What eddy-covariance measurements tell us about prior land flux errors in CO₂-flux inversion schemes

To guide the future development of CO₂-atmospheric inversion modeling systems, we analyzed the errors arising from prior information about terrestrial ecosystem fluxes. We compared the surface fluxes calculated by a process-based terrestrial ecosystem model with daily averages of CO₂ flux measurements at 156 sites across the world in the FLUXNET network. At the daily scale, the standard deviation of the model-data fit was 2.5 gCm ^-2d^-1; temporal autocorrelations were significant at the weekly scale (>0.3 for lags less than four weeks), while spatial correlations were confined to within the first few hundred kilometers (<0.2 after 200km). Separating out the plant functional types did not increase the spatial correlations, except for the deciduous broad-leaved forests. Using the statistics of the flux measurements as a proxy for the statistics of the prior flux errors was shown not to be a viable approach. A statistical model allowed us to upscale the site-level flux error statistics to the coarser spatial and temporal resolutions used in regional or global models. This approach allowed us to quantify how aggregation reduces error variances, while increasing correlations. As an example, for a typical inversion of grid point (300km × 300km) monthly fluxes, we found that the prior flux error follows an approximate e-folding correlation length of 500km only, with correlations from one month to the next as large as 0.6.