Abstract. Analysis of stratospheric transport from an observational point of view is frequently realized by evaluation of the mean age of air values from long-lived trace gases. However, this provides more insight into general transport strength and less into its mechanism. Deriving complete transit time distributions (age spectra) is desirable, but their deduction from direct measurements is difficult. It is so far primarily based on model work. This paper introduces a modified version of an inverse method to infer age spectra from mixing ratios of short-lived trace gases and investigates its basic principle in an idealized model simulation. For a full description of transport seasonality the method includes an imposed seasonal cycle to gain multimodal spectra. An ECHAM/MESSy Atmospheric Chemistry (EMAC) model simulation is utilized for a general proof of concept of the method and features an idealized dataset of 40 radioactive trace gases with different chemical lifetimes as well as 40 chemically inert pulsed trace gases to calculate pulse age spectra. It is assessed whether the modified inverse method in combination with the seasonal cycle can provide matching age spectra when chemistry is well-known. Annual and seasonal mean inverse spectra are compared to pulse spectra including first and second moments as well as the ratio between them to assess the performance on these timescales. Results indicate that the modified inverse age spectra match the annual and seasonal pulse age spectra well on global scale beyond 1.5 years of mean age of air. The imposed seasonal cycle emerges as a reliable tool to include transport seasonality in the age spectra. Below 1.5 years of mean age of air, tropospheric influence intensifies and breaks the assumption of single entry through the tropical tropopause, leading to inaccurate spectra, in particular in the Northern Hemisphere. The imposed seasonal cycle wrongly prescribes seasonal entry in this lower region and does not lead to a better agreement between inverse and pulse age spectra without further improvement. Tests with a focus on future application to observational data imply that subsets of trace gases with 5 to 10 species are sufficient for deriving well-matching age spectra. These subsets can also compensate for an average uncertainty of up to ±20 % in the knowledge of chemical lifetime if a deviation of circa ±10 % in modal age and amplitude of the resulting spectra is tolerated.

Abstract. Mean age of air (AoA) is a diagnostic of transport along the stratospheric Brewer–Dobson circulation. While models consistently show negative trends, long-term time series (1975–2016) of AoA derived from observations show non-significant positive trends in mean AoA in the Northern Hemisphere. This discrepancy between observed and modelled mean AoA trends is still not resolved. There are uncertainties and assumptions required when deriving AoA from trace gas observations. At the same time, AoA from climate models is subject to uncertainties, too. In this paper, we focus on the uncertainties due to the parameter selection in the method that is used to derive mean AoA from SF6 measurements in Engel et al. (2009, 2017). To correct for the non-linear increase in SF6 concentrations, a quadratic fit to the time series at the reference location, i.e. the tropical surface, is used. For this derivation, the width of the AoA distribution (age spectrum) has to be assumed. In addition, to choose the number of years the quadratic fit is performed for, the fraction of the age spectrum to be considered has to be assumed. Even though the uncertainty range due to all different aspects has already been taken into account for the total errors in the AoA values, the systematic influence of the parameter selection on AoA trends is described for the first time in the present study. For this, we use the EMAC (ECHAM MESSy Atmospheric Chemistry) climate model as a test bed, where AoA derived from a linear tracer is available as a reference and modelled age spectra exist to diagnose the actual spatial age spectra widths. The comparison of mean AoA from the linear tracer with mean AoA from a SF6 tracer shows systematic deviations specifically in the trends due to the selection of the parameters. However, for an appropriate parameter selection, good agreement for both mean AoA and its trend can be found, with deviations of about 1 % in mean AoA and 12 % in AoA trend. In addition, a method to derive mean AoA is evaluated that applies a convolution to the reference time series. The resulting mean AoA and its trend only depend on an assumption about the ratio of moments. Also in that case, it is found that the larger the ratio of moments, the more the AoA trend gravitates towards the negative. The linear tracer and SF6 AoA are found to agree within 0.3 % in the mean and 6 % in the trend. The different methods and parameter selections were then applied to the balloon-borne SF6 and CO2 observations. We found the same systematic changes in mean AoA trend dependent on the specific selection. When applying a parameter choice that is suggested by the model results, the AoA trend is reduced from 0.15 to 0.07 years per decade. It illustrates that correctly constraining those parameters is crucial for correct mean AoA and trend estimates and still remains a challenge in the real atmosphere.

<p><strong>Abstract.</strong> Mean age of air (AoA) is a diagnostic of transport along the stratospheric Brewer-Dobson circulation. While models consistently show negative trends, long-term time series (1975–2016) of AoA derived from observations show non-significant positive trends in mean AoA in the northern hemisphere. This discrepancy between observed and modeled mean AoA trends is still not resolved. There are uncertainties and assumptions required when deriving AoA from trace gas observations. At the same time, AoA from climate models is subject to uncertainties, too.</p> <p> In this paper, we focus on the uncertainties due to the parameter selection in the method that is used to derive mean AoA from SF<sub>6</sub> measurements in Engel et al. (2009) and Engel et al. (2017). To correct for the non-linear increase in SF<sub>6</sub> concentrations, a quadratic fit to the time-series at the reference location, i.e. the tropical surface, is used. For this derivation, the width of the AoA distribution (age spectrum) has to be assumed. In addition, to choose the number of years the quadratic fit is performed for, the fraction of the age spectrum to be considered has to be assumed. Even though the uncertainty range due to all different aspects has already been taken into account for the total errors on the AoA values, the systematic influence of the parameter selection on AoA trends is described for the first time in the present study. </p><p> In addition, a method to derive mean AoA is evaluated that applies a convolution to the reference time series. The resulting mean AoA and its trend only depend on an assumption about the ratio of moments. Also in that case, it is found that the larger the ratio of moments, the more the AoA trend gravitates towards the negative. The linear tracer and SF<sub>6</sub> AoA is found to agree within 0.3 % in the mean and 6 % in the trend. </p><p> The different methods and parameter selections were then applied to the balloon borne SF<sub>6</sub> and CO<sub>2</sub> observations. We found the same systematic changes in mean AoA trend dependent on the specific selection. When applying a parameter choice that is suggested by the model results, the AoA trend is reduced from 0.15 years/decade to 0.07 years/decade. It illustrates that correctly constraining those parameters is crucial for correct mean AoA and trend estimates and still remains a challenge in the real atmosphere. </p><p> Engel, A., Möbius, T., Bönisch, H., Schmidt, U., Heinz, R., Levin, I., Atlas, E., Aoki, S., Nakazawa, T., Sugawara, S., et al.: Age of stratospheric air unchanged within uncertainties over the past 30 years, Nature Geoscience, 2, 28, 2009.</p><p> Engel, A., Bönisch, H., Ullrich, M., Sitals, R., Membrive, O., Danis, F., and Crevoisier, C.: Mean age of stratospheric air derived from AirCore observations, Atmospheric Chemistry and Physics, 17, 6825–6838, <a href="https://doi.org/10.5194/acp-17-6825-2017" target="_blank">https://doi.org/10.5194/acp-17-6825-2017</a>, 2017.