Using Stacking of Predictive Distributions to Combine Multiple Emissions Estimates

Abstract

Statistical inference methods for estimating greenhouse gas emissions have advanced considerably, yet combining multiple independent estimates into a single, interpretable estimate in a rigorous and principled way remains a challenge. Here, we apply stacking of predictive distributions, a method taken from the statistical learning literature, to the problem of combining an ensemble of emission estimates within a Bayesian framework. Each ensemble member is assigned a weight according to how well it reproduces atmospheric observations, accounting for all uncertainties, with no single model assumed to be perfect and no opportunity to improve weighting through over-fitting. When a linear Gaussian framework is adopted, as is common in atmospheric flux inversion, model weights can be computed efficiently even for large observational datasets. We demonstrate the approach using satellite observations of methane from the Tropospheric Monitoring Instrument (TROPOMI) to quantify emissions for the USA. The approach has broad applicability to combining estimates derived from inverse modelling.

Plain-language Summary

There are many different methods to estimate greenhouse gas emissions, often producing different answers. We present a new approach that combines multiple estimates by giving more weight to those that best match real-world observations, while accounting for uncertainties and avoiding common statistical pitfalls. The method is computationally efficient and practical for large datasets, which we demonstrate using millions of satellite measurements of methane over the USA. This approach could be widely applied to other methods in the geosciences.