## Thermal inertia and rock abundance

Viking IRTM, MGS TES, MO THEMIS, and MER Mini-TES experiments have provided insights into the variation in grain size across the martian surface through measurement of the thermophysical characteristics of the regolith. Thermal inertia of the surface materials governs the daily thermal response of the surface to solar heating. The surface temperature due to absorption of solar radiation is the equilibrium temperature (Teq) and can be calculated by balancing the incoming (Fin) and outgoing (Fout) radiation from the planet. Fin is the amount of the solar flux absorbed over the planet's surface area which is exposed to the solar radiation:

where Ab is the bond albedo (Eqs. 4.3 and 4.4), which measures the amount of radiation reflected by the planet's surface. Thus the amount of radiation absorbed is (1 — Ab). The remainder of Eq. (4.6) is the amount of radiation received over the hemisphere in sunlight for a planet of radius R and distance r from the Sun. It is equivalent to Eq. (4.2). A rapidly rotating planet like Mars reradiates this absorbed energy from its entire surface; therefore the outgoing radiation emitted from the planet is

The radiation emitted by a blackbody is proportional to the surface temperature of the body and is given by the Stefan-Boltzmann law:

The Stefan-Boltzmann constant r=5.6705X10-8 W m-2 K-4. Thus Eq. (4.7) is the product of the surface area of the planet (4nR2) and the radiation emitted by that surface (rTe4q). Because the planet is not a perfect blackbody, we must also include the emissivity (e), which is a measure of how closely the object approximates blackbody emission (e for a blackbody = 1). Fin=Fout for a planet in thermal equilibrium, giving us the relationship for Teq:

Note that Teq depends only on the planet's heliocentric distance (r), Ab, and e, not its size (R). The observed temperature (effective temperature, Tef) is often higher than Teq; in the case of Earth and Mars, this is because of greenhouse warming by the atmosphere (Section 6.1).

Daytime sunlight heats up the surface material on Mars, but that heat is reradiated during the night. Large rocks can retain this heat longer than smaller material like sand because of their larger volume compared to surface area (V/A). This ability for materials to retain heat (thermal inertia, I) is related to the thermal conductivity (KT), density (q), and specific heat (cp) of the material:

The value of q can vary by about a factor of four for most geologic materials comprising terrestrial planet surfaces and cp varies by only about 10-20%. The largest changes in I result from KT, which can vary by up to three orders of magnitude (Christensen and Moore, 1992). Porosity, cohesiveness, and grain size are the major contributors to variations in KT and this is what dictates I for a particular region. Small particles, such as dust and sand, have low I values while higher I values correspond to rockier locations. Thermal inertia is sensitive to depths penetrated by a subsurface thermal wave of period P. This depth is the thermal skin depth (d):

Spectral and bolometric brightness temperatures derived from TES observations are used to calculate I variations across the martian surface (Jakosky et al., 2000; Mellon et al., 2000; Putzig et al., 2005). Figure 4.22 shows the global variation in I calculated from nighttime observations. Values of I range between 24 and 800 J m- K- s- across the martian surface. Low I values typically correlate with high-albedo regions, suggesting that these regions are dust-covered. Regions of higher I are rockier, although the apparent high I values near the north pole are an artifact resulting from measurements made near dawn when temperature variations are large. High I is often correlated with low albedo, interpreted to be regions of coarse-grained sediments, rocks, and bedrock exposures. A third region consists of

Figure 4.22 Thermal inertia provides information about particle sizes across Mars. This map, derived from TES data, shows the variation in thermal inertia across the planet. Areas of low thermal inertia, such as Tharsis, are dust-covered while regions of high thermal inertia, such as Valles Marineris and the rim of the Hellas impact basin, have high rock abundances. (Image PIA02818, NASA/JPL/ASU.) See also color plate.

Figure 4.22 Thermal inertia provides information about particle sizes across Mars. This map, derived from TES data, shows the variation in thermal inertia across the planet. Areas of low thermal inertia, such as Tharsis, are dust-covered while regions of high thermal inertia, such as Valles Marineris and the rim of the Hellas impact basin, have high rock abundances. (Image PIA02818, NASA/JPL/ASU.) See also color plate.

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Figure 4.23 Estimated rock abundances calculated from thermal inertia considerations are compared to observed rock abundances at the VL1, VL2, and MPF landing sites. The results for MPF rock abundance are consistent with landing site predictions before launch. (Reprinted by permission of American Geophysical Union, Golombek et al. [1999b], Copyright 1999.)

o MPF Far-Field

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Figure 4.23 Estimated rock abundances calculated from thermal inertia considerations are compared to observed rock abundances at the VL1, VL2, and MPF landing sites. The results for MPF rock abundance are consistent with landing site predictions before launch. (Reprinted by permission of American Geophysical Union, Golombek et al. [1999b], Copyright 1999.)

high I and intermediate albedo, interpreted as surfaces covered by duricrust interspersed with rocks and bedrock exposures (Mellon et al., 2000; Putzig et al., 2005).

High I generally translates to a rockier surface in the >0.1-0.15-m rock size range, so that I can be used to estimate rock abundances across the planet (Christensen, 1986). Rock abundance values range from 1% of the surface covered by rocks to a maximum of ~35% coverage, with a modal value of 6%. Predicted rock abundance has been compared with actual values at the five landing sites and generally the two are consistent (e.g., Golombek et al., 1999b, 2006) (Figure 4.23). The size-frequency distribution (SFD) of rocks follows a simple exponential curve, compatible with the distributions expected from the fracture and fragmentation of rocks (Golombek and Rapp, 1997).

Dust comprises a substantial portion of the martian soil and coats most of the rocks at the five landing sites. Winds often loft the dust into the atmosphere, transporting it around the planet. Local, regional, and global dust storms (Section 6.3.2) are the obvious manifestations of this dust transport, but the observation of dust devils (Figure 4.24) (Greeley et al., 2006) and atmospheric dust (Smith et al., 2000) indicates that transport of fine-grained particles occurs continuously. The dust particles are estimated to typically be <40-pm diameter and composed of ferric oxides.

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