Journal o[ l~blcanology and Geothermal Research, 56 ( 1993 ) 113-123 113 Elsex ier Science Publishers B.V.. Amsterdam

The formation of perched lava ponds on basaltic volcanoes: the influence of flow geometry on cooling-limited lava flow lengths

Lionel Wilson ~a' and Elisabeth A. ParfiW ~ ~Geological Sciences Dept., Brown Universio, Providepzce, RI 02912, L LS" l

bEnvironmental Science Division, Lancaster UniversiO', Lancas/er L,I 1 4 }Q, ( K

(Received July 30, 1992; revised version accepted Decemher 3, I¢1CC )

ABSTRACT

Analysis of the formation of morphologically distinctive perched lava ponds produced in effusive basaltic eruptions foeusses attention on the ways in which cooling and fluid dynamics interact to limit tile distance a lava flo~ can travel. If a previously channelised flow spreads laterally on encountering a sudden decrease in the slope of tile substratc or some other abrupt change in topography, its speed and thickness decrease progressively, ill a wa.x dictated by the requirements of mass and energy conservation. There is a consequent dramatic increase in heat loss from tile lava as it thins. Where a flow spreads approximately radially in this way, it ma} form a perched lava pond. The high heat loss limits the size of any such pond to be at most a few hundred meters under almost all circumstances. Pond size depends much more strongb on lava volume flux than on any other physical parameter involved in the system, and tile formation of these features provides a means of estimating eruption rates in paleo-eruptive episodes.

Introduction

Perched lava ponds are uncommon but dis- tinctive topographic features formed during some basaltic eruptions. Figures 1 and 2 show, respectively, examples from the 1968 eruption near Napau Crater (Jackson et al., 1975) and the 1974 eruption ofMauna Ulu (Tilling et al., 1987 ), both on Kilauea Volcano, Hawai'i. Both of these ponds are about 150 m in diameter and formed where a channelised lava flow with a relatively high volume flux encountered a re- gion of much flatter (nearly horizontal) to- pography than that on which it had previously been travelling.

In each case the flow spread out approxi- mately radially and soon stalled as a result of cooling and crust formation, forming a well- defined marginal levee enclosing a nearly cir- cular lava pond. Subsequent pulses of lava

('orrespondence to. L. Wilson.

flowed into the pond, sometimes overflowing the original levee and thus adding to the levee height, but more commonly thrusting slabs of cooling crust onto the vertically growing levee. In some cases, especially clear at Mauna Ulu, overflows formed short flow units extending down the outer face of the levee and onto the surrounding surface (Fig. 3 ), but this process only very slightly enlarged the horizontal pond dimensions.

In this paper we develop a simple model of the way in which cooling limits the motion of a lava flow with Newtonian rheology spread- ing approximately radially from a source, and compare this with the equivalent model of a channelised (i.e., constant width and thick- ness) flow. If a flow has developed a channel as part of the flow process, then radial spread- ing may be induced by a reduction in ground slope. However, many flows at Kilauea reuse existing channels and thus may spread radially simply by exiting the pre-existing channel. In

0377-0273/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.

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F()RMAFION OF PERCHED LAVA PONDS ON BASALFI(" \ OI_(aNOES I I 5

Fig. 2. P h o t o g r a p h o f a p e r c h e d lava p o n d f o r m e d in January 1974 at the base o f Mauna l.!lu, a laxa ,d~icld cmplaccd b c t ~ e c n May 1969 and July 1974 on the east rift zone o f Kilauea.

practice, a combinat ion of ground slope varia- tion and pre-existing topography probably lead to radial spreading. For both channelised and radial flow, the flow can lose heat freely to the atmosphere from its upper surface, i.e. we do not address tube-fed flows. We show that the difference in geometry has an extremely large effect, such that the subsequent travel distance of a radially-spreading flow will be at least an order of magnitude less than that of a channe- lised flow formed under the same condit ions of volume effusion rate and substrate slope. The travel distance of a radially-spreading flow is shown to be much more strongly dependant on the volume flux feeding it than on any other factor, and so ifa radially spreading flow comes to rest before any further changes in its geom- etry occur, and so forms a perched lava pond, the size of the pond is a good indicator of the volume flux of the lava which formed it.

Theoretical considerations

We begin by defining the equation of mot ion for a Newtonian lava and then combine this

with a suitable continuity equation, first for flow in a channel and then for a radially- spreading flow, in order to predict the distance the flow can move as a function of time. We then use a model of flow cooling as a function of time to deduce the maximum travel dis- tance of each type of flow. Consider a liquid with Newtonian viscosity lz and bulk density p moving with mean speed U and flow thickness D down an inclined plane with slope cf to the horizontal (Table 1 contains a list of all of the variables and symbols used). The equation of motion in the x coordinate direction is:

uOU=g sin ee KItU - D:p (1)

where g is the acceleration due to gravity and Kis a constant which depends on the cross-sec- tional geometry of the flow. K is related to the hydraulic radius of the flow (defined as the ra- tio of the cross-sectional area in motion to the length of the wetted perimeter) . For flows in a semicircular channel, K = 8. For flows in a rec- tangular channel K = 3 [ 1 + 2 ( D~ W~ ) ] 2, where W,. is the channel width. Thus, for flows which

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F O R M A T I O N O F P E R C H E D LAVA P O N D S ON BASALTIC V()LCANOES I 1 7

TABLE l

List of variables used

Symbol Meaning

C

D

K

T

[ ]

V H; X )(

h2

2 ll

P r

subscript implying lava moves in a channel depth of flowing lava the acceleration due to gravity geometric constant related to a flow's width to depth ratio subscript implying lava moves radially into a pond fraction of flow depth penetrated by cooling wave when motion stops (q2= 1/300) time needed for a batch of lava to travel a distance X

time after start of motion at which a flow stops due to cooling mean velocity of lava volume flux of lava width of channel in which lava moves coordinate in direction of lava motion maximum travel distance of a flow limited by cooling slope to the horizontal of the ground on which lava m o v e s

thermal diffusivity of lava ( 10 .6 mZ/s) distance penetrated by a cooling wave in time T Newtonian viscosity of lava (30 Pa s) bulk density of lava (2000 kg/m 3) time taken by a cooling wave to penetrate a distance 2

are very much wider than they are deep, K= 13; for flows which are three times wider than they are deep, K= 8.3; for flows which are twice as wide as they are deep, K= 12, etc. (for details of the definition and use of the hydraulic ra- dius of a flow, see Knudsen and Katz, 195,4, pp. 129-131). Equation (1) assumes that steady-state conditions prevail, i.e. there are no changes of velocity with time at a given loca- tion. This approximation is valid for almost all basaltic flows but fails for higher-viscosity la- vas (and for fluid lavas on sufficiently nearly horizontal ground) when melt cannot flow lat- erally fast enough to accomodate the flux from the vent and, in the extreme case of a very high viscosity flow, a dome forms over the eruption site and slowly relaxes after the eruption stops (Huppert et al., 1982). The equations given by Huppert (1982) can be used to estimate tile minimum ground slope, for a given lava vis-

cosity and effusion rate, needed for the steady- state approximation to be valid. For the effu- sion rates deduced below, this minimum slope is close to sin o~ = 0.003, an order of magnitude smaller than the typical slopes of shield vol- cano flanks.

The motion of the lava is determined by combining equation ( 1 ) with the appropriate continuity equation expressing conservation of the flowing material. We will assume below, for simplicity, that volume flux is conserved; if any significant density fluctuations occur in the flowing material, the more exact mass conser- vation equation would need to be used in- stead. This approximation is probably quite adequate for radially spreading flows for which, as we show below, the travel distances are rarely more than hundreds of metres. For channe- lised flows it is more likely that significant pro- gressive density increases will occur due to gas loss with increasing distance from the vent, as in the 1984 Mauna Loa flow (Lipman and Banks, 1987). Progressive density increase in this way will reduce the potential travel dis- tance of a flow, but only, as we show later in equation (14), in proportion to the cube root of the density change.

Figure 4 shows the geometries of lava mo- tion in a parallel-sided channel (left side) and lava dispersion onto a near-horizontal surface (right side), the latter being approximated as a radial flow into a semicircular region from a source at its centre of curvature. The singular- ity at the origin implied in this case if the mo- tion were strictly radial is avoided by making

[j Ig f~ ~ Xp~

Fig. 4. Diagram showing a plan view of the geometry of a channelised lava flow (left side) and a flow spreading out radially (right side) when no longer confined by local topography.

1 18 I,WILSONANDE.A P~,RFII!

the source have a small but finite size (in prac- tice the width of the channel feeding the pond). Comparison of Figures 1 and 2 with Figure 4 shows that the semicircular flow pattern is a poor approximation to the motion forming the pond at azimuths well beyond ~ 120 ° from the symmetry axis (i.e., that the ponds are more nearly circular than semi-circular), but even so it should account for the dynamics of most of the total lava volume involved.

To complete the analysis of the lava motion, we now use the geometries shown in Figure 4 to define the volume flux which is conserved in each case. For a flow in a channel of uni- form width, the volume flux V~ is defined by:

V~=U~D~W~ (2)

where We is the channel width, and b~ and D~ are explicitly the velocity and flow depth in the channel geometry case. Since the channel width does not change with x, both U~ and D,. are constant in this case; (0 U/Ox) is therefore zero in equation ( 1 ) and so the equation simplifies t o :

L~ = (D~pgsin a ) /K l t (3)

Each of Uc and D~ can be eliminated in turn between equations (2) and (3) to give:

D~ = ( V¢K~/Wcpg sin a ) '/~ (4a)

U~ --- ( V~pgsin a /WZKl t ) '/~ (4b)

The time, tc, needed for a given batch of lava in the flow to travel a distance x~ is:

tc=xclb~ (5)

since the velocity U~ is constant. Eliminating U~. with equation (2) we have:

t~=D~Wcxc/Vc (6)

We shall shortly use this expression for t~ to show how cooling will limit the motion of a channelised flow. However, we first derive the analogous expression to equation (6) for ra- dial flow motion.

For radial flow into a semicircular pond

( right side of Fig. 4 ), the continuity relation is:

vp = ~rxp Up Dp t 7 i

where the velocity and depth are Up and Dp, respectively, at a distance Xp from the centre of curvature. Since Vp now involves a depen- dence on Xp, it follows that both Up and Dp will be functions of Xp, and so in general it is no longer possible to neglect the term [U (0U/ Ox) ] in equation ( 1 ). However, we have inte- grated equations (1) and (7) simultaneously using numerical methods and find that, for values of V~ up to at least 1000 m3/s (much higher than any effusion rate recorded for a ba- saltic lava in historic time and comparable to the rates inferred for flood basalt eruptions - see summary in Wilson and Head, 1981 ), the analytical solutions obtained by neglecting the term [ U(OU/Ox) ] differ by less than 1% from the numerical solutions. We therefore proceed with the analytical development, since this makes it easier to compare the functional de- pendence on the variables in the two cases treated. Expressions for the variations of U,, and Dp with xp are found by eliminating each of Lp and Dp in turn between equations (3) and (7), giving:

V ( 8a

and

V~,pg sin oz] U~,(x) = ~ J

/3

(8b)

Both Up and Dp decrease with increasing Xp, with Up showing the most rapid change. Since Up is now a function ofxp, the time tp needed for a batch of lava to travel outward from its source is found by writing:

dx= Udt ~ 9 )

Substituting equation (8b) for U and integrating:

F O R M A T I O N OF P E R C H E D LAVe P O N D S ON BASALTIC V( )L( 'ANOES 19

tp "(p

0 XpO

- V~pgsin o~

/ 3 Vp

f X2/3dx ~.po

that is:

/r2K/z ]1/3(v.2/3 v.2/3 t p = ( 3 / 5 ) V ~ _ ~ p ---pO ~pg sin c~

(10a)

( lOb)

We shall find below that Xpo, having a value of at most a few metres, will generally be very much smaller than the distance at which the flow stops, so that we can approximate equa- tion (10b) by:

lp= ( 3 / 5 ) V~pgsino~ ~'P (11)

We now turn to the problem of determining the maximum distance to which a lava flow can travel by relating the travel times, given by equation ( l 1 ) for a radial flow and equation (6) for a channelised flow, to the t ime scale for cooling of a flow.

We treat the cooling of a fluid mafic lava flow using arguments developed by Hulme and Fielder (1977), based on an analogy with en- gineering models of the cooling of a fluid in a pipe, the walls of which are mainta ined at a much lower temperature that that of the fluid. This t reatment is supported by analyses of field observations of the travel distances of a large number of basaltic flows and of a few more sil- icic flows (Pinkerton and Wilson, 1988; Pink- erton and Wilson, 1992). In this model, mo- tion of a flow stops when a thermal cooling wave has penetrated to a distance which is some critical fraction of the thickness of the flow. Such a cooling wave propagates in prin- ciple from both the upper and lower surfaces of the flow, but almost all the heat loss takes place upwards due to the much larger temper-

ature gradient in that direction (as long as the flow is not confined in a tube). -[he distance 2 penetrated by a cooling wave in t ime r is given by:

"r=;,.2/tc (12)

as long as heat transfer is assumed to be en- tirely limited by the thermal diffusivity, ~c, of the flow material, rather than by the ability of the environment to remove the heat (this is a good approximation at times more than a t)w tens of minutes after a given batch of material has been erupted - - see Head and Wilson, 1986). get the cooling wave have penetraled to a distance which is some fraction q of lhe flow thickness D (i.e. 2 = qD) when motion of the flow ceases at some time r = T after erup- tion from the vent. Substituting for r and 5 in equation ( 12 ) gives the flow duration as:

T=(q2O2)/tc (13)

where k is -,. 10 6 m2/s for all silicates. Using a wide range of field measurements, Pinkerton and Wilson (1988, 1992) show that, as sug- gested by Hulme and Fielder (1977), q2 has a value close to ( 1/300).

We note that this model makes no at tempt to deal explicitly with changes which take place in lava rheology as a function of distance from the vent and hence time since eruption. In- stead, the model establishes a correlation be- tween the max imum flow length and the effu- sion rate, with the functional form of the relationship being that expected theoretically. The changes in rheological properties, the con- sequent deceleration and thickening of the flow, and the eventual cessation of motion, are all accommodated through the value found empirically for q2. This approach bypasses the many complications introduced by detailed considerations of variations in heat transfer ef- ficiency in the near-surface parts of a lava flow due to the presence of cracks, variations of bulk vesicularity, etc. (e.g., Crisp and Baloga, 1990), but appears to be justified by its suc- cess (Pinkerton and Wilson, 1988. 1992) in

120 l,. WILSON,AND E.A i 'ARFIJ I

predicting observed flow unit lengths for a large number of channelised flows for which the ef- fusion rate and flow width were recorded (Wolfe et al., 1988).

With these caveats, we now find the dis- tances to which our geometrically idealised flows can travel before stopping due to cool- ing. For motion in a channel, we equate Tgiven by equation (13) to tc given by equation (6). We explicitly identify D in equation ( 13 ) with Dc given by equation (4a) and write Xc = X~ for the distance travelled when flow ceases, giving:

Xc_l [- gc 14/3 F Kit 1 I/'3 - 300x [WTJ [ _ P g ~ o~ (14)

For the radial flow, we equate Tgiven by equa- tion ( 13 ) to tp given by equation ( 11 ), explic- itly identify D in equation ( 13 ) with Dp given by equation (8a) and isolate xp from the re- sulting expression. Putting xp=A], when the motion stops, we have:

Xv = 26 36 53 7~4jl~3pg sin c~ ( 15 )

Discussion

Examination of equations (14) and ( 15 ) shows the relatively weak dependence of flow length on the lava properties It and p, the envi- ronmental factors g and oe, and the geometric parameter K, especially in the case of motion in a pond; the most important control on flow length is clearly the volume flux V. It will be noted that both equations imply a weak in- verse relationship between maximum flow length and the product (pg sin ce ): a shallower slope or smaller lava density (or lower grav- ity) produces a longer flow. This apparently counter-intuitive result occurs because a flow with a fixed volume flux will travel faster and hence must be thinner on a steeper slope; the thermal consequences of the reduced thickness then more than outweight the higher speed in determining the distance travelled.

It is particularly instructive to compare the potential flow length for flows with the same volume flux and substrate slope but differing geometry. Consider a case where V= 200 m3/s (at the upper end of the range of common eruption rates in basaltic environments - - see values summarised in Wilson and Head, 1981); sin c~=0.025 (roughly the average along strike slope of the East Rift Zone of Ki- lauea); p = 2000 kg /m 3 (a moderately vesicu- lar basalt ); It = 30 Pa s (hawaiian basalts have viscosities close to this value on eruption ~ see Heslop et al., 1989) and K= 3, implying a rel- atively high ratio of flow width to thickness in the channel case. Then, for a channel I0 m wide, X~, the maximum distance travelled by a channelised flow, is 103 km, whereas X v, the maximum distance travelled by an unchanne- lised (ponded) flow, is only 339 m. Thus, i fa previously channelised flow begins to spread laterally (for whatever reason), the change in geometry can produce a dramatic difference in the subsequent distance that the flow can travel. We argue that this is the primary cause of the development of lava ponds such as those shown in Figures 1 and 2. Table 2 compares values ofX~, Xp and the ratio (Xc/Xp) for val- ues of V in the range 2 to 200 m3/s (encom- passing the vast majority of mafic eruptions ).

TABLE 2

The m a x i m u m travel dis tance o f lava in a channel , .k,, or m a semici rcular pond, .:t'~, as a funct ion of the lava vo lume f l ux I

t7 ( m3 / s ) Xp /m X,./km t, /.Vp

200 339 1!12 ~03 100 228 40.8 ,.79

50 154 16.2 i{~5 25 103 ~.43 i2 10 61.3 t.89 ~t

5 41.2 0.75 8 2 24.4 0.22 '~

Values are calculated f rom eqs. (14) and ( 15 ) using a chan- nel width o f 10 m for the channel ised flow and the following values for the other parameters in both geometries: a ground slope o f sin oe = 0.025, a lava densi ty o f p = 2000 k g / m ~, a la~a viscosity of/z = 30 Pa s and a geometr ic factor o f K = 3. imply- ing a relatively high ratio o f flow width to th ickness

FORMATION OF PERCHED LAVA PONDS ON BASALTIC VOLCANOES l 2 l

The ratio of the lengths of channelised and un- channelised flows is seen to decrease rapidly as the effusion rate decreases, but is always at least one order of magnitude.

Application to the lava ponds on Kilauea

The Mauna Ulu pond shown in Figure 2 has a diameter of 70-80 m which, for the above parameter values, implies a lava flow rate of 12.6-16.0 m3/s. The chief potential source of error lies in the value adopted for the pre-ex- isting slope of the ground on which the pond formed: we used sin oz= 0.025 to obtain these values. Equation ( 15 ) shows that Vp is propor- tional to (sin oz ) l/4, so a factor of 2 error in sin ol will produce only a 19% error in Vp. Unfor- tunately, no direct measurements of the flow rate were made at the t ime of the eruption, so no simple comparison can be made between the model and actual rates. However, it is possible to estimate the volume flux using the summit deflation recorded during pond formation. During eruptions on the two rift zones of Ki- lauea, the summit area of the volcano above the shallow magma chamber is commonly ob- served to deflate and tilt inwards (Dzurisin et al., 1984; Macdonald et al., 1986) as magma moves out of the chamber into a rift zone to be erupted. The amount of ground tilting is re- corded by tiltmeters located in a vault on the northwest rim of the caldera (Dvorak and Okamura, 1985 ). A number of attempts have been made to relate the amount of inward tilt to the volume of magma leaving summit stor- age. Dzurisin et al. (1984) calculated the ratio of the change in volume of magma in the chamber to the change of ground tilting to be 0.33X106 m3/~radian of tilt. Dvorak and Okamura ( 1985 ) est imated a value for this ra- tio of 0.45X 106 m3/#radian for the recent eruption at the Pu'u 'O'o vent. The lava pond at Mauna Ulu formed during a short-lived eruptive outbreak which lasted from 24th to 26th January 1974 (Tilling et al., 1987). This eruption was well defined in the tilt record

1 8 0 . 0 L , : ~ ~ . - - 1

-~ | Pond f o r m i n g I 7:3 [ e r u p t i o n I 1 7 6 . 0

2

1720 , / /

1 6 8 . 0 p.

E 1 6 4 . 0 1

E [ [ r

u~ 1 6 0 . 0 ~ . . . . " - i ] " [ 1 9 2 0 21 2 2 2 3 2 4 2 5 2 6 2 7 2 ~ 1 ;!9 3 0 :11

J a n u a r y 1 9 7 4

Fig. 5. Extract from the summit tilt record for Kilauea showing the deflation events associated with two eruptive episodes during the Mauna [Ilu eruption. The first of these episodes resulted in the formation of'the perched lava pond shown in Fig. 2.

(Fig. 5) and was associated with 5.1 /lradian of deflation which occurred over 35 hours, im- plying a deflation rate of 0.146 ¢tradian/hour. If we assume that the volume flux at the Mauna Ulu vent was equal to the volume flux of magma moving into the rift zone from the summit (i.e., that there were no changes in the volume of magma stored in the rift), and that all the lava erupted flowed down the channel and fed the perched pond, then the summit de- flation rate can be converted into a volume flux using the conversion factors quoted above. Us- ing factors in the range 0.33-0.45 × 106 m 3 /

¢tradian gives an estimated volume flux at Mauna Ulu of 0.048-0.066 × 106 m~/hour or 13.3-18.2 m3/s. This range is in remarkably good agreement with that (12.6-16.0 m3/s) est imated from our model. Thus, even given the uncertainties involved in converting the summit deflation into an equivalent volume flux, there seems little doubt that our model volume flux is of the right order of magnitude for the eruption.

The pond at Napau (Fig. 1 ) formed on top of lava which had recently flooded much of the interior of Napau crater and, although there is no detailed information on the topography of the flooded area, our visual appraisal suggests that it may be appropriate to assume a smaller value of sin oz for the Napau pond than that

122 L. WILSON AND E A P-kRFIT'[

used in producing Table 2 and in the Mauna Ulu calculation. If we take sin o~ = 0.008, about a factor of three smaller, then the pond radius of ~ 75 m implies a lava volume flux of about 10.7 m3/s. Again, no direct estimates of the volume flux into the pond were made during the eruption, but two estimates of the flux can be made, one using the deflation rate (as above) and the other using estimates of the erupted volume. The entire October 1968 eruption was associated with a summit defla- tion of 60/tradian and continued for 16 days (Klein, 1982). Although the pond-forming phase of the eruption lasted for only part of this time, the summit deflation rate can at least be used to make an order of magnitude estimate of the volume flux associated with the erup- tion and with pond formation. The deflation duration gives an average deflation rate of 0.156/tradian/hour which, using the conver- sion factors given above, yields estimates of the volume flux during the eruption of 14.4 to 19.5 m3/s. The volume of lava erupted is poorly known due to the large amount of drainback which occurred after the eruption ended (Jackson et al., 1975); however, an estimated erupted volume of ~9.5 × 10 6 m 3 (including drainback) gives an average volume flux of 6.9 m3/s. This value is likely to be a minimum as it assumes that eruptive activity was continu- ous over 16 days whereas it is known that there were periods during the eruption when little lava was being erupted (Jackson et al., 1975 ). The mean of the two estimates of the volume flux during the 1968 eruption, 14.4-19.5 m3/s and 6.9 m3/s, respectively, is 11.9 m3/s. This overall mean value is in very good agreement (perhaps fortuitously, given the uncertainties involved in making the estimates) with the volume flux estimated from the lava cooling model, 10.7 m3/s.

Summary

We have shown theoretically that, whenever a mafic lava flow spreads laterally by a large

amount (for example when the flow ceases to be confined to a channel, perhaps because it moves on to much flatter ground), there is ex- pected to be a dramatic reduction in the sub- sequent potential travel distance of the flow. The reduction factor will be one to two orders of magnitude, the exact value depending on the effusion rate - - see Table 2 - - and the slope change.

In some instances this spreading process may lead to the formation of a characteristic perched lava pond. The topographic require- ments for pond formation are that a reduction in ground slope or loss of channelisation on a sufficiently shallow slope should occur, lead- ing to the onset of mainly radial spreading, and should persist over a great enough area that the lava comes to rest as a result of the enhanced cooling efficiency before further changes in to- pography lead to significantly non-radial motion.

The size of such a pond, together with an es- timate of the slope of the surface on which it is emplaced, can provide a good estimate of the volume flux of lava in the flow which initially led to the formation of the pond.

The radii of two ponds produced in historic eruptions on Kilauea volcano, both ~ 75 m, imply lava volume fluxes between 10 and 20 m3/s. In both cases the eruption rate was also estimated using independent data (the defla- tion rate of the summit reservoir of the vol- cano), and essentially identical lava produc- tion rates are inferred from the two methods. These eruption rates fall well within the range observed for other historic eruptions of Ki- lauea (0.1-270 m3/s for a wide variety of eruptions and 0.35-8.3 m3/s for fissure vents --- see Jackson et al., 1975: Moore et al.. 1980: Wolfe et al., 1988 ).

Acknowledgements

The Scientist in Charge and members of staff of the U.S.G.S. Hawaiian Volcano Observa- tory kindly gave us access to their library of

F O R M A T I O N OF P E R C H E D LAVA P O N D S ON BASALTIC V O L ( ' A N O E S I 23

eruption reports and maps, and provided lo- gistic support. We thank reviewers Ken Hon and Greg Valentine for their comments on the manuscript; we particularly value Ken Hon's thoughtful discussion of how this model re- lates to his field observations. Financial sup- port was provided by NASA grants NAGW 2185 and NAGW 1873 (J.W. Head, Pl) and by the Leverhulme Trust. Peter Neivert sup- plied photographic skills.

References

Crisp, J.A. and Baloga, S.M., 1990. A model for lava flows wilh two thermal components. J. Geophys. Res., 95: 1225-1270.

Dvorak, J.J. and Okamura, A.T., 1985. Variations in tilt rate and harmonic tremor amplitude during the Janu- ar,~-August 1983 East Rift eruptions of Kilauca vol- cano, Hawai'i. J. Volcanol. Geotherm. Res., 25: 249- 258.

Dzurisin, D., Koyanagi. R.Y. and English, T.T., 1984. Magma supply and storage at Kilauea volcano, Ha- wai'i, 1956-1983. J. Volcanol. Geolherm. Res., 21: 177-206.

Head. J.W. and Wilson, L., 1986. Volcanic processes and landforms on Venus: theory, predictions, and obser- valions. J. Geophys. Res., 91: 9407-9446.

Heslop, S.E., Wilson, L., Pinkerton, H. and Head, J.W., 1989. Dynamics of a confined lava flow on Kilauea volcano, Hawai'i. Bull. Volcanol., 51:415-432.

Hulme, G. and Fielder, G., 1977. Effusion rates and rhcology of lunar lavas. Philos. Trans. R. Soc. London. Ser. A, 285: 227-234.

Huppert, H.E., 1982. The propagation of two-dimen- sional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech., 121: 43-58.

Hupperl, H.E., Shepherd, J.B., Sigurdsson, H. and Sparks,

R.S.J., 1982. On lava dome growth, with applical~on to the 1979 lava extrusion of the Soufriere of St. Vin- cent. J. Volcanol. Gcotherm. Res., 14:199-222.

Jackson, D.B., Swanson, D.A., Koyanagi, R.Y. and Wright, T.L., 1975. The August and October 1968 East Rift eruption of Kilauea volcano, ttawaii. I !.S. Geol. Surv.. Prof. Paper 890.

Klein, F.W., 1982. Patterns of historical eruptions at t la- wait an ~olcanocs. J. Volcanol. (ieolhcrnl. Rcs., 12: 1- 35.

Knudsen. J.G. and Katz, I).L., 1954. Fluid Dynanlics and Heal Transfer, McGra,a-Hill, New } ol-k, N'I', 243 pp.

Lipman, P.W. and Banks, N.G.. 1087. Aa tlo\~ dynam,cs, Mauna Loa 1984. [I.S. Geol. Surx., Prof. Pap., 13S0: 1527-1567.

Macdonald, G.A., Abbott, ~k.T. and Petcrson. F.L.. 1986. Volcanoes in the Sea: The geology of Hawaii. I !nix er- sity of Hawaii Press, Honolulu, 1 I,S.4.

Moore. R.B., Helz, R.T., Dzurisin, I)., Ealon, G.P., Knv- anagi, R.Y.. Lipman, P.W., Lockwood, J.P. and Puni- wai, G.S.. 1980. The 1977 eruption of Kilauea ~ol- cano, Hawai'i. J. Volcanol. (icolhcrm. Rcs., 7:IN9 210.

Pinkerton, H. and Wilson. L., 1988. The lengths of lava flows. Lunar Planet. Sci.,XIX:¢)37 938.

Pinkerton. H. and Wilson, L., 1992. Faclors controlling the lengths of channel-fed la~a llox~s. Bull Volcanol., in press.

Tilling, R.I., Chrislianscn. R.L., l)ufficld. W.,\., Endo, E.T., Holcomb, R.T., Koyanagi, R.Y., Petcrson, I) W. and Unger, J.D., 1987. The 1972-197'4 Mauna l!lu eruption, Kilauca volcano: an cxamplc of quasi-steady- state magma transfer. [ LS. Geol. Sur~., Prol. Pap. 1351), chapter 16.

Wilson, L. and Head, J.W.. 1981. ~sccnt and eruption of basaltic magma on the Earth and Moon. ,1. (}coph}s. Res., 86: 2971-3001.

Wolfe, E.W., Neal, C.A.. Banks, N.G. and I)uggan, 1 .,1., 1988. Geological observations and chronolog3 of eruptive events. U.S. Geol. Sur\.. Prof. Pap., 1463 1- 98.