An atmospheric inversion over the city of Cape Town: sensitivity analyses
Authors: Nickless Alecia , Rayner Peter J. , Scholes Robert J. , Engelbrecht Francois , Erni Birgit 
Published: June 2019

Abstract. An atmospheric inversion was performed for the city of Cape Town for the period of March 2012 to June 2013, making use of in situ measurements of CO2 concentrations at temporary measurement sites located to the north-east and south-west of Cape Town. This paper presents results of sensitivity analyses that tested assumptions regarding the prior information and the uncertainty covariance matrices associated with the prior fluxes and with the observations. Alternative prior products were considered in the form of a carbon assessment analysis to provide biogenic fluxes and the ODIAC (Open-source Data Inventory for Anthropogenic CO2 product) fossil fuel product. These were used in place of the reference inversion's biogenic fluxes from CABLE (Community Atmosphere Biosphere Land Exchange model) and fossil fuel emissions from a bespoke inventory analysis carried out specifically for the Cape Town inversion. Our results confirmed that the inversion solution was strongly dependent on the prior information, but by using independent alternative prior products to run multiple inversions, we were able to infer limits for the true domain flux. Where the reference inversion had aggregated prior flux estimates that were made more positive by the inversion – suggesting that CABLE was overestimating the amount of CO2 biogenic uptake – the carbon assessment prior fluxes were made more negative by the inversion. As the posterior estimates tended towards the same point, we could infer that the best estimate was located somewhere between these two posterior fluxes. The inversion was shown to be sensitive to the spatial error correlation length in the biogenic fluxes – even a short correlation length – influencing the spatial distribution of the posterior fluxes, the size of the aggregated flux across the domain, and the uncertainty reduction achieved by the inversion. Taking advantage of expected spatial correlations in the fluxes is key to maximizing the use of a limited observation network. Changes to the temporal correlations in the observation errors had a very minor effect on the inversion. The control vector in the original version consisted of separate daytime and night-time weekly fluxes for fossil fuel and biogenic fluxes over a 4-week inversion period. When we considered solving for mean weekly fluxes over each 4-week period – i.e. assuming the flux remained constant over the month – larger changes to the prior fossil fuel and biogenic fluxes were possible, as well as further changes to the spatial distribution of the fluxes compared with the reference. The uncertainty reduction achieved in the estimation of the overall flux increased from 25.6 % for the reference inversion to 47.2 % for the mean weekly flux inversion. This demonstrates that if flux components that change slowly can be solved for separately in the inversion, where these fluxes are assumed to be constant over long periods of time, the posterior estimates of these fluxes substantially benefit from the additional observational constraint. In summary, estimates of Cape Town fluxes can be improved by using better and multiple prior information sources, and particularly on biogenic fluxes. Fossil fuel and biogenic fluxes should be broken down into components, building in knowledge of spatial and temporal consistency in these components into the control vector and uncertainties specified for the sources for the inversion. This would allow the limited observations to provide maximum constraint on the flux estimates.