Practical identifiability analysis of large environmental simulation models

TLDR

Large environmental simulation models are often overparameterized, making many parameters poorly identifiable, and while sensitivity plots aid identifiability in small models, they cannot reveal near‑linear dependence in high‑dimensional models. This paper proposes a systematic local sensitivity‑analysis framework that introduces two interpretable identifiability metrics for large models. The first metric quantifies how model outputs change with individual parameters, and the second measures the near‑linear dependence among subsets of sensitivity functions, also allowing bias assessment when some parameters are fixed a priori. The metrics diagnose parameter subsets, guide selection for estimation, clarify the correlation matrix, and are validated through two illustrative case studies.

Abstract

Large environmental simulation models are usually overparameterized with respect to given sets of observations. This results in poorly identifiable or nonidentifiable model parameters. For small models, plots of sensitivity functions have proven to be useful for the analysis of parameter identifiability. For models with many parameters, however, near‐linear dependence of sensitivity functions can no longer be assessed graphically. In this paper a systematic approach for tackling the parameter identifiability problem of large models based on local sensitivity analysis is presented. The calculation of two identifiability measures that are easy to handle and interpret is suggested. The first accounts for the sensitivity of model results to single parameters, and the second accounts for the degree of near‐linear dependence of sensitivity functions of parameter subsets. It is shown how these measures provide identifiability diagnosis for parameter subsets, how they are able to guide the selection of identifiable parameter subsets for parameter estimation, and how they facilitate the interpretation of the correlation matrix of the parameter estimate with respect to parameter identifiability. In addition, we show how potential bias of the parameter estimates, due to a priori fixing of some of the parameters, can be analyzed. Finally, two case studies are presented in order to illustrate the suggested approach.