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The results of a high resolution Bayesian inversion over the City of Cape Town, South Africa, are presented, which used observations of atmospheric carbon dioxide from sites at Robben Island and Hangklip lighthouses collected over a sixteen month period from March 2012 until June 2013. A Lagrangian particle dispersion model driven by the regional climate model Conformal Cubic Atmospheric Model (CCAM) was used to provide the sensitivities of the observations to the surface sources and boundary concentrations. This regional climate model was dynamically coupled to the CABLE (Community Atmosphere Biosphere Land Exchange) model, which provided prior estimates of the biogenic fluxes. Prior estimates of the fossil fuel emissions were obtained from an inventory analysis specifically carried out for this inversion exercise, making use of vehicle count data, population census data, fuel usage at industrial point sources, and aviation and shipping vessel counts. The inversion solved for the actual concentration measurements at each site, which was made possible by the use of the Cape Point background site to provide information on the boundaries, and was necessary due to the effect of topography on the atmospheric transport, affecting particularly the sensitivity of the Robben Island site to the surface fluxes. Night-time observations were included, but allocated much larger errors compared to the daytime observations. The inversion was able to substantially improve the agreement between the modelled and observed concentrations, and able to better represent the diurnal cycle in the concentrations compared with the prior modelled concentrations. The mean bias in the modelled concentrations was reduced from −2.9 ppm, with interquartile range −9.1 to 3.7, for the prior modelled concentrations, to 0.5, with interquartile range −1.5 to 1.5, for the posterior modelled concentrations at Robben Island, and from a bias of 2.4 ppm in the prior modelled concentrations at the Hangklip site, with interquartile range −2.3 to 6.5, to a bias of 0.04, with interquartile range −1.1 to 0.8. The standard deviations of the posterior residuals at both sites were reduced to values below that of the observed concentrations. The inversion solved for working week and weekend fossil fuel emissions, and weekly biogenic fluxes, each split into day and night contributions, for each month; therefore six surface sources per week within each of the 10,201 surface pixels. The inversion was also allowed to solve for each of the four boundary concentrations (north, east, south and west), but these were provided with tight constraints provided by the background site. The inversion tended to reduce fossil fuel emissions over all months. During the warmer, drier months, the inversion increased the biogenic fluxes, but reduced the biogenic emissions during the cooler, wetter months. The uncertainty reduction in the total estimate for the domain over each month ranged between 8.6 to 40.0% for the biogenic fluxes and between 0.4 to 16.4% for the fossil fuel fluxes. Model assessment by means of the Chi squared statistic indicated that the mean statistic was 1.48 over all months, indicating that either the prior values for the model errors or the uncertainty in the fluxes was not specified high enough for some months. A companion paper on sensitivity analyses will address different options for the specification of the correlations between errors in the modelled concentrations, how these prior errors are determined, how correlations are determined between the prior fluxes, and how the state vector is specified. Greater confidence is given to the inversion's ability to correct the total flux within each pixel, rather than the individual flux estimates.

Original publication




Journal article


Atmospheric Chemistry and Physics Discussions


European Geosciences Union (EGU)

Publication Date



Bayesian Inverse Modelling, Carbon dioxide, Carbon dioxide emissions, Lagrangian particle dispersion model, conformal cubic atmospheric model, Carbon dioxide fluxes