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

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

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

The different methods and parameter selections were then applied to the balloon-borne

The Brewer–Dobson circulation (BDC) is the slow, overturning Equator-to-pole mass circulation in the stratosphere

Analysing global chemistry-climate models very consistently shows a speeding up of the BDC in the case of climate change and negative trends in AoA

Here, we want to focus on the uncertainties that arise from assumptions that are required to derive AoA from measurements. Those assumptions are necessary, as all tracers that are approximated as inert and measured in the atmosphere increase non-linearly. In our work, we will focus on

The latter also discusses the stratospheric lifetime of

In addition,

Still, the systematic uncertainty of the trend of mean AoA due to every single assumption of the specific methods has not been yet described. Investigating the method in a chemistry-climate model allows the use of diagnostics that are not available for the real atmosphere and thereby to better understand the uncertainties due to the particular assumptions.

In Sect.

The full information on the distribution of transport times is given by the actual age spectrum. The age spectrum is the distribution of transport times of trace gas concentrations to the location of interest

Sketch to illustrate the ratio of moments. The resulting age spectra from an inverse Gaussian with mean 4 years for values of

More detailed approaches considered two-peak age spectra

A well-established way to derive

In the real world, no perfectly linear increasing inert tracer is available. Often,

The resulting fit intervals for the fraction of input

Summing up, to perform this procedure one needs to choose the reference point, the fraction of the considered input and the ratio of the moments. Our aim is to systematically test the sensitivity of the derived mean AoA and AoA trends to those parameters.

Another method to infer mean AoA from a non-linear increasing tracer is to use a numerical convolution. Considering Eq. (

In the present study, we use the results of two simulations of the chemistry-climate model EMAC

The first simulation is a free-running transient hindcast simulation using EMACv2.51 with full interactive chemistry stretching from 1960 to 2011. This simulation was performed within the ESCiMo project

The second simulation, termed tranPul, is an EMACv2.53.0 run which is designed to resemble the RC1-base-07 simulation as closely as possible, for cost efficiency reasons however, without using interactive chemistry. This means that only the EMAC modules for dynamics, physics and diagnostics were used, namely AEROPT, CLOUD, CLOUDOPT, CONVECT, CVTRANS, E5VDIFF, ORBIT, OROGW, PTRAC, RAD, SURFACE, TNUDGE, TROPOP, and VAXTRA. For details on these submodels, refer to

The RC1-base-07 simulation is used to study the methods that are used to derive AoA from non-linear tracers, such as

Globally averaged

In the tranPul simulation, periodical pulses of an inert tracer were released at the surface in the range between 20

It is straightforward to derive mean AoA from linearly increasing tracers in models, as described in Sect.

Mean AoA derived from the idealized tracer from the RC1-base-07 ESCiMo simulation. July mean for the years 2001–2010.

Age spectra at 59

The ratio of moments calculated directly from the spectra as shown in Fig.

Mean ratio

As described in Sect.

The fraction of input was varied between 90 %, 95 % and 98 % and the ratio of moments between 0.7, 0.8, 1.0 and 1.25 years. This covers the range for the ratio of moments proposed in

The resulting trends for 40

Overview of the trend in mean AoA derived from

Figure

To build on what was already seen from Fig.

Mean absolute deviation of mean AoA calculated from

It is evident from Fig.

Figure

Ratio of moments derived from extended age spectra from the tranPul simulation at 20 hPa and 40

As shown in Fig.

Trends of mean AoA from 1975 to 2011

Since the reference location for the AoA calculation can also be varied in model calculations, we checked the effect on the resulting AoA and its trends. However, the different reference locations that have been tested do not show a strong influence on the resulting mean AoA or its trends. For example, an average of the concentration in the area between 20

We find that the sensitivity of the AoA trends derived from

Considering Eq. (

Coefficients

Another explanation for the variation in mean AoA might be the sensitivity of the lag time

Lag time

As described when discussing the polynomial coefficients, the

Now that the range for the polynomial coefficients

Mean AoA

It can be seen that for

To conclude the considerations why the AoA trend is sensitive to the parameter selection, it can be said that due to the shape of the

The latter analyses were done for both

As described in Sect.

Similar to Fig.

As Fig.

It has been shown here that the variation of the mean AoA trend due to the selection of parameters is larger than the internal variability (e.g. Fig.

Another question we consider is whether a second-order fit is appropriate to describe the

The convolution method enables us to avoid uncertainties about the amount of time considered and the function that is fitted to the time series. Still, there is a high sensitivity to the ratio of moments, and it remains open which ratio of moments describes the atmosphere best. Still, it is rather certain that larger ratios of moments are more realistic.

It is most valuable to put the results derived from the model data concerning parameters and methods of AoA calculations into context by testing whether we see the same tendencies in calculations of observed AoA. The mean age values are recalculated from the observations by

Trend in mean AoA derived from the observations for the fit method and the convolution method for the respective fraction of input and ratio of moments.

AoA trends recalculated from observations using the fit method and convolution method for different parameters. Within the presented decimals, the errors are equal.

In agreement with what we presented for the model data, there is little influence of the ratio of moments on the trend using the fit method for 98 % fraction of input, as was used in the calculations so far. For 90 % fraction of input, the trend becomes less positive and eventually even slightly negative for larger ratios of moments. Thus, we see the same tendencies towards smaller, respectively more negative trends for larger ratio of moments and smaller fraction of input.

Applying the convolution method for larger ratios of moments gives smaller positive trends, too. This confirms what we have seen from the model data. For both methods for the larger ratio of moments negative trends as seen in the models lay within the margins of error.

Figure

Overall our results show that the selection of parameters helps resolve the difference between model and observation AoA trends. Furthermore, it should be mentioned that

However, one should consider that the trend in

We investigated the sensitivity of the derivation of mean AoA to parameter choices that are necessary in the fit and convolution methods using a model as a test bed. References available in a model such as a linearly growing AoA tracer and age spectra allow specific testing of the methods.

In our analysis we were able to find a systematic variation of the mean AoA trend derived from

Investigating another method to derive mean AoA, namely the convolution method, showed the same relation of smaller negative AoA trends for a larger ratio of moments. The convolution method only assumes the ratio of moments. It provides very good agreement between AoA from

Applied to the balloon-borne observations was the fit method with a small ratio of moments (0.7 years) and a big fraction of input (98 %), which both tend to shift the trend towards more positive values. Based on model results, we find better agreement with a linear AoA tracer for ratio of moments of about 1.25 and a fraction of input of 95 %. Therefore, the parameter selection helps to resolve why the mean AoA trends found in

Our model results suggest using a ratio of moments larger than 0.7 years. Using a ratio of moments within the range 1.25–2 years is in line with what other 3d-model studies suggest

Testing the impact of the parameter choice on AoA derived from the balloon-borne observations shows the same sensitivities for fit and convolution method as seen in the model. Within the margins of error the trend in AoA from observations and EMAC agrees when assuming a large ratio of moments (2 years). However, as the ratio of moments in the real atmosphere is currently unknown, we cannot conclude whether such a large ratio of moments is realistic. Overall, understanding the systematic influence of the parameter selection on the trend of mean AoA provides further insight in addition to the existing work on the uncertainties of mean AoA and its trends. This work clearly highlights the benefits of the consistent model evaluation of methods that are applied to observations.

The ESCIMo data used in this study can be obtained through the British Atmospheric Data Centre (BADC) archive (

The initial concepts to derive mean AoA were initialized by HB and AE. HG and FF initiated the method evaluation. The simulation execution was done by RE with development contributions by FF. HB further contributed discussion and insight to the method evaluations. AE did the recalculation of the observational data. FF performed the data analysis and wrote the main parts of the paper. All the authors contributed in finalizing the paper.

The authors declare that they have no conflict of interest.

This article is part of the special issue “The Modular Earth Submodel System (MESSy) (ACP/GMD inter-journal SI)”. It is not associated with a conference.

We acknowledge project ESCiMo (Earth System Chemistry integrated Modelling), within which the EMAC simulations were conducted at the German Climate Computing Centre DKRZ through support from the Bundesministerium für Bildung und Forschung (BMBF). Further, we want to thank both anonymous referees for their reviews. Thanks to Romy Heller for providing a review prior to submitting.

Frauke Fritsch, Hella Garny and Roland Eichinger received funding by the Helmholtz Association under grant no. VH-NG-1014 (Helmholtz-Hochschul Nachwuchsforschergruppe MACClim). The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.

This paper was edited by Peter Haynes and reviewed by two anonymous referees.