Modelling of the Unresolved Spectrum
of the Earth
P.G.J. Irwin
Very Preliminary Report
24/10/01
Model Outline.
Disk-averaged spectra were calculated using a correlated-k radiative transfer model from
500-1700 cm-1 at a spectral resolution of 1cm-1. Spectra were calculated for different
months of the year and with the sub-spacecraft point at a range of latitudes and
longitudes.
The modelling required to do this contained the following elements:
1. A climate model was used to estimate the T/P/v.m.r. profiles and ground properties
for all latitudes and longitudes.
2. The observable disk was split into a number of bins of roughly equal areas.
3. For the chosen sub-spacecraft latitude and longitude, the zenith and azimuth angle of
each geographical position was calculated, and each profile (if on the visible disk)
averaged into the appropriate bin.
4. The averaged profile in each viewing bin was split into a number of layers with
appropriately placed cloud decks and path amounts calculated for the average
emission angle of each bin.
5. The thermal emission spectrum from each bin was calculated using the correlated-k
radiative transfer model.
6. The spectra from each bin were averaged using the projected area as a weight.
1. Climate Model.
1.1 Sources of Data
Climate data for this study comes mainly from the Goddard Distributed Active Archive
Center (GDAAC) Climatology Interdisciplinary Data Collection (CIDC). This contains
monthly means of over 70 physical parameters and comes on 4 CDs.
The data contained in the CIDC come from a variety of sources (which are described
below for those that were actually used) and are averaged into months over a number of
years. In all cases the data were further averaged for each month from 1980 to 1993
using an IDL routine average_cidc.pro.
Additional data for Ozone comes from the NASA/MSFC Global Reference Atmospheric
Model-1999 Version (GRAM-99) "atmosdat" data set.
Reference T/P/v.m.r. profiles for tropical, mid-latitude summer, mid-latitude winter, subarctic summer, sub-arctic winter come from AFGL (Anderson et al. (1986) (AFGL-TR86-0110).
1.2 Specific data choices for profiles
Ground temperature, ground pressure, near-ground temperature,
near-ground specific humidity.
These data come from the Goddard Data Assimilation Office (GDAO) data set (covering
the period 3/80 - 11/93).
Temperature profile.
The temperature profile as a function of pressure in the lower troposphere also comes
from GDAO data set (at 8 pressure levels between 1000 and 200 mb). The profile is
truncated at the lower end for pressures greater than the estimated ground pressure. The
upper part of the temperature profile is set to the AFGL reference profile closest in
season and latitude with vertical smoothing in the transition region to prevent excessive
vertical temperature gradients. The heights are then calculated assuming hydrostatic
equilibrium, setting the base height to 0 km.
CO2, CH4, CO, N2O and O2 profiles.
The v.m.r. profiles of CO2, CH4, CO, N2O and O2 are interpolated from the nearest
AFGL reference atmosphere to the pressures of the T/P profile.
Water vapour profile.
In the lower troposphere, these data come from the GDAO specific humidity data set. At
pressures below 200mb, they come from the nearest AFGL profile with a smoothed
transition between the two sources.
Ozone profile.
The ozone column amount in Dobson Units (where available) comes from the Total
Ozone Mapping Spectrometer data set covering the period (11/78 - 5/93). The vertical
profile between 0.01 and 20mb comes from the "atmosdat" GRAM-99 data set which is
zonally averaged in 10-wide latitude bins for all 12 months. The ozone profile for
pressures outside this range in the T/P profile are set to the nearest AFGL reference
profile, with smoothing at the transition. Once the vertical profile of ozone is established,
the column amount is calculated and compared to the TOMS estimate, where this is
available. If TOMS has a valid Column Amount estimate, then the ozone profile is scaled
to give the same. If TOMS did not measure a column amount (e.g. in polar winter) then
the profile is left unadjusted.
Clouds.
Cloud data come from the International Satellite Cloud Climatology Project (ISCCP) D2
(new version) data set covering the period(1/86-1/87) and (1/89-12/93). The particular
cloud products used were:
IR low cloud fraction(%), cloud top pressure (mb), cloud top temperature (K)
IR mid cloud fraction(%), cloud top pressure (mb), cloud top temperature (K)
IR high cloud fraction(%), cloud top pressure (mb), cloud top temperature (K)
2. Binning Scheme Definition
The observable disk is taken as being a perfect circle and the disk is split into a number of
sectors as shown in the figure below.
The radius R of the central circle is entered (as a percentage of the total radius). The
number of concentric rings is then calculated as INT((100-R)/R). Each ring is then split
up into a number of sectors where each sector has approximately the same area as the
central disk. Thus for the ring between radii r1 and r2, the number of sectors is:
NS = INT((r22- r12)/Acentral)
The binning scheme is defined by the IDL procedure subsector.pro.
3. Binning of data.
In order that both the zenith and azimuth of each geographical position in the climate data
set may be calculated, the latitude, longitude coordinates must be rotated twice. For the
sub-spacecraft latitude, longitude of lat_S, lon_S, the latitude-longitide coordinates of
each point in the climate data set (90-, ) are first rotated by an angle lon_S about the z-
axis, followed by a rotation of (90-lat_S) about the y-axis. The transformed zenith angles
and azimuth angles then identically the new coordinates (', '). This transformation is
performed by the IDL procedure subcalcbin.pro. The calculated zenith and azimuth
angles for all points on the globe with respect to a satellite over (45 N, 0 E) and at
infinite distance is shown below.
If '<90 then the data are allocated to the appropriate disk-bin and co-added with any
other data that are allocated to that bin. The average emission angle and geographical
latitude of each bin is calculated in the same way. This long process is performed by the
IDL program avcsector.pro. Once the data is averaged for each bin the following
output files are produced:
mon.dat
ASCII file containing the number of rings and sectors of the
binning scheme used and the averaged climate data variables
allocated to each bin. N.B. mon = jan, feb, mar, etc.
monSectorN_M.prf
Averaged radtran profile .prf file for ring N, sector M. The
central disk has N=1, first ring has N=2 etc. The central ring has
only one sector M.
monSectorN_N.pat
Averaged radtran path .pat file for each disk bin. File contains
the cloud top temperatures, pressures and cloud fractions and
also the ground temperature and layering scheme (described in
the next section).
4. Layering scheme
Once the data have been averaged into each disk-bin, the atmospheric profile is split into
a number of layers to facilitate the radiative transfer calculation. The layering scheme is
defined by the monSectorN_N.pat file via a new layering definition: muselayer. In this
scheme the T/P profile is first interpolated to the low, mid and high cloud top
temperatures to calculate the cloud top pressure most consistent with the averaged data
set. Three clouds are then placed (assumed to be of width 0.1km) with their tops at these
pressure levels and with their optical thickness  set to -log(1-cloud_fraction/100). The
vertical gaps between the clouds are split into 2 equally thick levels (in log(pressure)
coordinates). The gap between the bottom of the lower cloud and ground is split into 4
equal log(pressure) layers and the region above the clouds is split into 16 equal
log(pressure) layers. An extra 'cloud' layer of optical depth 1020 is substituted at the
ground and the temperature is set to that of the ground.
The layer and path amounts are then calculated using the usual Radtran path routines
within the combined layering and radiative transfer FORTRAN program Muse.
5. Radiative Transfer Calculation
This is done with using correlated-k and assuming thermal emission only. The pretabulated k-tables for each gas of interest cover the pressure and temperature range
reached by the terrestrial atmosphere and are tabulated in bins of width 1 cm-1, with
step 1 cm-1. The clouds are assumed to be non-scattering and to have no variation of
absorption cross-section with wavenumber. The program Muse takes the averaged .prf
and .pat file for each disk bin, runs the path routines to set up the .drv driver file and
calculates the spectrum which is output to an ASCII format .idl file.
6. Disk-averaging
This is done with the IDL routine museave.pro. The program reads all the output
spectra files monSectorN_M.idl and also the binning definition file mon.dat. The program
then calculates the projected area of each bin and co-adds the individual spectra using the
projected area as the weight.
7. Very Preliminary Results
Once the initial debugging was complete a test run was set up as follows.
Month: July
Radius of central disk: 20% of total radius.
Satellite longitude: 0 E.
Satellite latitudes: 90 S, 45 S, 0, 45, 90 N.
The disk-averaged spectra for these 5 cases is shown below.
Now the good news is that these look like the Voyager IRIS measurements of the Earth.
The bad news (if it is bad news for MUSE) is that they look almost identical! There are
small differences, but these are second order. In order to get inverted CO2 and O3 peaks
we clearly need the ground to be colder than the stratosphere. Also, we ideally want no
clouds since under these conditions of a temperature inversion, the cloud tops are slightly
warmer than the ground itself. On first inspection, this doesn't seem to happen too often,
although examples exist. If we consider the case where we are looking directly down on
the South Pole, and split the disk into rather more bins, setting the central radius to be
10% of the total radius, then cases of inversion are found:
However such areas seem rather small and are swamped by the radiance from the rest of
the planet which shows the O3 and CO2 features in absorption.
To show this I have plotted the averaged ground temperature in July as seen from above
the South pole.
You can just see the 220 K contour line which is well inside of Antarctica. In the absence
of cloud cover this region should, and does, have CO2 and O3 in emission. To see how the
binning scheme averages things, the plot below shows the average ground temperature in
each bin for the later case where R=10%.
Hence the binning scheme seems to work and reasonably represents the spatial variation
of the ground temperature. Even with this much finer binning scheme however, the
average remains very similar to the lower resolution R=20% case shown above.
Hence it would appear unlikely that for disk-averaged spectra we will ever in fact get
cancellation of the CO2 and O3 features, although I will continue working on this.
One area of the modelling which does worry me is that the climate data temperature
profiles only go up to 200mb and hence the stratosphere temperature profile does not
vary much from place to place. I am considering folding TOVS data (also form CIDC)
which contains estimates of the temperature in a layer 100-30mb. This may be important
although I get the feeling that the variable ground conditions are more important and
these should be well-modelled. Of course I may have overlooked something else so I
would appreciate any comments you might have on this.