Alan Gillespie1, Don Sabol1,

1
Temperature/Emissivity Separation

• Alan Gillespie1, Don Sabol1,
• William Gustafson1, Anne Kahle2, and Elsa Abbott2
• 1University of Washington, Seattle, WA
• 2Jet Propulsion Laboratory, Pasadena, CA

Crater summit of Mauna Loa, HI
2
Outline

• Introduction ASTER
• TIR radiative transfer
• Atmospheric compensation
• Temperature/emissivity separation algorithms
• ASTER TES algorithm
• Recover land surface temperatures and
  emissivities
• TES results (examples)
• Sources of error/uncertainty
• Noise, regression, atmospheric compensation
• TES performance

3
Introductory material

• ASTER on Terra a high-resolution imager for the
  Earths land surface
• Examples of ASTER data

4
ASTER

• Advanced Spaceborne Thermal Emission Reflection
  Radiometer
• Launched 19 December 1999 on Terra
• Terra instruments
• CERES
• MISR
• MODIS
• MOPITT
• ASTER

5
ASTER

• ASTER CHARACTERISTICS
• 14 Spectral Bands
• ASTER is the zoom lens for Terra (high spatial
  resolution)
• 15 meter VNIR (3 bands)
• 30 meter SWIR (6 bands)
• 90 meter TIR (5 bands)
• NEDT ? 0.25º K

TIR spectral bands
1.0 0.8 0.6 0.4 0.2 0.0
14
13
10
11
12
8 9 10
11 12 Wavelength (µm)
6
Why Multispectral TIR?
Salton Sea, California
Altyn Tagh, Xinjiang

• Emissivity spectra and surface temperatures can
  be calculated from multispectral TIR radiance
  measurements
• Surface temperatures are more accurate than
  one-channel brightness temperatures because
  emissivity is determined also
• Emissivity spectra can be used to determine
  surface composition

VNIR color composite
Surface temperature
TIR emissivity color composite
25 km
7
Why ASTER?

• MODIS/AVHRR suited for large regions
• Oceans, large forests
• ASTER better suited to analysis of fundamental
  components of landscapes
• Key applications
• Ecotome interfaces
• Land use (fractionation)
• Near-shore and estuarine phenomena
• Stream temperature
• Urban problems
• Geologic hazards
• Landslides
• Floods
• Volcanic eruptions

Summit caldera, Mauna Loa
TIR emissivity
8
Degrees of Freedom

• Four slides on the indeterminacy were added in
  LAquila and I dont have them here. The points
  were only for a homogeneous isothermal scene was
  it true that there were n1 unknowns, where n
  number of bands. For realistic cases matters
  were worse.
• The point was made that temperature was a
  fundamental parameter that governed heat
  conduction/diffusion (driven by gradients in
  temperature) but radiant temperature was harder
  to define because of inevitable mixing in a pixel
• Effective temperature and emissivity parameters
  were discussed and defined as what you estimated
  from radiant fluxes from finite scene elements

9
Snapshot temperatures

• A point was also made that remotely sensed
  temperatures were snapshots and were not
  representative (necessarily) of temperatures
  measured over longer time intervals
• The scene temperatures changed on various time
  scales, including seconds (leaves fluttering in
  wind) and minutes (gusts of wind cooling
  surfaces)
• MTI slides of the validation site in Hawaii were
  shown to emphasize this. The slides, from Lee
  Balicks (LANL) talk in Crete, showed images of
  the flat, homogeneous floor of a caldera with B G
  and R the same TIR band but different days and
  the floor showed worm-like color patterns related
  to different temperature patterns due to wind.
  Lee gave me permission to show the slides but not
  to distribute them.
• This snapshot problem afflicts all nadir
  instruments. Maybe a thermal MISR might help
  but it now is a fundamental limitation of the
  significance of temp images over land.
• Big-pixel imagers like MODIS dont have this
  problem so much because the temperature
  fluctuations go on a scales smaller than
  measurement and are averaged out

10
Emitted Thermal Radiation
Bl(T) c1p-1 l-5 (exp(c2(lT)-1)-1)-1 Ll(T) el
c1p-1 l-5 (exp(c2(lT)-1)-1)-1

• Plancks equation
• Reflectivity and Kirchhoffs Law

B blackbody radiance W m-2 sr-1 µm-1 L
surface radiance W m-2 sr-1 µm-1 l wavelength
c1, c2 constants e emissivity
T temperature K
rl 1 - el
r reflectivity
11
Emitted Thermal Infrared Radiation
400 K
Wavelength, µm
Reflected Solar
350 K
300 K
250 K
Radiance, W m-2 µm-1 sr -1
Cross-over region
Longwave IR
Mid IR
12
Radiative transfer Planck EquationWith
Emissivity and Atmosphere
Lx,y,l t x,y,l (ex,y,l Bl(Tx,y) rx,y,l (S ?
x,y,l S S Rxm,yn,l) ) S? x,y,l Bl(Tx,y)
c1p-1 l-5 (exp(c2(lT)-1)1)-1 B Blackbody
radiance c1, c2 constants ? W m-2 sr-1
µm-1 L radiance ? W m-2 sr-1 µm-1 l
wavelength e emissivity T temperature (K) r
reflectivity 1-e (Kirchhoffs law) x,y
position in scene S? downwelling atmospheric
irradiance ? W m-2 µm-1 S? upwelling atmospheric
path radiance ? W m-2 sr-1 µm-1 R radiance
emitted from adjacent scene elements ? W m-2 sr-1
µm-1 t atmospheric transmissivity
8 8
m-8 n-8
13
Atmospheric Effects - Transmissivity
1
0.9
0.8
0.7
0.6
ASTER TIR window
Transmissivity
0.5
0.4
Spectra are from different dates in Washington,
USA
0.3
0.2
0.1
Airborne MASTER channels
0
7.8
8.3
8.8
9.3
9.8
10.3
10.8
11.3
11.8
12.3
12.8
13.3
Wavelength, mm
14
Atmospheric Effects - Transmissivity
1
0.9
0.8
0.7
Spectra are from different dates in Washington,
USA
0.6
Transmissivity
0.5
0.4
0.3
0.2
0.1
0
7.8
8.3
8.8
9.3
9.8
10.3
10.8
11.3
11.8
12.3
12.8
13.3
Wavelength, mm
ASTER TIR image channels
15
Atmospheric Effects Path Radiance
3.5
3
2.5
Spectra are from different dates in Washington,
USA
2
Path radiance, W m-2 mm-2 sr-1
1.5
1
0.5
0
7.8
8.3
8.8
9.3
9.8
10.3
10.8
11.3
11.8
12.3
12.8
13.3
Wavelength, mm
ASTER TIR image channels
16
Estimation of Atmospheric Effects

• Usually done independently of image measurement
• Radiosonde for water, temperature profiles
• DEMs for pressure over image
• Atmospheric radiative transfer models (e.g.,
  MODTRAN) are used to predict values for
  parameters
• Measurement of water absorption bands (NIR, TIR)
  increasingly used for in-scene estimation on a
  pixel-by-pixel basis

17
Removal of Atmospheric Effects

• Subtraction of path radiance
• Normalization for transmissivity
• Iterative correction for downwelling
• Divide downwelling by pi (assumes Lambertian)
• Use best estimate of emissivity spectrum to
  estimate reflectivity spectrum
• In principle, iterations are better because each
  successive emissivity spectrum may be better than
  the one before. (Not necessarily true in the
  presence of noise)

18
Temperature/Emissivity Separation

• There are always at least (n1) unknowns
  (nmeasurements)
• Solutions for T and e are underdetermined
• Atmospheric parameters have been estimated
  independently
• Solutions can be badly underdetermined at low
  resolution (mixing and anisothermal scene
  elements)
• Common assumptions
• Isothermal, pure pixels
• Values for emissivities

19
Four basic solutions for T and e
Atm. unknowns
Measurements
Assumptions
Unknowns
Method Brightness temperature Color
Temperature Planck Draping Two-time
Approach Assume e1 solve for T
Measurements Radiance in 1 channel (1 time)
1
1
3
2
3
2
1
6
Assume e1e2 solve for e1 then for T
Radiance in 2 channels (1 time)
n
1
3n
Assume el 1 (unknown l) calculate blackbody
radiance at successively lower Ts when calc.
measured R(l) agree, T is correct
Radiance in n channels (hundreds) (1 time)
n1
12
4
0
4
No assumptions solve 4 simultaneous equations
Radiance in 2 channels 2 times
20
Brightness Temperature method
Assume e is known
1 measurement, 1 assumption, 2
unknowns 3 atmospheric unknowns are
found independently
Error in assumed emissivity
21
Color Temperature method
Radiance at 2 wavelengths is measured
emissivities are assumed to be the same
e1 R1 B(l1,T) e2 R2 B(l2,T) e1 e2
Solution loci
Measurement error lowers locus
Locus for 11µm
Locus for 9µm
22
Color Temperature method

If e1?e2 is violated, what are the consequences?
temperature error increases as (l1-l2)
decreases for most rock surfaces, errors
will exceed 5K for water and vegetation,
errors will be lt3K
e1-e2
23
Planck-Draping method
Approach assumes that the temperature at which
a Planck function touches the measured
spectrum gives the surface temperature (i.e., the
emissivity at that wavelength is 1.0)

Approach is used with field spectra and
can be used with hyperspectral images
Approach can be modified to assume the
maximum emissivity is lt 1
24
Two-Time, Two-Channel method

Approach estimate e1 and solve equation for e1
Solution occurs when estimated and calculated
values agree Use e1 R1,1 in Plancks equation
to solve for T1 From T1 R2,1 solve for e2
25
Two-Time, Two-Channel method

Solution occurs when the calculated e1 and the
estimated e1 are the same
26
Two-Time, Two-Channel method

• Measurement error of 0.01 causes error in
  emissivity of 0.033 and error in temperature of
  1.8K (for 9 11 µm, 300 350 K)
• Method is intolerant of changes in surface
  emissivity (e.g., due to rain, dew, dust)
• Method is intolerant of registration errors in
  scenes with high spatial variance

27
Temperature/Emissivity Algorithms

• Brightness temperature, color temperature, split
  window methods, Planck Draping methods
• Two-time approach (Day and night image)
• Magnifies noise
• Requires pixel-perfect registration
• Model emissivity, Normalized emissivity
• Inaccuracies tend to be 3 K
• Introduces tilts into the e spectrum
• Index approaches
• Alpha residual, MMD, TES approaches

28
Goal of TES

• Recovery of T/e for low/high-contrast test scenes
• 1.5 K
• 0.015 emissivity
• Consistency of e recovery (same scene, day/night
  or different days)
• 0.015 emissivity

29
TES - The Fundamental Idea
Calculate relative emissivity (fairly easy) and
use semi-empirical scaling relationship between
MMD of the normalized spectrum and Emin to
specify the absolute values of the emissivities.
30
TES - Regression

• Fundamental idea MMD vs Emin for a blackbody
  with a Gaussian reststrahlen band
• What happens when it is a greybody? (origin of
  scatter)
• What happens when there are many bands
  overlapping (like feldspar)? (Mixing issue)
• Original regression (76 spectra)
• Entire library
• Delete weird things to leave final regression
• Regression by material

31
MMD Regression - simulation
MMD regression is physically based provided
the spectrum has a gray-body continuum
interrupted by a simple (Gaussian) Reststrahlen
feature In reality, spectra of complex
materials violate this assumption, resulting in
scatter below the ideal regression line.

Simulated MMD regression line
32
TES Regression
1.00 0.95 0.90 0.85 0.08 0.75 0.70 0.65 0.
60
Minimum Emissivity
ASTER Default fit RMS 0.257 Linear Fit RMS
0.255 (R2 0.946)
0.0 0.1
0.2
0.3
0.4
Spectrum MMD
MMD Threshold (0.03)
33
TES Flow Diagram
Estimate normalized Emissivities taking S? into
account
Estimate spectral contrast (MMD)
low-contrast (water)
high-contrast (rock)
Estimate emin using the MMD vs. emin regression
Set eavg 98.7
Remove S? with Revised e estimate
Recalculate e
Calculate T
Gillespie. Et. Al, 1998, A temperature and
emissivity separation algorithm for Advanced
Spaceborne Thermal Emission and Reflection
Radiometer (ASTER) images, IEEE Transactions on
Geoscience and Remote Sensing, Vol. 36, no. 4,
1113-1126.
34
TES Validation Program

• High Contrast (substrate)
• Big Island, HI (lava flows)
• Railroad Valley, NV (playa)
• Low Contrast (water)
• Big Island, HI
• Lake Tahoe, CA
• Salton Sea, CA

35
TES Validation Results Lake Tahoe
TR 4 TR 3
TR 1 TR 2
ASTER Temperature Image
36
Lake Tahoe
courtesy Simon Hook (JPL)
37
TES Validation Results Lake Tahoe
Comparison of ASTER TES and Buoy Temperatures
1.00 0.50 0.00 -0.50 -1.00 -1.50 -2.00
03/12/2000 06/24/2000 08/04/2000 08/29/2000 09
/28/2000 11/07/2000 02/27/2001 02/28/2001 03/1
6/2001 06/03/2001 07/22/2001 08/22/2001 10/09/
2001 11/03/2001
ASTER TES Temp - Buoy Temp ( ºK)
Date
38
Lake TahoeASTER TES Mean Emissivities At Buoys
vs Laboratory Water Emissivity Spectrum
1.000 0.995 0.990 0.985 0.980 0.975
Emissivity
8.0 8.5 9.0
9.5 10.0 10.5
11.0 11.5
Wavelength (µm)
39
Salton SeaASTER TES Mean EmissivitiesLaboratory
Water Emissivity Spectrum
1.000 0.995 0.990 0.985 0.980 0.975 0.
970
Emissivity
8.0 8.5 9.0
9.5 10.0 10.5
11.0 11.5
Wavelength (µm)
40
The Classification Problem
Good
Salton Sea MMD examples
1.000 0.960 0.920 0.880
302.1 ºK
303.2 ºK
Aug 10 2001 Mean 0.024 S.D. 0.011
Good Bad Good pixels Bad pixels
305.8 ºK
Aug 07 2001 Mean 0.042 S.D. 0.023
Bad
8.0 8.5 9.0 9.5 10.0
10.5 11.0 11.5
Emissivity
Wavelength (µm)
Emissivity Images (R10, G 12, B 14)
41
Hawaiian RockValidation Sites
Saddle (6,600)
Mauna Loa Crater (13,045)
14 12 10 8 6 4 2 0
Altitude (feet X 1,000)
Punaluu (50)
0 2 4 6
8 10 12 14
16 18 20 22
Distance (feet X 10,000)
42
Mauna Loa Crater
N
Mean 2 s
Field Spectra Truth ASTER
1 KM
TIMS B 1 G3 R5
43
Mauna Loa Crater Results
0.03 0.02 0.01 0.00 -0.01 -0.02
Truth - ASTER TES (Emissivity)
05/04/00 06/05/00 10/20/00
12/05/00 01/01/01 01/02/01
08/29/01 11/17/01 01/11/02
Date
44
TES Regression Tuning
1.00 0.95 0.90 0.85 0.08 0.75 0.70 0.65 0.
60
Lab Spectra Caldera Spectra ASTER Default Linear
Fit
Minimum Emissivity
ASTER Default fit RMS 0.257 Linear Fit RMS
0.255 (R2 0.946)
0.0 0.1
0.2
0.3
0.4
Spectrum MMD
MMD Threshold (0.03)
45
Saddle Results
Mauna Kea
EMISSIVITY
Mean 2 s
Field Spectra Truth ASTER
5 KM
ASTER B 1 G2 R3
Mauna Loa
46
Saddle - Emissivity Results
0.03 0.02 0.01 0.00 -0.01 -0.02
Truth - ASTER TES (Emissivity)
05/22/00 12/05/00 01/01/01
01/17/01 05/25/01 11/17/01 01/04/02
Date
47
Punaluu
Altered
Weathered Surface
Original Surface
Weathered Surface
Original Surface
48
Punaluu
Mean 2 s
Field Spectra Truth ASTER
EMISSIVITY
05/04/00
WAVELENGTH (µm)
49
Punaluu
0.03 0.02 0.01 0.00 -0.01 -0.02
Truth - ASTER TES (Emissivity)
05/04/00 06/05/00 12/05/00 05/16/01
Date
50
Tabulated Results
Truth-Aster (Temps) Lake Tahoe 0.504 ºK
(0.62) Band 10 Band 11
Band 12 Band 13 Band
14 Truth-Aster (e) Lake Tahoe -0.007
(0.003) 0.002 (0.002) 0.007 (0.002) -0.007
(0.001) -0.003 (0.002) Salton Sea
-0.004 (0.005) 0.002 (0.007) 0.011 (0.009)
-0.008 (0.006) 0.001 (0.009)
Overall -0.004 (0.004) 0.002 (0.005) 0.006
(0.005) -0.004 (0.003) 0.000 (0.006)
Truth-Aster (e) Caldera 0.027
(0.001) 0.009 (0.006) 0.017 (0.006) 0.002
(0.006) 0.000 (0.006) Punaluu
-0.011 (0.006) 0.003 (0.006) -0.002 (0.004)
-0.016 (0.004) -0.015 (0.003) Saddle
0.011 (0.001) 0.009 (0.007) 0.006 (0.006)
-0.005 (0.004) -0.015 (0.004) Overall
0.009 (0.003) 0.007 (0.006) 0.007
(0.005) -0.007 (0.004) -0.010 (0.004)
51
Conclusions

• Accuracy is 1.5 K 1-sigma
• Precision 1.5 K 1 sigma (replication at one
  time/site)
• Repeatability is 1.5 K (replication at one site
  over time)
• Atmospheric effects are a major source of
  uncertainty (may be improved if MODIS atmospheric
  profiles for land surface are available)
• The standard products are validated, released,
  and ready for use