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Long, high-quality 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 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 present a novel curve fitting method and an ensemble-based approach that allows the uncertainty of the metrics to be quantified. We apply it here to the Northern Hemisphere CO2 dry air mole fraction time series. We use this ensemble-based approach to analyze different seasonal cycle metrics, namely the onset, termination, and duration of the carbon uptake period (CUP), i.e., the time of the year when the CO2 uptake is greater than the CO2 release. 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) and vice versa (upward zero-crossing date). However, we find that the upward zero-crossing date is sensitive to the skewness of the CO2 seasonal cycle during the net carbon release period. Hence, we propose an alternative method 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 (First-derivative threshold (FDT) method). Further, using the ensemble-based approach and an additional curve fitting algorithm, we show that (a) the uncertainty of the studied metrics is smaller using the FDT method than when estimated using the timing of the zero-crossing dates, and (b) the onset and termination dates derived with the FDT-method provide more robust results, irrespective of the curve-fitting method applied to the data. The code is made freely available under a Creative Commons-BY license, along with the documentation in this paper. [ABSTRACT FROM AUTHOR]

Long, high-quality 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 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 present a novel curve fitting method and an ensemble-based approach that allows the uncertainty of the metrics to be quantified. We apply it here to the Northern Hemisphere CO2 dry air mole fraction time series. We use this ensemble-based approach to analyze different seasonal cycle metrics, namely the onset, termination, and duration of the carbon uptake period (CUP), i.e., the time of the year when the CO2 uptake is greater than the CO2 release. 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) and vice versa (upward zero-crossing date). However, we find that the upward zero-crossing date is sensitive to the skewness of the CO2 seasonal cycle during the net carbon release period. Hence, we propose an alternative method 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 (First-derivative threshold (FDT) method). Further, using the ensemble-based approach and an additional curve fitting algorithm, we show that (a) the uncertainty of the studied metrics is smaller using the FDT method than when estimated using the timing of the zero-crossing dates, and (b) the onset and termination dates derived with the FDT-method provide more robust results, irrespective of the curve-fitting method applied to the data. The code is made freely available under a Creative Commons-BY license, along with the documentation in this paper. [ABSTRACT FROM AUTHOR]