An objective prior error quantification for regional atmospheric inverse applications

Assigning proper prior uncertainties for inverse modelling of CO2 is of high importance, both to regularise the otherwise ill-constrained inverse problem and to quantitatively characterise the magnitude and structure of the error between prior and "true" flux. We use surface fluxes derived from three biosphere models - VPRM, ORCHIDEE, and 5PM - and compare them against daily averaged fluxes from 53 eddy covariance sites across Europe for the year 2007 and against repeated aircraft flux measurements encompassing spatial transects. In addition we create synthetic observations using modelled fluxes instead of the observed ones to explore the potential to infer prior uncertainties from model-model residuals. To ensure the realism of the synthetic data analysis, a random measurement noise was added to the modelled tower fluxes which were used as reference. The temporal autocorrelation time for tower model-data residuals was found to be around 30 days for both VPRM and ORCHIDEE but significantly different for the 5PM model with 70 days. This difference is caused by a few sites with large biases between the data and the 5PM model. The spatial correlation of the model-data residuals for all models was found to be very short, up to few tens of kilometres but with uncertainties up to 100 % of this estimation. Propagating this error structure to annual continental scale yields an uncertainty of 0.06 Gt C and strongly underestimates uncertainties typically used from atmospheric inversion systems, revealing another potential source of errors. Long spatial e-folding correlation lengths up to several hundreds of kilometres were determined when synthetic data were used. Results from repeated aircraft transects in south-western France are consistent with those obtained from the tower sites in terms of spatial autocorrelation (35 km on average) while temporal autocorrelation is markedly lower (13 days). Our findings suggest that the different prior models have a common temporal error structure. Separating the analysis of the statistics for the model data residuals by seasons did not result in any significant differences of the spatial e-folding correlation lengths