Connecting the forward problem to the inverse problem in uncertainty quantification of Earth system models using fast emulators

TL;DR

This paper demonstrates how Gaussian process emulators can connect forward and inverse uncertainty quantification in Earth system models, guiding efficient Bayesian calibration and reducing parameter uncertainty.

Contribution

It introduces a non-iterative strategy using sensitivity analysis to identify informative observations for Bayesian calibration in Earth system models.

Findings

Emulators enable global sensitivity analysis with fewer model evaluations.

Diagnostic measures identify observation regions that improve Bayesian calibration.

Sensitivity-guided observations reduce posterior uncertainty in parameter estimates.

Abstract

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically plausible parameter distributions first be learned from observations. Bayesian inference offers a principled approach but can become ill-posed when observations weakly constrain parameters--a condition difficult to know prior to inference. Addressing this gap, we show that parameter sensitivity results from forward uncertainty quantification can guide a non-iterative strategy for identifying observations informative to Bayesian calibration. We explore both forward and inverse uncertainty quantification for parameterizations of atmospheric turbulence in the Weather Research and Forecasting (WRF) model. To overcome the computational bottleneck of $\mathcal{O}(10^5)$ model evaluations required for both analyses, we leverage Gaussian process emulators trained on several hundred WRF simulations. Using these emulators, we conduct a global sensitivity analysis across observation space, investigating how parameter contributions to output variance depend on quantity of interest, atmospheric stability, time-averaging length, and spatial location. We then introduce nondimensional diagnostic measures that systematically identify regions where a parameter's contribution to output variance exceeds observational noise and its independent effect exceeds interaction effects. We demonstrate that observations from these regions serve as a strong proxy for accurate Bayesian calibration and reduced posterior uncertainty. Through emulator-aided Bayesian inversion with synthetic observations, we show how parameter uncertainty can be systematically reduced by leveraging sensitivity information.