Reducing errors on estimates of the carbon uptake period based on time series of atmospheric CO₂

High-quality, long-time-series measurements of atmospheric greenhouse gases show interannual variability in the measured seasonal cycles. These changes can be analyzed to better understand the carbon cycle and the impact of climate drivers. However, nearly all discrete measurement records contain gaps and have noise due to the influence of local fluxes or synoptic variability. To facilitate analysis, filtering and curve-fitting techniques are often applied to these time series. Previous studies have recognized that there is an inherent uncertainty associated with this curve fitting, and the choice of a given mathematical method might introduce biases. Since uncertainties are seldom propagated to the metrics under study, this can lead to misinterpretation of the signal. In this study, we use an ensemble-based approach to quantify the uncertainty of the derived seasonal cycle metrics. We apply it to CO2 dry-air mole fraction time series from flask measurements in the Northern Hemisphere. We use this ensemble-based approach to analyze the carbon uptake period (CUP: the time of the year when the CO2 uptake is greater than the CO2 release): its onset, termination and duration. Previous studies have diagnosed CUP based on the dates on which the detrended, zero-centered seasonal cycle curve switches from positive to negative (the downward zero-crossing date, DZCD) and vice versa (upward zero-crossing date, UZCD). However, the UZCD is sensitive to the skewness of the CO2 seasonal cycle during the net carbon release period. Hence, we develop an alternative method proposed by Barlow et al. (2015) to estimate the onset and termination of the CUP based on a threshold defined in terms of the first derivative of the CO2 seasonal cycle. Using the ensemble approach, we arrive at a tighter constraint to the threshold by considering the annual uncertainty; we call this the ensemble of first derivative (EFD) method. Further, using the EFD approach and an additional curve-fitting algorithm, we show that (a) the uncertainty of the studied metrics is smaller using the EFD method than when approximated using the timing of the zero-crossing date (ZCD), and (b) the onset and termination dates derived with the EFD method provide more robust results, irrespective of the curve-fitting method applied to the data.