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Old February 4th 04, 12:27 AM
Ryan Pavlick
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Default 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
Stefan-Boltzmann 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,


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) * (sun-Mars distance)^2.

The sun-Mars distance being:

distance = (semi-major 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) =

H = half day length = -tan(dec)* -tan(lat)