# Spatio-Temporal Reconstructions of Global CO2-Fluxes using Gaussian Markov Random Fields

## TL;DR

This paper introduces a novel spatio-temporal reconstruction method for global CO2 fluxes using Gaussian Markov Random Fields, improving realism and computational efficiency over traditional approaches.

## Contribution

It develops a continuous domain flux modeling approach with GMRF, reducing aggregation errors and enhancing the representation of real-life fluxes.

## Key findings

- Flexible GMRF model with Matérn-like covariance
- Reduces aggregation errors in flux covariance
- Provides a more realistic space-time flux representation

## Abstract

Atmospheric inverse modelling is a method for reconstructing historical fluxes of green-house gas between land and atmosphere, using observed atmospheric concentrations and an atmospheric tracer transport model. The small number of observed atmospheric concentrations in relation to the number of unknown flux components makes the inverse problem ill-conditioned, and assumptions on the fluxes are needed to constrain the solution. A common practise is to model the fluxes using latent Gaussian fields with a mean structure based on estimated fluxes from combinations of process modelling (natural fluxes) and statistical bookkeeping (anthropogenic emissions). Here, we reconstruct global \CO flux fields by modelling fluxes using Gaussian Markov Random Fields (GMRF), resulting in a flexible and computational beneficial model with a Mat\'ern-like spatial covariance, and a temporal covariance defined through an auto-regressive model with seasonal dependence. In contrast to previous inversions, the flux is defined on a spatially continuous domain, and the traditionally discrete flux representation is replaced by integrated fluxes at the resolution specified by the transport model. This formulation removes aggregation errors in the flux covariance, due to the traditional representation of area integrals by fluxes at discrete points, and provides a model closer resembling real-life space-time continuous fluxes.