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 assumptions 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 photoclinometry 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

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 programphoempglobalcan 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).

File containing table of parameter values vs. phase for LL_EMP, MN_EMP. User datfile from which photomet loads the photometric function 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. LUNAR_LAMBERT_EMP #number of coefficients for Empirical Lunar Lambert L #approximation numllcoef=19 #the angles at which the coefficient values for Empirical Lunar #Lambert Lare calculated Count should = numbllcoef llphase =0.,10.,20.,30.,40.,50.,60.,70.,80.,90.,100.,110., 120.,130.,140.,150.,160.,170.,180. #values for Empirical Lunar Lambert 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 approximation numbeecoef=19 #the angles at which the coefficient values for Empirical Lunar #Lambert B approximation are calculated Count should = 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 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 MINNAERT_EMP numkaycoef=10 kayphase =0.,20.,40.,60.,80.,100.,120.,140.,160.,180. kval = numbeecoef=0 bphase= bval=

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