Basic principles of volcano radiometry

Robert WrightHawai’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:

• Lava flow cooling and motion• Volcanic energy/magma budgets• Lava eruption rates

• 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

Powe

r (M

W)

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

M = spectral radiant exitance (W m-2 m-1)T = temperature (K)= 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• 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)

M = 2hc2

5[exp(ch/kT)-1]

As before but……

M = spectral radiant exitance (W m-2 m-1)*C1 = 3.74151 108 W m-2 m-4

*C2 = 1.43879 104 m K= wavelength (m)

*of C1 and C2, 0.0027% and 0.0042%, respectively

Quantifying Blackbody Radiation

• A more useful form….

M = C1

5[exp(C2/T)-1]

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

• Stefan-Boltzmann Law• The radiant power from a blackbody is proportional to the fourth power of temperature

m = b/T

m = m b = 2898 m K

MT =T

MT = W m-2

= 5.669 10-8 W m-2 K-4

Quantifying Blackbody Radiation

Wien’s Law: turning point of the Planck function

Stefan’s Law: integral of the Planck function

• Planck’s Blackbody Radiation Law: spectral distribution of energy radiated by a blackbody as a function of temperature

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 m

Spectral radiance• Satellite sensors measure spectral radiance, not spectral exitance

L = M/

• L is the power emitted per unit area, per unit solid angle, in a given wavelength interval

• Common units are W m-2 sr-1 m-1

• Regarding angles……

• Degree, radian, steradian (sr)

• A steradian is the ratio of the spherical area to the square of the radius

• As/r2 = 4w

• 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 m)• 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

• So far, so good, but…….

• Planck’s blackbody radiation law describes the spectral emissive power of a blackbody

T = C2

ln[1+ C1/(5L)]

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

• 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

Temperature and emissivity

• ASTER (14, 12, 10; R, G, B)

• Reds = rocks higher in silica• Blues = rocks lower in silica (basalt)

Erta Ale volcano, Ethiopia

Blackbodies, Greybodies, & Selective Radiators

• Emissivity – capability to emit radiation

• Blackbody: = 1• Whitebody: = 0• Greybody: < 1• Selective radiator < 1

• Can be determined in the lab (ask Mike)

() = M(material, K)

M(blackbody, K)

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

ln[1+ c1/(5L)]

• Calculate atmospheric transmissivity over a wavelength range using radiative transfer model

e.g. MODTRAN/LOWTRAN

• Model specifies atmospheric properties

• Season (summer/winter/spring/fall)• Elevation• Location (maritime, urban, polar…)• Aerosols (urban, agricultural)• Gas concentrations (e.g. CO2 ppm)• Scattering model (i.e. multiple or single)

L[T(surface)]

T, H2O, SO2…. Altit

ude

L*

Atmospheric correction methods

• Radiative transfer modelling with parameters determined by simultaneous meteorological (radiosonde) data

Atmospheric correction methods

L[T(surface)]

T, H2O, SO2…. Altit

ude

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?