FluxPart-E: A Benchmark for Evaluating ${\mathrm{CO}}_2$ Flux Partitioning Methods

Estimating whether land ecosystems will keep absorbing part of our $\mathrm{CO}\_2$ emissions or begin releasing carbon requires separating two opposing fluxes—photosynthetic uptake ($\mathrm{GPP}$) and ecosystem respiration ($\mathrm{R}\_\mathrm{eco}$)—that are never measured directly: eddy covariance, the most prominent and least invasive method, observes only their net signal, the net ecosystem exchange ($\mathrm{NEE}$). $\mathrm{CO}\_2$ flux partitioning recovers $\mathrm{GPP}$ and $\mathrm{R}\_\mathrm{eco}$ from $\mathrm{NEE}$ and meteorological drivers under $\mathrm{NEE}=-\mathrm{GPP}+\mathrm{R}\_\mathrm{eco}$. It is an under-determined inverse problem: one constraint, two unknowns, closed only by assumptions that trade flexibility for identifiability, with noise, gaps, and abrupt events corrupting what little signal remains. It also inverts the usual supervised setting: the target is never observed, so a method is applied to the very data it fits. We introduce FluxPart-E, a benchmark and evaluation protocol that makes the problem measurable. Ground truth comes from two structurally distinct land surface models driven by meteorology at 188 observational sites, into which we reinject measurement-realistic noise, gaps, and dynamic rain pulse events. The protocol scores the latent decomposition into $\mathrm{GPP}$ and $\mathrm{R}\_\mathrm{eco}$ across defined stress regimes. FluxPart-E exposes failure modes—low data coverage, the edges of climate zones, peak temperatures—that leave detectable signatures in real eddy-covariance data, turning a domain problem into a concrete machine-learning challenge: injecting knowledge, transfer across space and time, and learning reliably under sparse, noisy, and shifting conditions to solve a real inverse problem.