Modelling surface temperatures on Mars
I am trying to model surface temperatures on Mars.
Coming up with insolation received at the various latitudes was fairly
simple, the equations are found at the bottom.
Assuming a known rate of insolation at each latitude from the
equations below, and a known albedo and thermal inertia for each
location on the surface. How would one find the surface temperature
for a location on the planet? I have thought of using the
StefanBoltzmann law, but I don't know how to account for the thermal
inertia of the surface. I am willing to discount the greenhouse effect
for now and assume a transparent atmosphere, but eventually the model
will increase in complexity.
If anyone has any insight please post here or email me,
rpavlick3[NO*SPAM]yahoo.com.
Thanks,
Ryan
Insolation Equations
____________________
The sun has an energy flux, Lo, applying the the inverse square law,
the flux density at Mars would be:
flux density at Mars = solar flux * (pi/4) * (sunMars distance)^2.
The sunMars distance being:
distance = (semimajor axis)(1  eccentricity^2) / (1 + eccentricity
cosine [solar longitude  longitude of perihelion])
Now the irradiance for a time of year and latitude can be found:
irradiance = flux density * cosine(zenith angle),
cozine(zenith angle) = sin(declination)sin(lat) +
cos(lat)cos(dec)cos(hour angle).
The solar declination is a function of solar longitude and the axial
tilt of the Mars,
sin(declination) = sin(obliquity)sin(solar longitude).
This can integrated to find:
daily insolation = (flux density/pi)(cos(dec)cos(lat)sin(H) =
sin(dec)sin(lat))
H = half day length = tan(dec)* tan(lat)
