Reconstructing Atmospheric CO2 with Flow Matching Models

Accurate estimates of the spatiotemporal distribution of atmospheric carbon dioxide (CO₂) are essential to evaluate and enforce international climate agreements as well as to infer fluxes of the greenhouse gas. However, current observations are spatially sparse, with satellite and in-situ measurements providing only partial coverage of the Earth’s surface and atmosphere. Atmospheric transport models are often used to infer CO₂ concentrations across unobserved regions by simulating how gases move and mix in the atmosphere. While physically grounded, these models are computationally intensive and notoriously difficult to calibrate with observational data, due to the complexity of atmospheric dynamics and the sparsity of available measurements.

This study investigates the use of generative machine learning for inpainting of CO₂. More specifically, we apply flow matching, an approach that generates samples from an unknown target distribution by iteratively transforming samples from a simple known noise distribution with a deep neural network. In a first step, we train a flow matching model on assimilation data from CarbonTracker (CT2022). This trains the model to respect the physical patterns of atmospheric CO₂ fields, turning it into an effective prior for data assimilation. In a second step, we test the trained flow matching model on conditional generation that is, reconstruction of atmospheric CO₂ from partial observations. For this, we artificially mask parts of the CT2022’s CO₂ in a way that emulates the availability of satellite measurements. In a third step, we infer global CO₂ by conditioning on the total column average CO₂ (XCO₂) measurements from NASA’s Orbiting Carbon Observatory-2 (OCO-2), comparable to other inversions from the OCO-2 v11 MIP, but using a novel approach.

Extensive evaluation against independent and held-out test-sets from in-situ and satellite measurements show physical consistency and decent agreement of the reconstructed global CO₂ fields from OCO-2 measurements. However, challenges remain: specifically, future research needs to alleviate spurious artifacts from the employed posterior conditioning method in both the artificial mask and particularly the conditioning on XCO₂ before the approach can become operational.

Our presented flow matching approach opens up new avenues of research. The prior parameterized by the flow matching model can be investigated itself. For instance, it is possible to perform feature extraction inside the latent space and hence purposefully explore counterfactual scenarios of CO₂ distributions by carefully tracing out paths in the noise distribution and analyzing the corresponding generated CO₂ samples.