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Thermal-Infrared imagingWhat is it?
- measurement of emitted radiation (temperature)- at one or more times (thermal inertia) - at one or more wavelengths (composition)
Why bother?
- see at night- temperatures- energy fluxes- material properties (resistance to
temperature change, i.e. thermal inertia)- composition (emissivities)
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Kirchhoff’s Law
ε = 1 - R
Wavelength (µm)
6 8 10 12 140.0
0.2
0.4
0.6
0.8
1.0
Emissivity Reflectance
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Restrahlen band: k maximized at fundamental vibration mode frequency
Christiansen frequency:n = 1, minimizing reflectance
Reflectance or emission spectrum results from combination of n, k variations
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Emissivity spectra of rocks
0.7
0.8
0.9
1.0
8 9 10 11 12 13 14
emiss
ivity
Wavelength, µm
Emissivity Spectra
limestone
dolomite
gypsum
varnish/ss
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Emissivity spectra of rocksEmissivity of rocks
0.5
0.6
0.7
0.8
0.9
1.0
8 9 10 11 12 13 14wavelength, µm
graniteanorthositebasaltduniteobsidian
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Emissivity spectra of approximate graybodies
Emissivity of soil & graybodies
0.80
0.85
0.90
0.95
1.00
8 9 10 11 12 13 14wavelength, µm
green grassconifersicesnowdry grassspodosol
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What compositions can be ���determined in the TIR?
Mostly vibrational resonance, not electronic processestherefore, relatively large molecules
Silicate minerals (SiO4-4); quartz (SiO2)
Sulfates (SO4-2); sulfur dioxide (SO2)
Carbonates (CO3-2); carbon dioxide (CO2)
Ozone (O3) Water (H2O)Organic molecules
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Thermal infrared spectral features of silicates (Clark, 1999)
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Death Valley, California
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Saline Valley, California
VNIR SWIR TIR
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Mauna Loa, Hawaii
MASTER VNIRdaytime
ASTER TIR,daytime
MTI TIR,nighttime
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Not all thermal images are dominated by solar heating of the surface
Enceladus
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Not all thermal images are dominated by solar heating of the surface
ASTER images of Yellowstone: VNIR (left) and TIR (right)
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A little about solving sets of equations
If you measure R there are 2 unknowns: ε and TIf you measure R at a different λ, there is another unknown ε
If you measure a spectrum of n bands, there are n+1 unknowns
You must have the same number of measurements as unknowns to solve a set of equations
How can you do this for TIR data?
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Temperature - Emissivity Separation
• Two-time two-channel method• Completely determined
• Model emissivity method• Assume ε10µm=0.96
• Normalized Emissivity method• Assume εmax=1
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Ruff et al. (1997)
But if εmax < 1 …
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Example of εmax < 1: chlorides
Osterloo et al. (2008)
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10.8 µm
290 336
T, K
290 308
T, K
1:30 pm
8:00 pm
Day/nightVis
Thermal inertia:dQ/dTResistance of matterto changing temperatureas heat is applied
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Morning
Veg Mapping - ThermalDay Night
Red = 10:00 amGreen = 2:00 pmBlue = 11:00 pm
Conifers cooler during day & warmer at night
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Sunlight heats planetary surfaces
in a sinusoidal pattern
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Surface temperature responds to heating (and lack of heating), but with a lag.
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Albedo
• The albedo of a planetary surface (A) is the percent of sunlight that it reflects.
• Albedo can range from A=1 (pure white) to A=0 (pure black). For Earth, average A is 0.39. For the Moon, average A is 0.12.
• The amount of sunlight absorbed by a surface is 1-A
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The effect of varying albedo on diurnal temperature curves
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Other physical quantities that affect temperature
• Thermal Conductivity (k) is a measure of the rate at which heat is conducted by a medium. krock < kwater < ksteel
• Specific heat capacity (C ) is a measure of the
amount of heat required to raise the temperature of a given amount of material by a certain number of degrees. Cwater > Crocks > Csteel
• Density (ρ) also important
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Thermal Inertia
• Thermal inertia is a measure of the resistance offered by a substance undergoing temperature changes. It is given by:
T.I. = (k ρ C)1/2
Units are J m-2 s-1/2 K-1 (tiu)
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The effect of thermal inertia on diurnal temperature curves
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Thermal inertia and albedo are the two parameters that fundamentally control the shape of the diurnal temperature curve.
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Thermal Inertia of Geologic Materials
T.I. = (k ρ C)1/2 • For most geologic materials, ρC only varies by a factor of two, whereas k varies by many orders of magnitude. • k is mostly determined by particle size, degree of induration. ⇒ A concrete sidewalk has a much higher thermal inertia than a sandy beach! Note that on Earth, the high C of water means moisture content also plays a big role in determining T.I.
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Blues indicate low TI ⇒ Fine-grained dust
Reds indicate high TI ⇒ Lots of rocks and outcrop
Martian Global Thermal Inertia Map
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Martian
albedo
Martian thermal inertia
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Very low T.I. on Saturn moons à high porosity?
Howett et al. (2010)
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Computation of Thermal Inertia
For terrestrial applications, commonly use “Apparent Thermal Inertia” (ATI).
ATI = N * (1-A)/ΔT The denominator just indicates that thermal inertia is inversely proportional to the diurnal temperature range. The numerator normalizes for amount of insolation absorbed by the surface.
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Terrestrial work mostly uses Apparent Thermal Inertia (ATI)
ATI = N * (1 – A) / ΔT
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Peace Vallis, Gale crater, Mars
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Hardgrove et al. (2010)
ΔT images of alluvial fans,
Death Valley & Owens Valley,
CA
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Columbus crater (Night IR over Day IR)
Figure from Baldridge et al. (2009)20 km
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+1250 m
+2250 m
Columbus crater (Night IR over Day IR)
20 km
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Columbus crater: CRISM data on HiRISE DEM
Polyhydrated sulfates
Kaolinite
Wray et al. (2011)
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Near-IR spectra allowed precise mineral identification
CRISM FRT 7D87
Gypsum (CaSO4·2H2O)
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Thermal IR spectral data allowed estimating abundances
Baldridge et al. (2013)
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But rough surfaces can complicate thermal IR unmixing… (because single scattering no longer dominates)
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Cavity EffectNorite rock with two drilled holes:
PHOTO
Thermal IR
Thermal IR spectra:
3D view (DTM resolution 0.002 m):
Modeled apparent emissivity: