifiability analysis of environmental models

Abstract

Identifiability of a system model can be considered as the extent to which one can capture its parameter values from observational data and other prior knowledge of the system. Identifiability must be considered in context so that the objectives of the modelling must also be taken into account in its interpretation. A model may be identifiable for certain objective functions but not others; its identifiability may depend not just on the model structure but also on the level and type of noise, and may even not be identifiable when there is no noise on the observational data. Context also means that non-identifiability might not matter in some contexts, such as when representing pluralistic values among stakeholders, and may be very important in others, such as where it leads to intolerable uncertainties in model predictions. Uncertainty quantification of environmental systems is receiving increasing attention especially through the development of sophisticated methods, often statistically-based. This is partly driven by the desire of society and its decision makers to make more informed judgments as to how systems are better managed and associated resources efficiently allocated. Less attention seems to be given by modellers to understand the imperfections in their models and their implications. Practical methods of identifiability analysis can assist greatly here to assess if there is an identifiability problem so that one can proceed to decide if it matters, and if so how to go about modifying the model (transforming parameters, selecting specific data periods, changing model structure, using a more sophisticated objective function). A suite of relevant methods is available and the major useful ones are discussed here including sensitivity analysis, response surface methods, model emulation and the quantification of uncertainty. The paper also addresses various perspectives and concepts that warrant further development and use.