Assessing the Intrinsic Uncertainty and Structural Stability of Planetary Models: 1) Parameterized Thermal-Tectonic History Models

Abstract

Thermal history models, that have been used to understand the geological history of Earth, are now being coupled to climate models to map conditions that allow planets to maintain surface water over geologic time - a criteria considered crucial for life. However, the lack of intrinsic uncertainty assessment has blurred guidelines for how thermal history models can be used toward this end. A model, as a representation of something real, is not expected to be complete. Unmodeled effects are assumed to be small enough that the model maintains utility for the issue(s) it was designed to address. The degree to which this holds depends on how unmodeled factors affect the certainty of model predictions. We quantify this intrinsic uncertainty for several parameterized thermal history models (a widely used subclass of planetary models). Single perturbation analysis is used to determine the reactance time of different models. This provides a metric for how long it takes low amplitude, unmodeled effects to decay or grow. Reactance time is shown to scale inversely with the strength of the dominant feedback (negative or positive) within a model. A perturbed physics analysis is then used to determine uncertainty shadows for model outputs. This provides probability distributions for model predictions and tests the structural stability of a model. That is, do model predictions remain qualitatively similar, and within assumed model limits, in the face of intrinsic uncertainty. Once intrinsic uncertainty is accounted for, model outputs/predictions and comparisons to observational data should be treated in a probabilistic way.