Estimate of Tephra Accumulation Probabilities for the 

U.S. Department of Energy’s Hanford Site, Washington

Open-File Report 2011–1064

U.S. Department of the Interior

U.S. Geological Survey
Estimate of Tephra Accumulation Probabilities for the 

U.S. Department of Energy’s Hanford Site, Washington

By Richard P. Hoblitt and William E. Scott

Open-File Report 2011–1064

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia 2011

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Hoblitt, R.P., and Scott, W.E., 2011, Estimate of tephra accumulation probabilities for the U.S. Department of 

Energy's Hanford Site, Washington: U.S. Geological Survey Open-File Report 2011-1064, 15 p.

[http://pubs.usgs.gov/of/2011/1064/].

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iii

Contents

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

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

Potential Tephra Sources and Eruption Magnitudes...................................................................................... 2

Probability Analysis........................................................................................................................................ 4

P(1): Annual Probability of Eruption ........................................................................................................... 5 

P(2|1): Mean Probability of Wind Direction................................................................................................. 5

P(3|2): Exceedance Probability of Tephra Accumulation............................................................................ 7

P(1 and 2 and 3): Estimate of Tephra Thickness that would be Equaled or Exceeded 

at the 1 x 10-4

Revised Probabilistic Tephra-Fall Map .......................................................................................................... 9

Annual Probability Level................................................................................................... 7

Conclusion................................................................................................................................................... 10

References Cited......................................................................................................................................... 11

Appendix 1. Discussion of Table 1 Highlighting Differences in Eruptive History Details from 

Compilations by Hoblitt and Others (1987) and Siebert and Others (2010) ...................................... 14 

Appendix 2. Tephra Data Used in Estimation of Annual Exceedance Probabilities ..................................... 15

1. Annual probability of exceedance for tephra fallout (in centimeters) at the Hanford Site in 

 south-central Washington State................................................................................................................. 8

Figures

2. Preliminary probabilistic tephra hazard map for Pacific Northwest revised from Hoblitt and 

 others (1987) and Scott and others (1995). ............................................................................................. 10

Tables

1. Mean annual probabilities of substantial (≥0.1 km3

2. Average wind directions (direction that the wind is blowing toward) in 16, 22.5°-sectors for nine 

 altitude ranges (in kilometers) for Quillayute, Washington, from January 1, 1973, through 

 June 30, 2010............................................................................................................................................ 6 

bulk volume) explosive eruptions of tephra 

 from the major Cascade volcanic centers in the U.S. and Canada (first three centers). ............................ 2 

3. Exceedance probabilities of tephra accumulations at 200 km distance from source volcano 

 for 14 VEI 4 and 5 eruptions from the global catalog (Appendix 2; Newhall and Hoblitt, 2002). ................ 7 

4. Exceedance probabilities and annual probabilities of exceedence of tephra accumulations 

 at the Hanford Site for the eruption data from table 3. ............................................................................... 8 
iv

Conversion Factors

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 centimeter (cm2) 0.001076 square foot (ft2

square meter (m

)

2

) 10.76 square foot (ft2

square centimeter (cm

) 

2

) 0.1550 square inch (ft2

square kilometer (km

) 

2

) 0.3861 square mile (mi2

Volume

)

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 (dm

) 

3

) 61.02 cubic inch (in3

liter (L)

) 

61.02 cubic inch (in3

cubic decimeter (dm

) 

3

) 0.03531 cubic foot (ft3

cubic meter (m

) 

3

) 35.31 cubic foot (ft3

cubic meter (m

)

3

) 1.308 cubic yard (yd3

cubic kilometer (km

) 

3

) 0.2399 cubic mile (mi3

Mass

) 

gram (g) 0.03527 ounce, avoirdupois (oz)

kilogram (kg) 2.205 pound avoirdupois (lb)

megagram (Mg) 1.102 ton, short (2,000 lb)

megagram (Mg) 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/cm

)

3

) 62.4220 pound per cubic foot (lb/ft3)
Estimate of Tephra Accumulation Probabilities for the U.S. 

Department of Energy’s Hanford Site, Washington

By Richard P. Hoblitt and William E. Scott

Abstract

In response to a request from the U.S. Department of Energy, we estimate the thickness of tephra 

accumulation that has an annual probability of 1 in 10,000 of being equaled or exceeded at the Hanford 

Site in south-central Washington State, where a project to build the Tank Waste Treatment and 

Immobilization Plant is underway. We follow the methodology of a 1987 probabilistic assessment of 

tephra accumulation in the Pacific Northwest. For a given thickness of tephra, we calculate the product 

of three probabilities: (1) the annual probability of an eruption producing 0.1 km3

 (bulk volume) or 

more of tephra, (2) the probability that the wind will be blowing toward the Hanford Site, and 

(3) the probability that tephra accumulations will equal or exceed the given thickness at a given 

distance. Mount St. Helens, which lies about 200 km upwind from the Hanford Site, has been the most 

prolific source of tephra fallout among Cascade volcanoes in the recent geologic past and its annual 

eruption probability based on this record (0.008) dominates assessment of future tephra falls at the site. 

The probability that the prevailing wind blows toward Hanford from Mount St. Helens is 0.180. We 

estimate exceedance probabilities of various thicknesses of tephra fallout from an analysis of 14 

eruptions of the size expectable from Mount St. Helens and for which we have measurements of tephra 

fallout at 200 km. The result is that the estimated thickness of tephra accumulation that has an annual 

probability of 1 in 10,000 of being equaled or exceeded is about 10 centimeters. It is likely that this

thickness is a maximum estimate because we used conservative estimates of eruption and wind 

probabilities and because the 14 deposits we used probably provide an overestimate. The use of deposits 

in this analysis that were mostly compacted by the time they were studied and measured implies that the 

bulk density of the tephra fallout we consider here is in the range of 1,000–1,250 kg/m3

. The load of 10 

cm of such tephra fallout on a flat surface would therefore be in the range of 100–125 kg/m2

Introduction 

; addition of 

water from rainfall or snowmelt would provide additional load. 

The following analysis re-examines the results of a probabilistic assessment of tephra 

accumulation in the Pacific Northwest that was part of a U.S. Geological Survey (USGS) report for the 

Nuclear Regulatory Commission published in 1987 (Hoblitt and others, 1987). In 2010, U.S. 

Department of Energy, Office of River Protection, Richland, Washington, contacted the USGS 

regarding tephra hazards and design of the new Hanford Tank Waste Treatment and Immobilization 

Plant (referred to hereafter as the Waste Treatment Plant), which is under construction at the 

Department’s Hanford Site in south-central Washington State. We were also contacted by the Defense 

Nuclear Facilities Safety Board, which is reviewing the design. During a conference call with these 

parties on August 18, 2010, we agreed to revisit the subject of tephra hazards for the new facility. The 

specific subject of interest was an estimate of the thickness of tephra accumulation that would have an 

annual exceedance probability of 1 x 10-4; that is, the thickness of tephra accumulation that would have 
2 

an annual probability of 1 in 10,000 of being equaled or exceeded. Our approach largely follows that of 

the 1987 report, but with some additional data and topics. 

Potential Tephra Sources and Eruption Magnitudes

Of the 16 major volcanic centers in the U.S. and Canadian Cascades volcanic arc, 14 have 

erupted since the disappearance of ice age glaciers about 12,000–15,000 years ago; only Mount Cayley 

and Mount Jefferson have been quiet (Scott, 1990; Hildreth, 2007). During this time period, three have 

produced substantial volumes (defined here as a bulk erupted volume of ≥0.1 km3

Table 1. Mean annual probabilities of substantial (≥0.1 km

) of tephra fallout on 

multiple occasions, seven have produced one such event, and six have not produced such tephra fallout. 

Hoblitt and others (1987) determined mean annual probabilities of a substantial explosive eruption at 

U.S. Cascade centers on the basis of the data in table 1 (modified slightly by additional information and 

the inclusion of Canadian centers; appendix 1). 

3

[U.S. data slightly modified from Hoblitt and others (1987) as described in appendix 1, which also explains differences with 

a recent compilation of worldwide data by Siebert and others (2010). Canadian data from Hildreth (2007) and Siebert and

others (2010); wind data from table 2. All volcanoes with no substantial eruptions are assigned a default value of 1 x 10

bulk volume) explosive eruptions of tephra from the 

major Cascade volcanic centers in the United States and Canada (first three centers). 

-5.]

Volcano

Time 

interval

(yr)

Explosive 

eruptions

≥0.1 km3

Mean 

annual

probability

Distance and 

azimuth from 

volcano to 

Hanford

(km)

Average 

probability of wind 

from azimuth 

direction (3–18 km 

altitude)

Mount Meager 12,000 1 8 x 10 550 SE -5 0.10

Mount Cayley 12,000 0 1 x 10 490 SE -5 0.10

Mount Garibaldi 12,000 0 1 x 10 450 SE -5 0.10

Mount Baker 12,000 1 8 x 10 300 SE -5 0.10

Glacier Peak 13,000 3 2 x 10 210 SE -4 0.10

Mount Rainier 10,000 1 1 x 10 175 E -4 0.17

Mount St. Helens 15,000 12 8 x 10 210 E -4 0.18

Mount St. Helens

1 

(Spirit Lake stage) 4500 9 2 X 10 210 E -3 0.18

Mount St. Helens 

(recent cluster)

1 

500 4 8 x 10 210 E -3 0.18

Mount Adams

1 

12,000 0 1 x 10 155 ENE -5 0.18

Mount Hood 15,000 0 1 x 10 210 NE -5 0.14

Mount Jefferson 15,000 0 1 x 10 270 NE -5 0.14

Three Sisters 12,000 1 8 x 10 325 NNE -5 0.07

Newberry Volcano 10,000 1 1 x 10 340 NNE -4 0.07

Crater Lake

(Mount Mazama) 12,000 3 3 x 10 450 NNE -4 0.07

Medicine Lake volcano 11,000 1 9 x 10 590 NNE -5 0.07

Mount Shasta 10,000 1 1 x 10 620 NNE -4 0.07

Lassen volcanic center 11,000 0 1 x 10 700 NNE -5 0.07

1 Value for Mount St. Helens from Hanford sector in table 2
3 

Because composite volcanoes such as those in the Cascades typically have episodes of more 

frequent activity for centuries to millennia alternating with apparently dormant intervals of roughly 

similar duration (for example, Crandell and Mullineaux, 1978; Crandell and others, 1979; Nathenson 

and others, 2007), the mean annual eruption probability can vary greatly depending on the time span 

selected. As shown in table 1, the eruption probability for Mount St. Helens, based on the average 

frequency of events during three time periods, ranges from 8 x 10-4 for the past 15,000 years (which 

includes a dormant interval of about 7,000 years) to 2 x 10-3 for the past 4,500 years (which includes 

several dormant intervals of 300–600 years) to 8 x 10-3 for the past 500 years (which includes two 

dormant intervals of 50–100 years). Mount St. Helens is the only Cascade center that one could argue 

strongly is in a period of increased eruptive frequency; thus we use 8 x 10-3

Five Cascade volcanic centers lie less than or close to 200 km of the Hanford Site and, except 

for Glacier Peak, lie at azimuths that have the highest probabilities (0.14–0.18) of being upwind. Glacier 

Peak and St. Helens have produced more than one substantial explosive eruption in the recent geologic 

past, Rainier one, and Adams and Hood none. A brief summary of each center follows. 

 in the following analysis. 

o Glacier Peak produced three large explosive eruptions in a brief time period shortly after the end 

of the last ice age, two of which deposited widespread tephra over eastern Washington (Gardner 

and others, 1998; Kuehn and others, 2009). Since then eruptive activity has consisted chiefly of 

lava dome extrusion and collapse accompanied by modest tephra production (Begét, 1982, 

1983).

o Mount Rainier has produced numerous eruptions of lava flows accompanied by modest 

explosive eruptions during the past 10,000 years, but only one substantial explosive eruption, 

which deposited pumice and ash over the eastern flank of the volcano about 2,200 years ago 

(Hoblitt and others, 1998; Sisson and Vallance, 2009). That event produced about 7.5 cm of 

tephra fallout at a distance of 25 km from the vent; the distal extent of this tephra is poorly 

known, but probably no more than a few millimeters fell at 200 km.

o Mount St. Helens has been the most prolific source of substantial explosive eruptions and 

accompanying tephra fallout in the Cascades since the end of the last ice age. As discussed 

above, the volcano has produced four significant explosive eruptions during the past 500 years 

(Hoblitt and others 1980; Carey and others, 1995; Mullineaux, 1996). These and a few older St. 

Helens eruptions have been studied in great detail and provide some of the most robust 

thickness-distance data in the world-wide sample analyzed in this report (appendix 2). 

o Mounts Hood and Adams have not produced substantial explosive eruptions or widespread 

tephra layers during their ~500,000-year lifespans. Effusion of lava flows (Adams) and lava 

domes (recent history of Hood) accompanied by modest tephra production have characterized 

these volcanoes (Hildreth and Fierstein, 1997; Scott and others, 1997). 

The rest of the Cascade centers lie 300–700 km from Hanford, are at less probable wind azimuths, and 

have low (10-4–10-5

On rare occasions during the past 1 million years, a few Cascade centers produced voluminous 

tephra eruptions measuring tens of cubic kilometers. Some of these eruptions are known to have been 

accompanied by caldera collapse. The most recent such event occurred about 7,700 years ago at Mount 

Mazama and created Crater Lake caldera; about 30 cm of tephra fell 500 km from the vent along the 

axis of deposition (northeast). Other such events near Mount Baker (~1 million years ago) and near 

Lassen Peak (610,000 years ago) are thought to have been of similar size (Hildreth, 2007). Studies of 

the Mazama system conclude that a volume of shallow silicic magma capable of producing another 

caldera-forming eruption will not accumulate for thousands of years (Bacon and others, 1997). From the 

nature of their eruptions over the past few thousand years, St. Helens, Rainier, Adams, and Hood are 

) annual probabilities of producing a substantial explosive eruption. 
4 

judged incapable of such activity (Hildreth, 2007). No other Cascade system is suspected to be primed 

to produce tens of cubic kilometers of tephra in a caldera-forming eruption during the next few centuries 

to millennia, so the annual probability of such an event appears negligible (~3 x 10-6

The following discussion refers to the Volcanic Explosivity Index (VEI; Newhall and Self, 

1982), a scale analogous to the magnitude scale for earthquakes. VEI is chiefly a function of bulk 

erupted volume and height of the eruption cloud. Only eruptions greater than VEI 3 (0.01–0.1 km

). 

3

) are 

capable of producing more than a millimeter of fallout at a distance of 200 km from a vent (table 3 in 

Newhall and Hoblitt, 2002). Cascade eruptions of the recent geologic past referred to as substantial 

(capable of producing centimeters or more of fallout at 200 km) include VEI 4 (0.1–1.0 km3; typically 

called large), 5 (1–10 km3; very large), and 6 (10–100 km3

The deposits of tephra falls analyzed in this report (appendix 2) are chiefly from a compilation 

by Newhall and Hoblitt (2002) that was used to develop a generic event-tree technique for forecasting 

the outcome of volcanic unrest and eruption. They used a worldwide dataset from 86 historical and 

prehistoric eruptions of VEI 4–8 to estimate exceedance probabilities of tephra-fall thickness at 

distances out to 200 km from the source volcano. We use a subset of 13 VEI 4 to 5 events from this 

compilation for which there exist measurements of fallout thickness at 200 km from the volcano, the 

approximate distance from Mount St. Helens to the Hanford Site. We add a fourteenth event by 

including measurements of tephra fallout at 200 km for the 1982 eruption of El Chichón, Mexico, 

(Varecamp and others, 1984) to the more proximal measurements given in Newhall and Hoblitt (2002). 

) events. As discussed above, the probability 

of a Cascade eruption in the high range of VEI 6 or larger in the near future is negligible, so such events

are not considered in the following analysis. On average, VEI 4 eruptions have an annual global 

probability of about 0.5—one about every 2 years; VEI 5 eruptions about 0.08—a little less than one per 

decade (fig. 2 in Newhall and Hoblitt, 2002).

Two of the events we include have been categorized elsewhere as VEI 6. The largest known 

eruption of St. Helens is the Yn eruption, which occurred about 3,800 years ago (Mullineaux, 1996). 

This eruption is categorized in the Smithsonian Institution’s global catalog as VEI 6 (Siebert and others, 

2010), but at most on the low end of the VEI 6 range, or about 15 km3

Probability Analysis

 (Carey and others, 1995; Gardner 

and others, 1998). Similarly, the 1991 eruption of Mount Pinatubo is listed as VEI 6 (Siebert and others, 

2010). However, the fallout deposit itself from that eruption probably ranks as VEI 5 (PaladioMelosantos and others, 1996; Scott and others, 1996). 

The annual probability of a given thickness of tephra accumulation from a given volcano at a 

given point is the product of three probabilities (Hoblitt and others, 1987): 

1. The marginal probability that the volcano will produce an eruption of a given magnitude in a given 

year, P(1);

2. The conditional probability that the wind will blow from the volcano toward the given point, P(2|1); 

and

3. The conditional probability that the eruption will deposit as much or more than the given thickness 

at the distance in question, P(3|2). 

The probability we seek is P(1 and 2 and 3) = P(1) * P(2|1) * P(3|2). 

Because the probability of more than one regional volcano becoming active in a given year is 

exceedingly small, the probabilities from individual volcanoes are effectively mutually exclusive. Thus 

the total annual probability will be the sum of the probabilities from each volcano in the region. 
5 

For the Hanford Waste Treatment Plant, we focus solely on Mount St. Helens. Decades of 

geological study have shown that St. Helens has a propensity for frequent large explosive eruptions; a 

propensity that is unusual even in a global context. As discussed above, other regional volcanoes—

Adams, Hood, Rainier, Glacier Peak, and Jefferson—do not contribute significantly to the total 

probability because of low eruption probabilities, low explosivities, greater distances from Hanford, less 

favorable azimuths, or combinations thereof (table 1). 

P(1): Annual Probability of Eruption 

St. Helens has been particularly active in the past approximately 500 years (table 1). During this 

interval it produced four large or very large (VEI 4–5) eruptions (Hoblitt and others, 1980; Carey and 

others, 1995; Mullineaux, 1996): May 18, 1980; 1800 CE, T tephra; 1482 CE, We tephra; and 1480 CE, 

Wn tephra. This results in a mean annual probability of a VEI 4–5 eruption of 0.008. 

A group of USGS physical volcanologists gathered at the Cascades Volcano Observatory (CVO)

on August 26, 2010, to discuss St. Helens’ current eruption probability. On a global basis, it is known 

that eruption frequency varies inversely with eruption magnitude—VEIn-1 is about 6 times more 

probable than VEIn 

P(2|1): Mean Probability of Wind Direction

(Newhall and Hoblitt, 2002). From this one may posit that volcanoes have a 

gestation period during which they accumulate a sufficient volume of gas-charged magma to trigger an 

explosive eruption. Most volcanologists agree with this hypothesis, and it is almost certainly true for 

some, perhaps most, volcanoes. Following this line of reasoning, the probability of a large explosive 

eruption decreases precipitously immediately after such an event. Some volcanologists at CVO argued 

that St. Helens’ explosive eruption probability is currently diminished because of a very large explosive 

eruption just three decades ago. There are two problems with this argument. First, there is a clear 

violation of the reduced eruption probability argument in the data for St. Helens itself—the We eruption 

occurred only two years after the Wn eruption. Second, even if the eruption probability is reduced, how 

do we quantify it? To be conservative in this analysis, we will retain the original estimate of St. Helens’ 

mean annual eruption probability, that is, P(1) = 0.008. 

To update the wind-direction probabilities used in an earlier report (Hoblitt and others, 1987; 

which used data in the 3–16 km altitude range), additional upper-air sounding data for Quillayute, 

Washington, were obtained from the National Climate Data Center. The Quillayute station has a long 

data record that is considered representative of the region. The dataset begins on January 1, 1973, and 

ends on June 30, 2010—a period of 13,694 days, or about 37.5 years. Soundings are typically taken 

twice daily. Many soundings were unsuitable for analysis because they contained untrustworthy or 

corrupted data, and many were unsuitable for specific altitude ranges because they did not extend to 

sufficiently high altitudes. 

Aside from the first data point, which is taken at ground level, data are collected at height 

intervals that vary during each sounding, and from one sounding to the next. Consequently, to obtain 

wind azimuth estimates at specified altitudes it is necessary to interpolate using bracketing data points. 

This provided the upper and lower limiting values for data series. To deal with discontinuity at 0/360 

degrees, we used the method of Mitsuta (Mori, 1986) to transform the wind directions before averaging. 

The data series were numerically integrated over the specified altitude range using the trapezoidal rule 

and divided by the altitude range to obtain an average wind direction for a given sounding. Average 

wind directions for individual soundings were sorted into sixteen 22.5-degree bins. Results are given in 

table 2.
6 

Table 2. Average wind directions (direction that the wind is blowing toward) in sixteen 22.5°-sectors for nine

altitude ranges (in kilometers) for Quillayute, Washington, from January 1, 1973, through June 30, 2010.

[Hanford row is a 22.5° sector centered on an azimuth of 80°—the approximate azimuth of Hanford from Mount St. Helens. 

The maximum value for the Hanford sector, 0.180 in the 3–18 km range, is used in exceedance calculations. Num., number 

of observations] 

Altitude Range, in kilometers

3 to 6 3 to 9 3 to 12 3 to 15 3 to 18 3 to 21 3 to 24 3 to 27 3 to 30

N 0.056 0.051 0.048 0.035 0.033 0.035 0.047 0.069 0.096

NNE 0.100 0.096 0.085 0.079 0.071 0.076 0.083 0.092 0.081

NE 0.141 0.133 0.134 0.135 0.138 0.124 0.111 0.079 0.060

ENE 0.148 0.152 0.154 0.172 0.179 0.173 0.130 0.091 0.062

E 0.133 0.143 0.151 0.162 0.174 0.169 0.141 0.117 0.093

ESE 0.119 0.127 0.127 0.139 0.144 0.142 0.138 0.131 0.109

SE 0.093 0.097 0.096 0.097 0.098 0.101 0.117 0.129 0.130

SSE 0.064 0.063 0.061 0.063 0.062 0.063 0.078 0.104 0.108

S 0.042 0.042 0.048 0.043 0.034 0.041 0.046 0.061 0.077

SSW 0.026 0.023 0.025 0.022 0.019 0.020 0.029 0.033 0.044

SW 0.013 0.013 0.014 0.012 0.009 0.009 0.013 0.015 0.020

WSW 0.010 0.009 0.010 0.007 0.009 0.008 0.009 0.011 0.015

W 0.009 0.009 0.008 0.007 0.007 0.006 0.008 0.008 0.009

WNW 0.009 0.008 0.008 0.006 0.006 0.006 0.008 0.009 0.012

NW 0.013 0.012 0.009 0.008 0.007 0.010 0.014 0.017 0.022

NNW 0.025 0.024 0.021 0.014 0.012 0.017 0.028 0.034 0.061

Hanford 0.144 0.149 0.152 0.164 0.180 0.175 0.141 0.105 0.073

Num. 15976 15007 14033 13574 13110 12259 11082 8511 3607

The bearing from Mount St. Helens to the Hanford Waste Treatment Plant is about 80°, which is 

close to the boundary between E and ENE sectors. These azimuths have the maximum probabilities for 

most altitude ranges, showing that the prevailing winds blow directly from St. Helens toward the site. 

From table 2 it is apparent that the mean probabilities change with altitude: they increase to a maximum 

at the 3–18 km range, then decrease as the upper altitude increases. Which range is most appropriate for 

this analysis? The maximum height of the sustained plume during St. Helens’ 1980 eruption was 19 km 

(Harris and others, 1981). The plume created by the initial explosion exceeded 30 km in height, but the 

conditions at the volcano that produced this event are no longer present. Plume heights derived from 

studies of geologically recent tephra deposits at St. Helens range from 11 to 31 km (Carey and others, 

1995). The plume heights of the largest eruptions of Mount Pinatubo in 1991 exceeded the radar ceiling 

of 24 km, but the height of the climactic eruption was estimated to be about 34 km on the basis of 

satellite data (Hoblitt and others, 1996; Koyaguchi and Tokuno, 1993). Plume height increases with VEI 

magnitude, and VEI 4 and 5 eruptions would be expected to typically produce plume heights at the 

upper ranges of those in table 2, that is, the ranges that exhibit decreasing probabilities. However, for 

this analysis, we shall use P(2|1) = 0.180—the maximum mean probability in the Hanford sector, as a 

conservative value. The Hanford sector is a 22.5° sector centered on an azimuth of 80°, which is the 

approximate azimuth from Mount St. Helens to Hanford. The maximum mean probability in the 

Hanford sector is slightly greater than the 0.161 probability derived from the wind analysis in the 1987 

report.
7 

P(3|2): Exceedance Probability of Tephra Accumulation

To determine the exceedance probability of accumulating a given thickness of tephra at a given 

point, we require empirical data on distance versus thickness. For the present analysis we will confine 

our attention to data from VEI 4, VEI 5, and two VEI 5–6 eruptions (Newhall and Hoblitt, 2002; 

appendix 2). From the global catalog, we only have 14 examples in this VEI range that contain reliable 

data at the 200 km distance (4 of these are from St. Helens) that is applicable to Hanford. The number of 

observations is small, chiefly because distal deposits tend to be thin and thin deposits are apt to be 

poorly preserved. A few millimeters of ash may last no more than a day or two before rain and wind 

redistribute it. Deposits from prehistoric eruptions are examined centuries to millennia after deposition, 

reducing the chance of preservation. Even deposits from recent eruptions are usually examined weeks to 

months after deposition. Because thick deposits are more apt to be preserved than thin deposits, thick 

deposits are probably over-represented in the dataset. 

Most of the tephra deposits in this data set were studied after some degree of compaction. We 

discuss the implications of this in a later section. 

To calculate tephra exceedance probability—the probability that an eruption will deposit tephra 

whose thickness at a given distance from its source will be greater than or equal to a specified value—

we first rank the empirical observations from highest to lowest, with the greatest value assigned a rank 

of 1. The exceedance probability for a thickness value of rank m is m/(n+1), where n is the number of 

data points. Results for the 14 eruptions with data extending to 200 km from source are tabulated in 

table 3.

Table 3. Exceedance probabilities of tephra accumulations at 200-km distance from source volcano for 14 VEI 4

and 5 eruptions from the global catalog (appendix 2; Newhall and Hoblitt, 2002). 

[In cases where thickness is the same for two layers, they are given the mean rank of their positions (for example, the rank 

of 12.5 is for the two same-thickness layers that occupy ranks 12 and 13); *, four tephra layers from Mount St. Helens] 

Thickness (cm) Rank Exceedance Probability

0.1 14 0.93

0.2 12.5 0.83

0.2 12.5 0.83

1 11 0.73

2* 9.5 0.63

2* 9.5 0.63

3 7.5 0.50

3 7.5 0.50

5 5.5 0.37

5 5.5 0.37

6* 3.5 0.23

6 3.5 0.23

7.5* 2 0.13

10 1 0.067

P(1 and 2 and 3): Estimate of Tephra Thickness that would be Equaled or Exceeded at the 1 x 10-4

We use P(1 and 2 and 3) = P(1) * P(2|1) * P(3|2) to estimate the tephra thickness that would be 

equaled or exceeded at the 1 x 10

Annual 

Probability Level

-4 level. First we multiply P(3|2), the exceedance probability for each 

thickness in table 3, by P(1) * P(2|1), that is, by 0.008*0.180. One of three terms—the eruption 

probability—only has one significant figure. Consequently the resultant annual tephra exceedance 
8 

probabilities are given to one significant figure in table 4 and figure 1. The tephra thickness that 

corresponds to an annual exceedance probability of 1 x 10-4

Table 4. Exceedance probabilities and annual probabilities of exceedance of tephra accumulations at the 

Hanford Site for the eruption data from table 3. 

 is 10 cm. 

[The annual exceedance probability is the product of the exceedance probability, the wind probability in the Hanford sector 

(0.180; table 2), and the St. Helens’ eruption probability (0.008; table 1). The eruption probability only has one significant 

figure; consequently the resultant annual exceedance probabilities are given to one significant figure, which results in 

several lines having the same value.]

Thickness (cm) Exceedance Probability

Annual Probability

of Exceedance

0.1 0.93 1 x 10

0.2

-3

0.83 1 x 10

0.2

-3

0.83 1 x 10

1 

-3

0.73 1 x 10

2

-3

0.63 9 x 10

2 

-4

0.63 9 x 10

3

-4

0.50 7 x 10

3 

-4

0.50 7 x 10

5

-4

0.37 5 x 10

5 

-4

0.37 5 x 10

6

-4

0.23 3 x 10

6 

-4

0.23 3 x 10

7.5

-4

0.13 2 x 10

10

-4

0.067 1 x 10-4

Figure 1. Annual probability of exceedance for various thicknesses of tephra fallout (in centimeters) at the 

Hanford Site in south-central Washington State.
9 

Each of the three probabilities used to reach this estimate is conservative. The mean annual 

eruption probability, based on activity of the past 500 years, is likely an overestimate due to a large 

explosive eruption just three decades ago. The mean wind direction probability is likely an overestimate, 

because we chose the altitude range with the highest value. Large eruptions are apt to send tephra to 

higher altitudes, where the average wind-direction probabilities are lower. The tephra accumulation 

exceedance probabilities are also likely overestimates because of sampling bias—thin distal deposits 

tend to be underreported. Consequently the estimated annual probability of equally or exceeding about 

10 cm of tephra at Hanford is likely not greater than 1 x 10-4

Because the deposits used in this analysis are chiefly from prehistoric eruptions or from 

historical eruptions whose deposits were subject to wetting and some degree of compaction before 

study, the 10-cm thickness estimated above does not consist of low-density, freshly fallen tephra.

Thickness of the May 18, 1980, deposit from Mount St. Helens is the only one of the 14 deposits 

analyzed that we are certain is uncompacted. In downwind areas, this deposit had an average in-place 

bulk density of about 450 kg/m

. 

3 (Sarna-Wojicki and others, 1981). Tephra fallout from two smaller 

eruptions in the summer of 1980 that was compacted during or soon after deposition by rain had average 

bulk densities of 1,000–1,250 kg/m3

. A similar difference in density was reported for uncompacted and 

compacted ash-fall deposits from the 1982 eruptions of El Chichón volcano in Mexico (Varecamp and 

others, 1984), and variably compacted tephra deposits of the 1991 eruption of Pinatubo volcano in the 

Philippines had a mean bulk density of about 1,000 kg/m3 (Paladio-Melosantos and others, 1996). 

Therefore, the 10-cm ash-fall thickness determined for Hanford probably represents a deposit whose dry 

bulk density would be in the range of 1,000–1,250 kg/m3

, and it would thereby impart an average tephra 

load of about 100–125 kg/m2

Revised Probabilistic Tephra-Fall Map

 on horizontal surfaces. Water falling with the tephra or added by later rain

or snow would provide additional weight. 

Maps showing the annual probability of the accumulation of 1, 10, and 100 centimeters or more 

of tephra fallout in the northwestern United States from Cascade sources were published in Hoblitt and 

others (1987), and the 1- and 10-centimeter maps were updated in hazard assessments for Cascade 

volcanoes published in the mid and late 1990s (for example, Scott and others, 1995). The maps were 

made from a process similar to that described above in the section on “Probability Analysis.” 

Probabilities were determined for each point in a grid covering the Pacific Northwest for eruptions from 

all Cascade sources; those probabilities were then contoured. The maps show how Mount St. Helens’ 

frequent and highly explosive eruptions dominate tephra probabilities in the region. In the 1987 map for 

10 centimeters or more of tephra, the 0.001 annual-probability contour passed through the Hanford area, 

whereas in the 1995 map the 0.0002 contour passed through Hanford. This near order-of-magnitude 

difference resulted chiefly from a labeling error on the 1987 contour lines—values of 0.1 x 10-x were 

labeled as 1 x 10-x. In retrospect we also found an error in the 1995 analysis in binning of wind data that 

has been corrected in the present calculations. The 1995 probability contours are displaced outward 

compared to those from the new calculations use to create figure 2, and the probability at a given site is 

about a factor of two higher in the 1995 calculations than in the present work. Two of the published 

maps (Mount Rainier, Hoblitt and others, 1998; and Mount Hood, Scott and others 1997) also had 

graphical errors that shifted the volcanoes and contours eastward from their correct positions. 
10

Figure 2. Preliminary probabilistic tephra-hazard map for Pacific Northwest, revised from Hoblitt and others 

(1987) and Scott and others (1995). Contours show the estimated probability of the accumulation of 10 

centimeters or more of tephra from eruptions of the 16 major volcanic centers (black triangles) in the Cascade 

volcanic arc. Contour pattern accentuates how Mount St. Helens’ explosivity and high eruption frequency 

dominate the probability analysis. Orange dot shows location of Hanford Waste Treatment Plant.

We have corrected these errors in a new version of the map for accumulation of 10 centimeters 

or more of tephra, which will replace the maps in existing USGS hazard assessments for Cascade 

volcanoes. On our new map (fig. 2), the 0.0001 contour of annual probability passes slightly west of the 

Waste Treatment Plant, consistent with the site-specific analysis presented above. 

Conclusion

The tephra accumulation thickness that would be equaled or exceeded at the Hanford Waste 

Treatment Plant at the 1 x 10-4 annual probability level is estimated to be about 10 cm. The values used 
11

to calculate this estimate are thought to be conservative, and consequently the estimate is considered 

conservative.

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14

Appendix 1. Discussion of Table 1 Highlighting Differences 

in Eruptive History Details from Compilations by Hoblitt 

and Others (1987) and Siebert and Others (2010) 

In table 1 we make minor changes to the values given in Hoblitt and others (1987, table 5-1) for 

the mean annual probabilities of a substantial (≥0.1 km3) tephra eruption at several volcanoes. In 

addition, table 1 also contains a few differences in the number of ≥VEI 4 (bulk volume of tephra ≥0.1 

km3

o Mount Baker—an eruption about 6,600 years ago, which is listed in Siebert and others 

(2010) as VEI 3, is included in Hoblitt and others (1987) and in this report as VEI 4 on 

the basis of its estimated volume of 0.1 to 0.2 km

) eruptions at several volcanoes compared to data in the Smithsonian Institution’s compilation of 

world volcanism by Siebert and others (2010). 

3

o Glacier Peak—Hoblitt and others (1987) list two large (≥0.1 km

 (Hyde and Crandell, 1978). 

3

o Mount St. Helens—we include three tephra deposits (layers Pu, Ps, and Yd) between 

2,500 and 4,000 years old in addition to the Hoblitt and others (1987) list, on the basis of 

work by Gardner and others (1998). Siebert and others (2010) include all of these save 

for one of the P layers. These additions do not affect the probability used in the 

exceedance analysis in this report, which is based on eruptions of the past 500 years. 

) eruptions at the end of 

the last ice age, but subsequent work by Gardner and others (1998) demonstrates that 

there were three. We do not include an eruption about 200 CE to which Siebert and 

others (2010) assign a VEI of 4+. The seminal study of the eruptive history of the 

volcano (Begét, 1982, 1983) describes the event as a prolonged period of lava-dome 

growth and collapse rather than a single explosive eruption and notes that only minor 

tephra has accompanied eruptions of the past 6,000 years. The eruption probability does 

not change at one significant figure.

o Three Sisters—in agreement with Siebert and others (2010), we add one event at Three 

Sisters, the Rock Mesa tephra (~0.1 km3

; Scott, 1987). The new eruption probability, 8 x 

10-5, is greater than the value in Hoblitt and others (1987), 4 x 10-5

o Medicine Lake volcano—Donnelly-Nolan and others (2007) describe two tephra layers 

≥0.1 km

, estimated from 1 

event in the past 25,000 years. 

3

, but on the basis of Ramsey and others (2009) we include the Glass Mountain 

tephra (0.18 km3) but not the Little Glass Mountain tephra (0.06 km3). This results in an 

increase in the annual eruption probability from 1 x 10-5 to 9 x 10-5. 
15

Appendix 2. Tephra Data Used in Estimation of Annual 

Exceedance Probabilities

Thickness versus distance data from 14 historical and prehistoric tephra fallout deposits were 

used to estimate annual exceedance probabilities for tephra accumulation at the Hanford Site in southcentral Washington State. The data are from a compilation by Newhall and Hoblitt (2002) and were 

selected for this analysis because they have measurements of tephra thickness at 200 km from vents, the 

approximate distance of Hanford from Mount St. Helens. Information regarding deposit A from El 

Chichón was supplemented at distances greater than 40 km by using observations from Varecamp and 

others (1984). Except for the May 18, 1980, deposit from Mount St. Helens, all of these thicknesses 

represent some degree of compaction from the time of deposition to the time of measurement. 

Thickness (in cm) at distance from vent (in km)

Volcano Date VEI

5 

km 1 10 km

15 

km

20 

km

30 

km

40 

km

50 

km

100 

km

200 

km

Agung May 1963 4 50 30 20 12 8 1 0.8 0.2 0.1

Lascar 1993 4 20 15 8 6 4 3 2 0.2

El Chichón

1982; deposit 

A 4 18 12 9 6 2 1 0.8 0.4 0.2

Soufrière St. Vincent 1812 4 5 3 

Askja 1875 4 35 33 30 26 23 20 8 5 

Cosegüina 1835 5 60 30 25 20 15 12 10 5 1 

St. Helens Wn 1480 5 150 120 100 50 22 16 5 2 

St. Helens May 18, 1980 5 20 11 11 11 9 7 3 3 2 

Usu ~580 yr ago 5 20 5 

Hudson August 1991 5 250 225 200 150 80 50 13 6 

St. Helens Ye ~3,500 yr ago 5 35 32 30 26 23 20 14 7.5

Santa Mariá 1902 5 100 84 75 60 50 40 30 10

Pinatubo June 15, 1991 5 40 2 30 27 25 18 16 14 5 3 

St. Helens Yn ~3,900 yr ago 5 150 2 140 120 110 90 80 60 20 6 

1 Volcanic Explosivity Index of Newhall and Self (1982)

2 Listed as VEI 5 in Newhall and Hoblitt (2002), but as VEI 6 in Siebert and others (2010)