A review of foundational methods for checking the structural identifiability of models: Results for rainfall-runoff

•Four screening methods have roles to play in understanding the non-identifiability.•Evolutionary algorithms can experience difficulties in convergence.•Model structure is shown to be a major factor in model non-identifiability.•Errors in data are not the major problem in our cases for parameter identification.•Objective function selection gives a partial resolution of identifiability issues. Checking for model identifiability has several advantages as outlined in the paper. We illustrate the use of several screening methods for assessing structural identifiability that should serve as a valuable precursor to model redesign and more sophisticated uncertainty analyses. These are: global evolutionary optimisation algorithms (EAs) that are being used increasingly to estimate parameters of models because of their flexibility; one and two-dimensional discrete model response plots with the latter showing trajectories of convergence/non-convergence; quadratic response surface approximations; and sensitivity analysis of combinations of parameters using Polynomial Chaos Expansion model emulation. Each method has a role to play in understanding the nature of non-identifiability. We illustrate the utility and complementary value of these methods for conceptual rainfall-runoff processes with real and ‘exact’ daily flow data, hydrological models of increasing complexity, and different objective functions. We conclude that errors in data are not primarily the cause of the parameter identification problem and objective function selection gives only a partial solution. Model structure reveals itself to be a major problem for the two more complex models examined, as characterised by the dotty/1D, 2D projection and eigen plots. The Polynomial Chaos Expansion method helps reveal which interactions between parameters could affect the model identifiability. Structural non-identifiability is seen to pervade even at modest levels of model complexity.