An atmospheric inversion over the city of Cape Town: sensitivity analyses

We present sixteen different sensitivity tests applied to the Cape Town atmospheric Bayesian inversion analysis from March 2012 until June 2013. The reference inversion made use of a fossil fuel inventory analysis and estimates of biogenic fluxes from CABLE (Community Atmosphere Biosphere Land Exchange model). Changing the prior information product and the assumptions behind the uncertainties in the biogenic fluxes had the largest impact on the inversion results in terms of the spatial distribution of the fluxes, the size of the aggregated fluxes, and the uncertainty reduction achieved. A carbon assessment product of natural carbon fluxes, used in place of CABLE, and the Open-source Data Inventory for Anthropogenic CO2 product, in place of the fossil fuel inventory, resulted in prior estimates that were more positive on average than the reference configuration. The use of different prior flux products to inform separate inversions provided better constraint on the posterior fluxes compared with a single inversion. For the Cape Town inversion we showed that, where our reference inversion had aggregated prior flux estimates that were made more positive by the inversion, suggesting that the CABLE was overestimating the amount of CO2 uptake by the biota, when the alternative prior information was used, fluxes were made more negative by the inversion. As the posterior estimates were tending towards the same point, we could deduce that the best estimate was located somewhere between these two posterior fluxes. We could therefore restrict the best posterior flux estimate to be bounded between the solutions of these separate inversions.

The assumed error correlation length for NEE fluxes played a major role in the spatial distribution of the posterior fluxes and in the size of the aggregated flux estimates, where ignoring these correlations led to posterior estimates more similar to the priors compared with the reference inversion. Apart from changing the prior flux products, making changes to the error correlation length in the NEE fluxes resulted in the greatest contribution to variability in the aggregated flux estimates between different inversions. Those cases where the prior information or NEE error correlations were altered resulted in greater variability between the aggregated fluxes of different inversions compared with the uncertainty around the posterior fluxes of the reference inversion.

Solving for four separate weekly inversions resulted in similar estimates for the weekly fluxes compared with the single monthly inversion, while reducing computation time by up to 75 %. Solving for a mean weekly flux within a monthly inversion did result in differences in the aggregated fluxes compared with the reference inversion, but these differences were mainly during periods with data gaps. The uncertainty reduction from this inversion was almost double that of the reference inversion (47.2 % versus 25.6 %). Taking advantage of more observations to solve for one flux, such as allowing the inversion to solve for separate slow and fast components of the fossil fuel and NEE fluxes, as well as taking advantage of expected error correlation between fluxes of homogeneous biota, would reduce the uncertainty around the posterior fluxes. The sensitivity tests demonstrate that going one step further and assigning a probability distribution to these parameters, for example in a hierarchical Bayes approach, would lead to more useful estimates of the posterior fluxes and their uncertainties.