Quantifying the uncertainties of advection and boundary layer dynamics on the diurnal carbon dioxide budget

[1] We investigate the uncertainties in the carbon dioxide (CO2) mixing ratio and inferred surface flux associated with boundary layer processes and advection by using mixed-layer theory. By extending the previous analysis presented by Pino et al. (2012), new analytical expressions are derived to quantify the uncertainty of CO2 mixing ratio or surface flux associated to, among others, boundary layer depth, early morning CO2 mixing ratio at the mixed layer or at the free atmosphere; or CO2 advection. We identify and calculate two sorts of uncertainties associated to the CO2 mixing ratio and surface flux: instantaneous and past (due to advection). The numerical experiments are guided and constrained by meteorological and CO2 observations taken at the Cabauw 213 m tower. We select 2 days (25 September 2003 and 12 March 2004) with a well-defined convective boundary layer but different CO2 advection contributions. Our sensitivity analysis shows that uncertainty of the CO2 advection in the boundary layer due to instantaneous uncertainties represents at 1600 LT on 12 March 2004 a contribution of 2¿ppm and 0.072 mg m-2s-1 in the uncertainty of the CO2 mixing ratio and inferred surface flux, respectively. Taking into account that the monthly averaged minimum CO2 surface flux for March 2004 was -0.55 mg m-2s-1, the error on the surface flux is on the order of 10%. By including CO2 advection in the analytical expressions, we demonstrate that the uncertainty of the CO2 mixing ratio or surface flux also depends on the past uncertainties of the boundary layer depth.