The Identifiability of Conceptual Hydrochemical Models

Estimating a uniquely best set of values for the parameters of conceptual hydrological models has long been a problem of considerable concern. More recent interest in using these models to determine the flow paths of water passing through catchments experiencing acidification has sharpened the focus of such concern on the role of tracer observations in model and parameter identifiability. The paper examines the question of a priori identifiability in both deterministic and stochastic frameworks. Working with relatively simple linear and nonlinear two‐store models, the deterministic analysis involves merely algebraic manipulation of the model's state space description. It is apparent that, while this form of analysis is of limited applicability (even with the assistance of systems of computer algebra), the availability of tracer observations enhances model identifiability in all the cases examined. More complex model structures, and the effects of model and observation uncertainty, can be explored within a stochastic framework based on filtering theory. It is found that the availability of two tracer signals does not necessarily improve identifiability beyond what is possible with just a single tracer measurement. There is also evidence of a basis for the cross referencing of identifiability results between the deterministic and stochastic frameworks.