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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