NASA-CR-204806

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. BI2, PAGES 24,51)9-24,519, DECEMBER 111, 1995

The dynamics of rapidly emplaced terrestrial lava flows

and implications for planetary volcanism

Stephen Baloga

Proxemy Research, Inc., Laytonsville, Maryland

NASA Goddard Space Flight Center, Greenbelt, Maryland

Paul D. Spudis

Lunar and Planetary Institute, Houston, Texas

John E. Guest

University of London Observatory, London, England

Abstract. The Kaupulehu 1800-1801 lava flow of Hualalai volcano and the 1823 Keaiwa

flow from the Great Crack of the Kilauea southwest rift zone had certain unusual and possibly

unique properties for terrestrial basaltic lava flows. Both flows apparently had very low

viscosities, high effusion rates, and uncommonly rapid rates of advance. Ultramafic xenolith

nodules in the 1801 flow form stacl_s of cobbles with lava rinds of only millimeter thicknesses.

The velocity of the lava stream in the 1801 flow was extremely high, tit least 10 m s _ (more

than 40 km h l). Observations and geological evidence suggest similarly high velocities for the

1823 flow. The unusual eruption conditions that produced these lava flows suggest a floodlike

mode of emplacement unlike that of most other present-day flows. Although considerable

effort has gone into understanding the viscous fluid dynamics and thermal processes that often

occur in basaltic flows, the unusual conditions prevalent for the Kaupulehu and Keaiwa flows

necessitate different modeling considerations. We propose an elementary flood model fl)r

this type of lava emplacement and show that it produces consistent agreement with the

overall dimensions of the flow, channel sizes, and other supporting field evidence. The

reconstructed dynamics of these rapidly emplaced terrestrial lava flows provide significant

insights about the nature of these eruptions and their analogs in planetary volcanism.

Introduction

The 1800-1801 eruption of the Hualalai volcano and the

1823 eruption of Kilauea volcano provide unique opportunities

for investigating the dynamics of rapidly emplaced lava flows.

These eruptions featured unusually high rates of discharge

combined with relatively low lava viscosities, conditions

thought to be present in certain planetary settings. The overall

dimensions, planimetric forms, and general morphologic characteristics of these Hawaiian flows seem to suggest physical

processes of emplacement that are usually considered commonplace in basaltic volcanism, for example, laminar viscous

fluid flow, cooling by radiation, incipient crystallization, and

the formation of an insulating surficial crust. However, it has

long been known that these flows are relatively unusual among

terrestrial basaltic eruptions [e.g., Stearns, 1926; Richter and

Murata, 1961] in featuring such high volumetric rates of effusion and low magma viscosities.

More than 50 years ago, Nichols [1939] correctly pointed out

that sufficiently slow-moving lava flows should be treated quantitatively by laminar viscous fluid dynamics, rather than a

semiempirical formalism for turbulent water flow. Nichols also

noted, in effect, the defining condition for a sufficiently slowmoving laminar flow, namely, that the movement of any iliaCopyright 1995 by the American Geophysical Union.

Paper number 95JB02844.

0148-0227/95/95J B-02844505.00

ment within the flow is locally parallel to all other filaments.

With noteworthy insight, Nichols [1939, p. 294] proclaimed that

inferences about the dynamics of lawl flows "can be determined only if it is known whether the flow was turbulent or

laminar." A slight overstatement of the case for viscous fluid

flow precedes this insightful remark, that "'gravity does not

succeed in making the liquid of low viscosity flow more rapidly

than the more viscous liquid, because the liquid of low viscosity

uses up energy in turbulence .... " When a free, unconfined

upper surface is present, additional volumetric flow rate can

always be used to increase the mean flow velocity, although this

is not as efficient for turbulent flows. Inferences drawn by

Nichols for the Alika flow of the 1919 Mauna Loa eruptkm and

a distal segment of the McCartys flow in New Mexico included

a laminar flow regime and flow adwmce rates of about 2 m/s

and (I.2 m/s, rcspectively.

Numcrous works treating lava emplaccmcnt with the concept of laminar, viscous tluid flow have appeared since Nichols'

publication. With the aid of more detailed observations of

basaltic lava flow emplacement, wc know today that thc concept of laminar flow with all elements moving in parallel is

certainly not always valid. In addition, advancc rates for many

basaltic lava flows havc been significantly greater than thc

range of values infcrrcd by Nichols.

Thc classical view of turbulence in fluid flow features statistically correlated, timc-dcpcndcnt fluctuations in thc components of flow velocity. We still cannot make the assertion of

turbulence in lava flows in the classical sense. Howcvcr, pure

24,5O9
24,51() BAI.()(;AET AI..:RAPII)I.Y I(MI'I.A('liI)_AV\ II.()WS

laminar flov,, is clearly somewhat of a special case due to

mixing, disruption of streamlines, irregular Ilov, bcd lopogl-aphy. breaks in slope, and other factors [sce Crisp and Baloga,

1994 I. It is unfortunate that the term "disrupted flow" [Daughertv and h'anzini, I_;(:] has never been ,_,i,h,V,, ,,ecepted in the

seientilic literature for naturally occurring conditions between

pt, rc laminar flow and clz,ssical turbulence.

Fiekl evidence and several critical observations indicate that

the cmplacenlenl of the 18t)0-1801 Hualalai and 1823 Kilauea

flows resembled a rapid flooding by lava, rather than a relatively slow-moving, laminar advance of a cooling and crystallizing viscous fluid. In this work we resurrect an approach that

has resided in desuetude tot more than half a century and

propose a floodlike model for low-viscosity, high effusion rate

flows. Wc show that a reconstruction of the llow dynamics

provides quantitative and qualitative results that arc consistent

with several types of field evidence. The dynamics of such flows

are sealed for gravity differences to illustrate the influence of a

planetary setting on these unique terrestrial analogs.

Geological Observations of the 1801 and 1823

Lava Flows

Reconstructing the dynamics of flow emplacement requires

several types of geological observations to ascertain the important physical processes that governed flow behavior. These

observations include the lluid behavior of the molten law_ at

wlrious stations ahmg the path of the flow, field evidence on

flow behavior and fluidity, and dimensional and morphologic

considerations. Details of the known and inferred properties of

the flows considered here arc summarized below.

The 1801 Hualalai Lava Flow

The geology of this flow. also known as the Kaupulchu fllow,

is described in detail by Richter and Murata [1961 ], McGetchin

aml Eichelbeg4('r [1975], ,hwkson et al. [1981], and Guest et al.

[ l'm5l. BricIly, it is an alkalic basaltic aa flow, having abundant

channels, erupted from a tissurc zone at about 1700 m elevation along the northwest rift of Hualalai volcano (Figure 1).

The llow trends down slope to the north for a distance of about

15 km to the sea and, from there, about another 5-6 km into

the ocean. The remaining deposit of lava is relatively thin at

the margins of the flow with thicknesses of 2-3 m near its

source vent and thickening only slightly at the margins to about

5-8 m near tile ocean.

The 1801 flow is rcmarkablc for its beds of xenolith nodules

[Richter and Murata, 1')611. The xenoliths appear to have been

emplaccd as _, cobble lag dcposit and, in some places, as an

ovcrbank levee deposit [Guest el al.. 1995 I. Rinds of lava on the

nodules (Figure 2) indicate that the effective viscosity of the

host [ava during nodule emplacement was extremely low, of

the order of 102-10 _ P ( 101-102 Pa s) [McGetchin et ul., 19"76].

l)rainagc is similar at all locations ahmg the path of tim flow

where nodule beds arc exposed. There is no evidence from the

rinds for a significant systematic change in viscosity, or other

rbcologic parameters, with distance from the vent.

The flow traversed the 15 km from the vent to the sea

extremely rapidly. The timescalc for the development of a

signilicant crust is typically tens of minutes to a few hours

[('risp and Bah{ga, 1990]. The lack of any significant crust on

the flow suggests an cmphtcement time of that order. This

infcrencc is also supported by the documented time of approximately 1 hour quoted by KilLs [1842 I. Guest et al. [1095] indcpcndently estimate a flow velocity near the vent of at least I(I m s _,

based upon the uphill i]o_, of lava around a preexisting cone.

Lava channels near the beds ofxenolith nodules can bc quite

large, up to 80 m across and 18 m deep (Figure 3). The

draina_,e ,_t"the ncuhl _"1:_a_ both toward the upper reach of

the flow and below the highway, the presence of lava overspills,

and the lack of a dramatic longitudinal increase in flow thickness, all provide evidence for a very low viscosity host fluid.

The 1823 Kilauea Lava Flow

The 1823 Keaiwa lava flow from the southwest rift zone of

Kilauea volcano also possesses several remarkablc features

that suggest unusual eruption conditions [Steams, 1926]. The

flow is a basaltic tholeiitic pahoehoe lava flow that changes to

a slabby aa surface at its distal margins. The flow vent is a linear

feature called the Great Crack and is between 1 and 1(1m widc (m

most places averaging about 3 m) and about 10 km in length

(Figure 4). The flow near its source vent is thin, ranging from 2 to

3(I cm. Nowhere does the flow thickness exceed about 2 m

[Stearns, 1926] and 1.5 m is a reasonable estimate of the average.

The tlow traveled down slope at an angle to its source vent. Thus

flow lengths vary from 1.5 to about 5 km. The total area of the

flow is about 25 km 2, of which some unknown but probably small

fraction is submarine [Swarm', 1926].

Observations of the eruption testify that lava issued from the

Great Crack very rapidly in the form of a sheet that quickly

flowed to the ocean, overwhelming a village and overtaking

fleeing natives [Ellis, 1842; Stearns, 1926]. Although this flow

contains no xenoliths, accretionary balls of lava display very

thin (centimeter size or smaller) layers of lava plastering, suggesting a very fluid magma. During the eruption, flow advance

was so rapid that the lava actually overrode a preexisting cone,

as occurred near the vent of the 1801 Hualalai lava flow. The

lava apparently went about 11 m up the side ofa prcflow cinder

cone (called the lava-plastered cones [Steams, 1926]). This

evidence suggests velocities of flow of at least 15 m s _, comparable to the velocity inferred for the 1801 Hualalai lava flow

[Guest et al., 1995].

Elementary Flood Model

The low viscosity of these lava flows and their rapid rates of

advance suggests a type of geologic mass movement more like

a precipitous flooding of lava than a relatively slow-moving,

viscous fluid flow. The residual deposits show that, for practical

purposes, viscosity changes along the flow paths were insignificant in both cases. This contrasts with other basaltic flows,

such as the IA flow from the 1984 Mauna [xm eruption, that

underwent a rheologic change of several orders of magnitude

during the 5 days of advance [Cri.sp et al., 1994; Moore, 1987].

Crystallization of microlites occurred during the adwmcc of the

Mauna Lea IA flow, as well as the formation of a thick crust.

As the viscosity increased toward the front of the flow, the

thickness increased dramatically to 25 m in places. Although

perhaps not as dramatic, many of the lobes of the Puu Oo

eruption showed significant thickening with distance from the

vent and a slowing of the advance rate that has been attributed

to rhcologic changes [Fink and Zimbelman, 1990]. Unlike the

1801 and 1823 eruptions, these flows were emplaced over periods, typically, of a few days.

For both the Mauna Lea 1A eruption and many of the

lobate Pu Oo flows, the duration of emplacement was sufficiently long that a significant crustal component formed on top
BALO(;AETAL.:RAPIDLYEMPI.ACEI) LAVAFLOWS 24.511

20 °

156 ° 155045 '

19045 ,

I I I

Zone L(km) Slope (o) W (m)

1 3.5 12.5 1400

2 4 9.5 1000-1300

3 5 3.8 1200

4 2.5 1.2 2000-3000

pACI F IG

0

flow

0 2 4 6 8 10km

I I I I I I

Contours in Meters

EXPLANATION

from1800-1801 Hualalai aJkalic volcanobasalt flows

• Nodule localities

• Vent area

Main roads

HU

l

Hainoa Crater

HUA LALAI VOLCANO

Keauho u

Figure 1. Sketch map of the island of Hawaii showing thc 18(11 Hualalai lava flow. After Guest et al. [1995].

Mcasurcments of reach length (L), tlow width (1¥), and slope (O) wcrc made from air photos and 7.5 min

U.S. Geol. Survey topographic maps of the Kiholo Quadrangle and the Kailua Quadrangle.

of a hot inner core. Once such allow bcct)mes established, the

streamlines within the flow tend to become parallel, although

some mixing and disruption often occurs, particuhtrly when

time-dependent or intermittent effects arc prescnt. Cracking,

mixing, and other processes expose the inner core causing an

important and significant thermal loss [Crisp and Baloga, 1990;

Cri,sp et al., 1994; Crisp and Bah_ga, 1994], but for the most part

the inner core of such slowly advancing, viscous 1tows remains

highly insulated from radiative losses.

Field observations of the 1801 and the 1823 Itows indicate

that the emplacement was rapid enough to prevent a signiticant crustal component from building up. It is likely that a high

dcgrcc of mixing continuously brought hot inner htycrs to the

surface. However, emplacement was so rapid that neither the

formation of a thick crustal layer or a marked change in the

bulk viscosity was able to occur, exccpt for lawl lrtm] the very

final stages of discharge.

Fluid dynamic effects observed in a variety of ditfcrcnt geologic mass movements were present in these flows, however.

Run-up is evident in both the 1801 and 1823 flows. The xcnolithic nodules are most evident, as one would expect from a

hydraulic type of flow, at breaks in slope [AIh'n, 197(I]. The

nodules themselves prcscnt the appearance of hydraulically

worked cobbles in a htg dcposit. The overall dimensions of the

Hualalai flows show a corresponding v,,idcning as the underlying

slope lessens. Field inspection provides the clear impression that

the directions of flow and the locations of the cmplaccd margins werc controllcd largely by the prccxisting topography as

opposcd to internal physical changes in the lava itself.

To describe the dynamics of these tlows, wc assume the local

conservation of fluid volume

;itt _JQ

w ,'it + i_x = 0 (1)
24,512 I_AI.O(iA I:'T AI..: RAPII)I.Y I:MPI.A('ED I.AVA FI.()WS

lqgurt' 2. Xcnolith nodules found in the l g01 f ttlakllai he, a ]low. Thin rinds (al_out I mrn or Ions) of host lava

on llic I_odulcs suggests an cxlremelv tluid, ]o_-visc'_siiv lava.

_hcre h isthe dcpth of the Ilmv, . is the _idth, C) isihc local

volumelric flow rate,.v rcprcsenls the distance along the path

of tile Ilo_', and I is lithe. The volunlelric llmv rate is Ihe

product of ihc eross-seelional [irc;l t)f lhc l]ow limcs lhc Illc';lll

vcloeitv, l:qualion ( I ) simply retluircs any spatial ehange in thc

local 11o_ tale to bc conlpcll,qilcd by :.i hlcal thickening of lhc

llm_ _iih lime.

Thc gcncric siatclneill of '_olulllC conservation in (1) pro-

\idcs lililc praclical value unlil ihc forill of lilt.' _olumeli-ic lit)w

talc is expliciily dclernlined by lhcoi-etical or empirical means.

(icnerally, ti Itowralc prescription fealUlCS ;,I depcndcncc t)ll

lhc underlying slopc, lile dcpih of the th>_, gravity, and paralllCicrs lh;il characlerizc lhc iesiMalicc of the l]lcdiunl It) t]tl'w

(e.g., viscosity and yield strength).

In spite of the liold cvidcncc for ;i highly Ihiid lava, one

might coiijecttlrt.' {ill ;.ikCl;ige tlm_ velociLv of the form

I y.q sin fill-'

u :3 /x (2)

characteristic of a laminar Ncwionian flow', where p is the

dcnsity, ,q is gr:.ivily, 0 is thc slope, and /,, is lhc viscosity.

["-Cltll.ltioI1 (2) in ell'cct defines ;l local l]owr;.ile needed to Make

( I ) ;ill explicit dilfcrcntial CqtliitiOll ftlr h. Applications of (2)

and (I) to la',a flows have been prcscnlcd in the literature [c.g.,

lialo<g,a mul Pied. IriS61 .

Fluid llo_ govcrncd bv (2) ma,+ bc cllariiclcrizcd by the

dinlcnsitlnless t{evnolds ilinlll'ucf

pldl

Re - (3)

/.t

As a rcfercnce, laboratory sit)flies of lluid Ilow in ppcs have

shtlwn Ihal tile transition Irom laminar tlow to classical turbuIcncc occurs for Reynolds numbers in ihc rangc from 2()01) It)

3ll(l(I. For highcr vahics, the onscl of classical Inrbulcrice is

dillicull lo prcvcnl, regardless of the gcomctry. For lower valtics, the flow has insulticicnl energy it) maintain lurbulencc.

Wc can examine the plausihility of (2) for the Igl)l llow

using lhe slope measurcmcnls lhai appear in Tablc 1. Field

obscrvalit)ns suggest a nlhlinlum thickness in the central parl

of tile flow of at least 5 i11. Mc(/clctiin and I_]ichc/het<'qer II9751

alld Mc(h'lchin el al. [ i<JT{,1;.irrivcd at ;.it1 eruplion viscosity of

I(t I- 10 e P;i s using pclmlogic consirainls and a rangl, of plausible cruplion lemperalures and volatile contcnls.

Table 2 shows hypothelical flow velocities given b}' (2) and

corresponding Reynolds numbcrs for the l,g01 flov, using a

conscrvativc estimate o15 m for the l]ow deplh, I IF Pa s for the

viscosity, and a density of 2.6 x 10 _ kg/m -_. These ch'mentary

CimlpUlations clearly indicalc lhat (2) is a poor choice. The

cxlrcmely high flow velocities and Rcynolds numbcrs are

grossly inconsistent with lhe concept of a lanlinar Newton)an

fluid llow, at least for dcscrihing the hlrgc-scale Iealuies of the

18()1 llow.

Many geologic lll:.lSS illl.l\ ClllCllls and fasl-movhlg fluids hearing various kinds of h_adings or suspensions exhibit a non-
BALOGAETAL.:RAPIDLYEMPLACEDLAVAFLOWS 24,513

2925-_

Main Channel

0

/

(1000m)

80 m =

....... ;i:... -Y

0

q I

(11300 In)

lOO

I I I I Contours in Feet

METERS

Figure 3. Topographic map of the area near the repeater station showing the dimensions of a huge lava

channel in which bedded layers of xenolith nodules are found, Channel dimensions taken from map, supplemented by field measurements. Topography from Jackson and Cla,_,ue [1982].

Newtonian or quasi-Newtonian behavior with a flow velocity

given approximately by

,,,"/,gSin O

" = \," C, (4)

where C l is a dimensionless friction coefficient that is determined empirically, or quasi-empirically, and may depend somewhat on the nature of the suspended material and the roughness of the underlying flowbed or the lateral confinement.

For simplicity, we have expressed the mean velocity in a
24,514 IIAI.()G,\ [!T AI_: RAPIDI.Y I_MPI.A('Id) I.AVA FI.()Vv'.',;

1823 Keaiwa Flow Kilauea Volcano, Hawaii

Area

Area 2

Area 1

N

1 0

lillil

1 2 3 4 5 km

I I I I I

Contour Interval = 200' = 61 m

\

\

0

Area L (km) Slope (o) W (m)

1 1.5-3.0 4.9 3000

2 3.5-4.6 5.0 1400

3 1.8-2.1 2.6 500

1823 tholeiitic basalt flows from Kilauea volcano

Fissure of Great Crack source vent for 1823 flow

Figure 4. Sketch map of the 1823 Kilauea h|va flow. Flow erupted from long fissure vent (Great ('rack) and

W;IS very lluid. Dimensional measurements v','ere made from the I: 1()0,()00 U.S. Geological Sur_,cy topographic

map: "'1 [itwaii Vt)leimocs National Park and Vicinity" (1986). Eslinlitlcs of lhc flow velocily reported bv (],ucsl

ctal. ] It)t,15] wcrc made near the northcrnmosl kipuka in area 2.

conventional form [scc Komar, 1980, equation u,)l thai nlakcs

('I dimensionless. Some authors [c.g.. l)augherly and l')ancini,

1965] use ;.t slightly different convention featuring a numerical

prcfaclor, usually 2, in the nUlllcralor t}f (,..1), but ('l remains

dinlcnsionlcss. Other spccitications like (4) feature explicitly

physical variables related to the resistance to ttow. such its lhe

average density or radius of transported particles, thus making

('_ a dimensioned constant. Consequently, some care is reqt, ircd in comparing the flow rcsistance parameters of dilltrent

geologic mass movements.

This general lorm of thc Ilow rate hits appeared in the

scicnlilic literature for over 2{1(I years in connection with

Table 1. I)imcnsional Data and Compulcd ('lmngus for the

1S01 tlualalai Lava Fh_w

Slope.

Zone I., km II', m dog h/h, .,/u,

I 3.5 14(10 12.5 1 1

2 4 1150 ¢L5 1.25 ( L9,";

3 5 121)() 3.8 1.64 {I.7 l

4 2.5 25(10 1.2 1.48 (I.3S

Scc Figure 1 I'or dclinition of zones. Ratios of Itow Ihiukn.:ss (h,,h,)

and llow velocity (u..'u,), rclali'_c to rulcrcncc \r;litlCS h_r Z, mc I. arc

conlpulcd fronl the lava ltood lllodcl.
I'_AI.OGA1'/1" AL: RAPIDI.Y I'_MPI.A('|'I) I.AVA FI.()WS 24,515

Table 2. [typothctical I:ltw_, Velocities and Reynolds

Numbers for IN()I t luahdai Fh)v,,

Zolle 11_ 111/_, l{t'

I 467 6 >', I(1'

2 358 5 ,: 10 =

3 144 2 × 1(1'

4 45 6 x 10 _

Flow velocities and Reynolds iltllllbt.'l-S arc inconsistent with Ihc

assumption of at laminar Ncwlonian [tow. Net text for lll¢[hod el

compuhilion alld paralllelcrs.

Chezy's formulatitm of flooding by ``valor in a conlincd channel.

Nevertheless, modern treatlncnts of the complex geologic materials in lahars, debris llows, and mud llows, slill clnbrace a

formulation like (4) and try to reline Ihe dcscriplion wilh

advances in theory or the use of empirical data. Frequcnlly,

these studies E/cus on ad.iuslnlcnls Io tile power ]a;,¢ dependence of the flow rate on the depth of the ltmv, lilL approprialc

value for the friction eoeffieienl, and the dependence of till

frictitm coetticicnt on the dilllcnsions of enlrained particles,

and similar considerations.

A small sampling of Iileralurc results pl'm,ridcs all indicalhm

tff the magnitude t/l' tile friction t,'oeflicicnis thai nfight bt,"

anticipated for diffcrenl types of geologic mass nlt)``,'t,'nlcnls thai

have been modeled by a lt)rin as sllo``vn ill (4). In a t,'tmlpara['l[¢

formulation for the asecnl dynamics of nlaars alld dialrcnles,

McGelchin and Ullrich I 1<J73]have used ;l frielion eoeltieienl of

0.1. Komar ligS0] cited a value of 0.11(i5 lor sedimcnl-hiden

turbulent waler ltooding. For water flowing in slnOt/l]l cenlcnl

channels, Jell)'O's 119251 obtained the cinpirical value of 11.(i()25,

a remarkable restilt which has wilhslotid till test of time

[H,'eUtltam, 1974] ill spite of signilicanl itdVallees ill both hydrology and metrology. With a ctmlpalablc ftlrnmlation, 1'1_,h11982] (see equation (10) arid Table S ill that reference, nt_ting

that C / is approximately .q/h _-) has olltained viihies approximately equivalent to the range 0.(11 to 1 from a kinematic wave

theory lor the movemcnl of lahars. For certain types of debris

flows, Takahashi [1980] (see equation (19) alld the subsequent

discussion ill thai reference) has tlblamcd 0.577 fronl clnpirical

studies.

We propose thc I]ow rate h.trnl shown ill (4) for lava flows

lhat were tmplaeed hy rapid ttooding, ralher than huninar,

viscous ltuid tlow. The gtwerning time-dependenl cqualion flu

the tlooding of hlva beconles

all i, ( h!t sil, 0)

w ;_t + ,_x hw \ (, = O. (5)

In general, this equation nlust bc supplcnlenlcd hy an appropriate boundary condition to cvaluale the hll]ucncc of timedependent changes in tile t,'ffUSlOn rate Oil file cvol``ing dowllstream Itow thickness. When detailed hfforlnation aboul ``,enl

eondilions is not available, steady stale st/lulions l]lily bc assumed as an ;,ipproxinlalion. This nlakts tile [hsl lt,'rln in (5)

irrelevant, but we lose the ability It) exphihl I]lh_'kncss ehallges

``vith time tit fixed stations along the path tit lhe llow.

At present, lhcrc is no experience wilh lhc applicalion of

such a forinulation io la``,a I]tv<vs. Spcciiically, the friclion cocflicicnt appearing in ihc dcnonlinator is ctmlplclcly unknt)v,'n

and the power law describing lhe response of lhc flow ralc to

lhe depth and underlying sh)pe is ptlsluhilcd. ('onsequenlly.

our approach is Io apply lhis intitle] It) fill I]OXVS illltl conlpal+e

lhc resulls with inclcpclldcni lield checks for consistency. We

,,','ill also compare the rcsulls v¢ilh the experience doculncntcd

ill lhc geologic literature for olhcr lypcs of mass Intwcnlcnts

wilh similar governing equations.

Dynamics of the 1801 Flow

The 18(11 cruplitm produced lava Ilows that overran four

relatively distinct zones on the villCallO during transit to tile

ocean. These zones are indicated on the skelch map appearing

as Figure 1. Measurements tie lile length tffeaeh reach (L), lilt."

width (1.1.'), and slope (0) wcrc made from air photos superiml)oscd till U.S. Gcohlgic ,_llrvcy topographic maps. As seen

ill Figure 1 and Table I, tbc width and slope are roughly

etlnslanl ill each zone. We assume thai lhe outer lllargills of

Ihc flow were emphlced during an early phase of tile eruption

and lhal lhc channels found ill all rcachcs wcrc Rmncd subsequcntly.

BeeatlS¢ 11o other information is availahle, Ihc eruption rate

is considered Io be constant during tile early phase of the

eruption. Will1 no lime-dependent ell'eels in (5), tile flow rate

I'l¢Ci)lllt_'s ;I Ct)llSCl'``'ed quantity (- Qll) along the llow path.

Thus

````here the subscript i indicates the vahic I/l" tile variable in zone

i.

t]tlualillns (Jr) and (6) pro,eitle all immediate COllsiralnl t)ll

ihc ratio of lhc ihickness of the flow ill each zone given by

1,, (w,) :'( sii, #,) ' '

h, - it', Sill 0,, (7)

where i denotes tile zone of inleresl and r hldieaies a reference

Zllne, The reference values are hiken as those of zone l. allhouoh all``' ZOlle could be elloscn.

Tahle I shows Ibc relative ihieknesses in each of the zones

hilsed Oil Ihc lllCilStll-ed values of lhc tlow widths and slopes.

This lypc of flow model produces a longitudinal thickness

prolile thai is relatively [lal ill spilc of the signiticanl changes in

slope and tlti``_ widlh ill lhe different zones. When lhe underlying slope ``,arialions and hileral spreading of lhe llow are

hiktn Jnlo account, vte expect Oll]y a modest thickening along

Ihc lh)w palh aeeordillg to lhe restllls ill Table 1.

We can also derive thc rclalivc vclocily of the l]ow in each of

lhe /ones by substilulhlg (7) into (4),

II r hrll' r

II, = h,ll', = (It', sin 0,/w, sin 0,) 1_. (8)

The rehitivc flow vclocilics arc also shown ill Table 1.

The prcdiclions of Ilow thickness and velocity ill Table 1 ;.ire

only relative values based Oll volume conservalion, lhe form of

the flow rale, and geometric ctmsidcralions. In effect, thcsc

predictions nlusl hc ealibralcd by independent informalion on

reference values in one of the zones. If we had independent

experience and knowledge of the frictitm cocllieicnt, this would

ilol be the ease.

Ficld observalions ill Zt)ll¢ I indicale Ihat the tlow must have

been at least 5 in deep, prestnnably during the early stage of

lhe cruptitm. By using this cslimalc as Ihe reference value, the

tlow thicknesses in the other zones are _ivell by (7). The numerical lhickncss vahics arc shown in Tablc 3. Although it is

dilticult Io establish flow lhickncsscs from postelnplacemenl
24,516 BALOGA I-Tl'AL.: RAPIDLY EMPLACED LAVA FLOWS

Table 3. Reconstructed Dynamics for the 1801 ttualalai

lA|va Flow

Zone 1 (Estimated)

h 5 m u 5 m,'s u 1(I m/s u 15 nl/s

Zone 2 6.2 4.9 9.8 14.6

(('omputcd)

Zone 3 S.2 3.5 7.1 11).6

((Mmpulcd)

Zone 4 7.4 1.9 3.8 5.7

(('omputed)

Transit lime, 71 35 24

rain

Flow rate. 35.01)(I 70,(X)(I 105,0(111

Ill _/S

('t 11.42 11.I I 0.05

Zone 1 values fi)r thickness and velocity arc estimated as described

in text. All other values arc computed fmrn the lawJ flood model.

conditions, wc consider the values in Table 3 to be consistent

with field observations.

Guest et al. [lt_t_5] have estimated a minimum local flow

velocity in zone 1 to bc at least Ill m/s. Using this as the

reference vah.c for (8) gives the zonal flow velocities shown in

Table 3. There arc uncertainties in such field estimates, so

Table 3 includes alternative reference choices (5 and 15 m/s)

for the flow velocity in zone 1 and the corresponding downstream velocities. Based on the observations of Guest et al.

[1995], wc consider the middle value (Ill m/s) to bc the best

estimate of the three alternatives shown in Table 3.

Three important characteristics of the emplacement can bc

reconstructed from the li_rnmlation above, namcty, total transit time fronl the vent to the ocean, the volumetric tlow rate,

and the friction coeflicicnt. Values for each of these quantities

with the three alternative reference velocities appear in Table

3. The transit time is computed from the relation

.I

I'=__, l-i (9)

The best estimate of the transit time from the crater to the

ocean is about 35 rain, which is consistent with the recorded

observations [Ellis, 1842]. Such a transit time is also consistent

with the lack of a significant crust formed on the surface of the

flow. For times nmch hmgcr than an hour, wc would expect to

find some evidence for a significant crust in the distal parts of

the llow, and this was not observed in the field.

The best estimate of the l]ow rate is 7 x 1(I4 m3/s. Even the

lowest value in Table 3 is more than a full order of magnitude

higher than the estimated peak of 3111/11nl _ s i |k_r the 1950

Mauna Loa eruption IMalin, 19811I. The volcanology literature

is replete with estimates of eruption rates. Itowever, these

estimates arc usually time-averaged over the entire duration of

eruption, so one rarely linds values approaching the 19511

Mauna koa value or the result wc have obtained for Hualalai.

The heretofore unknown friction coefficient was determined

by the equation

y sin oh

('_ = (10)

H 2

It may bc recalled that the range of wducs shown in Table 3 fi_r

the friction coefficient is common in the literature for lahars,

debris flows, and sediment-laden water floods, where similar

formulations of the flow rate have been used.

Perhaps the most convincing test of this formulation concerns the unusually large channels of the Hualalai flow complex. Near the repeater statkm, the largest channel is approximately rectangular in shape with a width that narrows to about

40 m and a depth of 18 m (See Figure 3). Field observations

indicate that this channel must have been completely filled at

some point during the eruption. Moreover, there is no field

evidence tor a ponding or staging area akmg the path of the

flow where law_ could have accumulated prior to a catastrophic

release.

We now examine the depth of flow in such a channel with

the inferred eruption rates and friction coefficients. As a minimum, the channel depth must satis_ the constraint,

', y sm

where h, is the depth of the channel, w is the measured width

of the channel, and Q and (it arc the inferred values from the

previous analysis. If the entire flow rate was confined to such a

channel, the computed depth of filling would bc more than

twice the measured depth for each of the flow rate/friction

coctficicnt pairs shown in Table 3.

An alternative approach is to compute the flow rate and flow

velocity necessary to fill such a channel. The results of these

computations are shown in Table 4. The flow rate in the channel is approximately one seventh of the previous estimates,

although the velocity of flow in the channel remains very high.

We might suspect the flow in the channel to be laminar late

in the eruption and attempt to abandon the flood model at this

stage. Using the familiar formula for the average flow velocity

shown in (2) with p = 2.6 × 103 kg/m _,g = 1[| m/s:, O = 8

degrees, tt - 18 m, and the conservative estimate p - 100 Pa

s(ll)00P),weobtainu - 3.9 × l0 s m/sandRe - 2 × 10".

For this conjecture to be remotely viable, there would have to

be new cvidcncc for a viscosity at least 2 orders of magnitude

higher than the McGetchin et al. [1976] estimate.

Wc consider this to bc an important check on the consistcncy of the previous Ilow rate estimates. Basaltic eruptions

often wane significantly in effusion rate from relatively high

peak values established early in the eruption. Channels typically torm after the early phase of the eruption and it is unlikely that the entire flow rate was conducted through this

solitary channel at the repeater station. Our flow rate estimate

in the channel is consistent with the hypothesis of a high

effusion rate early in thc eruption followed by a subsequent

waning.

Given the total w)lumc of lava that can be identified and

associated with this eruption, it is not likcly that high Itow rates

(approaching lip m3/s) werc maintained continuously h)r days

Table 4. Flow Rate and Velocity in Repeater Slation

Channel

('t Q' m_/s u. mls

0.42 5.5 × 111_ 7.6

(1.11 1.1 × I(¢ 15.2

0.(15 ].f) × IO4 22,8

Using the friction coclticicnt of previous computatiol s and dimensional data for channel, lhc ltow rates (Q) and velocities (u) arc

required to fill lhc channel.
BALOGAETAL.:RAPIDLYEMPLACEDLAVAFLOWS 24,517

orweeks. Otherwise, amuchmoremassiveedificewouldhave

beenconstructed fromthe1801eruption. Theflowrateinthe

channel attherepeaterstationsupportsasignificant dropin

theflowratefromthepeakvalueestablishedarlyin the

eruption.

Therelativelyhighvelocitiesinthechannel arguestrongly

forahighlyagitatedandforceful flowthatwouldbenecessary

tosuspendandtransport thenoduleload.Evidently, this occurred with such a highly mixed and agitated character that

significant internal temperature gradients were prevented during the rapid delivery to the distal reaches of the flow. Indeed,

the deposition of nodules in the deep channels supports the

continued drop in the effusion rate as the eruption waned.

The cause of the unusually high volumetric flow rate featured by this eruption remains somewhat unclear at present.

Guest et al. [1995] have attributed the high rate of discharge to

the near-Newtonian theologic properties of the host lava during both eruption and emplacement. Alternatively, a summit

crater about 250 m in diameter may have served as a reservoir

for molten lava. Field evidence clearly suggests that crater wall

collapse supplied at least some of exposed lava fows.

The overall dimensions of the flow and the behavior of the

eruption are consistent with a dynamic model of lava flooding.

The volumetric effusion rate during the early stage of eruption

appears to have been between 10 4 and 105 m3/s. This rate is

almost 2 orders of magnitude higher than the peak of the 195(I

Mauna Loa eruption and is comparable to eruption rates conjectured in the literature for large planetary lava flows. The

transit times from the vent to the ocean are also consistent with

the lack of a surficial crust, the low viscosity of the host magma

in the distal reaches, and the historical comments on the speed

of advance of the flow. It is clear that such high effusion rates

were not maintained for a long duration. The drop from the

high values shown in Table 3 is supported by the significantly

lower volumetric flow rates in the channel, as shown in Table

4. The waning character of the effusion rate is also supported

by the deposition of nodules exposed in the channels.

Dynamics of the 1823 Flow

The 1823 flow can be analyzed in a similar manner. Figure 4

shows a sketch map of the flow complex and suggests treating

the emplacement as three separate and distinct flows emerging

from different parts of the fissure. In each area the flow deposits each have a single width and slope along the path of the

flow from the Great Crack to the ocean. Flow continuity between the three areas cannot be applied as was done for the

1801 eruption because the lava did not advance from one area

to the next. Consequently, the dynamics of emplacement for

the 1823 flow cannot be reconstructed in as great detail.

Guest et al. [1995] have estimated a flow velocity of at least

15 m/s in area 2 about a kilometer from the Great Crack. First,

we compute the friction coefficient from the formula

Ct = 9 sin Oh u2 (12)

with the mean flow thickness taken as 1.5 m and the average

slope as shown in Figure 4. This gives C l = 0./1(157, a value

similar to that of sediment-laden flooding by water [Komar,

1980]. If the estimated flow velocity is conservatively decreased

to 10 m/s, the friction coefficient becomes 0.0128, which is

more typical of water.

The two velocity estimates (15 and 10 m/s) for area 2 correspond to transit times of 4.4 min and 6.7 min to the ocean.

The flow velocity must have remained essentially constant

along the flow path, as far as we know. The rapid emplacement

must have resembled an advancing, highly turbulent, floodlike

sheet. There was very little time for a crust or skin to form. The

thinness and fluidity of this flow suggests that it would naturally

follow the small-scale topography, thus mixing any cooler skin

into the interior.

For area 2 we find the eruption rates of 21,000 and 14,(100

m3/s for these two velocities estimates (15 and 10 m/s). These

rates seem very high by present-day experience, but this is

primarily due to the extent of the fissure (e.g., 1400 m parallel

to the direction of flow) and the lateral width of the flow.

In area I the slope is only marginally different from that of

area 2. The same flow velocity estimates are likely to be reasonable for this area as well. This part of the flow complex

probably added another 45,000 m3/s or 30,000 m3/s to the

eruption rate for estimated flow velocities of 15 m/s and 10 m/s,

respectively.

Toward the upper part of the Great Crack in area 3, the

slope is about a factor of 2 lower. Here the flood model can be

used to estimate the flow velocity of area 3. Based on the two

friction coefficients derived above, we obtain estimates of 10.8

and 7.2 m/s, respectively, in area 3. These results are also based

on an average depth of 1.5 m. These velocity estimates correspond to flow rates of 8100 and 5400 m3/s for area 3.

The flood model is hardly essential for these computations.

Thcy arc based primarily on the mapping of the flow, geometric considerations, and the field estimate of the velocity in one

of the areas. We have used the model only to compute the

friction coefficient and the velocity in area 3, which is a rather

minor contributor to the eruption rate.

The model does provide one very important aspect of support for these considerations. Specifically, the friction coetficient is about 10 or 21) times less than that obtained for the

1801 flow. Conceptually, this is qualitatively consistent with the

lack of an appreciable load in the 1823 magma and an emplacement that is even more rapid than that of the Hualalai

flOWS.

The conclusion we obtain for the 1823 flow is that it also had

a very high eruption rate, probably at least 21,000 m3/s. If the

three segments of the fissure were fed simultaneously, which

appcars likely, the eruption rate could have been roughly 3

times as high. As with the 1801 flow, this high eruption rate

probably persisted only for a short duration, perhaps on the

order of tens of minutes or less.

Scaling the Model for Planetary Applications

We now consider some implications of the lava flooding

model for volcanism in a planetary setting. As a basis of comparison, we consider the volumetric flow rates of a laminar

Newtonian fluid (equation (13)) and the lava flood model

(equation ( 14)):

g sin Oh3W

Q = --_,_-_- ..... (13)

Q= _i; Ct hW. (14)

To compare terrestrial analogs with lava flows in a planetary

setting, we suppose that the eruption rate, preexisting topog-
24.518 t-IALO(;At.71' AL.:RAPIDLYEMPLACEDLAVAFLOWS

raphy,andrheological propertiesremainthesamein both

settings. Ourchiefaimisthustoexaminetheinfucncedue

solelytochangesingravity.

Thefollowingexampleprovidesa comparisonbetweena

lavaflowontheEarthandtheMoon.Foreitherofthemodels

shownin(13)and(14),weobtaintherelation

9,S,_= ,J,,,hL (15)

Apriori,it issomewhat surprisingthat(15)holdsforboththe

Ncwtonianflowratebasedonalaminarflowandtheflood

modelthatismorecharacteristic ofdisrupted, possiblysuspension-laden, turbulent flow.Byrearranging(t5),andsubstitutingvaluesforthegravityoftheEarthandMoon,wcfind

h,,, = (g,./g,,,) k_h,. = 1.82h,.. (16)

A comparable flow on the Moon has a thickness almost twice

that of its terrestrial counterpart.

Why lower gravity produces systematically thicker flows on

planetary bodies with lesser gravity is evident from the corresponding velocity scaling:

It,

",,, = I (t,,]Y,_ I _:t, = 1.82 " (17)

I)uc to the lesser gravity on the Moon, a comparable flow

would advance almost twice as slowly. For the same eruption

rate and preexisting topography, the slower rate of advance is

the cause of the corresponding thickness increase. Equation

(17) is valid lk_r both of the flow rate models under consideration.

These considerations suggest that the 18{)1 ttualalai flow

could indeed bc quantitatively similar to hmar eruptions that

produced the lava flows at Marc lmbrium and other hmar

locations. Doubling the margin thicknesses of the 1801 |lows to

account for the lower gravity produces thicknesses comparable

to those of certain flow lobes in Mare Imbrium and elsewhere

on the lunar maria [Schaber et al., 197@

At one point during the Hualalai eruption, the central depth

in channels was at least 18 m. Comparable, but sustained,

eruption rates on the Moon or Mars could produce flows with

thicknesses between 10 and 30 m, just duc to the lower value of

gravity. Flow thicknesses in this range arc abundant on the

plains and shield w_lcanos on Mars and the lava flow lobes in

Mare Imbrium Unlike the Hualalai eruption, however, the

volumes of many of the planetary flows are at least an order of

magnitude larger than those of the Hualalai flow complex. The

lawl tlood model suggests that one primary difl_crencc is that

the duration of phmctary eruptions of this style persisted fi_r

orders of magnitude longer than their terrestrial analogs.

The high lluidities and high effusion rates of these terrestrial

eruptions might be analogous to conditions that once existed

on Mars, the Moon, and perhaps lo and Venus. Most lava

ltows thal have been identified on these surfaces arc probably

1 or 2 orders of magnitude thicker than the Kciawa lawt ltows,

although some authors have argued for similar eruption rates.

Our knowledge of planetary volcanism is limited by the resolution of availalqe images. Flows analogous to those at Kciawa

may indeed exist in numerous phmctary settings, but they

would not be disccrnablc with existing data. Flows with a relief

comparable to the 1823 flows, cvcn with adjustments for gravitational scaling, would go largely undetected, cvcn on the

Moon. tlowever, some thin hmar flows with vertical relief of

the order of meters have been suggested by (heeh 3' [1975].

This consideration has been thought to he the basis for the

scarcity of mappablc flow lobes on the young lunar maria for

some time [Schaber et at., 1976].

When plan form, vertical relief, and topographic slope could

be distinguished for law_ flows on planetary surfaces, many

authors have used models based on laminar flow to infer eruption, emplacement, and rhcologic conditions [e.g., Moore and

Schaber, 1975; Zimbebnan, 1985; Cattermoh,, 199(I; l, opesGautier; 1993, and references therein]. For the rapidly eraplaced terrestrial analogs considered in this work, we have the

benefit of knowing that they were rapidly cmplaced. Phtn form

and vertical relief comparable to available planetary data

would be of little assistance in choosing bctween a more convcntional laminar model and the rapid emplacement model wc

have employed. However, future studies will investigate the

existence of morphologic diagnostics indicative of a rapid emplacement phase in the early stage of a planetary eruption.

Conclusions

The planimetric lorm, dimensions, and general morphologic

character of basaltic flows do not guarantee that viscous fluid

dynamics for laminar flow are appropriate for describing the

essential character of emplacement. We have cw)kcd an elementary lava flooding model, similar to ones used lor a wide

variety of geologic mass movements, to explain the emplacement of low-viscosity tavas from eruptions with high eflusion

rates. Application of this approach to the 1801 flow of ltualalai

and the 1823 ilow of Kilauea produces quantitative results that

are consistent with several types of licld obser_'ations. The

inferred eruption rates for these flows are rather high by

present-day experience, ranging from 1(13 to 105 m_/s. The

friction coefficients obtained by this analysis are of the order of

l(t -" to I(I _, generally in the range anticipated from olher

types of geologic mass movements.

The 1801 Hualalai and 1823 Kilauca eruptions may indeed

be terrestrial analogs for many phmctary eruptions due to the

high fluidity and eruption rates. Our analysis suggests that the

eruptions of these terrestrial analogs must have bccn very brief

by planetary standards. Scaling of the terrestrial analogs for

gravitational changes indicates that llow thicknesses would

roughly double on the Moon, Mars, Mcrcu_', and [o, with

corresponding decreases in flow advance velocities. Judging by

the large volunacs of disccrnablc lava flows on planetary surfaces, the durations of eruptions must have bccn orders of

magnitude hmger than these unique terrestrial counterparts.

The transport model appearing in (1) relies on the assumption that the volume of a tluid element is a conserved quantity

during emplacement. Various field and thcoretical studies indicate that w_lumc conservation may be only an appr,_ximation

during the emplacement of a flow. Different aspects of this

issue arc given by, tot example, Moore 11987], Moore 11982],

Stasiuk et al. [1993 l, and Wadge [1981]. One natural extension

of the model presented hcrc is the addition of a rate term to

(1) to describe differences between the erupted and posternplacement w)lumes. Wc will reserve this extension For future

studies.

Rapidly moving, highly ltuid terrestrial lava flows n':ay bc less

rare than is commonly thought. An unusually fast-moving,

highly fluid flow with yet another composition was associated

with the 1977 eruption of the Mount Niragongo v,_lcano m

Zairc [Tazieff_ 1977]. A perched lawl lake of ncphclinitc composition was very rapidly drained in less than an hour. This
BALOGA ET AL.: RAPIDLY EMPLACED LAVA FLOWS 24,510

massive effusion resulted in flows with average velocity estimates of about 10-15 m/s and velocities early in the drainage

may have been significantly higher. This eruption may have

been analogous to the 18(}0-18(11 Kaupulehu eruption in that

lava flows appear to have been fed, tit least in part, by the rapid

draining of a topographically perched lava lake.

We expect the lava flooding approach to be appropriate t_)r

other fluid lava flows that arc emplaced too rapidly for laminar

flow conditions to prevail. When a transit time or an independent flow velocity estimate can be obtained, morphologic data

can be used to reconstruct the dynamics of the flow, as shown

in this work. When a transit time or an independent velocity

estimate cannot be obtained, a crude reconstruction of flow

dynamics may be conjectured by using the friction coefficients

obtained here and in future applications.

Acknowledgmenls. The authors express sincere gratitude for the

thorough and insightful comments by J. Fink, H. Pinkerton, and H. J.

Moore. Discussions and collaborative observations with G. J. Taylor

and R. Grcelcy are deeply appreciated. This work was supported by

the NASA Planetary Geology and Geophysics program. Participation

by P.D.S. represents LPI contribution 865.

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