A Numerical Model for Mars Atmosphere

The following numerical model, to be applied to the atmospheric model of Mars for use in the kinetic simulation of cellular life, is based on Coffin's [1] adaptation of Leith's [2] model. In this approach, surface temperatures are treated as variable quantities which are determined by the energy balance of the surface of Mars. Leith developed a two-dimensional zonal model. In 1967, a three dimensional model was considered out of reach for the computers at that time [1].

Coffin uses other models as comparisons. These include another Leith [3] model, one by Leighton and Murray [4] and one by Leovy [5]. Attempts are being made to obtain these references for comparisons to this group's effort. The Leighton and Murray model ignores most of the atmospheric effects and would be similar if this group's original simplistic approach were taken. We may use this as another comparison for the group's final output related to the surface condition on Mars at the expected time of the formation of the lifeforms that developed at the point of impact, causing the ALH sample to leave Mars.

Leovy simulates a diurnal variation of the surface using a one-dimensioanal calculation with a two-level atmospheric model. This model takes into account the Mars radiation budget with a little convection and some conduction.

Leith [2] defines an operator D/Dt as follows:

          D  =  d   +   u *    1       d    +  v * 1   d     w *  d
          -     -          ---------   -           - * -   +      --
          Dt    dt          a cos @    dg          a   d@         dp

This is used in the following horizontal momentum equations:

 
          Du   ( 2*W*sin @ + u tan @ ) * v =        1        d& 
          -- - (             --------)       -  ---------- * --  +  F(l)
          Dt   (                a    )           a cos @     dl


          Dv   ( 2*W*sin @ + u tan @ ) * u =    1   d& 
          -- - (             --------)       -  - * --  +  F(@)
          Dt   (                a    )          a   d@

Leith uses an energy fluctuation representation as follows:

          D@      1     ( P(0)) ^ g-1/g   dq
          -- =  ----  * -------         * --
          Dt    c(p)       P              dt

The hydrostatic equation is used for the vertical momentum equation:


                      dp
          gdz = - RT  --
                       p


Leith [2] considers the heat energy, dq/dt, with the components of solar radiation, long wave radiation, condensation and evaporation of CO2 and eddy diffusion as the means of convective transport. This provides a time rate of change of temperature at a geographical point.

Coffin [1] used a zonal model which "neglects" all terms involving derivatives in the same latitudinal direction.

Leith used a finite difference mesh with defined pressure levels of 0.1, 0.2, 0.4, 0.6, 0.8 and 1.0 of the mean surface pressure. There were 37 latitude values used from equator to either pole.

Leith defined boundary conditions for the vertical velocity and temperature. The vertical velocity was defined as W = Dp/Dt, with W=0 at p=0 and W(surface) = DP/Dt(surface). Temperature constraints were linked to the partial pressure of CO2.


REFERENCES

[1] Coffin, M.D., 1967. A Numerical Investigation of the Energy Balance of the Planet Mars, Ph.D. Dissertation.

[2] Leith, C.E., 1965. Numerical Simulation of the Earth's Atmosphere, Methods in Computational Physics, Vol. 4, Academic Press, New York.

[3] Leith, C.E., 1965. Convection in a Six-level Model Atmosphere, Lawrence Livermore Laboratory, California, UCRL 12415-T.

[4] Leighton, R.B. and B.C. Murray, 1966. Behavior of Carbon Dioxide and other Volatiles on Mars, Science, Vol.153, 136-144.

[5] Leovy, C., 1965. Note on Thermal Properties of Mars, The RAND Corporation, RM-4551-NASA.