Albedo and Thermal Inertia Determinations

INTRODUCTION

2.7 Albedo and Thermal Inertia Determinations

25 2.7 Albedo and Thermal Inertia Determinations

depth is much smaller than the object [Jakosky et al., 1990]. The magnitude of the phase angle induced differences could be a few degrees Kelvin [Jakosky et al., 1990].

Even ignoring possible errors in the decalibrated Viking IRTM data, there are other possible sources of the offset between Termoskan and IRTM. These include any bias in the Termoskan absolute preflight calibration, and any intrinsic difference in Mars' thermal emission between 197 6-7 8 and 198 9, including atmospheric effects such as clouds.

Not only are absolute temperature differences very small between Termoskan and IRTM, but also the thermal features in the Termoskan data qualitatively correlate very well with the lower resolution IRTM data, as seen in Figures 2.7 and 2.8. Thus, in both an absolute and a relative sense, I have a high degree of confidence in Termoskan's thermal channel and its calibration.

Termoskan sees thermal variations even at the limit of its spatial resolution. Figure 2.9 again shows Termoskan and IRTM data for 18°S latitude. The three curves represent different degrees of spatial averaging of the Termoskan data. Curve 1 is not averaged, i.e., it is a 1 pixel wide strip; curve 2 has 11 pixels averaged in a north-south direction; and curve 3 has 67 pixels averaged in a north-south direction. None of the curves are averaged in an east-west direction (whereas, Figures 2.7 and 2.8 were). Thermal features remain at the limit of resolution of the 1 pixel curve. For example notice the spike at approximately 115°W longitude (in Figure 2.9). This corresponds to the sunlit rim of a 6 km diameter crater.

The Instrument, the Data Set, and Validation 26

0 ...

N

0

<D N

z ⁰

0 l{l

IX N

u -

~if

_{a.. 0}

:2 """

~ ('.;

>-

0 0 CD

d: -18?0± 1 ?0 LA.T.; PIXELS WIDE= 1. 11,67; ±30 MIN. TOO

. - ----'--- l

'30 120 110

WEST LOf\:GITUDf

Figure 2.9: The lines represent Termoskan data centered upon -18 degrees latitude.

Curve 1 (top) has no averaging; it is a 1 pixel wide strip to which 10 K have been added uniformly to ease comparison with the other curves. Curve 2 (middle) has 11 pixels averaged in a north-south direction. Curve 3 (bottom) has 67 pixels averaged in a north- south direction and has had 10 K subtracted from it. Note that sharp features can be seen in the 1 pixel wide strip that average out at lower resolutions, e.g., the spike at approximately 115°W corresponds to the rim of a 6 km diameter crater.

27 2.7 Albedo and Thermal Inertia Determinations

interested in whether the visible channel signal can be converted to bolometric Bond albedo, which is the parameter necessary for the derivation of thermal properties.

Thermal inertia and bolometric Bond albedo are the two most important physical properties of a planetary surface that determine its diurnal temperature variations.

Thermal inertia, a bulk measure of the resistance of a unit surface area to changes in temperature, is commonly used to characterize the insulating properties of planetary surfaces. It is defmed as I= (kpcp)l(l. where k is the thermal conductivity, pis the density, and Cp is the specific heat. Low inertia materials exhibit the largest day-to-night surface temperature variations and the smallest thermal skin depths.

For the martian surface, thermal inertia is often expressed in units of 1Q-3 cal ^cm-2 K-1 sec-112 (e.g., in Kieffer et al., 1977). As a matter of convention, these units are used for thermal inertias throughout this thesis. To convert to SI units (J m-2 K-1 sec-112), multiply by 41.86. Several authors (e.g., Kieffer et al., [1977]; Palluconi and Kieffer, [1981]; and Haberle and Jakosky [1991]) have used brightness temperatures and thermal modelling to derive thermal inertias for the martian surface. These authors used IRTM data from multiple times of day to derive both inertia and bolometric albedo simultaneously.

T~rmoskan observed only a small area at more than one local time of day and those data are badly foreshortened. Thus, for essentially all the Terrnoskan data, inertias and albedos cannot be derived independently using observations at two times of day.

Therefore, the majority of the Termoskan data require bolometric albedo for thermal inertia determinations. Accurate bolometric albedos are particularly important for deriving inertias from Terrnoskan data because only daytime observations were obtained. Daytime temperatures are very dependent upon bolometric albedos.

Bolometric (Bond) albedo defmes the fraction of incoming solar flux over all wavelengths that is not absorbed by a surface. Surfaces with high bolometric albedos ("bright" surfaces) absorb less incoming solar flux than those with low bolometric albedos

The Instrument, the Data Set, and Validation 28

("dark" swfaces). Bolometric Bond albedo for a unit surface element is most simply defined as:

A=

pf

^q(a)da

where p is the total reflectivity of all wavelengths at 0° solar phase angle, a., and q(a.) is the variation of reflectivity over all wavelengths with increasing solar phase angle for the swface element Even the most comprehensive Mars albedo observations are limited by uncertainties in the local variation in q, in wavelength dependence, and in temporal and spatial variations in atmospheric scattering. Termoskan observed only the total visible intensity from Mars swface elements at a.

=

0°. The visible intensity observed included both swface and atmospheric components. Because Termoskan essentially did not observe shadows due to its zero phase angle geometry, the atmospheric contribution cannot be removed using the observed flux in shadowed areas as has been done with other data sets [e.g., Herkenhoff, 1989]. In addition to the other difficulties, the visible Termoskan data are largely dependent upon pre-flight calibration. Thus, even approximate estimates of Bond albedo from the Termoskan visible data alone will yield only low confidence results.

Another possible way to gain confidence in bolometric albedos derived from Termoskan data would be tying them to bolometric albedos derived from Viking IRTM solar band measurements. To test this possibility, I compared 1 o x 1 o averaged Termoskan dn (signal) values with the corresponding 1 o x 1 o binned albedos of Pleskot and Miner [1981]. Comparison strips were limited in latitude and longitude to lessen geometric and atmospheric effects. This increased the chances of tying the Termoskan data to the Viking albedos.

Figures 2.10 and 2.11 show representative examples of the comparisons. Figure 2.1 0, using data derived from observing session 2, shows a region with relatively large variations in albedo. Note the very high scatter within the data. A least squares fit to the

29 2.7 Albedo and Thermal Inertia Determinations

1 X 1 DEGREE TERMOSKAN ON AVERAG:::S VS. IRTM DERIVED 1 X 1 ALBEDOS

~ .---~--~--~--~--~--~--~---~--~--~--~--~---~

0

L{)

c)

~ 0 ~--L---L---L---~--~--~--~--~---L--~---L--~--~--~--_J

60. 80 100 120 140 160 180 200

TERMOSKAN ON VALUE

Figure 2.10: Termoskan visible dn vs. IRTM albedos - high contrast. Dots represent Termoskan 1° x 1° averages of visible channel dn (signal) values plotted versus IRTM I ⁰ x 1° bolometric albedos from Pleskot and Miner [1981]. The bin centers range from 3.5°N, 42.5°W to 4.5°S, 31.5°W. Note the large amount of scatter in the plot. The line

represents a linear least squares fit to the data with the following equation:

Albedo= (0.0009

±

0.0243) + (0.00143

±

0.00017)

*

(dn value).

lf)

0 0 w m

_J

<!

0 w

~ 0::

w

0

~ f-~

The Instrument, the Data Set, and Validation 30

1 X 1 DEGREE TERMOSKAN DN AVERAGES VS. IRTM DERIVED 1 X 1 ALBEDOS

o.f) N

ci

N 0

o.f)

ci

60 80 100 120 140 160 180 200

TERMOSKAN DN VALUE

Figure 2.11: Termoskan visible dn vs. IRTM albedos - low contrast. Same as Figure 2.11, but for a different region that has less albedo contrast. The bin centers range from:

14.5°S, 82.5°W to 16.5°S, 76.5°W. The line represents a linear least squares fit to the data with the following equation:

Albedo= (0.146 ± 0.016) + (0.00033 ± 0.00013)

*

(dn value)

31 2.8 Implications for Termoskan Studies

data gives a standard deviation in albedos derived from this method of 0.02 Uncertainties of this magnitude will introduce significant uncertainties in the detennination of thermal inertias. Figure 2.11 shows a region of low albedo variation, taken from panorama 3, for which the least squares fit is very different from that of Figure 2.1 0. Accuracy of this least squares fit is hampered by the small albedo variations at the scale of the 1 o x 1 o bins. The scatter in these and other plots combined with the variety of least squares fits and the uncertainties in the fits leads me to conclude that tying Tennoskan data to Viking albedos is potentially very inaccurate at these scales. The ties will be even more inaccurate and uncertain if attempted over larger scales. Thus, although I have not proven the Termoskan data to be intrinsically in error, I conclude that using the Tennoskan visible channel on its own or even with generalized ties to Viking data may introduce significant errors in derived absolute bolometric albedos, and significant errors in absolute thermal inertias.