AoA_from_convolution

tools to calculate the mean age of air from mixing ratios relative to a reference time series

How to use the code

0. Make sure to have the mandatory packages installed in your python environment:

   pandas
   numpy
   scipy
   matplotlib

   the code has been tested with the following package versions, but should work for a lot of other versions, too:

   pandas=2.1.1
   numpy=1.26.2
   scipy=1.11.3
   matplotlib=3.8.0

1. Download the package

2. E.g. create an empty python file (e.g. my_project.py) within your downloaded package

3. within my_project.py you can then use the SF6_to_AoA() and the CO2_to_AoA() functions to derive mean age from observations:

   
   # import everything from the run_convolution_method.py file into your current python session:

from run_convolution_method import *

Example to calculate mean age from SF6 mixing ratio values

Specify your observation date:

t_obs_sf6 = 2022.3 # float value in fractional year, single value only

have your SF6 mixing ratios ready, e.g.:

sf6mr = np.arange(9.5, 11, 0.1) # can be single value or array

decide on what value for the ratio of moments (rom) to use. I.e. the ratio of moments of the age spectrum

see e.g. Garny et al. (2024), Reviews of Geophysics

ratio_of_moments = 1.2 # single value only

calculate mean age from SF6 mixing ratios:

mean_age = SF6_to_AoA(t_obs=t_obs_sf6, SF6_obs=sf6mr, rom=ratio_of_moments)

print(mean_age)

obviously, if you want to calculate the mean age from variable observation dates, you need to

write some kind of for loop

%%

Example to calculate mean age from CO2 mixing ratio values (and CH4 values)

Specify your observation date:

t_obs_co2 = 2022.3 # float value in fractional year, single value only

have your CO2 and CH4 mixing ratios ready, e.g.:

co2mr = np.arange(400, 420, 0.5) # can be single value or array ch4mr = np.ones(co2mr.shape) * 1100.3 # must be the same size as co2mr

decide on what value for the ratio of moments (rom) to use. I.e. the ratio of moments of the age spectrum

see e.g. Garny et al. (2024), Reviews of Geophysics

ratio_of_moments = 1.2 # single value only

calculate mean age from SF6 mixing ratios:

mean_age = CO2_to_AoA(t_obs=t_obs_co2, CO2_obs=co2mr, rom=ratio_of_moments, CH4_obs=ch4mr)

print(mean_age)

WARNING: due to the propagation of the seasonal cycle in CO2 mixing ratios into the stratosphere,

only mean age values above a threshold of ca. 2.5 years are expected to be physically meaningful.

obviously, if you want to calculate the mean age from variable observation dates, you need to

write some kind of for loop