How to include stratospheric ozone depletion in C20C runs

The method of applying the trends to model ozone was designed by David Karoly and David Sexton, using SPARC trend estimates which are based on a variety of instruments: SAGE I/II, TOMS total column ozone, and ozonesondes in polar regions. Between 56^oS-56^oN, the trends are estimated above 20km from SAGE I/II data, and between the tropopause and 20km, the trends are estimated using the difference between TOMS column ozone data and SAGE I/II column ozone above 20km.

The SPARC data is here (big_endian) or here (little_endian).

1. Read in SPARC trend estimates (in Dobson Unit per km per decade), which are for each month, at latitudes {-88,-84,...,84,88} and heights {1.5,2.5,...,50.5km}. Note that the data are stored in both big_endian and little_endian byte orderings, so be sure to get the one that can be used on your local system. Here is some PVWave/IDL to set up array TRENDDU, LAT and HEIGHTS.

   f='trenddu_big_endian.dat'
   openr,unit,f,/f77,/get_lun
   lat=-88+4*findgen(45)
   heights=(1.5+findgen(50))*1000.0
   nht=n_elements(heights)
   heights=[0.0,heights]
   revht=reverse(heights)
   nl=n_elements(lat)
   trenddu=fltarr(nl,nht,12)
   readu,unit,trenddu
   
   

   In Fortran:

          dimension trenddu(45,50,12)
          open(10,file='trenddu_big_endian.dat',form='unformatted')
          read(10) trenddu
          close(10)
   

2. The trends are in Dobson Units per km per decade as a function of latitude, height and calendar month.

   To convert from DU/km to mass-mixing ratio in kg/kg at a given height of the atmosphere you need CONVC defined below and the density of air at that height in the atmosphere, rho_air_ht.

   dry_air_const = 287.05 ; J kg-1 K-1
   standard_depth = 1.0e-5 ; 0.01 mm O3 at stp is 1DU
   kilometre_depth = 1.0e3 ; 1000m for each DU km-1 datum
   scales = standard_depth/kilometre_depth
   standard_density = 1.0e5/(dry_air_const*273.15) ; p0/(R*T0)
   rmm_ozone = 48.0 ; 3*16
   rmm_air = 28.8 ; mixture
   air_density = air_pressure/(dry_air_const*air_temperature)
   mass_mixing_ratio = scales*standard_density*(rmm_ozone/rmm_air)*duperkm/air_density

   rho_air=1.
   convc=(1.0e-5/1.e3)*(1.0e5/(273.15*287.05))*(48/28.8)
   duperkm=mass_mixing_ratio*rho_air_ht/(convc*rho_air)
   mass_mixing_ratio=duperkm*convc*rho_air/rho_air_ht
   

3. First we calculate trends on the model grid in model units. HadAM3 model units are kg/kg.

   The procedure (explained in more detail below) is to only use trends in the lower stratosphere i.e. everywhere above the model tropopause. SPARC's troposphere does not quite match up with the model tropopause so any ozone lost below the model's tropopause is re-distributed between the model tropopause and 20km (this is only a minor correction and ensures that the total column loss of ozone below 20km is the same in both the model and the SPARC data set).

4. We also specified that we would always use climatological ozone values in the atmospheric level of the model at each latitude that contained the climatological monthly mean tropopause. This level would differ for each latitude and calendar month. We did this to avoid stratospheric ozone depletion occurring just below the tropopause which causes a negative radiative forcing. We also did this so that it was easy to separate stratospheric and tropospheric ozone trends. You may or may not choose to impose zero trends in the level which contains the model's climatological tropopause.

5. The procedure requires various inputs which are model-dependent and you will need to determine these to interpolate the SPARC trends onto the model climatology.
   1. The height of the top and bottom of each atmospheric level at each latitude for each month.
   2. The climatological height of the model tropopause at each latitude for each month.
   3. The climatological values of ozone used in the climate model.
   4. Estimate the model's climatological density of air in each atmospheric level at each latitude for each month. This is done by:

      rho_air_at_level=rho_air*pressure_difference_across_level_in_Pa/(g*height_difference_in_km).

   5. Convert climatological values of ozone used in the climate model to dobson units per km at each level by multiplying mass mixing-ratio by rho_air_at_level divided by CONVC (defined above).

6. The procedure is as follows:
   1. Interpolate the SPARC trends to the model's latitudinal resolution.
   2. For each month, latitude, and atmospheric level:
      • Using height of tropopause, determine fraction of level that falls above the model tropopause.
      • Determine fraction of each SPARC level that falls within the atmospheric level. Calculate total DU/km (called duperkm) that falls within atmospheric level. Calculate total DU in atmospheric level by multiplying by thickness of atmospheric level.
      • For that level, ozone trend in DU/km is duperkm*frac.
      • Apply minor correction to ensure total column change below 20km at each latitude is same in model as in SPARC data set. Calculate the total column ozone trend below the tropopause and add it to the layer between the tropopause and 20km in such a way that the adjustment at each level is the same percentage of the climatological ozone in that level as at the other levels. It is a good idea to check that the total column amounts are the same before and after the correction.

   3. Convert trends to kg/kg per year by multiplying by CONVC/rho_air_at_level and dividing by 10.

7. Stratospheric ozone starts in 1975. Prior to that only climatological ozone is used. Between 1975-1979 half the trend values estimated in steps 1-6 are applied to produce a data set of changing stratospheric ozone. After 1979, the full trends are applied. In HadAM3, we set a minimum ozone mass mixing ratio of 10e-11 kg/kg, mainly so that the radiation scheme did not have problems.

References