SCALE HEIGHTS AND MARS PRESSURE TRANSDUCER ERRORS
Scale Heights Are Key to Solving the Mystery of Mars (Updated 8/18/2016)
Atmospheric pressure decreases exponentially with altitude. In determining pressure for Earth, the formula for scale height is:
p = p0e-(h/h0)
where p = atmospheric pressure (measured in bars on Earth)
h = height (altitude)
P0 = pressure at height h = 0 (surface pressure)
H0 = scale height.
This page explores two published Martian scale heights: 10.8 and 11.1. It looks at what is expected to happen to pressure at various heights and depths (above and below what would correspond to mean sea level, or better phrased, the average elevation on Mars which is known as the mean areoid). The first two tables are based on a pressure of 6.1 mbar at the areoid. The next two tables assume that the Mars Pathfinder Tavis pressure transducer was functioning properly, and then extrapolate pressures from there at a depth of 3,682 meters below the mean areoid, back up to the mean areoid, and then on to all other indicated heights and depths. The last table is based on a 7.5 mbar pressure average often attributed to Dr. Robert Zubrin, using a 10.8 scale height. While the formula given above lists p as atmospheric pressure (measured in bars on Earth), the equivalent values for the Martian calculations are based on pressures there at the Mean Areoid. See column G of the spreadsheets. For an average pressure of 6.1 mbar, the Mars bar equivalent would be 6.1 mbar at mean areoid.
MARS AREOID DEFINITION: Geology.Com defines the Mars areoid as representing an equipotential surface of the Goddard Mars Gravity Model. The Mars areoid is an imaginary sphere with a center that coincides with the center of Mars and a radius of 3,396,000 meters. We can think of it as a reference elevation, similar to the zero elevation on Earth being mean sea level. (The radius used for the Mars areoid is very close to the average radius of Mars along its equator. That value is 3,396,196 meters.)
Of note on Table 1 are the pressures actually recorded just before and after dust devils passed or went over the Phoenix and Mars Pathfinder (MPF) landers. Note that based on a mean pressure of 6.1 mbar for Mars at the areoid, at the lower altitude Phoenix, (4,126 meters below mean areoid) we would have expected a pressure of about 8.938. The pressure recorded at the Phoenix site for its Sol 13 Event was about 8.425 mbar before dust devil passage, but it only dropped to 8.422 mbar at passage. Still, both values are close to what was expected in accordance with Table 1 (94.3% agreement). However, at the Pathfinder site (3,682 meters below mean areoid), the expected pressure was about 8.578 mbar, but the observed pressures were about 6.735 mbar before passage, and 6.7 mbar at passage. This is only around a 78.5% agreement for the MPF Sol 25 Event.
Above: Table 1 based on a scale height of 10.8 and an average pressure of 6.1 mbar at mean areoid. Below: Table 2 based on a scale height of 11.1 and an average pressure of 6.1 mbar at mean areoid.
On Table 2 pressures calculation are similar to those on Table 1, except that here a scale height of 11.1 was employed (not 10.8, as was used on Table 1). Based on a mean pressure of 6.1 mbar for Mars at the areoid, at the lower altitude Phoenix, (4,126 meters below mean areoid) we would have expected a pressure of about 8.846. The pressure recorded at the Phoenix site for its Sol 13 Event was about 8.425 mbar before dust devil passage, but it only dropped to 8.422 mbar at passage. So here the agreement was 95.2%. At the Pathfinder site (3,682 meters below mean areoid), the expected pressure was about 8.499 mbar, but the observed pressures were about 6.735 mbar before passage, and 6.7 mbar at passage. This is only around a 79.2% agreement for the MPF Sol 25 Event.
Table 3 below: An assumption was made that the Mars Pathfinder Tavis Pressure Transducer worked properly. All other pressures were derived from the MPF value using a scale height of 10.8.
Table 4 below: An assumption was made that the Mars Pathfinder Tavis Pressure Transducer worked properly. All other pressures were derived from the MPF value using a scale height of 11.1.
Figures 1 and 2 are adapted from graphs produced by Nelli et al. (2009).33 Their graphs included projections made from a General Circulation Model (GCM) with values hypothesized for 3 am, 9 am, 3 pm and 9 pm local time at Phoenix. We added Ls and data about day length for clarity. Phoenix landed in the Martian arctic in late spring. There was no sunset until Ls 121.1 on its 96th sol on September 1, 2008. By the time the mission ended there were about 16.7 hours of sun light each day.
The pressure data appears to be sol averaged, while the temperatures are not. But what kind of pressure drop would be expected if the average temperature dropped from 195K to 180 K, with a starting pressure of 8.5 mbar? The answer is about 7.85 mbar. The actual pressure at the end of the series shown on the graph is about 7.4 mbar, which is better than a 94% match with the prediction based on Gay-Lussac’s Law and a clogged pressure tube. However, when Phoenix landed on Mars on May 25, 2008, it was not yet summer. The summer solstice occurred on June 24, 2008. By that time there was no change in the temperatures evident on Figure 1, but pressure was running about 8.2 mbar. Using the same temperatures as above with an entering argument of 8.2 mbar the projected pressure would be 7.57 mbar. That is an agreement of 97.78%.
Unlike pressure calculations based on an inverse of normal temperature and pressure relationships that factor in RTG heat becoming available to Viking transducers, on Phoenix there was no RTG. If there was no heater, pressures would be expected to fall directly with the fall in ambient pressures. This happened, but there were indeed four heaters that were turned off just before the lander died.109 The third one operated the Surface Stereo Imager – and the meteorological suite of instruments. It was thought that electronics that operate the meteorological instruments should generate enough heat on their own to keep most of those instruments and the camera functioning. This sounds like there was no need to pump heat into the pressure transducer. If so, there may indeed have been slow cooling of the air trapped behind the clogged dust filter, with no timed heat pumps to cause pressure spikes seen with the Vikings and MSL.
There was nothing to keep Phoenix alive once it got too cold. Its death supposedly came when ice built up on and broke the solar arrays.110
References from our Basic Report:
33. Nelli, S.M., Renno, N. O., Feldman, W. C., Murphy, J. R., & Kahre, M. A.Reproducing Meteorological Observations at the Mars Phoenix Lander Site Using the NASA Ames GCM V.2.1, Lunar Planetary Science, XL, Abstract, Lunar Planet. Sci.,1732.pdf http://www.lpi.usra.edu/meetings/lpsc2009/pdf/1732.pdf
109. Dunbar, Brian. "NASA's Phoenix Mission Faces Survival Challenges." NASA. NASA, 28 Oct. 2008. Web. 10 Feb. 2015. http://www.nasa.gov/mission_pages/phoenix/news/phoenix-20081028.html
110. Dunbar, Brian. NASA. NASA, n.d. Web. 10 Feb. 2015. “Phoenix Mars Lander is Silent, New Image Shows Damage” http://www.nasa.gov/mission_pages/phoenix/news/phx20100524.html#.VNpJky6LWlI