                    ---------------------------------
                      HERMES: Model Map of Mercury
                    ---------------------------------
                    D.L. Mitchell  11 March 1991  UCB


	HERMES models the diurnal temperature variations in the subsurface
layers of Mercury.  For each element of a Hermographic longitude-latitude grid,
HERMES solves for the physical temperature of the crust as a function of depth
and time during the course of a Hermean solar day.  Next, the radiative
transfer equation is integrated and Fresnel coefficients are applied at the
crust-vacuum interface to obtain the brightness temperature of each element
as seen from Earth.  Finally, the Hermographic grid is converted to a
geocentric RA-Dec grid via coordinate rotations and a pixel image is generated
for use with the MIRIAD software. 

	The calculation of the physical temperature structure is controlled by
an input file called 'hermes.in' (the format of this input file is very
specific -- see example at end).  By editing this file, one can change the
position of Mercury in its orbit, the viewing geometry, and the observing
wavelength to handle any situation.  It is also possible to vary the physical
parameters of the crust: thermal inertia, electrical and thermal skin depths,
Bond albedo, infrared emissivity, and refractive index, in order to cover the
spectrum from a fine powder to solid rock.  The model includes temperature
dependent thermal conductivity and heat capacity -- the amount of radiative
heat conduction is adjustable, corresponding to varying degrees of porosity.
Finally, a constant heat flux may be included at the base of the thermal wave
to account for heat generated from core-mantle differentiation and radioactive
decay. 

	The depth and time resolution are adjustable up to 50 depth steps and
1000 time steps, which is more than sufficient to handle the most extreme
physical parameters.  The maximum resolutions in Hermographic longitude and
latitude are 3.6 and 9 degrees, respectively.  Generally, higher longitude
resolution is needed for short wavelength observations, which are sensitive to
the large day-night temperature contrast near the surface.  For example, a
resolution of about 6 degrees is adequate to model resolved 3mm observations. 

	HERMES creates two output files.  A log file ('hermes.log') contains 
a record of the input parameters and diagnostics of the numerical solution.  
The interpretation of

   CRANKN: cerr[ 6.5] =  -0.080    ferr[ 8.1] =   0.187    rerr =   0.004

is as follows:  subroutine CRANKN reports that the maximum convergence error
in the physical temperature structure is -0.080 K and occurs at a depth of 6.5
thermal skin depths.  "Convergence" is defined to be how well the solution
repeats from (Hermean solar) day to day.  The maximum deviation from thermal
equilibrium (i.e. constant net heat flux) is 0.187 K and occurs at a depth of
8.1 thermal skin depths.  Note that ferr > cerr in this case.  After only a few
solar days of calculation, the convergence accuracy is usually better than the
thermal equilibrium accuracy.  The best estimate of the "modeling error" is the
larger of cerr and ferr.  Finally, the imbalance between insolation and re-
radiation, averaged over a solar day at the surface, is 0.004 K.  One should
keep rerr as small as possible by adjusting the depth and time grid spacings. 

The interpretation of

	RADIATE: lon = 12.00  lat = 24.00   Tb = 412.31

is as follows:  subroutine RADIATE reports that the brightness temperature
(not including Fresnel limb darkening) at 12.00 degrees longitude and 24.00
degrees latitude (Hermographic coordinates) is 412.31 K, as seen from Earth.  
If Tb = 0, then the element is not visible from Earth.  There are four calls to 
RADIATE for each call to CRANKN due to north-south and mirror symmetries in the 
insolation pattern.

	The second output file is the pixel image which can be convolved with
an arbitrary beam for comparison with a BIMA image.  One can also Fourier
transform the model image to compare directly with visibility data.

	For additional information about the physics involved, the numerical
solution, and a general idea of how the thermal parameters vary with surface
composition, see "Thermal Microwave Emission from Mercury".

	The input file 'hermes.in' should look like this (the first line of
the file should start with 'Geometry ...'):

Geometry (18 May 1991):
------------------------------------------------------------------------------
229.13        | longitude of sub-earth point  (degrees)
1.11          | latitude  "      "       "    (degrees)
333.16        | position angle of N-pole  (degrees E from N)
3.685         | radius of Mercury's disk  (arc seconds)
319.16        | longitude of sub-solar point  (degrees)
20.04         | approximate time  (Mercury Hours)  exact if time < 0
------------------------------------------------------------------------------

Physical Parameters:
------------------------------------------------------------------------------
0.119         | bolometric (Bond) albedo  0.119
0.90          | infrared surface emissivity  0.90
0.0020        | thermal inertia (cal-cgs units @ 350K)  0.0020
1.0           | ratio of radiative to contact conductivity @ 350K
-60.0         | heat flux at base of thermal wave (cgs)  -60.0
1.80          | dielectric constant (real part)
0.8           | ratio of electrical to thermal skin depth (@ 350K)
89.21382      | observing frequency (GHz)
------------------------------------------------------------------------------

Grid Parameters:
------------------------------------------------------------------------------
15.0          | maximum depth (thermal skin depths)  15.0
1.11          | depth increment multiplier  1.11
30            | number of depth steps (max 50)  30
800           | number "  time    "   (max 1000)  800
25            | number of Hermographic longitude elements (max 50)  25
16            | number "       "       latitude     "     (max 20)  16
0.15          | cell size for 64 X 64 geocentric map  (arc seconds)
12            | maximum heat bomb iteration  in CRANKN  12
12            | maximum number of iterations in CRANKN  12
0.2           | maximum error in the temperature structure (K)  0.2 to 0.5
------------------------------------------------------------------------------
