Bull. Volcanol. Soc. Japan
Vol. 58 (2013) No. 1, pp. 291-306

ArticleEllipse-approximated Isopach Maps for Estimating
Ashfall Volume at Sakurajima Volcano
Yasuhisa TAJIMA＊, Keiji TAMURA＊＊,†, Takao YAMAKOSHI＊＊,Akira TSUNE＊＊＊ and Shinjiro TSURUMOTO＊＊＊＊,††(Received May 6, 2011 ; Accepted January 7, 2013)
In studies of volcanic tephra, it is usual that the overall volume of tephra is estimated ashfall volumes based on
representative locations within the ashfall area. The precision of the volume estimation largely depends on the numberof the locations. However, in the case of ongoing eruptions on island volcanoes, such as Sakurajima volcano, theobservation locations are usually limited. We therefore have developed a practical method for estimating ashfallvolume and distribution in such case. The method approximates the distribution of ashfall as ellipses, with the-1
distribution area (A) and thickness or weight of deposit (T) determined by A =αT . The ellipse-approximatedisopachs can be determined by using the direction of the ellipse axis and ashfall data at two points. In determing theellipse axis exactly, we usually need additional ashfall amounts from the other locations. We set 37 samplers around
Sakurajima volcano, and retrieved the samplers 15 times, from April to December, 2008. Using the propose method,
we are able to determine the volume of ash produced by small, continuous eruptions.
Key words : ashfall distribution; isopach; ellipse approximation; volume estimation; Sakurajima volcano

1．Introduction
The difficulty of ashfall volume estimation for small
islands or short intermittent eruptions in Japan is a major
issue, when forecasting the progress of volcanic eruptions.
Hence, we propose a tool for estimating ashfall volumeusing limited ashfall observation locations as inputs. Suchtool is useful in the case of ongoing eruptions when observation locations are usually limited.
Many authors have proposed methods to calculate the
distribution or volume of pyroclastic falls. The most advanced method is to produce an isopach map (lines of
equal thickness) of tephra deposits, based on many points
determined by geological surveys. Other approaches tovolumetric calculations include simulation models basedon the dynamics of the eruption column and existingmodels or codes (Ishimine, 2007). An isopach is a contour
line that shows the same thickness of tephra for a given
area. Whole ashfall volume can be estimated using
isopach map by applying integral calculus. Many studies
have shown that tephra thickness decreases exponentiallywith distance from the vent. Thorarinsson (1954) showed＊

Nippon Koei Co., Ltd., 2, Kojimachi, 4-chome, Chiyodaku, Tokyo 102-0083, Japan.
＊＊
Public Works Research Institute, 1-6 Minamihara,
Tsukuba-shi, Ibaraki 305-8516, Japan.
＊＊＊
Deep Ocean Resources Development Company, Ltd.,
1-3-15, Nihonbashi Horidome-cho, Chuo-ku, Tokyo
103-0012, Japan.
＊＊＊＊
Ministry of Land, Infrastructure, Transport and Tourism,
Osumi Office of River and National Highway, 1013-1

important results related to the exponential decrease intephra thickness with increasing distance from the source.
Porter (1973) considered that the correlation of thickness
and distance followed a power relationship for Hawaiian
tephra. Suzuki (1981) presented a logarithm approximation method that explained these correlations.
If the area and tephra thickness are correlated, then thevolume of tephra can be deduced. Rose et al. (1973)
estimated ashfall volume by integrating the plot of log (T)against log(A) with distribution area (A) and thickness orweight of deposit (T). Recently, ashfall deposits wereshown to follow exponential decreases of log(T) againstlog ( A ) for plinian tephra (Pyle, 1989). Fierstein andNathenson (1992) used two proximal and distal exponential rates (κ) of the plot of log(T) against log ( A ),which changed at the break in slope, in order to calculate
the volume. Bonadonna and Houghton (2005) used a
power method to estimate the volume of Plinian tephra
deposits. When using the exponential method or the
power formula, many isopachs are required to estimate theashfall volume over large areas accurately.
Shintomi, Kimotsuki-cho, Kimotsuki-gun, Kagoshima893-1207, Japan.
†
Sabo and Landslide Technical Center††
Ministry of Land, Infrastructure, Transport and Tourism,
Miyazaki Office of River and National Highway
Corresponding author: Yasuhisa Tajima
e-mail: tajima-ys@n-koei.jp292

Yasuhisa TAJIMA, Keiji TAMURA, Takao YAMAKOSHI, Akira TSUNE and Shinjiro TSURUMOTO

Fig. 1. Location of the Sakurajima volcano. Triangles denote active volcanoes.

Aramaki and Hayakawa (1982) developed a simple formula for the plot of log (T) against log(A), with a scaling
exponent (power) fixed at −1. Hayakawa (1985) estimatedthe ejecta volume as V=12.2 T×A (V: volume of tephra,
A: area, T: thickness of tephra) with a constant of 12.2.
This value of 12.2 was in agreement with results obtained
from the crystal concentration method (Walker, 1980; 1981),
in which the ejecta volume was estimated by the amount ofplinian tephra observed on the ground. However, Pyle
(1999) showed that the value of 12.2 was variable rather
than constant.
We consider the geometrical concept of ashfall distribution, which does not require the collection or estimation of ashfall distribution or volume over large areas.
For example, small island volcanoes require a volume
estimate only for the limited area around the volcano.
Recently, some authors considered that ashfall distribution
would approximate the elliptical forms (Froggatt, 1982;
Pyle, 1989; Sulpizio, 2005). Sulpizio (2005) calculated
the approximate volume of tephra using elliptical distributions. In this study, we have developed an ellipseapproximated isopach (EAI) method based on a simple
equation. We have applied this method to the volume

Fig. 2. Observation locations in Sakurajima. Solid circles denote locations of ash samplers for this study. Open circles
denote monthly observation points and camera marks used by the Osumi Office of River and National Highway.

Ellipse-approximated Isopach Maps for Estimating Ashfall Volume at Sakurajima Volcano

293

estimation of ashfall for ongoing eruptions of Skurajima
volcano (Figs. 1 and 2), which have produced frequent thermal columns from vulcanian or ash eruptions. The depositional ashfall (tephra) volume and the ejecta ashfall(tephra) volume of an eruption are different meaning(Koyaguchi, 1996). In this study, we use the word
“ashfall” to mean “depositional ashfall”.
2．Ellipse-approximated isopach (EAI) method
2-1 Area-versus-thickness relationshipWe use the relationship of the simple power function
between log(T) and log(A) (see Eq. 1), where A is the areaof one isopach, T is the thickness for that isopach, α is acoefficient and d is the exponent concerning T and A
shown in equation (1). In this study, area (A) is given insquare meters and thickness (T) in millimeters or grams
per square meter.
A=αT d(1)

It is uncertain whether the concept (d=−1) proposed
by Aramaki and Hayakawa (1982) is appropriate for small
phreatic, vulcanian or ashfall eruptions. We therefore
review the relationship between ashfall thickness and areafrom recent vulcanian and phreatic eruptions in Japan. We
use the described isopach maps to plot depositional area(m2) versus thickness (m). In this case, we convert g/m2 to
m, using a depositional density of 1.5 g/cm3 for the data
produced by Yoshimoto et al. (2005) and Takarada et al.
(2001).
At Shinmoedake volcano in the Kirishima volcanoes,
southern Japan, phreatic eruptions started at 14 : 50 JST on
February 17th, 1959, and continued for several days. An
isopach map was drawn from 50 to 0 cm (Fig. 3; Fukuoka
Meteorological Observatory, Kagoshima Local Meteorological Observatory and Miyazaki Local MeteorologicalObservatory, 1959). At Ontake volcano, central Japan,
phreatic eruptions started from approximately 05 : 20 JST
October 28th, 1979, until the following morning. The
isopach map was based on observations around thevolcano from October 30th to November 2nd, 1979 (Fig. 3;
Yamada and Kobayashi, 1988). At Usu volcano, northern
Japan, a phreatic eruption began on March 31st, 2000, from
13 : 07 JST until around 16 : 00. The small eruptions
continued until September 2001 (Yamasato et al., 2002).
Isopach maps were obtained for March 31st, April 1st and2nd, and April 4th, 2000 (Fig. 3; Takarada et al., 2001). At
Asama volcano, central Japan, an ash eruption started at
20 : 20 JST on September 1st, 2004 and some small
eruptions continued until December 9th, 2004 (Nakada etal., 2005). Isopach maps were obtained for eruptions
occurring on September 1st 20 : 02 JST, September 15th to
18th, September 23rd 19 : 44 JST, September 25th 18 : 36
JST, September 29th 12 : 17 JST, October 10th 23 : 10 JST,and November 14th 20 : 59 JST (Fig. 3; Yoshimoto et al.,2005). At Shinmoedake volcano, phreatic eruptions started

Fig. 3. Relationship between area (m2) and thickness (m)of isopachs in several examples. Dashed lines denotevulcanian or small magmatic eruptions. Solid lines
denote phreatic eruptions. Sm: Shinmoedake volcano
in Kirishima, Ot: Ontake volcano, Us: Usu volcano,
As: Asama volcano. Explanations of those isopachs areshown in section 2-1.

on August 22nd, 2008 and tremors continued for six hours,
from 16 : 34 JST (the Japan Meteorological Agency website). An isopach map was presented for this eruption(Fig. 3; Geshi et al., 2010). These results show that thearea-versus-thickness relationship is A=αT−1, and thatthe phreatic and magmatic ashfall eruptions show a rate ofsame decrease (d=−1) in Fig. 3. In addition, the 1959Shinmoedake, 1979-Ontake and 2008-Shinmoedake eruptions were comprised of multiple eruptions or a continuous
eruption; those cases also showed a rate of decrease (d=−1). Therefore, we adopt a simple formula with thescaling exponent (power) fixed at approximately −1, as
described by Aramaki and Hayakawa (1982). Regarding
shapes of isopach, we assume that the tephra distribution
approximates an ellipse that has the same aspect ratio (halfradius of orthogonal axis/half radius of calculation axis) in
concurrent eruptions (Fig. 4) with the correlation of A andT, following Eq. 1.
2-2 Formulation of EAI and the volume
The followings are three calculation ways of the ellipseapproximated isopach (EAI).
1) If the elliptical isopachs exhibit a fixed aspect ratio,
we can calculate the ellipse-approximated isopach using
one data point of the thickness or weight of the deposit andthe determined calculation axis (one data point calculation).
2) If we do not know the aspect ratio of the ellipticalisopach, we can calculate the ellipse-approximated isopach
using two data points of the thickness or weight, and the294

Yasuhisa TAJIMA, Keiji TAMURA, Takao YAMAKOSHI, Akira TSUNE and Shinjiro TSURUMOTO

Fig. 4. Schematic representation of isopach drawn by ellipse approximation. The figure shows the EAI method for two data
points. The x-axis represents the fixed dispersion (calculation) axis.

determined calculation axis (two data points calculation).
3) If the ellipse isopach does not exhibit an aspect ratioor an ellipse axis, we can calculate the ellipseapproximated isopach using three or more data points ofthe thickness or weight (multiple data points calculation).
Solution using one data point:
The elliptical isopach exhibits a fixed aspect ratio,
defined as
b
=c
a

(2)

where a is the calculation (ashfall distribution) axis of
the ellipse; b, the orthogonal axis; and c, the aspect ratio.
A point (x, y) on the ellipse is given by
2

2

y
x−a
+ 2 =1a2b(3)

The ellipse axes are determined from Eqs. 2 and 3 are
a=

2 2

2

c x +y, b=a×c2c 2x(4)

Solution using two data points:
If ellipses 1 and 2 have the similar ellipse shapes (Fig.
4), then
b1 b2
=
a1 a2

(5)

From Eq. 1, AT =α, and A1=π a1b1 and A2=π a2
b2. The relationship between ellipses 1 and 2 isT 1a 1b 1=T 2a 2b 2
From Eqs. 5 and 6,

(6)



T1
a2
=
a1
T2

(7)

P0 is source of ash distribution. If P2 on ellipse 2 moves
to a point on ellipse 1 using similar triangles shown bydash lines in Fig. 4, thenP 1=x 1,y 1, P 2'=

 TT x , TT y , P =0, 0
2

2

2

1

1

2

0

(8)

P1 and P2 on ellipse 1 are given by:2y 21
x 1−a 1+ 2 =1
2
a1
b1

(9)

 TT x −a  +  TT y  =1
2

2

2

1

1

2
1

a 21

2

2

b 21

(10)

The ellipse axes are determined from Eqs. 9 and 10 asfollows:

x 21y 22−x 22y 21
a 21y 21, b 1=(11)
2a 1x 1−x 21
T1
2 x 1y 22−
x 2y 21
T2
Solution using three data points:
If we consider three or more data points, any of the three
approaches may be used to derive the solution. The three
formulae are determined about the calculation axis (a),orthogonal axis (b), and calculation axis at a specified
angle (θ). Here we show only the basic formulae.
We consider ellipses 1, 2, and 3, which have similar
shapes:
a 1=







Ellipse-approximated Isopach Maps for Estimating Ashfall Volume at Sakurajima Volcano

295

Fig. 6. The aspect ratio and volume of ashfall vs. calculation axis azimuth of the EAIs by the trial calculationsof the two data points calculation. See the section 2-3
in the text for details of the calculation procedure.

nFig. 5. The ashfall distribution and a photograph of thesmall eruption at 12 : 56 JST on April 28th. The values
in the map are ash weights per square meter (g/m2).
The photograph was taken near NJ6 in Fig. 1.

b1 b2 b3
= =a1 a2 a3
Similarly to Eq. 6,(12)

T 1a 1b 1=T 2a 2b 2=T 3a 3b 3.

(13)

The three points move according to a rotation matrix, forexample:


x' 1
y' 1

=

x 1cos θ−y 1sin θ
x 1sin θ+y 1cos θ  
x' 2
y' 2

=

x 2cos θ−y 2sin θ
x 2sin θ+y 2cos θ



(14)

Eq. 14 is substituted into Eq. 11 and the two equations
are solved numerically. Under natural conditions, it is
impossible that three data points fit on an ellipse of one
aspect at the same time.
The ashfall volume is calculated using the EAI as
follows, using the distribution A =α T-1. The volume
integral is:

V= AdT=−αlog A n−−αlog A m

(15)

m

where m is the 104 m2 area used by Takarada et al.
(2001) and n is the area enclosed by the 0.1 g/m2 isopach.
The minimum observed thickness corresponded to aweight of 0.4 to 0.2 g/m2 for the 12 : 56 JST eruption on
April 28th at Sakurajima volcano (Fig. 5). Our fieldobservations determined the lower threshold of detectableashfall to be 0.1 g/m2.
In this study, we discuss how to calculate for EAI (eq.
11) and estimate for the volume of tephra (eq. 15) using thetwo data points calculation.
2-3 Relationship between ellipse axis and volume
of EAI
In this section, we demonstrate how to use the EAI
method namely how to choose two data locations and set
an ellipse axis. In the two data points calculation, it is very
important to determine the calculation axis of the ellipse
accurately. A trial calculation uses two data points fortentative ashfall amounts. The tentative amounts are set at
sampling locations HR1 (100 g/m2) and AR4 (50 g/m2) at
Sakurajima volcano (Fig. 7). Those are a value commonly
observed at Sakurajima. The calculation results include
ashfall volume and the aspect ratio of the ellipse, which isrotated from the calculation axis of the ellipse to one
degree clockwise from due east (Fig. 6).
The axis of the ellipse is regarded as non-existent on the296

Yasuhisa TAJIMA, Keiji TAMURA, Takao YAMAKOSHI, Akira TSUNE and Shinjiro TSURUMOTO

Fig. 7. The schematic representation of the results of thetrial calculations by the EAI method. We used thevirtual ashfall amount measured at two points (100g/m2 and 50 g/m2). The calculation axis is rotatedclockwise from east to north. The shaded area showswhere we cannot use ellipse approximation to obtaina solution. A solution is obtained for the white area by
ellipse approximation. In this case, we obtained thetrue circle solution at the dot-dashed line labeled “b/a=1.0”.

opposite side of the observation points (171 <θ< 4).
Firstly, the calculation axis of the ellipse is calculated to befour degrees clockwise from east. In this case, the aspectratio is greater than one, meaning that the calculation axis
is the short axis and the orthogonal axis is the long axis.
The EAI distribution is a long orthogonal axis, which is anunusual result under natural conditions. The results are thesame from 4° until 24° clockwise from due east (Fig. 7a).
A solution can not be got past 25° (24<θ≤87), because
the position of a low amount (50 g/m2) interchanges a highamount (100 g/m2) position for calculation axis in thisarea.
We must be careful in the case when the calculation axis
is close to the observation point, which is a common casefor the EAI calculation. The slight difference in the angleof the calculation axis leads to a larger change in the aspectratio and the ashfall volume (Fig. 6). If the interval of theangle is very small, the infinite volume is taken between
87° and 88°, which results in an extremely elongated ellipse(Fig. 7b). It is considered that the narrow lateral distribution of ashfall is due to a very strong wind over a long
period. The minimum ashfall volume occurred along 90°

Ellipse-approximated Isopach Maps for Estimating Ashfall Volume at Sakurajima Volcano(Figs. 6 and 7c) in this case. Next, the results are shown
for an EAI example in which the ellipse calculation axis islocated far from the observation points. The aspect ratio
and the ashfall volume are much larger when the calculation axis is further from the observation points (Fig.
7d; 90<θ<151). The calculation axis is over 150° clockwise from due east, and the aspect ratio is reversed between the long orthogonal and short calculation axes of theellipse (Fig. 7e; 151≤θ≤171), similar to Fig. 7a.
As described above, volume values from this calculation
using ashfall information from only two points are variable
depending on the axis. We will show how to determine
the numerical value of the direction of calculation axis forthe two data points calculation in Section 3, using theactual case of some eruptions at Sakurajima.
Ashfall sometimes distributes in concentric circles, as in
the case of the 1991 Mt. Pinatubo eruption (PaladioMelosantos et al., 1996; Koyaguchi, 1996). In such cases,
ashfall distributions cannot be constructed using the EAI
calculation. Additionally, the EAI cannot provide resultsin cases where the distribution meanders.
2-4 Determination for ashfall amount at a particular point on EAI
The EAI method can calculate the weight or thickness ata particular point, from the established ellipse distribution.
We calculate the half-radii of the short and long axes using
Eq. 16, to determine the aspect ratio at any point of theellipse. The calculation axis (a) is determined using Eq. 4,
by substituting the known aspect ratio (c) at a particularpoint, where the thickness (T) is required. Additionally,
the orthogonal axis (b) is determined using Eq. 4, and α isknown. Therefore, Eq. 1 is substituted into Eq. 16, allowing us to find the weight or thickness (T) at a particularpoint as follows:
T=α×π×a×b

1

(16)

2-5 Volume estimation by EAI for actual eruptions
The ashfall volumes of 2000 at Usu volcano (Takaradaet al., 2001; 2002) and those of 2004 at Asama volcano(Yoshimoto et al., 2005) were calculated when the distribution axis was already known. Takarada et al. (2001)
and Yoshimoto et al. (2005) estimated the segment isopachs volume using a log(T)-log(A) plot based on manyobservation locations. We estimated the volume using thedata points by Takarada et al. (2001) and Yoshimoto et al.
(2005). At first, we determined the direction of the major
ellipse axis by straight isopach distributions near the vent,shown in the original studies. Next, we chose two data
observation points for the calculation axis. The calculated
volumes vary depending on the selection of two points.
We compared the volumes obtained by actual observations(Takarada et al., 2001 and Yoshimoto et al., 2005) with thecalculated EAI method results, which were nearest to thoseof actual observations (Fig. 8). The calculated values of
EAI method are comparable to the actual observed values

297

Fig. 8. Relation between the total volume of ashfall deposits and the volume calculated by the EAI method in
the cases of the Usu 2000 eruptions and Asama 2004
eruptions (Table 1). The total volume of ashfall deposits
are from Takarada et al.(2001) and Yoshimoto et al.
(2005). Triangles denote the Asama eruptions in 2004,
and circles denote the Usu eruptions in 2000.

(Table 1).
3．Application of EAI method to Sakurajima eruptions
In this section, we explain how to determine the ashfallvolumes for the case at Sakurajima volcano.
3-1 Activity of Sakurajima volcano
Sakurajima is one of the most active volcanoes in Japan.
Since 1955, small eruptions frequently have occurred at
Minamidake crater (Kamo, 1974; Ishihara and Kobayashi,
1988; Ishihara, 1995). The pyroclasts, ballistics, and ashfalls have caused damage to houses and roads around thevolcano. On June 4th, 2006, a vent in Sakurajima volcano,named Showa crater, opened on the east flank of Minamidake (Yokoo and Ishihara, 2007; Iguchi et al., 2008). The
crater then produced small eruptions in June 2006, andfrom May to June 2007.
Small pyroclastic density currents occurred at 10 : 18
and 15 : 54 JST on February 3rd, and 11 : 25 JST on
February 6th, 2008 (JMA website). The surface activity
was quiet until early April 2008. At 00 : 29 JST on April
8th, an eruption produced density currents and an eruption
column more than 1 km above the vent. A small ashfall
eruption with lithic fragments began on April 8th, andsmall eruptions continued, with short breaks, until midJune. Small, short eruptions occurred after late June, andactivity ceased in September. In most cases, the eruptions
produced low columns, 500-3000 m in height. Showa andMinamidake craters have produced ashfalls even now.
3-2 Measurement of ashfall around the volcano
We applied our proposed method on the ashfall around
Sakurajima volcano. Ash samplers, which consisted of298

Yasuhisa TAJIMA, Keiji TAMURA, Takao YAMAKOSHI, Akira TSUNE and Shinjiro TSURUMOTO
Table 1. The results of volume calclations by the EAI method using the data points of
the Usu 2000 and Asama 2004 eruptions.

clear plastic cups of 7 to 8 cm diameter, were placed atthree locations between February and April 2008. We
tested the measurement error for this cup method at thesouthern and east part of the volcano set 13 samplers, andfound that the observation errors were less than 4 %. Afterthe increase in activity from April 2008, we placed
additional ash samplers at 37 locations around the volcano
on April 24th and 25th (Fig. 2). Ashfall deposits from thesamplers were collected at different time intervals ranging
from days to several weeks. The dates of retrieval wereApril 27th and 28th, May 1st, 7th, 9th, 18th, and 29th, June 5th
and 14th, July 4th and 12th, August 1st and 30th, September
23rd, and October 18th. The ashfall characteristics werenoted at the sampler locations in the field, after which thesamplers were carefully covered with clear plastic clingwrap and transferred to the laboratory. We soaked clumpsof ash in distilled water to separate out smaller flakes. The
deposit samples were dried and measured in terms ofgrams per square meter to determine the isopach. We
converted g/m2 to mm by applying the depositional densityof the fresh ashfall deposit after the April 3rd-7th eruptions
at sampling point AR1. We placed the ashfall deposits
into a mould in order to undisturb the samples, which wereTable 2. Density of ashfall deposited by eruptions between Feb. 3rd and 7th, 2008.

then used to measure the depositional density under dry
conditions. The resulting average depositional density is
1.5 g/cm3 (Table 2), showing that an ashfall depth of 1 mm
is equivalent to 1500 g/m2.
3-3 The determination processes of ashfall axis
During observation periods, we determined the approximate directions of ashfall dispersion as follows (Table 3).
Occasionally, observers remained at the volcano and noted

Ellipse-approximated Isopach Maps for Estimating Ashfall Volume at Sakurajima Volcano

the direction of the column. When we could not identify
the distribution axis, we used web-cameras and otherinformation. Our first source of eruption information was
the website of the Japan Meteorological Agency1) (JMA),
which immediately releases eruption information, categorized by eruption time, column height, column direction,
intensity, and other parameters. Next, we used images
from web-cameras set up at the Osumi Office for Riverand National Highway of the Ministry of Land, Infrastructure, Transport and Tourism (MLIT)2), and in the cityof Tarumizu3). Kagoshima University (KU) also provided archives of their web-camera images4), whichyielded valuable information for determining the column
direction (axis).
The determined ashfall directions described above usually have some uncertainties. Followings are the generalprocedure to determine the calculation axis exactly. If an
eruption occurred once during an observation period, wechose generally the maximum observed amount (weight or
thickness) at first near the expected distribution axis andnext the second or third-largest value for the two data
points of the EAI calculation. Next, we rotate an EAI
calculation axis by step intervals of 1 to 2 degrees aroundthe expected direction (we call this procedure as the stepseeking hereafter) and calculate EAI distribution repeatedly every degrees. We can calculate the ashfall amountsof nearby locations, where the actual amounts of ashfall
are measured using the EAI method and Eq. 16. Finally,
we determined the EAI calculation axis so that the differences between the calculated and measured ashfall
amounts become minimum value. The determination
process is more easily when the exact direction is determined by the observation.
3-4 An example of general determination of EAI;
June 28th, 2008 eruption
We explain how to determine the ashfall volumes for
one eruption recorded at 06 : 36 JST on June 28th alongwith small eruptions on the afternoons of June 28th and29th (JMA website). The ashfall of the small eruptions
would be negligible in amount. We retrieved the samplers
on July 5th. Ashfall was mainly found in the northernareas of the volcano. Ash weights of up to 263, 203 and155 g/m2 were recorded at sampling locations AM, FK1
and MU, respectively (Fig. 9). This ashfall originatedfrom Showa crater after an eruption at 06 : 36 JST on June
28th. Based on the amount of ashfall, the distribution axis
would pass through somewhere between locations AM andFK1. The angle of the EAI calculation axis was determined by the step seeking so that the calculation agreed
with the weight recorded at other locations (KM2, KM1,
1)

http : //www.seisvol.kishou.go.jp/tokyo/volcano.html
http : //www.qsr.mlit.go.jp/osumi/camera_sabo.htm
3)
http : //camera19.city.tarumizu.kagoshima.jp/
4)
http : //volceye.edu.kagoshima-u.ac.jp/sakurajima.html
2)299

KT1 and KT2) and limit of ashfall distribution (Table 3,
calculation No. C58). The calculation axis was 275°
clockwise from due east, and an EAI was drawn based on
the data of locations AM and FK1 (Fig. 9). The location
names and ashfall amounts of basic two data points and theappropriate ones are listed in Table 3. The estimatednumerical values of the degree of axis are also listed.
3-5 An example in the case of the multiple eruptions; May 2nd to 7th, 2008 eruptions
When the interval of eruptions is shorter than that of
retrieval of samples, it is very difficult to estimate theamount of each ashfall. We explain how to determine theashfall volumes in the case of May 2nd to 7th observation
period. During this period, four eruptions were recorded,at 06 : 34-06 : 50, 15 : 29, and 16 : 05-16 : 30 JST on May
6th and 06 : 38-06 : 54 JST on May 7th. Further smaller
eruptions with negligible ashfall amounts also occurred on
May 6th and May 7th (JMA website). During this period,
the ashfall samples were retrieved once. Based on theamounts of the ashfall samples, mainly four distribution
axes could be observed from the Showa crater towards
locations HM, KG, ST and HR1 (Fig. 10). The observed
ashfall informations suggested that these axes werecorresponded to those of 06 : 34-06 : 50, 15 : 29, and 16 :05-16 : 30 JST on May 6th; and 06 : 38-06 : 54 JST on May
7th eruptions, respectively (Fig. 10). The EAIs for thesefour eruptions were drawn, based on two data points
calculation located near the corresponding axis with thestep seeking using appropriate data points. Some locations
used for the calculations were affected by ashfall of other
eruptions, so that the affected weight must be taken awayfrom the weights collected at locations (Table 3, calculation No.C13 to No.C18). We could use the estimation
methods based on Eq. 16, as explained in 2-4.
3-6 The exceptional cases; April 11th, May 8th andJune 1st
When eruptions continue steadily for a long time and thewind direction changes gradually, an obvious distribution
axis cannot be determind for such eruptions. In this case,
we estimate the ashfall volume by isopach area drawn byhand. We examine the relationship of α= TA (α: coefficient; T: m, A: m2) from Eq. 1 to the volume of thedeposits. For example eruptions continued for over 2
hours, from 14 : 13-16 : 45 JST, on May 8th (JMA website)
and ash emission continued for some hours after 16 : 45
JST. The ashfall was mainly found in the northeast tonorth areas, and in the lower amounts in the northwest to
west to south areas of the volcano. First, we determined
four isopachs from the northeast to north by EAI (Table 3,
calculation No.C19 to No.C22). In the western part, we
produced the 30 g/m2 isopach by hand. The ashfall volumeof 11330 t on May 8th (Table 3) was estimated from therelation shown in Fig. 11. However, the main application
for this relationship is limited only valid for volumes lessthan 100,000 tons.

300

Yasuhisa TAJIMA, Keiji TAMURA, Takao YAMAKOSHI, Akira TSUNE and Shinjiro TSURUMOTO
Table 3.

List of Sakurajima eruptions from Feb. to Nov., 2008 and the results of the EAI volume calculation.

The day and time and eruption center are from the JAM website. uk: unkown. Thick horizontal lines show
collection times for ash fall samples. Multiple EAI distributions for one eruption were by continuously eruption
with wind direction change or wind direction change depending on height. Locations (loc.) show in Fig. 2.

Ellipse-approximated Isopach Maps for Estimating Ashfall Volume at Sakurajima Volcano
Table 3.

continued.

The “obs.” values are observation weight. The subtracted values (s.v.) are calculated using Eq.16. The “calc.”
values are weight for two data points calculation (calc.=obs.−s.v.). The “seeking” values are calculated weight onseeking point using Eq. 16. w, weak ashfall; x, no ashfall; c: other EAI calculation point.

301

302

Yasuhisa TAJIMA, Keiji TAMURA, Takao YAMAKOSHI, Akira TSUNE and Shinjiro TSURUMOTO

In the cases of April 11th and June 1st, we calculated theashfalll using only one observation location. In thesecases, we estimated the ashfall volume by the one data
point calculation with the averaged aspect ratio of EAI.
The aspect ratio of 0.21 was taken from average value inTable 3. The ashfall volumes were calculated to be 26990
t for April 11th and 1270 t for June 1st were estimated(Table 3, calculation No.C03 and No.C47).

Fig. 9. Spatial distribution of the amounts of the ashfall
based on the EAI calculation for 06 : 36 JST on June
28th at Sakurajima. The values are ash weights per
square meter (g/m2) and the values in parentheses arecalculated weights. P1 and P2 weights show in Table 3(Calculation No. C58).

4．Discussion
4-1 Comparison ashfall volume between EAI estimations and monthly MLIT observations
The Osumi Office of the MLIT, using 0.57 m-diameterdrum-type samplers, measured the weight of monthly ashfall in several observation locations (Fig. 2). To validate
our method, we compare the observed monthly weights
obtained by the Osumi Office with the accumulate weight
derived using the EAI distributions. We use Eq. 16 to
calculate the tephra thickness for eruptions at the six
observation locations of the Osumi Office shown in Table

Fig. 10. Spatial distributions of the amounts of the ashfall based on the EAI calculation for May 2nd to 7th eruptions. In thisperiod, four eruptions were recorded: from 06 : 34 to 06 : 50 JST on 6th (a: No.C13, C14), at 15 : 29 JST on 6th (b: No.
C15), 16 : 05 JST on 6th (c: No.C16, C17), and 06 : 38 JST on 7th (d: No.C18). The values are ash weights per square meter(g/m2) and the value in parentheses are calculation weights. P1 and P2 weights and calculation No. show in Table 3.

Ellipse-approximated Isopach Maps for Estimating Ashfall Volume at Sakurajima Volcano

Fig. 11. The relationship between α and volume of ash
deposit. The values of α and volume are shown in
Table 3.

4. The data from the six observed locations show apositive correlation with our calculations (Fig. 12, Table4). The observed values tend to be higher than thecalculated ones for some data points, due to the intervals
between observation locations. We note that the slightly
higher observation values would be caused sometimes bycontamination of the secondary ash.
4-2 Temporal variation of ashfall volume estimated by EAI method during 2008 activity
Using combined eruption informations and our observations at Sakurajima, we were able to determine the 68
directions of EAI dispersion and estimated 58 (66) eruption volumes (Table 3).
1) Volume for JMA classifications
According to the JMA classification scheme, the scaleof the eruptions covers seven categories (Q1-Q7). These
categories are determined by the area size (m2) of theeruption column by eye-watching observation. (Japan
Meteorological Agency, 1994). Based on our EAI data,
the average volume produced in the Q3 (medium) classification, which is most common at Sakurajima volcano, isabout 5000 t, whereas the average volume produced in theQ4 (rather much) classification is about 20000 t in thisstudy. Thus it is resonable to consider that the volume isdivided according to the classification of JMA as Q3 : Q4
=1 : 4 (Table 3).
2) Temporal change of ashfall volume during 2008
activity
During 2008, the first volcanic activity occurred fromFebruary 3rd to 7th. We estimated the ashfall volume ofeach eruption between February and October 2008, using
the EAI method which the exhaustively axis determined bygeological observation or JMA information (Table 3). The
daily and cumulative volumes of ashfall are shown in Fig.
13. An eruption occurred from April 8th to April 21st,
which continued until June 13th. During April 21st to June
3rd period the eruption rate increased. Ashfall amounts

303

Fig. 12. The relationship between monthly amount (fromMay to August) of ashfall observed by the Osumi
Office of MLIT and the monthly amount calculatedusing the EAI method. The Osumi Office observation
locations are shown in Fig. 2 (e.g. O-No.1). Plottedashfall amounts are over 10 g/m2.

Table 4. Ashfall volume of EAI estimations and monthly
Osumi Office observations.

were not collected for the eight eruptions that took placeon the 12th to the 25th of April. Instead we used the
medium-classification average volume of 5000 t (Table 3)
because the eruptions during this period were classified as“medium (Q3)” according to JMA. The peak volumes ofthe eruptions were clustered from May 6th to 23rd, 2008
(Fig. 13). The rate of eruption decreased in the next period
from June 14th to July 28th. The pace of activity subsequently changed during August, with a single eruption
every two or three weeks from the Showa crater; after
October, there were a number of very small eruptions from
the Minamidake crater. Using this method, we are able toreveal temporal change of the ashfall volumes, which isvery important information in predicting the progress ofthe ongoing eruption.
5．Conclusion
The EAI provided a swift geometric method for assessing ashfall eruptions. In many cases, the distributions
calculated using the EAI method correlated well with theobserved data for the Usu and Asama volcanoes, in whichsmall eruptions recently produced low columns. Under

304

Yasuhisa TAJIMA, Keiji TAMURA, Takao YAMAKOSHI, Akira TSUNE and Shinjiro TSURUMOTO

Fig. 13. Temporal changes of ashfall volumes determined by the EAI method. The column bars denote the daily ashfallvolumes determined by the EAI method, and the step line represents the cumulative volume.

these conditions, we could approximate the ashfall distribution as a single exponential function. The EAI method
is useful for small, continuous eruptions and for small
island volcanoes where terrestrial ashfall is naturally
limited to the area of the island. When using the EAI
method, it is important to determine the correct EAI
calculation axis and to confirm the fit between several
observation points and the calculated distribution.
Acknowledgments
We sincerely thank Mr. S. Shimomura and Mrs. K.
Kikuchi of the Research and Development Center Laboratory of Nippon Koei, and Mr. N. Takezawa of PWPI and
Mr. A. Kubota of Kagoshima University in the field. We
are grateful to the JMA for information, the prefecture ofKagoshima, the city of Tarumizu, and the Education
Department of Kagoshima University. We also thank Drs.
T. Kobayashi and N. Kinoshita of Kagoshima University,
Dr. M. Iguchi of Kyoto University, and Dr. H. Itoh of
Iwate Prefectural University for their helpful comments.
We also thank Dr. M. Ban editor and reviewers of thismanuscript who made devoted efforts in a long reviewing
process. We thank Mr. D. Uehara of Monashu University
for the helpful English comments. Finally, we deeply thankMrs. M. Tajima for her useful suggestions.
References
Aramaki, S. and Hayakawa, Y. (1982) Ash fall during theApril 26, 1982 eruption of Asama volcano. Bull. Volcanol.
Soc. Japan, 27, 203-215 (in Japanese with English abstract).
Bonadonna, C. and Houghton, B. F. (2005) Total grain-size
distribution and volume of ash fall deposits. Bull. Volcanol.,67, 441-456.
Fierstein, J. and Nathenson, M. (1992) Another look at thecalculation of fallout tephra volumes. Bull. Volcanol., 54,
156-167.

Froggatt, P. C. (1982) Review of methods of estimatingrhyolitic tephra volumes; application to the Taupo Volcanic
Zone, New Zealand. J. Volcanolo. Geotherm. Res., 14,301-318.
Fukuoka Meteorological Observatory, Kagoshima Local Meteorological Observatory and Miyazaki Local MeteorologicalObservatory (1959) Eruption of Shinmoedake, Kirishima
volcano, on 17 February, 1959 (Showa 34 Nen 2 Gatsu 17
Nichi no Kirishimayama Shinmoedake no Bakuhatsu). 16p(in Japanese).
Geshi, N., Takarada, S., Tsustui, M., Mori, T. and Kobayashi,
T. (2010) Products of the August eruption of Shinmoedake
volcano, Kirishima volcanic group, Japan. Bull. Volcanol.
Soc. Japan, 55, 53-64 (in Japanese with English abstract).
Hayakawa, Y. (1985) Pyroclastic geology of Towada volcano.
Bull. Earthq. Res. Inst., Univ. Tokyo, 60, 507-592.
Iguchi, M., Tameguri, T. and Yokoo, A. (2008) Volcanic
activity during the period from 1997 to 2007. In 10th Joint
Observation of Geophysics and Geochemistry (Iguchi, M.
ed), 1-18. Ann. Dist. Prev. Res. Inst., Kyoto Univ. Japan (inJapanese).
Ishihara, K. and Kobayashi, T. (1988) Recent volcanic activity
at Sakurajima volcano (Commentary on Photogravures).
Bull. Volcanol. Soc. Japan, 33, 269-271 (in Japanese).
Ishihara, K. (1995) Sakurajima. In National Project for Prediction of Volcanic Eruptions, 161-168. Japan Meteorological Agency (in Japanese).
Ishimine, Y. (2007) Overview of diverse computer simulations and their potential contribution to volcanology. Bull.
Volcanol. Soc. Japan, 52, 221-239 (in Japanese, withEnglish abstract).
Japan Meteorology Agency (1994) Manuals for volcanic
observations (Kazan Kansoku Shishin; volume of observation). Japan Meteorology Agency, 318p (in Japanese).
Japan Meteorology Agency Website. http : //www. seisvol.
kishou.go.jp/tokyo/volcano.html (7/22/2012).
Kagoshima University Website. http : //volceye.edu.kagoshimau.ac.jp/sakurajima.html (7/22/2012).
Kamo, K. (1974) Recent volcanic activity of SakurajimaEllipse-approximated Isopach Maps for Estimating Ashfall Volume at Sakurajima Volcano
volcano. Bull. Volcanol. Soc. Japan, 19, 48 (in Japanese).
Koyaguchi, T. (1996) Volume estimation of tephra-fall deposits from the June 15, 1991, eruption of Mount Pinatubo
by theoretical and geological methods. In Fire and mud,eruptions and lahars of Mount Pinatubo, Philippines(Newhall, C. G., and Punongbayan, R. S., eds), 583-600.
Philippine Institute of Volcanology and Seismology andUniversity of Washington.
Nakada, S., Yoshimoto, M., Koyama, E., Tsuji, H. and Urabe,T. (2005) Comparative study of the 2004 eruption with olderuption at Asama volcano and the activity evaluation. Bull.
Volcanol. Soc. Japan, 50, 303-313 (in Japanese with English
abstract).
Osumi Office of River and National Highway, of the Ministryof Land, Infrastructure, Transport and Tourism. Website:http : //www. qsr. mlit. go. jp/osumi/camera_sabo. htm (7/22/
2012).
Paladio-Melosantos, M. L., Solidum, R. U., Scott, W. E.,
Quiambao, R. B., Umbal, J. V., Rodolfo, K. S., Tubianosa,
B. S., Delos Reyes, P. J., Alonso, R. A. and Ruelo, H. R.
(1996) Tephra falls of the 1991 eruptions of Mount Pinatubo.
In Fire and mud, eruptions and lahars of Mount Pinatubo,
Philippines (Newhall, C. G., and Punongbayan, R. S., eds),
513-535. Philippine Institute of Volcanology andSeismology and University of Washington.
Porter, S. C. (1973) Stratigraphy and chronology of late
Quaternary tephra along the South Rift Zone of Mauna Kea
volcano, Hawaii. Geol Soc. Amer. Bull., 84, 1923-1940.
Pyle, D. M. (1989) The thickness, volume and grain size oftephra fall deposits. Bull. Volcanol., 51, 1-15.
Pyle, D. M. (1999) Widely dispersed Quaternary tephra in
Africa. Global and Planetary Change, 21, 95-112.
Rose, W. I., Bonis, S., Stoiber, R. E., Keller, M. and Bickford,
T. (1973) Studies of volcanic ash from two recent Central
American eruptions. Bull. Volcanol., 37, 338-364.
Sulpizio, R. (2005) Three empirical methods for the calculation of distal volume of tephra-fall deposit. J. Volcanolo.
Geotherm. Res., 145, 315-336.

305

Suzuki, T. (1981) “Thickness-Isopach area” curve of tephra.
Bull. Volcanol. Soc. Japan, 26, 9-23 (in Japanese withEnglish abstract).
Takarada, S. et al., (2001) Volcanic ashfalls from the Usu
2000 eruption and situation at the source area. Bull. Geol.
Surv. Japan, 52, 167-179 (in Japanese, with English abstract).
Takarada, S., Hoshizumi, H., Miyagi, I., Nishimura, Y.,
Miyabuchi, I., Miura, D. and Kawanabe, Y. (2002) Proximal deposits of the Usu 2000 eruption. Bull. Geol. Surv.
Japan, 47, 645-661 (in Japanese, with English abstract).
Tarumizu city website: http : //camera19.city.tarumizu.kagoshima.
jp/ (1/9/2009).
Thorarinsson, S. (1954) The eruption of Hekla 1947-48, part2, Ch. 3, The tephra-fall from Hekla on March 29, 1947.
Soc. Sci. Islandia. Reykjavik, 1-68.
Walker, G. P. L. (1980) The Taupo pumice: product of themost powerful known (ultraplinian) eruption? J. Volcanol.
Geotherm. Res., 8, 69-94.
Walker, G.P.L. (1981) Plinian eruptions and their products.
Bull Volcanol., 44, 223-240.
Yamada, N. and Kobayashi, T. (1988) Geology of the Ontakesan district. With Geological Sheet Map at 1 : 50,000, Geol.
Surv. Japan, 136p. (in Japanese, with English abstract).
Yamasato, H., Miyamura, J., Mori, H., Usui, Y., Sakuma, K.,
Watanabe, A., Sato, J., Takahashi, Y. and Sakai, T. (2002)
Eruptive activity inferred from infrasound associated withthe 2000 eruption of Usu volcano. Bull. Volcanol. Soc.
Japan, 47, 255-262 (in Japanese, with English abstract).
Yokoo, A. and Ishihara, K. (2007) Volcanic activity around
Showa crater of Sakurajima volcano monitored with infrared and video cameras. Annals of Disas. Prev. Res. Inst.,
Kyoto Univ., 50, 149-155.
Yoshimoto, M. et al. (2005) Mass estimation and characteristics of ejecta from the 2004 eruption of Asama volcano.
Bull. Volcanol. Soc. Japan, 50, 519-533 (in Japanese, withEnglish abstract).

(Editorial handling Masao Ban)

306

Yasuhisa TAJIMA, Keiji TAMURA, Takao YAMAKOSHI, Akira TSUNE and Shinjiro TSURUMOTO

桜島火山における楕円近似による火山灰堆積量の推定法について
田島靖久・田村圭司・山越隆雄・津根明・鶴本慎治郎

海に囲まれた火山島では観測できる場所が限られ，火山灰の堆積量を推定することが困難であった．また，火山灰が大量に降ることによって交通，健康，農作物へ影響を生じ，厚く堆積した斜面では土石流が発生しやすくなる．ゆえに火山灰の降下量（降灰量）や分布を迅速に把握する方法の開発は，火山学，防災学
上の重要な研究対象となる．このため桜島のように海に囲まれ観測場所が限られる火山での迅速かつより少ない点から火山灰の堆積分布・量を推定する方法を検討した．我々は等層厚線が相似の楕円に近似されると仮定し，各点から得られる楕円近似した等層厚線の軸比を一定とし，分布を幾何学的に単純化した．また，d
降灰観測データの豊富な噴火事例を検証した結果，面積= 層厚が A=αT （T: 層厚，A: 面積）とした場合，その減衰はほぼ−1 乗に近似可能である．これらの関係より，火口位置などを楕円の軸端点とし，火山灰堆
積分布に相当する分布軸が決められる場合，計算上 2 点の観測値から火山灰堆積量を推定することが可能となる．ただし，本手法では通常，計算軸を求める際に，計算に使用する 2 点以外の 1〜4 点程度の複数観測点の値が必要となる．本手法については分布軸が精度良く求められることと，複数の観測値を解析結果が矛盾なく説明できることを適応条件とした．本手法を用い桜島 2008 年の活動について 60 を超える噴火の火山
灰堆積量を推定した．推定した分布から特定の場所における月ごとの累積降灰量を計算した結果は観測量を再現可能である．2008 年の桜島の活動を日単位の堆積量として解析すると，ピークは 5 月 6〜23 日頃であったと推定される．本方法を適応することによって，これまで観測が難しかった火山島での火山灰堆積量観測が可能となる．