Basic principles of volcano
radiometry
Robert Wright
Hawai’i Institute of Geophysics and Planetology
Topics
• Heat and temperature
• Measuring lava temperatures remotely
• Measuring actual lava temperatures remotely
What is “temperature”?
• Internal energy = microscopic energy (kinetic + potential) associated with the random,
disordered motion of atoms and molecules contained in a piece of matter
• “Heat” is this energy (or part of it) in transit
• When a body is heated its internal energy increases (either kinetic or potential)
• Temperature = measure of average kinetic energy of the molecules of a substance
Why would we want to quantify temperature?
• Volcanism synonymous with heat
• Knowledge of the temperature of an active lava
body allows us to quantify:
• Variations in thermal energy output have been
shown to be a proxy for changes in the intensity of
volcanic eruptions, and can be used to track the
development of eruptions, and transitions between
eruptive phases
• Measurements of thermal emission allow the
chemistry of volcanic materials to be determined
Power (MW)
• Lava flow cooling and motion
• Volcanic energy/magma budgets
• Lava eruption rates
How can we measure temperature?
• Can perform in-situ measurements, although this has its drawbacks
• Localised in space and time
• Dangerous (or at least uncomfortable)
• Not as accurate as you might think (equilibration times, instrument “trauma”….)
• Fortunately, we can calculate the temperature of an object without touching it
Quantifying Blackbody Radiation
• Collisions cause electrons in atoms/molecules to become excited, and photons to be emitted
• In this way internal energy converted into electromagnetic energy
• Heated solids produce continuous spectra dependent only on temperature
• How can we quantify the relationship between internal kinetic energy (temperature)
and emission of radiation?
• Planck’s blackbody radiation law is a mathematical description of the spectral distribution of
radiation emitted from a perfect radiator (blackbody)
Ml =
2phc2
l5[exp(ch/lkT)-1]
Ml = spectral radiant exitance (W m-2 m-1)
T = temperature (K)
l= wavelength (m)
c = speed of light = 2.997925  108 m s-1
h = Planck’s constant = 6.6256  10-34 W s2
k = Boltzmann’s constant = 1.38054  10-23 W s K-1
Quantifying Blackbody Radiation
• A more useful form….
Ml =
C1
l5[exp(C2/lT)-1]
As before but……
Ml = spectral radiant exitance (W m-2 mm-1)
*C1 = 3.74151  108 W m-2 mm-4
*C2 = 1.43879  104 mm K
l= wavelength (mm)
*s of C1 and C2, 0.0027% and 0.0042%, respectively
Quantifying Blackbody Radiation
• Wien’s Displacement Law
• As the temperature of the emitting surface increases so the wavelength of maximum
emission shifts to shorter wavelengths
lm = b/T
lm = mm
b = 2898 mm K
• Stefan-Boltzmann Law
• The radiant power from a blackbody is proportional to the fourth power of temperature
MT = sT4
MT = W m-2
s = 5.669  10-8 W m-2 K-4
Quantifying Blackbody Radiation
• Planck’s Blackbody Radiation Law: spectral distribution of energy radiated by a blackbody
as a function of temperature
Wien’s Law: turning point of the Planck function
Stefan’s Law: integral of the Planck function
Quantifying Blackbody Radiation
• The spectral radiant exitance from an active lava varies by orders of magnitude
• Remote measurements of radiated energy provide a route for monitoring thermal emission and
quantifying surface temperature
Wavelengths of interest
• Given the temperatures of terrestrial lavas, we are interested in the wavelength region from
~1.0 to 14 mm
Spectral radiance
• Satellite sensors measure spectral radiance, not spectral exitance
Ll = Ml/p
• Ll is the power emitted per unit area, per unit solid angle, in a given wavelength interval
• Common units are W m-2 sr-1 mm-1
• Regarding angles……
• Degree, radian, steradian (sr)
• A steradian is the ratio of the spherical area to the square
of the radius
• As/r2 = 4pw
• We aren’t interested in hemispherical emissive power, rather the
emissive power in a particular direction
Satellite radiometry
• Radiometry: measurement of optical radiation (0.01 – 1000 mm)
• Satellite radiometry: radiometry from space!
• Many different satellite sensors currently in orbit that
can make the appropriate measurements
• But satellite radiometry of volcanoes is complicated by
two things:
• Lavas are not blackbodies
• Earth has an atmosphere
Calculating temperature from spectral radiance
• Invert modified Planck function to obtain temperature from spectral radiance
T=
C2
lln[1+ C1/(l5Ll)]
• So far, so good, but…….
• Planck’s blackbody radiation law describes the spectral emissive power of a blackbody
What is a blackbody?
• A perfect radiator, “one that radiates the maximum number of photons in a unit time from a unit
area in a specified spectral interval into a hemisphere that any body at thermodynamic
equilibrium at the same temperature can radiate.”
• All incident radiation is absorbed – Ideal absorber
• Emits energy at all wavelengths and in all directions at maximum rate possible
for given temperature – Ideal radiator
Temperature and emissivity
• Objects with the same kinetic temperature can have very different radiative temperatures
• Differences in apparent temperature of bodies with the same kinetic temperature tells us about
differences in their emissivity
• Temperature of a surface can’t be determined from spectral radiance unless we know its
emissivity
Erta Ale volcano, Ethiopia
• ASTER (14, 12, 10; R, G, B)
• Reds = rocks higher in silica
• Blues = rocks lower in silica (basalt)
Blackbodies, Greybodies, & Selective Radiators
• Emissivity – capability to emit radiation
Ml(material, K)
e(l) =
Ml(blackbody, K)
• Blackbody: e = 1
• Whitebody: e = 0
• Greybody: e < 1
• Selective radiator el < 1
• Can be determined in the lab (ask Mike)
Emissivity of some common lavas
• If you know how the emissivity of your target varies as a function of wavelength you can correct
for its effect
• Libraries of spectral reflectance (emissivity) available at http://speclib.jpl.nasa.gov/
Almost there……
• Inversion of Planck function only gives Apparent Radiant Temperature
• Apparent Radiant Temperature < True Kinetic Temperature
• Must account for emissivity AND the imperfect transmission of radiance by the atmosphere
Tkin =
c2
lln[1+ c1tlel/(l5Ll)]
Atmospheric correction methods
• Calculate atmospheric transmissivity over a wavelength range using radiative
transfer model
e.g. MODTRAN/LOWTRAN
• Model specifies atmospheric properties
T, H2O, SO2….
Ll[T(surface)]
Altitude
• Season (summer/winter/spring/fall)
• Elevation
• Location (maritime, urban, polar…)
• Aerosols (urban, agricultural)
• Gas concentrations (e.g. CO2 ppm)
t
• Scattering model (i.e. multiple or single)
L*l
Atmospheric correction methods
• Radiative transfer modelling with parameters determined by simultaneous meteorological
(radiosonde) data
t
T, H2O, SO2….
Ll[T(surface)]
Altitude
L*l
The transmissivity of a model atmosphere
• MODTRAN very easy to use, but…
• It is a model!
The transmissivity of real atmospheres
• The effect of the atmosphere varies
depending on the geography of the
volcano
• Volcanoes in low, wet, regions more
affected than those in cold/dry regions
Thermal remote sensing of active volcanoes
• Topics for the rest of the day:
• Which satellite sensors provide the
necessary data?
• How can we analyse lava surface
temperatures, physical/chemical properties
in detail using these data?
• How can these radiance/temperature
data be used for detecting and monitoring
volcanic thermal unrest?