Retrieval of Sizes and Total Masses of particles in Volcanic Clouds Using AVHRR Infrared Bands

Shiming Wen and William I. Rose
Department of Geological Sciences and Engineering
Michigan Technological University
Houghton, MI 49931

Poster presented at American Geophysical Union, Fall 1993 Meeting

ABSTRACT

The AVHRR sensor on polar orbiting NOAA satellites can discriminate between volcanic clouds and meteorological ones using two-band data in the thermal infrared. This paper is aimed at developing a retrieval of the particle sizes, optical depth and total masses of particles from AVHRR two-band data of volcanic clouds. Radiative transfer calculations are used with a semi- transparent cloud model that is based on assumptions of spherical particle shape, a homogeneous underlying surface and a simple thin cloud parallel to the surface. The model is applied to observed AVHRR data from a 13 hour old drifting cloud from the 19 August 1992 eruption of Crater Peak/Spurr Volcano, Alaska. The AVHRR data fit in the range of results calculated by the model, which supports its credibility. According to the model results, the average of effective particle radius in the test frame of this cloud is in the range of 2 to 2.5 um, the effective emissivity averages 0.6 and the optical depth is about 0.60 - 0.65. The total estimated mass of ash in the air amounts to 0.24 - 0.31 x 10^6 tons, which is about 0.7- 0.9% of the mass measured in the ashfall blanket. Sensitivity tests show that the mass estimate is more sensitive to the assumed ash size distribution than is to the ash composition.

BASIC THEORY

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A linear model for observed radiances:

Assumptions:

  1. The cloud approximates a planar homogeneous cloud layer parallel to the surface.
  2. The background surface is homogenous.
  3. The atmosphere above the cloud and between the surface and the cloud are clear window.

    (a)Radiative transfer equation

    (b)Eddington's approximation

    (c)Selected size distribution of particles:

    (d)Estimation of the total masses:

    (a) (b)

    (c) (d)

    THREE-BAND TEMPERATURE DIFFERENCE MODEL

    Assumptions and conditions:

    1. Silicates are the only kind of particle in the volcanic cloud, and the refractive index is from Andesite (Pollack et al., 1973).
    2. The shape of volcanic particles is spherical , therefore Mie theory can be used to calculate extinction cross section (sigma_e), asymmetric parameter (g), and single scattering albedo.
    3. The particle size distribution, n(r), is uniform and monodisperse within each pixel.
    4. The volcanic clouds are continuous, i.e. Ac=1.
    5. Knowing surface temperature: Ts=273 K
    6. AVHRR infrared bands: Band3 (3.55-3.95 um), Band4 (10.3- 11.3 um), Band5 (11.5-12.5 um).

      (a)Cloud-top temperature retrieval model

      (b)Particle radius retrieval model

      (c)Optical depth retrieval model

      (a) (b) (c)

    TWO-BAND TEMPERATURE DIFFERENCE MODEL

    (a)AVHRR band4 image of Spurr volcanic clouds The AVHRR Band 4 image of the Crater Peak/Spurr eruption cloud, August 19, 1992, 1338 GMT. The center square is the study frame, with an area of about 165 km 110 km. In the central part of the cloud shown Ac=1 for all pixels but at the edges sometimes this is not true.

    (b)Two-band temperature difference model Two-band temperature difference model at 10.8 m and 12 m. The near horizontal solid lines represent different effective radii, and the near vertical dashed lines represent the dependence of optical depth at 10.8 m with particle radius.

    (a) (b)

    (c)Retrieval of optical depth

    (d)Retrieval of effective radius

    (c) (d)

    DEPENDENCE OF REFRACTIVE INDEX

    Refractive index of different samples

    Band4 (Real,Imaginary), Band5 (Real, Imaginary)

    1. Andesite(54.15% SiO2)---- ( 2.0534, 0.60897),(1.8392, 0.13786)
    2. Basalt(53.25% SiO2)---- (2.1848 ,0.48812),(1.9051, 0.14670)
    3. Basaltic Glass(53.45% SiO2)----(2.1241,0.71211),(2.0129, 0.24037)
    4. Obsidian-little Glass, Mt. California,r hyolite(73.45% SiO2)----(2.0085,0.27476),(1.7281 , 0.18407)
    5. Obsidian-Lake County Oregon, rhyolite(76.20% SiO2)----(2.0268, 0.27882), (1.7410, 0.18462)
    6. Volcanic dust: two samples are averaged. The andesitic Irazu ash sampled during ashfall is dark grey with feldspar,and the Hawaii sample was lightly weathered vesicular basaltic glass ----(1.9700, 0.3700),(1.8000,0.18000)

      (a)refractive index of basalt The two-band temperature difference model with uniform size distribution and the Basalt (sample 2) refractive index.

      (b)rafractive index of basalt-glass The two-band temperature difference model with uniform size distribution and the Basalt glass (sample 3) refractive index.

      (c)refractive index of obsidian The two-band temperature difference model with uniform size distribution and the Obsidian (sample 4) refractive index.

      (d)refractive index of dust The two-band temperature difference model with uniform size distribution and the Volcanic dust (sample 6) refractive index.

      (a) (b)

      (c) (d)

      Pixel-scale retrieval of masses for different samples:

    DEPENDENCE OF SIZE DISTRIBUTION

    Efficiency facters for differnt size distributions

    Relationship of effective radius and efficiency factors at 10.8 m for different size distributions of particles. (1) (solid line ) is associated with uniform distribution, (2) (dotted line) with gamma, and (3) (dashed line) with lognormal distribution.

    (a)lognormal distribution

    (b)gamma distribution

    (a) (b)

    Frame scale retrieval of masses for different size distributions

    Mass calculations for different refractive index and distributions. The relatively higher calculated masses is due to the assumption of lognormal size distribution of particles, and lower calculated masses is due to the assumption of the volcanic ashes only containing glassy basalt component.

    CONCLUSION

    1. Volcanic clouds have negative brightness temperature differences (band 4 - band 5) only if they have a dominance of particles with radius less than 5 um.
    2. Our model works best when there is large difference between the temperature of the underlying surface and the volcanic cloud. The lowest temperature difference (band 4 - band 5) of the volcanic cloud is a linear function of the temperature difference between the underlying surface and the volcanic clouds (Ts - Tc).
    3. This method can be used to interpret volcanic clouds with a dominant effective radius between 0.8 and 4.3 m for uniform size distribution, between 0.1 and 17 um for lognormal size distribution.
    4. The mean radius and the optical depths within the test frame of a 13 hour old August 1992 Crater Peak/Spurr volcanic cloud are determined to be 2.8 m and 0.66, respectively, based on the two-band model. If lognormal size distribution is considered, the average of particle radius is about 0.62 to 0.78 m, the estimate of the mass of the volcanic cloud particles is about 42 - 56 X 10^3 tons in the frame, and about 0.24 - 0.31 106 tons in the whole cloud, which is about 0.7 - 0.9% of the total volcanic ash measured in the deposited ash blanket (36x106 tons).
    5. The mass estimate is more sensitive to the assumed ash size distribution than it is to the ash composition.