Prepared in cooperation with the U.S. Department of Energy, Office of River Protection

A Probabilistic Assessment of Tephra-Fall Hazards at 

Hanford, Washington, from a Future Eruption of 

Mount St. Helens

Open-File Report 2020–1133

U.S. Department of the Interior

U.S. Geological Survey
Cover. The Hanford pre-treatment facility, under construction, November 2016. USGS photo by Larry G. Mastin.
A Probabilistic Assessment of Tephra-Fall Hazards at 

Hanford, Washington, from a Future Eruption of 

Mount St. Helens

By Larry G. Mastin, Alexa Van Eaton, and Hans F. Schwaiger

Prepared in cooperation with the U.S. Department of Energy, Office of River 

Protection

Open-File Report 2020–1133

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DAVID BERNHARDT, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2020

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Suggested citation:

Mastin, L.G., Van Eaton, A., and Schwaiger, H.F., 2020, A probabilistic assessment of tephra-fall hazards at Hanford, 

Washington, from a future eruption of Mount St. Helens: U.S. Geological Survey Open-File Report 2020–1133, 54 p., 

https://doi.org/10.3133/ofr20201133.

Associated data for this publication:

Mastin, L.G., Van Eaton, A., and Schwaiger, H.F., 2020, Data used to develop a probabilistic assessment of tephra-fall 

hazards at Hanford, Washington: U.S. Geological Survey Data Release, https://doi.org/10.5066/P9VPFXQR.

ISSN 2328-0328 (online)
iii

Acknowledgments

This report was prepared under contract with the U.S. Department of Energy, Office of River 

Protection (DOE/ORP). Except for a few minor formatting changes, the removal of a few tables, 

and the addition of a second appendix, it is identical to a report submitted to DOE/ORP.
iv

Contents

Acknowledgments........................................................................................................................................iii

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

The Explosive History of Mount St. Helens ......................................................................................4

What We Learned from the Eruption of 1980 ..........................................................................4

Older Tephra Deposits.................................................................................................................6

Methods.........................................................................................................................................................10

Inputs ...........................................................................................................................................................10

Eruption Source Parameters ............................................................................................................12

Erupted Volume ..........................................................................................................................12

Plume Height...............................................................................................................................12

Grain-Size Distribution..............................................................................................................14

Non-Aggregating Particles .............................................................................................14

Mean Aggregate Size (μagg).............................................................................................14

Mass Fraction Aggregating Ash ....................................................................................15

Secondary Physical Parameters......................................................................................................16

Meteorological Inputs........................................................................................................................17

Model settings.....................................................................................................................................17

Modeling Methodology...............................................................................................................................18

Results ...........................................................................................................................................................19

Deposit Thickness and Mass Load..................................................................................................20

Airborne Concentration .....................................................................................................................22

Grain-Size Distribution.......................................................................................................................25

Discussion.....................................................................................................................................................27

Results in the Context of Inputs........................................................................................................27

Comparison with Measured Airborne Concentrations ................................................................29

The Implications of Uncertain Fall Velocity....................................................................................31

Conclusions...................................................................................................................................................32

References Cited..........................................................................................................................................32

Appendix 1: Particle Characterization......................................................................................................38

Introduction...................................................................................................................................................38

Methods and Data .......................................................................................................................................39

Size Analysis of Volcanic Ash...........................................................................................................40

Sieving .........................................................................................................................................40

Laser diffraction.........................................................................................................................40

Sedigraph....................................................................................................................................41

Shape Analysis of Volcanic Ash.......................................................................................................42

Results and Discussion...............................................................................................................................43

Particle-Size Distributions.................................................................................................................43

Morphology of the Volcanic Ash Particles.....................................................................................46

Conclusions...................................................................................................................................................48
v

Appendix 2: Effect of Extremely Large Eruptions of Mount St. Helens on Tephra-Fall Thickness 

and Airborne Ash Concentration at the Hanford Site, Washington.......................................49

 by Larry G. Mastin, Michael Clynne, Manuel Nathenson, John Pallister, and 

Alexa Van Eaton

Introduction...................................................................................................................................................49

Size of the Largest Eruptions at Mount St. Helens.................................................................................49

Probability of an Eruption Larger than the Yn .........................................................................................50

Effect of Large Eruptions on our Model Results.....................................................................................51

Conclusions...................................................................................................................................................54

Figures

1. Maps and images from the May 18, 1980, eruption at Mount St. Helens............................5

2. Graphs showing particle-size distributions of tephra-fall from the May 18, 1980, 

eruption at Mount St. Helens......................................................................................................7

3. Map and graphs showing thickness of the Yn and 1980 deposits at Mount St. Helens...9

4. Model grid used by the Ash3d model for simulations ..........................................................10

5. Illustration of the two types of probability density functions used to assign 

parameter values in this study .................................................................................................11

6. Correlations between plume height and eruption rate or erupted volume ......................13

7. Diagram showing processes that influence the distribution of fine, distal ash...............14

8. Graphs showing settling velocity versus transport distance and diameter for 

particulate matter falling at Hanford, Washington ...............................................................16

9. Distribution of inputs used in the simulation..........................................................................18

10. Graphs of probability of exceedance of a given tephra thickness or ash 

concentration versus thickness and concentration.............................................................19

11. Calculated values of tephra-fall thickness in a “1-in-10,000-year event” ........................20

12. Maps of tephra deposition for four runs whose deposit thickness at Hanford is 

closest to “1-in-10,000-year event” .........................................................................................21

13. Tephra-fall duration at Hanford, Washington, versus eruption duration ..........................22

14. Graphs showing airborne ash concentration versus time for eruption simulations.......24

15. Graphs showing grain-size distributions at Hanford, Washington, for several 

model runs at varying conditions.............................................................................................25

16. Contrasting ash-cloud shapes from small and large eruptions..........................................28

17. Graph of slopes of lines on plots of log thickness versus square root of 

area covered ...............................................................................................................................29

18. Sketches showing airborne particle sampling tools ............................................................30

19. Diagram showing control volume into which ash is falling at the mass 

accumulation rate.......................................................................................................................31

20. Illustration of the path that might be taken by aggregates or particles falling near 

the intake of an HVAC system of generic design ..................................................................32

 1.1. Scanning electron microscope images of volcanic ash used in this study ......................39

 1.2. Schematic showing the particle characterization methods used on different sizes 

for this study ................................................................................................................................40

 1.3. Images showing steps of particle-shape analysis ................................................................43
vi

 1.4. Histograms showing particle-size distributions from sieve-laser diffraction 

analysis of each volcanic ash sample collected in the field...............................................44

 1.5. Comparison of parent versus resuspended ash from Portable laboratory experiments, 

using material from Mount St. Helens, Washington, and the Valley of Ten Thousand 

Smokes, Alaska...........................................................................................................................45

 1.6. Histograms showing comparison of the particle-size distribution of the proximal 

May 18, 1980, ash sample from this study (gray bars) with other samples from 

the same eruption.......................................................................................................................46

 1.7. Histogram of feret diameters from each of the samples analyzed for shape...................47

 1.8. Plots showing the results of particle-shape analysis on the three samples of 

volcanic ash.................................................................................................................................47

 2.1. Graph showing the number of Cascade eruptions versus age, in thousands of 

years before present..................................................................................................................51

 2.2. Graphs showing volume and thickness of tephra deposits indicated by model runs ....52

 2.3. Graphs showing the cumulative distribution function and the probability 

distribution functions as a function of dense-rock equivalent volume .............................53

Tables

1. List of variables .............................................................................................................................2

2. Tephra deposits from large Plinian eruptions of Holocene age at Mount St. Helens, 

Washington....................................................................................................................................8

3. Summary of procedures used to assign eruption source parameters in 

each simulation...........................................................................................................................11

4. Values of secondary physical parameters and model settings used in 

each simulation...........................................................................................................................11

5. Total grain-size distribution from the 1980 deposit and used in this study ......................12

6. Mass fraction of fine ash assigned to different size bins for aggregates ........................15

7. Mass fraction of fine ash in selected recent eruption deposits.........................................15

8. Threshold values of tephra-fall thickness in millimeters and airborne 

concentration at different exceedance probabilities...........................................................20

9. Table of runs yielding deposit thicknesses close to T10K ......................................................21

10. Table of runs producing ash concentrations close to Cmax,10K..............................................22

11. Table of runs producing ash concentrations close to Cmax,2k ...............................................23

12. Table of runs producing ash concentrations close to Cmax,1k ...............................................23

13. Run numbers producing ash concentrations at Hanford, Washington, 

close to Cavg,10K .............................................................................................................................23

14. Grain-size distribution at Hanford, Washington for runs where T≅T10k .............................25

15. Grain-size distribution at Hanford for runs producing ash concentrations 

close to Cmax,10K......................................................................................................................................................................................................................26

16. Grain-size distribution at Hanford for runs producing ash concentrations 

close to Cavg,10K .............................................................................................................................27

17. Estimated range of uncertainty in secondary physical parameters and their possible 

effects on results ........................................................................................................................28
vii

18. Measurements of suspended particle concentrations made during 

volcanic eruptions ......................................................................................................................30

19. Tabulated fall velocities of ash aggregates from different sources ..................................31

 1.1. Volcanic ash samples used in particle characterization.....................................................39

 1.2. Particle-size distributions using combined sieve-laser diffraction analyses, 

shown as cumulative percent less than a given size fraction............................................41

 1.3. Sieve-sedigraph particle-size distributions, shown as cumulative weight percent 

less than a given size fraction ..................................................................................................42

 1.4. Particle shape descriptors used in this study .......................................................................43

 1.5. Samples and number of particles used in shape analysis..................................................43

 2.1. Thickness of the largest tephra layers at Mount St. Helens, at 8–11 kilometers from 

the vent.........................................................................................................................................50

 2.2. Number of eruptions in the Smithsonian Institution’s Global Volcanism Program 

Volcanoes of the World Database, listed by size ..................................................................50

 2.3. Effect of the addition of a small number of high-volume simulations on the 

tephra-fall thickness, maximum airborne ash concentration, and average airborne 

ash concentration at Hanford, Washington, having an annual probability of 

one in 10,000 ................................................................................................................................52

 2.4. Values of tephra-fall thickness, maximum airborne ash concentration and average 

airborne ash concentration at Hanford, Washington...........................................................54
viii

Conversion Factors

International System of Units to U.S. customary units

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

kilometer (km) 0.5400 mile, nautical (nmi) 

meter (m) 1.094 yard (yd) 

Area

square meter (m2) 0.0002471 acre 

hectare (ha) 2.471 acre

square hectometer (hm2) 2.471 acre

square kilometer (km2) 247.1 acre

square centimeter (cm2) 0.001076 square foot (ft2)

square meter (m2) 10.76 square foot (ft2) 

square centimeter (cm2) 0.1550 square inch (ft2) 

square hectometer (hm2) 0.003861 section (640 acres or 1 square mile)

hectare (ha) 0.003861 square mile (mi2) 

square kilometer (km2) 0.3861 square mile (mi2)

Volume

cubic meter (m3) 6.290 barrel (petroleum, 1 barrel = 42 gal)

cubic meter (m3) 264.2 gallon (gal) 

cubic decimeter (dm3) 0.2642 gallon (gal) 

cubic meter (m3) 0.0002642 million gallons (Mgal) 

cubic centimeter (cm3) 0.06102 cubic inch (in3) 

cubic decimeter (dm3) 61.02 cubic inch (in3) 

liter (L) 61.02 cubic inch (in3) 

cubic decimeter (dm3) 0.03531 cubic foot (ft3) 

cubic meter (m3) 35.31 cubic foot (ft3)

cubic meter (m3) 1.308 cubic yard (yd3) 

cubic kilometer (km3) 0.2399 cubic mile (mi3) 

cubic meter (m3) 0.0008107 acre-foot (acre-ft) 

cubic hectometer (hm3) 810.7 acre-foot (acre-ft) 
ix

Multiply By To obtain

Mass

gram (g) 0.03527 ounce, avoirdupois (oz)

kilogram (kg) 2.205 pound avoirdupois (lb)

metric ton (t) 1.102 ton, short [2,000 lb]

metric ton (t) 0.9842 ton, long [2,240 lb]

Density

kilogram per cubic meter 

(kg/m3

) 

0.06242 pound per cubic foot (lb/ft3

) 

gram per cubic centimeter 

(g/cm3

)

62.4220 pound per cubic foot (lb/ft3

) 

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F = (1.8 × °C) + 32.

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C = (°F – 32) / 1.8.

Conversion Factors—Continued

Abbreviations

DOE/ORP U.S. Department of Energy, Office of River Protection

DRE Dense-rock equivalent

ECMWF European Centre for Medium-Range Weather Forecasts

ERA European Centre for Medium-Range Weather Forecasts reanalysis

GSD grain-size distribution

GVP Global Volcanism Program

HVAC heating, ventilation, and air conditioning 

MSH Mount St. Helens

pdf probability density function

PM particulate matter

SEM scanning electron microscope

TSP total suspended particulates

USGS U.S. Geological Survey

VEI Volcanic Explosivity Index

VTTS Valley of Ten Thousand Smokes

WTP Waste Treatment and Immobilization Plant

A Probabilistic Assessment of Tephra-Fall Hazards at 

Hanford, Washington, from a Future Eruption of 

Mount St. Helens

By Larry G. Mastin, Alexa Van Eaton, and Hans F. Schwaiger

Abstract

Hanford, Washington (USA) is the construction site 

of a multi-billion-dollar high-level nuclear waste treatment 

facility. This site lies 200 kilometers (km) east of Mount St. 

Helens (MSH), the most active volcano in the contiguous 

United States. Tephra from a future MSH eruption could pose 

a hazard to the air intake and filtration systems at this plant. In 

this report, we present a probabilistic estimate of the amount 

of tephra that could fall, and the concentrations of airborne ash 

that could occur at the Hanford Site during a future eruption. 

Mount St. Helens has produced four large explosive eruptions 

in approximately the past 500 years, suggesting that its annual 

probability of eruption (P1) is roughly 4/500 = 0.008. Assuming 

that a large eruption occurs, we calculate the probability (P3|1) 

of a given fall deposit thickness or airborne concentration at 

Hanford by running about 10,000 simulations of ash-producing 

eruptions using the atmospheric transport model Ash3d. In each 

simulation, we calculate the pattern of tephra dispersal, deposit 

thickness at Hanford, and airborne ash concentration at ground 

level. As input for each simulation, we choose meteorological conditions from a randomly chosen time in the historical 

record between 1980 and 2010, using data from the European 

Centre for Medium-Range Weather Forecasting (ECMWF) 

Reanalysis (ERA) Interim model. The volume (dense-rock 

equivalent) of each simulated eruption is randomly chosen 

from a uniform probability distribution on a log scale from the 

range of magma volumes (0.008–2.3 cubic kilometers [km3]) 

estimated for late Holocene eruptions at MSH. Plume heights 

and durations of each eruption are chosen using empirical 

correlations between volume, height, and eruption rate, which 

account for the fact that larger eruptions have higher plumes 

and last longer. We construct summary tables of final deposit 

thickness (T), maximum ground-level airborne concentration 

(Cmax), and average ground-level airborne concentration (Cavg) 

during tephra-fall for each run. Each table is sorted and ranked 

by decreasing value of T, Cmax, or Cavg. Conditional probabilities 

(P3|1) are derived by dividing rank by n+1, where n is the total 

number of successful runs. For example, a deposit thickness 

of 5.10 centimeters (cm) from run 446 is ranked 123 of 9,785 

successful runs, yielding P3|1 = 123/9,786 = 0.01257. Its annual 

probability is P=P1·P3|1=0.008×0.01257=0.000101. By interpolation, the deposit thickness (T10k) having an annual probability 

of 1 in 10,000 (P= 0.0001) is 5.11 cm. Analogous concentration 

values are Cmax,10k=3,819 and Cavg,10k=1,513 milligrams per cubic 

meter (mg/m3), respectively. Independent calculations using the 

known mass accumulation rate of the deposit (Ṁd=0.001–0.006 

kilograms per square meter per second [kg/m2/s]), aggregate 

fall velocities (u=0.3–0.8 meters per second [m/s]), and the 

simple formula C= Ṁd / u, yield similar results, although highly 

variable fall velocities add significant uncertainty. This formula 

implies that deposit accumulation rates of millimeters (mm) to 

greater than 1 cm per hour, which are not uncommon during 

heavy ash fall, are associated with airborne concentrations of 

102–103 milligrams per cubic meter (mg/m3). These concentrations are much higher than published measurements (10−3–101

mg/m3), which record only suspended particles sampled in 

sheltered areas. During heavy ashfall, most fine ash falls as 

aggregates. Whether such aggregates will be ingested into air 

ducts will depend on the aggregate size and fall rate, the fragility of the aggregates, the air duct geometry, intake velocity, 

and other factors.

Introduction

Radioactive waste generated during World War II and the 

Cold War were originally contained in 177 underground tanks 

at the Hanford Site near Richland, Washington. In support of 

its nationwide environmental cleanup of nuclear facilities, the 

U.S. Department of Energy (DOE), Office of River Protection 

(ORP) is constructing a facility and supporting infrastructure 

(the Waste Treatment and immobilization Plant [WTP]) to 

retrieve, process and vitrify this waste for permanent storage. 

An explosive eruption from Mount St. Helens (MSH) could 

potentially deposit enough ash at Hanford to temporarily 

disrupt site operations (for example, WTP). DOE Standards that 

provide criteria and guidance for natural phenomena hazards 

analysis (for example DOE-STD-1020, Section 8) require 

that this be stated in probabilistic terms. For this project, it is 

interpreted to mean, “What deposit thickness and airborne ash 

concentration could be expected at Hanford given a Mount St. 

Helens eruption with an annual exceedance probability of 1 

in 10,000?” We notate the thickness and concentration values 

at this threshold as T10K and C10k, respectively (see table 1 for 

a list of variables). This report provides a methodology to 

quantify these values.
2 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

In 2011, Hoblitt and Scott (2011) found that ashfall at the 

Hanford site would most likely come from MSH, rather than 

Mount Rainier, Hood, Adams, or other regional volcanoes. 

Hoblitt and Scott (2011) also estimated T10K empirically from 

volcanological and meteorological data, by breaking the problem into three components:

1. What is the annual probability of a large ash-producing 

eruption (P1) from MSH? Hoblitt and Scott noted that 

four large eruptions had occurred at MSH in approximately the past 500 years, suggesting that 

P1≅ 4/500=0.008. 

2. Given a large eruption, what is the probability that wind 

will be blowing toward Hanford (P2|1)? From historical 

records they concluded that (P2|1)≅ 0.18.

3. Given an eruption with wind blowing toward Hanford, 

what is the exceedance probability of a given amount 

of ash fall (for example, 1, 5, or 10 centimeters [cm]) at 

Hanford (P3|2)? To address this question, they examined 

the thickness of 14 large eruptions whose deposits 

could be tracked 200 kilometers (km). The thickest 

deposited 10 cm, suggesting P3|2=1/(14+1)=0.067 

of greater than 10 cm thickness. The product 

P1·P2|1·P3|2=0.008·0.18·0.067 is about 1 in 10,000, 

implying that T10K≅10 cm.

Snow and Nelson (2012) used this result, and an assumed 

deposit density of 1,125 kilograms per cubic meter (kg/m3), to 

calculate an approximate mass load (M) of 112 kilograms per 

square meter (kg/m2). Assuming a settling rate of u=1.7 meters 

per second (m/s) and an ashfall duration of Dd=12 hours 

(hrs; 43,200 seconds [s]), they calculated an airborne tephra 

concentration at ground level of C=M/(Dd·u)= about 1,500 

milligrams per cubic meter (mg/m3). Airborne concentrations 

this high could be economically challenging to filter.

A more sophisticated analysis could provide a more 

robust result. The erupted magma volume, plume height, 

eruption duration, and size distribution resulting from the next 

large eruption are uncertain; but a reasonable range of estimates can be made from past eruptions at Mount St. Helens 

and from eruptions of similar size around the world. Given 

specified inputs, the tephra-fall thickness at Hanford can be 

calculated using transport models such as the U.S. Geological 

Survey (USGS) Ash3d model (Schwaiger and others, 2012).

The purpose of this study is to use a Monte Carlo procedure and approximately 10,000 model simulations to calculate 

probabilities of exceedance of specified levels of ashfall or 

airborne concentration (P3|1), given an eruption whose size 

and other characteristics range within likely bounds for Mount 

St. Helens. The probability P3|1 replaces the product P2|1⋅P3|2

from Hoblitt and Scott (2011). Combined with P1, our results 

yield new values of tephra-fall thickness (T10K) and maximum 

(Cmax,10k) or average (Cavg,10k) airborne ash concentration having an annual probability of occurrence of 1 in 10,000. Key 

inputs for each simulation are assigned following Monte Carlo 

procedures, using methods similar to other studies (Stirling 

and Wilson, 2002; Hurst and Smith, 2004; Mastrolorenzo and 

others, 2008; Amigo, 2013; Bear-Crozier and others, 2016).

Table 1. List of variables.

[Abbreviations: DRE, dense-rock equivalent; hr, hour; kg, kilogram; kg/m2, kilogram per square meter; kg/m3, kilogram per cubic meter; kg/m2/s, kilogram per 

square meter per second; kg/s, kilogram per second; km, kilometer, km2, square kilometer; km3, cubic kilometer; m, meter; m/s, meter per second; m2/s, square 

meter per second; mm, millimeter; mg/m3, milligram per cubic meter; mg-s/m3, milligram-seconds per cubic meter; yr, year]

Variable Description Units

A Area on ground surface m2

a,b,c Ellipsoid semi-axes m

C Airborne ash concentration mg/m3

Cmax Maximum airborne concentration during the period of Tephra-fall mg/m3

Cavg Average airborne concentration during the period of Tephra-fall (dosage divided by fall duration) mg/m3

Cmax,10K Value of the maximum airborne ash concentration at Hanford having a recurrence interval of 10,000 yrs mg/m3

Cavg,10K Value of the average airborne ash concentration at Hanford having a recurrence interval of 10,000 yrs mg/m3

Cmax,2K Value of the maximum airborne ash concentration at Hanford having recurrence interval of 2,000 yrs mg/m3

Cavg,2K Value of the average airborne ash concentration at Hanford having recurrence interval of 2,000 yrs mg/m3

Cmax,1K Value of the maximum airborne ash concentration at Hanford having recurrence interval of 1,000 yrs mg/m3

Cavg,1K Value of the average airborne ash concentration at Hanford having recurrence interval of 1,000 yrs mg/m3

De Eruption duration hrs

Dd Duration of ash fall hrs

d Particle diameter mm
Introduction 3

Table 1. List of variables.—Continued

Variable Description Units

de Eruption dosage (airborne concentration times time) mg-s/m3

dz Vertical nodal spacing km

F Particle shape factor (≡(b+c)/2a)

H Plume height above sea level km

Hbestfit Plume height above the vent calculated by equation 3 km

Hv Plume height above the vent km

Kx Diffusion coefficient in the horizontal direction m2

/s

k Suzuki constant

k0,k1,k2 Slopes of lines on plots of log thickness versus square root of area covered km−1

M Mass load of tephra deposit kg/m2

Ṁd Mass accumulation rate of deposit kg/m2

/s

m Deposit mass kg

m63 Mass fraction ash in the deposit <0.063 mm

mfines Mass fraction of a deposit moved into the aggregate size classes

mp,i Mass fraction of non-aggregating particles of size class i

n Number of successful runs

P Annual exceedance probability of a given tephra-fall thickness T or airborne ash concentration C. 

P=P1⋅P2|1⋅P3|2 (Hoblitt and Scott, 2011), or P=P1⋅P3|1 (this study)

P1 Annual probability of eruption, from (Hoblitt and Scott, 2011) (=0.008)

P2|1 Probability of wind blowing toward Hanford given that an eruption has occurred, from Hoblitt and Scott (2011)

P3|2 Probability of exceedance of a given tephra thickness given that an eruption has occurred, and that the wind is 

blowing toward Hanford. From Hoblitt and Scott

P3|1 Probability of exceedance of a given tephra thickness or ash concentration given that an eruption has occurred

Qm Mass eruption rate kg/s

T Tephra-fall thickness mm

T10K Tephra-fall thickness at Hanford having an annual probability of P=0.0001 (the “1-in-10,000-year event”) mm

T2K Tephra-fall thickness at Hanford having an annual probability of P=0.0005 (the “1-in-2,000-year event”) mm

T1K Tephra-fall thickness at Hanford having an annual probability of P=0.001 (the “1-in-1,000-year event”) mm

t

d Arrival time of ashfall, in hours after the start of the eruption hrs

u Settling velocity m/s

V Erupted volume (DRE) km3

Vmin Minimum erupted volume used in model simulations. (volume in DRE) km3

Vmax Maximum erupted volume (DRE) used in model simulations. Equal to the volume of largest eruption likely to 

occur for the purposes of this study

km3

zv Elevation above the vent m

 Particle size. =−log2(d), where d is particle diameter in millimeters

p,i

Size of non-aggregating particle of class i 

μagg Median aggregate size 

ρp Density of particle kg/m3

ρagg Density of aggregate kg/m3

ρd Density of deposit kg/m3

ρm Density of magma kg/m3

σagg Standard deviation in aggregate size 
4 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

An accompanying study, appendix 1, characterizes the 

size and shape of tephra particles that have been tested for 

resuspension properties as part of this Department of Energy 

Ashfall Project (Etyemezian and others, 2019). The appendix 

was added as a means of publishing results that were contracted by DOE. A second appendix (appendix 2) describes 

a follow-up study that examines the effect that rare, very 

large events might have on our estimates of T10k, Cmax,10k, and 

Cavg,10k. This follow-up study was taken in response to concerns 

expressed by the Defense Nuclear Facilities Safety Board that 

our original study, which did not consider such events, could 

understate the hazard.

The Explosive History of Mount St. Helens

Mount St. Helens is the most active and among the most 

explosive volcanoes in the Cascade Range of North America. 

The Cascade Range extends along the west coast from Lassen 

Peak (California) in the south to Mount Garibaldi (British 

Columbia) in the north, roughly the same range of latitude 

where the Juan de Fuca Plate subducts beneath the North 

American Plate at a rate of about 40 millimeters per year 

(mm/yr) (Coltice and others, 2017). Globally, volcanic arcs 

with the highest rate of volcanism are those whose subduction rates are high. The subduction rate of the Juan de Fuca 

Plate beneath North America is in the middle of the range of 

subduction rates observed worldwide (as much as 80 mm/yr). 

Magma production rates along the Cascade arc are modest in 

comparison with, for example, those volcanic arcs of Indonesia or the southern Andes. 

Volcanism along the Cascade arc has persisted for tens of 

millions of years, but most individual volcanoes, like Mount 

St. Helens or Mount Rainier, are only hundreds of thousands 

of years old. Mounts Rainier, St. Helens, and other Cascade 

volcanoes are built on eroded volcanic centers from past geologic periods. Mount St. Helens, for example, sits atop igneous 

rocks with an age of 28–23 mega-annum (Ma) (Evarts and 

others, 1987). Mount Rainier overlies rocks of age 36–14 Ma 

(Vance and others, 1987). Rocks of present-day Mount Rainier 

erupted less than 500,000 years ago (500 kilo-annum [ka]) 

(Sisson and others, 2001). All Mount St. Helens rocks are 

younger than about 300 ka (Clynne and others, 2008), and 

most of the Mount St. Helens edifice is younger than 4 ka—

younger than the pyramids of Egypt.

Stratovolcanoes, such as the main Cascade Range peaks, 

primarily erupt during stages lasting centuries to millennia. At 

Mount St. Helens, the current, highly active stage (the Spirit 

Lake stage) has continued since 3.9 ka; earlier stages extended 

from 16–10 ka (Swift Creek), and 28–18 ka (Cougar stage; 

(Pallister and others, 2017). Brief periods of quiesence are 

between these stages of activity.

In the past 4,000 years, MSH has produced nine mapped 

tephra deposits that can be traced tens, hundreds, or even 

greater than 1,000 kilometers from the volcano (Westgate, 

1977; Zoltai, 1989; Carey and others, 1995; Mullineaux, 

1996). By comparison, ash-producing eruptions from the 

neighboring volcanoes of Mounts Adams, Hood, and Rainier 

have been few and small during this period. At 8 kilometers 

from the vent, for example, the thickest post-4 ka tephra 

deposit from MSH (Yn of table 2) is about 2 meters (m) 

thick (Mullineaux, 1986; Carey and others, 1995). For 

comparison, at 7 km distance from Rainier, the thickest post4 ka Rainier deposit (the C tephra) is about 30 centimeters 

(cm) (Mullineaux, 1974); and at 6 km from Mount Adams, 

the thickest layer (layer 23 of Hildreth and Fierstein [1997]) 

is less than 10 cm. At Mount Hood, the only post-4 ka tephra 

deposits were produced when domes growing south of the 

summit collapsed and avalanched down the steep south flank, 

releasing clouds of debris. Such deposits are decimeters 

thick near Timberline Lodge, 5 km south of the vent (Scott 

and Gardner, 2017). Thus, we infer that the tephra hazard to 

Hanford is primarily from eruptions of Mount St. Helens.

What We Learned from the Eruption of 1980

The May 18, 1980, eruption gave us vivid images of the 

hazard ash poses in central Washington. It also demonstrated 

some key processes that have influenced how we have set up 

this modeling study.

The May 18, 1980, eruption followed 2 months of precursory activity; seismicity started on March 20 and included 

many earthquakes of magnitude 3, 4, and even 5. Dramatic 

deformation of the volcano’s north flank (growth of the 

“bulge”) was underway within a few days of the onset of 

seismicity. Phreatic (steam) eruptions from the summit started 

March 27 and continued through early May. The climactic 

eruption on May 18, however, was not preceded by any 

uptick in seismicity or deformation rate in the hours or days 

preceding the event.

The May 18 eruption started with gravitational collapse 

of the north flank of the volcano, which had been destabilized 

by intrusion of a magma body into the upper edifice. At 

8:32 a.m. local time, the north flank abruptly slid outward, 

uncorking the magma body whose gases expanded northward 

as a pyroclastic density current that destroyed about 600 

square kilometers of forest. As the pyroclastic current rode 

over the ground surface, it entrained air and became buoyant, 

lifted off the ground from an area about 10 km north of the 

summit, rose to about 32 km in the atmosphere, and expanded 

as an umbrella cloud to about 150 km in diameter (Sparks and 

others, 1986; Holasek and Self, 1995) (fig. 1B).

Within a few tens of minutes after the flank collapse 

(Christiansen and Peterson, 1981), a vertical Plinian column 

began rising from the volcano’s decapitated summit, reached 

about 15 km above sea level, and fluctuated between 13 and 

17 km for the next 9 hours (Harris and others, 1981). In the 

first few hours, airborne ash moved downwind from both the 

Plinian column and the umbrella cloud. In the afternoon, ash 

injected by the Plinian column was supplemented by fine ash 

rising buoyantly from pyroclastic flows that avalanched down 

the volcano’s north flank (fig. 1D). 

The resulting ash cloud moved eastward at an average 

speed of 100 kilometers per hour (km/hr), reaching Yakima, 

Washington around 9:45 a.m. Pacific Time; Pasco, Washington 
Introduction 5 Figure 1

49 ̊48 ̊47 ̊46 ̊45 ̊

124 ̊ 122 ̊ 120 ̊ 118 ̊ 116 ̊ 114 ̊

50 μm

C. Yakima ash

B. From Toledo, looking Southeast, 8:45 a.m.

Rocky Kolberg, Wikimedia Commons 

E. Yakima, noon

U.S. Forest Service photo

F. 

USGS photo by Daniel Dzurisin

Moses Lake

Quarter for scale

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Ritzville

A. Mass load map, 1980

Hanford

WASHINGTON

200 KILOMETERS

100 MILES

100 0

50 0

50302010510.50.10.01

EXPLANATION

Grain-size in figure 2MeasurementsMass load, in kilogram 

per square meter 

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Pacific Ocean

IDAHO

MONTANA

OREGON

Pyroclastic flows

D. Looking east, 1:50 p.m.USGS Joe Rosenbaum photo

WASHINGTON

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116° 120° 124°

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km

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Ritzville bulge

G. Isopach map

TB7 SW412 DZ21_8

DZ20_20

CAREY66

CAREY20

Figure 1. Maps and images from the May 18, 1980, eruption at Mount St. Helens. 

A, Mass load map of 

the May 18, 1980, Mount St. Helens tephra deposit, digitized from figure 338 of Sarna-Wojcicki and others (1981). 

B, Composite photograph of the growing umbrella cloud, taken from Toledo, Washington around 

8:45 a.m. Wikimedia Commons photo by Rocky Koberg. 

C, Scanning electron microscope 

(SEM) image of ash collected in Yakima, Washington, 144 kilometers (km) downwind. 

D, Plume and 

pyroclastic flow activity at the vent around 1:50 p.m. USGS photograph by Joe Rosenbaum. 

E, Image of 

Washington Street, Yakima, taken around noon on May 18, 1980. U.S. Forest Service photograph. 

F, 

Tephra-fall thickness at Moses Lake, 250 km downwind. USGS photo by Daniel Dzurisin. 

G, Isopach map of 

the deposit, digitized from figure 336 of Sarna-Wojcicki and others (1981). km3, cubic kilometers; mm, 

millimeter; USGS, U.S. Geological Survey; μm, micrometer.
6 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

around 10:45; Spokane around noon; and Missoula, Montana 

at about 3:00 p.m. (Sarna-Wojcicki and others, 1981). Although 

the plume reached heights of 32 km (15 ±2 km for the Plinian 

phase), the cloud’s leading edge that passed over central 

Washington was around 10–12 km elevation, where wind 

speeds were highest.

The tephra-fall deposit from this eruption (fig. 1A) is one 

of the world’s most thoroughly studied. Within days, field crews 

drove north-south transects across Washington State, stopping 

regularly (red dots, fig. 1A) to measure the thickness (T) of the 

deposit, and collect ash from measured areas (A) on the ground 

or on flat surfaces such as the roofs of cars, stairs (fig. 1F), or 

sidewalks. The fresh deposit had not yet been altered by wind or 

by rain, allowing scientists to sample to distances of more than 

600 km, where thicknesses were a fraction of a millimeter. The 

samples were dried and weighed to obtain a mass (m), and to 

calculate a mass per unit area (M= m/A) and a deposit density 

(ρd=M/T) at each location. Maps of both thickness (fig. 1G) and 

mass load (fig. 1A) were created by contouring these data.

Like new-fallen snow, these deposits were light and 

fluffy. Bulk deposit densities in central Washington and beyond 

averaged 450 kg/m3 and decreased to less than100 kg/m3

beyond 500 km distance (Sarna-Wojcicki and others, 1981). 

Rainfall rapidly compacted the ash, as observed when sampling 

deposits from May 25 and June 12 eruptions, which were 

accompanied or shortly followed by rain and had densities of 

1,000 to 1,250 kg/m3 (Sarna-Wojcicki and others, 1981). Grainsize distributions were also analyzed from many samples, and 

then combined in a weighted sum to estimate the grain-size 

distribution of the entire erupted mass (Carey and Sigurdsson, 

1982; Durant and others, 2009).

Several key findings were noted:

1. The overall grain-size distribution (fig. 2G) was 

exceedingly fine, with more than 60 percent of the 

erupted mass consisting of particles finer than 0.06 

mm diameter. Beyond about 200 km distance, greater 

than 75 percent of ash was less then 0.06 mm diameter (Durant and others, 2009). Much of the fine ash 

consists of the walls of burst pumice bubbles. The fine 

grain size has been linked to both the bubble sizes in 

the magma (dominantly 0.01–0.022 millimeters [mm] 

(Genareau and others, 2012)) and the milling of ash 

within pyroclastic flows (Dartevelle and others, 2002).

2. The median grain size of the ash decreased downwind 

to about 300 km distance, then remained constant at 

greater distance (Carey and Sigurdsson, 1982; Durant 

and others, 2009).

3. The grain-size distribution (GSD) at about 25–200 km 

distance was bimodal (fig. 2A–C). A coarse mode 

of particles a few tenths of a millimeter in diameter 

dominated at proximal distances (fig. 2A, B), but they 

decreased in both median size and in mass fraction 

with distance and disappeared from the size distribution beyond about 200 km (fig. 2D). A fine mode of 

particles with a median size of 8–16 micrometers did 

not change significantly in median size but increased in 

abundance with distance.

4. Isopach maps showed that both deposit thickness 

and mass load decreased with distance, but they then 

increased again to form an intriguing secondary maximum about 290 km downwind (fig. 1G), near the town 

of Ritzville, Washington (Sarna-Wojcicki and others, 

1981). At this distance, about 93 percent of the tephra 

is smaller than 0.06 mm. Particles of this size, falling 

from a 15-km-high plume, would not have deposited at 

this distance under these wind conditions if they were 

falling individually.

5. These observations indicate that the fine ash modes in 

figure 2A–F fell as clusters, so that their fall velocity 

was independent of the size of individual particles. 

The increased ashfall near Ritzville suggests either 

that the clusters had a narrow range of fall velocities 

(0.66–0.78 m/s; (Mastin and others, 2016)), causing 

them to land at a similar location, or that there was a 

change in the ash cloud that led to rapid sedimentation 

once the plume reached Ritzville. These ash clusters 

could be observed during active fallout. In Pullman, Washington for example (390 km downwind), 

aggregates were captured on wet, painted cardboard 

and described as delicate clusters 0.25–0.5 mm in 

diameter, composed of particles from less than 0.001 

to 0.04 mm in size (Sorem, 1982). Nearly all aggregates disintegrated on landing and left little evidence 

of their existence in the deposit. 

The bulk volume of the May 18, 1980, deposit, was 

estimated at 1.1 km3 and was calculated by determining the 

area within each isopach line, multiplying each isopach area 

by the isopach thickness, and then summing (Sarna-Wojcicki 

and others, 1981). Using the measured average deposit 

density and assuming a magma density of 2,000–2,600 kg/

m3, Sarna-Wojcicki and others (1981) estimated the bulk 

tephra volume to be equivalent to about 0.20 to 0.25 cubic 

kilometers (km3) of dense-rock-equivalent (DRE) magma. 

Later, the estimate was revised to 0.33 km3 (Criswell, 1987; 

Pallister and others, 1992).

Older Tephra Deposits

Field geologists, in the past five decades, have identified 

and named at least a dozen sets of tephra beds at Mount St. 
Introduction 7

men20-7413_fig02

0.001 0.031 1

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Figure 2. Graphs showing particle-size distributions of tephra-fall from the May 18, 1980, eruption at Mount St. Helens. 

A–F, Particle-size distributions of the deposit at different distances from the source, based on grain-size analyses 

published in Durant and others (2009). Names of samples analyzed are listed on the figure. Locations of these samples 

are shown in figure 1A. G, Total grain-size distribution (TGSD) for combined deposit. Blue bars give the mass fraction 

in a given bin. Blue lines with dots give the cumulative mass fraction coarser than the given size. Black dashed line is 

0.063 millimeters (mm). km, kilometer.
8 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Helens (Mullineaux, 1986). Table 2 lists all the tephra deposits 

from large eruptions of Holocene age at MSH. All such eruptions occured during the Spirit Lake Stage, since 3.9 ka. Carey 

and others (1995) estimated that the size of these eruptions 

ranged from 0.1 to about 4 km3 DRE (table 2). There are, 

however, large uncertainties in these estimates. To illustrate, 

figure 3A shows the map of deposit thickness (cm) used by 

Carey and others (1995) to estimate the volume of the largest Holocene tephra deposit, the 3.5 ka Yn. Red dots indicate 

locations where thicknesses were measured. Contour lines 

of equal thickness (isopachs) are interpolations of the thickness measurements. Note that, for this prehistoric deposit, the 

isopachs are constrained by fewer field measurements than the 

1980 deposit 

(fig. 1A). The thinnest isopach in figure 3A is 20 cm in contrast 

to 0.5 mm on the 1980 map (fig. 1G). In addition, the Yn on 

map figure 4A only extends about 40 km from of the volcano, 

in contrast to about 800 km on the 1980 map. Within 40 km 

distance, the 1980 deposit contained only about six percent of 

its total volume (Carey and others, 1995). 

Deposit volume can be estimated by determining the area 

within each isopach line and plotting the log of the isopach 

thickness versus the square root of the area encompassed 

within each isopach line. For a well-mapped deposit like that 

of May 18, 1980, the data can be fit with two straight lines as 

shown, and the area under those lines can be integrated to give 

a bulk volume (fig. 3B).

Published Yn data define only the proximal line segment 

(red line, fig. 3C). Carey and others (1995) used published 

data from other deposits to argue that a distal line segment 

should intersect the proximal one at a point where thickness is 

about 12 percent of T0 (T1, fig. 3C); and the line should have a 

slope of about 0.01 to 0.015. From this assumed second line 

(blue dashed line, fig. 3C), Carey and others (1995) estimated 

about 15 km3 bulk erupted volume, with an uncertainty of 

±60 percent. Carey and others (1995) converted 15km3 bulk 

erupted volume to 4 km3 DRE assuming a deposit density 

of 600 kg/m3 and a magma density of 2,300 kg/m3. Carey 

and others (1995) did not present the data used to derive the 

second line or show a plot like figure 3C in their paper.

Recent work has revised the volume of most Mount St. 

Helens tephras downward. Nathenson (2017) plotted ln(T) 

versus sqrt(A) for Yn and noted that data points for the four 

isopach lines (black dots, fig. 3C) followed the proximal trend 

line to a point well beyond T1, where the distal line should 

intersect. Thus, Nathenson concluded that the Yn could 

not have the volume inferred by Carey and others (1995). 

Nathenson (2017) extrapolated the thicknesses using thinning 

trends (black lines, fig. 3C) from deposits documented by 

Sulpizio (2005). For each deposit in table 2, Nathenson (2017) 

estimated three volumes based on thinning trends in which 

less than 30 percent, 30–70 percent, or greater than 70 percent 

of the deposit lay within a proximal region of high thinning 

rates. For the Holocene eruptions in table 2, Nathenson’s 

(2017) volumes are 0.008–2.3 km3 DRE—much smaller than 

the 0.1–4.0 km3 of Carey and others (1995). Nathenson (2017) 

showed that Carey and others’ (1995) volume estimates could 

not be derived using the methodology described in their paper. 

For this reason, we consider values of Nathenson (2017) to be 

more authoritative.

The Yn represents deposit from the largest eruption in 

the past 10,000 years from MSH, and we take it to be the 

largest (volumetrically) likely to occur for the purposes of our 

analysis. We call this volume Vmax and use it as the maximum 

eruption volume modeled.

Volumes of tenths or hundredths of a cubic kilometer are 

several times more frequent than those of cubic kilometers 

(table 2). This trend is important in our modeling procedure 

and is described later.

Table 2. Tephra deposits from large Plinian eruptions of Holocene age at Mount St. Helens, Washington.

[For prehistoric eruptions, ages (column 2) are taken from Nathenson (2017). Columns 3–6 give approximate volumes of the deposits, as bulk tephra (columns 3 

and 4), and dense-rock equivalent magma (DRE, columns 5 and 6). Volumes in columns 3 and 5 are from Carey and others (1995); those in 4 and 6 are revisions 

by Nathenson (2017). For the 1980 eruption, the erupted volume (DRE) of 0.3 km3 for the Plinian fall deposit is from Pallister and others (1992). Abbreviations:

cal yrs B.P., calendar years before present (where present is 1950 C.E.); C.E., common era; DRE, dense-rock equivalent; km3, cubic kilometer; yr, year]

Deposit name Age Bulk volume, in km3 DRE Volume, in km3

Carey Nathenson Carey Nathenson

1980 1980 C.E. 1.1 1.1 0.3 0.3

T 1800 C.E. 1.5 0.12–0.34 0.4 0.031–0.089

We 1482 C.E. 1.5 0.15–0.80 0.4 0.039–0.21

Wn 1479 C.E. 7.7 0.71–1.4 2.0 0.19–0.37

Pu 2500–2900 cal. yrs B.P. 0.8 0.030–0.18 0.2 0.008–0.047

Ps 2550–2900 cal. yrs B.P. 0.4 0.031–0.18 0.1 0.008–0.047

Ye 3300–3500 cal. yrs B.P. 3.5 0.5–1.5 0.9 0.13–0.39

Yn 3500 cal. yrs B.P. 15.3 1.6–8.8 4.0 0.78–2.3

Yb 3850–3900 cal. yrs B.P. 1.2 0.044–0.26 0.3 0.011–0.068
Introduction 9

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EXPLANATION

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Figure 3. Map and graphs showing thickness of the Yn and 1980 deposits at Mount St. Helens. A, Measured 

thicknesses of the Yn deposit at Mount St. Helens and isopach contours of the thickness distribution, digitized 

from figure 3A of Carey and others (1995). B, Plot of log thickness (T) versus square root (sqrt) of the area 

encompassed within each isopach line for the May 18, 1980, deposit (fig. 1G). C, Plot of log thickness versus 

square root of area within each isopach for the Yn deposit (fig. 3A). Blue dots are the area within isopach lines 

in figure 3A (the lines had to be extrapolated to form closed polygons to derive these data points). Red line is the 

best-fit line through these points. Blue dashed line is the distal line inferred by Carey and others (1995) to derive 

a bulk tephra volume of 15.3 cubic kilometers (km3). Black lines were distal lines inferred by Nathenson (2017) to 

derive his estimated tephra volumes. km, kilometer.
10 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Methods

To simulate tephra transport and deposition, we use 

the model Ash3d, developed by the U.S. Geological Survey 

(Schwaiger and others, 2012). Ash3d is an Eulerian, finite-volume, advection-diffusion model that divides the atmosphere 

into a three-dimentional grid of cells (fig. 4). In each cell, at 

each time step, atmospheric properties such as wind vectors, 

temperature and pressure are linearly interpolated from the 

nearest cells in a numerical weather prediction model.

The column of cells above the volcano (fig. 4B) act as 

source nodes, meaning that at each time step, a mass of ash is 

added to each node and distributed vertically using the following equation (Suzuki, 1983), with an adjustable constant k that 

modulates the degree to which mass is concentrated near the 

top of the column:

(1)

where

Qm is the mass eruption rate (kilograms per 

second [kg/s]),

Hv is plume height above the vent; and

zv is elevation (above the vent) within the plume.

Within each cell, at a given time step, Ash3d calculates 

the flux through cell walls as tephra is: (1) advected by wind, 

(2) settles by gravity, and (3) spreads by turbulent diffusion. 

Advection and settling are calculated through the Donor-Cell 

Upwind method using a Lax-Wendroff scheme (LeVeque, 

2002, Chapter 6) in which flux in each direction is calculated 

sequentially (dimension splitting). Diffusion is calculated 

using an implicit Crank-Nicolson method in each coordinate 

to keep time steps reasonable (Schwaiger and others, 2012). 

Diffusion rates are calculated using a specified diffusion 

constant Kx. The calculations are done sequentially for each 

of a series of grain-size classes. These size classes represent 

individual particle sizes, or aggregates of particles. Particles 

or aggregates are assumed to be ellipsoidal in shape, with a 

specified diameter d, density ρ, and shape factor F ≡ (b + c) 

/ 2a, where a, b, and c are the semi-major, intermediate, and 

semi-minor axes of an ellipsoid, respectively. The diameter d

is assumed to equal (a + b + c) / 3, and the volume is assumed 

to equal πd3 / 6. The settling rate of particles or aggregates is 

calculated using relations of Wilson and Huang (1979).

Inputs

We define four categories of model inputs. The 

first category consists of eruption source parameters as 

conventionally defined in Mastin and others (2009), such as, 

erupted volume (V), plume height (H), duration (De), and a 

GSD characterized by parameters defined later. The source 

parameters differ from one simulation to the next, using 

Source nodes

Model grid

Hanford

B

A

Figure 4. Model grid used by the Ash3d model for simulations. A, Full view of the model grid. B, Close-up of the grid in 

southern Washington State, highlighting the source nodes above Mount St. Helens, and the Hanford, Washington site. Grid 

spacing is 0.1° latitude and longitude.

dQ

dz Q k z H k z HH k k

m

v

m v v v

v

  

  

2 1 1

1 1

( / ) exp( ( / ))

[ ( ) exp( )]
Inputs 11

procedures described below and summarized in table 3. Many 

of the parameter assignments involve randomly selecting the 

value of a variable from within a probability density function 

(pdf). The types of pdfs we use are uniform (fig. 5A) in which 

the probability of a given value is equal within a min–max 

range; and Gaussian (fig. 5B), in which the probability is 

highest at a mean value and decreases at a rate defined by the 

standard deviation.

The second category includes secondary physical parameters such as the Suzuki constant k; particle shape factor F; 

densities of particles (ρp), the deposit (ρd), and magma (ρm); 

and the diffusion coefficient Kx. These parameters do not vary 

between simulations. Rather, we use values that have been 

found to accurately reproduce mapped deposits in other studies (table 4). The third category consists of meteorological 

parameters: the wind field, atmospheric pressure, and temperature, which are used to calculate particle advection and 

fall velocities. These values are obtained from the output of an 

external meteorological model. The fourth category includes 

model settings such as vertical and horizontal cell spacing, which have been adjusted to give an acceptable balance 

between model accuracy and speed.

Table 3. Summary of procedures used to assign eruption source parameters in each simulation.

[Abbreviations: DRE, dense-rock equivalent; km, kilometer; km3, cubic kilometer; mm, millimeter; pdf, probability density function; ρm, density of magma;

Qm, mass eruption rate]

Parameter Method of assignment

Erupted volume (V) We choose randomly from a uniform pdf on a log scale, extending from Vmin=0.008 to Vmax=2.3 km3

 DRE.

Plume height (Hv) We calculate Hv from V using equation 3, and then add a random value, sampling from a Gaussian pdf with a mean 

of zero and a standard deviation of 2.9 km.

Eruption Duration (De) We calculate the eruption rate from the plume height using equation 2, and then calculate the duration by 

converting erupted volume to mass (assuming ρm=2,500 kg/m3) and dividing by the rate Qm.

Grain-size distribution We assume that all fine ash aggregates and characterize the fine ash fraction using two adjustable parameters, its 

fraction of the erupted mass (mfines) and the size of aggregates (μagg). We choose mfines, from a Gaussian pdf that 

has a mean of 0.5 and standard deviation of 0.15, based on considerations explained in the text. We choose 

μagg from a Gaussian pdf having a median of =2.4 (0.189mm) and a standard deviation of =0.1 (±7 percent). 

The aggregates are divided into five bins with mass fractions as shown in table 6 for median aggregate size 

σagg=0.1. For particles that do not aggregate, we use sizes and mass fractions derived from the May 18, 1980, 

deposit (Durant and others, 2009), with two modifications: (1) we consolidate particles greater than 2mm, 

which generally deposit at less than 100km distance, into a single d = 2mm size bin; and (2) we adjust the mass 

fraction in each bin equally so that the sum in all these bins, plus mfines, equals 1. 

Eruption start time We randomly choose a start time within the period January 1, 1980, to January 1, 2010.

min max

mean

standard

deviation

A. Uniform pdf

B. Gaussian pdf

probability probability

Figure 5. Illustration of the two types of probability density 

functions (pdf’s) used to assign parameter values in this study: 

uniform (A) and Gaussian (B).

Table 4. Values of secondary physical parameters and model 

settings used in each simulation.

[Abbreviations: asl, above sea level; kg/m3, kilogram per cubic meter; 

km, kilometer]

Physical Parameter or setting Value

Model domain 45–49°N

123–113°W

0–35 km asl (30 percent higher 

than plume)

Vent location 122.18°W

46.2°N

Vent elevation 2.00 (km)

Nodal spacing 0.1° horizontal

2.0 km vertical 

Diffusion coefficient (Kx) 0

Suzuki constant (k) 8

Particle shape factor (F) 0.44

Deposit density (ρd) 1,000 kg/m3

Magma density (ρm) 2,500 kg/m3

Aggregate shape factor (F) 1.00
12 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Eruption Source Parameters

We ran approximately 10,000 Ash3d simulations using 

a modified Monte Carlo approach. We did not use a straight 

Markov Chain Monte Carlo method, in which all key inputs 

are randomly assigned, independently of the others, because 

some inputs were correlated. For example, larger-volume 

eruptions tend to have higher plumes, and longer durations. 

Below, we explain how these relations are considered.

Erupted Volume

We choose volume (V) from a uniform pdf on a log scale 

ranging from 0.008–2.3 km3 DRE—the range estimated by 

Nathenson (2017); table 2) for Holocene Mount St. Helens 

eruptions. Eruptions smaller than 0.008 km3 are unlikely to 

impact the Hanford site. Our choice of a log scale implies 

that 0.1 km3 eruptions are about 10 times as likely as 1 km3

eruptions and reflects the greater frequency of small eruptions 

in the Holocene record.

Plume Height

Larger-volume eruptions produce higher plumes. On 

May 18, 1980, for example, Mount St. Helens erupted ash for 

about 9 hours at an average rate of 2×107 kg/s (Carey and Sigurdsson, 1985). The Plinian phase (after 9:00 a.m.) produced 

a plume that fluctuated around 14 km above the vent (Harris 

and others, 1981). The much larger June 15, 1991, eruption of 

Mount Pinatubo in the Philippines expelled close to 1×109 kg/s 

of magma for several hours (Koyaguchi and Tokuno, 1993), 

producing a maximum height of 34–39 km above the vent 

(Holasek and others, 1996). The smaller Eyjafjallajökull eruption in Iceland on April 14–18, 2010, emitted an average mass 

rate of 5–10 × 105 kg/s (Gudmundsson and others, 2012) and 

produced plume heights about 4–8 km above the vent (Arason 

and others, 2011).

Historical eruption data illustrate this relationship. 

Because big eruptions produce higher plumes than small ones, 

the plume height for each simulation cannot be chosen independently from erupted volume. Data have been published for 

a few dozen recent eruptions for which average plume height, 

erupted mass, and duration have been recorded (Wilson and 

others, 1978, table 3; Sparks and others, 1997, table 5.1; 

Mastin and others, 2009, table 1). The correlation observed in 

equation 2 is based on a few dozen examples (fig. 6A; (Mastin 

and others, 2009):

, (2)

where 

Hv is the plume height in kilometers above the 

vent; and

Qm is the mass eruption rate, in kg/s. 

The best-fit exponent of 0.241 is similar to a theoretical 

prediction of 0.25 (Morton and others, 1956) and to previous 

empirical relations (Wilson and others, 1978, eq. 2; Sparks and 

others, 1997, eq. 5.1).

Table 5. Total grain-size distribution from the 1980 deposit (column 3) and used in this study (column 4).

[Mass fractions in column 3 are estimated by Durant and others (2009, supplementary file number 3 of their paper) by integrating the deposit to a distance of 

about 670 kilometers. Column 4 gives formulas used to calculate mp,i if mfines is known. Density values are calculated as described in the text. Size of particles 

() is −log2(d),where d is particle diameter in millimeters. Abbreviations: kg/m3, kilogram per cubic meter; mm millimeter; mp,i, mass fraction of nonaggregating particles of size class i]

Size of particles, in  Diameter, in mm

Mass Fractions Density of particles, in kg/m3

1980 mp,i (this study)

≤-4.0 16.0000

-3. 5 11.3137 0.0007 490

-3.0 8.0000 0.0019 490

-2.5 5.6569 0.0021 490

-2.0 4.0000 0.0047 665

-1. 5 2.8284 0.0058 1,292

-1.0 2.0000 0.0056 0.0727(1-mfines) 2,003

-0. 5 1.4142 0.0084 0.0294(1-mfines) 2,350

0.0 1.0000 0.0141 0.0493(1-mfines) 2,005

0.5 0.7071 0.0214 0.0748(1-mfines) 2,248

1.0 0.5000 0.0459 0.1605(1-mfines) 2,624

1. 5 0.3536 0.0723 0.2528(1-mfines) 2,644

2.0 0.2500 0.0532 0.1860(1-mfines) 2,639

2.5 0.1768 0.0292 0.0766(1-mfines) 2,706

H Q v m = 0 3 0 241 . .
Inputs 13

Table 5. Total grain-size distribution from the 1980 deposit (column 3) and used in this study (column 4).—Continued

Size of particles, in  Diameter, in mm

Mass Fractions Density of particles, in kg/m3

1980 mp,i (this study)

3.0 0.1250 0.0330 0.0577(1˗mfines) 2,691

3.5 0.0884 0.0460 0.0402(1˗mfines) 2,730

4.0 0.0625 0.0602 2,698

4.5 0.0442 0.0700 2,640

5.0 0.0313 0.0799 2,581

5.5 0.0221 0.0829 2,570

6.0 0.0156 0.0790 2,670

6.5 0.0110 0.07174 2,670

7.0 0.0078 0.0575 2,670

7.5 0.0055 0.0429 2,670

8.0 0.0039 0.0327 2,670

8.5 0.0028 0.0261 2,670

9.0 0.0020 0.0207 2,670

9.5 0.0014 0.0138 2,670

10.0 0.0010 0.0094 2,670

10.5 0.0007 0.0063 2,670

≥11.0 0.0005 0.0029 2,670

Log volume, in cubic kilometers dense-rock equivalent

Height above vent, in kilometers

−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 .5

−20

0

20

40

Log rate, in kilograms per second

3.5 4 4.5 5.5 6.5 7 7.5 8.5

Height above vent, in kilometers

0

20

40

60

5 6 8

Data

Best fit

+/− σ

EXPLANATION

Figure 6. Correlations between plume height and eruption rate or erupted volume. A, Plume height above the 

vent (kilometers) versus log of eruption rate (kilograms per second) using historical data tabulated in Mastin 

and others (2009) (blue diamonds). The red solid line is a best-fit curve through these data, and the dashed lines 

give the ±1σ standard error in prediction. B, Plume height above the vent versus total erupted volume (cubic 

kilometers [km3] dense rock equivalent [DRE]) for the same historical eruptions.
14 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Total erupted volume also correlates with plume height 

(Carey and Sigurdsson, 1989; Mastin and others, 2009, 

Table1). A best-fit curve through historical data (fig. 6B) give

(3)

where

Hbestfit is plume height above the vent; and

 V is erupted volume in km3 DRE. The standard 

error in prediction (1σ) based on this 

correlation is about 5.8 km. 

We assign plume height using relationship (3), but then 

add a random number using a Gaussian pdf with a mean of 

zero and standard deviation of 2.9 km—half the standard error 

in the regression. We arbitrarily reduced the standard deviation 

of the Gaussian adjustment from 5.8 to 2.9 km to avoid having 

negative plume heights near the low end, and unrealistically 

high plumes (higher than 45 km) at the high end.

Grain-Size Distribution

The grain-size distribution (GSD) is challenging to 

parameterize because several processes can accelerate the 

fallout of fine ash; including particle aggregation, scavenging 

by rainfall, and bulk instabilities in the cloud (fig. 7). The 

Ash3d model does not explicitly account for these processes. 

Rather, we empirically adjust the input GSD, so fine ash is 

represented as aggregates of given size, shape, and density.

Our method to characterize distribution of both particles 

and aggregates in each simulation involves three groups of 

parameters: (1) one-dimensional arrays of the mass fractions 

(mp,i) of particles too large to aggregate, along with their size 

(p,i) and density (ρp,i); and single parameters defining (2) the 

median aggregate diameter (μagg), and (3) the mass fraction of 

fine, aggregating ash erupted (mfines).

Non-Aggregating Particles

To assign mp,i, we start with mass fractions of each size 

p,i from the 1980 deposit (table 5, column 3). We assign 

densities (ρp,i) to each size fraction using measured proportions of mafic crystals, feldspar, lithics, pumice, and glass 

fragments (Carey and Sigurdsson, 1982), assuming a density 

of 3,200 kg/m3 for mafic crystals, 2,600 kg/m3 for feldspars, 

2,900 kg/m3 for lithics, 490 kg/m3 for large pumice (≤1) 

(Klug and Cashman, 1994), and 2,670 kg/m3 for small glass 

fragments ( ≥ 4.5). For intermediate-sized pumice or glass 

(1 <  < 4.5), the density was interpolated linearly between 

490 and 2,670 kg/m3.

Next, we consolidate all particles larger than 2 mm 

in diameter into a single 2 mm bin, dramatically speeding 

computation time. Particles larger than 2 mm diameter will 

almost certainly fall out upwind of Hanford. Under the wind 

and plume conditions of 1980, for example, nearly all particles 

larger than 0.25mm diameter would have fallen out upwind 

(fig. 8A).

Mean Aggregate Size (μagg)

Third, we divide mfines into five aggregate classes having 

a narrow Gaussian size distribution with a standard deviation 

σagg = 0.1 (table 6). The narrow σagg is justified by recent Ash3d 

modeling (Mastin and others, 2016) that optimally fits deposits 

of four well-documented eruptions with nearly the identical 

aggregate-size distributions (mean μagg = 2.4 ± 0.1, standard 

deviation σagg ≤ 0.1). These eruptions—Mount St. Helens 

(May, 18, 1980); Crater Peak, Mt. Spurr, Alaska (September, 

16–17, 1992); Ruapehu, New Zealand (June, 17, 1996); and 

Redoubt, Alaska (March, 23, 2009)—ranged widely in magma 

type, plume height, eruptive volume, mass fraction fine ash, 

and atmospheric temperature and water content, suggesting that 

these parameters are robust. 

H V bestfit   25 9 6 64 10 . . log ( )

Secondary thickening Sharp front?

Path taken by aggregates that form 

in the rising column (Ash3d) Path taken by aggregates that form 

in the downwind cloud

Deposit

Fine

aggregates

Instability, overturn

Freezing elevation

Fall of larger tephra

±Hydrometeor formation

Coarse

aggregates

Figure 7. Diagram showing processes that influence the distribution of fine, distal ash. These include 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 and others, 2009).
Inputs 15

Although μagg is tightly constrained, we vary it slightly 

between simulations by sampling from a pdf having a mean of 

2.4 and standard deviation of 0.1.

Mass Fraction Aggregating Ash 

The mass fraction of aggregating ash (mfines) was very 

high in the 1980 deposit, altering the pattern of fallout and 

contributing to the secondary maximum in thickness near Ritzville (Carey and Sigurdsson, 1982). But mfines almost certainly 

will vary in future MSH eruptions. If we define mfines to contain 

all ash of  ≥ 4 (d ≤ 0.063mm), and 75 percent, 50 percent, 

and 25 percent, respectively, of size bins  = 3.5, 3, and 2.5 

(following Mastin and others (2016)), then mfines in the 1980 

deposit is about 0.7 (table 5, column 3). The fraction smaller 

than 0.063 mm (m63) in the 1980 deposit is about 0.6.

Recent research suggests that mfines may increase in future 

events with eruption size, magma silica content, and the size 

and abundance of pyroclastic flows (Rose and Durant, 2009) 

Mastin and others, 2009). However, these relations are hard 

to document in historical events. Consider silica content for 

example. Rose and Durant (2009) found m63 (a proxy for 

mfines) to be at least 0.3 in several silicic deposits, but m63 was 

only 0.08–0.12 in the silicic 2011 Cordon Caulle eruption 

(Bonadonna and others, 2015a). Another consideration is eruption size. Among the eruptions in table 7, m63 in the two largest 

ranges widely from 0.08–0.12 (Cordon Caulle) to 0.6 (MSH). 

Entries in table 7 support the notion that pyroclastic flows (pf) 

generate fine ash, with m63≥0.4 among the three pf-producing 

eruptions at MSH and Spurr. Still, the small dataset prevents 

us from extracting robust relationships.

In the absence of better data, we still lean toward the 

notion that future MSH eruptions will produce substantial 

quantities of fine ash. MSH eruptions tend to be large, silicic, 

and in the past have involved much pyroclastic-flow activity. 

If mfines in 1980 was 0.7, we doubt it will be 0.1 in the next 

eruption. But the uncertainty is large, and the high m63 content 

in 1980 (relative to other eruptions) suggests mfines may be 

lower in the future. Thus, for model simulations, we assign 

mfines using a Gaussian pdf with a mean of 0.5 and a standard 

deviation of 0.15.

Table 6. Mass fraction of fine ash assigned to different size bins for aggregates.

[Abbreviations: μagg median aggregate size; mfines, mass fraction of a deposit moved into the aggegate size classes]

μagg −0.2 μagg −0.1 μagg μagg +0.1 μagg +0.2

Fraction 0.06mfines 0.24 mfines 0.40 mfines 0.24 mfines 0.06 mfines

Table 7. Mass fraction (m63) of fine (smaller than 0.063 mm) ash in selected recent eruption deposits. 

[Entries are in order of decreasing erupted volume (V, in dense-rock equivalent). SiO2 refers to the weight percent SiO2 in the melt, a proxy for magma viscosity. “V” refers to the erupted volume, in cubic kilometers (km3

) dense-rock equivalent (DRE). Pf? indicates whether pyroclastic flows occurred during this 

eruption which could have milled fine ash. Max. dist. is maximum distance in kilometers (km) from the vent of the most distal sample used to calculate the 

total grain-size distribution]

Deposit SiO2 wt% V km3 Pf? m63 Max. dist. km

Cordon Caulle, 20111,2 72 0.24 0.08–0.12 100

Mount St. Helens, 19803,4 70 0.2 x 0.6 630

Fuego, 19745,6 54 0.02 0.03 150

Spurr, August 18,19927,8 60–75 0.015 x 0.4 370

Spurr, September 17–18, 19927,8 60–75 0.015 x 0.4 385

Redoubt, March 23, 20099,10 68 0.0016 0.27 300

Ruapehu, 199611,12 62–65 0.001 0.03 180

1

Bonadonna and others (2015b)

2

Castro and others (2013)

3

supplemental file number 3 in Durant and others (2009)

4

Rutherford and others (1985)

5

Rose and others (2008)

6

Roggensack (2001)

7

Durant and Rose (2009)

8

Nye and others (1995)

9

Mastin and others (2013)

10Coombs and others (2013)

11Bonadonna and Houghton (2005)

12Nakagawa and others (1999).
16 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Secondary Physical Parameters

The following physical parameters are assigned nonchanging values that have been found to optimally fit mapped 

deposits:

•	 Suzuki constant (k). This parameter, which is used in 

equation 1, controls the vertical distribution of mass 

in the source nodes (fig. 4B). Higher values of k (for 

example k ≳ 8) concentrate most of the mass in the 

upper 20 percent or so of the column. A top-heavy 

column produces a prominent, realistic secondary 

thickening of the deposit but also produces an 

unrealistic decrease in the proximal deposit thickness 

(fig. 8 of Mastin and others [2016]). We chose a value 

of k = 8 to balance these two features.

•	 Particle shape. We use the drag coefficient formula of

Wilson and Huang (1979) to calculate settling velocity, assuming particles settle at their terminal velocity. 

Wilson and Huang (1979) approximate particles as 

ellipsoids with a shape factor F = (b + c) / 2a, where 

a, b, and c are the semi-major, intermediate, and semiminor axes of the ellipsoids, respectively. Wilson and 

Huang (1979) measured these axes dimensions for a 

collection of volcanic ash particles. We use a shape 

factor of 0.44, which corresponds to the average of 

their measured values. We assume aggregates are 

round, consistent with previous work (Mastin and 

others, 2016). Aggregate shape strongly influences the 

depositional pattern, especially at distances of greater 

than 100 km (fig. 6 of Mastin and others [2016]).

200

400

600

800

1,000

2,500

EXPLANATION

Density of material, in kg/m3

0 500 1,000 1,500

Transport distance, in kilometers

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Average settling velocity, in meters per second

Distance of Hanford

0.35

0.30

0.25

0.21

0.18

0.15

0.13

0.11

0.09

0 0.1 0.2 0.3 0.4 0.5

Diameters, in millimeters

A B

Settling velocities that 

would fall at Hanford

Aggregate 

diameter (mm) 

Aggregates

Particles

Fallout upwind

of Hanford

Figure 8. Graphs showing settling velocity versus transport distance and diameter for particulate matter 

falling at Hanford, Washington. A, Transport distance versus average fall velocity, assuming a 15.1 meters per 

second (m/s) wind speed, equal to the average wind speed at Mount St. Helens between 0 and 15 kilometer 

(km) elevation on May 18, 1980, and a fall distance of 15 km. The vertical shaded bar represents the distance 

of the Hanford site. Horizontal shaded bar is the fall velocity at which objects falling from 15 km elevation 

would land at Hanford. Labels on dots give the average diameter (millimeters [mm]) of a round aggregate 

having a density of 600 kilograms per cubic meter (kg/m3) and the given fall velocity, as calculated by Wilson 

and Huang (1979). B, Fall velocity at pressure=1 atmosphere (atm), Temperature=298.15 Kelvin (K), versus 

diameter, for round falling objects. Red lines represent aggregates (densities less than or equal to 800 kg/m3). 

Black lines represent particles (densities greater than or equal to 1,000 kg/m3). Objects falling at faster than 

about 1.2 m/s from 15 km under these wind conditions would land upwind from Hanford. All particles having 

densities greater than or equal to 1,000 kg/m3 and diameters greater than 0.25 mm would fall faster than about 

1.2 m/s and would therefore land upwind of Hanford.
Inputs 17

•	 Density of individual particles (ρp,i). The density 

of individual particle classes (table 5) is calculated 

according to its componentry as explained in the 

mean aggregate size section of this report. 

•	 Deposit density (ρd). Ash3d calculates mass per unit 

area (M) and converts (M) to deposit thickness (T)

assuming a density (ρd) of 1,000 kg/m3. This value 

of (ρd) is intermediate between new-fallen densities, 

which ranged from less than 100 to more than 

1,000 kg/m3 at Mount St. Helens in 1980 (SarnaWojcicki and others, 1981), and higher densities that 

follow rain or compaction. Densities of 400–2,000; 

1,150–1,350; 200–800; and 1,200–1,300 kg/m3 have 

been measured at Pinatubo (Paladio-Melosantos and 

others, 1996); Eyjafjallajökull (Bonadonna and others, 

2011); Redoubt Volcano (Scott and McGimsey, 1994); 

and Chaitén (Alfano and others, 2011) respectively. 

Using a value of ρd = 1,000 kg/m3 also conveniently 

implies that T = 1 mm when M = 1 kg/m2. Changing 

the deposit density from 1,000 kg/m3 would change T, 

but not M. The relationship is linear; in other words, 

using a value of 500 kg/m3 would double the value of 

T; using 2,000 kg/m3 would reduce T by half. 

•	 Magma density (ρm). Ash3d converts the input value of 

erupted volume, km3 DRE, into mass, in kg, assuming 

a magma density of 2,500 kg/m3. Like deposit density, 

the magma density is hard-coded into Ash3d and is a 

round number that lies within the range of observed 

densities. Magma contains melt, whose density ranges 

from about 2,200 to 2,600 kg/m3 depending on composition, temperature and dissolved volatile content 

(Lange, 1994; Ghiorso and Sack, 1995). It also contains crystals whose densities range from about 2,500 

to 3,200 kg/m3 depending on crystal type, composition, and temperature (Berman, 1988). The percentage 

of crystals in magma ranges from 0 percent to greater 

than 60 percent, and in MSH magmas from above 30 

to 50 percent by volume (Gardner and others, 1995). 

Erupted masses calculated using our assumed magma 

density of 2,500 kg/m3 are about 8 percent greater 

than those using 2,300 kg/m3 as reported by Carey and 

others (1995) for MSH magmas, but this difference is 

well within the uncertainty in deposit volumes.

•	 Diffusion Coefficient (Kx). Mastin and others (2016)

systematically varied Kx from 0 to 3,000 square 

meters per second (m2/s)in MSH test simulations and 

found that non-zero values of Kx did not measurably 

improve the agreement compared to Kx = 0. However, 

setting Kx > 0 increased runtime by a factor of three. 

Thus, we set Kx = 0 for these simulations.

•	 Aggregate size bins. We use five aggregate size bins 

with the mass fractions of each bin assigned as shown 

in table 6 and as described in the mean aggregate size

section of this report.

Meteorological Inputs

The wind and other meteorological conditions are varied in 

each simulation by randomly picking a start time between January 1, 1980, and January 1, 2010. For meteorology we use data 

from the ERA Interim model (Dee and others, 2011), published 

by the ECMWF. It has a roughly 79 km horizontal spacing 

between model nodes, 3-hour time intervals, and 60 pressure 

levels in the atmosphere extending to 0.1 hectopascal (greater 

than about 60 km). The data extend back to January 1, 1979. 

The Interim-ERA data had to be reformatted to be read by 

Ash3d, which took about a month of processing time. A small 

percentage of the 65,700 files did not reformat successfully, 

resulting in failure of 2.1 percent of the simulations.

Model settings

We chose a horizontal nodal spacing of 0.1 degree 

(table 4), 8 x 11 km at this latitude, which tested well in earlier 

work (Mastin and others, 2016). Meteorological features 

smaller than a few times the 79 km nodal spacing of the ERA 

Interim model were not captured.

We chose a small model domain to maximize efficiency 

of calculations under the assumption that ash would be 

transported primarily to the east, toward Hanford from Mount 

St. Helens. The small domain may miss instances, however, 

in which ash takes a roundabout route outside the domain 

before arriving at Hanford. To evaluate this effect, we also ran 

1,000 simulations using a larger model domain (125–111°W, 

43–51°N). A small number of runs produced slightly higher 

values of T or airborne ash concentration (C), increasing T10k

by 6 percent and Cmax,10k by 3.5 percent. This inaccuracy is 

small relative to other uncertainties.

During test runs we found a surprising relation between 

model resolution and T or C. For a thousand test runs, increasing horizontal resolution from 0.2 to 0.1 to 0.05 degrees, 

increases T on average by about 10–20 percent and C by 

about 20–40 percent, although results differ widely from 

run to run. With increasing resolution, the solution does not 

converge on a single, more accurate result as Eulerian model 

tests normally predict (LeVeque, 2002; Schwaiger and others, 

2012). We think this relation results from the fact that ash is 

released in a single column of source nodes (fig. 4B) having 

a footprint (nodal area on the ground surface) determined by 

the nodal spacing. In higher-resolution runs, the same mass of 

ash occupies a smaller footprint, hence its airborne concentration is greater and, as it falls out, the deposit is thicker. This 

greater concentration is advected downwind. At nodal spacings smaller than the source region, model accuracy does not 

improve because the model is unable to capture the physics 

of the rising and spreading ash column. An optimal spacing 

would be roughly equal to the horizontal dimension of the 

volcanic plume at the neutral buoyancy elevation. This dimension increases with eruption size, from tens to hundreds of 

kilometers, for the range of eruption sizes considered here. We 

conclude that choosing a constant nodal spacing may introduce an uncertainty of tens of percent in the result.
18 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Model testing found that varying vertical cell spacing 

(dz) between 0.5 and 2 km has less than 10 percent effect 

on deposit thickness but as much as 30 percent on airborne 

concentration. The insensitivity in T seems to imply that most 

tephra is falling vertically. Halving vertical spacing quadruples 

run time; hence we chose dz = 2 km for speed. Ash3d 

interpolates linearly between the nearest nodes in the ERA 

Interim model (in which spacing is tens of meters at ground 

level) to obtain pressure, temperature, and wind vectors at 

each height.

Ash3d does not calculate wet deposition, which would 

require difficult assumptions of the size and density of falling 

ashy raindrops. Ash3d can incorporate topography, but the 

implementation uses a crude cut-cell method, which creates a 

brickwork pattern of topography, sometimes creating deposit 

artifacts on the upwind sides of mountain ranges. Topography 

around Hanford is fairly subdued, and test runs with and 

without topography produced nearly identical values of T and 

C. Thus, we did not include topography.

Modeling Methodology

We attempted a total of 10,000 simulations using these 

inputs. Table S1 of the accompanying Data Release (Mastin and 

others, 2020) lists the inputs for each run. Histograms (fig. 9) 

illustrate that the input distributions resemble the pdfs specified.

0.008 km3

2.3 km3

A

−3 −2 −1

log volume, km3 DRE

Volume, km3 DRE

0

500

1,000

n

1/1/19801/1/2010

1980 1990 2000 2010

B

Start date

0

200

400

mean=−0.03

std=2.91

C

−0 −5 0 10

0

1,000

2,000

n

mean=0.50

std=0.15

D

0 0.2 0.4 0.6 0.8 1

mfines

0

1,000

2,000

3,000

mean=2.40

std=0.11

E

2.0 2.2 2.4 2.6 2.8

agg

0

2,000

4,000

n

10−2 10−1 100

10−2 10−1 100

0

20

40

Vent elevation

F

G

0 5 10 15 20

Duration, hrs

0

1,000

2,000

3,000

n

std mean

0 1

5

H 102

100

Volume, km3 DRE

n

n

Hbestfit−HV, km

Duration D, hrs

Ha, km

Figure 9. Distribution of inputs used in the simulations. A, Histogram of the number of simulations versus the log of erupted volume. 

Horizontal bars give Nathenson’s (2017) range of volumes for eruptions listed in table 2. B, Distribution of eruption start dates. C, 

Distribution of plume height above or below Hbestfit calculated from equation 3. D, Distribution of mfines used in simulations. E, Distribution 

of μagg. F, Plume height versus erupted volume. The red line represents Hbestfit; the yellow dashed lines represent Hbestfit ± 2.9km. Points are 

densest near Hbestfit, as quantified in figure 9C. G, Distribution of eruption durations. H, Duration versus log volume. Magenta lines in A

through E give theoretical distributions defined in table 3. DRE, dense-rock equivalent; Hbestfit, plume height above the vent calculated by 

equation 3; Hv, plume height above the vent; hr, hour; km, kilometer; km3, cubic kilometer; mfines, mass fraction of a deposit moved into the 

aggregate size classes; n, number of successful runs; std, standard deviation; μagg, median aggregate size.
Results 19

Two hundred fifteen simulations (2.1 percent) failed 

because of corrupt wind files, but the remaining runs are 

enough for the analysis. Table S2 (Mastin and others, 2020) 

gives tephra thickness, arrival time, fall duration, and 

grain-size distribution at the Hanford site (46.5507° N., 

119.489° W.) for each run.

In each simulation, the total C in the ground-level node at 

Hanford was recorded at each time step (roughly every minute 

or so) as long as ash was in the air. The maximum value of C

in each simulation was taken as Cmax. The dosage (product of 

concentration times time) was calculated as de=Σ Ci ∆t

i

, where 

Ci is the airborne concentration at each time step and ∆t

i is 

time-step duration. This dosage was divided by the time over 

which ash was falling (Dd) to obtain an average concentration 

Cavg. For both the maximum and average airborne concentration, about 56 percent of simulations gave less than 1 mg/

m3, and 60 percent gave less than 2 mg/m3. Dosage is used to 

define aircraft engine tolerance (Clarkson and others, 2016), 

and may be relevant when considering the amount of ash 

required to clog air filters.

For each run, documented in Mastin and others (2020), 

we tabulated inputs (table S1 of Mastin and others (2020)), 

thickness and fall duration (table S2), maximum airborne 

concentration, and dosage (table S3). Thickness was ranked 

in decreasing order (table S4) and each thickness value was 

assigned a probability P3|1, equal to its rank divided by (n+1), 

where n is the number of successful runs. In the notation of 

Hoblitt and Scott (2011) P3|1 =P2|1 ⋅ P3|2, tables S5 and S6 are 

analogous to table S4, but they list maximum and average 

airborne ash concentration respectively rather than thickness. 

Plots of P3|1 versus thick-ness and concentration are given in figure 

10. About 60 percent of the simulations deposited no tephra at 

Hanford. Sixty-one percent deposited less than 0.1 mm, 88 percent 

less than 3.5 mm, and 94 percent 15 mm or less.

Results

Following the methodology above, the ranked values of 

thickness and concentration were interpolated to give T, Cmax, 

and Cavg at specified exceedance probabilities (table 8 and 

fig. 10). For the 10,000-year recurrence interval, T10K = 51.1, 

Cmax,10K = 3,819 and Cavg,10K = 1,513 mg/m3.

The values of T10K and Cmax,10K were also calculated as a 

function of the number of runs completed (n; fig. 11). Changes 

in T10k or Cmax,10k with n result from changes to the statistical 

distribution as n changes. Ideally, T10k and Cmax,10k should converge on a stable value with increasing n. After about 5,000 

runs, T10K is within about 5 percent of its final value, whereas 

more than 6,000 are required to bring Cmax,10K within 5 percent 

of its final value.

P3|1 =0.0125

P3|1 =0.0625

P3|1 =0.125

T10k = 51 mm

T2k = 12 mm

T1k = 3 mm

A

20 40 60 80

0 20 40 60 80

100

Mass load M, kg/m2

P3|1 =0.0125

P3|1 =0.0625

P3|1 =0.125

B

Maximum

Average

C avg,10k =1,513 mg/m3

C avg,2k = 457 mg/m3

C avg,1k = 164 mg/m3

C max,10k =3,819 mg/m3

C max,2k =1,090 mg/m3

C max,1k = 3,72 mg/m3

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

Airborne concentration C, in milligrams per cubic meter

0

0.05

0.1

0.15

0.2

0.25

0.3

Probability P 3|1

100 120

Deposit thickness T, in millimeters

0

0.05

0. 1

0.15

0. 2

0.25

0. 3

Probability P 3|1

EXPLANATION

Figure 10. Graphs of probability 

of exceedance of a given tephra 

thickness or ash concentration 

(P3|1) versus thickness and 

concentration. A, Plot of 

exceedance probability P3|1 versus 

deposit thickness. B, Plot of P3|1

versus ground-level maximum 

(Cmax) and average (Cavg) airborne 

ash concentration in milligrams 

per cubic meter (mg/m3). The 

exceedance probability is the 

probability that any eruption will 

result in tephra-fall thickness (T) 

or airborne ash concentration (C) 

exceeding the value given on the 

x axis. kg/m2, kilogram per square 

meter; mm, millimeter.
20 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Table 8. Threshold values of tephra-fall thickness in millimeters (which is equal to mass load in kilograms per square meter) and 

airborne concentration at different exceedance probabilities (P3|1).

[Abbreviations: Cmax, maximum airborne concentration during the period of tephra fall; Cave, average airborne concentration during the period of tephra fall; mg/

m3, milligram per cubic meter; mm, millimeter; T, tephra-fall thickness]

Probability P3|1 Recurrence years T, in mm Cmax, in mg/m3 Cavg, in mg/m3

0.0125 10,000 51.1 3819 1513

0.050 2,500 16.3 1350 574

0.0625 2,000 12.2 1090 457

0.125 1,000 2.9 372 164

30

40

50

60

70

T10k, in mm

Cmax,10k, in mg/m3

Final value

+5%

−5%

30

40

50

60

70

M, in kg/m2

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

Number of runs

3,000

3,500

4,000

4,500

5,000

Final value

+5%

−5%

A

B

Figure 11. Calculated values of tephra-fall thickness in a “1-in-10,000-year event” (T10K; A) and maximum airborne 

ash concentration (Cmax,10K ; B) as a function of the number of runs. Horizontal dashed lines give the final value; dotted 

lines give the final value plus or minus 5%. kg/m2, kilogram per square meter; M, mass load of tephra deposit; mm, 

millimeter; mg/m3, milligram per cubic meter; P3|1, probability of exceedance of a given tephra thickness or ash 

concentration given that an eruption has occurred; %, percent.

Deposit Thickness and Mass Load

Among four simulated deposits where T T10k (fig.12)

deposition patterns range widely, but in each case the dominant 

wind was blowing toward Hanford. Among ten runs with 

T T10k (table 9), Erupted volumes are in the upper half 

of the input range (0.62–2.01 km3). Average accumulation rates 

(T/Dd) ranged widely, from 3.6 to 23.2 millimeters per hour 

(mm/hr; 1 to 6 grams per square meter per second [g/m2/s]). 

Previous estimates of airborne concentration have 

assumed that Dd are comparable to De, but a plot of these 

two parameters for all runs (fig. 13) shows surprisingly little 

correlation. When Dd > 0, Dd > De about two thirds (66 percent) 

of the time, with a difference (Dd − De) of about 2.6±2.5 hours 

(mean ± standard deviation). Greater fall duration may result 

when slower, low-elevation winds cause ashfall to linger. 

Shorter fall duration may result when Hanford lies near the 

edge of a deposit and catches a brief, passing cloud.
Results 21

men20-7413_fig12

A. Run 1453

C. Run 0446 D. Run 0695

B. Run 4788

Figure 12. Maps of tephra deposition for four runs whose deposit thickness at Hanford is closest to T10k. ASL, above sea 

level; cm, centimeter; DRE, dense-rock equivalent; ECMWF Interim ERA ,European Centre for Medium-Range Weather 

Forecasts Interim Reanalysis; km, kilometer; km3, cubic kilometer; mm, millimeter; UTC, coordinated universal time.

Table 9. Table of runs yielding deposit thicknesses close to T10K.

[Deposit arrival time (t

d

) is in hours after the eruption start, when the deposit thickness first exceeded 0.01 millimeters. Fall duration (Dd) is the time period over 

which the deposit was falling at a rate exceeding 0.01 millimeters per hour. Abbreviations: asl, above sea level; hrs, hours; km, kilometer; km3, cubic kilometer; 

mm, millimeter]

Rank P3|1

Run

number T, in mm t

d

, in hrs Dd, in hrs V, in km3 DRE H, in km asl De, in hrs mfines

118 0.0121 2305 51.85 2.8 15.5 0.98 30.8 4.28 0.41

119 0.0122 5896 51.7 3.3 10.5 0.38 28.9 2.23 0.55

120 0.0123 4473 51.38 3.5 13.3 2.02 31.1 8.36 0.48

121 0.0124 1453 51.26 2.5 7.2 2.01 31.4 7.99 0.61

122 0.0125 4788 51.2 5.4 16.4 1.42 28.9 8.09 0.71

123 0.0126 446 50.97 2.2 9.3 2.05 27.8 14.14 0.56

124 0.0127 695 50.79 1.4 6.4 0.62 28.5 3.84 0.55

125 0.0128 743 50.71 2.6 5.8 1.82 34.8 4.59 0.51

126 0.0129 6274 50.62 2.1 14.3 1.88 28 12.51 0.70

127 0.013 6124 50.62 8.8 12.1 0.99 29.8 4.93 0.53
22 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

13

0 5 10 15 20 25

Eruption duration, in hours

0

5

10

15

20

25

Fall duration, in hours

Figure 13. Tephra-fall duration at Hanford, 

Washington, versus eruption duration, excluding model 

runs for which fall duration is zero. If fall duration at 

Hanford were comparable to eruption duration in each 

simulation, these dots would be concentrated near the 

diagonal line.

Table 10. Table of runs producing ash concentrations close to Cmax,10K.

[Abbreviations: asl, above sea level; DRE, dense-rock equivalent; hrs, hours; km, kilometer; km3, cubic kilometer; mg/m3, milligram per cubic meter; mg-s/m3, 

milligram-seconds per cubic meter; mm, millimeter]

Rank P3|1 Run Number Cmax, in 

mg/m3 t

d

, in hrs Dd, in hrs Dosage,in 

mg-s/m3 T, in mm V, in km3 DRE H, in km asl De

, in hrs

118 0.0121 6,775 3,900 4.2 12 4.77E+07 36.6 0.6 28.5 3.6

119 0.0122 7,132 3,890 14.7 7.7 3.63E+07 21.4 1.8 29.9 8.99

120 0.0123 7,943 3,880 9 6.4 4.17E+07 24 0.6 25.8 5.43

121 0.0124 5,355 3,880 6 18.4 6.09E+07 37.4 0.9 24.9 10.07

122 0.0125 3,330 3,830 5 5.6 2.56E+07 39.8 1.6 32.2 5.66

123 0.0126 5,551 3,800 3.4 6.1 4.89E+07 74.5 1.8 34 5.16

124 0.0127 3,046 3,790 7 9.4 3.54E+07 21.4 0.4 21.6 9.17

125 0.0128 8,227 3,780 6.2 13.5 5.58E+07 39.3 0.5 30.8 2.11

126 0.0129 7,921 3,780 8.1 4.5 2.27E+07 8.6 0.9 31.4 3.57

127 0.0130 5,175 3,780 2.2 11 6.14E+07 96.6 1.5 32.8 5.08

Airborne Concentration

For runs where Cmax ≅ Cmax,10k, key inputs are summarized 

in table 10; similar lists for Cmax ≅ Cmax,2k, Cmax ≅ Cmax,1k and 

Cavg ≅ Cmax,10k are given in tables 11–13. When Cmax ≅ Cmax,10k, 

erupted volumes for runs in table 10 are 0.4–1.8 km3 DRE. For 

the same runs, tephra starts falling at Hanford 2.2–14.7 hours 

after the eruption starts and falls for 4.5–18.4 hours. Deposits 

are 9–96 mm thick, and average accumulation rates are 2.3–

19.1 mm/hr. Concentration versus time (fig. 14A) is mostly 

Gaussian in shape with peak values that last only a few hours 

before dropping to less than 80 percent of the peak value. 

Dosages (fig. 14D, table 10) range from 3.5×107 to 6.1×107

milligram-seconds per cubic meter (mg-s/m3), reflecting the 

range of time over which these concentrations persisted.

Grain-Size Distribution

Tephra fall deposits at Hanford have coarser grain-size 

distributions in simulations where T ≅ T10k (table 14, fig. 15A) 
Results 23

Table 11. Table of runs producing ash concentrations close to Cmax,2k.

[Abbreviations: asl, above sea level; DRE, dense-rock equivalent; hr, hour; km, kilometer; km3, cubic kilometer; mg/m3, milligram per cubic meter; mg-s/m3, 

milligram-seconds per cubic meter; mm, millimeter]

Rank P3|1 Run Number Cmax, in 

mg/m3 t

d

, in hrs Dd, in hrs Dosage, in 

mg-s/m3 T, in mm V, in km3DRE H, in km asl De

, in hrs

607 0.062 6,851 1,100 7.7 7 1.10E+07 6.8 0.4 23.6 6.14

608 0.0621 5,580 1,100 5.1 4.9 8.11E+06 7.1 0.2 27.3 1.83

609 0.0622 3,228 1,100 3.1 4.7 1.28E+07 13.9 0.3 23.5 4.28

610 0.0623 7,841 1,090 8.7 5.3 8.78E+06 5.7 0.1 22.3 1.79

611 0.0624 7,368 1,090 1.9 12.2 3.41E+07 73.4 2.3 29.6 11.62

612 0.0625 5,594 1,090 5.4 10.4 2.02E+07 11.5 0.3 26.4 2.86

613 0.0626 5,453 1,090 3.6 7 5.64E+06 3.7 0.7 27.8 4.53

614 0.0627 1,670 1,090 1.7 3.7 8.16E+06 15.2 0.2 22.6 2.92

615 0.0629 534 1,090 1.9 6.4 1.73E+07 34.5 0.6 25.5 5.9

616 0.0630 8,916 1,080 5.3 19.8 3.42E+07 23.1 1.2 26.8 9.62

Table 12. Table of runs producing ash concentrations close to Cmax,1k.

[Abbreviations: asl, above sea level; DRE, dense-rock equivalent; hr, hour; km, kilometer; km3, cubic kilometer; mg/m3, milligram per cubic meter; mg-s/m3, 

milligram-seconds per cubic meter; mm, millimeter]

Rank P3|1 Run Number Cmax, in 

mg/m3 t

d

, in hrs Dd, in hrs Dosage, in 

mg-s/m3 T, in mm V, in km3DRE H, in km asl De

, in hrs

1219 0.1246 9,484 374 13.5 6.5 1.99E+06 3.7 1.27 24.6 14.99

1220 0.1247 8,694 374 3.9 3.2 2.70E+06 1.5 0.02 15.2 2.1

1221 0.1248 73 374 7.4 9.8 4.48E+06 8.0 1.26 27.1 9.69

1222 0.1249 8,777 373 2.4 10.2 5.43E+06 7.3 0.33 20.8 8.38

1223 0.125 7,033 373 3.0 6.6 4.76E+06 4.4 0.22 21.8 4.46

1224 0.1251 5,875 372 4.0 4.1 2.74E+06 1.5 0.02 14.3 2.45

1225 0.1252 5,098 372 4.1 4.3 2.58E+06 1.8 0.04 16.2 3.25

1226 0.1253 4,692 372 8.2 15.2 8.07E+06 4.5 0.56 24.2 7.14

1227 0.1254 2,510 372 4.3 4.2 2.74E+06 1.7 0.02 14.9 2.66

1228 0.1255 1,149 372 4.9 8.2 4.60E+06 2.6 0.04 15.0 4.6

Table 13. Run numbers producing ash concentrations at Hanford, Washington, close to Cavg,10K.

[Abbreviations: asl, above sea level; DRE, dense-rock equivalent; hr, hour; km, kilometer; km3, cubic kilometer; mg/m3, milligram per cubic meter; mg-s/m3, 

milligram-seconds per cubic meter; mm, millimeter]

Rank P3|1 Run Number Cavg, in 

mg/m3 t

d

, in hrs Dd, in hrs Dosage, in 

mg-s/m3 T, in mm V, in km3DRE H, in km asl De

, in hrs

118 0.01206 5,175 1,555 2.2 11 6.14E+07 96.6 1.5 32.8 5.08

119 0.01216 8,332 1,554 4.5 19.9 1.12E+08 66 1.7 28.9 9.58

120 0.01226 9,899 1,546 5.1 5.9 3.27E+07 23.1 1.2 28.7 7.12

121 0.01237 5,945 1,542 5.1 11.4 6.35E+07 43.2 1.1 25.7 10.67

122 0.01247 1,320 1,515 10 8.8 4.77E+07 30.9 1.6 28.3 9.85

123 0.01257 2,129 1,510 5.2 9.1 4.95E+07 38.2 1.1 28.9 6.57
24 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Table 13. Run numbers producing ash concentrations at Hanford, Washington, close to Cavg,10K.—Continued

Rank P3|1 Run Number Cavg, in 

mg/m3 t

d

, in hrs Dd, in hrs Dosage, in 

mg-s/m3 T, in mm V, in km3DRE H, in km asl De

, in hrs

124 0.01267 167 1,506 4.6 6.3 3.42E+07 23.2 0.2 20.7 4.84

125 0.01277 9,642 1,497 1.8 8.6 4.66E+07 94.2 1.1 28.7 6.65

126 0.01288 8,701 1,494 4.7 9.8 5.28E+07 32.1 0.5 22.8 8.57

127 0.01298 530 1,490 9.7 8.7 4.64E+07 22.2 1 24.1 12.41

0 5 10 15 20

0

2,000

4,000

Concentration, mg/m3

6,775

7,132

7,943

5,355

3,330

5,551

3,046

8,227

7,921

5,175

0 5 10 15 20

Time, hours after eruption start

0

5

10

Dosage, mg−s/m3

10 7

6,775

7,132

7,943

5,355

3,330

5,551

3,046

8,227

7,921

5,175

0 5 10 15 20

0

500

1,000

1,500

Concentration, mg/m3

6,851

5,580

3,228

7,841

7,368

5,594

5,453

1,670

534

8,916

0 5 10 15 20

0

200

400

Concentration, mg/m3

9,484

8,694

73

8,777

7,033

5,875

5,098

4,692

2,510

1,149

A

B

C

D

EXPLANATION

EXPLANATION

EXPLANATION

EXPLANATION

Run number

Run number

Run number

Run number

Figure 14. Graphs showing airborne ash concentration versus time for eruption 

simulations shown in tables 10 (A), 11 (B), and 12 (C). Airborne ash dosage versus 

time (D) is also shown for eruptions listed in table 10. Numbers in the legends 

refer to the run numbers. mg/m3, milligrams per cubic meter; mg−s/m3, milligramseconds per cubic meter.
Results 25

than those where Cmax ≅ Cmax,10k (table 15) or Cavg ≅ Cavg,10k

(table 16), as observed in the m63 column of these tables. 

The m63 for the T ≅ T10k runs correlates poorly with mfines

in the input (table 9), and plume heights for runs with a 

coarse grain-size are also not especially high, suggesting 

that wind speed plays a strong role in determining grain-size 

distribution.

Table 14. Grain-size distribution at Hanford, Washington for runs where T≅T10k.

[Rows 3–12 and columns 2–10, give the mass fractions of the particle size indicated in row 2. Falling aggregates are included in the ≤0.063 millimeter (mm) size 

class. No size classes larger than 1 mm were present in these results]

Run

Number

Aggregate diameter, in mm

1.000 0.707 0.500 0.354 0.250 0.177 0.125 0.088 ≤0.063

6,775 0.0000 0.0000 0.0000 0.0001 0.0435 0.1749 0.0318 0.0001 0.7497

7,132 0.0000 0.0000 0.0000 0.0000 0.0076 0.1147 0.0036 0.0000 0.8742

7,943 0.0000 0.0000 0.0000 0.0000 0.2648 0.7061 0.0010 0.0006 0.0274

5,355 0.0000 0.0000 0.0043 0.5912 0.3632 0.0064 0.0014 0.0004 0.0331

3,330 0.0000 0.0000 0.0000 0.0000 0.0001 0.0443 0.0206 0.0016 0.9334

5,551 0.0000 0.0000 0.0000 0.0428 0.8582 0.0662 0.0017 0.0004 0.0308

3,046 0.0003 0.0162 0.2174 0.7216 0.0415 0.0001 0.0001 0.0001 0.0026

8,227 0.0000 0.0000 0.0000 0.0338 0.8840 0.0712 0.0004 0.0000 0.0104

7,921 0.0001 0.0036 0.0651 0.5708 0.3468 0.0028 0.0002 0.0001 0.0105

5,175 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0515 0.0138 0.9345

0

0.2

0.4

0.6

0.8

1

Mass fraction

A. Runs where T is near T10k

2,305

5,896

4,473

1,453

4,788

446

695

743

6,274

6,124

0

0.2

0.4

0.6

0.8

1

Mass fraction

B. Runs where Cmax is near Cmax, 10k 

6,775

7,132

7,943

5,355

3,330

5,551

3,046

8,227

7,921

5,175

2 0.25 0.125 0.0625

Diameter, in mm

1 0.5

EXPLANATION

EXPLANATION

Run number

Run number

−1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

Figure 15 (pages 25–26). Graphs showing grain-size distributions at Hanford, Washington, for several 

model runs at varying conditions. A, Grain-size distributions at Hanford for model runs in table 9, where 

tephra fall thickness (T) is close to the 1-in-10,000-year event thickness (T10K). B, Grain-size distributions 

for model run numbers in table 10, where the maximum airborne concentration during the period of tephra 

fall (Cmax) is close to the value of the maximum airborne ash concentration at Hanford having a recurrence 

interval of 10,000 yrs (Cmax,10K). C. Grain-size distributions at Hanford for model runs in table 13, where the 

average airborne concentration during the period of tephra fall (Cavg) is close to Cavg,10K. Numbers in the 

explanation refer to the run numbers. p, particle diameter in millimeters (mm).
26 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

men20-7413_fig15

0

0.2

0.4

Mass f

1,453

4,788

446

695

743

6,274

6,124

0

0.2

0.4

0.6

0.8

1

Mass fraction

B. Runs where Cmax is near Cmax, 10k 

6,775

7,132

7,943

5,355

3,330

5,551

3,046

8,227

7,921

5,175

−1 −0.5 0.5 1.5 2.5 3.5

0

0.2

0.4

0.6

0.8

1

Mass fraction

C. Runs where Cavgis near Cavg, 10k

5,175

8,332

9,899

5,945

1,320

2,129

167

9,642

8,701

530

−1 0 1 2 3 4

EXPLANATION

EXPLANATION

Run number

Run number

2 0.25 0.125 0.0625

Diameter, in mm

1 0.5

Diameter, in mm

Figure 15 (pages 25–26).—Continued

Table 15. Grain-size distribution at Hanford for runs producing ash concentrations close to Cmax,10K.

[Rows 3–12, columns 2–10, give the mass fractions of the particle size indicated in row 2. Falling aggregates are included in the ≤ 0.063 millimeter (mm) size 

class. No size classes larger than 1 mm were present in these results]

Run

Number

Aggregate diameter, in mm

1.000 0.707 0.500 0.354 0.250 0.177 0.125 0.088 ≤0.063

6,775 0.0000 0.0000 0.0000 0.0000 0.0006 0.1359 0.1107 0.0033 0.7495

7,132 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0549 0.0010 0.9432

7,943 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0549 0.0056 0.9393

5,355 0.0000 0.0000 0.0000 0.0000 0.0000 0.0034 0.0742 0.0038 0.9185

3,330 0.0000 0.0000 0.0000 0.0021 0.7786 0.1793 0.0036 0.0011 0.0353

5,551 0.0000 0.0000 0.0000 0.0099 0.9011 0.0527 0.0010 0.0000 0.0353

3,046 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0574 0.0046 0.9376

8,227 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.1462 0.0075 0.8453

7,921 0.0000 0.0000 0.0000 0.0000 0.0000 0.0238 0.1233 0.0051 0.8478

5,175 0.0000 0.0000 0.0000 0.1277 0.8491 0.0185 0.0005 0.0002 0.0040
Discussion 27

Table 16. Grain-size distribution at Hanford for runs producing ash concentrations close to Cavg,10K .

[Rows 3–12, columns 2–10, give the mass fractions of the particle size indicated in row 2. Falling aggregates are included in the ≤ 0.063 millimeter (mm) size 

class. No size classes larger than 1 mm were present in these results]

Run

Number

Aggregate diameter, in mm

1.000 0.707 0.500 0.354 0.250 0.177 0.125 0.088 ≤0.063

5,175 0.0000 0.0000 0.0000 0.1277 0.8491 0.0185 0.0005 0.0002 0.0040

8,332 0.0000 0.0000 0.0000 0.0000 0.0000 0.0246 0.0218 0.0007 0.9529

9,899 0.0000 0.0000 0.0000 0.0000 0.0217 0.3946 0.0523 0.0014 0.5300

5,945 0.0000 0.0000 0.0000 0.0000 0.0016 0.1338 0.0438 0.0014 0.8194

1,320 0.0000 0.0000 0.0000 0.0000 0.0000 0.0017 0.0508 0.0031 0.9444

2,129 0.0000 0.0000 0.0000 0.0000 0.0001 0.0597 0.0504 0.0032 0.8867

167 0.0000 0.0000 0.0000 0.0000 0.0000 0.0222 0.0246 0.0001 0.9531

9,642 0.0000 0.0000 0.0022 0.6295 0.3366 0.0046 0.0013 0.0002 0.0256

8,701 0.0000 0.0000 0.0000 0.0000 0.0001 0.0184 0.0293 0.0008 0.9515

530 0.0000 0.0000 0.0000 0.0000 0.0001 0.0761 0.0552 0.0015 0.8671

Discussion

In this section we consider these results in the context 

of their inputs, and the implications of the results for hazards 

at Hanford.

Results in the Context of Inputs

Our T10K value of 51 mm is about half the 10 cm 

estimated by Hoblitt and Scott (2011); but our estimate of 

Cavg,10k (1,513 mg/m3) is nearly identical to the estimate of 

Snow and Nelson (2012) (1,500 mg/m3). These results bear 

some scrutiny in the context of our inputs.

In choosing inputs, we used best estimates with no 

intent to add conservatism. Minimum and maximum erupted 

volumes (Vmin and Vmax, respectively) for example, were 

chosen on the basis of Nathenson’s (2017) estimated range 

for Holocene MSH eruptions rather than those of Carey and 

others (1995), because the former are better documented and 

reproducible. However, Nathenson’s volume estimates are 

lower by at least a factor of two than those of Carey and others 

(1995). Our estimate of T10k, half that of Hoblitt and Scott 

(2011), is consistent with this. Our choice of a logarithmic 

probability distribution for V was based on the abundance of 

small eruptions rather than large ones in the geologic record. 

The paucity of observations precludes a more specific sizefrequency relationship, but a different one could alter the 

frequency of the largest eruptions, which strongly control T10k

and C10k.

Our choices of plume height and duration are also 

important. H and De are derived by correlation from V, with 

uncertainties indicated by the scatter of data in figure 6. 

Eruption rate is proportional to roughly the fourth power of 

plume height in kilometers above the vent (equation 2); thus, 

overestimating plume height by 20 percent would double the 

eruption rate and reduce eruption duration by half, essentially 

doubling the average airborne concentrations during the fall 

period. We consider it unlikely however that durations were 

systematically over- or underestimated by a factor of two; 

eruption durations in table 9, for example (2–14 hrs for volumes of 0.6–2.0 km3

), do not appear out of line with observed 

durations for similar-sized eruptions (see table 1, Mastin and 

others (2009)).

Other parameters such as k, F, and ρp have uncertainties 

whose possible effects are listed in table 17. Most of these 

effects have never been explored.

Our results may be conservative in one respect. Eruptions 

larger than about 1 km3 DRE produce umbrella clouds that 

drive ash radially outward, a process not included in this 

version of Ash3d. Umbrella spreading produces clouds that 

are circular (fig. 16B) in contrast to the fan shape of clouds 

of smaller eruptions (fig. 16A). Umbrella clouds spread ash 

over a wider area, reducing the maximum deposit thickness 

immediately downwind (Mastin and others, 2014), and 

making the statistical worst-case (thickest) scenario not so 

bad. In 1991, Pinatubo produced the biggest umbrella cloud in 

recent decades (fig. 16B), and erupted about three times more 

magma (6–10 km3 DRE (Koyaguchi, 1996)) than the largest of 

our simulations (2.3 km3 DRE).

The dispersal of ash can be quantified by contouring 

the thickness distribution of an ash deposit as shown in 

figure 1G for the 1980 deposit, and then constructing plots of 

log thickness versus sqrt(A) as in figure 3B. Data can be fit 

with a best-fit line of slope k0 (fig. 3B), although well-mapped 

deposits like MSH 1980 are better fit with two lines, of slopes 

k1 and k2 (fig. 3B). Lower absolute slope values reflect broader 

dispersal. Fierstein and Nathenson (1992) compiled slopes for 

27 published deposits. Plotted as a function of the bulk deposit 
28 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Table 17. Estimated range of uncertainty in secondary physical parameters and their possible effects on results.

[The range of uncertainty in these parameters are estimates. Abbreviations: cm, centimeter; DRE, dense-rock equivalent; m2/s, square meter per second; kg/m3, 

kilogram per cubic meter]

Parameter(s) Value used Uncertainty Estimated effect

Diffusion 

coefficient

Kx

0 m2/s 0–1,000 m2/s? Increasing Kx

 could decrease max. thickness values in the deposit, and increase the 

deposit footprint area, by tens of percent. It would likely decrease T10k by a small 

fraction, though this is unverified. Effect on airborne concentration is unknown.

Suzuki 

constant k

8 about 4–12 In a given simulation, changing k could increase or decrease thickness values at 

Hanford by tens of percent depending on winds and plume height. Effect on T10k

or C10k is not known.

Particle shape 

factor F

0.44 about 0.3–1 This parameter affects the settling velocity of larger particles that do not aggregate. 

The effect would vary from one simulation to another. How much it would affect 

T10k or other key outputs is not clear.

Deposit 

density ρd, 

1,000 kg/m3 about 500–1,400 kg/m3 Varying ρd

 would have no effect on mass load at Hanford (M). But because T=M/ρd, 

it would directly affect T10k. Changing ρd to 1,125 kg/m3 from 1,000 for example 

would change the value of T10k from 5.11 to 4.54 cm.

Magma 

density ρm, 

2,500 kg/m3 about 2,200–2,800 kg/m3 Erupted volumes (DRE) are converted to erupted mass by multiplying by magma 

density. Increasing or decreasing ρm by 10–20 percent would increase or decrease 

erupted mass, deposit mass load at Hanford, and T10k and C10k by the same amount.

Wind

Vent

200 km upwind

Umbrella cloud

E tna E yja MSH Pinatubo

0 100 200 300 400 500 600

0

50

wind

C

B. Pinatubo

Horizontal extent (km)

100 km

Vent No umbrella cloud

A. Eyjafjallajökull

N

25 km

Figure 16. Contrasting ash-cloud shapes from small and large eruptions. A, The National Aeronautics and Space Administration Earth 

Observatory image of the shape of the cloud from the eruption of Eyjafjallajökull (Eyja), Iceland, on May 7, 2010. Under a modest mass 

eruption rate of 5–10 x 106 kilograms per second (kg/s), the cloud emanates from a point source, advects downwind in the ambient wind 

field, and widens into a fan-like shape because of turbulent diffusion. B, Japanese geostationary meteorological satellite (GMS) visible 

image of the shape of cloud from the 1991 Pinatubo eruption, which produced one of the highest mass eruption rates in the past century, 

4–20 x 108 kg/s (Koyaguchi, 1996). The massive eruption formed a large, circular umbrella with radial winds that drove ash hundreds of 

kilometers upwind. C, Height and lateral extent in kilometers (km), of some plumes produced by recent eruptions: Etna in 2001 (Scollo 

and others, 2007), Eyjafjallajökull in 2010 (Arason and others, 2011), Mount St. Helens (MSH) in 1980, both the initial phase (8:30–9:00 a.m. 

Pacific Daylight Time [PDT]) and later (9:00 a.m.–5:00 p.m. [PDT], and Pinatubo in 1991 (Holasek and others, 1996).
Discussion 29

volume (fig. 17), the absolute values of these slopes generally 

decrease with increasing erupted volume. The upwarddecreasing trend starts when bulk (not DRE) volumes exceed a 

few cubic kilometers—near the top of the range of volumes we 

are modeling. The decreasing trend likely reflects the increasing 

dominance of umbrella-cloud dispersal for larger eruptions.

Comparison with Measured Airborne 

Concentrations

Our estimates of airborne ash concentration for Cavg,10k

(1,519 mg/m3) are orders of magnitude higher than any that 

have been measured. At Soufrière Hills, Montserrat (Searl and 

others, 2002), Eyjafjallajökull, Iceland (Thorsteinsson and 

others, 2012), and Mount Spurr, Alaska (Gordian and others, 

1996) for example, measured concentrations did not exceed 

several milligrams per cubic meter (table 18). On May 18, 

1980, measurements in central Washington ranged as much as 

33 mg/m3 (Bernstein and others, 1986). However, a review of 

methods reveals why these values differ from ours.

Measurements like the one that recorded 33 mg/m3 in 

Yakima in 1980 were taken from a device that resembled a 

small weather station with a birdhouse roof (fig. 18A). Beneath 

that roof, air was drawn into a funnel-shaped intake and 

through a filter (Doug Jager, U.S. Environmental Protection 

Agency, Seattle, written commun., 2017). The filters were 

weighed every 24 hours, yielding an average value for total 

suspended particulates. Unpublished worksheets of the 

Yakima measurement from the Washington State Department 

of Ecology (unpublished data, 1980) indicate that, on May 18, 

1980, the filter was withdrawn before 24 hours. In Colville, 

Wenatchee, and elsewhere, filters clogged before the end of 

the 24-hour period and concentrations could not be reported.

Measurements near Yakima provide evidence for how 

much total ash could have been airborne. Wanapum Dam lies 

51 km northeast of Yakima, directly down the 1980 dispersal axis. As at Yakima, about 10 mm (8 kg/m2

) of ash fell at 

Wanapum Dam on May 18, 1980; but at Wanapum, workers 

laid out trays and recorded mass accumulation rates (Scheidegger and others, 1982), which averaged about =2.5 × 10-4

kg/m2/s for a 9-hour period. Assuming a fall rate of u=1.5 m/s 

(Durant and others, 2009; Snow and Nelson, 2012), total 

airborne concentration during the fall period would have been 

about = about 160 mg/m3—several times the suspended concentrations measured at Yakima.

During large eruptions, it is not uncommon for downwind 

areas to receive centimeters of ash in a few hours. For example, the Volcanic Explosivity Index (VEI) 6, 1912 NovaruptaKatmai eruption deposited greater than 30 cm (consolidated) 

of ash on Kodiak Island, about 170 km downwind from the 

10-2 10-1 100 101 102 103

Log bulk volume, km3

10-3

10-2

10-1

100

Log of absolute value of k0 or k2, km-1

k0

k2

Trend line

Range of volumes

modeled in this study

Slopes k0 and k2 for other eruptions

versus bulk volume

EXPLANATION

Figure 17. Graph of slopes of lines on plots of log thickness 

versus square root of area covered (k0 and k2) compiled from 

mapped deposits in table 6 of Fierstein and Nathenson (1992), 

as a function of bulk deposit volume. Red box represents the 

range of bulk volumes used in this study. One cubic kilometer 

(km3) bulk equals about 0.4 km3 DRE, using the values for 

magma density (2,500 kg/m3) and deposit density (1,000 kg/m3) in 

our study. km−1, reciprocal kilometer. 
30 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Table 18. Measurements of suspended particle concentrations made during volcanic eruptions.

Abbreviations: mg/m3, milligram per cubic meter; km, kilometer; PM10, particulate matter smaller than 10 micrometers in diameter; PM2.5, particulate matter 

smaller than 2.5 micrometers in diameter.

Eruption Concentration Reference Comments

Mount St. Helens, 

May 18, 1980

As much as 

33.4 mg/m3

(Bernstein and others, 1986) Measured in Yakima, Washington from filter measurements of 

a cyclone-type instrument. Concentration represents total 

suspended particles. (Bernstein and others, 1986). Unpublished 

measurements included 17.3 mg/m3 in Spokane, and 15.3 mg/m3

in Coeur d’Alene (Center for Disease Control, 1980). In Colville, 

Wenatchee, and elsewhere, filters clogged before the end of the 

24-hour period and concentrations could not be reported.

Mount Spurr, 

August 18, 1992

3 mg/m3 PM10 (Gordian and others, 1996) Measured in Anchorage, 100 km downwind from the source. 

80 percent was between PM2.5 and PM10. Values are 24-hour 

averages using an Anderson and Head sampler.

Soufrière Hills, 

1996–2000

“up to several 

mg/m3”

(Searl and others, 2002) Respirable dust concentrations measured with cyclone filters and 

DustTrak instruments in Plymouth, Cork Hill, Salem, and North, 

Montserrat, between September 1996 and June 1997.

Eyjafjallajökull, 

2010

> 13 mg/m3 (Thorsteinsson and 

others, 2012)

10-minute average PM10 concentration measured in Vík, Iceland, 

May 7, 2010, 40 km southeast of Eyjafjallajökull Volcano.

Direction of ash fall

Direction of 

intake airflow

Suspended ash

Falling ash

B

A

Sheltered

intake

Figure 18. Sketches showing airborne particle sampling tools. A, Sketch showing the approximate design of 

airborne particle samplers of the type used in Yakima, Washington, in May, 1980. Sketch downloaded from appendix 

B of 40 CFR Part 50, 2017. B, Illustration of falling ash and suspended ash, showing how falling ash may fail to be 

drawn into the sheltered intake because of its fall velocity.
Discussion 31

volcano (Fierstein and Hildreth, 1992). In 1932, Malargüe, 

Argentina received about 10 cm of ash from the 18-hourlong VEI 6 eruption of Cerro Azul (Quizapu), Chile, 106 km 

upwind (Hildreth and Drake, 1992). Assuming u = 1.5 m/s, 

a fall rate of 1 centimeter per hour (cm/hr; ≅ 0.003 kg/m2/s) 

translates to C ≅ 1,800 mg/m3. Average accumulation rates for 

runs in tables 10 and 13 are in this range.

Estimates using assume a control volume (fig. 19; Snow 

and Nelson, 2012) in which all mass enters from above, and 

no mass leaves. We think this method is robust and that C > 

1,000 mg/m3 is reasonable given known accumulation rates, 

but fall velocity adds a level of uncertainty.

The Implications of Uncertain Fall Velocity

Aggregates used in our study have a settling velocity of 

about 0.35–0.85 m/s (tables 11 and 16) and are assumed not to 

change as they move downwind. But real aggregates may form 

as the cloud descends and fall faster late in transport (fig. 7). 

For example, Durant and others’ (2009) estimates of 1.5 m/s 

were based on rate of 1980 cloud descent. If the 0.25–0.50-mmdiameter aggregates described by Sorem (1982) had a density 

similar to the deposit density at this location (about 500 kg/m3

(Sarna-Wojcicki and others, 1981)), their fall velocity would 

have been 0.85 to 1.9 m/s (fig. 8B). Measurements of u in other 

studies range from about 0.05 to 4 m/s (table 19). 

This wide range adds uncertainty to C. Both Ash3d and 

the control-volume method calculate airborne concentration as 

downward flux through a control volume. Lower fall velocities 

imply higher airborne concentrations. If aggregate fall velocities are 0.4–4 m/s (Taddeucci and others, 2011), rather 

0.3–0.8 m/s, then airborne concentrations could be several 

times lower than we estimate.

Control

volume

Tephra falling at velocity u

Tephra deposit accumulating at mass rate Ṁd

1m

1m

1m

Figure 19. Diagram showing control volume into which ash is falling at the mass accumulation 

rate Ṁd.The average fall velocity is u. Dimension of the grid cells are shown in meters (m).

Table 19. Tabulated fall velocities of ash aggregates from different sources.

[Abbreviations: km, kilometer; kg/m3, kilogram per cubic meter; mm, millimeter; m/s, meter per second; MSH, Mount St. Helens]

Value Explanation

1.5 m/s Estimated by Durant and others (2009) at MSH 1980 as an average between the cloud (11.5 km) and ground level, based on 

a 1 hour 46 minute time delay in Spokane between arrival of the cloud overhead and the first tephra-fall.

0.4–4 m/s Velocities of hundreds of falling dry aggregates measured 7 km downwind of Eyjafjallajökull in high-speed video by 

Taddeucci and others (2011). Aggregates were mostly 1±0.5mm diameter and had densities of < 100 to > 1,000 kg/m3.

0.05–0.5 m/s Measured by James and others (2002) on loose, dry aggregates created in the laboratory by electrostatically charging 

pumice particles. 
32 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Falling aggregates

and particles

Fall

path

Path of

air flow

HVAC

air intakes

Disintegration

on impact

Figure 20. Illustration of the path that might be taken by 

aggregates or particles falling near the intake of an HVAC 

system of generic design. Air drag from flow into the intake, 

along with the gravitational force, will determine whether 

individual particles or aggregates are ingested. Some 

aggregates may disintegrate on impact near the intakes, 

increasing suspended particle concentrations.

Conclusions

One the basis of about 10,000 model simulations, we 

estimate maximum and average airborne ash concentrations for 

the “1 in 10,000-year” event at Hanford, Washington, of about 

3,800 and 1,500 mg/m3, respectively. These are order-of-magnitude estimates with large uncertainties, but we are confident 

that airborne concentrations of about 103 mg/m3 are possible, 

given known deposit accumulation rates elsewhere. We emphasize that these estimates are of total airborne ash; both falling, 

and in suspension. They are not comparable to most air quality 

measurements, which measure only suspended ash.

Falling particles differ from suspended ones in that their 

movement is no longer well coupled to the air. Air moving 

toward an HVAC air intake (fig. 20) may not draw them in. 

The fraction of falling ash ingested depends on the nearby 

flow field as well as the size, shape, and density of falling 

material. Some aggregates may disintegrate upon impact 

(fig.20), locally increasing the suspended concentration

Assessing the ash ingestion rate into a Hanford HVAC system 

is beyond the scope of this project. It may involve uncertainties as great as those in this study.

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38 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Appendix 1: Particle Characterization

Introduction

The purpose of this appendix is to characterize the size 

and shape of volcanic ash particles that could affect Hanford 

from a future eruption, and to provide supporting data for 

related modeling and experimental studies on ashfall and 

resuspension. A careful analysis of particle size and shape 

would not be necessary if volcanic ash were composed of 

smooth, uniform spheres akin to beach sand. But the reality 

is somewhat more complex. For example, ash from explosive 

eruptions like the May 18th, 1980 eruption of Mount St. 

Helens (MSH) consists of fragments of silicate glass, denser 

mineral crystals, and pieces of host rock blown out by the 

eruption. These components are present in varying proportions 

depending on the eruption dynamics and transport history, 

leading to a complex distribution of sizes and shapes at any 

given site (fig. 1.1). Here, we characterize some of the key 

physical properties that influence the aerodynamic properties 

of volcanic ash, and their entrapment by air intake filters, 

focusing on particle size and shape. We have analyzed samples 

of volcanic ash sourced from three primary locations: (1) the 

proximal MSH 1980 deposit, (2) distal MSH 1980 deposit, 

Yak_1000x_vesicular

3a

6b

MSH1-29a VTTS6a

MSH1-25a

MSH1-15a

Proximal Mount St. Helens Valley of Ten Thousand Smokes

Bubble wall

Elongate 

bubbles

Vesicular

glass

Vesicular

glass

Crystal

A

B

C

G

H

I

Distal Mount St. Helens (Yakima)

Yak_23b

Yak_1000x_mossy

Mossy

Poorly

vesicular

D

E

F

Dense 

glass

Vesicular

glass

Mossy

Vesicular

Vesicular

Bubble 

wall
Methods and Data 39

Figure 1.1 (page 39). Example of scanning electron microscope (SEM) images of volcanic ash used in this study. Arrows point to 

particle morphologies discussed in the text. Note scale bar on each image; magnification ranges from 270x to 370x. A–C, Images of 

proximal Mount St. Helens (MSH) ash deposit derived from pyroclastic flows on the afternoon of May 18, 1980, (sample MSHb1sub). 

Note the variety of grains present, from vesicular glass (containing abundant bubbles), to poorly vesicular or dense glass, and a smaller 

proportion of irregular, mossy grains. D–F, Images of distal MSH ashfall from May 18, 1980, collected from Yakima, Washington, roughly 

78 kilometers west of Hanford, Washington (sample MSH1980-C.RUSSELL). This material contains less vesicular glass overall. G–I, 

Volcanic ash from the Valley of Ten Thousand Smokes, Alaska, derived from tephra-fall deposits of the 1912 Novarupta-Katmai eruption 

(sample subVTTS2a). Note the abundance of vesicular glass and bubble wall shards. μm, micrometer.

and (3) 1912 Novarupta-Katmai eruption from Alaska’s 

Valley of Ten Thousand Smokes (VTTS). These samples 

span a range of eruption and transport styles yet are all within 

the plausible range of Cascades eruptive activity and are all 

dacitic in composition. This approach allows us to address a 

key question in context with the modeling and experimental 

work—what ranges of particle sizes and shapes would we 

expect to fall at Hanford during the next highly explosive 

eruption in the Cascades?

Methods and Data

To address the issues described above, particle size 

distributions were analyzed for 10 samples of volcanic ash, 3 

of which were selected for additional shape analysis (table 1.1, 

fig. 1.2). All analyses were completed at the U.S. Geological 

Survey Cascades Volcano Observatory in Vancouver, Wash., 

by Alexa Van Eaton (laser diffraction, shape analysis) and 

Katherine Norton (sieve, sedigraph).

Table 1.1. Volcanic ash samples used in particle characterization. 

[Collection locations give latitude and longitude in decimal degrees. Abbreviations: DRI, Desert Research Institute; km, kilometer]

Sample ID Analyses Collection location Description

MSH-B1sub sieve, sedigraph, 

laser, shape

Mount St. Helens, Wash.,

46.26957, −122.18092

Field sample from the “ramp” 8 km north of Mount St. Helens, 

derived from pyroclastic flows on the afternoon of May 18, 1980 

SUBVTTS1a sieve, sedigraph, 

laser

Katmai, Alaska

58.40150, −155.38569

Field sample of 1912 Plinian fall deposits from the Valley of Ten 

Thousand Smokes, 25 km from Novarupta 

SUBVTTS2a sieve, sedigraph, 

laser, shape

Katmai, Alaska

58.40150, −155.38569

—as above

SUBVTTS3a sieve, sedigraph, 

laser

Katmai, Alaska

58.29762, −155.23869

—as above, 10 km from Novarupta 

SUBVTTS4a sieve, sedigraph, 

laser

Katmai, Alaska

58.29762, −155.23869

—as above, 10 km from Novarupta 

SUBVTTS5a sieve, sedigraph, 

laser

Katmai, Alaska

58.35327, −155.30924

—as above, 18 km from Novarupta 

SUBVTTS6a sieve, sedigraph, 

laser

Katmai, Alaska

58.35327, −155.30924

—as above, 18 km from Novarupta 

MSH-Hop_3.17.2017 laser DRI lab Lab sample of ash resuspended during experiments on MSH material

VTTS_

Hop_3.21.2017

laser DRI lab Lab sample of ash resuspended during experiments on VTTS1, 

VTTS2, and VTTS5 material

MSH1980-C.

RUSSELL

laser, shape Yakima, WA

46.60202, −120.41813

Field sample of ashfall collected on May 18, 1980, during the first 

few hours of ashfall, 144 km from Mount St. Helens
40 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

men20-7413_fig01.02

Sieve

Laser diffrac�on

Sedigraph

Shape analysis

1 μm

32

1 mm

2 4 8 16 63 125 250 500 2 4 8 16

Diameter

10 9 8 7 6 5 4 3 2 1 0 –1 –2 –3 –4 Phi scale

Figure 1.2. Schematic showing the particle characterization methods used on different sizes for this study. Note size bins are 

based on a logarithmic phi scale (ø) shown in italics, where ø = –log2(D), and D is the particle diameter in millimeters (mm) and 

micrometers (μm).

Size Analysis of Volcanic Ash

In conventional methods of particle size analysis, the 

coarser material is assessed by sieving, which involves 

passing the sample through progressively smaller meshes 

and weighing the fractions retained. This approach 

becomes unreliable for particles much smaller than about 

63 micrometers (μm), so more sophisticated methods are 

required for the fine-grained material. In this study we have 

used a combination of laser diffraction and sedigraph to 

analyze the finer particles and merge results with sieve data 

where appropriate. Both laser diffraction and sedigraph have 

strengths and weaknesses. One benefit of the sedigraph is 

that it measures settling velocities of particles (in water), 

which may provide useful information for calculating settling 

velocities in air. Key benefits of laser diffraction are that it 

can cover a wider range of sizes (0.4 μm to 2 millimeters 

[mm]) and analyze very small amounts of sample (typically 

less than 0.2 grams [g]). Results from these two methods 

would be identical if the particles were perfect spheres 

with uniform densities and optical properties. But the 

natural complexity of volcanic ash means that sieving, laser 

diffraction, and sedigraph techniques each provide slightly 

different measurements of “diameter”, despite being robust 

and established methods that have been used in particle size 

analysis for decades. 

Sieving

All samples containing particles larger than 1 mm were 

dry sieved (table 1.1) to obtain the distribution of sieve diameters from 31.5 mm to 63 μm. To prepare the sample, aggregates were lightly crushed with a mortar and rubber-tipped 

pestle. The material larger than 4 mm was hand-sieved at standard intervals of 8, 16, and 31.5 mm. Then the fraction finer 

than 4 mm was passed through a stack of sieves using an automated shaker for 10 ± 2 minutes, using sieve meshes of 2 mm, 

1 mm, 500 μm, 250 μm, 125 μm, and 63 μm, plus a catch pan. 

Material retained on each sieve and pan was weighed to the 

nearest 0.1 gram. The cumulative particle size distribution was 

recorded as weight percent retained by each sieve and merged 

with fines analysis where appropriate (table1.1), as describe

in the following sections.

Laser diffraction

Laser diffraction measures the optical diameters of 

particles less than 2 mm. For this study, the method was only 

applied to volcanic ash sieved below 1 mm, using a Beckman 

Coulter LS 13 320. The technique works by shining a 780 nm 

laser beam through a well-mixed dispersion of particles in 

water. The cross sectional areas of tumbling particles scatter 

the light into a diffraction pattern, which can be converted to 

a size distribution using Mie theory and some assumptions 

about the optical properties of the grains. With our instrument 

configuration, a sample mass of 0.1–0.2 g is typically enough 

for a standard analysis. This enabled analysis of the airborne 

material collected from resuspension experiments in the lab 

(table 1.1), which did not provide enough material for the 

sedigraph. To prepare the sample, a test portion of volcanic 

ash smaller than 1 mm was transferred to a plastic vial with 

50–100 milliliters (ml) of Calgon solution and shaken by 

hand to disperse any aggregates. Using a plastic pipette, 

the dispersion was transferred to the instrument’s Aqueous 

Liquid Module and sonicated for 60 sec before analysis. The 

sample was analyzed 3 times for 60 seconds each, and an 

average of the three runs was used. A single optical model 

was applied to all volcanic ash samples used in this study 

(all are dacitic in composition), using values of 1.5 for the 

real refractive index and 0.0005 for the absorption coefficient 

based on comparison with published studies (Ball and others, 

2015) and the International Organization for Standardization 

(ISO) lookup table (ISO, 2009). The results give volume 

percent finer for each size class. Note that laser diffraction 

measures volume rather than weight percent (like sieving and 

sedigraph), but results are comparable if a constant particle 

density is assumed. For samples that were sieved (table 1.1), 

the laser diffraction and sieve data were combined by scaling 

the laser diffraction results to the whole sample using the 
Methods and Data 41

known proportion of ash smaller than 1 mm determined 

from sieving. Data are provided in table 1.2. We have binned 

the laser data into half-phi intervals (see fig. 1.2) although 

higher-resolution bins are also available in the data archive. 

We included additional size classes at 2.5 and 10 micrometers 

(particulate matter [PM]2.5 and PM10, respectively) because 

of their relevance to resuspension and air filtration systems 

(highlighted rows in table 1.2).

Sedigraph

Sedigraph analysis was performed on all the sieved samples (table 1.1). This method determines the settling diameter 

of particles less than 63 μm by measuring their gravitational 

fall velocity in water and assuming perfectly spherical 

shapes. The Micromeritics SediGraph III 5120 uses the relative absorption of a low-energy X-ray beam to estimate the 

concentration of particles in suspension at different heights, 

at known times during the analysis. Conversion to a particlesize distribution is performed through a combination of Beer’s 

Law and Stokes’ Law, assuming a constant particle density of 

2.615 grams per cubic centimeter (g/cm3) and water temperature of 35 °C (refer to ISO, 2001; Webb, 2004). The analysis 

requires 1.5 to 3 g of material for reliable results. To prepare 

the sample, a sufficient mass of the fraction finer than 63 μm 

fraction was placed in a cup, wetted with deionized water and 

dispersed using 1 milliliter (mL) of dispersing agent and a 30 

second burst with an ultrasonic probe. Then the dispersion was 

Table 1.2. Particle-size distributions using combined sieve-laser diffraction analyses, shown as cumulative percent less than a given 

size fraction.

[Size bins are given in half-phi intervals from 1 micrometer (μm) to 1 millimeter (mm), and whole-phi intervals from 1–16 mm. Extra bins were added for PM10 

and PM2.5]

Method Diameter, 

in μm

MSHB1subsubVTTS1asubVTTS2asubVTTS3asubVTTS4asubVTTS5asubVTTS6aMSH_

Hopper

VTTS_

Hop_3

MSH1980-

C.RUSSELL

laser 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1

laser 1.4 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.3

laser 2 0.4 0.1 0.1 0.2 0.3 0.1 0.1 2.1 1.1 0.9

laser 2.5 1.5 0.3 0.2 0.9 1.1 0.1 0.1 9.4 6.5 2.0

laser 2.8 2.4 0.4 0.3 1.4 1.8 0.2 0.2 15.2 11.1 2.7

laser 3.9 6.1 0.9 0.5 3.8 4.7 0.2 0.3 37.7 30.0 5.5

laser 5.5 10.9 1.4 0.8 6.8 8.2 0.4 0.4 59.7 50.0 8.7

laser 7.8 16.6 2.0 1.1 10.1 12.2 0.5 0.6 75.1 66.0 12.1

laser 10 21.6 2.4 1.4 12.8 15.4 0.6 0.8 82.7 74.9 14.7

laser 11 23.6 2.6 1.5 14.0 16.8 0.7 0.8 85.0 77.8 15.8

laser 15.6 32.9 3.4 1.9 19.0 22.8 1.0 1.1 92.5 87.3 20.3

laser 22.1 43.4 4.4 2.6 25.6 30.5 1.4 1.6 97.2 94.4 24.6

laser 31.3 53.5 5.7 3.5 33.0 38.9 2.0 2.2 99.0 97.9 28.3

laser 44.2 63.0 8.1 5.3 41.9 48.5 3.1 3.5 100.0 99.9 32.1

laser 62.5 71.3 12.3 8.7 51.6 58.7 4.7 5.6 100.0 100.0 35.0

laser 88.4 78.1 18.5 14.2 60.2 67.4 7.2 9.0 100.0 100.0 37.8

laser 125 84.5 27.4 22.5 68.1 74.9 10.7 13.8 100.0 100.0 41.5

laser 176.8 89.8 38.7 33.6 74.6 80.7 15.7 20.6 100.0 100.0 51.9

laser 250 93.8 52.3 47.6 80.2 85.0 23.9 30.6 100.0 100.0 74.2

laser 353.6 96.6 66.1 62.1 84.9 88.6 36.8 44.7 100.0 100.0 90.9

laser 500 97.7 76.7 74.0 89.2 92.0 54.4 61.4 100.0 100.0 97.3

laser 707.1 98.3 84.1 82.4 93.4 95.5 72.3 76.9 100.0 100.0 99.8

sieve 1,000 98.9 90.4 89.8 95.7 97.4 89.4 90.3 100.0 100.0 100.0

sieve 2,000 99.6 95.4 96.0 99.4 99.2 94.1 95.4 100.0 100.0 100.0

sieve 4,000 100.0 97.9 98.8 99.9 100.0 96.6 97.3 100.0 100.0 100.0

sieve 8,000 100.0 99.2 99.9 100.0 100.0 98.3 97.9 100.0 100.0 100.0

sieve 16,000 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
42 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

introduced to the sedigraph for analysis. Recorded values for 

the mass of each size class were scaled to the whole sample 

using the known proportion of ash smaller than 63 μm determined from sieving (table 1.3).

Shape Analysis of Volcanic Ash

Particle morphology exerts a first-order control on the 

aerodynamic behavior of volcanic ash (Wilson and Huang, 

1979). The particle sizes most likely to clog HVAC filters 

are in the range of 10 micrometers diameter and smaller (For 

example, Azimi and others, 2014). Particles in this size range 

are challenging to isolate and work with in the lab owing to 

the effects of electrostatic attraction in low-humidity environments (Miura and others, 2002; James and others, 2003). In 

our analysis, the 32–63 μm fraction was chosen as a reasonable compromise between imaging the finest particles and 

ensuring reliable results by minimizing electrostatic aggregation and touching grains during sample preparation.

Some of the useful ways to categorize particle shape 

include measurements of form (elongate versus equant) and 

roughness (jagged versus smooth) (Liu and others, 2015). To 

quantify the relevant parameters (table 1.4), we examined twodimensional projected areas of unpolished grains using images 

from a scanning electron microscope. The areas are projected 

because they are based on two-dimensional images of complex 

three-dimensional objects, rather than flat thin sections or polished surfaces (fig. 1.3). This approach was chosen because it 

allows examination of the surface features and a better intuition 

for the overall appearance of volcanic ash in its natural state.

Bulk ash samples were sieved between 32–63 μm, sonicated in deionized water for 2–3 minutes to remove adhering 

fines, and oven dried. Particles were dusted onto pin-type 

scanning electron microscope (SEM) stubs and carbon coated 

using a Denton Vacuum Desk Sputter Coater. Typical SEM 

operating conditions used a working distance of 15–17 mm 

and accelerating voltage of 20 kilovolts (kV) in backscatter 

mode. Images were collected at a magnification of 55x or 

more and saved as 1024 x 1024 TIFF files, providing about 

20–40 grains per image and a resolution of at least 0.63 pixels 

per μm. Then images were processed using digital thresholding to distinguish the particles from background. Where necessary, a line was manually drawn (2 pixels wide) to separate 

touching grains and those touching the edge of the image but 

still greater than 98 percent within the field of view. Next, the 

image was converted to binary (black and white) and used as 

input for ImageJ (software version 1.50c4). Within ImageJ, 

the scale was specified according to the pixel resolution of the 

image, and the following measurement routines enabled: (1) 

area, (2) shape descriptors, (3) perimeter, (4) fit ellipse, and 

(5) feret diameter (table 1.4). Particles were excluded from 

analysis if they were less than 200 square micrometers (μm2) 

area or touching the edges of the processed image. Resulting 

outlines were numbered and saved. More than 1,000 particles 

were analyzed from each of the three samples. The number of 

pixels per particle (pixel density) is an important factor in data 

quality, with previous studies showing consistent results with 

at least 750 pixels per particle (Liu and others, 2015). Therefore, we only include results from the particles defined by 750 

pixels or more (table 1.5).

Table 1.3. Sieve-sedigraph particle-size distributions, shown as cumulative weight percent less than a given size fraction.

[Size classes are binned into whole-phi intervals from 1 micrometer (μm) to 16 millimeters (mm), (see fig. 1.2). (–) indicates negative values that were rounded 

up to zero]

Method Diameter, in 

μm

MSH-B1sub subVTTS1a subVTTS2a subVTTS3a subVTTS4a subVTTS5a subVTTS6a

sedigraph 1 0.9 0.1 – 4.0 5.4 – 0.1

sedigraph 2 4.9 0.3 0.4 6.3 7.6 0.3 0.3

sedigraph 3.9 10.0 0.5 0.5 8.3 10.3 0.4 0.4

sedigraph 7.8 21.8 1.1 1.2 11.8 15.0 0.9 0.9

sedigraph 15.6 41.3 2.4 2.1 17.5 23.5 1.7 1.6

sedigraph 31.3 57.9 6.8 5.7 27.0 36.6 4.3 3.9

sieve 62.5 67.7 13.7 11.7 33.0 43.6 8.5 8.0

sieve 125 85.0 32.8 31.1 48.4 59.8 19.5 18.9

sieve 250 94.7 60.1 60.8 62.2 72.6 40.3 39.3

sieve 500 98.1 81.7 82.2 81.9 87.2 72.9 71.6

sieve 1,000 98.9 90.4 89.8 95.7 97.4 89.4 90.3

sieve 2,000 99.6 95.4 96.0 99.4 99.1 94.1 95.4

sieve 4,000 100.0 97.9 98.8 99.9 100.0 96.6 97.2

sieve 8,000 100.0 99.2 99.9 100.0 100.0 98.3 97.9

sieve 16,000 100.0 100.0 100.0 100.0 100.0 100.0 100.0
Results and Discussion 43

men20-7413_fig01.03

A B C

Figure 1.3. Images showing steps of particle-shape analysis. A, Original scanning electron microscope (SEM) 

image in backscatter mode. B, Processed image used as input for ImageJ analysis, after thresholding the 

particles and converting to black and white. C, Output image showing the outlines included in analysis. Within 

the software file, each particle outline is numbered, giving it a unique reference ID. μm, micrometer.

Table 1.4. Particle shape descriptors used in this study.

Area Area of particle within outline, including bubbles

Perimeter Length of the outside boundary of the particle

Major Major axis of a best fit ellipse

Minor Minor axis of a best fit ellipse

Circularity 4 π × [Area/Perimeter]2

 with a value of 1.0 indicating a perfect circle

Feret Maximum caliper, the longest distance between any two points on particle boundary

MinFeret Minimum caliper, the shortest distance between any two points on particle boundary

Aspect ratio Ratio of long to short axes (Major / Minor)

Roundness 4 × Area / (π × Major2

)

Solidity Morphological roughness (Area / Area of a convex hull)

Pixel density Number of pixels contained within the particle

Form Factor Measure of form and roughness (4 π × Area/Perimeter2

)

Axial ratio Ratio of intermediate to long axes (Minor / Major)

Table 1.5. Samples and number of particles used in shape analysis.

[Sample ID corresponds to table 1.1. Note that only particles defined by 750 pixels or more were included in results]

Sample ID Location Particles analyzed Particles of ≥750-pixel density

MSHB1-sub Mount St. Helens, Wash. 1,601 1,029

MSH1980-C.RUSSELL Yakima, Wash. 1,640 1,087

subVTTS2a Katmai, Alaska 1,004 815

Results and Discussion

Particle-Size Distributions

Full results of the measured size distributions are 

tabulated in spreadsheet A1 in the accompanying data 

repository (Mastin and others, 2020). Size distributions 

of the volcanic ash from Mount St. Helens and Valley of 

Ten Thousand Smokes samples show several key features 

(fig.1.4). First, the 10 samples of primary volcanic ash sho

marked variations in the content of particles less than or equal 

to 10 μm (PM10), from less than one percent in the coarsest 

samples from the Valley of Ten Thousand Smokes, to 22 percent in the proximal MSH sample. Particles smaller than 2.5 

μm (PM2.5) range from 0.2–2 percent (fig. 1.4, table 1.2). 

In contrast, the airborne ash collected during resuspension 
44 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

men20-7413_fig01.04

0

5

10

15

20

25

1 3.9 15.6 62.5 250 1,000 16,000

%

Diameter, micrometers

A

MSH-B1sub

0

5

10

15

1 3.9 15.6 62.5 250 1,000 16,000

%

C

subVTTS1a

0

5

10

15

1 3.9 15.6 62.5 250 1,000 16,000

%

D

subVTTS2a

0

5

10

15

1 3.9 15.6 62.5 250 1,000 16,000

%

E

subVTTS3a

0

5

10

15

1 3.9 15.6 62.5 250 1,000 16,000

%

F

subVTTS4a

0

5

10

15

20

1 3.9 15.6 62.5 250 1,000 16,000

%

Diameter, micrometers

G

subVTTS5a

0

5

10

15

20

1 3.9 15.6 62.5 250 1,000 16,000

%

Diameter, micrometers

H

subVTTS6a

0

5

10

15

20

25

1 3.9 15.6 62.5 250 1,000 16,000

%

Diameter, micrometers

B

MSH1980-

C.RUSSELL

Mount St. Helens, Washington

Valley of Ten Thousand Smokes, Alaska

Proximal MSH Distal MSH

Figure 1.4. Histograms showing particle-size distributions from sieve-laser diffraction analysis of each 

volcanic ash sample collected in the field. Note values are reported as percent within each size class, rather 

than cumulative percent as shown in table 1.2. Size bins are in half-ø increments from 1 micrometer to 1 

millimeter (mm), and whole-ø increments from 1–16 mm. %, percent.
Results and Discussion 45

experiments (fig. 1.5) is almost entirely less than 32 μm and 

contains significantly more PM10 (75–83 percent) and PM2.5 

(7–10 percent). These numbers vastly underestimate the 

PM2.5 fraction because particles smaller than 2.5 μm were 

removed during the lab’s collection process. The implication is 

that primary ashfall from an explosive eruption could transport 

significant quantities of extremely fine ash to Hanford, but 

resuspension by the wind would concentrate and re-entrain the 

sizes most relevant to air filtration systems.

Another observation is that the proximal sample of MSH 

1980, collected 8 km from the volcano, contains substantially 

more fine ash than the distal fall deposit that landed in eastern 

Washington (fig. 1.4). Table 1.2 shows that the proximal 

sample is 71 percent finer than 63μm compared to 35 percen

at Yakima. The difference in PM10 content is somewhat less 

marked (22 percent versus 15percent). The finer-graine

nature of the proximal ash is clearly seen in figure 1.6A, which 

includes two additional ashfall samples that landed within 80 

km of Hanford (reported by Durant and others, 2009). The 

contrast between proximal and distal samples mainly reflects 

their transport histories during different phases of the eruption. 

In this case, the proximal sample was sourced from the outer 

edges of pyroclastic flows on the afternoon of May 18. These 

ground-hugging currents simply did not travel as far as the 

higher-altitude vertical plumes, so all their mass—even the 

finest particles—deposited closer to the volcano. The key 

message is that both samples are useful for evaluating the 

range of possible size distributions transported by a Mount St. 

Helens eruption. To demonstrate this, figure 1.6B shows the 

proximal sample alongside the total grain-size distribution of 

the entire May 18, 1980, fall deposit from Durant and others 

(2009), which integrates several ashfall samples at different 

sites to reconstruct the original size population as it exited the 

volcano. The two plots show roughly comparable amounts of 

PM10, suggesting that the proximal sample is well within the 

expected range of size distributions produced by the May 18, 

1980, eruption.

0

5

10

15

20

25

1 3.9 15.6 62.5 250 1,000 16,000

%

Diameter, micrometers

Mount St. Helens

0

5

10

15

20

25

1 3.9 15.6 62.5 250 1,000 16,000

%

Diameter, micrometers

Valley of Ten Thousand Smokes

Cutoff at 

2.5 μm

Resuspended

MSHb1sub

Resuspended

subVTTS2a

Figure 1.5. Comparison of parent versus resuspended ash from Portable In Situ Wind ERosion Lab (PI-SWERL) 

laboratory experiments, using material from Mount St. Helens, Washington, and the Valley of Ten Thousand Smokes, 

Alaska. Grain-size distributions are from sieve-laser diffraction data in table 1.2. The size distributions of resuspended 

ash from the two locations are nearly identical, despite very different parent material. The PI-SWERL laboratory 

instrument is designed to sample only the particles coarser than 2.5 micrometer (μm) “aerodynamic” diameter from the 

resuspended ash (labeled cutoff in this plot), although laser diffraction does show a small amount of material less than 

2.5 μm “optical” diameter. %, percent.
46 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

men20-7413_fig01.06

0

5

10

15

20

25

0.4 1.0 2.8 7.8 22.1 62.5 177 500 2,000 16,000

%

Diameter, micrometers

Distal MSH (MSH1980-

C.RUSSELL)

76 km west of Hanford (Durant

et al.)

37 km East of Hanford (Durant

et al.)

0

5

10

15

20

25

0.4 1.0 2.8 7.8 22.1 62.5 177 500 2,000 16,000

%

Diameter, micrometers

A

Total grain size 

distribution for

entire fall deposit 

(Durant et al .)

Ashfall near

Hanford

Proximal ash sample 

(MSHb1sub)

Proximal ash sample 

(MSHb1sub)

Yakima (this study)

76 km W ( Durant et al. )

37 km E ( Durant et al .)

B

Mount St. Helens – Proximal vs. distal

Figure 1.6. Histograms showing comparison of the particle-size distribution of the proximal May 18, 1980, ash sample from 

this study (gray bars) with other samples from the same eruption. A, Compares with three samples collected from the Hanford, 

Washington area, including the Yakima, Washington sample analyzed in this study (MSH1980-C.RUSSELL) and sites 37 kilometers 

(km) east (DZ 21_12) and 76 km west of Hanford (DZ 20_6) reported by Durant and others (2009). B, Compares with the total grainsize distribution of the entire May 18, 1980, fall deposit reported by Durant and others (2009). %, percent.

Morphology of the Volcanic Ash Particles

Results of shape analyses are tabulated in spreadsheet A2 

of the data repository (Mastin and others, 2020). The aerodynamic properties of volcanic ash and entrapment by filters 

are both influenced by the shape of the particles (Wilson and 

Huang, 1979). Figure 1.7 shows distribution of long axes in 

each of the three samples, based on feret diameter. Although 

these particles were sieved between 32–63 μm, their long 

axes are generally much larger, in the range of 60–100 μm, 

owing to the presence of elongate particles, particularly in 

the sample from the Valley of Ten Thousand Smokes (subVTTS2a). Figure 1.8A illustrates this particle elongation 

with a plot of axial ratios, which is the ratio of intermediate 

to long axes. The VTTS sample contains higher proportions 

of elongate grains compared to the proximal and distal MSH 

ash, perhaps reflecting differences in the style of magma fragmentation. For example, magma breakage may have occurred 

along bubble walls that were more elongate than in the Mount 

St. Helens 1980 magma. Elongate bubbles are visibly more 

common in scanning electron microscope (SEM) images of 

the VTTS ash (fig. 1.1H).

Another important observation is particle roughness, 

which is strongly affected by the presence of vesicular glass. 

The distal MSH sample from Yakima is an outlier in this 

regard. Both in terms of solidity (fig. 1.8b) and form factor 

(fig. 1.8c), it contains significantly more particles with smooth 

outlines, indicating less vesicular glass. Lower vesicularity 

is linked to the magma ascent and fragmentation processes 

associated with the earliest phase of the May 18th eruption. 

The sample was collected during the first few hours of ashfall 

in Yakima, at a time when the eruption was expelling a less 

vesicular batch of magma known as the cryptodome. The 

cryptodome magma rose slowly in the volcanic edifice and 

had time to partially degas before generating the lateral blast 

and its associated far-traveled ash plume (Hoblitt and Harmon, 
Results and Discussion 47

men20-7413_fig01.07

0.

0.05

0.1

0.15

0.2

0.25

0.3

20 40 60 80 100 120 140 160 180 200 220 240

Frequency

%

Feret diameter, micrometers

Yakima (n = 1,087)

MSH (n = 1,029)

VTTS (n = 815)

Convex hull Ellipse Feret diameter Figure 1.7. Histogram of feret diameters (in 

micrometers [μm] ) from each of the samples 

analyzed for shape, where n gives the number 

of grains used for each sample (meeting 

or exceeding the threshold of 750 pixels 

per particle). The green bar is from Yakima, 

Washington, sample MSH1980-C.RUSSELL; the 

yellow bar is from Mount Saint Helens (MSH), 

sample MSHb1sub; and the dashed black line 

is from the Valley of Ten Thousand Smokes 

(VTTS), sample subVTTS2a. The particles 

were sieved between 32–63 micrometers for 

analysis, but their feret diameters (long axes) 

are mainly in the range of 60–90 μm owing to 

the presence of elongate grains. Note that 

the Valley of Ten Thousand Smokes sample 

contains the longest feret diameters for the 

same sieve fraction, indicating a greater 

proportion of elongate grains. %, percent.

0%

10%

20%

30%

40%

0.1 0.3 0.5 0.7 0.9 1.1

Frequency

Axial ratio (form)

0%

10%

20%

30%

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Frequency

Form factor (form and roughness)

0%

20%

40%

60%

80%

0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

Solidity (morphological roughness)

Yakima MSH VTTS

B

C

A

EXPLANATION

Figure 1.8. Plots showing the results of particle-shape analysis 

on the three samples of volcanic ash. A, axial ratio, or ratio of 

intermediate to long axes. B, Solidity which is a measure of particle 

roughness. C, Form factor, which is sensitive to both form and 

roughness. The green bar is from Yakima, Washington, sample 

MSH1980-C.RUSSELL; the yellow bar is from Mount St. Helens (MSH), 

sample MSHb1sub; and the dashed black line is from the Valley of Ten 

Thousand Smokes (VTTS), sample subVTTS2a. Note that the Valley 

of Ten Thousand Smokes (VTTS) sample has the lowest axial ratios 

because of elongate particles, and distal Mount St. Helens (MSH) 

(Yakima) has the highest values of solidity and form factor owing to 

poorly vesicular particles.
48 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

1993). This is quite a different scenario from the later phases 

of the May 18th eruption (and the 1912 eruption Novarupta) 

which involved actively vesiculating magma that rose 

quickly to the surface and erupted as vertical Plinian columns 

(Gonnermann and Houghton, 2012). The key message here is 

that different magma fragmentation processes can produce fartraveled volcanic ash in the Cascades, leading to deposition of 

different particle shapes. And yet, despite the clear differences 

among samples in terms of eruption dynamics and particle 

morphologies, they do plot in a relatively consistent range, 

with most axial ratios in the range of 0.4–0.8, solidity 0.85–

0.90, and form factor 0.45–0.75 (fig. 1.8).

Conclusions

An analysis of particle size and shape distributions of 

volcanic ash from the May 18, 1980, eruption of Mount St. 

Helens and 1912 eruption of Novarupta, Alaska (Valley of 

Ten Thousand Smokes), reveals several observations relevant 

to the hazards of ashfall impacting Hanford from a future 

eruption in the Cascades.

1. Particle-size distributions transported to the Hanford 

area by a Mount St. Helens eruption will vary greatly 

depending on the dynamics of eruption and transport, 

but a reasonable expectation is that the content of PM10 

(particles smaller than 10 μm) could be less than 1 percent 

to greater than 20 percent, with PM2.5 comprising as 

much as 2 percent of the ashfall deposit by mass. 

2. Resuspension of the ashfall deposit by wind will preferentially loft the material less than 32 μm, leading to a 

substantially greater proportion of PM10 in the airborne 

population (much greater than 70 percent by mass).

There are distinct differences in particle morphologies of 

the three ash samples analyzed in this study, related primarily 

to magma fragmentation processes. But overall, they show 

a relatively consistent range of shape parameters, with most 

axial ratios in the range of 0.4–0.8, solidity 0.85–0.90, and 

form factor 0.45–0.75.
Size of the Largest Eruptions at Mount St. Helens 49

Appendix 2: Effect of Extremely Large Eruptions of Mount St. Helens on TephraFall Thickness and Airborne Ash Concentration at the Hanford Site, Washington

by Larry G. Mastin, Michael Clynne, Manuel Nathenson, John Pallister, and Alexa Van Eaton

Introduction

In December 2018, the U.S. Geological Survey’s 

Cascades Volcano Observatory submitted the main body 

of this report to the U.S. Department of Energy’s Office of 

River Protection (DOE-ORP), estimating the thickness and 

airborne ash concentration that could occur at the Hanford, 

Washington, facility with an annual probability of 1 in 10,000 

during a future eruption of Mount St. Helens (MSH). To make 

this estimate, we ran approximately 10,000 model simulations 

of a hypothetical MSH eruption, randomly sampling erupted 

volumes within the range that are recorded in the Holocene 

stratigraphic record at MSH. The largest Holocene tephra 

deposit at MSH, the Yn, has a dense-rock-equivalent 

(DRE) volume between 0.8 and 2.3 cubic kilometers (km3; 

Nathenson, 2017). The maximum volume we used for our 

modeling, 2.3 km3 DRE, was a key input.

In July 2019, DOE-ORP forwarded us the Staff Factual 

Accuracy Check and Staff Review of our analysis, written by 

the Defense Nuclear Facilities Safety Board (DNFSB) staff. 

The Accuracy Check noted some key concerns, specifically:

1. The maximum eruption volume used in our 

analysis was “non-conservative”. The DNFSB 

staff cited an International Atomic Energy Agency 

document, IAEA-TEC-DOC-1795, Volcanic 

Hazards Assessments for Nuclear Installations, 2016 

(International Atomic Energy Agency, 2016), which 

recommends that volcanic hazard assessments for 

nuclear facilities consider volcanic activity extending 

back 10 million years. “Including data from 10,000 

years to 10 million years ago would have resulted in 

a larger estimated maximum erupted volume (Vmax) 

and would therefore increase anticipated ashfall 

thickness and concentration values.” The DNFSB 

staff was not persuaded by previous assessment and 

appraisal from the U.S. Geological Survey (USGS) 

that the magma system for Mount St. Helens was 

different during pre-Holocene time, and that larger 

pre-Holocene eruptions did not reflect the current 

composition and (or) size of the magma system.

2. The maximum estimated volume for the Yn, 

2.3 km3, was used as an absolute upper bound and 

we did not consider aleatoric variability and epistemic uncertainty.

The USGS provides this report to address those concerns. 

In our modeling, we chose the Yn as the upper endmember 

because it was the largest Holocene eruption, and because 

it occurred in a magma system that in some way resembles 

the current one. We did not examine older eruptions because 

the lack of adequate geological and physical evidence makes 

estimates of their size impractical; however, we should at 

least consider the probability of eruptions bigger than the Yn. 

In this report, we examine evidence of larger eruptions, run 

additional models, and reach three conclusions: (1) that the 

Yn eruption is likely the largest at Mount St. Helens over at 

least the past 50,000 years; (2) that the annual probability of 

larger eruptions is likely about 10-5 or less, and (3) that including eruptions larger than the Yn in our analysis, weighted by 

their probability, does not change our estimates of thickness 

or airborne concentration by more than a few tens of percent, 

for the 1-in-10,000 year event. These variations are within the 

range of other uncertainties in our analysis.

Size of the Largest Eruptions at Mount 

St. Helens

The oldest rocks that make up Mount St. Helens are a 

few hundred thousand years old (Clynne and others, 2008). 

The area around the volcano was glaciated several times 

before about 10 kilo-annum (ka) and older tephras were 

mostly removed; thus, older tephras are known primarily from 

distal locations. The biggest late-Pleistocene tephras known 

from MSH are the C-set tephras (Mullineaux, 1996), at least 

four of which are exposed in the eastern Washington Palouse 

(Busacca and others, 1992). The younger two correlate 

with Cw and Cy (Busacca and others, 1992), with ages in 

the 45–50,000-year range. One of the two older C tephras 

was dated at 83±8.3 ka by thermoluminescence (Berger and 

Busacca, 1995), and it is not a C tephra recognized proximally. 

The age of the fourth Set C tephra was estimated by deposition 

rate to be as old as about 120 ka and is also probably not 

preserved proximally. 

We have no estimates of the volume of these older 

eruptions, but in the most comprehensive study of MSH 

tephras, Mullineaux (1996) implies that they were big. In his 

abstract, and his summary of Ape Canyon Stage volcanism, 

Mullineaux (1996) describes a late Set C tephra (probably Cy) 

as the largest known Mount St. Helens tephra of Pleistocene 

age. “One of them erupted near the end of Ape Canyon 

time, records one of the largest [italics ours] volume tephra 

eruptions known for MSH and has been recognized as far 

away as Nevada.”. Also, in the abstract and discussion of 

Spirit Lake Stage volcanism (Mullineaux, 1996, abstract)) 
50 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

states: “One of the coarse layers, layer Yn, is the largest 

volume Holocene tephra known from Mount St. Helens.” 

Carey and others (1995) echo that statement: “Layer Yn 

(3,510 years before present.) represents the highest intensity 

and largest magnitude eruption at Mount St. Helens in postglacial times.”

The best available indicator of the size of late-Pleistocene 

tephras, relative to the Yn, is their thickness at comparable 

distances along their dispersal axes (table 2.1). The Cb tephra 

is about 100 centimeters (cm) thick at 8–11 kilometers (km) 

downwind (Mullineaux, 1996, Fig. 11). At the same distance 

downwind, Cw is 40 cm and Cy is 60 cm, and the other Set C 

tephras are thinner. Yn is about 200 cm thick, and 120–180 cm 

at 18 km (Carey and others, 1995, Fig. 3c; Mullineaux, 1996, 

Fig. 40B). Also at 8–10 km distance, the Wn, the second 

largest Holocene tephra, is 180 cm thick (Carey and others, 

1995, Fig. 7a; Mullineaux, 1996, Fig. 61E). In these proximal 

locations, the Yn is the thickest known MSH tephra. Studies 

of distal Cascade tephras from the American West or Canada 

(Jensen and others, 2019) also recognize the Yn as being the 

most widespread Mount St. Helens tephra. 

There are caveats with this conclusion of course. Exposures of the Pleistocene tephra set C-set are sparser than of 

Holocene tephras; and for this reason, we are less confident 

that the C-set thicknesses observed at 8–11 km distance are 

along the dispersal axis. Moreover, because exposures degrade 

with time, the older tephras at distal sites will be less prominent. Despite those caveats, we have found no evidence of any 

MSH tephras thicker than the Yn.

Table 2.1. Thickness of the largest tephra layers at Mount St. 

Helens, at 8–11 kilometers from the vent.

[Data from Mullineaux (1996, Table 4). Abbreviations: cm, centimeter; 

km, kilometer]

Unit Thickness at 8–11 km distance (cm)

Wn 180

Yn 200

Cy 60

Cw 40

Cb 100

Probability of an Eruption Larger than 

the Yn

Even if the Yn were the biggest of the MSH tephra eruptions, the probability of a larger eruption must be greater than 

zero. In order to assign the size and probability of this larger 

eruption, we must consider a larger dataset.

The world’s volcanic activity is chronicled by the Smithsonian Institution. Their Global Volcanism Program Volcanoes 

of the World (GVP) Database (https://volcano.si.edu/) lists all 

known historical eruptions worldwide, plus all older Holocene eruptions that are known from deposits rather than direct 

observations. Where possible, the size of each eruption is 

assigned using the Volcanic Explosivity Index (VEI); a complicated ranking that uses both plume height and tephra volume to derive a number from 0 to 8. Considering only tephra 

volume, eruptions of VEI 3, 4, 5, 6, and 7 have bulk volumes 

exceeding 0.01, 0.1, 1, 10, and 100 km3 respectively. Nathenson (2017) estimates the bulk volumes of the 1980, the Wn, 

and the Yn tephra deposits as 1.1, 0.7–4, and 2–9 km3 respectively, ranking them all as VEI 5 on this scale. Nathenson’s 

(2017) 9 km3 maximum tephra volume for the Yn converts to 

our modeled maximum dense-rock-equivalent (DRE) volume 

of 2.3 km3, using Nathenson’s densities of 600 kilograms per 

cubic meter (kg/m3) and 2,300 kg/m3 for the deposit and the 

magma, respectively. 

Nathenson’s (2017) volume estimate for the Yn ranks 

it as a large VEI 5 eruption. Among all eruptions in the GVP 

database, eruptions of size VEI 6 and larger (roughly, those 

bigger than the Yn) are about three times less common than 

VEI 5 (table 2.2, columns 2 and 3). However, some types of 

volcanoes are more capable of large eruptions than others. The 

GVP data indicate for example that of 6,049 eruptions from 

stratovolcanoes (of which MSH is one) 127 are VEI 5 (column 

4), and 24 are VEI 6 or greater. Thus VEI 6 or greater eruptions compose less than 0.5 percent of all eruptions, and about 

2 percent of VEI 3 or greater eruptions.

Within the Cascade Range, scattered layers record the 

infrequent occurrence of very large tephra eruptions. Nathenson (2012, Table 4) has tabulated about 20 Cascade tephras 

with deposit volumes (V) greater than 5 km3, and 12 with 

(V) greater than10 km3, since 1.2 Ma. The volumes that form 

Table 2.2. Number of eruptions in the Smithsonian Institution’s 

Global Volcanism Program (GVP) Volcanoes of the World 

Database, listed by size (VEI) (Global Volcanism Program, 2013). 

Eruptions with no size assignment are listed under “??”.

[Abbreviations: km3, cubic kilometer; VEI, Volcanic Explosivity Index; 

%, percent]

Volume (km3) All GVP Stratovolcanoes

VEI Bulk Count Percent Count Percent

?? 2,251 23 1,318 22

0 1×10−5–1×10−4 804 8 174 3

1 0.0001–0.001 1,208 12 772 13

2 0.001–0.01 3,741 38 2,481 41

3 0.01–0.1 1,127 11 808 13

4 0.1–1 504 5 342 6

5 1–10 177 2 127 2

6 10–100 52 0.5 24 0.4

7 100–1,000 8 0.1 3 0.0
Effect of Large Eruptions on our Model Results 51

this tally are mostly educated guesses using thicknesses 

extrapolated from a few outcrops or inferred from the size of 

a caldera. Some volumes have since been revised downward 

(Nathenson, 2017). But if we take these numbers at face value 

and plot them as a function of age (fig. 2.1), we can assess 

the eruptive frequency from the steepness of the curves. The 

frequency of eruptions with bulk volumes greater than 5 km3

(the blue curve of fig.2.1) appears dramatically greater in the 

past few tens of thousands of years than at earlier times. We 

do not think that this indicates an increasing rate of activity; 

more likely, it is an artifact of preservation. Tephra deposits get buried or eroded with time, and the smaller deposits 

disappear. The magenta curve of figure 2.1 represents the 

larger eruptions and shows a more constant rate since about 

600 ka—a trend that suggests the record may be more complete over this time. The last 300 ky shows a rate somewhat 

higher—perhaps twice as high as the overall average since 

600 ka. Ten eruptions with V > 10 km3 since 600 ka implies a 

Cascade-wide annual probability of 1.6×10-5. The somewhat 

higher rate in the past 300 ky suggests an annual probability 

of about 3×10-5. Whether this probability is evenly distributed 

among all 18 volcanoes of the Cascade Range is debatable. 

MSH is currently the most explosive volcano, but geodetic, 

seismic, and petrologic data make it uncertain whether its 

magma body is large enough to feed such an event. If evenly 

distributed so that the annual probability of a VEI 6 or greater 

eruption is the same at all volcanoes, the annual probability 

of a larger than 10 km3 (bulk) eruption at MSH would be 

roughly 3 × 10-5 / 18 ≅ 2 × 10-6. If concentrated at MSH, the 

annual probability of a VEI 6 or greater there could be an 

order of magnitude higher. Corresponding recurrence intervals (RVEI6+) of a larger than 10 km3

 (bulk) eruption at MSH 

would be about 50,000 to 500,000 years. At this rate, we 

would expect at least a few such eruptions in the more than 

300,000-year history of MSH. In the geologic record, we see 

no evidence for any such eruptions.

Effect of Large Eruptions on our Model 

Results

Our analysis and that of Hoblitt and Scott (2011), noted 

that MSH produced 4 large explosive eruptions in roughly the 

last 500 years. Nathenson’s (2017) volume estimates suggest 

that these were VEI 3 or larger. To first order, the recurrence 

interval R of these events is about one per century. If the recurrence interval (RVEI6+) for VEI 6 or greater eruptions is between 

50,000 and 500,000 years, then the conditional probability of a 

VEI 6 or greater eruption, given the occurrence of an eruption, 

would be roughly R/RVEI6+=0.0002 to 0.002. That is, for every 

VEI 6 or greater eruption, we would expect between 500 and 

5,000 smaller (VEI 4–5) eruptions.

Including these larger eruptions with their appropriate 

conditional probability would require that we add between 

2 and 20 larger eruptions to the roughly 10,000 we have run 

already. We have actually run 1,000 additional simulations 

with volumes of 2.3–40 km3 DRE. In table 2.3, we examine 

the effect on the thickness (T10k), maximum (Cmax,10k), and average (Cavg,10k) airborne ash concentrations of adding 1, 10, 100, 

Eruptions >5 km3

Eruptions >10 km3

Figure 2.1. Graph showing the number of 

Cascade eruptions versus age, in thousands 

of years before present. Figure modified from 

Nathenson and others (2012, fig. 14). Blue line 

shows all eruptions with tephra volumes greater 

than about 5 cubic kilometers (km3); magenta 

line shows all eruptions with tephra volumes 

exceeding about 10 km3.
52 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

or all 1,000 to the simulations already run. Our objective is 

to examine the sensitivity of model results to different probabilities of high-volume eruptions. Volumes of these additional 

runs were assigned randomly using a uniform cumulative 

distribution on a log scale (fig. 2.2A). Model inputs and outputs from these runs is posted in tables BS1–BS3 of Mastin 

and others (2020). New values of the T10k, Cmax,10k, and Cavg,10k

airborne ash concentrations at Hanford, having an annual 

probability of 1 in 10,000, were calculated using the same 

methodology as in our main report.

Table 2.3 shows that changes to T10k, Cmax,10k, and Cavg,10k

from the addition of these runs are less than 40 percent, even 

when all 1,000 of the large-volume runs are added. The small 

effect is due in part to the fact that most simulations produced 

no deposit at Hanford (red dots, fig. 2.2b).

A second reason for the small effect is that we left most 

of the volume distribution intact, changing only the upper 

(high-volume) tail. Here, we also consider the effects of 

entirely different volume distributions. Figure 2.3A shows 

the cumulative distribution function for our standard uniform 

distribution (V = 0.008 – 2.3 km3 DRE), compared with 

four others: our standard with 100 (“hi-V”) high-volume 

runs added; our standard with 1,000 (‘hi-V 10 percent”) 

high-volume runs added; a uniform distribution from 0.1 – 

4 km3 based on MSH tephra volume estimates in Carey and 

others (1995) and used in an analysis reported to DOE in 2017 

(“Carey”); and a new, hypothetical distribution (“Hypo”). The 

hypothetical distribution was constructed by starting with the 

Table 2.3. Effect of the addition of a small number of highvolume simulations on the tephra-fall thickness (T10k), maximum 

airborne ash concentration (Cmax,10k) and average airborne ash 

concentration (Cavg,10k) at Hanford, Washington, having an annual 

probability of one in 10,000.

[Abbreviations: mg/m3, milligram per cubic meter; mm, millimeter; yr, year; 

%, percent; ∞,infinity]

Number (%) 

of runs added

RVEI6+

yrs

T10k, mm

Cmax,10k

mg/m3

Cavg,10k

mg/m3

0 (0%) ∞ 51.1 3819 1513

1 (0.01%) 1×106 51.1 3819 1513

10 (0.1%) 1×105 51.1 3856 1529

100 (1%) 1×104 51.8 3849 1568

1,000 (9.3%) 1×10−3 62.6 4071 2083

100 101 102

Volume, km3 DRE

0

200

400

600

800

1,000

Cumulative numer of runs

0 100

Run number

0

50

100

150

200

250

Thickness at Hanford, mm

VEI 5 VEI 6 VEI 7

50

Figure 2.2. Graphs showing volume and thickness of tephra deposits indicated by model runs. 

A, Cumulative volume distribution of the 1,000 large-volume model simulations. Blue dashed line 

depicts a volume of 2.3 cubic kilometers (km3) dense-rock equivalent (DRE). Black dashed lines 

separate Volcanic Explosivity Index (VEI) 5, 6, and 7 eruption sizes, using bulk tephra volume 

as the defining quantity for these VEI ranges and assuming tephra and DRE densities of 1,000 

and 2,500 kilograms per cubic meter (kg/m3) respectively. The volumes are sampled from a 

distribution that is uniform on a log scale from 2.3 to 40 km3 DRE. B, Tephra deposit thickness at 

Hanford, Washington, as a function of the run number, for the first 100 model runs. Model runs 

with exactly zero thickness (T) at Hanford are represented by red dots, while those with T > 

0.000 millimeters (mm) are blue.
Effect of Large Eruptions on our Model Results 53

standard distribution but increasing the frequency of larger 

eruptions under the assumption that the volumes of older 

deposits are toward the larger end of the uncertainty range. 

In particular, we assumed: (1) that most (about 95 percent) 

Holocene eruptions in the stratigraphy are at least VEI 4 in 

size; (2) that about 1 percent of eruptions in this record are 

VEI 6 or greater; and (3) that among eruptions in the VEI 4–5 

range, about two thirds will be VEI 4, based on global trends 

(table 2.2). The percentage of VEI 6 or greater eruptions in 

this distribution (1 percent) is 5 to 50 times greater than the 

percentage we estimated earlier, based on Cascade Rangewide large eruption frequencies. The hypothetical distribution 

includes volumes extending to 40 km3 DRE. The probability 

density functions for these distributions are in figure 2.3 B–D.

For each of these distributions, we calculated values 

of T10k, Cmax,10k, and Cavg,10k (table 2.4). Values based on the 

100

Log volume, km3 DRE

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cumulative distribution

VEI 3 VEI 4 VEI 5 VEI 6

A

Std

hi-V

hi-V (10% )

Carey

Hypo

0

0.2

0.4

pdf

Standard

B

0

0.5

1

pdf

Carey

C

10-2 100 102

Log volume, km 3 DRE

0

0.5

1

pdf

Hypothetical

D

Figure 2.3. Graphs showing the cumulative distribution function and the probability distribution 

functions as a function of dense-rock equivalent (DRE) volume in cubic kilometers (km3). A, 

Example cumulative distributions of DRE volume. Std (black line) is the the standard distribution 

used in our analysis; hi-V (high volume, dashed red line) is the modification to the standard 

distribution, with 100 (1 percent) high-DRE-volume eruptions added (barely distinguishable from 

the Std curve); hi-V (10 percent; dotted red line) is the modification to the standard distribution, 

with 1,000 (10 percent) high-volume eruptions added; Carey (dashed magenta line) is the volume 

range of Holocene eruptions used in an earlier version of our analysis, based on Mount St. Helens 

Holocene volume estimates of Carey and others (1995); and Hypo (solid green line) is a hypothetical 

distribution as explained in the text. Alternating gray and white zones show the regions where 

erupted volumes match the ranges for Volcanic Explosivity Index (VEI) 3, 4, 5, and 6, when 

calculated by converting dense-rock equivalent volume to bulk volume using assumed densities 

of 1,000 kilograms per cubic meter (kg/m3) for the deposit and 2,500 kg/m3 for the magma. B–D

Probability density function (pdf) versus DRE volume showing: B, this study’s standard distribution 

(with 1 percent and 10 percent hi-volume additions shown as a red dashed and red dotted 

lines, respectively); C, the volume distribution of Carey and others (1995); and D the hypothetical 

distribution illustrated in A.
54 A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens

Table 2.4. Values of tephra-fall thickness (T10k), maximum 

airborne ash concentration (Cmax,10k) and average airborne ash 

concentration (Cavg,10k) at Hanford, Washington, based on the 

distributions of eruptive volume given in figure 2.3.

[Abbreviations: mg/m3, milligram per cubic meter; mm, millimeter]

Distribution T10k

mm

Cmax,10k

mg/m3

Cavg,10k

mg/m3

Standard 51.1 3,819 1,513

Standard+100 large runs 51.8 3,849 1,568

Carey 105 7,387 3,018

hypothetical 55.1 4,410 2,148

Carey and others (1995) DRE volume distributions were 

presented in a DOE meeting on October 2, 2017, and were 

based on about 10,000 additional simulations. Those for the 

hypothetical distribution were calculated by taking 3,000 of 

the about 11,000 runs (the original about 10,000 plus the 1,000 

high-volume runs), to produce a population with the volume 

distribution shown. 

The hypothetical distribution increases T10k about 8 percent relative to the standard distribution. Cmax,10k and Cavg,10k

are 15 percent and 42 percent higher, respectively, than the 

standard distribution. In summary, these new values are within 

a few tens of percent of the ones we reported. The Carey and 

others (1995) DRE volume distributions, which we think 

overestimates volumes, gives T10k roughly equal to the 100 

mm value estimated by Hoblitt and Scott (2011), and concentration values about two times greater than our results using 

the standard distribution.

Conclusions

In the conclusions section of our original report, we 

characterized our results as order-of-magnitude estimates with 

large uncertainties. We also noted in the discussion section 

that these were “best estimates”, made with no intent to add 

conservatism. We have taken seriously the concern that our 

modeling did not consider a finite probability of an eruption 

larger than 2.3 km3 DRE. In addressing this issue, we have 

shown (1) that there are no known eruptions from Mount St. 

Helens that are larger than 2.3 km3 DRE; (2) that Cascades 

eruptive history suggests an annual probability of a larger 

eruption to be on the order of 10−5 or less; and (3) that when 

one adds larger eruptions to our dataset, using appropriate 

conditional probabilities, the calculated thickness and concentration at Hanford are still within a few tens of percent of our 

original calculations.

Menlo Park Publishing Service Center, California 

Manuscript approved for publication November 9th, 2020

Edited by John Mark Brigham

Layout by Kimber Petersen

Illustration support by JoJo Mangano
Mastin and others—A Probabilistic Assessment of Tephra-Fall Hazards at Hanford, Washington, from a Future Eruption of Mount St. Helens—Open-File Report 2020–1133

ISSN 2328-0328 (online)

https://doi.org/10.3133/ofr20201133