holland's formula and volcano.pdf

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1/36

-

AFGL-TR-76-0127

rnOP

~

ENTM. RESEARO l PAP

~~~

NO.

566

~~

Rise of

Volcanic

Eruption Clouds:

~

Relationship

Between

Cloud

Height and

~

Eruption

Intensity

MARK

S

ETTLE

,

iLt

,

USAF

22

June 1976

D D C

APP I

V.d

hr

publi

c rs

~

sss.

d

stv1

bu t

~

on

TERRESTRIAL

SCIENCES

DIVISION

PROJECT 8607

AIR FORCE GEOPHYSICS

LABORATORY

HANSCOM

APS,

MASSACHUSETTS

01731

AIR

F

ORCE SYSTEMS

COMMAND

,

USAF


2/36

;

~~~~~~~~

~~

j .

4

~~~

J

~

I

~~~~~~~~~~~~~~~

4

This

technical

report

has

been reviewed

and

is

approved

for publication

.

4

FOR

THE

COMMANDER:

(

iAef Scientist

Qualifled

requeslors

may obtain

additional

copies from

the

Defense

Documentation Center.

AU

others

should

apply

to

the

National

Technical

Information Service.

ft

S


3/36

Unclass i

fied

S ( CI J R I T V

CL A S S I F I C Af l O lA OF TI l lS P A G E (WA.,, 0.1 .FnI.,. d)

~

REPORT

DOCUMENTATION PAGE

BEFORE

COMPI

ET NG

IORM

AFGI rR

~

7 G - i .

27

,

A

~

~~~~~~~~~~~~~

3

R E C I P I E N T

~

s

C A T A L O G NU M B ER

S T Y P E OF

RE PoRT

A PERIOD

COVEREy

~

E L A T IO

~~

SHIP BE

~~ ~

E E N c L d

~

D

H EIG H T

scientific. Interim.

A N D E

,

I

~

U P T I O N

,

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NTENS

IT

~~

6 P E R F O R M I N G OR

G.

RE P ORT

N U M B E R

t. CONTR

ACT OR

GRANT N U M B E R (. I

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~~~~~~

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M a r k J

t t l eJ

1st

Lt

,

B

P E R U OR M IN G

O R G A N I Z A T I O N

N A M E

A N D

A D D R E S S

P R O G R A M

E L E M E N T P R O J E C T

.

T A S K

A i r Force

Geophysics

La

b

or a t

or

y

(LWW)

~

J

~~~~

~~~~~~~~~~

j W O R

~~~~~~~~~~~~~~~~~~~~~~

7

M assach u se tt s

01731

~~~~

Th2F

~~~~~~~~~~~~~~

ii C O N T R O L L I N G

O F F I C E

N A M E A N D A D D R E S S

.

t2. REPfl

~~~~~~~~~

_ --

1

A i

r

Force

Geophysics Laboratory (LWW)

//

22

Jun.

~~

76

Hanscom AFB

~~

R

UMP

AG ES

M assachus e tt s 0 l7

~~

1

_

_________________________

4 M O N I T O R I N G A G E N C Y

N A M E

A A O D R E S S ( I I dIfle,.,, 1

I Co nI o II lng

Office)

15. S E C U R I T Y C L ASS.

~

/

151. ,

~

p

~

rI)

-

Unclass i f i ed

a I

yes

~

-

~~~

~~~~~~~

-

D E C L A S SI F I C A T I O N DOWNG

~~~~~~~~~~~

~

.

~~

L*

.TB

~~~~

w 0 r .T

E M E N T (ol fbi.

R.porI)

A p p r o v e d

for u b

ic

~~

el

~~ ~

e; distribution

u n l i m i t e d

.

~

~~~

i

7. D ISTRIBIJ AT E M E N T

ft

~

ot eflf.,Ad 10

810Kb

25 I

5/l.,on

f

frOm

R.s.o,I)

It. S U P P L E M E N T A R Y

N O T E S

I

19. KEY

W R

~

5

Coofr,,

~

..,,.

. . ..

,d.

If n4 c

~~

o4fy

m.d

id.nhiVy by

Slosh n nb.f)

Volca

n

ic er

u

p

t io

n

s T

h er

m al plumes

Cloud rise

Infrared

sources

St ra t osp

he

re

Atmospheric dust

20. A B S T R A C T (Coma,,.. . on

,o.,00 Ma . f

nc y

.nd Id.nlif

y b

y

SImS

n..mb.f)

The

rise

of eruption clouds

is produced

b

~

y

the

up w

~

d

momentum

and

thermal

buoyancy of volcanic dust and

gas

,

F

li.e

~

e procesns

~

.p

1ay important roles in

other

phenomena.

The

expansion

of a

turbulent

j e t

in

free flow

( that

is

,

uncori f ined

by

lateral

boundaries)cis

controlled by

t h e

rate

at

w h ic h th e

f o r w a r d

momentum

of

the

jet

is

dissipated. Th

~

thermal

buoyancy

of industrial

waste

gases provides

a

mechanism

for moving

~

iich waste

Hq

~

teria 1

~

upward through

the atmosphere

and ensuring

their dispersal

over

a w i d e area. The

r isc

of

OD

~~~~~~~~

~

473

E D I T I O N

OF

I NOV

ES

IS

O B S O L E T E

Unclassified

S E C U R I T Y C L A S S I F I C A T I O N OP

T H I S

P A G E (WI,.n 0.1.

PsIsrod)

~~~~~~~~~~~~~~

~

.

~~

-

~

0

~

.-

~~~~~~~~

~

-

~

___________ _____________________

.--

_ _ _

_ _ _ _ _ _ S _ _ _ _ _ _ _ _


4/36

,

-----

-- -

~

.

-

~~~~~~~~

..- aoar

Unclass ified

-

. - .

-

.

20

. Abstract

( C on t i nued) -

4

,

volca n ic

eruption clouds can

be modelled

after hese a

~

wWana1ogous

p h e n o m e n a

.

I

n

t h i s report average

e j e c t i o n

velocities

~

at a volcanic vent

ranging

f r o m

20

rn/sec to 200

rn / s ec are assumed to represent a w i d e

range

of eruption

in

t

e

n

si

t

y,

f rom

S

t r o

m bolian t

o

V

u

lc a

n ia

n

t yp es

,

ef

er

u

p4k

~~

.

9

For

eruption

veloc i t ies

vary

ing f r o m 20

rn / s ec

to

200

rn / s ee

,

cloud heights estimated by the

t u r b u l e n t j e t model range

from

1500

m to

6500

m

( m i d - l a t i t u d e

e r u p t i o n )

w hi l e

c lo u d

hei

ghts estimated

b

y

the

industrial

plume models range f r o m 900

m

to

10

,

000

rn

. These es t imates are

considered

to

be

roug

hl

y co m parabl e in v

ie w

of t h e assumptio

ns

and extrapolations

i n v o lv e d in app ly

in g t

hese

m

odels

to

explosiv

e

eruption

c o n d i t i o n s a n d agree

q u i t e w el l

with

reported heights of

er

u p t io n clouds.

The f a c t t ha t comparable es t imates of c lo u d height are pro-

5

du

i

~~

y

~

th

~

t

wo very

d i f f e r e

nt

model s

su gges t s t ha

t

bo

t

h

mo m

e

ntu

m an d

~

,

thermal buoyancy

play

an

i m p o r t a n t

role t h r o u g h o u t t h e m a i n portion of an

er

u p t io n

c l oud t

s

t rajectory.e

~

Fo r these eruption conditions

(20

rn/sec

~

w

0

~

~~

200

rn /see)

,

nei ther

moinntum

nor

thermal

buoyancy appears

to

dominate

the

process of cloud rise to altitudes

of 10 km above an

actively erupting

volca

nic vent. A n

order

of

magnitude

variation

in

eruption velocity

f rom

20

rn/sec to w

0

= 200

rn/sec

results

in

a

factor of

3

to

4

increase

in

avera

ge c l oud

h e i

gh t

p r e d i c t e d b

y

th e

t u r b u l e n t volcanic j e t

model

and a

factor

or 2 5

i

ncrease

in

median

c lo u d h e ig h t p r e d i c t e d

b

y a selec t g r o u p

of

i n d u st r i a 1

~

p lu me

models

. H o w e v e r

,

bo th models

also

demonstrate t ha t

changes in

crossi

w ind

v e l o c i t y

b

y

factors of 2 to 5 can result in variations in

cloud

h e ig h t

of

si m

i l a r magni

t u d e . T he r e f o r e

,

reported

h e i

gh ts of eruption clouds w i t hou t

refer-

ence to local crosswind conditions a t

th e

t i m e of an

eruption

cannot

be

directl

y

compared to gau ge the relative exp

losiveness

of d i f f e r e nt

v o l c a n i c

eruptions

.

a

~~

_

Unclass i f ied

SE P T . a c ( i r i A, -

pn .

.

5

~

.

~~~

, .::

.


5/36

-

~~~~~

w ;-

~

-

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.-

-

~~~~

~~~

~~~~~

- -

~~~~~

-

~

~ ~~

-

~~

~~~~

P r e f a c e

The author is gra te fu l to Torn Webb

, C h u c k W o o d

,

and John Cronin

for cr i t i-

call

y rev iewing e a r l i e r v e r s i o n s of

th i s

repor t

,

and to Elaine Robson for

h e r effor t

arid

pa t ience

in

p r e p a r in g

the m a n u s c r i

pt .

Boff

S.cft

~

oI

~~~~~

I

D D C

---

--i

~

-..j

DEC

22

~

/K

UPECIAL

J

~~~

D

-SuurU

U

~

~~~~~~

-

. a

~~~~ ~~~~

--

.-


6/36

____

C

ontents

1.

IN T R O D U C T I O N

7

2.

P U R P O S E OF TH IS

STUDY

9

3. E R U P T I O N C L O U D RISE

ESTIMATES

10

3.

1

Turbulent Jet

Flow

in

t h e Atmosp

he

r

e

10

3.

2 Rise of Industrial

Plumes

15

4 DISCU SSION

22

5. C

O

NC

L

US IONS

25

RE FE

R

ENCES

27

BIBLIOGRAPHY

31

APPENDIX A:

Observe

d Eruption Cloud

Heights

35

I l tustrat ons

1. The

Centerline Velocity

of a

Turbulent

Volcanic

Jet

(heavy li

nes)

Compared

w i t h

Averaged

Crosswind

Velocities

( l ight lines)

at

Variou s Altitudes

14

2. Parameters

Employed in

the Industrial

Plume

Formulae

Used for

Predicting

Plume

Rise

17

5

-

~~~

ID

PAGE

Bt

2IC

NO?

~~~~~~

-

~~~~~~~~~~

~~


7/36

~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~

**

~~~~~~~~

Tab les

1.

E r

u p t i o n ( loud Hei

ght

Estimates

21

A l . Observed Er u p t io n

(

loud

H e i g h t s

36

6

-mc

~~~~~~

.

~~~

..

.

,

~~

~~~~~~~~~~~~

_

~~

_

_ _ _

~

-

-,

~~~~~~~~~~~~~~

-

~~~~~~~~

~

l

~

.5 -


8/36

-

-

-

---

-

-

-

Rise

of

Vo lcan i c

Erupt ion

C lo ud s :

R ela tio ns h i

p

Between

Cloud

Heig

ht

and

Eruption Intensity

I.

I\TQtH)

(: T IO\

E xp

losive

volcanic e

ruptions inject

large

q u a n t i t i e s of ash and

gas

i n to

th e

ea

r t h

s a t

mosphe r e

. The

l eng th

of t ime these

d i f f e r e n t volcanic

products reside

i

n the

at mosp

here can vary

f r o m

several

hours

to several years . A s

a result

,

an

individual

er

u

p

t ion

ca

n p r odu

c

e

m et eorolog

ical e f f e c t s t ha t

range

in t ime from

several days

to

several

years

and

can

range in

space

f r o m a localized

region to

the

entire

planet

.

R e g i o n a l

meteorology

can be

significantl

y altered b

y a maj o r

ex p

losive

erup-

t ion

.

Airborne

ash and

volcanic

gases can

e f f e c t i v e l y

insulate

the

earth

s

surface

,

modif

y

ing

diurnal

temperature

variations

and

producing a shor t - te rm

warming of

the

region.

R a i n w a t e r from clouds

contaminated

wi th

volcanic

gases can

be

highly

acidic and

may

pollute local ground

water

.

The

long

term

atmospheric

effects

of an

eruption

are

produced

by particulate

dust and

gases

t ha t have

much

longer atmospheric

residence

times. Major

explo-

sive

eruptions

can

have a

significant

impact on the

chemical budget

and

radiation

budget of

d i f f e r e n t

portions of the

atmosphere.

Volcanic

eruptions

appear

to be

the dominant

source

of

atmospheric

chlorine

1

w h i c h plays an

important role in

(Received for publication

22 June

1976)

1.

R y a n

,

J .A . ,

and

Mukherjee

,

N . R .

(1975)

R evs .

Geophys. and

Space

Sci.

13:650-688.

7

I

I

--

-


9/36

T

~~

.

T-

.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

5-

~~

~

r3

~~~~~~~~~~~~~~~~~~~~~~~~~

-

----5..

1/I I I IC

c h e m i c a l

r e z a - t I I l f l . s

in the s t r a t

I

.5phere

.

Sulp

h u r diox

ide

ga

s produced b

y

t o1 I

~~

I t ) Z (

a - r u p o ,n

~

is

ti i

-d

a t

i v - l v I l I n l a r sour c e

of

a t m o s p h e r i c sul p

hu r

3

hut ca n

si

g n i f i c a n t l y

inc

c:

- a- 1

~

-

Ii

n -

~

tv

of

the

s t ra tosp

h e r i c

aerosol layer b

y

gas

phase

\ u I

: a tj o f l

t I

.50l 1)1 1

1tt I : a r t i

~~~

The

i n j e c t i o n

of

l a r ge

quant i t ie s

of s i l i c a t e

dust part id

a -

-. . j t 1 p

h it r ga -o-

. i n t o t h e a t m o s p h e r e can produce a cooling

of

th e

E:a

r U s s u rt : o

a

I \

r t - -

,- :

~

-

OIL

g

lobal

albedo

or

an

i n c r eas ed greenhouse w a r m i n g

III Ih e -, ux t a I e due t i h a -

j I l l i t . thesc

volcanic

producL. t o i n f r a r e d

r a d i a t i o n

a n i t t e d f t a

h . I t t

I , ( ja

,-

.

Th e ore t t e a l

c a l c u l a t i o n s

of

Pollack et al

7

m d i

c a N - t h a t

a- ,

Ia

~~

I

- I ) ,

.1

~~

j I

lt

- . t - t t l t

o u t

of the a t m o s p h e r e

,

global cooling

l a c on es Ut a

~~~

I

-t -

I tn

1

1 1 1

~~

.

The

i t n - , I - x

II

f l p : I ( - t

of a

p a i - t o - u l a r

e r u p t i o n

is

la rge l

y

d e t e r m i n e d

b

y

the

: a l t i

~

ttde.s at w h i c h

, l l - t a i i

Iu

~

t

I l l

ga

~

en ter and are mixed into the

a t m o s p

he r e

.

P r e c i

pi ta t ion

in

t h e

t r o p o sp h e r e e f fec t i ve l

y

\Y

ashes these ma ter i a l s out of t h e lower

a t m o s p

he

re.

T r o p o s p h e r i c

w e a t h e r

s

st e

ii

~

i

also

mix

l a rg e

a i r

mas s e s over

rela-

t ively

shor t per iods of t ime

rap

id l y reducing

t h e concen t r a t ion of volcanic produc ts .

The

lower

boundary

of

the

t roposp

h e re is the e a r th s

su r f a c e

which provides a

v a r i e t y

of geologica l

,

biolog

ical and anthropogenic

s inks

for

a i r bor ne

volcanic

product s .

Long t e r m a tm o sp

her ic e f fec ts f rom individual erup t ions a re

t h e r e f o r e

l imi ted

to erup t ions tha t succeed in penet ra t ing

the

upper levels of the

t r o p o s p h e re

and introduce

volcanic

dust and

gas i n t o

the s t r a t o s p h e r e

.

8

,

9

The a ve r a ge

heig h t

of

the

t ropopause

var ies

lat i tudinal l

y

f ro m a p p r o x im a te l

y

9

km at

the

poles to

ap p ro x i m a t e ly 16

km

at the

equator

.

The r i s e of an erupt ion cloud is controlled b y the

upward

m o m en t u m

of

ash an d

gas

at the mouth of

a volcanic vent

and b

y

the

t h e rm a l buoyancy of the volcanic

gases.

The

init ia l r i s e of dust and gas in an eruption cloud is largely d e t e rm i n ed

by

the

exit veloci ty

of the

mater ia l .

A t higher

a l t i tudes

the init ia l m o m en t u m of th e

volcanic

dust and

gas

has

been

subs tant ia l l

y

diss ipa ted

and the

subsequent r i s e of

the eruption cloud is predominant l

y

dete rmined by the

re la t ive

buoyancy of

the

hot

volcanic

gases

.

This t r ans i t ion

is s o m e t i m e s

ref lected

in

the

mor p

hology of th e

2.

Rowland

, F. S.

,

and Molina

,

M . J .

(1975)

Revs,

Geoph

ys. and

Space

Sd.

13:135.

3. Kellogg, W

.

W .

,

Cadle

,

R. .

,

A l l e n

,

E

.R.

,

Lazarus

,

A

.

L.

,

and Martell

,

E.K

.

( 1 9 7 2 )

Scie

n ce

175:587-596.

4.

Harker

,

A

.B. 1975) J.Geophys.Res.

24:3399-3401.

5. Lazru s

,

A

.L .

,

and Gand ru d

,

B.

W . ( 1 9 7 4 )

J . G eop

h

ys.Res.

79:3424-3431.

6.

Dyer

,

A.J . and Hicks

,

B , B .

( 1 9 6 8 )

Q u a r t . J .R o y . M e te or o l . Soc. 94:545-5

~

4.

7

.

Po

~~

ek

,

J .B .

,

Toon

,

O . B .

, Sagan

,

C. ,

Summe r s

,

A.

,

Baldwin

, B. ,

an d

Van Camp, W. 1976)J.

Geophys.

Res.

81:1071-1083

.

8

.

Lamb

,

H,

-

1. 1970) Phil. Trans.

Roy.

oc. London 266:425.

9 .

C

ronin

,

J.F.

1971)

Science

172

:847-84fl

.

8

_ _

~~~~~~

_

--

~~~~~

.-_

-

~~~~~~

. --

-

~~~~


10/36

-

~~~~~

- -

~~~~~

~~~~~~~~~~~~~~~~~~

--

-

-----.

~~~~~

- -----

~~~~~~~~~~~~~~~~~~~

~~~~

--

~~~~~~~

~

.----.

---

~~~~~

,

~

_

.

-

_P

~~~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

e ru p t i o n cloud

. The

l o n er

p i t t i o r t

of t h e

cloud I

o f l t t i l f l . ,

a

l a r g e r -

( i r t I

(

~

n t I -

a t ion of

~

i

~

l

i 1

E - ) c -i - t a and

c a n

a p p e a r much

d a r k e r

than

t h e

u p p e r - por t i on

of

t i t i

-

- I I

,u l

-

In

such

t t S C S the

l o w e r

p o r t i o n

of the

cloud

i,s , n : c t t t :

es

r - e f er x - a - , I

t o as t h e ash

cloud

s

w h c - r e a . s the

uppe r

,

li g h t e r -

co lo r - ed

por t ion

is

so m e t im e s

h -

t e d

the

va p

o

r

c l o u d . In oth

er

instances

eruption clouds have a u n i f o r m

g r e y

appearance

.

H epor ted

hei

g

hts of erup t ion clouds

genc-ral l

y

i - e l i - i -

to

he

m a x i m u m he ig

h t

h i t h e

condensed vapor

cloud

observ e d

a h , v e

an

t o - t i v e l y erup t ing vo lcan ic ven t .

~

i g ni f

i r a l t

z 1 t : t I

u t t 5

of

p a r t i c u l a t e

dust and gas may ac tua l l

y

r i s e

beyond t h e t o p of

t h e

I se r v a h l e cloud.

The m a x i m u m

height

of an

eruption cloud

is

r e l a t e d to

the i n t e n s i t y

of the

exp los ive e rup t ion .

The

mo st

in tense

exp los ive

e ru p t i o n s

a r - c

c h a r a c t e r i z e d

b y

e j e c t i o n velo c it i e

~

on

the or de r of h u n d r e d s of

me te r s pe r

second and

la rge

m a s s

f l u x

r a t e s .

In the

past the

c l a s s i f i c a t i o n of

d i f fe ren t

s ty

les of

exp

losive

erup t ion

has been q u a l i t a t i v e l

y

based upon a

var ie ty

of

par -amete r s

,

inc luding

t h e

v i sc o s i t y

and chemica l compos i t ion of t h e

e r - u p t e d

m a g m a

,

and

the vio lence of

a

p a r t i c u l a r

e rupt ion

m eas u red in

t e r m s

of h

iss

of l i fe

or

the extent of p ro p e r t y

d c - s t r u c t i l h n .

10

M o s t c l a s s i f i c a t i o n

sc he me s

include a g en e ra l d e s c r i p t i o n of

the

size and s t r u c t u r e

of the

e rup t ion

cloud

as s o c i a t ed w i t h a

part icular-

t

~

pe o f exp

losive e rupt ion

. Such

d e sc r ip t i o n s sugges t t h a t the

s i z e

of an

erupt ion cloud is a p p r o x im a te ly

c or r e l a t e d

w i t h erup t ion in tens i t

y,

w i t h

sma l l clouds

,

r - i s i n g

to heig

hts of

se ve r a l

hundred

m e t e r s

,

as s o c i a t ed

with

weakl

y - e x p

los ive St rombol ian-s ty

le erup t ions

,

and

larger-

cl oud s

,

r i s i ng

to hei

ghts

of

s evera l k i l o m e t e r s

,

associa ted

w i t h vi

olent l y-explosive

Vulcan ian-stvle eruptions. Thus

the

height of an

eruption

cloud can be

considered

to

he

an

approximate index

of eruption

i n t ens i t y . R e p o r t s

of

t h e

he ights

of erup t ion

clouds

observed in remote areas

,

where ground-based observat ions of active

erup t ions ar

e

h aza rd o u s

or-

imposs ib le

,

have

been used

t o

qua l i ta t ive l y gauge

th e

r e l a t i v e

in tens i ty

of such erup t ions

.

-

P1

RP O

4 OF This

STi

U\

The ph

ysica l

processes

which are

respons ible for

the rise

(If

e r u p t i o n clouds

the upward mOmentum and thermal bu

oyancy

of

the erupted m ator i a l

p

lay impor-

t a f l l

- e I c - --

~

in

othe r phenomena .

The expansion of a

tu rbulent

je t in f ree flow

( t h a t

i s ,

unconfined b

y

l a t e r a l boun daries)

is control led b

y the ra te a t

which

the fo rward

~~

,

) ; ( f l t U f l 1

of

the

jet

is diss ipa ted

.

The s t r u c t u r e

of

tu rbu len t j e t s

is a c las s ica l

10

.

MacDonald

,

G . A .

( 1 9 7 2 )

Volcanoes, Pr e n t i c e - H a l l

,

Englewood

Cliffs

,

N

. J .

,

i10 op.

-

I

_____

5---

.5-

--

-

----

-

~~~~~

- -

~~~~~

~~~~~~ ~~~~~~~~~~~~~~~~~~~

--


11/36

-

~

~~~~~

zr

~~~~

- 5 -

--1.--- ;,

------,,,-

~~

--, -

~

..---

~~~~~~~~~

-

---- --- - - - - -

-

-

------ -

--- -

~

---

I t f l u i d

) I ( & t i a ) i i ( s . i i i e -

tb

~~

r n n i

il h o o v a n i - v

of

r n d u . s t r - i a l

wash-

~~~~~

p

-

-v

I d a

-

,

a

n

- a - i - h t m

l

i i i

h r

ii l o v i n g

such

n : -

~~

e- m a t e r i a l s u p w a rd s

t h r - o u g h

t l i t

at

:l ,

- i t i s -

e :i

~~

1 e n s u r i n g t h i e l

,

d i

~

p - r . s : i 1

o v e r a w i d e a r e a . T h e r e l e a se

and

di s

p a - c

-

j : i

of

such

i n d u s t

- i a l

e l l h t i c -

i t s

i n t h e : m t r n o s p

l t c - r e h a v e been desc r ibed b

y

a

i t t

.

a

i i t v of t h a

n

i - t i c n t l an d

a - c : p t i O a l

~

t u I t i ( - 5

( s i c

,

f o r -

t- x : i i t

p

le

,

.su xi I l a v h

~

J3 r

~~~~

1 2

)

1 } :

r

i s e

of v o l c a n i c

, - r u n

i

j O

- h

ulL

i - t i n t

i c -

m o d

el led

a f t e r t h e se

t n l

i

a n al - g e u

p h e n o m en a .

d o - h i

~~~

- 1

t i l l -

tI - \ -

a -l - ) a -

h

i n his

- i t i d v

t o investigate

lie

- i - h t m l

i1 1 i

~~

hi

p

between

c- i -o p t

u i

c - I , i i i I - i d

tu

tu c

t-t

O condi t io n s

at a

volcanic

vent

.

T h e pu

- p o s e

of

t h i s

s tud i

~

t n I -h - i t :

( I )

to

i c - I I - d -

: t I i r I e

if t h e

r - m -

,e

of

erup t ion c louds

e d ,

r n n i n a n t l v

c o n t i - o l l e d

l i v

( l i e

i n i t

,

~

it n : a - i t u m or

t h e r - nal

b u o y a n c y of vol-

canic p r o d u c t s ; and

2 )

to I c - t i -

t i - i i i -

if t h e I c - i g h t - of e r u p t i o n

clouds

are

an

a c c u

- a t e r-e

flect ion

of

r e l a t i v e ecu p t i o n

I

it e i t - it

I

F

~~

Pli lJ\

1 1 1 1

I)

RI

I

I RI

~

I I-

:1. 1

1 urba,

I

-nt

j . - t

F

a,

~

s

in t h e-

~

t r11aa

~

p

Ii i ra -

D e s c r i p t i o n s of t h e s t r u c t u r e

of

er-option

clouds have been made

pr inc i

pall

y

b

y g r o u n d - b a se d o b s e r v e r s who have

r e p o r t e d the

shape

and s i ze of such

clouds .

Hi

g

h l y

v a r - i a h l e

~

inds

,

la rge

quan t i t i es of p a r t i c u l a t e ash

,

and

o ccas io n a l e l ec t r i ca l

( i r a

-i

a s s o c i a t e d w i t h

e rupt ion c louds make ae r i a l o b s e rv a t i o n s

d i f f i c u l t

(see

,

f o r

c - x : c i : :

p le

,

T h o r - a m - i n s s o n

and Vonnegut

13

).

As

a

r - e s u lt

,

v e ry

l i t t le is k n o w n about

t h e i n t e r n a l

s t r - u c t u r e o f erup t ion

clouds

or

about

v a r i a t i o n s

in

local m et eo ro l o g i ca l

c i

I i t i

n i

( t o r

e x a m p

le

,

t e m p e r a t u r e

gr - ach i e n t s

,

humid i ty ,

or wind

s t r u c tu r e )

in

the v i c i n i t y o f erup t ion c louds .

A n a p p r o x i m a t e model of

t h e

in te rna l

s t ru c t ure

of e rupt ion

clouds

may

poss ibl

y

he

t , i - o v i d c - I

by

t u d j e

~

of s i m i l a r

l

y shaped

c lo u d - f o r m

s t ru c t u re s s u ch as

experi-

menta l conver t

i v , -

plumes

(Benech

14

)

,

models

of

cumulus c loud format ion

(Squires

and

T u r n i - r

1

~~

)

,

a n d e x p e r i m e n t a l

l e t s

( 1- f i d

y

and

F r i e dla n d e r

16

;

M or r is

17

).

E jec t ion

11. S c h h i c h t i n g ,

II

.

( 1 9 6 8 )

Boundary

Layer

T h e o ry , Mc G ra w -H i l l

,

N e w York

,

7 14

pp .

12

. Br i g g s

,

G . A .

( 1 9 6 9 )

Pl u m e

R i s e , AEC

Cr i t i ca l

R e v i e w

Series

USAEC

,

Report

TID-25075

,

Il l

pp .

13

. T h o ra r i n s s o n ,

a.

,

and

Vonnegut

,

B.

( 1 9 6 4 )

B u l l . A m . 1\ Ieteor ol. Soc. 45:

440-444

.

14

. Benech

,

B.

( 1 9 7 6 )

J . A p p

l.

Me te o r

.

15:127-137

.

15

.

Squires

,

P.

, and

T u r n e r

,

J .

5

.

( 1 9 6 2 )

Tel lus

1 4 : 4 2 2 - 4 3 4 .

i i ;

. ru d

y,

G . M . ,

and

F r i e d l a n d e r

,

D. K .

( 1 P 6 4 )

J. A m . I n s t .

Chem.

E n g i .

10:

11

5-124

.

17

.

M o r r i s

,

D

.

c.

.

( 1 h 6 8 )

Bu ll

.

Am

. Me t e o r . Soc.

4 ( 1

:1054- 1058

.

10

---

--


12/36

-

-

-

~~~

.

5-

~~~~~~~

~

-

-

-

-

--

-

-

--

~~~

--

~~

~~

v t - b c

i t i e

ul ,

erv - u l

d u r i n g

e x p l o s i v e v o l c a n i c eruption .s

((

houet et al

i

)

a

r -c

t

~

- p i i

- tu

1l

~

m u c h

g re tm ti - m- t h o u

u p

d r a f t v c - l o c i t i e s produced

b

- o n v e c t i v e

p r o c e s s e s

i n

h i -

: a t i u i , s p h e r e

. Erup t ion ve lo

- i t i e ;

c u r - r e s p o n d l i t o r c c

l o s e l y

to e x i t

c o n d i t i o n s

at

the

m o u t h

of

a

c- t

t h a n t o u p

d r : c t t v e l o c i t i e s

at

t h e base

o f

cumulus clouds

o r-

e x p e r i m e n t a l

t h e r - m a l

plumes .

In

addition

,

the t e m p e r a t u r e c o n t r a s t

b e t w e e n

volcanic g a. -

1es

and

the

ar tibi ent

atmosp

here

is more nearly

approximated b

y s o m e

types of e x p e r i m e n t a l j e t s

( fo r

e x a m p

le

,

(

al laghan

and

Rugger i

19

) than

by

uprl raf ts

as s o c i a t e d w i t h cumulus cloud formation

.

The

expans ion of a

t u rbu l en t j e t

in

f r ee

f l o w ( t h a t

is

unconfined

b

y

l a t e r a l

boundar ie s )

is

t h - t - r - r i t i n e d

by

the

rate at w h i c h the

f o r w a r - d

m o m e n t u m

of t h e jet is

d i s s i p a t e d .

11

,

2 0

S i m i l a r l

y the i n i t i a l

r i s e

of an erupt ion cloud

i s

pr inc i

pall

y

d e t e r m i n e d

b

y the upward m o m e n tu m

of dust

and

gas

e jec ted

f rom a volcanic vent

.

The

i n t e r n a l

s t r u c t u r e of

a

tu rbu len t

je t may

s e r v e as a

s i m p l e

,

f i r - s t -o rder

model

of the

internal

structu i- e of

an explosive

eruption

cloud

near

the

volcanic vent

w h e r

e

t

h

e

r

ise

of

d u

st

and

gas is contro l led b

y

the

i n i t i a l upward

m o m e n tu m of

these

materials

. One me

thod

of ext imating

the atmosp

heric penetration

of

a

turbulent volcanic

let

IS to

compare the

upward

veloci ty of t h e

jet w i t h

c r o s sw in d

veloc i t i es above the volcanic vent at

var ious

a l t i tudes . The in i t ia l

upward

momen-

tum

of the volcanic

dus t

and

gas

can

be cons idered to be

ef fec t ive l

y

a r r e s t e d

at

t h e a l t i

tude a t which the ve

r

t ic al ve lo

ci

t

y

of t

he je

t

,

a

,

becomes

co m p arab l e

to

the local crosswind velocity,

u

. Experimental

studies

of t h e ac tua l

behaviour

of

a

t u r b u l e n t j e t in

a c r o s s w i n d

h a v e

b e e n

r e p o r t e d

b

y K e f f e r and Baines

21

and

- 22

P a t r i c k

.

The variat ion of v e r t i ca l velocity

w w i t h

range

f r o m a volcanic vent

can

be

~

e5cr ibed

b

y an ex p res s i o n for

tu rbu len t

jet f l o w :

11

w (x

,

z)

i

~~~~

2

( 1)

i+ f l

~~

)

18

. Chouet

, B.

,

Hamisev icz

,

N

.

,

and

McGetch in

,

T . R . ( 1 9 7 4 ) J . G e o p

h

y

s . Res .

79:4961-4976

.

19. Callaghan

,

E.

E.

,

and

Rugger i

, H . S. ( 1 9 4 8 ) Inves t iga t ion

of

the

Pen e t r a t i o n

of

an

A i r

Je t Directed

Perp

~~

dicul to

an

A i r

Stream,

Repor t N A CA -

TN -l 6 1 5

,

National A d v is o r y

C o m m i t t e e for A e r o n a u t i c s .

20. P

ai

,

S.

( 1 9 5 4 )

Fluid Dynamics

of

Je ts

,

Van

Nostrand

,

New York

,

2 2 1

pp .

21.

Keffer

,

T.

F.

,

and

Baines

,

W

,

D.

( 1 9 6 3 )

J. Fluid Mech.

15:481-497

.

22. Pa t r i ck

,

M

. A .

( 1 9 6 7 )

Trans . Inst. Chern.

Eng.

(

L o n d o n )

45:16-3 1

.

11

--

~~~~~~

-

~~~~~~

~~~~~~~~~~~~~~ ~~~~~ ~~~~~~~~

,

~~~~~~

- L

~~

:

~r


13/36

n

it - i - c -

K

( 1 .

1)

F 0

.

0 2 5 6 b \i

I I

1

3K x

~~

.5

~~~~~~~~

x h i c , r i i o n t a l

d i -

~

t

o n c e

m e a s u r e d

f r o n t

et

c c n t e r lj n e

( m e t e r - )

z =

~~

rt i ca l d i s tance i t i e a s u

- a- d

f rom t h e

n i c , u t h

of

t h e

vent

(meter )

ave-rage

e x i t

v e - l o d i t \ at the vent

( m i t e t i -

-

se c )

b h a l f w i d t h o f t h e

t

,

taken h e re as one -ha l f

t i n -

vent

d i a m e t e r

(me te r )

This equat ion is app

l i c ab l e

to t h e

reg

ion in w h i c h

t u rbu l en t

f l o w

is

f u l l y developed

,

w h i c h

n o r m a l l

y oc c u r s

at

a

hu

-

, i n s t r - e a n t r - a n g e

t ,f

a p p ro x i m a t e l y 10 vent

d i a m e t e r s .

2

A l o n g the cen t e r l i n e of t h e

je t

,

(t

h a t is

,

d i r e c t l y

tm h o v c - t h e volcanic v e n t )

x

= 0 and

E

q.

( 1 )

r educes to

3 K

-

w ( z )

~~~

(2 )

B i n

~

z

0

In or de r to app ly t h i s

t u rbu l en t j e t

i n i o d , )

to -x p

los

i v e

erup t ion cond i t ions

,

it

is

nece ssar-y

to a s s u m e an av e rag e e x i t v

~

- 1 o c i t v

for

t h e

e t - u p t e d

ash and eas

.

Q u a n t i t a t i v e d e sc r ip t i o n s of d i f f e r e n t t

~

pea-

of

t - x p lo .-

~

i

vt

i - r u j t i nis in terms of

e jec t ion v e l o c i tL - s

or

m as s

f l u x ra tes are

l i m i t e d

. Q

u : i h i t a t i v e l y

,

erup t ion

in tensi ty

i.

~

cons idered

to he r e l a t e d

to the ex p los iveness of d i f f e r e n t

v p u -

s of e ru p t i o n s

.

10

(

houet et a118 have

o b se r v e d

gas

e x i t

v e l o c i t i c - s dur ing i nd iv idua l ex p los ive b u r s t s

of

Stron iho l ian - tvpe e rup t ions t h a t

r

ange

f rom

110 m sec t o 2 0

m

-

a-c

. In the

past

,

p a r o x y s m a l e x p l o s ive erup t ions have been accompan ied

by r -

~

- p e r - t s of

repeated

thunder and t h e f i r i n g

of ships

guns

at some

d i s t a n c e

f rom

h e : t c t i v - l

~

e ru p t i n g

-

~

u , 1 r an e

,

su g g e s t i n g that

gas

exit

v e l o c i t y

f luc tuated

around

t h e

s ; u -

of sound

~~

300 rn s e - i - . Such r - e p o r t . s

o ccu r r ed

dur ing

the 1883

K r a k : m t t

e r u p t i o n s

1

a n d t h e

1902

eruption

of Santa Maria Volcano

in

Guatemala.

4

Thus

~~~

a

~~~

a

~~

e x i t vc

l c , r i t i c

of a p p r o x im a te l

y

300 itt see

may

be

t en ta t ive l

y assoc

iated

w i t h

m a s s i v e P l i n i a n

sc a l e e r u p t io n s .

23. Symons

,

G . J .

(1888)

The Erupt ion of Kraka toa

and

Subs equen t P h e n o m e n a ,

Repor t of

t h e Kraka toa co m m i t t ee of the Royal Sccict v

,

r e p r i n t e d

by

I

I e l i o

l

s -i ociates

,

Inc.

,

Tucson

,

A r i z o n a

,

1974.

24

.

R ose

,

W. . 1972) Bulletin Volcanologique 36: 2 5-4

.

12

-

~~~

- - -

~~~~~~

-

~~~~~

~-


14/36

In this

s t u d y

t h e

m m l a x i r l m u t i c

heig

ht of an e r u p t i o n c l o u d

a

i l l

Is -

:c ,

~~

m u i e c I to

be

i-

e l :i

t ed to

liii- ti m e a

~

-

-

r : c g c - c I c

-up t

ion

vt -b

- i ty c c f

g:c

and f i n e

a ,}c

at

t he i r to u t h m

of

:i

vok -anic ven t

. In otiier

ac

r-ds

,

f l u c t u a t

1 105

in e rupt ion

y e cc

i t t -

a r - c

m a t e on s id

em -cd to be im l ) o i - t a n t

in

c h - t - mu

i r i i r i g t i m e he i

g

ht

( i f

a n

e rup t ion c loud

.

A v e r - a g . -

exit

velin- itie-i

ranging fr-omit

20

nm / s e - c -

t o 200 m rm -ec t i r e t i s s u t

( - ( h

to m

(pr a

s (n t

i

a

m dc -

m t c m i g e i t

erup t ion

in tens it s-

,

f r - o m i t

St

x - m c m ii b o l i a n

t i c

V o k - a n i a n

t

y i c e

~

of c - t - u p t i o n

.

M u c h

l

a r g a - r

e t - u p t i o n

v e l c c c i t i e s on

t ime

em -

c U r

If 600 i i i

/

~

ec

h a v e

l i c e - tm

i n f e r - r e d

for t i n -

b a l l i- I

m u -

t

r - a r m s

lation of

l a r g e

h , l c

,c

Ls of

e

~

cc

t o a

r i d

f o r t i r e f o r ni at ion c

~

f

( - c o

n i c l a

r \

c - n - o t t - c s

c o m r i n i or r l y

i c h u s t - r e a - c I i t

h i s t : c r t c e s of

s e v - c a l

k i l o m e t e r - s

Im -

c c m n

volcanic

v -r t t s

.

2

Such

v c l c c ( i t i e s

a r e

p r - o h a b l y

r io t r e p r e se n t a t i v e

oh

aver-age

e x i t

c

onditions

d u r

i n g

air e r u p t i o n

b u t

r a t h e r

are

a s s o c i a t e d

w i t h

t r a n s i e n t explosive pulses

.

I - i g i m i - e

I

pr-esents

t h e

v a r - i a t i o n

of

c e n t e r - l i n e

~

c - t v e l o c i t y

w i t h a l t i tude

descr ibed

I c y

1 : 1 .

( 2 ) for

:m

c i r c u l a r -

vent w i t h

d i a m e t e r

D 100

m

over a

r

ange

o

f

e rupt ion

i n t e n s i t y

( t h a t

is

,

d i f f e r e n t va lues of erup t ion ve loc i ty w

0

).

Also shown in Figure 1

is

a se

ries

of ver-tical wind profiles

repmesenting

averaged winter crosswind con-

d

itions in

the

Northern

Hemisp

here.

These

averaged

wind

profiles

show

that

zonal

w e s t e r l

y

f l o w

is s t r o n g e r

at

m id - l a t i t u d e s

(Washington

D

.

C. and Flor ida) than at

su b p o ia r l a t i tudes

(Greenland

and the

A l e u t i a n s ) .

A t

a p a r t i cu l a r

a l t i tude the cen t e r l i n e velocity a long the je t

r e p r e s e n t s

the

m a x i m u m u p w a rd

ve loc i ty

of any par t

of

the e rupt ion

cloud. The m ax i m u m

height

t

o w h i c h

vo lcan ic

dust a n d gas wil l r i se as a result of thei

r

ini t ial mo m en tum can

be

a p p r o x im a te l

y

e s t im a te d

as the al t i

tude at w h

i

ch the j e t centerl ine

v e l o c i t y

equals

the local

c

rosswind

veloc i ty .

Fi gure 1 indicates

that for an eruption

veloci ty

of

-

~~~~

20 m sec Strombolian- scale eruptions) the

hei

g

ht of an e rupt ion cloud may

vary

~

c c n n n

~~

l 1500

-

2000

m

at mid-latitudes to

~

H

~~

3500 - 4000 in at

sub

polar

l a t i t u d e s ; w h i l e for an

erup t ion

veloci ty of w = 200

m/sec

(Vulcanian-scale

erup-

t i c , m i s )

t i s - b m e i g h t of an erup t ion cloud

may

vary

f rom

iliF

5000 - 6500

in

at m id-

l a t i i

u d e

~

,

I c ,

~

I l

- 11000

-

17000

m at

subpolar

la t i tudes

.

These

are

maximum

e,timates

of atmospheric penetration based up o n t

he ce nt

erl i

n e

ve l

oc i ty

of the je t

,

not

t h e

a v e - r a g e et

y e l

c i t y

at a p a r t i cu l a r

a l t i tude .

These

-l

oud height

.st int ate s

indicate that an order-of-magnitude

increase

in

e ru p t i

o

n v e - l c c c i t t - s h o u l d r e - c o l t in

a fac tor

of

3

increase

in

the average

he igh t

of an

erup t ion

cloud produced

by

a

m i d - l a t i t u d e e rupt ion

,

and a s l ight l

y

l a rge r

fac tor of

4 increase in the

avera ge h e ig h t

of an

eruption

cloud produced b

y an eruption at

su b pola r l a t i tudes . This method c c f es t im a t ing the he ight of an erupt ion cloud also

i nd i ca t e s

the

impor t an t

in f luence

t h a t

c rossa- inds

have on cloud

he ight . For

a

p a r -

t i c u l a r v a l u e

of

er

u p t io n

v e l o c i t y t h e

average

h e ig h t of an e r u p t i o n

loud

produced

at su b p o l a r l a t i t u d e s

is a p p r o x i m a t e l

y t w i c e t h e

average he igh

t to which an eruption

cloud

w o u l d

r i s e

in the

s t r onge r

w es t e r l

y

f l o w

tha t

occurs

at

m i d - l a t i t u d es

.

2 5

.

Fudal i

,

H .

1-

. ,

and Melson

,

W . G.

(1972)

Bulletin Volcanologique 33:383-402.

13

--

-

--

--.---------.--


15/36

-

-

~~~~~~

0

~~~~~

-

~~~~

~ ~~~~~~~~~~~~~~~~~

~~~~~~~~~

J E

T

CE N T ER LI N E V E

L O C I T Y

I

rn/sec

______

10 rn / sec

100

rn / sec

I

~

r

~

y

r T rv

7_

~

_T_

rI

~

r

I

T H U L E

A L E U T I A N

GREENLAND

~~

I S L A N D S

FLORIDA

10

-

-

9 -

-

8 -

-

WASHINGTON

.

DC

-

-

w

a

5 -

-

4 -

-

3 -

-

2

w

0

20 0 rn / s e

w

0

.IOO

rn/sec

I

-

w

0

20

rn/ sec w

0

.5

0 rn/sec

-

0

m c m l

rn/sec 10 r n / s e c

100

rn/sec

C R O S S W I N D

V

EL O C I T Y

Figure 1.

The

Centerline

Velocity of

a T u r b u l e n t

Volcanic

Jet (heavy

lines)

Co rn -

pared

w i t h

Averaged

Cro s s w i n d Velocit ies ( l i

ght

l ines) at

Var ious A l t i t u d e s .

Je t

cen ter l ine ve loci ty is calcu la ted b

y Eq.

(2 ) for different

values

of w

,

t h e eruption

velocity

at a

volcanic vent. Eruption velocities ranging from 20

m /

~

ec

to 200

rn / s ec are

as sumed to represent

a

w i d e variation in

e r u p t i o n

i n t e n s i t y , f

r

om

Strombolian-scale

erupt ions

to

Vulcanian-sca le

e ru p t i o n s ;

a

vent

d i a m e t e r

D = 100

in

has been as s umed in

all

calcu la t ions . Wind

prof i les a re

averages

fo r

t h e

win ter season

in

th e

N o r t h e r n

Hemisphere.

[ H andbook of

Geophys.

and

Space

Environments

1965)

,

Tables 4-12 through 4-18.

1

14


16/36

-

-

-

-

-c----

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-

-

--:---

--------.-------

- --- - -

,

----- - --

- --------- -

~

--

~~~~~~~~~~~~~~~~~~~

--

~~

:

~~~~~

C ross w i n ds

c a r t

fo

r -ce

an

e r - u p t i o n

cloud

to

bend o c - r and become h o r i z o n t a l

downrange

of

the volcanic

vent . Tle

ac tua l t r a j e c t o r y of an

erup t ion

cloud i t m th e

pr e se nc e of the prevai l ing

c r - t c s s w i n d s

sh

o w n in l-

i

gure

1

can

be

roug

h l

y

a n t i c i pated

b y

the

angle formed b y

t h e

in tersec t ion

of individual

w i n d profiles and

je t

c e n t e r -

l ine

ve loc i ty

c ur ve s . The

a

100

n i /

sec e rupt ion

ve loc i ty

c u r - y e

shown in

1- i g u r e

1 converges at a s m a l l

ang

le w i t h the w i n d p r - o f i l e

for

Thule

,

Gi-eenland

at

an

a l t i t ude

of 12

km. A

c o m p a r i so n

of these

t w c ,

curves ind ica tes t h a t h o r i z o n t a l

c r o s sw in d veloci t i es

a r e

70

percent

as s t ro n g as t ime

v e r t i c a l

center- l ine

ve loc i ty

of

the volcanic

e t

over

a l t i tudes

of

8 t o 12 km

. A n e rupt ion

of t h i i

in tens i ty

into

this

c x - o s s w i n d

e n v i r o n m e n t would thus produce an

e r - u p t n ) n

cloud t h a t

bends

in a

wide

a r c

f r - om

t h e

local v e r t i c a l

d i r e c t i o n . In co n t r a s t

the

- 100

r n / s e c

e rupt ion

~

- e - l c c it v c ur ve

in t e r se c t s

the

w i n d

prof i le

for

Washington

,

D.

C. at

a

much

l a r g e r

ang

le a t an a l t i tude

of

:isoo rn

.

In

th is case

,

the

eruption cloud would bend

th rough a niuch s m a l l e r arc in ntaking

the

t r a n s i t i o n front

p redominan t ly

v e r t i ca l

to

p r - e d o m n i n a n t l

y

h o r i z o n t a l motion

.

F i g u r e

1

ind ica tes

t h a t the

average

a t m o s p h e r i c

penetr-a t ion

of an erupt ion

cloud produced b

y

a

tu rbu len t volcanic

jet should be grea te r

for

e ru p t i on s o ccu r r i n g

at subpola r

la t i tudes

,

w h e r e zonal w e s t e r l

y

f l o w in

the

mid- t roposp

he r e is gener-

a l l y

a e a k e r t h a n at

midd le

la t i tudes

.

As

nt ent ioned p rev i o u s l

y,

the

a ve r a ge height

o f t h e

t ropopause is

lowest

n e a r -

the

poles

~

9 k m ) so

that di rec t

in t roduc t ion

c cf

volcanic dus t and

gas

i n t o the

s t r a t o s p

here

may,

on

the

a ve r a ge

,

be more eas i l

y

acco m p

l i shed

b y

ex p los ive erup t ions at sub

polar

la t i tudes (for examp

le

,

195 ( 1

B e i v m i a n n

y e r u p t i o n

in

K a m c h a t k a ;

1912 K a tm a i erup t ion in Alaska) .

Simi lar l

y,

zonal w es t e r l

y flow

iii sub t rop

ical la t i tudes is

weak

in c ompa r i son with

the

mid-

l a t i t u d e

w e

t c n - l i e s

.

However-

,

the

average

he i

ght

of

the t ropopause is gr e a t e s t in

e q u a to r i a l reg ions

~

1( 1

km). Thus

mas s ive

Pl in i a n - s ty l e erup t ions are general l

y

requ i red

to

d i r e c t l

y

in t roduce

volcanic dust and

gas

into

the

s t r a to s phere

at sub-

t r o p ical

la t i tudes

(for example

, 1883 Krakatoa eruption in

Indonesia;

1963 Mt.

A gtmng

erupti

on

in

Bali).

:i.2 h i s . o f

I

nc lu

=1 Ii sI P

I

urne

~

Waste gases and fine p a r t i cu l a t e

m a t e r i a l

released f rom

indust r ia l s mokes tacks

fornt p

lumes that a r e s o m e t i m e s c lea r l

y visible.

The

r a t e

at

which indus tr ia l

e f f luents en ter the

atmospher-e

,

though widely var iable

,

is generall

y

s imi l a r to

some

f o r m s of fumarol ic

and

weakl

y-explos ive

volcanic

act ivi ty. The m a x i m u m

gas

d i s ch a rg e r a t e s

of

c c c m , t m e r c i a l

power

p

l an t s a re on the

order of

l0

~

m

3

/ s ec

(Table 5. 1

,

R e f

12)

in

c ompa r i son

to

a

peak gas flux of 2

X

~~~

m

3

/sec

obser

ved

in

the

in i t ial

phases of individual exp

losive

b u r s t s f ro m a volcanic

vent at Stromboli

by C hc iu e t

et

al

18

The

r a t e

a t which t h e r m a l

energy

is released b

y such indus t r i a l

15

-

-

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

---

-

.

-

-

~~

- -

.

~

~~~~~~~~~~~~~~~~~

-

~

-


17/36

-

~~~~~ ~~~~~~~~~~~~ ~~~~~~~~~

-

t a c i h i t i e s is t y p i c a l l y

l ess

than

S

y

~~~

c a l

se c

,

whereas

the gas

pha se t r a nspor t

c c f t r e a t away f rom t h e

surface

of t h e

permanent lava lake at the

Nyir-angongo

-

-

8 26

\

c

.

c l c a r i c c

has

been

e s t im a te d

to

be

10

ca l / sec

b

y

D el s em m e (see

also

m i l ( c z u

ru

~~~~

.

E r - o p t i o n

cloud

heigh t s

of

s evera l

hundred m e t e r s

observed

for Strombolian-

s ty

le ct-options

(see

A

~~ ~

endix A ) a r e c ompa r a b l e

to the

plume he i

g

hts repor ted

for

a

v a r i e t y

of i n d u s t r i a l

s ou rces

(see

,

for example

Briggs

28

).

In

the

case of ma jor

exp

losive e rupt ions

( t h a t

is

, V u l can i an - s ca l e e ru p ti o n s ) exit condi t ions at

volcanic

y e n / s

d i f f e r

s ign i f i can t l

y

f rom those commonl

y

found at the mouths

of

i n d u s t r i a l

s m o k e s t a c k s

.

1 - x i t

veloci t i es and m a s s

flux ra tes

assoc ia ted

with majo r

ex p

losive

e r u p t io n s

grea t l

y

exceed the

r a t e at which indus t r i a l

e f f luents typ

icall

y en t e r th e

a t r i o s p

he r e . (Fo r e x a m p

le

,

T hor a r ins son

and Vonnegu

t

13

e s t i m a t e

that

dur ing

th e

in i t ia l

s t a g e s of the

19( 13

S u r t e sy

et - up t io n i

,

thermal energy was emi t t ed a t a

ra te

-

10

-

-

in

excess of

10

cal sec . ) As a r e su l t

,

e rupt ion

clouds produced b

y Vu

lcanian -

style

erup t ions can eas i l y

dwarf

most

in d u s t r i a l

p

l u m es

. The crosswind environ-

ment

into

which

indus t r i a l

ef f luen t s

and

volcanic

dust

and

gas are emi t t ed may

also

be

qu i te d i f fe ren t .

Explosive

erup t ions c o m m o n l

y

occur

at the

s u m m i t s

of

large

s t r a tovo lc a noe s w h ere

c ro s s w i n d s are

l ikely to

be

considerabl

y

s t ronger

than

those typica l l

y encountered b

y

indus t r ia l e f f luents .

A var ie ty of t h eo re t i ca l and em p i r i ca l

ex p re s s i o n s

have

been proposed

to

e s t i m a t e

the

maxirnunt r i se

he i

g

hts

of

in

d u s t r i a l

plumes

. Appl ica t ion

of

t h e s e

indus t r i a l l

y- ba se d fo rm u l ae to ex p

losive

erup t ion

c o n d i t i o n s

involve

s

an

extrapola-

t i on

of these

various

expressions

b e y o n d

t h e range of ex i t c o n d i t i o n s fo r w h i c h t h e y

w e r e

developed.

As ment ioned

prev ious ly ,

t h e re is

an ap p ro x i m a t e

c or r e spond-

en ce be t w een the he ights

of

p

lumes produced b

y

large

i n d u s t r i a l sour c e s and

th e

he i

ghts

of

erupt ion clouds

produced

b

y

a e n k l y - e x p

los ive

S t r o rnbol ian-s ty le

erup-

t ions . A t these

scales v e r t i c a l

p e n e t r a t i o n

of

the

a tm o sp

h e re b

y indus t r ia l

l ) l u f l i e s

and

e rupt ion clouds

is

roughl

y compar-able. Extr-apola t ion

of i n d u s t r i a l l

y-based

plume r i s e e xpr e s s ions

beyond

this

scale

to

m o r e

explosive

e rupt ion cond i t ions ia

employed

he r e

as

a

me a ns

of

inves t i

ga t ing

t h e

r -e la t ionshi

p

be tween the

he igh t s

of

erupt ion clouds and e rupt ion

in tens i ty .

The

r i s e of

i n d u s t r i a l

p

lumes is predom-

inantl

y cont ro l l ed b

y

the

t he r ma l buoyancy of

i n d u s t r i a l

e f f luents .

E s t im a te s

of

the heights of erup t ion

clouds

based

upon

the

behavior of i n d u s t r i a l plumes

can

be

co m p ared w i t h

repor ted cloud hei

g

hts and e s t i m a t e s of

erupt ion

cloud

h e i

ght

based

upon

the

tu rbulent jet model in order to

assess

the r e l a t i ve

impor tance

of t h e r t -mt a l

buoyancy in

the rise of

eruption

clouds.

26.

D

elsemme

,

A , (1960) Centre

N a t i o n a l

de

V o l c a n

,

P

u

bl

.

7: 1199-70 7

.

27.

Shintozuru

,

D.

( 1 9 6 8 )

Bul le t in

Volcanologi

que

32:383-394

.

28 . Br i

ggs

,

G . A .

(1971)

Nuclear

Safe t

y

12:15-24.

1(1

-

- - - - - -

------

~~

-- - - -

- _

---

-- -

_- -

--

- - - _

-

--- -

- - -

~~

--- --

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


18/36

-

-

__

~

w v c

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.

__=

~~~~

-,=_-_--__-

_

-

~~

___-

_

~

_ _-.--,. --_

_ _____

-

--

__ _ -

---

-

-------

.

--

--

-

-

-a-

~

_

-

~~

The

r i s e of i n d u s t r i a l

p lumes

e m a n a t in g f rom smoke s t a c ks has been found to

d epend

upon :

( I )

the

v e l o c i t y of

the e f f l u e n t

at

the mouth of

the

stack

,

( 2 ) th e

t em p era t u re co n t r a s t

between

the

e

ffluent and the

ambient

a tmosphe r e

,

(3) th e

m c c

ss sectional area of the stack

,

4)

the average crosswind

speed

at

the

heigh t

it w h i c h the effluent is

re leased

,

and

(5 )

the thermal s t r u c t u r e of the

a t m o s ph e r e

( t

h a t is

,

the var ia t ion o f

envir-on inenta l


w i t h

height) .

The

fo l lowing

f o r m u l a e

emp

loy v a r io u s

combinat ions of t he se pa r a me te r s to es t i m a t e the maxi-

m u m

heig

hts of

indust r ia l p lume-s

(see

al so

Figure

2) .

These fo rmulae have been

2

d i s cu s s ed in

g r - e a t e i -

d

e t a i l

b

y

Briggs .

-

ERUPTION

CLOUDS

THER

~

AL PLUME MODEL

-

_

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-

~~~~~~~~~~~~

~~~~

Fi

gure

2.

Parameter-s

E m p l o y e d i n the I n d u s t r i a l

P l u m e

Forntu lae

Used

for Pre-

d i c t i n g

P l u m e

R i s e

.

29. Briggs

,

G

. A .

(116 8)

M o m e n t u m a n d b u o y a n c y e f f e c t s

,

i

n

M e t e o r o l o g y

and

Atomic

E n e r g

~

,

D.

Slade ( E d )

,

U S A E C

R e p o r t T I D

24190 .

17

-

~~~~

--- -

--

-

-- .---

_ -

_--__-

_--

-

-

--

---

-

- - - -- - .--_--

-- - - - - -

--- -

-- - -

_

_

---

_-------

-

--.

_- -

-

~~~~~~~~~~~~~

~~

~


19/36

-

_--

--

-

-

-

- - _ -

-

;----

1.

l c i l l a t m h

( O a k

I t i i .

l

gc-) I - i c r t i i i ib i

1

( I

tV

c 3 )

~~

h

I

.

- d )

~~

c c

4 . 0

~

o

5

s-

-

(Q

11

is h e a t

f l u x in

i - a l

s e e )

2 .

f ) a v i n l s o n - B r -y a t m h

_

i i

c r n i u l a

1

( I t i S 4 )

~~

I

I )

~~~

_

~

.

4

(I

.

.

B o s an qu c t

F o r - n m u l a

32

f

Stable

conditions

,

w i n d

y

1957)1

0

.

6 l 5 X

0

1

2

i

~

l l

A u

f

1

+ f

2

2

1 - 2

((;2)

0 .57 )

(See

Bosanque t

32

for

definit ion of var iables

A and

X ;

values

of

func t ions

and

1

9

a r e

g iven

in t abu lar

f o r m a t )

4 .

13o-sanquet

Forn-

m u l a

3 2

[Stable

conditions

,

calm

( 1 9 5 7 ) 1

~~i i =

O

.

666

( g Q

~~~

T \

1 4

( t + t

)

3/4

- .

t

3 / 4

0 .

2 8 3 ( Q

~

/2

2

~

T

j

0

2

0

a

~

w

/

(See Bo sanque t

12

for

definit ion

of

var iables

a

,

t

and t

0

;

Q

is

effluent

d i s ch a rg e

ra t e

in

m

3

/

sec)

5. Stiimke

Formula

3

~

(1963 )

=

I

.

SD

(-;

~

--)

+

6 5 . 0

D

3 12

( A

T )

l / 4

30

.

Holland

,

J . Z.

( 1 9 5 3 )

USAEC

Repor t ORO-99

,

Weather Bureau

, Oak R i d

ge

T cnn.

31.

Davidson

,

W

.

I-

.

( 19 5 4 )

l

r - a n s

. C o n f .

m d .

Wastes , 1 4 t h Annua l

Meeting,

pp. 38-55

,

Indus t r i a l

h

ygiene Foundat ion of A m er i ca .

32

.

B o sa n q u e t

,

C .

H.

( 1 9 S 7 )

J. I

nst . Fuel

30:322328.

33. St

~

rn k e

, H.

( 1 9 6 3 )

1

.

S. A t o m i c

Energy

Co m m i s s i o n

Repor t

ORNL-TR-077

Oak

R i d g e N a t i o n a l

Labo

a t o r y .

18

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-

~~~

-

~~

-

----

- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-

- -

~~~~

-d

.


20/36

-

_ _

~~~~~~~~~~

-

~~~~~~~~~~~~

-

~~~~~~~~

i r i

~~

u s

i - c r

c i i l a

1

(

~~

a d h c 1 c c c c r i c l m t i c c i c - \%

in ( h

y

( l t l I c

~

d ) J

~~

i

L 0 (

~~

~

7

. l i i g

~

.

Ic c i1 l

u l a

~

t ah c I c - c a c n c h i t I c c r t

~~

c a l r i m

(

l d di

c d ) I

1

.

_ I

4

~~

h

. 0

h i - c e

~~

1 I p lume r i s e h e i g h t

d cc

c v i -

ven t

(m )

I)

v e n t d i a m e t e r

(

or )

v e t - t i c a l

exit

v e l o c i t y

a t

vc - r r t

mouth (n t

see)

u a v e r a g e c

r c , s - c w i n d

speed

(m u

sec- )

~

T

d i f f e m - e n c e in a b s c c l u t e

t empera tu r -e

be tween

a n m b i e n t a i r and

e f f l u e n t

gas

( K)

T

-

absolu te

t e m p e r - a t u r - e

of

e f f l u e n t s tack

gas

(

K)

T

a

absolu te

t e n i p e r - a t u r e of ambient a t m o s p h e r e

(

K)

buoyancy

f l u x

1-

-

g

~

41)

w

( D )

2

(n t

4

/ s e c

3

)

S

=

a tm o sp h e r i c

s t a b i l i t y

p a r a m e t e r

-

~~~~

-

~~~~~~~

-_

(1

,

- s e e

2

)

9 8

K

r F

-

~

1000

in

-

-

-

d

.

r e n v i r o n m e n ta l l apse

r a t e

=

aT

: dZ

(

K

n i t )

g

grav i ta t iona l a c c e l e r a t i o n

(9

.

8 ru

see

2

)

These various formulae a r e based upon both

l a b o r a to r y

ex p e r i m en t s

and

obser-

vat ions

of

t h e ac tua l behav io r of indus t r ia l p

lumes

. Each f o r m u la

produces r eas on-

ab l y a c c u r a t e

e s t i m a t e s of

p lunt e

r i s e

w h en

ap p

l ied to ce r t a i n

types of

meteorolog-

iea l

condit ions and

a

spec i f ic

r - a n g e

o f e f f l u e n t

s o u r - c - c

s l r i - n g t h i .

N o single

t echn ique

can

a c c u r a t e l y

predic t

p lume

he i

g

ht in all cases

.

h - c r

e x a m p le

,

t h e Holland (Oak

H i d g e )

formula

i s based

upon

w i n d

tunnel e x p e r i m e n t s and e m p i r i c a l

o b se r v a t i o n s

at re la t ive l

y sm a l l

power

p

lants opera t ing in t h e 1 9 50

s

. W h e n ap p

l i ed

to

e x p l o s i v e

e r - u p t i o n

c o n d i t i c c .

t h e

Holland

(Oak

R i d g e ) f o r m u l a

; c m - e c h i c t s u n r e a s o n a b l y

l a rg e

cloud

h e i g h t s . (Fo r

values

of g r e a t e r t h a n

l 0

~~

e a l/ se

t h e h olland formula

1

-

-

--

- -


21/36

~~~~~

-

~~~~~~~

pm -

(

-d h

m ( - ts

et -up t i on

c l oud

h e ig

h t s o

n t he order

of 50 km.

)

The

r e m a i n i n g

e q u a t i o n s

p u -

e

-

~

ented

a bc ,v - produce r e a l i s t i c e s t i m a t e s of e rupt ion

cloud height when ap p

lied

t c c

e x p l o s i v e

e r u p t i o n

cond i t ions

a s su n ed

in

this

s tud

y.

By co n s i d e r i n g

s evera l

methods

of

e s t i m a t i n g plume height

it

is

poss ible to make a meaningful e s t ima te

of

e r u p t i o n

cloud

he i

g

ht based upon the

behavior

of indus t r i a l p lume s .

l able

I p r e s e n t s the

c - a l c u l a t e d

heig

hts of erupt ion clouds above an activel

y-

e r u p t i n g v

c l r - a n i c

vent

for

the

case

of

a

volcanic ga-s

(T

,

= 373

K)

en t e r i n g th e

ambient a t m o s p

here

(T

a

S

2 7 3

K)

v i a a

c i r cu la r

vent

o

d ia me te r

U

100 in. It

has

been

as s u m ed he r e

t h a t

the

e rupted gases

expand rap

id l

y and cool

f rom

th e


at w h i c h

the m ag m a

is

e rupted to

100

C

such that they e f fec t ive l

y exi t

the

c r a t e r

at

the

l a t t e r t e m p e r a t u r e. Small changes in

T

a

or

T

5

w i l l not

gr e a t l

y

affec t cloud

height e s t i m a t e s

in Table 1. These e s t ima te s

have been rounded to

the

neares t 100 in

in recogni t ion

of

the

l a rge

ex t rapo la t ions involved in ap p

l

y

ing

th e

i n d u s t r i a l p lu m e f o r m u la e to ex p

losive

erupt ion condi t ions.

Actua l

observa t ions

of

the

he ig

hts of

e rupt ion

clouds

are commonly es t imated

to the

neares t k i l o m e t e r

(see

A ppendix

A ) .

A v a r i e ty

of

combinat ions of erupt ion veloci ty

and

crosswind

veloci ty

has been chosen to r ep res en t an i nc rease in erupt ion in tens i ty

f rom th e

l e f t

to r igh t

of

Table

1.

Exp

losive erup t ions typ ica l l

y occur at the s u m m i t s

of

l a rge

s t ra tovolcanoes

w h ere

average

crosswind

veloc i t ies a re on the order

of

10 to 30

n i s e c .

Est ima ted he ights of e rupt ion

clouds

v a ry

f ro m 900

-

10

,

000

m for

Strombolian-

sc a l e e ru p t i o n s

(w

0

=

20

m/sec)

to

3 2 0 0

-

8500

m

for

Vulcanian-scale eruptions

W

~

200 m/sec)

in Table

1

. The

S tn

~

mke formula

appears

to

pred ic t unr e a sona b l

y

l a r ge

cloud

heig

hts

(

~~

H 10

kin ) for r e l a t i v e l

y

sma l l

,

St r omool ian-sca le erup t ions

(w

20

in

see);

and the

Briggs

and Bosanque t fo rm u l ae

for calm condi t ions may

be cons

idered

to

be

inappropr ia te fo r

the

upper

levels

of

the

a tmosp

here

w h ere

c ro s s w i n d veloc i t ies a re usual ly

grea te r

than

5

n t / s e c

.

A more se lec t ive range

of

e s t ima te s can he based upon the

D a v id so n - B r y a n t

,

Bosanque t (stable condi t ions ,

w i n d y)

and

Brigg s

( s tab le

condi t ions

,

w i n d y )

fo rmulae

.

D is r e ga r d ing

the

Stiimke

f o r m u la

,

e s t i m a t e s of cloud height in

the

pres ence of a

c ro s s w i n d

vary

f r o m

900 -

4000 in for Strombolian-scale eruptions

(w

20

n-

c / s e c )

to

3200 - 8400

in

for

Vulcanian-sca le e rupt ions

(w

0

=

200

rn / s ee ) . Based upon these e s t i m a t e s

,

it

would

appear t h a t an order of magni tude var ia t ion in

e r u p t io n

veloci ty

will

not

neces s a r i l

y

resul t

in a major change in e rupt ion

cloud

heigh

t

. A compar i son of the median

value of c l oud h ei ght selec t ed f r om t he range

of estimates

predicted for these tw o

cases of e ru p t i o n condi t ions

suggests

t h a t an

or de r

of

magnitude inc reas e

in erup-

Hon

i n t e n s i t

y should result in a f a c t o r of

2.

5 increase in m e d i a n c l oud h e i g h t .

A

c ompa r i son of

t h e D a v id so n - B r y a n t

,

Bosanque t ( s tab le condi t ions

,

w i n d

y )

,

and Briggs

(stable

conditions

,

windy) fo rm u l ae for an

eruption velocity

of

w

0

= 200

r n / s e c

under

d i f fe rent

c ro s s w i n d cond i t ions

ind ica tes t h a t

cloud height

varies f rom

20

-

- ---

_______

-_


22/36

--

-

~~~~~~~~~~~~~~~~~~~~~~~~~

--

-

~~~~~~~~~~~~~~~~~~~~~

I

-

~~~~~

I

-

o

~~~~~~~~~

-

,

I

-

~

1

~~~

:

i

~

C

nfr

-

-

~~~~~~~~~~~~

~

ncr

o c

~

C

C

C

-

0 - 0

0 : 0

7 - .

0.. I

C

~

l t- c n- c c

-

~

: -

~~~

-

~~

-

-

~

,=

C 1 - e

- e -

I-.

- - -

, - -

-

-

U

Hr

:;

I E

o ~~~~~~

0 0

C

0. O

~~~

O

~~

-

~~

- ,

0 1 0

0

0

~~~~~~~~ =

~~~~~~~

~~~~

,

~~

I

S~~~

E

I

~~~~

e I c l o - o o o

~~~

o

[ o l o

o

I o

o

0 - 0 0 - 0 0

0 0

l

0 0 0

-=

- c-, -)

C)

I

0 0

C

C)

-)

f i 4

0

~~

-t

I

I

0 cc en

-

cc

~~

in .f

~

~~~~

~~

O -

-

I

~~

I

J

I

~~~~~~~~

-

~

~~

~~~~~~~~~~~~~~~~~~ ~~~~

n . e

-

~ ~ ~

~~~

-

~~

-

~~~~~

L-.

.-----

~~ ~~~~~~~

I

~

L

-

~~~~~~~

-

-

-_

-c

-

-

~~~~~~~~~~~~~~

-

~~ ~~~~~

~

~~~~~

~~~~~~~~~~~~~~~

--

~ ~~~~~~~~

5

~

9

~~~ ~~~~~~~~

21

__


23/36

_

~

~~

_

~

_

~

z =

~~~~~~~~~~~~~~~~~~~~~~

--

- _

~~~~~~~~~~~~~~~~~

~~~~

-

~~

_

~~

~~~~~~~~~~~~~~~~~~~~

-

-

-

~~

I

= 3700

8 4 0 0 in t c r

c r c

~~

sWj i td

u 10

i t t / s ec

to

~~

1 = 3200 53

00

in

he i r

er o s -

.-

w

ind

u

20 m

s e c -

.

T h u s v a r i a t i o n s

in

c - r m s s w i n d

condi t ions may potent ia l l

y

he

as

s ign i f i can t as

v a r - i a t i o n s

i n n erup t ion

velocity

in

d e t e r m i n i n g

the

hei

g

h t

of an erup-

t i o n cloud.

In

addit ion ,

Table I d e m o n s t r a t e s that var ia t ions in the t h e rn t a l

st ruc-

t u u - e

of t h e a t m o s p h e r e

(F)

can also I t a v e an impor tan t influence on e rupt ion

cloud

h e i g h t .

I.

I ll

=

~

I

The p

h ys ica l m i t e c h a n i s m s responsible for

the r i se

of

an

erup t ion cloud

a re th e

u p w a u - d n a c n t e n t u m and

t h e r m a l

buoyancy

of the

volcanic dust and

ga s .

Each of th e

ana logous phenomena

employed

l u e r e

to model the

r i s e

of an e rupt ion

cloud is p r i n -

ci

pa l lv dependent on

c O O

of

these

two ph

ysica l

n mec ira n -n i s ms .

By compar ing

cloud

h e i g h t e s t i m a t e s

produced

by

these

t w o

ve ry

d i f fe ren t models

,

i t

may

be poss ible

i r e c - r -

w h i c h

c1 t h e t w n m e c h a n i s m s pla s a mor e

in t ipo r - t an t

role

in the

r i s e

of

v c , l can i c

e r u p t i o n c louds .

I - : s t i m a t e s of

e

r - o p t i o n

cloud

height

based

upon t h e

tu rbu len t je t

model

a r e a

- l e a s u r e

of a t m o s p h e r i c pene t ra t ion produced

by

t h e upward

m o m e n t u m

of

volcanic

dust and gas . Cloud

height

e s t ima te s based u p o n the

i n d u s t r i a l

p

l u m e m odels a re

a m tr e a s u r e

of

a tm o sp

h en - i c

p e n e t r a t i o n produced b

y

t ire thermal buoyancy

of

volcanic

gas . For e rupt ion

v e lo c i t i e s

vary

ing

f r - o r - n

20 t o 200

m

see

,

cloud

heights

e s t i m i t a t e d

by

t h - - tu rbu len t j e t model

r

ange f rom

1500

-

6500

rn

ut-

rid-latitude eruption in

Figure

1)

,

w h ereas cloud

heigh t s

e s t im a te d b

y

t l t e i n d u s t r i a l plunte models range

f r o n t 900

-

8400 m

(p re fe r r ed

models

neg lec t ing Str i imke

F o r m u l a and

calm con-

dit ions

in

Table

1).

T he se e s t ima te s

o f

cloud heigh t a re

consider-ed

to

be roug

h l

y

contparab le in view of the as s u m p t i o n s

and

ext rapola t ions involved in

appl

y

i n g the

models to exp

losive

erupt ion condi t ions . The

fact

t h a t g en e ra l l y

s i m i l a r

e s t i m a t e s

of

cloud hei

ght are

produced

by two very

d i f fe ren t

models sugge s t s

t h a t

both

m it o i t i e n -

t u r n

and t h e rm a l

buoyancy

p lay an impor tan t ro le t h roughou t

t h e

u

~

t a i n

por t ion

of

an

e

ruption clouds

traject

ory.

For

these eruption

c

onditions 20 i i i sec

~

w

~

200

n t - s e c t n e i t h e r m o m e n tu m

nor

t h e r m a l buoyancy appears to domina te t h e

) n a c c ( 5

S

~

f

cloud

r i s e

to a l t i tudes

of

10 km above an ac t ive ly-erup t ing volcanic

vent .

Both

the

t u rbu l en t jet and the i n d u s t r i a l

plume

models ind ica te

t h a t

for con-

s tan t

crosswind

condi t ions

ire

height

of

an e rupt ion cloud should i n c r e a s e

as erup-

t ion intensi t

y

( t h a t

is

,

a ve r a ge erup t ion ve loc i ty

w

0

)

i nc r e a se s . A n

o r d e r -

of rt t a g-

n i tude

var ia t ion

in erup t ion

ve loc i ty

front

w

0

20

n t -

sec

to

=

200

n i t

sec

r e s u l t s

in a fac tor

of 3

to

4 inc reas e

in

average

cloud height predic ted

b y

t h e tu rbu len t

volcanic

j e t model

,= n d

a fac tor

of

2. 5

i nc r e a se

in median cloud hei

ght

pred ic ted

by

the se lec t group

of

indus t r i a l p

lume

models

holland's formula and volcano.pdf

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