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Modelling surface temperatures on Mars



 
 
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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,
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) * (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) =
sin(dec)sin(lat))

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