VOL. 83, NO. B4 JOURNALOF GEOPHYSICALRESEARCH APRIL 10, 1978

The Control of Volcanic Column Heights by Eruption Energeticsand Dynamics

L. WILSON,x R. S. J. SPARKS,T. C. HUANG, AND N. D. WATKINS9'

GraduateSchool of Oceanography,University of Rhode Island, Kingston,Rhode Island 02881

The heightreached by a volcaniceruption column, together with the atmosphericwind regime,controls the dispersalof . Column height is itself a function of vent radius,gas exit velocity,gas content of eruption products, and efficiencyof conversionof thermal energy contained in juvenile material to potential and kinetic energyduring the entrainmentof atmosphericair. Different heightswill be attained for the sametotal energyrelease depending on the styleof the eruption:a discreteexplosion produces a transient plume, whereas a prolonged release of material forms a maintained plume. A maintained eruptionplume will alsobe formedif discreteexplosions occur within a few minutesof one another,and eruptionsproducing large volumesof tephra commonly lead to maintainedplume formation. Observed eruption columnsfrom eight eruptionswith cloud heightsin the range 2-45 km and volume rates of productionin the range l0 to 2.3 X l05 m3/s are comparedwith predictedvalues deduced from theoreticalrelationships for fluid convection.Theoretical model heights were calculated in two ways:first, for a wide range of eruptive conditionsby using a dynamic model of eruption column formation and second,by usinga theoreticalformula relatingheight to rate of thermal energyrelease. Results from the two calculationswere found to agreewell and furthermoreshowed satisfactory agreement with the eight observations.Expected cloud heights can be usefully expressedas a function of heat releaserate, expressedas the equivalentvolume eruptionrate of magma,for three differentvalues of the efficiencyof heat use. The resultsimply that many eruptionsinvolve highly efficientuse of the releasedheat, which indicatesthat the particlesizes in theseeruptions are sufficientlysmall to allow rapid heat transferto air entrained into the column. For certain combinationsof vent radius, gas exit velocity, and gas content, column collapseto form pyroclasticflows shouldoccur. Cloud heightshave beencalculated for a wide range of permutationsof these parameterscorresponding to the onset of collapse. The maximum theoreticalheight expectedfor a stable maintainedplume is about 55 km, correspondingto a volume eruption rate of 1.1 X 1tYm3/s.

INTRODUCTION dispersedashin downwind sediment core traverses [Huanget, Discrete layers and dispersedash zones have al., 1975'Watkins and Huang, 1977]. Cloud heights f•0r'•the now beendocumented as a minor but significantcomponent of eruptionsrepresented were computed by usinga simplemodel all deep-seasediments. Because tephra are often highly dis- whichrelates cloud heights and net paleowind velocity profiles tinctive, at least in Pleistocenesediments, single eruptive epi- to thedownwind sorting of volcanicash particles. In prinCiPle, sodescan frequentlybe identifiedby usinga variety of parame- the cloudheight can be expressedin termsof the total energy ters such as ash morphology, glass chemistry, the glass whichis required to injectmaterial to theheight deduc6d•and refractive index, and mineralogy. This characteristic,and the theambient conditions in theatmosphere by usingthe th.e0ret- fact that ashhorizons are generallydistributed over very large icaltreatment of Mortonet al. [1956],which considers turb u- areas during single eruptions, is the basis of the well-known lentgravitational convection of both a continuousplume a'.nd valueof tephradeposits in definingstratigraphic relationships. an instantaneoussource. The relationshipused in our earlier, Ash horizons are, however, potential indicatorsof several papers assumes,however, an instantaneousexplosion and other important geologicalprocesses. A substantialpropor- yieldsthe minimum explosive energy required to attaina gi9.en tion of the ejecta from explosivevolcanic eruptions is depos- cloudheight. Were an eruptionto take placeover many d0•ys, ited in the oceanseither by direct fallout or by reworking of for example,the columnheight would dependon the rate of subaerial tuffs. Generally, it is difficult to trace all but the energyrelease rather than the total energy,and an instanta- largest su.baerial depositsto distancesgreater than 150 km neousexplosion would not be an appropriatemodel. • even in depositionalenvironments which favor preservation. Thefour principal factors which control atmospher ic dis- In contrast,tephra in deep-seacores often appear to be well persalof ashparticles are the wind velocity profile jnl,the preserved.Therefore crucial information on the productivity atmosphereduring the entire period of theeruption, the varia- of individual volcanoes, volcanic regions, and global vol- tionof thewind velocity during the eruption, the eruption canismis more likely to be found in abyssalsediments. Abys- columnheight, and the spatialdistributions of particles':of sal tephra can alsoyield potentialinformation on the volcanic differentsizes within the column.The growthof eruption cloud height and net paleowind velocity for an eruption or columnsand the way in which eruption cloud height is con- eruptive series. trolledby the rate of releaseofkinetic and thermal eruption Two of the authors have studiedthe downwind dispersalof energiesare the principal concernsof this paper. • volcanicash from severalsources by systematicanalyses of the Models of the structureof eruption columnshave recently beenpresented by Wilson[1976] and Sparksand WilSon [1976].On the basisof both theoretical[Wilson, 1976] and • Also at Lunar and PlanetaryUnit, EnvironmentalScience Depart- empirical[Blackburn et al., 1976]evidence they proposed that ment, LancasterUniversity, Lancaster,LAI 4YQ, United Kingdom. eruption columnscan be convenientlyconsidered in two re- •' Now deceased. gions.In the lowerpart of the column,where gas and ejecta Copyright¸ 1978 by the American Geophysical Union. are dischargedat a high velocity,the momentum(kinetic Paper number 7B 1126. 1829 0148-0227/78/047B-I 126503.00 1830 WILSONET AL.: VOLCANICCOLUMN HEIGHTS energy)of the mixture dominatesthe motion. This regioncan reach its maximum potential height. We emphasizethat the be modeledas a high-speedgas jet, or alternatively,the mix- two stylesof activity are end-membersof a continuousspec- ture can be consideredas a projectedslug. The choiceof model trum of eruption stylesand thusthe divisionof our modeling for this region dependson the style of activity, principally the into two typesis arbitrary but convenient. frequencyof explosionsfeeding the column. During this stage A fundamental difference between the two models is in the the mixture deceleratesrapidly as it interactswith the atmo- quantity of energyexpended in reachinga given height. In the sphereand entrains air. As the column decelerates,buoyancy instantaneoussudden explosion the releasedcloud has to do forces increase,air is heated, and momentum is decreaseduntil work in displacingthe atmosphereas it risesas well as lose eventually, buoyancy becomesdominant. In the upper part energyowing to turbulent mixing with the atmosphereat the of the column, where buoyancy dominates the motion, the column sides. In the maintained plume the atmospherehas column essentiallybehaves as a convectiveplume. Uprise ve- already been displaced,so the only sourceof energyloss is at locities are moderate, and decelerations are slow. the column sides.We shall comparethe two modelsfor erup- In' most eruption columnsthe lower gasjet regionmakes up tion cloud growth with relevant data for severalhistoric erup- less than 10% of the total column height. Thus as a first tions. approximation,models of convectiveplumes may be appropri- MAINTAINED PLUMES ate for understandinghow cloud height is determined.In this paper we investigatevarious theoreticaltreatments of atmo- Theoreticalcalculations. There have been many attempts spheric convection and_apply them to the problem of the to relate heights of convectiveclouds to conditions at their relationshipbetween eruption energetics and cloudheight. We bases,often in connection with the releaseof effluent gases also compare the theoreticalmodels with observationaldata. from industrial processes.The applicationof thesetreatments has beensummarized by Briggs[ 1969]and Settle [ 1978].Settle ERUPTION CLOUD HEIGHT draws attention to the need to distinguishbetween formulae Heights of eruption columnshave been used as indicesof basedon the initial kinetic energysupply and thosebased on the relative 'intensity' or 'explosivity' of different eruptions the initial thermal energy. The observedconvective structure [Knox and Short, 1964; Shaw et al., 1974]. It is therefore of many suchcolumns suggests that modelsbased on the rate important to develop a detailed understandingof the factors of thermal energy releaseare likely to be applicableto most which control eruption column height. explosivevolcanic eruptions, where the degreeof magma frag- Observationssuggest that two common modesof eruption mentation is sufficientto yield high efficiencyof heat release. can be distinguishedwhich lead to eruption columns[McBir- Wilson[1976] attemptedto take accountof both factors in ney, 1973]. One involvesthe occurrenceof suddendiscrete deriving heights of maintained (Plinian) eruption columns, explosionswhich generallylast only a few minutes or hours. usingdynamic equations to follow motionsin the lower gasjet Examplesof such canonlike explosions[McBirney, 1973].are part of the column, where the initial kinetic energyis rapidly the 1938 and 1947 eruptions of Asama [Minakami, 1950], lost. He also usedarguments based on conservationof energy explosionsduring the 1976 eruption of Augustine to deducefinal cloud heights. It was demonstratedthat the [Hobbs et al., 1977], explosionsduring the 1975 eruption of main effectof the high-speedgas thrust part of the columnwas Ngauruhoe [Nairn and Self, 1978], and the 1968 explosionsof to initiate the rapid entrainment of atmosphericair. In all Arehal volcano [Fudali and Melson, 1972]. casesthe initial density of the erupted fluid was greater than The other style of eruption is characterizedby a continuous that of the atmosphere,and mixing and heating of air within dischargeof gas and entrained ejecta which has been com- the gas thrust region was therefore required to produce a pared to a fire hose by McBirney [1973]. Such eruptionsmay mixture less dense than the atmosphereso that thermal con- pulsate and may even be the result of closely spaced ex- vectioncould be initiated. Thesefacts suggest that the heights plosions,but the eruptioncolumn fed by the explosionscan be of columnrise calculated by Wilson shouldbe compatiblewith regardedas a maintained plume. Such eruptionstypically last the results of calculations based on thermal energy release for tens of minutes to severalhours. Examplesof suchevents alone. Such a correspondencewould be of great value in are the opening Plinian phase of the 1947 eruption simplifying the use of these calculations,since the rate of [Thorarinsson,1954] and phasesof the 1975Ngauruhoe erup- thermal energyrelease at a vent can be easilyspecified in terms tion [Nairn and Self, 1978]. of the averageradius of the vent and the velocity,density, and The two contrastingstyles of eruptionclearly must be repre- temperatureof the erupting fluid, togetherwith an efficiency sentedby different physicalmodels. In a suddendiscrete ex- factor to account for the thermal energylost to the system plosion the height of the column is related to the total energy when coarsehot clastsleave the column.This efficiencyfactor released,whereas in a maintained, continuouslyfed plume the is related to the degreeof fragmentation,as will be discussed column height is related to the rate at which energyis supplied later. to the plume. Thus, as was stressedearlier, if the column There are a number of simple formulae available to relate heightsare deducedfrom geologicaldata on tephra, the way in cloud height to thermal energy release. The discussionof which they are relatedto eruption energeticswill be dependent Briggs [1969] showsthat the formula proposedby Morton et on whether a maintained plume or instantaneousexplosion al. [1956] is essentiallyidentical to that derived by Briggsand model is assumed. other authorsto give the total rise heightH of a buoyant The criterion for an instantaneousexplosion is that the plume in a stable atmosphere.The Morton et al. formula is duration of the explosionis short in comparisonwith the rise expressedas time of the cloud. The criterion for a maintainedplume is that = + there is a continuoussupply of material at the base of the column. A maintained plume model is still valid even if the whereH is measuredin meters,Q is therate of productionof supply does not continue indefinitely, provided it is main- thermal energyat sourcein kilowatts, and n is the ratio of the tained for a time comparableto that neededfor the cloud to verticalgradient of absolutetemperature (the environmental WILSON ET AL.' VOLCANIC COLUMN HEIGHTS 1831

dominatedby the solid phasefor gascontents of a few percent z by weight, and so s, the specificheat, is taken as 1.1 X 10-a J o 4o kg-• K-•. Equation (2) applies,strictly, only to the vertical rise of an LiJ •0 -- eruptioncolumn in a still atmosphere(no wind). A numberof formulae for the rise of industrial plumes [Briggs, 1969] in- 0 clude a dependenceof cloud height on wind speed.However, ß, 20 -- (2) should•be applicable to most large explosiveeruptions, since the upward velocity of the cloud is commonly much greater than the transversewind velocity over much of the -r- I0 -- column height and sincethe rate at which a particle-richplume (eruption column) is bent over by the wind shouldbe much

• 0 smaller than the correspondingrate for a particle-poor plume 0 i I i -J 0 I0 20 30 40 becausethe initial upward momentum is less rapidly domi- nated by the addition of horizontal momentumfrom the en- CLOUD HEIGHT (km),FROM WILSON (1976) trained air. For strong winds and moderate- to small-sized Fig. 1. Comparisonof cloud heightsdeduced from the theoretical eruption columnsthe effectof wind on column height may be treatment of Wilson [1976] and from (2), derived from the work of significantand is discussedin detail by Briggs[ 1969]and Settle Morton et al. [1956]. [1978]. We have compared(2) to Wilson's[1976] cloud heightsby lapserate) to the adiabaticdecrease in temperaturewith height taking 10 setsof valuesof u, r, and N for which Wilson gives (the adiabatic ). This formula givesthe final height heightsand insertingthese values into (3) and (4) to give•, that a buoyantplume will reachin a stabledensity-stratified usingan efficiencyfactor F = 0.7. Thesevalues of • were fluid. A numberof simplifyingassumptions are madeby Mor- insertedinto (2) to find H. Figure 1 showsthe resultsof this ton et al. [1956], but the formula satisfactorilyagrees with method with a least squaresregression line. The two methods observations[Briggs, 1969]. For an environmentallapse rate give closelycomparable estimates of cloud height,and there is in a standardatmosphere of 6.5øC/km and an adiabaticlapse a strong correlation with small variance about the bestfit line rate of 9.8øC/km, (1) can be reexpressedas derived from different principles. /-/: 8.2 TM (2) Factorscontrolling efficiency of heat use. The relationship between the height reached by an eruption cloud and the whereH is in metersand Q is the steadyrate of releaseof controlling conditions at the vent is critically dependent on thermalenergy in watts.Q is relatedto the conditionsat the two factors:the ratio of kinetic to thermal energyreleased (per vent by unit time and per unit massof eruptedmaterial) and the extent 0: •mrr•s(O- Oa)F (3) of magma fragmentation(essentially the particle size distribu- tion of the ejecta in the column). In explosionswith a high in which fl, u, s, and 0 are the bulk density,velocity, specific content of nonjuvenile lithies, for example, in some heat, and temperatureof the erupting fluid; 0a is the temper- eruptions, the amount of thermal energymay be substantially ature to which the eruptionproducts ultimately cool (•270 K reduced. For sufficientlyhigh initial velocitiesof gas and frag- in mostcases), r is the vent radius,and F is an efficiencyfactor ments the rate of kinetic energy releasemay exceed that of of heat usage.The bulk density• is relatedto the densityof the thermal energy release. However, for most eruptions where magmatic gas /gg,the density of the pyroclastspro, and the predominantly high temperaturejuvenile lava and gasesare weight fractionsof gas and pyroclastsN and Xm: produced,thermal energywill be shownto be the main factor in controlling cloud heights. Thus F in (3) is primarily con- l_xm +N (4) trolled by the degreeof magma fragmentation. fi Pm P• In some subaerial eruptions, high-temperaturelava frag- If it iS assumedthat the predominantgas Js water and that ments and gases are injected into the atmosphere at high the eruptin8fluid is at atmosphericpressure, then for • - 1200 velocity. In the lower part of an eruptioncolumn, pyroelastics K, p• is O.18 kg/m•. The thermalproperties of the magmaare and gas are rapidly deceleratedas work is done againstgravity and air friction. The subsequentconvective rise of the column is influencedby the particle size oistribution in two ways. TABLE 1. Heat Loss Related to Tephra Fragment Size Large clastshave a high ratio of inertia to drag force and can decouple relatively easily from the gas motion. The time Gas Velocity Particle Diameter u, m/s d,* cm Time t,]. s needed for thermal waves to cross such particles may be greaterthan their residencetime in the column, so little of their 10 0.06 0.04 heat can be utilized in raisingthe temperatureof the surround- 30 0.4 1.6 ing gasesand driving convectivemovement [Sparksand Wil- 100 3.0 90.0 300 50.0 2.5 X 104 son, 1976]. Small clasts, however, may be essentiallyfrozen 500 220.0 4.8 X 105 into the gas motion, so that the gas and fine particle mixture 700 600.0 3.6 X 106 can be consideredas a compound fluid and the particlescan readily supply heat to drive convectionon the time scalesof *Values of particle diameter d for which the terminal velocity in most eruptions. steamat 1200 K is equal to the givengas velocity u when the particle density is 1000 kg/m •. A convenientmeasure of the easewith which fragmentscan ]-Times t needed for substantialheat loss from particleswith the decouplefrom the gas movementsis the ratio of the terminal stated diameters. velocitiesof suchfragments in thegas to the absolutegas 1832 WILSON ET AL.: VOLCANIC COLUMN HEIGHTS

TABLE 2. Calculations of Kinetic Energy Contribution to Total estimateat least70% efficiencyin the useof the heat in selected Energy in ExplosiveVolcanic Eruptions Plinian columns. Table 2 showsthe relative importanceof kinetic and thermal Initial Velocity Kinetic Energyas Percent Uo,m/s of Total Energy energy in many eruptions. The available kinetic energy per unit massof eruptedmaterial is taken as •U02,where U0is the 10 0.01 mean initial velocity of the eruption products.This energyis 30 0.09 essentiallyderived by expansionof the gas phase.The avail- 100 0.9 300 7.9 able thermal energyis taken to be 70% of the heat which would 500 19.2 be liberated in cooling magma from 1200 K to 300 K. No 700 31.8 allowance has been made in Table 2 for the latent heat liber- ated by magma crystallization or vitrification or the minor amount of thermal energy in the gas, and so the relative importanceof kinetic energymay be overestimatedby asmuch velocities.If this ratio is much lessthan unity, particlesand gas as 10%. It is clear therefore that thermal energy release is will traveltogether. Table 1 showsthe diametersof clastsof completely dominant in all eruptions involving highly frag- density of 1.0 X 1!Y kg/m 3 for which the terminal velocity in mented magma. hot steamat 1200 K (calculatedby the method of Walker et al. [1971]) is equalto the absolutegas velocity for a rangeof gas INSTANTANEOUS EXPLOSIONS velocities. Clasts much smaller than the size shown will not ß Certain types of volcanicactivity appear to meet the crite- decoupleeasily from the gas motion. Also given are the times rion of an instantaneousexplosion. Often sucheruptions con- neededfor thermalwaves to passfrom the centerto the edgeof sist of short detonations in which a cloud of ejecta is dis- suchparticles and hencefor significantheat lossto occur. chargedinto the atmosphere.Examples of this type of activity, It is clear that the efficiencyof heat use is of fundamental often described as vulcanian explosions, have been docu- importance in driving a convectiveeruption column, and its mented to be the characteristicrecent activity of Asama in role can be consideredin two extreme examples.If the pyro- Japan [Minakami, 1950] and to have occurred during the clastsconsist largely of coarseejecta where the ratio of termi- activity of Augustine volcano in Alaska in January 1976 nal velocity to absolutegas velocity in Table 1 is great'erthan [Hobbs et al., 1977]. The best definition of an instantaneous unity, little of the heat will be utilized to drive a convective explosionis one which suppliesejecta to the cloud for a time column. Hawaiian lava fountains which produce pre- that is short in comparisonwith the time requiredto reachthe dominantly large spatter pieceshave poorly developedcol- maximum cloud height.The cloud from one explosionshould umns. The height of lava fountainsis mainly controlledby the be substantiallydissipated before the next explosion.Eruptive kinetic energyof the burst. Similarly, Strombolian explosions cloudstypically take only a few minutesto riseto closeto their generally are poorly fragmented. For example, Self et al. maximum height. For example, the 1947 eruption cloud of [1974] estimate that only 5% of the 1973 ejecta in the 1973 Hekla rose to 20 km above the vent in 5 min, a rise rate of 67 eruption of Heimaey were finer than 1 min. Walker [1973]also m/s [Thorarinsson,1954]. Similarly, the August 14, 1947, ex- documentsthe relatively low degreeof fragmentationin many plosion of Asama roseto over 3.5 km in 100 s, a riserate of 35 cinder conesformed from Strombolian activity. m/s. Clearly, an eruption can be modeled as an instantaneous On the other hand, if the ejecta consistlargely of ash-sized event only if the explosionor explosionsoccur over a discrete material such that the ratio in Table 1 is less than unity, period of less than a few minutes. Many eruptions, such as virtually all the magmaticheat can be convertedinto mechani- Hekla 1947, are either continuousdischarges of ejecta or re- cal energy to drive the convectivecolumn. peated explosionslasting many minutes, hours, or days, and columns can be so modeled because the magma is usually the maintainedplume model is regardedas being more appli- sufficientlyfragmented that much of the thermal energycan be cable. utilized in driving convection. For example, Susuki et al. Morton et al. [1956] give the height of a cloud in a standard [1973] showthat at least 55% of the ejectain the 1667Tarumai atmospherefrom an instantaneousevent as P!inian depositare finer than 1 mm. On the basisof the grain size characteristicsof the deposits,Sparks and Wilson [1976] H = 1.37QTM (5)

TABLE 3. Data on Historic Eruptions

AverageVolume Eruption Rate,* Cloud Duration, Eruption mA/s Height,t km hours Source

Hekla 1947 17,000 24 0.5 Thorarinsson[1954, 1968] Hekla 1970 3,333 14 2 Thorarinssonand Sigoaldason [1972] Soufriere1902 11,000-15,500 14.5-16 2.5-3.5 Andersonand Flett [1903], Carey and Sigurdsson[ 1977] Bezymianny1956 230,IJ00 36-45 0.5 Gorshkoo[1959, 1961] Fuego 1971 640 l0 l0 Roseet al. [1973],Bonis and Salazar [1973] Heimaey19735 50 2-3 Selfet al. [1974] Ngauruhoe1974 10 1.5-3.7 14 Self[1974] SantaMaria 1902 17,000-38,000 27-29 24-36 Rose[1972],Sapper[1904]

*Data on volume rate of eruption are given in terms of the denserock equivalentof magma. tCloud heightsare above the top of the volcano, not sea level. •:The data on Heimaey refer to the first weeksof the eruption. WILSON ET AL.: VOLCANIC COLUMN HEIGHTS 1833

50 rock (densitya = 2500 kg/m 8) erupted per second,since this is the parameterthat is most commonly quoted in the literature.

40- BEZYMIANNY,I The appropriate modificationto (2) gives E O = •6s(0- OA)F (6)

30- SANTA MARIA , 1902 Thus threemeasurements are requiredfor eacheruption' the HEKLA,1947© volume of ejecta, the time interval during which it is erupted, and the correspondingcloud height. Most commonly, only 20- overall average values of b are quoted from total volumesof HEKLA,1970 SOUFRIERE, 1902 ejecta, and total eruption durations and maximum cloud FUEGO ,1971 IO- heightsare generallygiven. Unfortunately, there are very few eruptions for which all three of these observationsare accu-

1973 rately known. 0 I I I I Table 3 showsdata for eight eruptionsin which reasonable I0 I0 2 103 I0 4 105 106 confidencecan be placed. The two Hekla eruptionsare both VOLUME ERUPTION RATE, mS/see Plinian events in which there was a continuous ejection of Fig. 2. Plot of observederuption cloud heightsagainst volume material into the atmosphere [Thorarinsson, 1954, 1968; eruption rate for eight explosive eruptions. Error bars have been Thorqrinssonand Sigvaldason,1972]. The Soufriere,Santa included where there is sufficientinformation (Table 3) to assess Maria, Ngauruhoe, and Fuego eruptionswere also recordedas variationsin both parameters.Three theoreticalcdrves are shownfor F values(see text) of 1.0, 0.7, and 0.3 using(2). continuous dischargesof tephra and gas mixtures into the atmosphere from andesitic stratovolcanoes[Anderson and Flett, 1903; Rose, 1972; Sapper, 1904; Carey and Sigurdsson, where H is in meters and Q is in joules. Data for the few 1977;Self, 1974;Rose et al., 1973;Bonis and Salazar, 1973]. eruptionswhere sucha model may apply are comparedwith The Fuego eruption produced minor volumes of pyroclastic this formula later. flows, but thesevolumes are not included in our calculations of THE ROLE OF EXTERNAL WATER ON COLUMN 6. The explosionof Bezymiannyin 1956 also producedpyro- DYNAMICS AND CLOUD HEIGHT clasticflows [Gorshkov,1959, 1961], but thesevolumes are not included in our calculations of 6; again, only the air fall The modelsdeveloped thus far assumethat the gasdriving volume is utilized here. Little of the heat contained in the the columninto the atmopsherewas originallydissolved in the ejecta which formed the pyroclasticflows is used to drive the magmaand constitutesonly a few percentof the eruptedmass. column.The 1973Heimaey eruption consisted of Strombolian The bulk of the heat exchangewas consideredto occur be- explosions in whichthe frequencyof explosion(one per sec- tween air entrained into a column and the hot pyroclasts. ond) in the early phasesof the activity wassuch that the plume Anotherimportant class of explosiveeruption, hvwever, occurs above the vent could be regardedas being continuouslyfed. whenabundant groundwater or seawatermixes with theerupt- Generally, on windy days the maximum column height was ing productsbefore they are dischargedinto the atmosphere. difficult to estimate, but on still days, column heights of. 2-3 In the caseof phreatomagmaticactivity a greatdeal of the heat km were recorded [Self et al., 1974]. exchangemay be betweenmagma and water, and the column Figure 2 showsthe relationshipsbetween maintained cloud dynamicscontrolling cloud height may be very different.In height and volume eruption rates calculated from (2)-(4). this situationfor mixingratios of water to magmaof lessthan Considering the simple theoretical basis of the calculations about0.335, a largeproportion of the thermalenergy is used and the vagariesof the field estimates,the calculationscoin- to transformthe water into steam.Because the heat of vapor- cide well with the recordedcloud heights.The theoreticallines ization of water is 580 cal g-X, coolingof the magmacan be are calculatedfor efficiencyfactors F = 1.0, 0.7, and 0.3. For substantialfor mixing ratios in the range0.1-0.3. If the mix- all the eruptionsexcept Heimaey the observedcloud heights ture of pyroclastsand steamthen rises,the thermal energy used in vaporization can only be recoveredby the con- / / / / / / densationof the steam.If condensationoccurs, the phase e,,,,_e _e,,•, ,,,' / / changefrom steam to waterdroplets requires a largechange in • •o•'• /.' / // // ,,* , volume.This will be partiallycompensated by the mixingof / air into the column duringcondensation, but nonetheless,a substantialincrease in densitymust occur. It is under such conditionsthat basesurge clouds are believedto form in both • 10•6 nuclear explosionclouds and phreatomagmaticeruptions [Moore, 1967].In sucha situationa substantialproportion of • 10•5 the thermal energy is not used to drive convection. Con- sequently,cloud heightsshould be lower in a phreatomag- • iOl• matic eruption than in a magmaticeruption with the same • / /I H• ID•Y IWEEK IMONTH lYEAn volume rate of production. •0 i00 103 104 105 106 COMPARISONS WITH OBSERVATIONS ERUPTION DURATION (minutes) For comparisonof the theoreticalheights with heightsob- Fig. 3. Diagram of selectedvolcanic eruptions illustrating the servedin actual eruptionsit is usefulto expressthe average relationshipsof cloud height (diagonal lines) to eruption duration and rate of releaseof thermalenergy in termsof the averagerate of total energy. The total energyestimated assumes use of all the avail- magma productionb, given as the equivalentvolume of dense able thermal energy (F = 1.0). 1834 WILSON ET AL.: VOLCANIC COLUMN HEIGHTS coincide with theoretical curvesfor which the efficiencyfactor assumea temperature of 1200 K, the values of Q for these is high.Settle [1978]also shows similar relationships, utilizing three events are about 10'8, 3.3 X 10TM, and 3.3 X 10TM J, formulae for plume rise and comparing them with some re- respectively.Corresponding calculated cloud heights,when (5) corded eruption cloud heights. is used,are 59, 8, and 8 km. The observedheights were 43, 3.5, There is a tendency for the larger eruptions, notably the and 7-9 km. In two cases therefore the cloud heights are 1902 Santa Maria and the 1947 Hekla columns, to be some- significantlydifferent from theoreticalestimates based on the what higher than would be predictedby using an F value of formula for a discreteexplosion. There is an obvious discrep- 1.0. This observationis even more striking when it is consid- ancy in the Asama cases,where similar volumesof material led ered that an F value of 1.0 is most improbable. One reasonfor to very different cloud heights. Possiblereasons for the differ- this discrepancyis that the cloud heights are the maximum encesinclude the presenceof cold country rock or the presence observedwhereas the volume rates of eruption are time aver- of coarseclasts in the ejecta, sinceeither factor would lead to aged. In thesetwo casesand probably in many other eruptions our having overestimatedQ. Finally, substantialdepartures there is evidencethat the volume rate of eruption can fluctuate from the standard atmosphereused in computingthe constant considerably.This has been documentedfor the Hekla erup- in (4) may also result in different heights[Settle, 1978]. In the tion and inferred for other eruptions, such as Santa Maria, by Bezymiannycase a maintainedplume model appearsto match reverselygraded deposits.The maximumcloud the data much better (Figure 2). Until many more data are heightsmay reflect the peaks in volume eruption rate rather recorded from discrete explosions, the use of (5) must be than the average.Another factor is that there may be signifi- treated with caution or at least qualified as involving a mini- cant departuresfrom the value of n in (1). Vertical temperature mum energy release. gradientsalso have a role in controllingcloud height, as is THEORETICAL LIMITS ON CLOUD HEIGHT illustrated by Settle [1978]. The data in Figure 2 indicate that the assumption of a standard atmosphereis reasonable,but According to the simple model presentedthus far there the scatter in data may partly reflect variations in vertical should be no limit to the height of an eruption column if large temperaturegradients in eachcase. enough volume eruption rates occur. In practice, there is a The Heimaey eruption illustrates the importance of the limit to the volume rates of eruption which can produce high mechanismand type of eruption in cloud formation. Another eruption columns. column was produced by lava entering the sea during this It was noted above that all eruptivemixtures are discharged eruption. This column consistedlargely of white steam and into the atmospherewith a density greater than that of their reached much greater heights than the eruptive column. The surroundings.If sufficient air can be entrained as a column qtrombolian activity at Heimaey did not fragment the magma rises,the column eventually becomesless dense than the atmo- grea.tly, lessthan 5% of the ejectabeing finer than 1 mm [Self sphere,and convectionensues. For certain combinationsof et al., 1974] and the median size being greater than 1 cm. |n vent radius, gas content, and gas velocity, however, the col- such a situation the efficiencyfactor could be expectedto be umn is still more densethan the atmosphereafter all the initial low, and indeed, the best match of data with theory is for a kineticenergy is expended,and the collapseof the column and low value of F. the formation of pyroclasticflows result. These relationships We have shown above that for most maintained plumesthe have been investigatedby Sparksand Wilson[1976] and Wil- thermal energy releaseexceeds the kinetic energy release,so son [1976], who found that the conditionsleading to collapse that Q in (2) canbe regardedas a goodapproximation to the involve large vent radii, low gas velocities,and low gas con- total energy release rate. If H is interpreted as the average tents. Generally, column collapseoccurs at high volume rates cloudheight during an eruption,then Q canbe takenas the of productionbecause t• increaseswith increasingvent radius total energyreleased divided by the eruptionduration. Figure and decreasinggas content. But t• decreaseswith decreasing 3 shows the result of plotting total energy releasedagainst gas velocity, and so the relationshipsare not simple. Sets of eruption duration. In logarithmiccoordinates, lines of con- permutationsof vent radius,gas content, and eruption velocity stantslope represent constant values of Q andhence particular are given by Sparks and Wilson[1976] and Wilson[1976] for cloud heights,as indicated.Analyses of particle sizedata in eruptioncolumns on the point of collapsefor F = 0.7. We used traversesof abyssalcores can in principleyield estimatesof (3) and (4), together with a = 2500 kg/m 3 for denserock, to cloud heights for eruptions in the Pleistoceneand Pliocene deduce the correspondingvolume rates of eruption, and we [Huanget al., 1975].These heights, on the maintainedplume then applied (2) to obtain cloud heightsjust before collapse. model, can be directlyexpressed in termsof energyrelease rate Figure 4 summarizesthese results,showing maximum vol- and hencevolume eruption rate. Furthermore, if estimatesof ume eruption rate, and hence maximum cloud height, as a the duration of any eruption can be made, the total energy function of vent radius for three valuesof eruptionvelocity. At releasedand volumeerupted can be ascertained;alternatively, the point of collapse, only two of the three variables (gas if the total volume of an ash horizon can be estimated, the content, gas velocity, and vent radius) are independent,the energyreleased and eruptionduration can be calculated.It is third being controlled by the other two. The gas contents stronglyemphasized that the estimateof energyreleased does implied are therefore also shownin Figure 4. At any point in not correspondto the total thermal and kinetic energyof an the diagram, collapseof the column would be expectedwhen eruption unlessthe efficiencyfactor is 1.0. In the eruptions any combination of an increasein vent radius, a decreasein considered in Table 3 a value of F close to 1.0 seemsaccept- gas velocity, or a decreasein gas content occurred. Various able, but there are other typesof eruption, notably phreato- calculationsand observationsimply that eruptionvelocities in magmaticeruptions, where F will be much lessthan 1.0. excessof 700 m/s are unlikely to occur on earth [McGetchin Three eruptionsof short duration for which data are avail- and Ullrich, 1973; Wilson, 1976], and so Figure 4 implies that, able are those of Bezymiannyin 1956 [Gorshkot;,1959, 1961] the largestvolume eruption rate that can lead to a maintained and Asama in June 1938 and August 1947 [Minakami, 1950]. eruption column is 6.5 X 10• m3/s, correspondingto a column If we use the quoted total volumesof material liberated and height of 48 km. Greater heightsshould occur only very rarely, WILSON ET AL.' VOLCANIC COLUMN H•iC;HTS 1835

at the University of Rhode Island. This program has generatedthis • 106 o and many other contributions, and Norman Watkins created and r" cz inspiredmany new approachesand conceptsthrough this program.

m Hiscolleagues and a greatmany earth scientists will miss this dynamic and versatile man. -- 3xlO 5 m Researchfor this study was supportedby the Division of Earth Sciences,National ScienceFoundation, grant EAR76-22319, and the _ 105 -I Program of SubmarineGeology and Geophysics,National Science o z Foundation,grant OCE-74-22347-A03. Researchwas also supported by NATO researchgrant 1222. M. Settle and S. Self are gratefully acknowledgedfor helpful discussionsconcerning parts of this study. -- 104 ..•

m 10:5 REFERENCES Anderson,T., and J. S. F!ett, Report on the eruptionsof the Soufriere in St. Vincent in 1902, and on a visit to Montagne Peleein Marti- nique, 1, Phil. Trans. Roy. Soc. London,200, 353-553, 1903. 0 I00 200 :500 400 õ00 600 Blackburn, E. A., L. Wilson, and R. S. J. Sparks, Mechanismsand VENT RADIUS (M) dynamicsof Strombolian activity, J. Geol. Soc. London,132, 429- Fig. 4. Combinationsof ventradius, gas velocity, and gascontent 440, 1976. which are predictedto be at the criticalboundary between column Bonis, S., and O. Salazar, The 1971 and 1973 eruptions of volcan collapseand columnconvection according to the modelof Sparksand Fuego, Guatemala, and somesocio-economic considerations for the Wilson[1976]. Three curvesare shownfor gasvelocities of 200, 400, volcanologist,Bull. Volcanol.,37(3), 394-400, 1973. and 600 m/s. The maximumcloud height and impliedvolume erup- Briggs,G. A., Plumerise, Critical ReviewSeries, Rep. TID.25075, pp. tion rate areshown as a functionof ventradius for eachgas velocity. 1-81, At. Energy Comm., Washington, D.C., 1969. The value of the weight fractionof gas N is uniquelyfixed at this Carey, S., and H. Sigurdsson,The eruptions of Soufriere and Mt. boundary,and sothe impliedgas fractions are shownas dotted curves. Peleein 1902and a mixedsurface tephra layer in the Tobagotrough (abstract), Eos Trans. AGU, 58, 528, 1977. Fudali, R. F., and W. G. Meison, Ejecta velocities, for any increasein volumeeruption rate would leadto column pressureand kinetic energyassociated with the 1968 eruption of collapse.Even if the factor F in (3) is increasedto 1.0 and a Arehal volcano, Bull. Volcano!., 35, 383-401, 1972. velocityof 700 m/s is used,the maximumcloud heightin a Gorshkov,G. S., Giganticeruption of the volcanoBezymianny, Bull. Volcano!., 20, 77-109, 1959. standardatmosphere is increasedto 55 km, and the maximum Gorshkov, G. S., The Kamchatka Valley of Ten ThousandSmokes, eruption rate to 1.1 X 11Ym*/s. Proc. Pac. Sci. Congr. 9th, no. 12, 237-239, 1961. Hobbs, P. V., L. F. Radke, and J. L. Stith, Eruptions of the St. CONCLUSIONS Augustinevolcano: Airborne measurementsand observations,Sci- 1. A model relatingeruption column height to the release ence, 195, 871-873, 1977. Huang, T. C., N. D. Watkins, and D. M. Shaw, Atmospherically rate of thermal energy(proportional to volume rate of erup- transportedvolcanic glass in deep-seasediments: Volcanism in sub- tion of magma) hasbeen investigated and found to be reason- Antarctic latitudesof the South Pacificduring late Plioceneand ably consistentwith field observations.Cloud heightsranging Pleistocenetime, Geol. Soc. Amer. Bull., 86, 1305-1315, 1975. from 2 to 45 km from eighteruptions fit a formulafor a steady Knox, J. B., and N.M. Short,A diagnosticmodel using ash fall data maintained plume in a standard atmosphereand a model to determineeruption characteristicsand atmosphericconditions during a major volcanicevent, Bull. Volcano!.,27, 5-24, 1964. basedon conservationof energy. McBirney, A. R., Factorsgoverning the intensityof explosiveande- 2. For 'instantaneous'explosions there is insufficientdata siticeruptions, Bull. Volcano!.,37, 443-453, 1973. to confirmavailable relationships between explosion yield and McGetchin, T. R., and W. G. Ullrich, Xenoliths in and dia- cloud height. Instantaneousmodels can be applied only to tremeswith inferencesfor the moon,Mars, and Venus,J. Geophys. Res., 78, 1833-1853, 1973. eruptionsin which there is a singlediscrete explosion lasting Minakami, T., On explosiveactivities of andesiticvolcanoes and their lessthan a fewminutes because clouds initially rise a• tensof fore-runningphenomena, Bull. Volcano!.,lO, 59-87, 1950. metersper second. Moore, J. G., Basesurge in recentvolcanic eruptions, Bull. Volcano!., 3. There are sometypes of eruptionin whichthe magma 30, 337-363, 1967. heat utilization in driving the column is not efficient.These Morton, B. R., G. Taylor, and J. S. Turner, Turbulent gravitational convectionfrom maintainedand instantaneoussources, Proc. Roy. include Strombolian eruptions where the fragmentationis Soc., Ser. A, 234, 1-23, 1956. poor and little heat is given to the column becauseof large Nairn, l., and S. Self, Explosiveeruptions and pyroclasticavalanches fragmentsize, some vulcanian explosions in whichthe magma from Ngauruhoein February 1975,J. Volcanol.Geotherm. Res., in may havecooled to a low temperatureor a largeproportion of press, 1978. Rose, W. l., Jr., Notes on the 1902 eruption of Santa Maria volcano, cold countryrock is ejected,and phreatomagmaticeruptions Guatemala, Bull. Volcanol., .•6(1), 29-45, 1972. in which much of the thermal energyis used in vaporizing Rose, W. l., Jr., S. Bonis, R. E. Stoiber, M. Keller, and T. Bickford, externalwaters and recoveryof this energycan occuronly if Studiesof volcanicash from two recentCentral Americanerup- condensation occurs. tions, Bull. Volcano!.,37(3), 338-364, 1973. 4. For magmatic eruptions, a theoretical limit to cloud Sapper, K., Die vulkanischenEreignisse in Mittelamerika in Jahre 1902, Neues Jahrb. Mineral. Geol. Palaeonto!., 39-90, 1904. height of 55 km on the earth in a standardatmosphere is Self, S., R. S. J. Sparks, B. Booth, and G. P. L. Walker, The 1973 predictedbecause at high volume rates of eruption, column HeimaeyStrombolian scoria deposit, Iceland, Geol. Mag., III, 539- collapseoccurs to form pyroclasticflows rather than high 548, 1974. convective columns. The maximum theoretical volume rate of Settle, M., Volcaniceruption clouds and the thermal power output of explosiveeruptions, J. Volcanol.Geotherm. Res., in press,1978. productionthat can leadto the formationof a stableeruption Shaw,D., N. D. Watkins,and T. C. Huang,Atmospherically trans- column is 1.1 X 11Ym3/s. ported volcanic glass in deep-seasediments: Theoretical consid- erations,J. Geophys.Res., 79(21), 3087-3094, 1974. Acknowledgments. Norman Watkins lost his life in November Sparks,R. S. J., and L. Wilson, A modelfor the formationof ignim- 1977as a resultof a tragicillness. He wasthe creatorand driving force brite by gravitational column collapse,J. Geol. Soc. London,132, of the recentresearch program on volcanicash in deep-seasediments 441-451, 1976. 1836 WILSONET AL.: VOLCANIC COLUMN HEIGHTS

Susuki, T., Y. Katsui, and T. Nakamura, Size distribution of the Walker, G. P. L., L. Wilson, and E. L. G. Bowell, Explosivevolcanic Tarumai Ta-b pumicefall deposit,Bull. Volcanol.Soc. Jap., 18, 47- eruptions,I, The rate of fall of pyroclasts,Geophys. J. Roy. Astron. 63, 1973. Soc., 22, 377-383, 1971. Thorarinsson, S., The Tephra Fall from Hekla on March 29th, 1947, Watkins, N. D., and T. C. Huang, in abyssalsediments east The Eruption of Hekla 1947-48, vol. II, part 3, pp. 1-78, H. F. of the North Island, New Zealand:Chronology, paleowind velocity, Leiftur, Reykjavik, 1954. and paleoexplosivity,N. Z. J. Geol. Geophys.,20, 179-198, 1977. Thorarinsson,S., On the rate of lava and tephra productionand the Wilson, L., Explosive volcanic eruptions, III, Plinian eruption col- upward migration of magma in four Icelandic eruptions, Geol. umns, Geophys.J. Roy. Astron. Soc., 45, 543-556, 1976. Rundsch.,57(3), 705-718, 1968. Thorarinsson,S., and G. E. Sigvaldason,The Hekla eruption of 1970, Bull. Voicanoi.,36(2), 269-288,1972. (Received June 24, 1977; Walker, G. P. L., Explosivevolcanic eruptions--A new classification revised November 14, 1977; theme,(•eoi. Rundsch., 62, 431-446,1973. acceptedNovember 28, 1977.)