Basic principles of volcano radiometry

1. Basic principles of volcano radiometry Robert Wright Hawai’i Institute of Geophysics and Planetology

2. Topics • Heat and temperature • Measuring lava temperatures remotely • Measuring actual lava temperatures remotely

3. 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

4. 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 Power (MW)

5. 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

6. Quantifying Blackbody Radiation 2phc2 Ml = l5[exp(ch/lkT)-1] • 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 = 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

7. Quantifying Blackbody Radiation • A more useful form…. C1 Ml = l5[exp(C2/lT)-1] • As before but…… • Ml = spectral radiant exitance (W m-2mm-1) • *C1 = 3.74151  108 W m-2mm-4 • *C2 = 1.43879  104mm K • = wavelength (mm) • *s of C1 and C2, 0.0027% and 0.0042%, respectively

8. 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 lm = b/T lm = mm b = 2898 mm K MT = sT4 MT = W m-2 s = 5.669  10-8 W m-2 K-4

9. 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

10. 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

11. Wavelengths of interest • Given the temperatures of terrestrial lavas, we are interested in the wavelength region from ~1.0 to 14 mm

12. 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-1mm-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

13. 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

14. Calculating temperature from spectral radiance C2 T = lln[1+ C1/(l5Ll)] • 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

15. 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

16. 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

17. Erta Ale volcano, Ethiopia • ASTER (14, 12, 10; R, G, B) • Reds = rocks higher in silica • Blues = rocks lower in silica (basalt)

18. Blackbodies, Greybodies, & Selective Radiators • Emissivity – capability to emit radiation • Blackbody: e = 1 • Whitebody: e = 0 • Greybody: e < 1 • Selective radiator el < 1 • Can be determined in the lab (ask Mike) Ml(material, K) e(l) = Ml(blackbody, K)

19. 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/

20. 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 c2 Tkin= lln[1+ c1tlel/(l5Ll)]

21. Atmospheric correction methods • 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*l Altitude t T, H2O, SO2…. Ll[T(surface)]

22. Atmospheric correction methods • Radiative transfer modelling with parameters determined by simultaneous meteorological (radiosonde) data L*l Altitude t T, H2O, SO2…. Ll[T(surface)]

23. The transmissivity of a model atmosphere • MODTRAN very easy to use, but… • It is a model!

24. 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

25. 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?