Mars Climate Code Introduction with Block Diagram and Pseudocode

Modeling Solar Heating

The sun is the source of energy for all planets in our solar system. Its radiation provides the heating of the planet and the energy necessary for the formation of the food chain of our Earth. Mars suffers from its location being further from the Sun. It also suffers from an eccentricity of orbit that causes variations that life here on Earth would have difficulty in adjusting.

The heating of a planet is, as has been alluded to in previous sections here, related to the albedo of the planet, i.e. the reflectance of that energy back into space. Mars has a varied surface, and albedoes that range from 0.34 for the brightlands and 0.17 for the darklands. The polar caps present an albedo of approximately 0.45 [Abell, 1978]. The sun has been monitored and its radiation (integrated over the spectrum) is well known. Also well known is the fact that the solar radiation is by no means a true constant.

The solar radiation not only varies over its 11 year sunspot cycle, but also presents variations even to a daily cycle and yearly cycle. We really are unsure how much solar radiation has varied over the period of the existence of the planets.

Modeling Thermal Radiation

Mars, like the Earth, re-radiates some of the solar energy it sees as thermal radiation out to space. The thermal radiation from Mars arises mostly from its surface, since its atmosphere is so much finer than our own planet's atmosphere, which does have a more significant role in the re-radiation of the solar energy [Abell, 1978].

The Martian atmosphere emits weakly under unobscured surface conditions. When dust stjorms are present, the atmosphere absorbs sunlight directly and also radiates more effectively. The effect of increasing dust in the atmosphere is to reduce diurnal temperature variation at the surface. On the other hand, the dust enhances atmospheric thermal variation [Abell, 1978].

Other components causing thermal radiation from the surface of Mars is the dissipation of mechanical energy of winds, of wind waves, atmospheric tides and the energy transferred by the precipitation of carbon dioxide and possibly water, at least at the poles.

The Computer Model

Overview of Program

The current Mars climate program was based upon a previous program written by Harold Geller for Physics 590 (Atmospheric Physics) applied to the Earth. It consists of a MAIN.FOR program that first has an include statement for the purposes of using the PLOT.FOR routine provided by Liam Gumley (this is to be expunged for use on this effort), a former colleague of Harold's at Goddard Space Flight Center. Variables are then declared, as is typical. Next, the values of the Martian specific parameters to be used (defined in the comments section) are set to their respective values for program use. Next, the program initializes certain parameters for the display subroutine.

The program then queries the user for a sun/mars angle from which it can determine a distance parameter. This one distance parameter will be used as the Martian distance for all following calculations within the program. The user is next presented with a menu from which he can choose the desired display and calculations.

The seven choices that were developed are as follows (some of these will be expunged for this effort):

    1) Display the physical characteristics [originally Earth's now Mars]
    2) Display the current Earth temperature profile [to be expunged]
    3) Display the current Mars temperature profile
    4) Display the Earth temps over 5 b.y. for 30% case [to be expunged]
    5) Display the Mars temps over 5 b.y. for 30% case 
    6) Display the Earth temps over 5 b.y. for 70% case [to be expunged]
    7) Display the Mars temps over 5 b.y. for 70% case [to be combined with #5]
Selection 1 now simply displays the Martian parameters which are used in some of the calculations in the program. These include the diameter, radius, density, length of a Martian day, obliquity, eccentricity, solar orbit period, scale height, albedo, and semi-major axis.

Selection 2 calls a sub-routine which is the original program used in the homework problem defined by Professor Summers for Physics 590 in 1991. This selection will be deleted.

Selection 3, using the same assumptions for Mars as was used in the development of the homework model for Earth, displays the current temperature profile of Mars versus latittude based upon the model results. The user should be aware that the Sun/Mars orbital ellipse angle entered in the beginning of the program, determines the distance used in this routine before it is used to display a temperature profile.

Selection 4 calls a sub-routine, which is the converted program used in the old homework problem with a major exception. The homework problem assumed that the solar radiation was greater now by 30% than at a time some 5 billion years ago. This sub-routine was written with the assumption that the solar radiation was actually 30% greater at the formation of the planet than it is now (which is not in line with current theories of stellar evolution). Furthermore, in the original homework assignment, it was unclear how to allow the ice/snow line to be determined. For this subroutine I calculate the temperature at the equator using the land/ocean mean albedo for no ice/snow present, and keep the albedo at that value until the temperature is noted as falling below a value which would have ice form (water ice on Earth, solid CO2 on Mars).

Selection 5, once again using the same modeling assumptions from the original homework assignment, develops a of curves depicting the surface temperature of Mars over the 5 billion years of its existence. This selection assumes that the solar radiation was 30% greater at the formation than it is now and the distance used is based on the user entry for the Sun/Mars orbit angle. Also, in the original problem, I used the -10 degree Celsius value as the demarcation for ice/snow on Earth. For Mars I taken into consideration that the polar caps consist mostly of carbon dioxide so I used the break point of -78.5 degrees Celsius, taken from the Handbook of Chemistry and Physics as the value that carbon dioxide melts.

Selection 6 calls a sub-routine, which is the converted program used in the original homework problem, again with the difference being that it was modified to assume that the solar radiation at the start of its lifetime was 70% greater than it is now. This selection will be expunged from the code.

Selection 7, once again using the same modeling assumptions from the original homework assignment, displays a series of curves depicting the surface temperature over the 5 billion years of its existence. This selection differs from Selection 5 in that the solar radiation is assumed to have been 70% greater at the time of formation. Again, the value for the setting of the snow/ice line was -78.5 degrees Celsius, as noted for Selection 5, above.

Additional Considerations

The orbital eccentricity of the planet Mars itself is a major factor in Martian temperature changes on the planet's surface.

Other considerations in the variability of the temperature on the surface of Mars includes the obliquity. Polaris has not always been the north polar star. Our own planet has wobbled over a period of approximately 22,500 years, and seen the axis point in different directions.

William Ward, 1973, studied the variability of the Martian obliquity and discovered two periodicities that would of course contribute to the variability of the Martian surface temperature. One of these periodicities occurs over a time of about 120,000 Earth years and the other occurs at a period of about 1.2 million Earth years. Although the investigator did not include temperature predictions in his discussion of these orbital perturbations, the effects on the temperature curves would be significant in the time-dependent views.

Besides the long-term shifts in the obliquity, there has been a shift in the Martian elliptic orbit known as the precession of the perihelion. Einstein's General Theory of Relativity was used to explain the precession of the orbit of Mercury, which is only 43 arc seconds per century. The effects are dependent on the orbital eccentriciy and the closeness to the sun. In the case of Mercury, the orbital eccentricity is 0.206 or about 2.2 times the eccentricity of Mars [Abell, 1978]. Nonetheless, the precession of the perihelion of Mars is a real consideration when viewing the scenario in time of billions of years.

The computer model used in this investigation does not currently take into account the transmission coefficient of the atmosphere. Gerard De Vaucouleurs investigated the theoretical surface temperature of Mars and produced plots that would be useful as a matter of comparison to the results of this model as well as an example of the influence of the thickness of the atmosphere on the temperature profile from any model. These theoretical results should be compared with those obtained from Viking data [Kaplan, 1988]. One must also keep in mind, that if one truly desires to model the situation on Mars back to some 5 billion years ago, one would have a thicker atmosphere to contend with at that time.

Another aspect that theoreticians have examined is the temperature and pressure relationships to the major constituent of the atmosphere, namely carbon dioxide. In 1966, Leighton and Murray proposed that carbon dioxide, being the major component of the polar caps, determined the atmospheric pressure by the vapor pressure over the caps.

According to this theory, the amount of atmosphere is a function of polar temperature. This is due to the nature of the carbon dioxide vapor pressure curve. An explanation of this theory was a part of the doctoral thesis of Owen Toon in 1976 [Toon, 1976]. In essence, there would be a raising of the overall atmospheric mass if the temperature at a pole increases somewhat, and we have demonstrated that is the case just caused by the eccentricity of orbit. An increase to the atmospheric mass causes the atmospheric contribution to the polar heat balance to become important.

Also of interest to the temperature situation on Mars is the contribution of ozone heating in the Martian atmosphere. This is discussed in the recent literature [Lindner, 1991 and Esperak et al, 1991]. Lindner comes to the conclusion that ozone is a "minor, although nonnegligible, heat source in the martian atmosphere." He notes that there is an observed hemispherical asymmetry in ozone abundance, which he believes not to be a significant factor in the observed hemispherical asymmetry of the polar caps.

Espenak et al present ground-based infrared measurements of the global distribution of ozone in the martian atmosphere which is significantly lower than the only other measurements made of ozone on Mars, that by Mariner 7. The spacecraft reported some 20 times the amount of ozone over the south polar cap as is now reported by the ground-based measurements. The question to pose is whether this ozone reduction is a remnant of a mechanism on Mars which is similar to the south pole reduction on Earth?

Block Diagram of the Mars Climate Code

The following is a conceptual block diagram consisting of components alluded to in the discussion above regarding the Mars climate model for the Team #3 term project:

                 ------------------
                 |     Input      |
                 |    Mars/Sun    |
                 |     Angle      |
                 ------------------
                         |
                         |
                 -------------------
                 |    Calculate    |
                 |  Solar Energy   |
                 |     at Mars     |
                 -------------------
                         |
                         |
                         |
                 -------------------
                 |   Select Menu   |
                 |      Choice     |
                 -------------------
                         |
                         |
           ---------------------------------------------------
           |                     |                           |
           |                     |                           |
  -----------------      -----------------          -------------------
  |  Choose to    |      |  Choose to    |          |     Choose to   |
  |   Calculate   |      |  Calculate    |          |     Calculate   |
  |      all      |      |  Temperature  |          |    Temperature  |
  |   Parameters  |      |  and          |          |   and Pressure  |
  |  and Display  |      |  Pressure on  |          |    on Mars for  |
  |  Them to User |      |  Mars for the |          |   the Past Five |
  -----------------      |  Present Day  |          |   Billion Years |
          |              -----------------          -------------------
          |                      |                           |
          |                      |                           |
  -----------------      -----------------          -------------------
  |  Calculate    |      |  Calculate    |          |     Calculate   |
  | All Parameters|      | Solar Energy  |          |   Solar Energy  |
  | and Disply    |      | Arriving at   |          |   Arriving at   |
  |   to User     |      |     Mars      |          |       Mars      |
  -----------------      -----------------          -------------------
          |                      |                           |
          |                      |                           |
  -----------------      -----------------          -------------------
  |   Return to   |      |   Derive      |          |      Derive     |
  |  Main Menu    |      |  Temperature  |          |    Temperature  |
  -----------------      |  Using Solar  |          |   Using Solar   |
                         |  Constant and |          |    Constant and |<----+
                         |  Distance and |          |   Distance and  |     |
                         |  Newton's Law |          |   Newton's Law  |     |
                         |  of Cooling   |          |   of Cooling    |     |
                         -----------------          -------------------     |
                                 |                           |              |
                                 |                           |              |
                         ------------------          -------------------    |
                         |   Derive       |          |      Derive     |    |
                         | Pressure From  |          |   Pressure From |    |
                         |  Temperature   |          |    Temperature  |    |
                         |    and CO2     |          |    and CO2      |    |
                         | Vapor Pressure |          |  Vapor Pressure |    |
                         |   References   |          |    References   |    |
                         ------------------          -------------------    |
                                 |                           |              |
                                 |                           |              |
                         ------------------          -------------------    |
                         |   Pass to      |          |     Pass to     |    |
                         |  Atmosphere    |          |    Atmosphere   |    |
                         |    Module      |          |      Module     |    |
                         ------------------          -------------------    |
                                 |                           |              |
                                 |                           |              |
                         -------------------          -------------------   |
                         |   Calculate     |          |    Calculate    |   |
                         | New Temperature |          | New Temperature |   |
                         |  for Air Mass   |          |  for Air Mass   |   |
                         |   based upon    |          |   based upon    |   |
                         |  interactions   |          |  interactions   |   |
                         | with other air  |          | with other air  |   |
                         |  masses nearby  |          |   masses nearby |   |
                         -------------------          -------------------   |
                                 |                           |              |
                                 |                           |              |
                         -------------------          -------------------   |
                         |    Pass New     |          |   Pass New      |   |
                         |  Temperatures   |          |   Temperatures  |   |
                         |  of air masses  |          |  of air masses  |   |
                         |   to files      |          |   to files      |   |
                         |   for use in    |          |   for use in    |   |
                         | life simulation |          | life simulation |   |
                         -------------------          -------------------   |
                                 |                           |              |
                                 |                           |              |
                         ------------------          -------------------    |
                         |  Return to     |          |     Calculate   |    |
                         | Main Menu for  |          |   Solar Energy  |    |
                         |  Further       |          |    Output for   |----+
                         |  Instructions  |          |     Previous    |
                         ------------------          |  Billion Years  |
                                                     -------------------

Pseudocode of the Mars Climate Code

The pseudocode for the Mars climate code is presented as follows (note that this is being modified and will not be identical to the final implementation):

read_user_input of solar_mars angle

calculate_solar_energy
  use_distance
  use_solar_constant
  use_angle_of_sun

display_menu
 get_user_choice

if user_choice = display_parameters
  calculate physical_parameters
    display mars_distance
    display mars_ellipse_angle
    display mars_day
    display mars_year
    display mars_diameter
  endif

if user_choice = display_mars_present_climate
  calculate physical_parameters
  calculate mars_temperature
  send mars_temperature to atmosphere_function
  return mars_temperature_over_latitude
  send mars_temperature_over_latitude to life_simulation
 endif

if user_choice = display_mars_climate_past

  until past_age is five_billion_years_ago
   calculate physical_parameters
   calculate mars_temperature
   send mars_temperature to atmosphere_function
   return mars_temperature_over_latitude
   send mars_temperature_over_latitude to life_simulation
   decrement past_age
   calculate solar_constant
   return

  endif

if user_choice = no_more_output_desired
  exit program


REFERENCES

Abell,G.O. Drama of the Universe (Holt, Rinehart and
     Winston, San Francisco, 1978).
Espenak, F. et al Icarus 92, 252-263 (1991).
de Vaucouleurs, G. Physics of the Planet Mars (Faber and
     Faber Limited, London, 1954).
Kaplan, D. Environment of Mars (NASA Technical
     Memorandum 100470, Washington, D.C., 1988).
Leighton, R.B. and Murray, B.C. Science 153, 134-144
     (1966).
Lindner, B.L. Icarus 93, 354-361 (1991).
Toon, O. Climatic Change on the Earth and Mars
     (University Microfilms International, Ann Arbor, 1976).
Ward, W.R. Science 181, 260-262 (1973).