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Supplementary electronic material
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Related to the manuscript “Pyroclastic flow erosion and bulking processes: comparing field-
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based vs. modeling results at Tungurahua volcano, Ecuador” (by J. Bernard et al.)
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1. Image acquisition
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Images of the deposits were captured at right angles to the outcrop surface with a 12 Mpx
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digital camera. Several images were obtained using different zoom magnifications on a same
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site to capture grain shape and componentry on a large size range (~50 cm to ~0.2 cm). A 45
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x 45 cm graduate square was used for scale on each image, and allowed us to check for
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distortion effects (Figure 2 of the main text).
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2. Detailed protocol
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Our image analysis protocol comprised 3 steps including masking, segmentation and object
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recognition. Exclusion masks are defined on each image to ensure that 1) a single clast is not
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counted twice on two images of the same part of an outcrop captured at different
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magnification, and 2) possible optical distortion near the edges and corners of the images are
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discarded (correction of the such distortion is performed in Sarocchi et al., 2011). The high
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resolution images are then segmented to obtain discrete representative clast populations
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according to their lithological origin. Current automated recognition softwares (e.g. van der
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Berg et al., 2002 for thin sections) are unable to perform accurate object recognition of
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images from natural outcrops because of uneven brightness, low color contrasts and
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overlapping object contacts (Jutzeler et al., 2012). For this reason, we manually isolated on
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the computer screen all recognizable clasts using PhotoshopTM CS5 software suite. Discarding
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all objects smaller than 20 pixels in diameter (which corresponds to an error on the area of
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less than 1% in the case that one pixel of the object is misrepresented, cf. Shea et al., 2010),
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our protocol yields object populations in the range of 1000-3400 clasts per sample.
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3.
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The digital sampling protocol based on acquisition and treatment of images of thin sections,
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rock cuts and sedimentary deposits is a powerful geoscientific tool (e.g. vesicle and crystal
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size distributions: Shea et al., 2010; clast-fiamme shape and size distributions: Jutzeler et al.,
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2012; optical granulometry: Sarocchi et al., 2011; and references therein). The segmented
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images obtained above yield a two dimensional (2D) information on three dimensional (3D)
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objects. Extraction of 2D data (circle equivalent area and diameter) of each clast is conducted
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with SPO (Shape Preferred Orientation) image analysis software (Launeau and Robin, 1996).
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The scaling tool (Figure 2) is then used to standardize clasts parameters of all images of a
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same digital sample by converting pixel sizes into centimeters. To convert 2D to 3D
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information we performed a stereological correction based on the mathematical approach of
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Sahagian and Proussevitch, (1998, and references therein) implemented by Shea et al. (2010),
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and illustrated in Figure 3. The geometrical bin size of Sahagian and Proussevitch (1998), in
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which each size bins is 10-0.1 time smaller than the previous one, is used between 0.05 and
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62.95 cm.
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The clasts whose apparent diameter occurs in a size bin i are automatically counted to
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determine the object number density per unit area NAi (cm-2, Figure 3). The whole dataset of a
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given digital sample is merged applying the magnification cutoff technique of “minimized
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ΔNA” solution of Shea et al., 2010 (Figure 3). Detailed stereology unfolding equations used in
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this study assume spherical particles. For a given digital sample, the number density NVi of
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spherical objects of size i per unit volume is obtained by correcting the whole merged NAi
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value extracted from 2D data with 1) the probability of intersection Pi of a sphere through its
Stereological conversions
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̅ ˈ) of
maximum diameter in a bin of given size and 2) the mean projected height (𝐻
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Underwood (1970), which corresponds to the characteristic diameter of each bin (Sahagian
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and Proussevitch, 1998; Shea et al., 2010). The volume fraction Vƒi of a clast population of
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size i in a given bin is expressed by multiplying NVi by the volume of a single equivalent
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sphere of the considered bin. Our large set of high resolution images allows us for each digital
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sample to extract large clast populations (in this study, > 30 objects) on an extended size
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range (as recommended by Shea et al., 2010). Each image includes areas, called here “digital
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background” where fragments are too small to be identified in the componentry analyses. The
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obtained Vƒi values given as a function of the geometrical binning are converted to 3D grain
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size on phi-scale (ϕ = - log2 (d), Krumbein (1938) where d is the clast diameter (in mm).
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4. Componentry and conduit-derived correction
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Deciphering the control of erosion on PDC dynamics requires estimating the amount of
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juvenile (essential) and non-juvenile (accessory and accidental) material in the deposits.
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Based on the identification keys detailed in the main text body, a componentry nature (i.e.
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juvenile vs. non-juvenile) is assigned to all outlined clasts during the segmentation step. 2D
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componentry ratios are reconstructed for each sample (Figure 3) and converted to 3D data
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using the stereological unfolding application. Please, see the main text for the description of
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clast’s nature.
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Moreover, our data are corrected from conduit-derived non-juvenile fragments using
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componentry analysis performed by Eychenne et al. (2013) on tephra fall deposits from the
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same 2006 eruption. Our mass balance results isolate thus only the non-juvenile fraction in the
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2006 PDC deposits which derives from the eroded substratum.
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5.
Mass conversion
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For a given 0.5  interval, the mass of each componentry sub-classes (cf. section 3 above) is
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obtained by multiplying its volume fraction (obtained from the stereological suite) by its
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specific density values. Here, we used the density values measured on the coarsest fall
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particles of the same 2006 Tungurahua eruption by Eychenne and Le Pennec (2012) which
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are: 1) for juvenile products, 1.7 g.cm-3 for scoriaceous andesite and 2.6 g.cm-3 for blocky
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andesite, 2) for non-juvenile products, 2.7 g.cm-3 for old lavas, 2.5 g.cm-3 for oxidized
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material and 1.0 g.cm-3 for pumices.
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The mass fraction corresponding to the whole recognized part of the digital sample is
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calculated by summing the mass fraction obtained at each 0.5 ϕ interval. The digital
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background fraction is used to take into account the mass proportions of the fine un-
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recognized fraction of the deposit, assuming that juvenile and non-juvenile volume and mass
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proportions in the digital background are similar to those in the smallest recognized phi class
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of the sample (usually -1 ϕ). Hall et al. (2013) found that the fine-grained fraction of the 2006
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Tungurahua PDCs (<2 mm and called matrix) can contain 5-10 vol. % lithic clasts, which is
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consistent with the values assumed here for the digital background composition.
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6. References
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Jutzeler M, Proussevitch AA, Allen SR (2012) Grain-size distribution of volcaniclastic rocks
1: A new technique based on functional stereology. Journal of Volcanology and Geothermal
Research 239-240:1-11
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Krumbein, W.C., 1938. Size frequency distributions of sediments and the normal phi curve.
Journal of Sedimentary Research, 8(3): 84-90.
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Underwood EE (1970) Quantitative stereology. Addison-Wesley Publishing CO, Reading,
Mass. 274 pp.
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van den Berg EH, Meesters AGCA, Kenter JAM, Schlager W (2002) Automated separation
of touching grains in digital images of thin sections. Computers & Geosciences 28(2):179-190