Energy Efficiency Investments at Holland's Largest Pension Plan
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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
-
8/10/2019 holland's formula and volcano.pdf
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
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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
,
I
,
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
C
~~~~~~
~
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 _ _ _ _ _ _ _ _
-
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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
~
.
~~~
, .::
.
-
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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
~~~~ ~~~~
--
.-
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8/10/2019 holland's formula and volcano.pdf
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?
~~~~~~
-
~~~~~~~~~~
~~
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~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~
**
~~~~~~~~
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 -
-
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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
--
-
-
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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
_ _
~~~~~~
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~~~~~
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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-
--
-
----
-
~~~~~
- -
~~~~~
~~~~~~ ~~~~~~~~~~~~~~~~~~~
--
-
8/10/2019 holland's formula and volcano.pdf
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
---
--
-
8/10/2019 holland's formula and volcano.pdf
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
-
8/10/2019 holland's formula and volcano.pdf
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
-
~~~
- - -
~~~~~~
-
~~~~~
~-
-
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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
--
-
--
--.---------.--
-
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-
-
~~~~~~
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
-
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-
-
-
-
-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
-
-
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
---
-
.
-
-
~~
- -
.
~
~~~~~~~~~~~~~~~~~
-
~
-
-
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-
~~~~~ ~~~~~~~~~~~~ ~~~~~~~~~
-
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
-
- - - - - -
------
~~
-- - - -
- _
---
-- -
_- -
--
- - - _
-
--- -
- - -
~~
--- --
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
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-
-
__
~
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
t e m p e r a t u r e
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
-
~~~~
--- -
--
-
-- .---
_ -
_--__-
_--
-
-
--
---
-
- - - -- - .--_--
-- - - - - -
--- -
-- - -
_
_
---
_-------
-
--.
_- -
-
~~~~~~~~~~~~~
~~
~
-
8/10/2019 holland's formula and volcano.pdf
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
.
-
8/10/2019 holland's formula and volcano.pdf
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
-
-
--
- -
-
8/10/2019 holland's formula and volcano.pdf
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
t e m p e r a t u r 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
-
- ---
_______
-_
-
8/10/2019 holland's formula and volcano.pdf
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
__
-
8/10/2019 holland's formula and volcano.pdf
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