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

Tk Tk L e t Pre-processing 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  m)

Converting DN to L Satellite measures spectral radiance but stores digital numbers First, need to convert sensor response (DN) to spectral radiance ( L ) Sometimes this is already done for you ( e.g. MODIS Level 1B product) W m -2 sr -1  m W m -2 sr -1  m -1 MODIS band 21 (3.959  m)

e.g. Landsat Thematic Mapper (TM) L = DN [( L max – L min )/255] + L min (mW cm -2 sr -1 m m -1 ) where L min and L max are given by…. Band L min L max Or you might have to do it….. Converting DN to L TM band 5 (2.22  m) DN = 203

Night-time vs. day-time data Erta Ale Mayon At wavelengths shorter than ~4  m 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

The contribution of sunlight 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 Wooster and Kaneko, 2001

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 And we can do this from space or using field-based instruments But first…… T kin = C2C2 ln[1+ C 1 /( 5L l )]

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

We can use L l 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 Single-band radiometry

Field radiometer data: Santiaguito Sahetapy-Engel et al., 2004

i=1 Multi-band radiometry: un-mixing mixed pixels Active lavas rarely thermally homogenous Measured L integrated over all radiators present within the pixel at the time of sampling 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 n L n ( ) = S f i L (, T i )

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) 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 The “dual-band” method T f h T 1- f h L 1 = f h L ( 1, T h ) + f c L ( 1, T c ) L 2 = f h L ( 2, T h ) + f c L ( 2, T c )

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 m m & 2.22 m m) It is common to assume T h in order to to calculate T c and f, as T h is less variable than T c or f (Oppenheimer, 1991) f T c (°C) T h = 900°C TM band 5 TM band 7 L 5 = f h L ( 5, T h ) + f c L ( 5, T c ) L 7 = f h L ( 7, T h ) + f c L ( 7, T c ) 30 m T f h T 1- f h

Wavelength (  m) Spectral radiance (Wm -2 sr -1 m m -1 ) 500°C 300°C 200°C 150°C Bi-spectral temperature retrievals Issues The TM sensor saturation/dynamic range/spectral resolution limits measurement range Is the assumption of isothermal crust and cracks realistic?

The thermal complexity of real lava surfaces 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

i=1 n L n ( ) = S f i L (, T i ) 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”

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

Mount Etna, October 1998 Field spectrometers Analytical Spectral Devices FieldSpec FR (3-10 nm, 0.35 – 2.5  m) 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 contiguous bands between and 2.57  m 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

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 Minimisation routine converges to a one or two component solution Why? Noisy data/limited spectral coverage/signal to noise ratio/uncertainty in  and  Mixture-modelling with Hyperion i=1 n L n ( ) = S f i L (, T i )

Other hyperspectral resources AVIRIS Airborne spectrometer 224 contiguous bands between 400 and 2500 nm MIVIS Airborne spectrometer 102 bands 0.43 – 12  m (VIS = 20; NIR = 8; MIR = 64; TIR = 10) Many others (all airborne); HYDICE, CASI…

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  m 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