Recalibrating neural network estimates of net ecosystem exchange in a Bayesian synthesis inversion

Using neural networks to upscale eddy covariance measurements is a common approach to obtain global estimates of net ecosystem exchange (NEE) and thereby the land carbon sink. Unfortunately, this approach suffers from a limited representativeness of eddy covariance sites of the global picture, resulting in discrepancies between such data-driven bottom-up estimates of the land-atmosphere fluxes in comparison to independent top-down products from atmospheric inversions. Here, we introduce a novel method to bridge both approaches: recalibrating the last neural network layer in a Bayesian synthesis inversion. In other words, we find the least squares estimate of the last neural network layer weights, by first transporting the deep features and then inverting the covariance matrix of transported features to obtain a least squares estimator against atmospheric observations. This approach is possible because atmospheric tracer transport of CO₂ is a linear operator with respect to the surface fluxes. It is also computationally tractable due to a small number of degrees of freedom, namely just the regression coefficients for the approximately 50 deep features. For comparison, modern CO₂ inversions typically model the land surface flux with over 1000 parameters, which requires them to leverage variational or ensemble approaches for optimization.

 

The NEE estimates recalibrated using atmospheric data differ significantly from those obtained through pure eddy covariance training within the FLUXCOM-X framework. Namely, the recalibrated estimates show increased agreement with observational data from atmospheric measurement stations, when transported with the atmospheric transport model TM3. Surprisingly, this agreement does not necessarily arise from a greater agreement of global flux maps with results from the Jena CarboScope inversion. Here, the approach may suffer from low robustness of deep features or from regridding fluxes to a lower resolution before transporting them. We discuss ways to alleviate these limitations and outline what our results mean for improving neural network estimates of NEE.