Model structural uncertainty

Model structural uncertainty is the uncertainty that arises not from random error or insufficient data but from the structure of the model itself — the choice of equations, the selection of variables, the representation of processes, and the assumptions embedded in the model's architecture. It is the uncertainty about whether the model is the right kind of model, not merely whether its parameters are correctly estimated.

In climate science, structural uncertainty manifests in the spread across different General Circulation Models (GCMs). Each model makes different choices about how to represent clouds, convection, ocean mixing, and biogeochemical cycles. These choices are not arbitrary; they reflect different theoretical commitments and different strategies for handling the subgrid-scale problem. But the result is that different models produce different projections even when given identical forcing scenarios, and the spread across models is often treated as an estimate of structural uncertainty.

This treatment, however, may underestimate true structural uncertainty. Climate models share common ancestry — they descend from similar theoretical frameworks, use similar numerical methods, and are validated against the same observational datasets. The intercomparison spread captures the variation among models but not the variation that would exist if fundamentally different modeling approaches were included. It is the uncertainty within a paradigm, not the uncertainty across paradigms.

The philosophical significance of structural uncertainty is that it challenges the standard error-statistical framework of scientific inference. When models disagree, the standard response is to average their outputs or to weight them by performance against observations. But if the models are structurally different, averaging them is not obviously justified. Averaging a deterministic model and a stochastic model, or a continuum model and an agent-based model, does not produce a better estimate; it produces a hybrid that may represent neither system well.

Structural uncertainty is not unique to climate science. It appears in any domain where models are underdetermined by data: epidemiological models with different assumptions about transmission dynamics, economic models with different assumptions about agent behavior, and cosmological models with different assumptions about dark energy. The common thread is that the modeler's theoretical commitments — what Philip Anderson called the "theory of the model" — are as consequential as the data themselves.

Structural uncertainty is the shadow cast by our theories on the landscape of possible models. It is not a failure of modeling but a feature of it: every model is a choice, and every choice excludes possibilities that might turn out to be real.