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CHAPTER 4
North Data Set 36 TABLE 4.1
Northern Data Set Results
Wavelength 2cm 6cm
Whole Disk Dielectric Constant 2.34
±
.05 2.70±
.09 Whole Disk Sub-surface Density (g cm-3Ja
1.24±
0.06±
0.16 1.45±
0.10±
0.18 Whole Disk Brightness Temperature 193.2K±
l.Ob 191.2K±
0.6bNormalized Brightness Temperaturec 189.0K ± l.Ob 187.1K ± 0.6b 1.85cm Bright. Temp., Klein (1971Y 187K ± 12 -
2.7cm Bright. Temp., Mayer et al. (1971)c 185K ± 12 - 2.8cm Bright. Temp., Andrew et al. (1977)c 194.3K ± 3.6d - 2.8cm Bright. Temp., Doherty et al. (1979)c 195.2K ± 2.7d -
6cm Bright. Temp., Kellerman (1971)c - 196K ± 27
North Polar Cold Region Bright. Temp. 125.9K ± 2.0b 150.1K ± 2.0b North Polar Cold Region Extent 69.7° ± 0.3 66.2° ± 0.6
North Polar Cap Extent, James (1982) 70.8°
North Polar Cap Extent, Iwasaki (1984) 67.4°
aThe first error is the least squares error and the second error is due to the scatter in dielectric constants for powders of varying origins. (c. f. Campbell and Ulrichs, 1969)
bThese are formal errors only and estimates of the absolute calibration errors are ±5°at 6cm and ±7°at 2cm.
cThese temperatures have been normalized to a solar distance of 1.524AU using an R0·25 power law for comparison purposes.
dThese measurements were published as functions of longitude and the error shown here is actually the variation over longitude.
workers, giving us confidence that the calibration is good. Much of the discrepancy that is present can be attributed to the fact that different observations were taken at different seasons, different sub-earth time of day, and at different wavelengths. Few other workers have published estimates of the whole-disk dielectric constant. This is because the polarized signal is much harder to measure accurately. Because the VLA has so many baselines, the signal-to-noise inherent in this measurement can be increased. The accuracy with which the model whole-disk brightness temperatures (estimated from the thermal modeling using the fitted whole-disk dielectric constants) agree with the actual whole-disk brightness temperatures will play a crucial role in
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the next chapter.
4.2 North Polar Cold Region
The results of the North Polar Cold Region fitting are also listed in Table 4.1, along with some estimates of the extent of the North Polar Cap at this season as measured by other observers. Note the strong agreement between the latitude of the edge of the North Polar Cap and the estimated edge of the North Polar Cold Region.
The brightness temperature of the North Polar Cold Region differs between the two wavelengths and is much colder at 2cm than the temperature at which C02 sublimates under Martian surface conditions. This is due mostly to the combination of two different effects, one of them physical and one a result of the method of observation.
The first, and most straightforward of these effects, is that the resolution of the 6cm data is one third that of the 2cm data. The estimate of the edge of the North Polar Cold Region from the fit of the lower resolution, 6cm, data will have a larger non-formal error than the estimate from the fit of the 2cm data, which is higher in resolution. If the edge of the North Polar Cold Region is fixed at the 2cm value of 70°
N (i.e., the latitude is no longer a free parameter), then the brightness temperature of the North Polar Cold Region at 6cm is only 142K. The second contribution to the difference can be most easily understood by noting that the region which is sampled by the 6cm emission is, roughly, three times deeper than the region sampled by the 2cm emission. Since the radio absorption length of C02 frost is very large (it can vary between some tens of wavelengths to over one hundred wavelengths depending on the density of the C02 and the soil content, Simpson et al., 1980), it is possible, at certain latitudes, to 'see' through the seasonal frost layer to the ground below, which can be warmer at depth than the sublimation temperature of C02 • As will be seen
North Data Set 38
shortly this is exactly the situation that occurs at the season during which the North data set was obtained.
The behavior of the seasonal wave and can be understood through the following, simple argument: At all latitudes, the C02 cap is seasonal. This means that sometime during the year the surface gets much warmer than the C02 sublimation temperature (Keiffer et al., 1977). Assuming the transport of C02 is relatively efficient, the surface temperature remains near the C02 sublimation temperature. Therefore, the sub- surface temperature will always be warmer than the sublimation temperature of C02 ,
converging at some depth to the seasonal average (assuming minimal heat flow from the deep interior and across latitude ranges). Solutions for the heat equation under these circumstances show that, at a latitude of about 65°N, the temperature at a depth of one seasonal thermal skin depth, about llOcm, will be around 10 to 15 degrees warmer than the C02 sublimation temperature during the season in which our measurements were taken.
Figure 4.1 illustrates this warming with depth. The two curves shown in Figure 4.1 are the diurnally averaged kinetic temperature as a function of depth for two seasons. They were computed using the thermal model described in Chapter 3, using a value of 6.5 for the thermal inertia and a value of 0.25 for the albedo. The solid line corresponds to the season during which the North data set was taken. The dotted lines corresponds to late summer in the northern hemisphere. Both were calculated for a latitude of 62.5° N. Note the positive thermal gradient for the line corresponding to the season during which the North data set was taken. In late fall the thermal gradient is just the opposite as the summer heat wave propagates into the sub-surface.
In addition, the C02 frost acts as a dielectric 'film' coating the surface so that the angle of emission from the sub-surface to the frost is much nearer the vertical than it would be if the emission were to come directly through the surface-atmosphere
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