USGS

Isis 2 Documentation


shadow_tau Documentation

SHADOW_TAU - Estimate optical depth tau from shadows.
This program uses level-surface and shadow image intensites to estimate
atmospheric optical depth tau.  The input is a table with one line per
image point to be modeled, listing the image ID, incidence, emission,
and phase angles, and the radiances (DN in a "level 1" calibrated image)
of a level unshadowed area and a nearby shadow.  On output, model results
for the optical depth and albedo of the surface are appended to the
end of each line. The surface and atmosphere models use the same assump-
tions as the "photomet" photometric correction software so the resulting
optical depth estimate will be useful for processing images with that
program.  (In other words, the optical depth calculated by this program
is model-dependent but it is exactly the model-dependent value that will
produce the most effective photometric correction in "photomet".)  Since
the only planet this program will be used for (the only one apart from
Earth with modest atmospheric optical depths) is Mars, most of the
parameters default to appropriate values for Mars.

References cited in individual help entries:

Chandrasekhar, S., 1960.  Radiative Transfer. Dover, 393 pp.

Hapke, B. W., 1981. Bidirectional reflectance spectroscopy
   1: Theory. J. Geophys. Res., pp. 86,3039-3054.

Hapke, B., 1984. Bidirectional reflectance spectroscopy
   3: Corrections for macroscopic roughness. Icarus, 59, pp. 41-59.

Hapke, B., 1986. Bidirectional reflectance spectroscopy
   4: The extinction coefficient and the opposition effect.
   Icarus, 67, pp. 264-280.

Johnson, J. R., et al., 1999, Preliminary Results on Photometric
   Properties of Materials at the Sagan Memorial Station, Mars,
   J. Geophys. Res., 104, 8809.

Kirk, R. L., Thompson, K. T., Becker, T. L., and Lee, E. M.,
   2000. Photometric modelling for planetary cartography.
   Lunar Planet. Sci., XXXI, Abstract #2025, Lunar
   and Planetary Institute, Houston (CD-ROM).

Kirk, R. L., Thompson, K. T., and Lee, E. M., 2001.
   Photometry of the martian atmosphere:  An improved
   practical model for cartography and photoclinometry.
   Lunar Planet. Sci., XXXII, Abstract #1874, Lunar
   and Planetary Institute, Houston (CD-ROM).

McEwen, A. S., 1991. Photometric functions for photo-
   clinometry and other applications.  Icarus, 92, pp. 298-311.

Tanaka, K. L., and and Davis, P. A., 1988, Tectonic History of
   the Syria Planum Provice of Mars, J. Geophys. Res., 93, 14,893.

Thorpe, T. E., 1973, Mariner 9 Photometric Observations of Mars
   from November 1971 through March 1972, Icarus, 20, 482.

Tomasko, M. G., et al., 1999, Properties of Dust in the Martian
   Atmosphere from the Imager on Mars Pathfinder, J. Geophys. Res.,
   104, 8987

PROGRAMMER: Randolph Kirk, U.S.G.S., Flagstaff, AZ

ParmDescriptionDefault
FROM
Input datafile name with
ID/inc/ema/phase/flat/shadow
NONE
TO
Output datafile name with
Inputs/tau/albedo
NONE
FUNC
Type of photometric function
model used for surface:
LAMBER, LOMSEL,
MIN, LUNLAM, MN_EMP, LL_EMP,
HAPHEN, HAPLEG, HAPH_S, HAPL_S
HAPHEN
K
Minnaert exponent for MIN
1.0
L
Lunar-Lambert weight for LUNLAM
1.0
DATAFILE
File containing table of
parameter values vs. phase
for LL_EMP, MN_EMP
"$ISISDATA/photom.mars.sav"
WH
Single-scattering albedo for
HAPHEN, HAPLEG, HAPH_S, HAPL_S
0.52
HH
Opposition surge width for
HAPHEN, HAPLEG
0.170
B0
Opposition surge strength for
HAPHEN, HAPLEG
0.025
THETA
Macroscopic surface roughness
in degrees, for HAPHEN, HAPLEG
30.0
HG1
Henyey-Greenstein asymmetry
parameter for single particle
phase function in HAPHEN, HAPH_S
-0.213
HG2
2nd Henyey-Greenstein parameter
controls mix of +HG1, -HG1
components for HAPHEN, HAPH_S
0.0
BH
Coefficient of P1(cos(phase))
in Legendre single particle
phase function for HAPLEG,
HAPL_S
--
CH
Coefficient of P2(cos(phase))
in Legendre single particle
phase function for HAPLEG,
HAPL_S
--
ATMOS
Type of atmospheric scattering
model
I1	1st approx. Isotropic
I2	2nd approx. Isotropic
A1	1st approx. Anisotropic
A2	2nd approx. Anisotropic
H1	1st approx. Hapke
H2	2nd approx. Hapke
H2
WHA
Single-scattering albedo of
atmospheric particles.
0.95
BHA
Used only with ATMOS=A1, A2.
Coeff of P1(phase) in single
particle Legendre phase fn.
--
HGA
Used only with ATMOS=H1, H2
Coeff of single particle
Henyey-Greenstein phase fn.
0.68
HNORM
Atmospheric shell thickness
normalized to planet radius.
0.003

ADDITIONAL NOTES:

ParmDescription
FROM
Filename of input textfile.  Input file must have image-id,
inc, ema, phase, dn-flat, dn-shadow on each line.
TO
Filename of output textfile.  Output file will have image-
id,inc, ema, phase, dn-flat, dn-shadow plus tau and albedo
on each line.
FUNC
This parameter selects the type of photometric function
model used to describe the planetary surface.  Any surface
photometric function can be used in combination with any
type of atmospheric photometric model (ATMOS).  The parameters
used differ between the photometric functions.

PHOTOMETRIC FUNCTIONS

TAE     Full name                       Parameters
___     _________                       __________

LAMBER  Lambert                         none
LOMSEL  Lommel-Seeliger ("lunar")       none
LUNLAM  Lunar-Lambert function          L
MIN     Minnaert function               K
LL_EMP  Lunar-Lambert empirical         DATAFILE
MN_EMP  Minnaert function               DATAFILE
HAPHEN  Hapke - Henyey-Greenstein       WH,HG1,HG2,
                                        HH,B0,THETA
HAPLEG  Hapke - Legendre                WH,BH,CH,
                                        HH,BH,THETA
HAPH_S  Hapke - Henyey-Gr. smooth       WH,HG1,HG2
HAPL_S  Hapke - Legendre smooth         WH,BH,CH

The functions are defined as follows, where phase is
the phase angle, and u0 and u are the cosines of the
incidence and emission angles, respectively

Lambert
FUNC=u0

Lommel-Seeliger
FUNC=u0/(u0+u)

Minnaert
FUNC=u0**K * u**(K-1)

Lunar-Lambert ("lunar" part is Lommel-Seeliger)
FUNC=(1-L)*u0 + 2*L*u0/(u0+u)

Minnaert empirical
FUNC=B(phase) * u0**K(phase) * u**(K(phase)-1)

Lunar-Lambert empirical
FUNC=B(phase) * ((1-L)*u0 + 2*L*u0/(u0+u))

Used with the two empirical functions, the file
named in DATAFILE contains a table of triplets of
phase, B(phase), and K(phase) or L(phase).  These
values will be spline-interpolated to calculate B
and K or L at the needed phase angles.  The program
pho_emp_global can be used to calculate values of
B and K or L that will provide a fast approximation
to Hapke's model with any particular set of parameter
values.  See description of DATAFILE for formatting
of the file and examples and McEwen (1991) for the
original description of these fast approximate
photometric functions.

Hapke - Henyey-Greenstein
Complete Hapke (1981; 1984; 1986) photometric model
with Henyey-Greenstein single-particle phase function
whose coefficients are HG1 and HG2, plus single scattering
albedo WH, opposition surge parameters HH and B0, and
macroscopic roughness THETA.

Hapke - Legendre
Similar to the previous except that the single particle
phase function is a two-term Legendre polynomial with
coefficients BH and CH.

Hapke - Henyey-Greeenstein smooth
Substantially simplified version of Hapke-Henyey-Greenstein
function that omits the opposition effect as well as the
(very slow) macroscopic roughness correction.  For a smooth
model with opposition effect, use the full Hapke-Henyey
function with THETA=0.

Hapke - Legendre smooth
Simplified Hapke model with Legendre single particle phase
function, no opposition surge, and no roughness correction.

McEwen (1991) has compiled Hapke parameter estimates for
many planets and satellites from a variety of sources.

The following Hapke parameters for Mars are from Johnson
et al. (1999) for IMP data of Photometry Flats (soil)
and may be reasonably representative of Mars as a whole.
Note that (HG1, HG2=1.0) is equivalent to (-HG1, HG2=0.0)

Band    WH     B0     HH    HG1    HG2
Red    0.52  0.025  0.170  0.213  1.000
Green  0.29  0.290  0.170  0.190  1.000
Blue   0.16  0.995  0.170  0.145  1.000

Kirk et al. (2000) found that Mars whole-disk limb-darkening
data of Thorpe (1973) are consistent with THETA=30, but
results of Tanaka and Davis (1988) based on matching
photoclinometry of local areas to shadow data are more
consistent with THETA=20 when the domain of the fit is
restricted to small emission angles (=< 20 degrees).
K
Exponent that governs limb-darkening in the Minnaert
photometric function: FUNC=u0**K * u**(K-1). Values
generally fall in the range from 0.5 ("lunar-like",
almost no limb darkening) to 1.0 (Lambert function).
L
Weight that governs limb-darkening in the Lunar-Lambert
photometric function: FUNC=(1-L)*u0 + 2*L*u0/(u0+u).
Values generally fall in the range from 0 (Lambert
function) to 1 (Lommel-Seeliger or "lunar" function).
DATAFILE
User datfile from which photomet loads the photometric func-
tion parameters for the Minnaert empirical (MN_EMP) and
lunar-Lambert empirical (LL_EMP) functions, which use a table
to describe how the parameters of the empirical function
vary with phase angle.  Program pho_emp_global can be used
to calculate the parameter values that best approximate a
Hapke model with a given set of parameters.

The file may contain sets of values for both functions,
generally intended to represent the same Hapke model
(same planetary surface).  Here is an example for Mars.

##################################################
##  File: ~/$ISISDATA/photom.mars.sav           ##
##  Description: This file is  the Mars  lookup ##
##    file for  default  photometric correction ##
##    parameters for the photometric correction ##
##    program, "photomet".                      ##
##  Author: K. Teal Thompson                    ##
##  Data: Randy L Kirk                          ##
##  Date of Last Revision:  2003 Feb 11         ##
##################################################
##  Use # at the beginning of the line for      ##
##  comments.                                   ##
##  Use , to delineate the coefficient values.  ##
##  New line starts new parameter.              ##
##  formatting for coeffs: (f15.8)              ##
##  declaration for coeffs: real*8              ##
##  declaration for line: character*256         ##
##################################################
LUNAR_LAMBERT_EMP
# number of coefficients for Empirical Lunar Lambert L appro
ximation
  numllcoef=19
# the angles at which the coefficient values for Empirical L
unar Lambert L
# approximation are calculated (ALL ON ONE LINE!) Count shou
ld = numllcoef.
  llphase =0.,10.,20.,30.,40.,50.,60.,70.,80.,90.,100.,110.,
120.,130.,140.,150.,160.,170.,180.
#the values for Empirical Lunar Lambert L (ALL ON ONE LINE!)
  lval =0.946,0.748,0.616,0.522,0.435,0.350,0.266,0.187,0.11
8,0.062,0.018,-0.012,-0.027,-0.035,-0.036,-0.037,-0.031,-0.0
12,0.010
#number of coefficients for Empirical Lunar Lambert B approx
ximation
  numbeecoef=19
# the angles at which the coefficient values for Empirical L
unar Lambert B
# approximation are calculated (ALL ON ONE LINE!) Count shou
ld = numbeecoef.
  bphase=0.,10.,20.,30.,40.,50.,60.,70.,80.,90.,100.,110.,12
0.,130.,140.,150.,160.,170.,180.
#the values for Empirical Lunar Lambert B (ALL ON ONE LINE!)
  bval=1.000,1.010,0.987,0.940,0.882,0.819,0.756,0.697,0.639
,0.581,0.522,0.458,0.391,0.324,0.259,0.199,0.138,0.066,0.000
END
MINNAERT_EMP
  numkaycoef=10
  kayphase =0.,20.,40.,60.,80.,100.,120.,140.,160.,180.
  kval =
  numbeecoef=0
  bphase=
  bval=
END
(end of DATAFILE example)
WH
Single-scattering albedo of surface particles, used if
FUNC=HAPHEN, HAPLEG, HAPH_S, or HAPL_S.  See Hapke (1981).
Not to be confused with albedo WHA of the atmospheric
particles.
B0
Magnitude of the opposition effect for the surface, used
if FUNC=HAPHEN, HAPLEG, HAPH_S, or HAPL_S.  See Hapke (1984).
HH
Width parameter for the opposition effect for the surface,
used if FUNC=HAPHEN, HAPLEG, HAPH_S, or HAPL_S.  See Hapke
(1984).
THETA
"Macroscopic roughness" of the surface as it affects the
photometric behavior, used if FUNC=HAPHEN or HAPLEG.
This is the RMS slope at scales larger than the distance
photons penetrate the surface but smaller than a pixel.
See Hapke (1986).  The roughness correction, which will
be evaluated if THETA is given any value other than 0.0,
is extremely slow.
HG1
Asymmetry parameter used in the Henyey-Greenstein model
for the scattering phase function of single particles
in the surface, used if FUNC=HAPHEN or HAPH_S.  See Hapke
(1981).  The two-parameter Henyey-Greenstein function is
P(phase) = (1-HG2) * (1-HG1**2)/(1+HG1**2+2*HG1*COS(PHASE))**1.5
         +    HG2  * (1-HG1**2)/(1+HG1**2-2*HG1*COS(PHASE))**1.5
HG2
Second parameter of the two-parameter Henyey-Greenstein
model for the scattering phase function of single particles
in the surface, used if FUNC=HAPHEN or HAPH_S.  This
parameter controls a the proportions in a linear mixture
of ordinary Heneyey- Greenstein phase functions with
asymmetry parameters equal to +HG1 and -HG1.  See HG1 for
the full formula.
BH
When FUNC=HAPLEG or HAPL_S, a two-term Legendre polynomial
is used for the scattering phase function of single
particles in the surface
P(phase) = 1 + BH * P1(COS(PHASE)) + CH * P2(COS(PHASE))
BH is not to be confused with the Legendre coefficient BHA
of the phase function for atmospheric particles, used when
ATMOS=A1 or A2.
CH
When FUNC=HAPLEG or HAPL_S, a two-term Legendre polynomial
is used for the scattering phase function of single
particles in the surface
P(phase) = 1 + BH * P1(COS(PHASE)) + CH * P2(COS(PHASE))
ATMOS
Only used with GENMOD=ALBAT, or TOPAT, this parameter controls
the type of model used for atmospheric photometric correction.
I1, A1, H1 all use the first order scattering approximation,
whereas I2, A2, H2 use the second order approximation, and so
are slower but more accurate and are generally preferred.

Models I1 and I2 use Chandrasekhar's (1960) solution for
isotropic scattering.  They require only the parameters TAU,
WHA, and HNORM, plus the corresponding values at the reference
condition that the image will be normalized to, TAUREF and
WHAREF.

Models A1 and A2 use Chandrasekhar's solution for anisotropic
scattering described by a one-term Legendre polynomial.  The
coefficient of this term BHA and the value for the reference
condition BHAREF are required in addition to the parameters
also used by the anisotropic models.  The anisotropy of the
Legendre function is fairly weak so the Hapke models are
preferred as a description of the martian atmosphere.

Models H1 and H2 are an approximation for strongly anisotropic
scattering that is similar in spirit to Hapke's model for a
planetary surface.  The Chandrasekhar solution for isotropic
scattering is used for the multiple-scattering terms, and a
correction is made to the singly-scattered light for anisotropic
particle phase function.  In particular, a one-term Henyey-
Greenstein function with parameter HGA (and HGAREF in the
reference condition the image is normalized to) is used.  The
parameters used by the isotropic models are also required.
See Kirk et al. (2001).

Values of the photometric parameters for Mars, adopted from
Tomasko et al. (1999) are:

Band    WHA     HGA
Red    0.95     0.68
Blue   0.76     0.78
WHA
Single-scattering albedo of atmospheric particles, used in
all atmospheric models.  Not to be confused with albedo WH
of the surface particles.
BHA
Coefficient of P1 (cosine) term of atmospheric particle phase
function, used in A1 and A2 atmosphere models.  Not to be
confused with corresponding coefficient BH for the surface
particles.
HGA
Henyey-Greenestein asymmetry parameter for atmospheric particle
phase function, used in H1 and H2 atmosphere models.  Not to be
confused with corresponding parameter HG1 for the surface
particles.
HNORM
Atmospheric shell thickness normalized to planet radius,
used to modify angles to get more accurate path lengths near
the terminator.  (Ratio of scale height to the planetary
radius).

Last updated: Jan 31 2005
File: pdfs2.html

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