Uncertainties in the CO2 buget associated to boundary layer dynamics and CO2-advection

The relationship between boundary layer dynamics and carbon dioxide (CO₂) budget in the convective boundary layer (CBL) is investigated by using mixed-layer theory. We derive a new set of analytical relations to quantify the uncertainties on the estimation of the bulk CO₂ mixing ratio and the inferred surface flux. This analysis of the uncertainties is done as a function of boundary layer depth, morning vertical CO₂ distribution, which also includes the CO₂ vertical gradient in the free atmosphere (FA) and the carbon dioxide horizontal advection. We apply these relations for two prototype convective boundary layers observed at the Cabauw tower in The Netherlands: one CBL is near the free convective regime and the other is largely influenced by advection of CO₂.

We find that at midday CO₂ mixing ratio in the boundary layer and CO₂-inferred surface flux are mainly sensitive to the early morning CO₂ mixing ratio in the boundary layer and in the FA, just above the inversion. From the sensitivities the actual errors of CO₂ mixing ratio and inferred surface flux are calculated by assuming typical errors on the variables considered. Notice that the contribution of the error of each analyzed variable on the CO₂ budget depends on the sensitivity and on the uncertainty of the variable understudy. Consequently, although CO₂ mixing ratio or the inferred surface flux have small sensitivity to some of the analyzed variables, errors in these variables can have a non-negligible contribution to the errors in the CO₂ mixing ratio and in the inferred CO₂ surface flux. This is the case of the CO₂ vertical gradient in the FA.

Focusing on the CO₂ advection, we find that errors lead to notable uncertainties in the simulated CO₂ mixing ratio even on diurnal time scales. This is due to the fact that these errors are of the order of the advection rates. This finding is very relevant since CO₂-horizontal advection is a contribution to the CO₂ budget characterized by large uncertainty in its quantification either by using measurements or modeling. Furthermore, CO₂ mixing ratio errors due to advection are history dependent and hence even small systematic errors can increase to cause substantial errors in the CO₂ mixing ratio. Similar conclusions can also be drawn regarding to the inferred CO₂ surface flux. Our findings stress the fact that advection plays an important role on the CO₂ budget even when diurnal time scales are studied.

We complete the analysis of the uncertainties in the CO₂ budget by studying the role of large-scale subsidence on the CO₂-budget. We will show as an example that by introducing a deviation of approximately 1 cm/s in the subsidence velocity, we obtain differences of 4 ppm in the CO₂ mixing ratio and 50% of the inferred CO₂ surface flux. Consequently, not only horizontal but also vertical advection uncertainties, studied here as large-scale subsidence, lead to significant errors in the CO₂ mixing ratio and in the inferred CO₂ surface flux even on diurnal time scales.