SHDOMPPDA - Plane-Parallel SHDOM for Data Assimilation
OVERVIEW
SHDOMPPDA computes unpolarized radiative transfer in a plane-parallel
medium for either collimated solar and/or thermal emission sources of
radiation. The shdomppda_fwd_tl_adj module contains subroutines that
perform the forward, tangent linear, and adjoint radiative transfer
models. The forward model outputs top of atmosphere monochromatic
radiances (in reflectance units or brightness temperature) for a number
of specified directions. SHDOMPPDA inputs mixing ratio and number
concentration profiles for any number of hydrometeor species. It
performs optical property calculations from the hydrometeor profiles
(and a pressure profile) using scattering tables as a function of mass
mean radius. SHDOMPPDA also inputs pressure, temperature, water vapor
and ozone profiles, which are passed to user provided molecular
absorption routines. Molecular Rayleigh scattering is calculated for
wavelengths shorter than 1 micron. Currently only Lambertian surface
reflection is supported, though the underlying routines also support
the RPV BRDF model.
Using the SHDOMPPDA_FWD_TL_ADJ Module
The shdomppda_fwd_tl_adj module contains six subroutines:
READ_SCATTERING_TABLES reads all scattering table files
FORWARD_COLUMN_RADIANCE forward radiative transfer for one column
TANLIN_COLUMN_RADIANCE tangent linear of forward RT
ADJOINT_COLUMN_RADIANCE adjoint of forward RT
DEALLOC_COLUMN_RADIANCE releases memory allocated by forward RT routine
DEALLOC_SCATTERING_TABLES releases memory allocated for scattering tables
READ_SCATTERING_TABLES reads the single scattering information for all
the hydrometeor components and channels that are subsequently used. It
is called once before the radiative transfer routines are used.
FORWARD_COLUMN_RADIANCE is called once for each channel and set of
column and surface parameters. It allocates arrays that may be used by
the tangent linear or adjoint routines. The TANLIN_COLUMN_RADIANCE and
ADJOINT_COLUMN_RADIANCE routines MUST be called after
FORWARD_COLUMN_RADIANCE and with the same data for the input parameters
(with the same names). DEALLOC_COLUMN_RADIANCE should be called after
finishing with one column, that is, after the last of the forward,
tangent linear, or adjoint routines is called.
For a list of the specific input and output parameters for each
subroutine, see the comments at the beginning of each routine in
shdomppda_fwd_tl_adj.f90. See demo_shdomppda.f90 for an example of the
use of most of the above routines, and see the run_demo_shdomppda.csh
script on how to run the demonstration program. The comments for the
two key subroutines are copied below (the tangent linear and adjoint
routines have similar argument lists).
SUBROUTINE READ_SCATTERING_TABLES (NCOMP, NCHAN, SPECIESZRANGE, &
SCATTABDIR, SCATTABFILES)
! Reads the tables of single scattering properties as a function of
! mean mass radius for the needed hydrometeor species and all the
! NCHAN channels (over all platforms). If the SPECIESZRANGE(2,I) is
! negative for a component than those scattering table files are not read.
! The SPECIES2TABLE module array is made, which converts from hydrometeor
! species number (1 to NCOMP) to the scattering table number (1 to NSCATTAB)
! in the tabulated properties arrays. The module arrays for the tabulated
! scattering properties (NRTAB, RTAB, WAVELEN1, WAVELEN2, PARDENS,
! EXTINCTTAB, SSALBTAB, NLEGTAB, LEGENTAB) are allocated and filled in here.
!
! Inputs:
! NCOMP number of hydrometeor components or species
! NCHAN number of wavelengths
! SPECIESZRANGE height range (in km) for each hydrometeor species
! SCATTABDIR scattering table directory for all files
! SCATTABFILES scattering table files for all components and channels
!
! Outputs:
! No output arguments. Routine sets global variables in module.
SUBROUTINE FORWARD_COLUMN_RADIANCE (NZ, ZLEV, TEMP, PRES, VAPMIXR, O3MIXR, &
TOPMOLECTAU, TOPTEMP, INDEXABS, &
NCOMP, MIXR, CONC, SPECIESZRANGE, &
SFCPRES, TEMPSKIN, SFCALBEDO, &
ICHANSCAT, NOUT, MUOBS, PHIOBSREL, &
SRCTYPE, SOLARFLUX, SOLARMU, WAVELEN, &
NMU, NPHI, SPLITACC, SOLACC, &
UNITS, RADOUT)
! Computes the upwelling radiance for the specified atmospheric state
! in the specified directions.
! Allocates many of the module global arrays (deallocate with
! DEALLOC_COLUMN_RADIANCE).
! Model levels are treated as SHDOMPP layer boundary levels with the
! cloud mixing ratio linearly interpolated and integrated to get the
! hydrometeor mass in each layer. The hydrometeor water paths are
! obtained from the mixing ratios and pressure profiles; ZLEV is
! used only for speciesZrange, not for optical properties.
!
! Inputs:
! NZ number of model levels
! ZLEV model height levels (km) (from bottom to top of atmosphere)
! TEMP model temperature profile (K)
! PRES model pressure profile (mb)
! VAPMIXR model water vapor mass mixing ratio (g/kg)
! O3MIXR ozone mixing ratio (ppmv) at model levels
! TOPMOLECTAU equivalent top layer (above model top) molecular optical depth
! TOPTEMP equivalent top layer temperature (K)
! INDEXABS absorption channel index number (<=0 for no absorption call)
! NCOMP number of hydrometeor species input
! MIXR model hydrometeor mass mixing ratio profiles (g/kg)
! CONC model hydrometeor concentration profile for each species (#/kg)
! SPECIESZRANGE lower and upper range of layers to allow each species (km)
! SFCPRES model surface pressure (mb)
! TEMPSKIN model surface skin temperature (K)
! SFCALBEDO surface Lambertian albedo
! ICHANSCAT channel number for indexing into scattering tables
! NOUT number of output radiance directions
! MUOBS viewing cosine zenith angles
! PHIOBSREL viewing azimuth angles relative to solar azimuth (deg; 0 is forw$
! SRCTYPE radiation source type: 'S'=solar, 'T'=thermal, 'B'=both
! SOLARFLUX solar flux on a *horizontal* surface (W/m^2 um)
! SOLARMU cosine solar zenith angle (must be < 0)
! WAVELEN wavelength (microns) for thermal source
! NMU number of discrete ordinate zenith angles in both hemispheres
! NPHI number of discrete ordinate azimuth angles in 2\pi
! SPLITACC adaptive layer splitting accuracy (0.03 to 0.0003 recommended)
! SOLACC SHDOMPP solution accuracy (1E-6 to 1E-7 recommended for adjoint
! accuracy even though that is not needed for radiance accuracy)
! UNITS output units: 'R' for reflectance (relative to SOLARFLUX),
! 'T' for EBB brightness temperature
! 'W' for radiance output (W/(m^2 ster um))
! Outputs:
! RADOUT reflectance or brightness temperature vector
ACCURACY ISSUES
The accuracy of SHDOMPPDA output radiances is determined by the angular
resolution, chosen by NMU and NPHI, the spatial resolution, chosen by
SPLITACC (and the MAXDELTAU parameter), and the solution convergence,
chosen by SOLACC. A good choice for solar reflection problems is
NPHI=2*NMU, but for high Sun or low viewing zenith angles or a more
isotropic phase function a smaller NPHI could be accurate. For thermal
emission problems set NPHI=1. Note: NPHI is the number of azimuth
angles in 0 to 2*pi, but only the range 0 to pi is actually used
internally. There is seldom any point in having the SPLITACC and
SOLACC parameters set very small if the accuracy is limited by low
angular resolution (small NMU). However, a smaller SOLACC parameter is
required for good tangent linear and adjoint accuracy than is required
for good forward model accuracy. How the actual accuracy depends on the
input parameters should be investigated with a convergence test for
problems similiar to the ones you want to carry out. Also see the
SHDOMPPDA journal article for results that offer some guidance.
MAKING SCATTERING TABLES
Two programs are provided for making the scattering tables input to
SHDOMPPDA: make_mie_table2 and make_ice_table2. These tables give the
optical properties (extinction, single scattering albedo, and Legendre
coefficients of the phase function) as a function of the particle size
distribution mean mass radius. Mass mean radius is chosen for SHDOMPPDA
instead of effective radius because it can be directly calculated from
the input hydrometeor mass mixing ratio and number concentration without
further assumptions about the particle size distribution and shape.
MAKE_MIE_TABLE2
Make_mie_table calculates the single scattering properties of gamma or
lognormal distributions of spherical particles and outputs the results
in a scattering table. If the particle type is water or ice then an
integration across the specified wavelength band may be performed. If
an aerosol particle type is chosen then the index of refraction of the
aerosol is specified.
For water or ice particles an integration across the wavelength range
may be done. In this case a series of Mie calculations are performed at
a specified wavelength spacing using the correct index of refraction for
each wavelength. The alternative is to use the Planck function averaged
index of refraction and central wavelength, which takes less computation
but may be less accurate (depending on the spectral band width). For
solar wavelengths (< 3 um) the Planck function is for a solar
temperature (5800 K), for longwave wavelengths (> 5 um) the Planck
function is for an atmospheric temperature (270 K), while between 3 and
5 um a straight average is used.
If an aerosol particle type is chosen then the particle bulk density of
the aerosol is specified. The density is needed because the output
scattering table extinction is normalized for a mass content of 1 g/m^3.
The gamma distribution of cloud droplet sizes is
n(r) = a r^alpha exp(-b*r)
where r is the droplet radius, and a, b, alpha specify the gamma
distribution. The number concentration of droplets is
N = a Gamma(alpha+1)/ b^(alpha+1), where Gamma is the gamma function.
The effective radius of the distribution is r_eff = (alpha+3)/b, while
the effective variance is v_eff = 1/(alpha+3). A typical value for
water clouds is v_eff=0.1 or alpha=7. For ice clouds a typical value is
alpha=1 or 2. An exponential distribution is obtained with alpha=0. A
large value of alpha gives close to a monodisperse distribution.
The lognormal distribution of cloud droplet sizes is
n(r) = a/r exp( -[ln(r/r0)]^2 / (2*sigma^2) )
where r0 is the logarithmic mode of the distribution and sigma is the
standard deviation of the log. The number concentration of droplets is
N = sqrt(2*pi)*sigma*a. The effective radius of the distribution is
r_eff = r0*exp(2.5*sigma^2) and the effective variance of the
distribution is v_eff = exp(sigma^2)-1. A common value for water clouds
is sigma=.35, or v_eff=0.130, and a common value for aerosol distributions
is sigma=0.7.
The maximum radius of the distribution is specified by the user because
it is the critical determinant of the Mie calculation computer time.
There are often microphysical reasons for truncating the theoretical
size distribution; for example, one might say that the cloud droplet
mode ends at a radius of 50 microns. For a narrow gamma distribution
(alpha=7) of cloud droplets, a maximum radius of only twice the largest
effective radius gives virtually the same optical properties as the
untruncated gamma distribution. For a wide lognormal distribution, as
might be used for an aerosol distribution, a much larger maximum radius
relative to the largest effective radius would be required if no
truncation was desired. If there is truncation make_mie_table uses an
iterative procedure to adjust the size distribution modal radius to
achieve the desired mean mass radius. Thus one can be assured that the
size distributions have the mean mass radii reported in the output
scattering table even if there is truncation of the theoretical
distribution. The number and spacing of the integration steps over the
size distribution is controlled by the GET_NSIZE and GET_SIZES
subroutines. The default formula is DELX = max(0.01,0.03*X**0.5),
where X is the size parameter (2*pi*r/lambda, lambda=wavelength)
and DELX is the integration step. This integration spacing is
adequate for most purposes, but can be easily changed if higher
accuracy is sought.
Make_mie_table2 Input Parameters
Parameter Description
WAVELEN1 wavelength range (microns) for this band
WAVELEN2 for monochromatic choose WAVELEN1=WAVELEN2
PARTYPE particle type: W=water, I=ice, A=aerosol
if PARTTYPE='A' then the index of refraction is input,
otherwise tables for water and ice index are used.
AVGFLAG 'A' for spectral average over the wavelength range (for
PARTYPE='W' or 'I'), 'C' to use the central wavelength.
DELTAWAVE wavelength interval for averaging (micron)
RINDEX aerosol complex index of refraction (negative imaginary part)
PARDENS aerosol particle bulk density (g/cm^3)
DISTFLAG 'G' for gamma distribution or 'L' for lognormal distribution
ALPHA distribution shape parameter (either alpha in gamma distribution
or sigma in lognormal distribution). Effective variance
= 1/(alpha+3) for gamma, exp(alpha^2)-1 for lognormal.
NRTAB number of effective radii entries in Mie table
SRTAB starting effective radius (micron) in Mie table
ERTAB ending effective radius (micron) in Mie table
MAXRADIUS maxium particle radius in size distribution (micron)
MIEFILE output Mie scattering table file name
MAKE_ICE_TABLE2
Make_ice_table2 calculates the shortwave single scattering properties of
gamma distributions of mixtures of six shapes of ice crystals and outputs
the results in a scattering table. The ice crystal scattering properties
were produced by Ping Yang and are described in these articles:
Yang, Ping, K. N. Liou, Klaus Wyser, David Mitchell, 2000:
Parameterization of the scattering and absorption properties of
individual ice crystals. J. Geophys. Res., 105 (D4), 4699-4718.
Yang, P., H. Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar,
M. I. Mischenko, and Q. Fu, 2005: Scattering and absorption property
database for nonspherical ice particles in the near-through
far-infrared spectral region. Appl. Optics, 44,5512-5523.
The scattering properties are tabulated in "yang2005_ice_scatter.db"
for 65 wavelength from 0.20 to 100 microns and 45 particle lengths from
2 to 9500 microns. The six ice crystal shapes are 1=aggregate, 2=solid
column, 3=droxtal, 4=hollow column, 5=hexagonal plate, 6=bullet rosette.
(see the second article for pictures of these shapes and more information).
The phase functions have been modified for this distribution by
convolving the portions with scattering angles less than 10 degrees by a
gaussian with 0.25 degree rms width and by adjusting the forward peak
height to normalize each phase function. The reasons for doing this is
that the original phase functions with the largest size parameters would
require a huge number of Legendre series terms to be represented for
SHDOM and also were not properly normalized. The number of Legendre
terms required for the smoothed forward peak phase functions is 2500.
The smoothing of the forward peak will not affect the radiative transfer
results significantly for nearly all applications (one application where
it could be an issue is sun photometry, but the TMS approximation in
SHDOMPP is already poor for that application).
Make_ice_table2 reads the "yang2005_ice_scatter.db" database file to
produce a scattering table file for gamma size distributions with a
sequence of mean mass radii for a mixture of particle shapes. The shape
mixture can vary throughout the size distribution because the mixing
fractions depend on the particle maximum diameter. The mixing fractions
of the six particle shapes are specified with a mixture file. The
format of the shape mixture files is:
one header line
Dmax F1 F2 F3 F4 F5 F6 (Fn are the fractions for each shape)
Dmax is the maximum particle diameter (e.g. the length of a column).
Dmax must increase in the file. The mixing fractions are interpolated
in Dmax between entries in the mixing table. The mixing fractions of
the smallest Dmax in the table are used for smaller Dmax database
values, and fractions for the largest Dmax in the table are used for
larger Dmax database values.
The scattering properties are averaged over the desired spectral range
using linear interpolation between wavelengths in the database. The
gamma distributions are in terms of the equivalent volume spherical
diameter (Dv), not the particle length. The "b" parameter of the gamma
distribution [n(D) = a Dv^alpha exp(-b*Dv)] is adjusted iteratively to
achieve the correct mean mass radius. The user specified mean mass
radius may not be achievable for a particular particle shape and size
distribution width, in which case a different range of mean mass radius
or a narrower distribution (larger alpha) will have to be chosen. The
extinction in the output scattering table is normalized for
distributions with an ice water content of 1 g/m^3 assuming an ice
density of 0.916 g/cm^3. The output mean mass radii are logarithmically
spaced between SRTAB and ERTAB.
Make_ice_table2 Input Parameters
Parameter Description
ICESCATDB filename of the ice scattering database
(i.e. yang2005_ice_scatter.db)
WAVELEN1 wavelength range (microns) for this band
WAVELEN2 for monochromatic choose WAVELEN1=WAVELEN2
SHAPEMIXFILE input ice particle shape mixing file name
NRTAB number of mean mass radii entries in scattering table
SRTAB starting mean mass radius (micron) in scattering table
ERTAB ending mean mass radius (micron) in scattering table
ALPHA gamma distribution shape parameter
ICETABFILE output scattering table file name
SHDOMPPDA DISTRIBUTION FILES
shdomppda.txt this documentation file
demo_shdomppda.f90 demonstration program calls forward and adjoint
shdomppda_fwd_tl_adj.f90 SHDOMPPDA module with main routines to use
molec_absorption_interface.f90 dummy molecular absorption module
shdomppda.f90 forward SHDOMPPDA subroutines
shdomppda_ftls.f90 tangent linear SHDOMPPDA subroutines
shdomppda_ads.f90 adjoint SHDOMPPDA subroutines
make_mie_table2.f90 Mie program to make scattering tables
mieindsub.f subroutines for Mie code
make_ice_table2.f90 program to make ice crystal scattering tables
makefile make file to compile distribution programs
run_demo_shdomppda.csh example script to run demo_shdomppda
make_scat_tables.csh example script to
put.c utility program for the scripts
rams_twomom2_y360.dat RAMS X-Z slice used in JAS paper
goes_ch1_cloud.scat GOES channel 1 scattering table for cloud droplets
goes_ch1_ice.scat GOES channel 1 scattering table for pristine ice
goes_ch4_cloud.scat GOES channel 4 scattering table for cloud droplets
goes_ch4_ice.scat GOES channel 4 scattering table for pristine ice
Baum_MODIS_shape_mixture.dat Bryan Baum's MODIS ice crystal mixture recipe
yang2005_ice_scatter.db database for making ice scattering tables
(not in distribution, obtain separately)