a forward and inverse modeling approach using thermal imagery
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a forward and inverse modeling approach using thermal imagery
A FORWARD AND INVERSE MODELING APPROACH USING THERMAL IMAGERY Matteo Cerminara, in collaboration with Tomaso Esposti Ongaro, Sébastien Valade & Andy Harris
Time 1
Image 1
Time 2
Image 2 Image 3
Time 3
(A.2)
(A.1)
Image Processing
Electromagnetic model
time-averaged 1D Plume model
Time-averaging and resampling
z
U(z)
U
(B.1)
+
turbulent entrainment
1D balance: Mass, Momentum Energy
- Image dilatation - Image rotation
Experimental TIR Image
b(z) (z),T(z)
control volume
- Radiative heat transfer (Schwarzshild's equation) - Electromagnetic absorption (Mie's theory) - Material emissivity
Synthetic TIR Image
100
500
450 80
350
60
z [m]
300 250
40
200 20
150 100
0
80
400
Inversion model 1D fit (axis) 2D fit (image)
50
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60
300 z [m]
400
0 −200 −150 −100
100
500
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(C.1)
(B.2)
+
250
40
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(C.2)
20
150 100
0
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−50
0 x [m]
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0 −200 −150 −100
−20
Plume properties retrieval
−50
0 x [m]
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(e.g., mass eruption rate, gas content, mean particle diameter)
GRAPHICAL ABSTRACT
2
MOTIVATION Measure eruption source parameters: MER, Temp., Density, GSD… Invert data globally, using information from the whole TIR video Measure indirectly what cannot be seen directly: opaque plumes This is possible by coupling: infrared emission/absorption ⟷ fluid dynamics of volcanic plumes 3
EMISSION/ABSORPTION OF AN HETEROGENEOUS MEDIUM TIR wavelengths ≈ 7-14 μm Optical regime for d > 8 μm Absorption coefficient of particles proportional to their bulk density Schwarzschild’s equation
Optical thickness
specific absorption coefficient for particles: A1mm ≈ 1 m2/kg A0.1mm ≈ 10 m2/kg 4
VOLCANIC GASES ABSORPTION COEFFICIENTS 1
spectral response water vapor SO2 CO2
800
0.9 0.8
ACO = 5.908 m2/kg
0.7
2
600
400
104 103 102 101 100 10-1 10-2 10-3 -4 10
AH
2
0.6
2 O = 0.1145 m /kg
0.5 0.4 8
10
12
14
16
0.3
18
200
0.2 ASO = 5.139 m2/kg
0.1
2
0 8
10
12 14 wavelength [µm]
16
18
0
spectral response
specific absorption coefficent [m2/kg]
1000
Absorption coefficient of gases depends also on the camera spectral response visibility of Air with 1 g/kg of H2O is approximatively 10 km 5
Thus, having the temperature T and the phases density ρ along an optical ray allows to find the TIR intensity IL impacting the camera In volcanic ash plumes, T and ρ can be found in the 3D spatial domain through 1D integral models A fast analytical plume model is used to find T and ρ in a fast way, once 7 parameters are given at the “vent”: FORWARD APPROACH entrainment velocity radius temperature ash mass fraction water mass fraction specific absorption coefficient of the mixture (depending on GSD, and mass fractions of SO2 and CO2) 6
DATA FROM SANTIAGUITO ERUPTION OCCURRED IN 2005
Averaged image Fluctuations Time window: 45-255 s Eddy turnover time ≈ 5 s 7
INVERSION PROCEDURE A cost function is identified, measuring the “distance” between the observed and measured averaged image Its minimum is searched using the genetic algorithm, to find the best vent parameters fitting the observation, globally 8
SYNTHETIC TIR IMAGE AND DIFFERENCE WITH OBSERVATION 100
500
10
450
9
400
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350
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300
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250
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80 400 350 60
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z [m]
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0 50 0 −200 −150 −100
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9
SYNTHETIC VS OBSERVED ALONG THE PLUME AXIS 110 100 90 80
Plume radius: Mass flux: Velocity: Temperature: Air mass fraction: H2O mass fraction: Ash mass fraction: GSD Sauter diameter:
23±1 m 13±2 tons/s 7.5±0.9 m/s 103±3° C 40±6 % 20±3 % 41±6 % 2.3±0.8 mm
Mass:1.9±0.4 Ktons 1/3 H2O 2/3 Ash d = 450 μm, σ=500 μm (log-normal) D = 2.34±0.09 (power law) 12
INPUT DATA NEEDED
Averaged TIR image of the plume: min. time window ≈ 10D/U TIR image of the background atmosphere (good visibility needed) Atmospheric condition profiles SO2/H2O and CO2/H2O mass fractions (for GSD retrieval)
FUTURE DIRECTIONS Compare with steam-ash experimental plumes in air Application of the technique to other volcanic eruptions Fast and robust method
application to real-time monitoring
Use TIR data with thinner wavelength window Couple the TIR model with 3D plume models (ASHEE) synthetic TIR videos of the plume (umbrella?)
