Download Document

High-temperature mixture-modeling:
retrieving lava surface temperatures
from infrared satellite data
Robert Wright
Hawai’i Institute of Geophysics and Planetology
Lecture topics
Pre-processing – isolating the thermally emitted radiance
Single-band temperature retrievals
Bi-spectral temperature retrievals
Multi/Hyper-spectral temperature retrievals
Pre-processing
Ll
• The satellite measures the
spectral radiance from the lava
surface which we know is related
to its temperature, but….
• The spectral radiance is not
directly related to the lava surface
temperature because it is
modulated by….
• Surface emissivity (< unitary)
• Atmospheric absorption (< unitary)
• Solar radiation (< 4 mm)
t
e
Tk
Converting DN to Ll
• Satellite measures spectral radiance but stores digital numbers
• First, need to convert sensor response (DN) to spectral radiance (Ll)
• Sometimes this is already done for you (e.g. MODIS Level 1B product)
MODIS band 21 (3.959 mm)
27.38 W m-2 sr-1 mm-1
5.70 W m-2 sr-1 mm-1
Converting DN to Ll
• Or you might have to do it…..
• e.g. Landsat Thematic Mapper (TM)
Ll = DNl[(Lmaxl – Lminl)/255] +Lminl
(mW cm-2 sr-1 mm-1)
where Lminl and Lmaxl are given by….
Band
1
2
3
4
5
7
Lminl
-0.15
-0.28
-0.12
-0.15
-0.037
-0.015
Lmaxl
15.21
29.86
20.43
20.62
2.719
1.438
TM band 5 (2.22 mm)
DN = 203
Night-time vs. day-time data
Mayon
• At wavelengths shorter than ~4 mm
Earth’s surface reflects increasing
amounts of energy
• Active lavas emit energy prodigiously at
these wavelengths
• So when using short-wave infrared data,
we need to isolate the thermally emitted
portion of the at-satellite radiance before
we can invert measurements of spectral
radiance to obtain temperature
Erta Ale
The contribution of sunlight
Wooster and Kaneko, 2001
• Dacite at 360 °C (left) and 220 °C (right)
• Solid curve = reflected radiance; dashed curve = emitted radiance
• Temperatures chosen so that emitted component equals reflected
Correcting for the reflected light component
• Simplest method: use lab reflectance spectra to deduce reflection component
• But if we don’t know this (or can’t assume it is valid) need to derive a scene-dependent
correction from the image itself
“Mean” method
• Choose sample of pixels containing similar
material but which are not emitting energy at
the wavelengths employed
• Determine mean reflectance of these pixels
• Subtract from the hot-spot pixels to isolate the
thermally emitted radiance
“Per-pixel” method – preferred
• Choose sample of pixels containing similar
material but which are not emitting energy at
the wavelengths employed
• Determine empirical relationship between
VNIR and SWIR wavelengths
• Use this on a pixel-by-pixel basis to isolate
the volcanic signal
High temperature radiometry
• Now we can convert (thermal) spectral radiance to kinetic temperature by inverting the Planck
function
Tkin =
C2
lln[1+ C1/(l5Ll)]
• And we can do this from space or using field-based instruments
• But first……
Thermal characteristics of active lava surfaces
• What do we mean by the “ temperature” of an active lava? (see Pinkerton, 1993)
Short-wave vs long-wave infrared radiometry
Landsat TM
7, 5, 3 (RGB)
• High-temperature radiators emit lots of EMR at short-wave infrared wavelengths
• Short-wave data better than long-wave data for remote sensing high temperature surfaces
• The reverse is true for lower temperature surfaces
Single-band radiometry
• We can use Ll measured over a single waveband to calculate the temperature of the emitting
surface
• This assumes that the pixel/Instantaneous Field of View/Field of View is thermally homogenous
• In reality Pixels/IFOV/FOV are rarely thermally homogenous
• Long wavelengths less accurate for high temperatures
Field radiometer data: Santiaguito
Sahetapy-Engel et al., 2004
Multi-band radiometry: un-mixing mixed pixels
• Active lavas rarely thermally homogenous
• Measured Ll integrated over all radiators present
within the pixel at the time of sampling
n
Ln(l) = SfiL(l, Ti)
i=1
• A single temperature will fail to describe the actual
sub-pixel temperature distribution
• So w need methods for un-mixing the mixed thermal
emission spectrum
The “dual-band” method
• Model assumption: active lava surfaces can be described in terms of an isothermal crust within
which isothermal cracks expose molten lava (Rothery et al., 1988)
Tc @ 1-fh
Th @ fh
L1 = fhL(l1, Th) + fcL(l1, Tc)
L2 = fhL(l2, Th) + fcL(l2, Tc)
• Radiance measured at a single wavelength is weighted
average of that emitted by these two end-members
• Three unknowns: two measurements of radiance at
separated wavelengths allows the sub-pixel temperature
distribution to be determined if one of the unknowns can be
assumed
Dual-band solutions
• Model accommodated Landsat TM sensor design, which was the best available at the time
• Only two wavebands are available with TM at any time (bands 5 & 7; 1.65 mm & 2.22 mm)
• It is common to assume Th in order to to calculate Tc and f , as Th is less variable than Tc or f
(Oppenheimer, 1991)
850
750
650
550
L5 = fhL(l5, Th) + fcL(l5,
Tc )
L7 = fhL(l7, Th) + fcL(l7,
Tc )
Th = 900°C
TM band 5
TM band 7
30 m
Tc @ 1-fh
450
Th @ fh
350
55
105
250
150
50 -6
10
5
5
10-5
55
10-4
255
255
105
f
10-3
10-2
10-1
Bi-spectral temperature retrievals
Spectral radiance (Wm-2sr-1mm-1)
Issues
• The TM sensor saturation/dynamic range/spectral resolution limits measurement range
• Is the assumption of isothermal crust and cracks realistic?
1000
500°C
100
300°C
1000
200°C
10
150°C
1
0.1
0
1
2
Wavelength (mm)
1
2
3
3
The thermal complexity of real lava surfaces
200
400
600
800
1000
1200
Temperature (°C)
• Real lava surfaces exhibit a continuum of temperatures between eruption temperature and
ambient
• Impossible to resolve this level of complexity
• How well does the dual-band method perform?
• How complex does the mixture-modelling have to become in order to characterise this
distribution
Characterising sub-pixel temperature
distributions
• High resolution FLIR images
• Calculate integrated emission spectrum from
FLIR data
• Un-mix this spectrum to retrieve the size and
temperature of the sub-pixel “components”
n
Ln(l) = SfiL(l, Ti)
i=1
Resolving sub-pixel temperature distributions
• Sophistic to talk of resolving discrete temperatures
• In fact, we are only concerned with which value of n will allow us to retrieve a set of T and f that
convey the main statistical properties of the sub-pixel temperature distribution (mean, modes,
range, skewness)
• n = 5 to 7 seems to do it (model spectra computed from field data)
• Can’t really work with hypo-spectral data, which leads us to……
• Field spectrometers
• Hyperspectral imaging
Field spectrometers
Mount Etna, October 1998
• Analytical Spectral Devices FieldSpec FR (3-10 nm, 0.35 – 2.5 mm)
• Can resolve the size and temperature of the emitting objects in the manner previously
described
• Curve fitting algorithms rely on the difference in radiance between several wavelengths
rather than the absolute flux, as field-spectrometers difficult/impossible to calibrate in the field
• Use for field validation of satellite data over active volcanic features
Space-based hyperspectral imaging
• Earth Observing-1 Hyperion
• Launched November 2000
• 242 contiguous bands between 0.357 and 2.57 mm
at 10 nm resolution
• 196 calibrated and unique bands
• Technology testing mission (scheduled life 18 months)
• Still collecting data; many volcano images available
Night-time Hyperion data of active lava lake
Mixture-modelling with Hyperion
• Assume nothing in the fit (0 < T < 1200 °C, 0.0 < f < 1.0)
• Perform least-squares minimisation of corrected Hyperion spectra to model spectra described
by
n
Ln(l) = SfiL(l, Ti)
i=1
• Minimisation routine converges to a one or two component solution
• Why? Noisy data/limited spectral coverage/signal to noise ratio/uncertainty in e and t
Other hyperspectral resources
• AVIRIS
• Airborne spectrometer
• 224 contiguous bands between 400 and 2500 nm
• MIVIS
• Airborne spectrometer
• 102 bands 0.43 – 12 mm (VIS = 20; NIR = 8; MIR = 64; TIR = 10)
• Many others (all airborne); HYDICE, CASI…http://hydrolab.arsusda.gov/rsbasics/sources.php
Issues to be resolved
Sensor measurement range
• Sensor saturation is catastrophic when using hypo-spectral data
• It’s also a problem when using hyper-spectral data
• Dynamic ranges tinkered with in ASTER design (but no substantive improvement)
• Logarithmic or dual gain settings required to provide unsaturated data for the most active lava
surfaces (e.g. large channel-fed ‘a‘ā)
Spectral resolution: SWIR/MIR/TIR retrievals
• Ideally, data in the 4 and 12 mm atmospheric window would also be available as this would
• Provide information regarding the temperature of lava with T < ~100 ºC
• Allow for more robust least-squares temperature solutions
Conclusions
• Detailed temperature retrievals offer the potential for constraining lava flow thermal budgets,
surface integrity, dome surface structure, calibrating low spatial resolution thermal observations
• Methods for doing this have been established and have evolved and been improved