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 tephra. 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 magma 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 eruption rate 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 volcanic ash 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