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

Thermal history models, historically used to understand Earth's geologic history, are being coupled to climate models to map conditions that allow planets to maintain life. However, the lack of structural uncertainty assessment has blurred guidelines for how thermal history models can be used toward this end. Structural uncertainty is intrinsic to the modeling process. Model structure refers to the cause and effect relations that define a model and are assumed to adequately represent a particular real world system. Intrinsic/structural uncertainty is different from input and parameter uncertainties (which are often evaluated for thermal history models). A full uncertainty assessment requires that input/parametric and intrinsic/structural uncertainty be evaluated (one is not a substitute for the other). We quantify the intrinsic uncertainty for several parameterized thermal history models (a subclass of planetary models). We use single perturbation analysis 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 model feedback (negative or positive). A perturbed physics analysis is then used to determine uncertainty shadows for model outputs. This provides probability distributions for model predictions. It also tests the structural stability of a model (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. Plain Language Summary The Earth's internal energy is the source of tectonics, volcanism, and geologic activity, all of which effect the surface conditions of our planet. Thermal history models have been used to help understand how this energy, and associated tectonic-volcanic-geologic activity, has evolved over the Earth's history. These models are now being adopted to map conditions that allow for life on planets beyond our own. However, the uncertainty of these models has not been fully assessed which casts a cloud over how their predictions should be viewed. Here we investigate the uncertainty of thermal history models using several techniques. Our results indicate that model predictions should be viewed in a probabilistic sense which breaks from the way they have traditionally been used for Earth application. These results can also be extended to the exoplanet community. They suggest that efforts to delineate conditions that allow for planetary life will need to proceed under a probabilistic umbrella.