A conceptual framework to quantify the influence of convective boundary layer development on carbon dioxide mixing ratios

Abstract. Interpretation of observed diurnal carbon dioxide (CO₂) mixing ratios near the surface requires knowledge of the local dynamics of the planetary boundary layer. In this paper, we study the relationship between the boundary layer dynamics and the CO₂ budget in convective conditions through a newly derived set of analytical equations. From these equations, we are able to quantify how uncertainties in boundary layer dynamical variables or in the morning CO₂ distribution in the mixed-layer or in the free atmosphere (FA) influence the bulk CO₂ mixing ratio.

We find that the largest uncertainty incurred on the mid-day CO₂ mixing ratio comes from the prescribed early morning CO₂ mixing ratios in the stable boundary layer, and in the free atmosphere. Errors in these values influence CO₂ mixing ratios inversely proportional to the boundary layer depth (h), just like uncertainties in the assumed initial boundary layer depth and surface CO₂ flux. The influence of uncertainties in the boundary layer depth itself is one order of magnitude smaller. If we "invert" the problem and calculate CO₂ surface exchange from observed or simulated CO₂ mixing ratios, the sensitivities to errors in boundary layer dynamics also invert: they become linearly proportional to the boundary layer depth.

We demonstrate these relations for a typical well characterized situation at the Cabauw site in The Netherlands, and conclude that knowledge of the temperature and carbon dioxide profiles of the atmosphere in the early morning are of vital importance to correctly interpret observed CO₂ mixing ratios during midday.