ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-9399-2016Adjusting particle-size distributions to account for aggregation in
tephra-deposit model forecastsMastinLarry G.lgmastin@usgs.govVan EatonAlexa R.DurantAdam J.U.S. Geological Survey, Cascades Volcano Observatory, 1300 SE Cardinal
Court, Bldg. 10, Suite 100, Vancouver, Washington, USASection for Meteorology and Oceanography, Department of Geosciences,
University of Oslo, Blindern, 0316 Oslo, NorwayGeological and Mining Engineering and Sciences, Michigan Technological
University, 1400 Townsend Drive, Houghton, MI 49931, USALarry G. Mastin (lgmastin@usgs.gov)28July201616149399942019January201631March201612June201614June2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/9399/2016/acp-16-9399-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/9399/2016/acp-16-9399-2016.pdf
Volcanic ash transport and dispersion (VATD) models are used to forecast
tephra deposition during volcanic eruptions. Model accuracy is limited by
the fact that fine-ash aggregates (clumps into clusters), thus altering patterns
of deposition. In most models this is accounted for by ad hoc changes to model
input, representing fine ash as aggregates with density ρagg, and a
log-normal size distribution with median μagg and standard
deviation σagg. Optimal values may vary between eruptions. To
test the variance, we used the Ash3d tephra model to simulate four deposits:
18 May 1980 Mount St. Helens; 16–17 September 1992 Crater Peak (Mount
Spurr); 17 June 1996 Ruapehu; and 23 March 2009 Mount Redoubt. In 192
simulations, we systematically varied μagg and σagg,
holding ρagg constant at 600 kg m-3. We evaluated the fit
using three indices that compare modeled versus measured (1) mass load at
sample locations; (2) mass load versus distance along the dispersal axis;
and (3) isomass area. For all deposits, under these inputs, the best-fit
value of μagg ranged narrowly between ∼ 2.3 and 2.7φ (0.20–0.15 mm), despite large variations in erupted mass
(0.25–50 Tg), plume height (8.5–25 km), mass fraction of fine (< 0.063 mm) ash (3–59 %), atmospheric temperature, and water content between
these eruptions. This close agreement suggests that aggregation may be
treated as a discrete process that is insensitive to eruptive style or
magnitude. This result offers the potential for a simple,
computationally efficient parameterization scheme for use in operational
model forecasts. Further research may indicate whether this narrow range
also reflects physical constraints on processes in the evolving cloud.
Introduction
Airborne tephra is the most wide reaching of volcanic hazards. It can extend
hundreds to thousands of kilometers from a volcano and impact air quality,
transportation, crops, electrical infrastructure, buildings, water supplies,
and sewerage. During eruptions, communities want to know whether they may
receive tephra and how much might fall. Volcano observatories typically
forecast areas at risk by running volcanic ash transport and dispersion (VATD)
models. As input, these models require information including eruption
start time, plume height, duration, the wind field, and the size
distribution of the falling particles. Of these inputs, the particle-size
distribution is perhaps the hardest to constrain.
Particle size (along with shape and density) determines settling velocity,
which controls where particles land in a given wind field. For different
eruptions, the total particle-size distribution (TPSD) can vary. Large
eruptions produce more fine ash than small ones for example; and silicic
eruptions produce more than mafic (Rose and Durant, 2009). The TPSD is
difficult to estimate (e.g., Bonadonna and Houghton, 2005), hence, estimates
exist for only a handful of deposits. Even in cases where the TPSD is known,
the raw TPSD, entered into a dispersion model, will not accurately calculate
the pattern of deposition (Carey, 1996).
This inaccuracy results from the fact that complex processes, not considered
in models, cause particles to fall out faster than theoretical settling
velocities would predict. These processes include scavenging by hydrometeors
(Rose et al., 1995a), gravitational instabilities
that cause dense clouds to collapse en masse (Carazzo and Jellinek, 2012; Schultz
et al., 2006; Durant, 2015; Manzella et al., 2015), and aggregation, in
which ash particles smaller than a few hundred microns clump into clusters.
The rate of aggregation, as well as the type and size of resulting aggregates,
depends on atmospheric processes such as ice accretion, electrostatic
attraction, or liquid-water binding, whose importance varies from place to
place.
Although one VATD model, Fall3d, calculates aggregation during transport for
research studies (Folch et al., 2010; Costa et al., 2010), no operational
models consider it. Instead, aggregation is accounted for by either setting
a minimum settling velocity in the code (Carey and Sigurdsson, 1982;
Hurst and Turner, 1999; Armienti et al., 1988; Macedonio et al., 1988), or,
in the model input, adjusting particle-size distribution by replacing some
of the fine ash with aggregates of a specified density, shape, and size
range (Bonadonna et al., 2002; Cornell et al., 1983; Mastin et al.,
2013b). These strategies will probably prevail for at least the next few
years, until microphysical algorithms replace them.
These adjustments are mostly derived from a posteriori studies, where model inputs have
been adjusted until results match a particular deposit. It is unclear how
well the optimal adjustments might vary from case to case. For model
forecasts during an eruption, we need some understanding of this
variability. This paper addresses this question, using deposits from four
well-documented eruptions. We derive a scheme for adjusting TPSD to account
for aggregation, optimize parameter values to match each deposit, and then
see how much these optimal values vary from one deposit to the next.
Background on the deposits
The IAVCEI Commission on Tephra Hazard Modeling has posted data from eight
well-mapped eruption deposits, available for use by modeling groups to
validate VATD simulations (http://dbstr.ct.ingv.it/iavcei/). Of
these, we focus on eruptions that lasted for hours (not days), where the
TPSD included at least a few percent of ash finer than 0.063 mm in diameter,
and where data were available from distal (> 35 km) sample
locations. Four eruptions met these criteria: the 18 May 1980 eruption of
Mount St. Helens, the 16–17 June 1996 eruption of Ruapehu, and the 16–17 September and 18 August 1992 eruptions of Crater Peak (Mount Spurr), Alaska.
The August Crater Peak eruption was already studied using Ash3d
(Schwaiger et al., 2012) and therefore not included here,
reducing the total to three. To these we add event 5 from the 23 March 2009
eruption of Mount Redoubt, Alaska. Although an Ash3d study was made of this
event (Mastin et al., 2013b), aggregation has been
unusually well characterized in recent years (Wallace et al., 2013; Van
Eaton et al., 2015).
Maps of the deposits investigated in this work: (a) Mount St.
Helens, 18 May 1980; (b) Crater Peak, 16–17 September, 1992; (c) Ruapehu, 17 June 1996; and (d) Redoubt, 23 March 2009. Isomass lines for Mount St.
Helens were digitized from Fig. 438 in Sarna-Wojcicki et al. (1981); for Crater Peak from Fig. 16 in McGimsey et al. (2001); for Ruapehu from Fig. 1 of Bonadonna and Houghton (2005);
and for Redoubt from Wallace et al. (2013). Isomass values are all in kg m-2. Colored
markers represent locations where isomass was sampled, with colors
corresponding to the mass load shown in the color table. Black dashed lines
indicate the dispersal axis. Sample locations for Mount St. Helens taken
from supplementary material in Durant et al. (2009),
for Redoubt from Wallace et al. (2013), for Crater Peak
from McGimsey et al. (2001), and for Ruapehu, from data posted
online at the IAVCEI Commission on Tephra Hazard Modeling database
(http://dbstr.ct.ingv.it/iavcei/) (Bonadonna and Houghton,
2005; Bonadonna et al., 2005).
Input parameters for simulations. Vent elevation is given in
kilometers above mean sea level.
Parameter(S)Mount St. HelensSpurrRuapehuRedoubtModel domain42–49∘ N, 124–110∘ W; 0–35 km a.s.l.59–64∘ N, 155.6–141.4∘ W; 0–17 km a.s.l.39.5–37.5∘ S, 175–177∘ E; 0–12 km a.s.l.60–64∘ N, 155–145∘ W; 0–20 km a.s.l.Vent location122.18∘ W, 46.2∘ N152.25∘ W, 61.23∘ N175.56∘ E, 39.28∘ S152.75∘ W, 60.48∘ NVent elevation (KM)2.002.302.802.30Nodal spacing0.1∘ horizontal 1.0 km vertical0.1∘ horizontal 1.0 km vertical0.025∘ horizontal 0.5 km vertical0.07∘ horizontal 1.0 km verticalEruption start date (UTC) (YYYY.MM.DD)1980.05.181992.09.171996.06.16 1996.06.172009.03.23Start time (UTC)15:3008:0320:30 02:0012:30Plume height, km a.s.l.See Table 2138.515Duration, hoursSee Table 23.64.5 2.00.33Erupted volume km3 DRE0.2 (total)0.0140.000643 0.0003570.0017Diffusion coefficient D0000Suzuki constant K8888Particle shape factor F0.440.440.440.44Aggregate shape factor F1.01.01.01.0
Time series of plume height and total erupted volume used in model
simulations of the Mount St. Helens ash cloud. H is plume height in
kilometers above sea level (a.s.l.), V is erupted volume in million cubic
meters dense-rock equivalent (DRE). The time series of plume height
approximates that measured by radar (Harris et al., 1981). We calculated a
preliminary eruptive volume for each eruptive pulse using the duration and
the empirical relationship between plume height and eruption rate
(Mastin et al., 2009). This method
underestimated the eruptive volume, as noted in previous studies
(Carey et al., 1990). Hence, we adjusted the volume of each
pulse proportionately so that their total equals the 0.2 km3 DRE
estimated by Sarna-Wojcicki et al. (1981). For the last two
eruptive pulses, start times in UTC, marked with asterisks, are on 19 May in
UTC time. All other start times are on 18 May.
Below are key observations of these events. Deposit maps are shown in Fig. 1, digitized from published
sources.
The 18 May 1980 deposit from Mount St. Helens remains among the
best documented of any in recent decades (Durant et al., 2009;
Sarna-Wojcicki et al., 1981; Waitt and Dzurisin, 1981; Rice, 1981). This 9 h eruption expelled magma that was dacitic in bulk composition but
contained about 40 % crystals and 60 % rhyolitic glass (Rutherford et
al., 1985). The eruption start time (15:32 UTC) and duration are well
documented (Foxworthy and Hill, 1982); the time-changing plume
height was tracked by Doppler radar (Harris et al.,
1981) and satellite (Holasek and Self, 1995) (Table 2). The
deposit was mapped within days, before modification by wind or rainfall, to
a distance of ∼ 800 km and to mass load values as low as a few
hundredths of a kilogram per square meter (Sarna-Wojcicki
et al., 1981). Estimated volume of the fall deposit in dense-rock equivalent
(DRE) is 0.2 km3 (Sarna-Wojcicki et al., 1981) based
on what fell in the mapped area. A TPSD was estimated by Carey and
Sigurdsson (1982) and later by Durant et al. (2009) to contain about 59 % ash < 63 µm in
diameter (Table S1 in the Supplement), with a modal peak in particle size that coincided with
the median bubble size of tephra fragments (Genareau et al.,
2012). Some fine ash may have been milled in pyroclastic density currents on
the afternoon of 18 May and in the lateral blast that morning. A secondary
maximum in deposit thickness in Ritzville, Washington (∼ 290 km downwind) was inferred by Carey and Sigurdsson (1982) to have
resulted from fine-ash aggregating and falling en masse, perhaps as the cloud
descended and warmed to above-freezing temperatures
(Durant et al., 2009). Wind directions that were more
southerly at low elevations combined with elutriation off pyroclastic flows
in the afternoon to feed low clouds, producing a deposit that was richer in
fine ash along its northern boundary than in the south (Waitt and
Dzurisin, 1981; Eychenne et al., 2015). Aggregates sampled by Sorem
(1982) in eastern Washington consisted mainly of dry clusters 0.250
to 0.500 mm in diameter, containing particles < 0.001 mm to more
than 0.040 mm in diameter, though no aggregates were visible in the fall
deposit except at proximal locations (e.g., Sisson, 1995). The
eruption began under clear weather conditions. Clouds increased throughout
the day. Some precipitation in the form of mud rain was noted within tens of
kilometers of the vent (Rosenbaum and Waitt, 1981), probably
due to entrainment and condensation of atmospheric moisture in the rising
plume. But no precipitation was recorded at more distal locations during the
event.
The 16–17 September 1991 eruption from Crater Peak, Mount Spurr,
Alaska, was the third that summer from this vent. The eruption start time
(08:03 UTC, 17 September) and duration (3.6 h; Eichelberger et al., 1995) were seismically
constrained. The maximum plume height measured by U.S. National Weather
Service radar (Rose et al., 1995b) increased for the
first 2.3 h and then fluctuated between about 11 and 14 km above mean
sea level (a.m.s.l.) until the plume height abruptly decreased at 11:10 UTC. The
andesitic tephra consisted of two main types – tan and gray, which were both
noteworthy for their low vesicularity (∼ 20–45 %) and high
crystallinity (40–100 %) (Gardner et al., 1998). The
deposit was mapped rapidly after the eruption (Neal et al., 1995;
McGimsey et al., 2001) to a distance of 380 km and mass loads as low as
0.050 kg m-2. This deposit displays a weak secondary thickness maximum
260–330 km downwind. Durant and Rose (2009) derived a TPSD for
this deposit, estimating about 40 % smaller than 0.063 mm. Milling in
proximal pyroclastic flows that accompanied this eruption
(Eichelberger et al., 1995) could have contributed
fine ash. The eruption occurred at night under clear skies
(Neal et al., 1995).
The 17 June 1996 eruption of Ruapehu produced a classic weak
plume that was modeled by Bonadonna et al. (2005), Hurst and
Turner (1999), Scollo et al. (2008), Liu et al. (2015), and Klawonn et al. (2014), among others.
The main phase involved two pulses, one beginning 16 June at 19:10 UTC and
lasting 2.5 h and the second at 23:00 UTC and lasting approximately 1.5 to 2 h. Ash-laden plumes reached to about 8.5 km a.m.s.l.
based on satellite infrared images (Prata and Grant, 2001). The
deposit was mapped out to the Bay of Plenty (190 km), sampled at 118
locations to mass loads less than 0.01 kg m-2, and yielded a total mass
of about 0.001 km3 DRE (Bonadonna and Houghton, 2005).
Ejecta consisted mainly of scoria containing 75 % glass and 25 %
crystals, with glass containing about 54 wt % SiO2
(Nakagawa et al., 1999). A TPSD estimate based on the
Voronoi tessellation method (Bonadonna and Houghton, 2005) suggested
that ash < 0.063 mm composed only about 3 % of the deposit. A
minor secondary thickness maximum was constrained by mapping at about 160 km
downwind (Bonadonna et al., 2005) (Fig. 1c). Although some
witnesses at distal locations observed loose, millimeter-sized clusters
falling, no aggregates or accretionary lapilli were present in the deposit
(Klawonn et al., 2014). The eruption was not accompanied by
significant pyroclastic density currents and occurred during clear weather.
Event 5 of the 23 March 2009 eruption of Redoubt Volcano, Alaska,
erupted through a glacier and entrained a variable amount of water into a
high-latitude early-spring atmosphere. It began at 12:30 UTC, lasted
about 20 min on the seismic record (Buurman et al.,
2013), and sent a plume briefly to about 18 km as seen in both National
Weather Service NEXRAD Doppler radar from Anchorage, and a USGS mobile
C-band radar system in Kenai, Alaska (Schneider and
Hoblitt, 2013). Within a few days after the eruption, the deposit was mapped
by its contrast with underlying snow in satellite images (NASA MODIS), and
sampled for mass load and particle-size distribution at 38 locations, at distances up to ∼ 250 km and mass loads as low
as 0.01 kg m-2 (Wallace et al., 2013). During Ash3d
modeling of this eruption, Mastin et al. (2013b) found
that wind vectors varied rapidly with both altitude and time, making the
dispersal direction highly sensitive to both the plume height (which varied
from ∼ 12 to 18 km during the 20 min eruption) and the
vertical distribution of mass in the plume. In the deposit, Wallace et al. (2013) described abundant frozen aggregates with size
decreasing with distance from the vent, from about 10 mm at 12 km distance.
Schneider et al. (2013) attributed the high
(> 50 dBZ) reflectivity of the proximal plume in radar images,
and a rapid decrease in maximum plume height over a period of minutes, to
formation and fallout of ashy hail hydrometeors in the rising column. Van
Eaton et al. (2015) combined analysis of the aggregate
microstructures with a three-dimensional (3-D) large-eddy simulation to show that the ash
aggregates grew directly within the volcanic plume from a combination of wet
growth and freezing, in a process similar to hail formation.
These eruptions vary from weak (Ruapehu) to strong (Redoubt) plumes, from
mid-latitude (St. Helens, Ruapehu) to high-latitude (Spurr, Redoubt), from
dry (Ruapehu) to relatively wet (Redoubt), from basaltic andesite (Ruapehu)
to dacite (St. Helens), and from ∼ 3 to 59 % ash
< 0.063 mm in diameter. Inferred aggregation processes range from
dry (Ruapehu) to wet within the downwind cloud (St. Helens), to liquid plus ice
in the rising column (Redoubt).
Illustration of the path taken by coarse aggregates that fallout
in proximal sections, less than a few plume heights from the source (left),
and fine aggregates that fall out in distal sections (right). Among distal
fine aggregates, we show the path taken by those that might have formed
within or below the downwind cloud as hypothesized by Durant et al. (2009) (red dashed line), and those that were
transported downwind without changing size, as calculated by Ash3d (blue
dashed line). Also illustrated are some key processes that might influence
the distribution of fine, distal ash, including development of gravitational
instability and overturn within the downwind cloud (Carazzo
and Jellinek, 2012), and the development of hydrometeors as descending ash
approaches the freezing elevation (Durant et al.,
2009).
MethodsThe Ash3d model
We model these eruptions using Ash3d (Schwaiger et
al., 2012; Mastin et al., 2013a), an Eulerian model that calculates tephra
transport and deposition through a 3-D, time-changing wind field. Ash3d
calculates transport by setting up a 3-D grid of cells, adding
tephra into the column of source cells above the volcano, and distributing
the mass in the column following the probability density function of Suzuki
(Suzuki, 1983), modified by Armienti et al. (1988):
dQmdz=Qmk21-z/Hvexpkz/Hv-1Hv1-1+kexp-k,
where Qm is the mass eruption rate, Hv is plume height above
the vent, z is elevation (above the vent) within the plume, and k is a
constant that adjusts the mass distribution. Suzuki (1983)
defines this function as a “probability density of diffusion” of mass from
the column as particles fall out. Here we regard it as a simplified
parameterization of mass distribution with no implication for physical
process.
At each time step, tephra transport is calculated through advection by wind,
through turbulent diffusion, and through particle settling. For wind
advection, simulations of Mount St. Helens, Crater Peak, and Redoubt use a
wind field obtained from the National Oceanic and Atmospheric
Administration (NOAA) NCEP/NCAR Reanalysis 1 model (RE1)
(Kalnay et al., 1996). For the Ruapehu
simulations we used a local 1-D wind sounding, which gave more accurate
results as detailed below. The RE1 model provides wind vectors on a global
3-D grid spaced at 2.5∘ latitude and 2.5∘ longitude, and 17 pressure
levels in the atmosphere (1000–10 hPa), updated at 6 h intervals. Ash3d
calculates turbulent diffusion using a specified diffusivity D
(Schwaiger et al., 2012, Eq. 4). D is set to zero for
simplicity, though later we show the effect of different values of D.
Settling rates are calculated using relations of Wilson and Huang
(1979) for ellipsoidal particles. Wilson and Huang define a
particle shape factor ≡F(b+c)/2a, where a, b, and c are the
maximum, intermediate, and minimum diameters of the ellipsoid, respectively.
Wilson and Huang measured a, b, and c for 155 natural pyroclasts. From data
published in Wilson and Huang, we calculate an average F of 0.44, which we
use in our model. For aggregates we use F= 1.0 (round aggregates).
Other model inputs include the extent and nodal spacing of the model domain;
vent location and elevation; the eruption start time, duration, plume
height, erupted volume, diffusion coefficient D, and a series of particle-size classes and associated densities. The size classes may represent either
individual particles or aggregates. These input values are given in Tables 1
and 2.
Adjusting particle-size distributions to account for aggregation
In deriving a particle-size adjustment scheme we found it necessary to
prioritize the type(s) of processes and products we wish to replicate. The
rate and type of ash aggregation are known to vary with both eruptive
conditions and meteorology. Large aggregates, including frozen accretionary
lapilli, form near the source and are abundant in phreatomagmatic deposits
(Van Eaton et al., 2015; Brown et al., 2012; Houghton et al., 2015). They
are associated with particles colliding in moist, turbulent updrafts within
a rising plume (Fig. 2) or an elutriating ash cloud. These near-source
aggregates commonly exceed 1 cm diameter (Wallace et al., 2013; Swanson
et al., 2014; Van Eaton and Wilson, 2013). In contrast, the low-density
aggregates that produced the Ritzville Bulge, 230 km downwind from Mount St.
Helens, are thought to have been triggered by mammatus cloud instabilities
(Durant et al., 2009) as the cloud descended, warmed, and ice melted
into liquid water (red line, Fig. 2). These aggregates tend to be smaller
than a millimeter, and form in the cloud hundreds of kilometers downwind
from the source (Sorem, 1982; Dartayat, 1932). At Mount St. Helens
and perhaps other places, investigators found evidence for both large, wet,
proximal accretionary lapilli (Sisson, 1995) and distal, dry
aggregates (Sorem, 1982). The latter type deposited over a larger
area, involved a greater fraction of the total erupted mass, and affected a
greater population. Thus, it is the latter process whose deposits we wish to
reproduce.
Aggregation is also a highly size-selective process. The threshold size
below which most particles aggregate and above which they do not varies with
moisture and electrical charge, ranging from several tens of microns under
dry conditions, to hundreds of microns when liquid water is present
(Gilbert and Lane, 1994; Schumacher and Schmincke, 1995; Van Eaton et
al., 2012). Our aggregation scheme is too crude to distinguish the threshold
size as a function of atmospheric conditions; hence, we use a broad range
such that for ϕ>= 4, all ash aggregates; for ϕ<= 2, no ash aggregates.
For 4>φ> 2, the mass fraction that
aggregates varies linearly with φ from 1 (when ϕ=4) to 0
(when φ=2).
Total particle-size distribution for each of the deposits studied:
(a) Mount St. Helens, (b) Crater Peak (Mount Spurr), (c) Ruapehu, and (d) Redoubt. Gray bars show the original TPSD before aggregation. Black bars
show the sizes not involved in aggregation; red bars show sizes of aggregate
classes used in Figs. 11–14.
Statistical measures of fit used in this paper.
NameFormulaExplanationPoint-by-point methodΔ2=∑i=1Nmm,i-mo,i2∑i=1Nmo,i2The mass load mo,i observed at each sample location i is compared with modeled mass load mm,i at the same location. Squared differences are summed to the total number of sample points N, and normalized to the sum of squares of the observed mass loads.Downwind thinning methodΔdownwind2=1M∑j=1Mlogmm,j/mo,j2The log of modeled mass load mm,j at a point j on the dispersal axis is compared with the observation-based value mo,j expected at that location based on a trend line drawn between field measurements along the axis (Fig. 4). Differences between mm,j and mo,j are calculated on a log scale, squared, and summed.Isomass area methodΔarea2=∑i=1LAm,i-Ao,i2∑i=1LAo,i2This method calculates the area Am,i of the modeled deposit that exceeds a given mass load i by summing the area of all model nodes that meet this criterion. It then takes the difference between Am,i and the area Ao,i within same isomass line mapped from field observations. The sum of the squares of these differences, normalized to the sum of the squared mapped isopach areas, gives the index Δarea2.
The TPSDs used to model these four eruptions are listed in Table S1 and
illustrated as gray bars in Fig. 3. Particle sizes that do not aggregate
according to this scheme are illustrated as black bars. We assume that the
aggregates collect into clusters having a Gaussian size distribution of mean
μagg, and standard deviation σagg (insets, Fig. 3). For
deposit modeling, we ignore the small fraction of the erupted mass that goes
into the distal cloud, typically a few percent (Dacre et al., 2011;
Devenish et al., 2012).
In our study, the aggregated ash mostly deposits as a secondary thickness
maximum. Different choices of a threshold size for particle aggregation
would influence the mass building the secondary maximum. For Mount St.
Helens, about 10 % of the erupted mass lies between φ= 2 and
φ= 4. For Spurr, Ruapehu, and Redoubt, the percentages are 28,
6, and 11 %. These values reflect the variability in mass of the
secondary maximum that could result from different choices of the
aggregation-size threshold.
Aggregate density: different processes influence aggregate
density
Wet ash (> 10–15 wt % liquid water) rapidly produces
sub-spherical pellets with density > 1000 kg m-3
(Schumacher and Schmincke, 1991; Van Eaton et al., 2012); drier
conditions lead to electrostatically bound clusters (Schumacher and
Schmincke, 1995; Van Eaton et al., 2012) with density in the hundreds of
kilograms per cubic meter range (James et al., 2002; Taddeucci et al.,
2011). Taddeucci et al. (2011) estimated densities ranging
from < 100 to > 1000 kg m-3 in dry aggregates
photographed falling 7 km from the Eyjafjallajökull vent. For
simplicity, we hold ρagg constant at 600 kg m-3, toward the
middle of the observed range but higher than that of some dry aggregates.
Optimal aggregate sizes that we derive later in this paper are determined by
this assumed density, and may be larger or smaller than actual aggregate
sizes.
Statistical measures of fit
For each eruption, we have done a series of model simulations, first using
the TPSD without considering aggregation, and then systematically varying
σagg and μagg to include the effects of aggregation. We
compare the resulting modeled deposit with the mapped deposit using three
methods presented in Table 3. Each has advantages and disadvantages.
The point-by-point index Δ2 compares model
results with sample data collected at specific locations (dots, Fig. 1). It
offers the advantage that the comparison is made directly with measured
values, not with interpreted or extrapolated contours of data. But Δ2 can be influenced by errors in the wind field, which cannot be
adjusted in the model. More importantly, Δ2 can be dominated
by differences in proximal locations where mass per unit area is greatest,
and where near-vent processes, such as fallout from the vertical column, are
not accurately simulated. For these reasons, we exclude proximal data,
within a few column heights distance from the vent, from the calculation of
Δ2.
The downwind thinning index Δdownwind2
compares modeled mass per unit area along the downwind dispersal axis with
values expected at that distance based on a trend line drawn from field
measurements (Fig. 4). The comparison is not made directly with measured
values (a disadvantage). However, the method does not suffer the limitation
of over-weighting proximal data, and, more importantly, it still provides a
useful comparison when wind errors cause the modeled dispersal axis to
diverge from the mapped one.
The isomass area index Δarea2 compares
the area within modeled and mapped isomass lines. It is based on traditional
plots of the log of isopach thickness versus square root of area (Pyle,
1989; Fierstein and Nathenson, 1992; Bonadonna and Costa, 2012), which are
assumed to accurately depict the areal distribution of tephra while
minimizing the effects of 3-D wind on the distribution (Pyle, 1989).
Figure 5 shows plots for our four eruptions, using the log of isomass rather
than isopach thickness to avoid problems introduced by varying deposit
density.
The index Δarea2 is assumed to be insensitive to effects of
wind (an advantage). However, model results are compared with isopach lines
that are interpretive and may not be well constrained, depending on the
distribution and number density of sample locations.
Mass load versus downwind distance along the dispersal axis for
the deposits of (a) Mount St. Helens, (b) Crater Peak (Mount Spurr), (c) Ruapehu, and (d) Redoubt. Squares indicate sample points within 20 km of the
dispersal axis, with the grayscale value indicating the distance from the
dispersal axis following the color bar in (a). The dash trend lines
represent interpolated values of the mass load that are compared with
modeled values to calculate Δdownwind2.
Sensitivity to various input values
We ignore complex, proximal fallout and concentrate on medial to distal
areas, about 100 to ∼ 500 km downwind at Mount St. Helens, for
example. There, under the average wind speed (15.1 m s-1) that existed
below about 15 km, tephra falling from 15 km at average settling velocities
of 0.4–1.5 m s-1 would deposit within this range (Fig. 6a). Tephra
falling at 0.66–0.78 m s-1 would land 290–340 km downwind, the distance
of the secondary maximum at Ritzville. A wide range of aggregate diameters
d could fall at this rate depending on density ρagg (Fig. 6b).
Log mass load versus the square root of the area within isomass
lines mapped for the (a) Mount St. Helens, (b) Crater Peak (Spurr), (c) Ruapehu, and (d) Redoubt deposits. Also shown are best-fit lines, drawn by
visual inspection, using either one line segment (Ruapehu, Redoubt) or two,
where justified (Spurr, St. Helens). Triangular markers are marked with
labels indicating the approximate percentage of the deposit mass lying
inboard of these points, as calculated using equations derived from
Fierstein and Nathenson (1992).
(a) Transport distance versus average fall velocity, assuming a
15.1 m s-1 wind speed, equal to the average wind speed at Mount St.
Helens between 0 and 15 km, and a fall distance of 15 km. The vertical
shaded bar represents the distance of Ritzville. Labels on dots give the
average diameter of a round aggregate having a density of 600 kg m-3
and the given fall velocity. (b) Average fall velocity between 0 and 15 km
elevation, versus aggregate diameter, for round aggregates having densities
ranging from 200 to 2500 kg m-3. The horizontal shaded bar represents
the range of average fall velocities that would land in Ritzville. Fall
velocities are calculated using relations of Wilson and Huang (1979), at 1 km elevation intervals in the atmosphere, from 0 to
15 km, then averaged to derive the values plotted.
Other factors listed below can also affect the results.
Aggregate shape: aggregate shape can strongly affect the
settling velocity and thus where deposits fall, as illustrated in Fig. 7.
For simplicity, we use round aggregates (F= 1.0).
Suzuki k: simulations of Mount St. Helens (Fig. 8) show
that increasing the Suzuki factor from 4 to 8 increases the prominence of a
secondary thickness maximum. But at k>∼ 8, the
proximal deposit becomes unrealistically thin. Our simulations use k= 8 to
replicate the known prominent secondary thickening while minimizing
unrealistic thinning of proximal deposits.
Aggregate size: the transport distance is highly sensitive
to aggregate size. Reducing aggregate diameter d from 0.250 to 0.217 to 0.189 mm increases transport distance at Mount St. Helens from 300 to 366 to
448 km,
respectively (Fig. 6a). In simulations that use a single, dominant
aggregate size, these variations produce conspicuous changes in the location
of a secondary maximum (Fig. 9). Decreasing size also decreases the percent
of erupted mass that lands in the area shown in Fig. 9: from 63 to
35 to 15 % for d= 0.165, 0.143, and 0.125 mm, respectively (φ= 2.6, 2.8.3.0). At d= 0.1 mm (φ= 3.3), only 4 % of the
erupted mass lands in the mapped area.
This constrains the range of aggregate sizes we may use in our simulations.
Sparse observations suggest that > 90 % of erupted mass falls
as an observable deposit while less than several percent is transported
downwind as a distal cloud (Wen and Rose, 1994; Devenish et al., 2012).
To ensure a similar relationship in our simulations, nearly all of the
aggregate-size distribution must be coarser than about 0.1 mm. At the
proximal end, for Mount St. Helens, Durant et al. (2009) found that most
fine ash fell at distances > 150 km. This implies aggregate sizes
coarser than about 0.32 mm (φ= 1.6) (Figs. 6, 9). To ensure that
the tails of our aggregate-size distribution land in the area of interest,
we must vary μagg values within a narrow range of about
1.9–3.1φ (0.27–0.12 mm), and σagg within a small
fraction of this range. We assume that similar constraints apply to all
deposits in this study.
Deposit maps for simulations using a single size class
representing an aggregate with phi size 1.9 and density 600 kg m-3,
using three shape factors: (a)F=0.44, (b)F=0.7, and (c)F=1.0. Inset
figures illustrate ellipsoids having the given shape factor, assuming
b=(a+c)/2.
Deposit map for simulations using a single size class representing
an aggregate with F=1.0, phi size 2.4φ and density 600 kg m-3. (a), (b), and (c) illustrate the deposit distribution using
Suzuki k values of 4, 8, and 12, while (d) illustrates the deposit
distribution resulting from release of all the erupted mass from a single
node at the top of the plume. Inset plots schematically illustrate the
vertical distribution of mass with height in the plume for each of these
cases. Simulations used other input values as given in Table 1. Colored dots
represent sample locations with colors indicating the sampled mass load, as
in Fig. 1a.
Results of Mount St. Helens simulations using a single size class
of round aggregates in each simulation: φ=1.8, 2.0, 2.2, 2.4, and
2.6 in (a), (b), (c), (d), and (e); (f) shows the mapped mass load,
digitized from Fig. 438 in Sarna-Wojcicki et al. (1981). Markers in each
figure provide the sample locations, with colors indicating the mass load
measured at each location, as shown in the color bar. Lines are contours of
mass load with colors giving their values. The mass load values of the
contour lines, from lowest to highest, are 0.01, 0.1, 0.5, 1, 5, 10, 20, 30,
50, 80, and 100 kg m-2.
Fall-velocity model: different fall-velocity models are used
in different tephra dispersion models. These models give slightly different
results, and it should be noted that our results are specific to our choice
of the Wilson and Huang fall model.
Finally, we note that key parameters, such as particle density, shape, Suzuki
k, etc., are held constant for all four eruptions even though they may vary
from one eruption to another. Such parameters cannot easily be scrutinized
when setting up simulations during an eruption. An objective is to see how
well “standard” values, even if locally unrealistic, can reproduce
observations.
Results
We ran simulations at μagg=1.9,2.0,2.1…3.1φ,
and σagg 0.0, 0.1, 0.2, and 0.3φ. The latter used 1, 5,
7, and 11 aggregate size classes, respectively, in each simulation, with the
percentage of fine ash assigned to each bin given in Table 4. Our
calculations of Δ2 and Δdownwind2 only included
sample points, whose downwind distance lies within the range indicated by the
trend lines in Fig. 4.
Percentage of fine ash assigned to different size bins for different
values of σagg. The mass fraction mφ in each bin
(φ) was calculated using the equation for a Poisson distribution,
mϕ=1/2πexp-ϕ-μagg2/2σagg2. Values of mφ were then adjusted
proportionally so that their sum added to 1.
Contours of Δ2 (left column), Δdownwind2 (middle column), and Δarea2 (right column)
as a function of σagg and μagg for deposits from Mount
St. Helens (top row), Crater Peak (Mount Spurr, second row), Ruapehu (third
row), and Redoubt (bottom row). The values of these contour lines are
indicated by the color using the color bar at the right. Maximum and minimum
values in the color scale are given within each frame. The best agreement
between model and mapped data is indicated by the deep blue and purple
contours; the worst is indicated by the yellow contours. Regions of each
plot where agreement is best is indicated by the word “Lo”.
Figure 10 shows contours of Δ2, Δdownwind2, and
Δarea2 as a function of σagg and μagg
for each of these four deposits. Values are given in Tables S3–S6. Although
the three indices compare different features of the deposit, they provide
roughly similar optimal values of μagg. For Mount St. Helens, for
example, the best-fit value of μagg is about 2.4φ using
Δ2 (Fig. 10a), 2.5φ using Δdownwind2
(Fig. 10b), and 2.7φ using Δarea2 (Fig. 10c).
Optimal values of σagg are 0.1, 0.1, and 0.2, respectively. For
Crater Peak, optimal μagg values are 2.6φ, 2.5φ,
and 2.0φ, respectively, while for Ruapehu they are 2.3φ,
2.5φ, and 2.5φ. For both Crater Peak and Ruapehu, optimal
values of σagg range from 0.0 to 0.2. For Redoubt, optimal
values are disparate: μagg= 2.5φ, 2.5φ, and
<2φ, respectively. The Redoubt deposit is the least constrained
by field data and the most difficult to match due to the complex wind
conditions.
Results of the Mount St. Helens simulation that provides
approximately the best fit to mapped data (μagg=2.4φ and
σagg=0.1φ). (a) Deposit map with modeled isomass
lines and dots that represent field measurements with colors indicating the
field values of the mass load, corresponding to the color bar at left. The
black dashed line indicates the dispersal axis of the mapped deposit whereas
the solid black line with dots indicates the dispersal axis of the modeled
deposit (the latter lies mostly on top of the former and obscures it). The
modeled dispersal axis was obtained by finding the ground cell in each
column of longitude with the highest deposit mass load. (b) Log of modeled
mass load versus measured mass load at sample locations. Black dashed line
is the 1:1 line; dotted lines above and below indicate modeled values 10 and
0.1 times that measured. Gray dots lie outside the range of downwind
distances covered by trend lines in Fig. 4 and therefore were not included
in the calculation of Δ2. (c) Log of measured mass load (black
and gray dots), and modeled mass load (black line with dots) versus distance
downwind along the dispersal axis. The black dashed line is the same trend
line as in Fig. 4a. Gray dots were not included in the calculation of
Δdownwind2. (d) Log of mass load versus square root of area
contained within isomass lines. Black squares are from the mapped deposit,
red squares from the modeled one.
Results of the Crater Peak (Mount Spurr) simulation that provide
a good fit to mapped data (μagg=2.4φ and σagg=0.1φ). The features in the sub-figures are as described in Fig. 11. “CP” in (a) refers to the Crater Peak vent.
Results of the Ruapehu simulation that provide a good best fit
to mapped data (μagg=2.4φ and σagg=0.1φ). The features in the sub-figures are as described in Fig. 11.
Results of the Redoubt simulation that provide a reasonable fit
to mapped data (μagg=2.4φ and σagg=0.1φ). The features in the sub-figures are as described in Fig. 11.
Figures 11–14 show results for each of these eruptions using μagg= 2.4φ (0.19 mm) and σagg= 0.1φ. The sizes
of particles and aggregates used to generate these figures is given in Table S2. For all deposits these values are close to optimal, depending on which
criterion is used. Similar figures for other values of μagg and
σagg are provided as Figs. S005–S212.
Figures S001–S004 show simulations using the original particle-size
distribution, with no aggregation. Tephra fall beyond a few tens of
kilometers is strongly underestimated in all these runs, especially for the
three eruptions that contain more than a few percent fine ash. Values of
Δ2, Δdownwind2, and Δarea2 are
also higher than most simulations that use aggregates (Tables S3–S6). For
Mount St. Helens, Crater Peak, Ruapehu, and Redoubt, the percentages of the
erupted mass landing in the mapped area are very low: 29, 42,
88, and 59 %, respectively.
Optimal aggregates obtained from our study are similar in size but denser
than those found optimal by Cornell et al. (1983) for the
Campanian Y-5 (μagg= 2.3φ, ρagg= 200 kg m-3) deposit. The unknown wind field during the prehistoric Campanian
Y-5 eruption makes it difficult to compare the optimal value of Cornell et al. (1983) to
the results here. Folch et al. (2010) matched the Mount St. Helens deposit
using a similar aggregation scheme, but with aggregates of density 400 kg m-3 (compared with our 600 kg m-3) and diameter of 0.2–0.3 mm
(compared with our ∼ 0.2 mm). Their results are broadly
consistent with ours.
Mount St. Helens
For the Mount St. Helens case, the modeled deposit follows a dispersal axis
(solid black line, Fig. 11a) that matches almost exactly with the mapped one
(dashed line). The agreement reflects both the faithfulness of the numerical
wind field to the true one and the appropriateness of other inputs, such as
k, that influence dispersal direction. The measured mass loads in Fig. 11a,
indicated by the color of markers, agree reasonably well with modeled mass
loads indicated by colors of the contour lines, except along the most distal
transect, where modeled loads are essentially zero, whereas measured loads are
about 10-1 kg m-2. Figure 11b shows that modeled and measured mass
loads generally agree within a factor of 3 or so, except for those same
distal, low-mass-load measurements, to the lower left of the legend label
(those where modeled values are truly zero do not show up on this plot).
Figure 11c shows that the modeled mass load (black line with dots) contains
a secondary thickening at about the same location mapped (dashed line). It
also has roughly the same downwind shape, in contrast to results using
σagg= 0.2 and 0.3 (Figs. S027–S028), in which the secondary
thickening is broader and thinner than observed. However, the modeled mass
load is consistently less than measured, especially at the most distal
sites. In Fig. 11d, the log of modeled mass load versus square root of area
shows reasonable agreement with mapped values until mass loads are less than
about 1 kg m-2, where they diverge.
Notably, modeled mass loads somewhat underestimate the measured values along
the dispersal axis in Fig. 11c. The underestimate reflects the fact that the
input erupted volume of 0.2 km3 DRE (Table 1) was based on estimates by
Sarna-Wojcicki et al. (1981), which lies within the mapped
area in Fig. 11a, yet only about 78 % of the modeled mass landed within
this area. Reducing the mean aggregate size to 2.6φ (0.164 mm, Fig. S036)
improves the fit somewhat along distal parts of the transect but
degrades it near Ritzville; the finer size moves the secondary maximum
too far east and reduces the percentage deposited to ∼ 65 %.
Modeled mass load of the Mount St. Helens eruption for four cases
using μagg=2.4φ, σagg=0.1φ, and
different diffusion coefficients: (a)D=0 m2 s-1, (b)3×102 m2 s-1, (c)1×103 m2 s-1, and
(d)3×103 m2 s-1. Other inputs are as given in
Tables 1 and 2. Lines are isomass contours of modeled mass load and colored
dots are sample locations. Colors of the dots and lines give the mass load
corresponding to the color table.
Atmospheric temperature profiles during the eruptions at Mount St.
Helens, Crater Peak (Spurr), Ruapehu, and Redoubt volcanoes. Profile for
Mount St. Helens is for 18 May 1980, 18:00 UTC, interpolated to the location
of Ritzville, Washington (47.12∘ N, 118.38∘ W). For
Crater Peak (Spurr) the profile is for 17 September 1992, 12:00 UTC,
interpolated to the location of Palmer, Alaska (61.6∘ N,
149.11∘ W). For Ruapehu the temperature profile is for 17 June
1996, 00:00 UTC, interpolated to the location of Ruapehu. For Redoubt the
sounding was for 23 March 2009, 12:00 UTC, at 62∘ N, 153∘ W. All soundings were taken from RE1 reanalysis
data available at http://ready.arl.noaa.gov/READYamet.php. For Mount St. Helens, the
freezing elevation was also checked using data from the North American
Regional Reanalysis model (Mesinger et al., 2006), available at the same NOAA
site, and found to be 3.3 km, similar to that given below by the RE1 model.
Modeled mass load of the Ruapehu eruption for four cases using
μagg=2.4φ, σagg=0.1φ, and
different diffusion coefficients: (a)D=0 m2 s-1,
(b)1× 102 m2 s-1, (c)3×102 m2 s-1, and
(d)1×103 m2 s-1. Other inputs are as given in
Table 1. Lines are isomass contours of modeled mass load and colored dots
are sample locations. Colors of the dots and lines give the mass load
corresponding to the color table.
In Fig. 11a, the modeled deposit is also slightly narrower than the mapped
one. Adding turbulent diffusion, with a diffusivity D of about 3×102 m2 s-1 (Fig. 15) visually improves the fit, and was
likely important during this eruption due to high crosswind speeds that
increased entrainment (Degruyter and Bonadonna, 2012; Mastin, 2014). But
adding diffusion slightly increases Δ2, improving fit on
deposit margins at the expense of the axis. Ignoring turbulent diffusion
also decreases run time by ∼ 3×, from ∼ 30 to 10 min,
yielding faster results under operational conditions. Results with
other models may vary depending on model setup and configuration.
Crater Peak (Mount Spurr)
At Crater Peak (Mount Spurr), results in Fig. 12a also show good agreement
between the modeled dispersal axis and the mapped one (which is constrained
by fewer sample locations than the Mount St. Helens case). The isomass lines
in this plot are jagged and irregular due to effects of topography in this
mountainous region. The modeled location of secondary thickening in Fig. 12c
agrees with the mapped location, about 250–300 km downwind. Although Fig. 12c shows a tendency for the model to underestimate the mass load along the
dispersal axis, there is less tendency to underestimate the mass load in the
most distal locations as has occurred at Mount St. Helens. In Fig. 12d, the
areas covered by modeled isomass lines are comparable to the mapped values,
down to mass loads approaching 0.1 kg m-2.
Ruapehu
For Ruapehu (Fig. 13), simulations using the NCEP Reanalysis 1 numerical
winds produced an odd double dispersal axis, whose average did not correspond
well with the mapped direction of dispersal (Fig. 1c). To improve the fit we
used the 1-D wind sounding provided for this eruption at the IAVCEI Tephra
Hazard Modeling Commission web page (http://dbstr.ct.ingv.it/iavcei/). Use of a 1-D wind sounding seems
justified in this case because this deposit covers a smaller area than the
others, making a 3-D wind field less important in calculating transport. The
resulting dispersal axis (Fig. 13a) agrees with the mapped one out to about
140 km distance, beyond which it strays eastward, reaching the coast, 180 km
downwind, about 10 km east of the mapped axis. This slight difference is
enough to cause misfits in point-to-point comparisons at measured mass loads
of ∼ 10-1 kg m-2 (Fig. 13b).
The modeled mass load along the dispersal axis (Fig. 13c) agrees with
measurements to about 60–90 km distance. At 100–200 km, modeled values level
off and show a hint of secondary thickening at ∼ 180 km, in
agreement with the mapped deposit (Figs. 1c and 13c), although the mapped
secondary thickening is more prominent.
A large discrepancy is also apparent at distances of less than 60 km, where
mass load along the dispersal axis (Fig. 13c) and the area covered by thick
isomass lines (Fig. 13d) are greater than that for the mapped deposit. The
implication is that too much mass is dropping out proximally in the model.
Underestimates of isomass area at greater than or equal to 10-1 kg m-2 (Fig. 13d) also show that too little is falling distally. Simulations (not shown)
that raise the plume height or increase k to concentrate more mass high in
the plume do not improve the fit. The discrepancy may reflect the coarse
TPSD – 50 % of which is coarser than 1 mm (compared with 2, 12,
and 8 % for the other three deposits in Table S1). An additional
simulation used the TPSD derived from technique B of Bonadonna and Houghton (2005)
(Table S1), which divides the deposit into arbitrary sectors,
and calculates a weighted sum of the size distributions in each sector
following Carey and Sigurdsson (1982). Technique B yields a finer
average particle size than technique C, which uses Voronoi tessellation to
sectorize the deposit. But the finer particle size of the technique B TPSD
does not improve the fit. Further exploration of this discrepancy is beyond
the scope of this paper, but other possible causes could include release of
different particle sizes at different elevations, or complex transport in
the bending of the weak plume that cannot be accommodated in this model.
A second, smaller discrepancy is that the modeled deposit is narrower than
the mapped one (Fig. 1c). As at Mount St. Helens, deposit widening due to
cross-flow entrainment is likely. Increases in entrainment resulting from
cross flow is widely known to both increase plume width and decrease its
height for a given eruption rate (Briggs, 1984; Hoult and Weil, 1972;
Hewett et al., 1971; Woodhouse et al., 2013). Adding turbulent diffusion, we
get a visually improved fit when D=∼3×102 m2 s-1 (Fig. 16), consistent with findings by Bonadonna et al. (2005)
based on the rate of downwind widening of isomass lines.
This diffusivity is also similar to the visual best-fit value for Mount St.
Helens (Fig. 15).
Despite the uncertainty in TPSD, simulations that systematically vary μagg and σagg fit best in Fig. 10g, h, and i when μagg is about 2.3 to 2.5. Results similar to those presented in Fig. 13c
use other values of μagg (Figs. S109–S160) and show a secondary
maximum migrating downwind as μagg increases, coming into agreement
with the mapped distance at μagg= 2.3 to 2.5φ (0.20–0.18 mm), where errors in Fig. 10g, h, and i are the lowest.
Redoubt
This deposit is the second smallest in our group, the least well constrained
by sampling, and the only one in our group not known to include a secondary
thickness maximum. Mastin et al. (2013b) modeled this
deposit using numerical winds from the North American Regional Reanalysis
model (Mesinger et al., 2006). During that eruption, the winds at
0–4 km, 6–10, and > 10 km elevation were directed toward the
northwest, north, and northeast, respectively, with the highest speeds at
6–10 km. Mastin et al. (2013b) found that the modeled cloud developed a
north-oriented, northward-migrating wishbone shape with the west prong at
low elevation and the east prong at high elevation. Mastin et al. (2013b) also found
that the modeled dispersal axis and the mass load distribution roughly
agreed with mapped values for a plume height of 15 km, k= 8, and a particle-size adjustment that involved taking 95 % of the fine ash (< 0.063 mm) and distributing it evenly among the coarser bins. In this study we use
the same plume height and k value, a different wind field (RE1), and explore
a different parameterization for particle aggregation.
In Fig. 14a, the modeled dispersal axis diverges about 20∘
westward from the mapped axis. We do not correct this divergence by
adjusting mass height distribution, since the optimal values of μagg and σagg can still be obtained from Δdownwind2
and Δarea2. As with the Crater Peak (Spurr) simulations, the
isomass lines are jagged and patchy, an artifact of high relief. (The most
distal sample location lies at 4.3 km elevation on the west shoulder of
Mount Denali.) Although the value of μagg (2.4φ, 0.19 mm)
portrayed in Fig. 14 is close to optimal in Fig. 10j, many sample points do
not plot in Fig. 14b because the modeled mass load is zero, and most values of
Δ2 are high (0.99) largely because of the disparity in axis
dispersal directions and the consequent fact that sample points lie outside
the modeled deposit. The reason that Δ2 shows a clear minimum,
around μagg= 2.4φ (0.19 mm) in Fig. 10j, is apparent from
Figs. S161–S212, which show that, as μagg decreases in size, the
modeled deposit extends farther north and takes a clear turn to the
northeast, overlapping more with the mapped deposit. These figures also
illuminate why Δdownwind2 is optimal at μagg= 2.3;
i.e., modeled and mapped loads come into best agreement along the
dispersal axis for aggregates of this size. Δarea2 is
optimized at μagg<2 because the area of the 1 kg m-2 isomass diverges below the mapped value, and the area of the 0.01 kg m-2 isomass diverges above observed, as aggregate size increases.
The isomass lines are drawn based on sparse data and are the least reliable
of the data sets used in this comparison.
Discussion and conclusions
The overall derived values of μagg have a narrow range between
∼ 2.3 and 2.7φ (0.15–0.20 mm), despite large variations
in erupted mass (0.25–50× Tg), plume height (8.5–25 km), mass
fraction of fine (< 0.063 mm) ash (3–59 %), atmospheric
temperature, and water content between these eruptions. The value of this
narrow range depends strongly on other inputs, such as particle density,
shape factor, and Suzuki factor. Values assigned here may not always be
representative. Aggregate density for example is frequently less than 600 kg m-3; different assumptions on particle or aggregate shape could
significantly change our results. Moreover, our result is partly an artifact
of our choice to optimize fit to deposits at medial distances of several
tens to hundreds of kilometers. Including more proximal sample points may
have given optimal aggregate sizes that spanned a wider range, as used for
example in aggregation schemes for Vesuvius (Barsotti et
al., 2015) or Iceland (Biass et al., 2014). Despite these
considerations, the similarity in optimal values of μagg between
these four eruptions is noteworthy.
The overall agreement in modeled mean aggregate size (μagg)
suggests that accelerated fine-ash deposition may be treated as a discrete
process, insensitive to eruptive style or magnitude. It seems unlikely that
these varied eruptions would produce aggregates of the same size, density,
and morphology. A combination of processes removed ash, and our approach
captures these processes implicitly, ignoring the microphysics.
What sort of processes could evolve in the cloud? Some possibilities are
illustrated in Fig. 2. The evolution starts with ejection of particles from
the vent, with size ranging from microns to meters. For an eruption having
the TPSD of Mount St. Helens, the rising plume would have contained
106–108 particles per cubic meter with diameter between
10 and 30 µm that collided with larger particles many times per second. High collision
rates and the availability of liquid water in the plume would have led to
rapid aggregation. Freezing of liquid water and riming would have shifted
the maximum possible size of aggregates towards millimeter to centimeter sizes. Mud rain,
observed falling at Mount St. Helens (Waitt, 1981), and ice
aggregates collected near the vent at Redoubt (Van Eaton et
al., 2015), are evidence of these processes.
In the downwind cloud particle concentrations were lower, turbulence was
less intense, a smaller range of particle sizes existed, and, for all four
eruptions, atmospheric temperatures near the plume top were well below
freezing (Table 5), leading to presumably slow aggregation rates. However,
at least two other processes may help settle ash from downwind clouds. One
is gravitational overturn. Experiments (Carazzo and
Jellinek, 2012) have observed that fine ash settles toward the bottom of ash
clouds as they expand and move downwind, accumulating gravitationally
unstable particle boundary layers that eventually overturn and cause the
entire air mass to settle rapidly. At Eyjafjallajökull in 2010,
gravitational convective instabilities formed within 10 km of the vent,
presumably as a result of accumulation of coarse ash over a period of
minutes (Manzella et al., 2015). The development of fine-ash
particle boundary layers presumably takes longer, perhaps hours, although
the underlying processes remain a subject of active research.
A second process is hydrometeor growth. In some cases, magmatic and (or)
externally derived water in the eruption cloud may condense on ash particles
and initiate hydrometeor growth. Both hydrometeor growth and gravitational
overturn have been suggested to produce the mammatus clouds that developed
in mid-day over central Washington on 18 May 1980 and signaled mass settling
(Durant, 2015; Durant et al., 2009; Carazzo and Jellinek, 2012). Mammatus
descent rates are typically meters per second (Schultz
et al., 2006), much faster than the settling rate of individual ash
particles (< 0.1 m s-1) or even of ash aggregates (<∼ 1 m s-1, Fig. 6).
The extent to which these processes operated at Crater Peak, Ruapehu, and
Redoubt is unknown. Cloud structures were not observed during the nighttime
eruptions of Redoubt and Crater Peak (Spurr). Although virga-like
structures can be seen in some near-vent photos of Ruapehu
(Bonadonna et al., 2005, Fig. 9a), we have seen no
documentation of such instabilities farther downwind.
For operational forecasting, these mechanisms cannot be considered in any
case, because no operational model has the capability to resolve these
processes. The fact that these eruptions can all be reasonably modeled using
similar inputs for aggregate size is convenient, even if the processes
involved are not specified in the model. The agreement suggests that model
forecasts can still be useful during the coming years. Future work will
focus on the development of more sophisticated algorithms that account for
cloud microphysics.
The Supplement related to this article is available online at doi:10.5194/acp-16-9399-2016-supplement.
L. Mastin conceived the study, did the model simulations, and wrote most of
the paper. A. Van Eaton provided advice on aggregation processes. A. Durant
provided the data for Mount St. Helens and Crater Peak, and advice on
aggregation processes that occurred during those two eruptions.
Acknowledgements
We are grateful to the IAVCEI Commission on Tephra Hazard Modeling for
posting data on key eruptions that could be used for this
study.Edited by: M. TescheReviewed by: A. Folch, M. de' Michieli Vitturi, A. Neri, and one anonymous referee
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