Towards the validation of a traceable climate model hierarchies

Abstract

Background It is a common practice to use a simple model to explain the mechanisms or processes that occur in a much more complex, complete and computationally expensive model. Many such examples can be found in climate change research.

Objective This paper uses two illustrative examples to show how we can quantitatively relate the mechanisms or processes observed in a simple climate model to similar mechanisms in a more complex one.

Method A simple model can only explain a more complex solution’s mechanisms if outcomes are tested over a broad range of inputs. By carefully sampling the full set of inputs for both the simple and complex models, we can robustly compare the process or mechanistic outcomes, statistically, between them. Thus, by examining the similarity or differences in the relationship between the inputs and outputs. The method can reject an incorrect simple model.

Results The examples are, first, analytic and numerical solutions to the heat equation and, second, the 1948 Stommel model of horizontal ocean circulation and a more complex quasi-geostrophic ocean model. We quantitatively state how similar the simple model’s mechanisms are to the mechanisms in the more complex representation. In addition, when a simple solution may be correct, we give the percentage of the variance of the complex model’s outcomes that is explained by the simple response along with an uncertainty estimate.

Conclusion We successfully tested a methodology for robustly quantifying how the physics encapsulated by a simple model of a process may exhibit itself in another, more complex formulation. Suggestions are given as a guide for use of the methodology with more complex and realistic models.