The development of near-vent volcanic ash cloud layers due to inhomogeneous atmospheric turbulence and relationship to wind shear
Marcus Bursik, Qingyuan Yang, Adele Bear-Crozier, Michael Pavolonis, Andrew Tupper
TThe development of near-vent volcanic ash cloud layersdue to inhomogeneous atmospheric turbulence andrelationship to wind shear
Marcus Bursik , *ORCID: 0000-0002-9312-5202, Qingyuan Yang Adele Bear-Crozier , Michael Pavolonis and Andrew Tupper Center for Geohazards Studies,University at Buffalo, Buffalo NY USA Earth Observatory of Singapore,Nanyang Technological University, Singapore Bureau of Meteorology, Melbourne, Australia NOAA Cooperative Institute forMeteorological Satellite Studies University of Wisconsin, Madison WI USACorrespondence: mib@buffalo.edu; Tel.: +1-716-645-4265January 7, 2021
Abstract
Volcanic ash clouds often become multilayered and thin with distance from the vent.We explore one mechanism for development of this layered structure. We review dataon the characteristics of turbulence layering in the free atmosphere, as well as examplesof observations of layered clouds both near-vent and distally. We then explore andcontrast the output of volcanic ash transport and dispersal models with models thatexplicitly use the observed layered structure of atmospheric turbulence. The resultssuggest that the alternation of turbulent and quiescent atmospheric layers provides onemechanism for development of multilayered ash clouds by modulating the manner inwhich settling occurs.
Keywords: ash cloud; volcanic cloud; Pinatubo
Volcanic ash is a multi-billion dollar economic hazard to aviation, as shown during the2010 eruptions of Eyjafjallaj¨okull, Iceland [
Casadevall , 1994;
Mazzocchi et al. , 2010]. Itis also a risk to flight safety, with hundreds of encounters of varying severity recorded,and several instances of multiple engine flame-out in flight. The International Airways a r X i v : . [ phy s i c s . a o - ph ] J a n olcano Watch (IAVW), which seeks to safely separate aircraft from volcanic ash inflight, relies on detecting areas of ash and forecasting its future movement [ Tupper et al. ,2007]. However, the forecasting of ash presence and concentration is generally poorlyresolved vertically, although there is some progress in this direction, e.g., [
Heinold et al. ,2012;
Kristiansen et al. , 2015]. Aircraft flying in a supposedly ash-contaminated regionat a particular altitude may encounter no ash or significant and potentially damagingamounts, due to the high degree of ash stratification with altitude. The improvedunderstanding and forecasting of stratification would assist enormously in managingthe hazard and support the continuing development of the IAVW.Photography and satellite imagery of numerous volcanic eruptions show that strati-fication or layering of volcanic clouds is a fundamental aspect of volcanic cloud develop-ment (Fig. 1). Lidar backscatter data have been key in defining this layered structurein distal regions (Fig. 2). Volcanic layers can be stratospheric as well as tropospheric.Figure 1: Photograph and tracing of eruption of Redoubt volcano, AK, 21 Apr 1990, showing plumeovershoot, main umbrella intrusion and particle rich secondary intrusion. Tracings show growth ofcloud layers through different time steps (numbered solid lines), long dashed where partly obscured.White dashed line, tropopause. Modified from
Woods and Kienle [1994]The layers form and separate by numerous processes, some unique to volcanicclouds. The primary volcanic cloud layer near the vent, such as the volcanic umbrellacloud or anvil cloud, arises from the driving of hot eruptive gas and ash parcels outwardaround their equilibrium level, or neutral buoyancy height [
Sparks et al. , 1997]. Ashaccretion, ash re-entrainment, source variability – injection of ash at different altitudeswith changing eruption rate and wind fields, and gas-ash separation cause develop-ment of multiple layers [
Holasek et al. , 1996a;
Tupper et al. , 2004;
Thorsteinsson et al. ,2012]. Double diffusion and convective sediment flux to a single [
Woods and Kienle ,1994;
Bursik , 1998;
Hoyal et al. , 1999a, b;
Carazzo and Jellinek , 2012] and multiple[
Carazzo and Jellinek , 2013] levels by descending fingers that intrude below the level ofa major volcanic cloud layer have been observed, and recreated in the laboratory. Assuggested by brightness temperatures over the surface of near-vent clouds and ground igure 2: (a) CALIOP nadir LIDAR total attenuated backscatter (along track shown in (b))showing complex layering of Eyjafjallajokull ash cloud on 8 May, 2010, isotherms (kelvins, blackdotted lines) and tropopause (black solid line). (b)
Aqua-MODIS RGB false color image [
Pavoloniset al. , 2013] of North Atlantic capturing this ash cloud (pink hues).based photography, umbrella clouds can be solitary, accompanied by a single lower in-trusion resulting from re-entrainment and column-edge downflow [
Woods and Kienle ,1994;
Bursik , 1998] or accompanied by lower level skirt clouds [
Barr , 1982], which mayor may not contain ash. Mechanical unmixing of particulate-laden and gaseous vol-canic cloud components has been noted as a further cause of volcanic layer formation[
Holasek et al. , 1996b;
Fero et al. , 2009], perhaps enhanced by gravity current slumpingof the particle laden component [
Prata et al. , 2017].In contrast to the well-defined and complex layers discussed above, volcanic ashtransport and dispersal models (VATDs), used to forecast ash cloud motion, display ayering of only a single ash cloud, if derived from wind shear; or after the fact froma numerical inversion for variable source height, which is otherwise assumed a fixedparameter ([ Kristiansen et al. , 2015]. Although horizontal, planview resolution can begood, VATDs thus have difficulty in reproducing the vertical thickness and multilay-ering of distal volcanic clouds [
Devenish et al. , 2012;
Folch et al. , 2012;
Heinold et al. ,2012]. In VATDs, dispersal in the vertical direction is commonly described by a singlevertical diffusivity, κ z , which in many models is taken to have the same value as thehorizontal diffusivity, κ h ; the result is then uniform or isotropic ash dispersion. The formation mechanism and morphology of distal ash cloud layers are poorly under-stood, and one potential mechanism for their formation and characteristics is the sub-ject of the present contribution. Our working hypothesis is that, with particle settling,the structure of the atmosphere itself can cause layer formation, through the processof enhanced suspension in vertically restricted regions of high turbulence. Given thatthe mechanism explored herein results from the properties of the atmosphere itself, itmay be the primary, distal layer-forming mechanism. Understanding the reason forthe occurrence and morphology of specific ash-rich cloud layers is critical for correctlycharacterizing extended persistence of ash in the atmosphere, especially when multipleseparate layers occur together. Satellite sensors penetrate only partially into the high-est layer of an optically thick cloud, and satellite remote sensing algorithms are mostsensitive to the column integrated ash properties, when multiple optically thin layersare present. A correct understanding of layer formation and morphology is also criticalfor any attempts to construct VATD models capable of producing output consistentwith observations of vertical dispersion.
Volcanic clouds both create turbulence and are subject to ambient atmospheric tur-bulence. In volcanic clouds near the vent, turbulence is created by both the Rayleigh-Taylor and Kelvin-Helmholtz mechanisms, as the clouds intrude into the atmosphereas gravity currents. Kelvin-Helmholtz instability is driven by the shear between theintruding cloud and the atmosphere [
Britter and Simpson , 1981]. Rayleigh- Taylor in-stability is driven by convective sedimentation, fingering and local, eddy scale densityreversal [
Woods and Kienle , 1994;
Holasek et al. , 1996b;
Chakraborty et al. , 2006].Information of sufficient resolution in the vertical direction to discover and char-acterize the layered structure of the atmosphere is obtained from airborne measure-ment campaigns or rawinsonde balloon releases [
Dehghan et al. , 2014;
Cho et al. , 2003;
Pavelin et al. , 2002]. Several methods have been developed to derive turbulence fromrawinsonde and other high-resolution data.
Vasseur and Vanhoenacker [1998] mea-sured changes in the refractive index structure parameter for radio waves, as turbu-lence causes changes in the refractive index, based on rawinsonde pressure, tempera-ture, humidity, wind speed and wind direction data.
Clayson and Kantha [2008] used ariations in the potential temperature profile from an idealized profile to calculate theThorpe scale, and derive turbulent dissipation and diffusivity. These estimates can bemade for single rawinsonde profiles with simple calculations. There are drawbacks ofcourse to extrapolating such high-resolution or point data to a regional scale becauseof spatial and temporal inhomogeneity; the troposphere is highly transient and spa-tially variable [ Clayson and Kantha , 2008;
Thouret et al. , 2000]. Tropospheric isobaricsurfaces are not necessarily parallel to the earth’s surface, especially at fronts and inmountain waves
Sharman et al. [2012]. Fronts are associated with tropopause folds,non-horizontal isobaric surfaces separating cold from warm air, and turbulence in foldsis generated by local dynamic and convective instabilities. Mountain waves form as thedensity stratified atmosphere flows past the lee side of a mountain or mountain range.These waves can break, resulting in local turbulence concentrated in non-horizontallayers.In the free atmosphere, parameters such as moisture content and temperature donot change monotonically with height; there are regions of relatively homogeneous,convecting or turbulent air, separated by regions in which parameters vary rapidly[
Vasseur and Vanhoenacker , 1998;
Sharman et al. , 2012]. Both the stratosphere and thetroposphere are layered on scales of O [0 . − km ] [ Maekawa et al. , 1993;
Wilson et al. ,2014], but the layers in the troposphere tend to be more transient and discontinuous[
Gage et al. , 1980]. In the troposphere, layers of high turbulence, including high verticalturbulence, can be indicated by constant relative humidity (RH) or mixing ratio, q [ Choet al. , 2003]. RH is thus an important proxy for turbulence intensity. (Atmosphericmoisture is also important in aiding plume lift, especially in plumes from weak sources,or at low latitude, where the moisture content is high [
Sparks et al. , 1997;
Tupperet al. , 2009]). As a result of the layering, large-volume or bulk turbulence is highlyanisotropic ( κ h (cid:29) κ z ), and only within thin, well-defined layers is it approximatelyisotropic ( κ h,local ≈ κ z,local ) [ Gage et al. , 1980].
Data are available from a number of sources on the shape and structure of both near-vent and distal ash clouds. In the near-vent region, data tend to be more limited,due to the greater optical depth. Nevertheless, cloud brightness temperature (BT) asmeasured from nadir-looking geostationary and low-earth orbiting satellites providesmuch useful information, as the topography of the top of the near-vent clouds can bequite variable, with a distinct high point or swell above the central vent that mightbe many kilometers above the top of the main umbrella cloud [
Fero et al. , 2009].In addition, airborne and ground-based photography and videography have providedextensive data on the features at the base of the main umbrella or anvil, and within theunderlying cloud layers. Visible satellite imaging of the near vent cloud top consistentlyreveals strong, well-defined three-dimensional vortex structures above the vent, whichevolve to smooth, somewhat more diffuse structures in the umbrella cloud [
Pougetet al. , 2016].Although the air can be choked with opaque, diffuse ash bodies that extend toground level near vent (Fig. 3a, b), and although gravitational intrusions, such asumbrella clouds, are wedge-shaped by nature and therefore of variable depth (Fig. 3c),measurements have been made of the ∆BT between cloud top and edge of the maincloud. The results suggest that umbrella clouds at the vent typically encompass depths f O [5] km (Fig. 1; Table 1), which makes a large mass of ash available for transportat sometimes high levels. Some of the lower near-vent clouds also become distal clouds(Fig. 3d). In some cases, therefore, it might be possible to find the entire troposphereand even lower stratosphere charged with ash, or only a distinct layer or two of O [5]km depth.Figure 3: (a) Eruption of Pinatubo, June 15, 1991. Emission from vent as well as pyro-clastic flows results in ash injecting into the atmosphere at all heights up to 40 km. Inthe public domain. (b)
Eruption of Grimsvotn, May 22, 2011. Ash injected in um-brella cloud (above), and in lower intrusion from secondary, ash-rich cloud (below). Um-brella at 18-20 km. Modified from . (c) Eruption of Calbuco, April 22, 2015. Ash injected in single umbrella cloud at c. 15 km. Modifiedfrom https://volcano.si.edu/volcano.cfm?vn=358020 . (d) Eruption of Eyjafjallaj¨okull, April24 and May 1, 2010. Ash injected at multiple heights in relatively quiescent atmosphere on April24. On May 1, under windy conditions, ash mostly injected from single downwind plume. Modifiedfrom photographs by M. Gudmundsson.In the distal region, airborne lidar, EARLINET-AERONET and CALIOP datatypically show much thinner, more discontinuous cloud structures (Fig. 2). Threeseparate tabulations of distal ash cloud layer data for the Eyjafjallaj¨okull plume havebeen published [
Jonsson et al. , 1996;
Ansmann et al. , 2011;
Winker et al. , 2012]. Thesedata suggest that distal clouds from this tropospheric eruption were typically 0.3-3 kmthick, made up of 2-3 layers, with individual layers of 0.3-1.4 km depth, and maximumage of 129 h (¡ 1 week) (Table 2).
Vernier et al. [2013] using CALIOP data, discerned able 1: Measured main, near-vent, upper volcanic cloud depth from top to cloud edge. Measuredfrom geostationary imagery in first scene after eruption start (photography for Redoubt). Datafrom Bear-Crozier et al. [2020]; and
Pouget et al. [2013] and
Holasek et al. [1996a] (below divider)
Volcano Eruption start date Height, kmASL Depth, km No. layers
Tinakula Oct 20, 2017, 2350 UT 16.6 4.9 1Tinakula Oct 20, 2017, 1930 UT 15.1 3.4 1Rinjani Aug 1, 2016, 0345 UT 5.5 4.0 1Manam Jul 31, 2015, 0132 UT 13.7 9.2 † † † Depth possibly overestimated. two or more well-defined layers in the cloud from Puyehue-Cordon Caulle three weeksafter the eruption. Some of the layers showed fold or wrap-around structures (Figure1a in
Vernier et al. [2013]), perhaps related to vertical-plane chaotic mixing [
Pierce andFairlie , 1993]. Clouds were up to 3 km thick, with individual layers of 0.1-2 km depth,in the upper troposphere-lower stratosphere (UTLS), centered on the tropopause at 8-14 km altitude. On July 12-13, 1991, 26 days after the last major eruption of Pinatubo,a lidar flight noted numerous stratospheric layers [
Winker and Osborn , 1992]. The datashowed a number of well-defined layers of 0.5-1 km depth between about 14 and 25km altitude (Figure 1 in
Winker and Osborn [1992]). Along much of the line of flightthere were two layers, but in places there were up to five. In all studies cited above,distal ash layers were horizontal or tilted relative to the horizon, and had extents inthe cross-transport direction of hundreds of km in the troposphere (Eyjafjallaj¨okull),to thousands of km in the stratosphere (Puyehue, Pinatubo). Ash is retained longerin the stratosphere than in the troposphere as suggested by the data cited herein.Once the particles have propagated far from vent (¿11 hr in the case of a largeeruption, e.g., Pinatubo), they no longer retain significant memory of source condi-tions [
Fero et al. , 2009]. Back trajectories of distal ash clouds for Eyjafjallaj¨okulland Puyehue-Cordon Caull´e are generally consistent with theoretically possible cloudheights at the source [
Winker et al. , 2012;
Vernier et al. , 2013]. However, it is notclear that ash was injected at these altitudes at the source, given uncertainties in ver-tical parcel motion and settling speed, or lack of incorporation thereof in the models[
Madankan et al. , 2014;
Vernier et al. , 2013]. It is at least possible that some cloudlayers were generated at distance from the volcanic source.The data presented herein, in text, Figures 2, 3, and Tables 1, 2, suggest thatthe number of layers increases with time, and the depth decreases (see also
Dacreet al. [2015]). Volcanic source conditions are eventually lost after an eruption, meaning able 2: Measured distal Eyjafjallaj¨okull cloud depths from CALIOP lidar. Data from Winkeret al. [2012] (top),
Marenco et al. [2011] (middle) and
Schumann et al. [2011] (lower section). Notethat number of layers varies with spatial position.
Date Cloud Heightrange Depth Age, hr No. lay-erskm ASL km
Apr 15 20100415 1 . − .
23 0.51 < . − .
50 0.58 30 > . − .
27 0.67 24 > . − .
28 0.76 42 1Apr 17 20100417-b 0 . − .
00 0.61 42 1Apr 18 20100418-a 3 . − .
59 0.81 66 –Apr 18 20100418-b 3 . − .
49 0.86 66 –Apr 19 20100419-a 3 . − .
26 1.06 71 –Apr 19 20100419-c 2 . − .
94 0.45 30 –Apr 19 20100419-d 4 . − .
20 0.41 114–126 –Apr 20 20100420 0 . − .
88 1.08 20–24 –May 4 20100504 2 . − . − . − . − . − . − . − . − . − . − . − . − . − . − > . − . −
108 1Apr 19 20100419-3 3 . − . −
108 1Apr 22 20100422-4 0 . − . −
50 diffuseApr 23 20100423-5 2 . − . − > . − . . − > . − . −
129 1May 13 20100513-8 2 . − . . − . −
78 1 tiltedMay 16 20100516-9 3 . − . − > . − . − > . − . −
100 1May 18 20100518-12 4 . − . − > that the atmosphere completely controls cloud shape. Layers are more transient in thetroposphere than in the stratosphere, as mentioned for certain eruptions (also, cf. datain Table 1 with 2; [ Thouret et al. , 2000]). In summary, the features of volcanic cloudsinclude the following:1. Near-vent clouds often evolve from sharply defined with clear eddy or vortexstructure to diffuse or diaphanous, into distal, thin well-defined layers with sharp,smooth boundaries2. There are often multiple distal layers . Collocation in position in planview is common (stacking), but not pervasive4. Sometimes distal cloud forms are horizontal; sometimes sloping or tilted relativeto horizontal5. Separate particle clouds exist, not only separate gas and ash clouds6. Horizontal extent (cid:29) vertical extent7. Vertical extent of near-vent layers is O [5] km, which with time results in8. Vertical extent of single, distal layers being O [0 . −
1] kmThe present contribution seeks to provide explanations for some of these features.
The advection-diffusion equation forms the basis for all VATD models. To illustratedifferences and potential problems in implementation of VATD and the underlyingphysics, in this section, we introduce two zeroth-order simplifications. Our goal is tocontrast the basic behavior of an ash cloud under conditions of isotropic (or constant κ h and κ z ) turbulence, as assumed in the models, and layered turbulence, as we findin the atmosphere. We base our modeling on generation of synthetic atmospheres withand without multiple turbulent layers separated by relatively quiescent air.In the case of isotropic turbulence, we begin by assuming Cartesian coordinates,( x, y, z ), with velocity components, ( u, v, w ). The three components of the turbulentdiffusivity, ( κ x , κ y , κ z ) are the same, κ . The concentration of particles in the i -sizefraction, C i , varies in time, t and space as: ∂C i ∂t + ∂∂x ( uC i ) + ∂∂y ( vC i ) + ∂∂z ( wC i ) = ∂ ∂x ( κC i ) + ∂ ∂y ( κC i ) + ∂ ∂z ( κC i ) + Φ (1)where Φ represents the source/sink function, which in the case of ash clouds is mostlyrepresented by aggregation and disaggregation of small particles. In the present case,such processes are set to zero. We assume a two-dimensional system with a point-source in time and space, w = w s , the settling speed, and that, following a streamtube,the motion of the volcanic cloud can be characterized by a single downwind coordinatedirection s – for which the axis is everywhere tangent to the plume centerline, e.g.,[ Wright , 1977;
Hopkins and Bridgman , 1985] – and speed U in that direction. Underthese assumptions, the advection-diffusion equation becomes: ∂C i ∂t + ∂∂s ( U C i ) + ∂∂z ( w s C i ) = ∂ ∂s ( κC i ) + ∂ ∂z ( κC i ) (2)with the well-known solution for the impulse initial condition [ Csanady , 1980;
Robertsand Webster , 2002]: C i ( s, z, t ) = C i πκt exp (cid:20) − ( s − s − U t ) + ( z − z − w s t ) κt (cid:21) . (3)It is reasonably clear that the solution is a Gaussian in ( s, z ), in which ash spreads,settles and is blown downwind with time.In the second case, of layered turbulence, more realistic for the free atmosphere, weassume particles filling a layer of finite vertical extent. Due to its internal turbulence, oncentration varies in t but not in s or z within the layer, C i ( s, z, t ) = C i ( t ). Thereis no flux at the upper boundary of such a layer, as any particles injected upwardsby eddies will settle back down into the layer. There is a flux boundary condition atthe lower boundary where κ z →
0, and in this case, the advection-diffusion equationbecomes, at the lower boundary: ∂∂t ( C i ) + ∂∂z ( w s C i ) = 0 (4)If furthermore it can be assumed that some particles near the cloud base fall from theturbulent layer when their weight overcomes the internal turbulence at the lower cloudedge, thus developing a step-like concentration gradient at the base of the streamtube,then: C i ( t, z ) = H ( z ) C i ( t ) (5)where H ( z ) is the Heaviside step function, then: ∂∂t ( C i ) + ∂∂z ( w s C i ) = ∂C i ∂t + w s C i ∂H ( z ) ∂z = 0 (6)Integrating through the layer depth, h : ∂C i ∂t (cid:90) h dz = − w s C i (cid:90) h δ ( z ) dz (7)we obtain: dC i dt = − w s h C i (8)which has solution: C i = C i exp (cid:18) − w s ( t − t ) h (cid:19) (9)In the quiescent layer below the boundary, particles only settle and are advecteddownwind, there is no turbulence mechanism to enhance persistence within the layer.Thus, turbulent layers can retain particles longer than do quiescent layers becauseof continuing re-entrainment in eddies. Particles fall relatively rapidly through thequiescent layers because of uninhibited settling, sometimes even enhanced by the effectsof convective sedimentation [ Hoyal et al. , 1999a], which is not included in the presentmodel.Based on similarity theory, the timescales for the processes under the differentparticle transport conditions arising in different layers can be used to examine theconditions under which diffusion or settling dominates. From Eq 3, the timescale ofvertical diffusion, τ , through a layer of depth, h , is given as τ = h κ . From Eq 9,the timescale of settling through the same layer, τ , is τ = hw s . The ratio of the twotimescales indicates domination of particle transport by settling or dispersion in thevertical direction. The ratio is given by the dimensionless group,Π :Π = τ τ = hw s κ (10)In the following section, we explore results from these simplifications and the sim-ilarity analysis, as well as numerical solutions to more complicated cases. Numericalsolutions are provided for the Ash3D VATD model [ Schwaiger et al. , 2012], as well asboth Eulerian and Lagrangian model codes (Table 3). Results
Following from Eq 3, spread from a point source in a VATD model, with isotropicturbulence and a wind of constant speed with height, is shown in Figure 4a, b. Ashdiffuses and progressively spreads from the source as the center of mass descends atthe settling speed. Using a higher settling speed, the rate at which the center of massdescends increases, but the rate at which the particles disperse from the center of massremains constant. Thus, at any one height below the source, particles with a highersettling speed should be spread less distance from the source.
Cloud concentration (mg/m
Cloud concentration (mg/m
Cloud concentration (mg/m
Distance, km H e i gh t, k m Figure 4: Cross sections through Ash3D output, with: (a) instantaneous source, showing advection,settling and isotropic dispersal of ash. 10 min after release. (b) instantaneous source, showingadvection, settling and isotropic dispersal of ash. 120 min after release. (c) maintained source,showing advection with wind shear, settling under isotropic turbulence. 10 min after release. (d) maintained source, showing advection with wind shear, settling in isotropic turbulence. 120 minafter release. Note that maintained source and wind shear result together in elongated dispersalpattern, and layer development. Red cross, source location. a b l e : S i m u l a t i o np a r a m e t e r s . D u r a t i o n r e f e r s t o e m i ss i o n f r o m v e n t . P a r a m e t e r κ = c o n s t κ = c o n s t L a y e r e d A t m o - s ph e r e w i nd = c o n s t w i nd s h e a r S i m u l a t i o n t y p e A s h D A s h D L ag r a n g i a n - L ag r a n g i a n - E u l e r i a n S o u r ce t y p e P o i n t P o i n t P o i n t P o i n t L a y e r S o u r ce h e i g h t , k m . . . . . − . P a rt i c l e s i ze , µ m S e tt li n g s p ee d , m / s . . A m o un t . k m . k m p a r ce l s p a r ce l s p a rt i - c l e s D u r a t i o n . h r . h r I n s t a n t a n e o u s I n s t a n t a n e o u s I n s t a n t a n e o u s T u r bu l e n t l a y e r h e i g h t s ––24 − , . − k m . − . , − . k m . − . , − . k m W i nd s p ee d m / s a ll e l e v B e l o w . k m : m / s m / s m / s m / s . t o21 . k m : i n c r e a s i n g t o50 m / s . t o23 . k m : d ec r e a s i n g t o10 m / s A b o v e . k m : m / s ispersion in the presence of wind shear is shown in Figure 4c, d. The sheardistorts the dispersal pattern from the idealized, spherically symmetric pattern seenin the constant wind field, causing an elongation in the dispersal pattern centered atthe wind speed maximum. Because the deformation is by simple shear, cloud thinningdoes not occur. Wind-shear produced elongation thus creates a volcanic cloud layerthat continues to deepen by diffusion.In a layered atmosphere, we refer to Eq 10 to explore asymptotic behavior. In layersfor which Π >
1, the diffusivity is low relative to the settling speed, the timescale ofdiffusion is therefore long, hence motion is controlled by settling. In layers for whichΠ <
1, the diffusivity is high relative to the settling speed, the timescale of settlingis long, hence motion is dominated by diffusion. Note also that as h increases, thetimescale of diffusion increases faster than does that for settling, meaning it becomesmore likely the particles will exit a layer by settling than by diffusion. For a typicaldiffusivity of κ = 1 m /s in the UTLS [ Wilson , 2004] at 10 km altitude, and layerof depth h = 1 km, the critical settling speed, w s,crit , dividing settling from diffusiondominated motion is c. 1 m/s, which would correspond to a pumice particle of diameterc. 100 µ m at about 2400 kg/cu m (e.g., [ Scollo et al. , 2005]).Results for a simple layered system are shown in Figures 5 and 6. These figuresare simplified from the observations of
Cho et al. [2003], who point out two layers ofespecially striking turbulence from 2-2.7 km and 3.8-4.2 km (Fig. 5a), but do not givespecific values for turbulence intensity in any layers. We therefore apply turbulence inthese two layers through a Lagrangian random walk, and in other layers, no turbulence.Particles in the turbulent layers, then, initiate the random walk, being “stuck” withinthe eddies of the turbulent layer (Fig. 5b). Consider the lower boundary of a layerwith strong turbulence. All the particles there are subject to a random walk. Theyhave a 50% percent probability of going up, and a 50% probability of going down.Those particles sent above the lower boundary due to turbulence are sent to a positionhigher above the boundary than their original position at the boundary. This willgive them a greater chance to spend a longer time in the turbulent layer, whether ornot one considers settling. Thus, for those layers dominated by the random walk anddispersion, Π <
1, Eq 9 holds, and the behavior seen in Figures 5 (purple layers) and6 (red and blue lines) occurs. Particles accumulate in the lowermost turbulent layers(e.g., blue curve in Figure 6), and once reaching a peak, settle out only slowly. Thus,the lower, turbulent layers are the most likely ones in which to observe particles onlonger timescales.The two modes of behavior, isotropic diffusion and layered diffusion, contraststarkly, as seen in explicitly comparing VATD output with that from the Lagrangian-1model (Table 3; Fig. 7). Isotropic diffusion alone cannot lead to generation of ashlayers away from source, but layered diffusion can, even in a constant windfield.
In the present work, we have presented data and models on near-vent and distal volcaniccloud morphology and loading. We have performed numerical experiments comparingdispersal in an atmosphere with constant κ and wind, constant κ and wind shear, andvariable κ z with height. The observational data suggest that more distal clouds ofdepth O [0.1 to 1] km develop from near-vent clouds of depth generally 1 − igure 4: Model of concentration of particles in layered atmosphere. Upper and lower layers arenot turbulent; middle layer turbulent. of specific humidity squared, ( dq / dz ) = [ q ( z + ! z ) ! q ( z )] /( ! z ) ; the Brunt ! Va¨isa¨la¨ frequency squared, N =( g / " q )[ q ( z + ! z ) ! q ( z )]/ ! z , where g is the gravitationalacceleration, q is the potential temperature, and " q is themean potential temperature; and the gradient Richardsonnumber, Ri = N /( dU / dz ) . Also, in order to assess thethermodynamic effects of humidity on stability, we com-puted N v and Ri v where the differenced q quantities arereplaced by the virtual potential temperature q v for unsat-urated conditions and by the equivalent potential temper-ature q e for saturated conditions.[ ] For statistics comparing ! and I to the gradientquantities, we interpolated ! and I to the same 1-m altitudegrid used above in order to have exact coincidence.
4. Discussion of Results [ ] Figure 1 indicates the locations of the vertical pro-files used in this paper. One sees that virtually all of the datawere taken over water.[ ] Figure 2d gives the probability distribution func-tion (PDF) of the number of data points used with respectto latitude. The PDFs in Figures 2a to 2c are divided intothe free troposphere (solid lines) and the boundary layer(dashed lines). One can see that most of the data pointswere taken in the lower to midtroposphere. The relativehumidity PDFs show a very dry mode for the freetroposphere (but with a non-negligible tail at wet values)and a very wet mode for the boundary layer (notsurprising since almost all the profiles were over water).The broad tail in the free tropospheric relative humidityPDF should give us a significant amount of data withwhich to examine the potential effect of humidity on CATgeneration.[ ] Before we go on to discuss the statistics, let uslook at an example profile. Figure 3 shows the verticalprofiles of temperature ( T ), q , N , ( dU / dz ) , and log ! .For vertical gradient quantities ! z = 100 m was used.For the ! calculation ! t = 0.05 s was used. The verticallines at log ! = ! Ri " Figure 4.
PDFs of log ! and log I for ! t = 0.05 s (solid),0.25 s (dashed), and 0.5 s (dash-dotted). Also PDFs of log( dq / dz ) for ! z = 10 m (solid), 100 m (dashed), and 1000 m(dash-dotted). The left-hand column is for free troposphericdata and the right-hand column is for boundary layer data. Figure 3.
Vertical profile taken at 30 ! N, 131 ! E, on March31, 2001, around 0430 UT. The vertical lines at log ! = ! Ri " Table 1.
Turbulence Parameters in the Free Troposphere ! t , s ! , m s ! I ! ! ! ! ! ! ! ! ! ! ! ! Table 2.
Turbulence Parameters in the Boundary Layer ! t , s ! , m s ! I ! ! ! ! ! ! ! ! ! ! ! ! GTE 5 - D o w n w i ndd i s t an c e , m Figure 5: Turbulent tropospheric layers (shaded) indicated by constant mixing ratio ( q ), highturbulent energy dissipation rate (log " ), and bounded by high shear (( dU/dz ) ). Modified fromCho et al. (2003). Last panel: paths of two volcanic particles settling through the turbulent layers,in which suspension is enhanced. Figure 5: (a)
Turbulent tropospheric layers (shaded) indicated by constant mixing ratio ( q ), highturbulent energy dissipation rate (log ε ), and bounded by high shear (( dU/dz ) ). Modified from Cho et al. [2003]. Shaded layers are used in simplified layer models Lagrangian-2 and Eulerian(Table 3) (b)
Lagrangian paths of two volcanic particles settling through the turbulent layers, inwhich suspension is enhanced. This is output from model Lagrangian-2.Figure 6: Eulerian model (Table 3) of number of particles in layered atmosphere. Middle layeris not turbulent (green dashed curve); upper and lower layers are turbulent (red and blue solidcurves)downwind clouds occur at heights consistent with the original eruption column heightsfor both tropospheric and stratospheric eruptions. The depth range of the distal layers, eing markedly less than the near-vent depth range, and the common stacking of moredistal ash cloud layers, suggest that their development is controlled by atmosphericprocesses. The observations are consistent with the working hypothesis that the lay-ering of the atmosphere in turbulence intensity, causing alternating suspension andsettling dominated behavior of particles, is a cause of distal layer morphology.The present model outputs (Figs. 4, 7) are consistent with those of VATD andbacktrajectory models that layers can be produced under conditions of certain sourcecharacteristics or wind shear [ Devenish et al. , 2012;
Folch et al. , 2012;
Heinold et al. ,2012;
Winker et al. , 2012;
Vernier et al. , 2013]. The model outputs assuming theatmosphere has multiple turbulent layers support the working hypothesis regardingthe effects of an atmosphere layered with respect to turbulence intensity. Thus, inaddition to the near-vent, volcanic and sedimentation processes causing formation ofvolcanic layers, processes associated with atmospheric layered turbulence also producelayering in ash clouds. These are often multilayered due to multiple, alternating layersof turbulent and quiescent air. The distal ash layers furthermore scale to the depth ofthe alternating turbulent and quiescent layers in the atmosphere, which are O [0 . − Concentration, g/cu mAB
Figure 7: (a)
Cross section through Ash3D output (Table 3), with instantaneous source and nowind shear, showing advection, settling and isotropic dispersal of ash. (b)
Cross section throughLagrangian-1 dispersion model (Table 3 with turbulence layered atmosphere, showing advection,settling and non-isotropic ash dispersal. Red × is point of origin for particles, and color gradientis scaled to concentration in both.Because of the alternating turbulent and quiescent structure in the troposphere andstratosphere, volcanic ash clouds tend to separate vertically over time, lending to themthe distinct layering or banded appearance in imagery. The turbulent layers retainparticles longer than the quiescent layers because the turbulence retains particles insuspension. Particles fall more rapidly through the relatively quiescent layers (lower κ z ) by single particle settling, or because of convective sedimentation. he results suggest that to better model the position and morphology of ash cloudsfor aviation safety and other purposes in VATDs, the vertical characteristics of theatmosphere need to be better resolved than is typical at present. Because of theimportance of turbulence and moisture to layer formation, it is critical that these twoparameters especially be estimated well, and at as high a vertical resolution as possible. Abbreviations.
The following abbreviations are used in this manuscript:AERONET AErosol RObotic NETworkBT Brightness TemperatureCALIOP Cloud-Aerosol Lidar with Orthogonal PolarizationEARLINET European Aerosol Research Lidar NetworkIAVW International Airways Volcano WatchRH Relative HumidityUTLS Upper Troposphere - Lower StratosphereVATD Volcanic Ash Transport and Dispersal
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