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Keywords:

  • plume modeling;
  • plume dynamics;
  • volcanic eruption;
  • climate impact of volcanoes

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Model Description and Experimental Setup
  5. 3. Results
  6. 4. Conclusions
  7. References
  8. Supporting Information

[1] Many of the past large volcanic eruptions like Tambora in 1815, Krakatau in 1835, and Pinatubo in 1991 were secondary so called co-ignimbrite eruptions that were forced over a large area instead of a point source as in the Plinian case. Previous modeling studies were based on one-dimensional plume models. We used the fully three-dimensional plume model ATHAM (Active Tracer High-Resolution Atmospheric Model) to investigate the dynamics and the resulting plume heights of co-ignimbrite eruptions in an idealized setup. Ash particles as well as a sulfur dioxide (SO2) tracer are included in the model. In the analysis we focus on the behavior of SO2 since the neutral buoyancy height is an ill-defined parameter for gravitationally settling particles. In contrast to Plinian plumes the co-ignimbrite plumes develop from multiple updrafts resulting in significantly reduced neutral buoyancy heights. At least a two-dimensional modeling framework is necessary to capture the relevant dynamical features.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Model Description and Experimental Setup
  5. 3. Results
  6. 4. Conclusions
  7. References
  8. Supporting Information

[2] Volcanic eruptions emit large amounts of gases and particles into the atmosphere. Since ash particles are quickly removed from the atmosphere only volcanic gases have atmospheric residence times long enough to have a climatic effect. For example, stratospheric sulfate formed from volcanic sulfur dioxide (SO2) can impact global climate for several years [Robock, 2000]. Often volcanic plumes develop from gas particle mixtures with a bulk density above that of the atmospheric environment. Hence, these plumes only become buoyant by entraining ambient air. Otherwise the column will collapse and form a pyroclastic flow. Co-ignimbrite (secondary) plumes develop when the pyroclastic flow becomes buoyant by entrainment or gravitational settling of particles [Sparks et al., 1997]. The most recent example for such an event on a large scale was the eruption of Mt. Pinatubo in 1991 [Holasek et al., 1996]. However, much larger events took place in the past where tens of kilometers wide pyroclastic flows developed [Branney and Kokelaar, 2002] with umbrella clouds that may have covered continental scales.

[3] Baines and Sparks [2005] investigated the height of co-ignimbrite plumes utilizing a simple one-dimensional model [Sparks et al., 1997; Woods, 1988]. They justified the use of a one-dimensional model by arguing that co-ignimbrite like Plinian eruptions can be characterized by a single lift off. They found that the height of the umbrella cloud significantly increases with the size of the source. This stationary one-dimensional model does not differentiate between the maximum and neutral buoyancy height (NBH). Here we will investigate the effect of the size of the initial pyroclastic flow on the evolution of the co-ignimbrite cloud, its maximum overshooting and NBH using a three-dimensional numerical model. The results will show a qualitatively different behavior than for Plinian plumes and suggest that neither NBH nor the maximum overshooting depends linearly on the size of the source.

2. Model Description and Experimental Setup

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Model Description and Experimental Setup
  5. 3. Results
  6. 4. Conclusions
  7. References
  8. Supporting Information

[4] The Active Tracer High-Resolution Atmospheric Model (ATHAM) was originally developed to study volcanic plumes from Plinian eruptions [Oberhuber et al., 1998; Herzog et al., 2003; Textor et al., 2003]. However, since ATHAM is conceptually an atmospheric circulation model for cloud resolving scales extended with a concept for dynamically active tracers, the model can and has already successfully been applied to study biomass burning plumes [Trentmann et al., 2002], pyro-cumulus clouds from large wild fires [Trentmann et al., 2006], and shallow cumulus clouds [Guo et al., 2007]. Modules for different physical processes in different complexity can be selected as needed for the application under consideration.

[5] The dynamical core of ATHAM solves the compressible Euler equations for momentum, pressure and temperature of a gas particle mixture [Oberhuber et al., 1998]. The sub-grid turbulence closure scheme differentiates between the horizontal and vertical directions [Herzog et al., 2003]. The cloud microphysics predicts the mass of hydrometeors in liquid and ice phase [Herzog et al., 1998]. An extension exists to simulate particle aggregation [Textor et al., 2006]. Additional modules include radiation [Langmann et al., 1998], gas phase chemistry [Trentmann et al., 2002] and gas scavenging by hydrometeors [Textor et al., 2003].

[6] In the presented simulations particle aggregation was not considered since this does not significantly impact the initial plume development [Textor et al., 2006]. Radiation was not included since the radiative forcing is orders of magnitude smaller than the volcanic forcing. Gas phase chemistry was not considered since the time scales for the oxidation of SO2 in the atmosphere are in the order of one month [Hoff, 1992]. Gas scavenging by hydrometeors was switched off for simplicity and because it is inefficient for weakly-soluble gas species like SO2 [Textor et al., 2003].

[7] In ATHAM prognostic equations are solved on a three-dimensional Cartesian grid. For sensitivity studies ATHAM can be used in a two-dimensional mode. The Cartesian two-dimensional version performs simulations on a vertical slice of the three-dimensional model. In addition, cylindrical coordinates can be used for axisymmetric problems. Grid stretching allows for the use of a higher spatial resolution in the model centre than at the model boundaries.

[8] The model domains and the size of the initial layers of a hot mixture of gas and ash (“hot pillows”) for each simulation are listed in Table 1. The initial ash layer is located at the model center where the horizontal resolution is highest and kept constant within the ash layer. Away from this layer the spatial resolution increases gradually reaching several kilometers at the lateral boundaries and around 700 m at the top boundary. As in Baines and Sparks [2005] the initial gas ash layer has a circular shape. In addition to their sizes we considered smaller co-ignimbrites with initial radii between 10 km and 2.5 km. Table 2 lists the properties of the initial gas particle mixture. The temperature of the initial gas ash layer is 500°C plus a random perturbation with maximum amplitude of 5°C. The total ash content is adjusted so that the bulk density at the top of the initial gas ash layer equals the density of the surrounding atmosphere.

Table 1. Size, Ash and Sulfur Loading for the simulated Idealized Co-ignimbrite Eruptions
RadiusVertical ExtentInitial Ash LoadingSO2 LoadingModel DomainFinest Spatial Resolution
70 km2.33 km2.57 1013 kg3.84 1011 kg750 × 750 × 50 km3500 × 500 × 100 m3
50 km1.66 km9.60 1012 kg1.45 1011 kg600 × 600 × 50 km3500 × 500 × 100 m3
30 km1.00 km2.03 1012 kg3.12 1010 kg350 × 350 × 50 km3500 × 500 × 100 m3
10 km1.00 km2.24 1011 kg3.45 109 kg275 × 275 × 50 km3200 × 200 × 100 m3
5.0 km1.00 km5.61 1010 kg8.63 108 kg250 × 250 × 50 km3100 × 100 × 100 m3
2.5 km1.00 km1.37 1010 kg2.11 108 kg200 × 200 × 50 km3100 × 100 × 100 m3
Table 2. Temperature and Composition of the Ash Particle Mixture Used in All Simulations of Idealized Co-ignimbrite Eruptionsa
 Properties of Ash Particle Mixture
  • a

    A random temperature perturbation with a maximum amplitude of 5 °C has been added to the initial mixed hot gas and ash layer. The exact amount of lapilli is adjusted in each simulation so that the bulk density of the mixture at the top of the initial gas ash layer equals the environmental density at the same height.

Temperature500 ± 5 °C
Fine ash (r = 100 μm)7% by weight
Ash (r = 300 μm)18% by weight
Lapilli (r = 2 mm)40–42% by weight
Water vapor3% by weight
SO21% by weight

[9] Since SO2 injections are important for the climatic effect of a co-ignimbrite eruption and since the neutral buoyancy height is an ill-defined parameter for gravitationally settling particles, only the simulated SO2 distributions are discussed in the following and used to determine plume height. We distinguish between maximum plume height and neutral buoyancy height. The maximum plume height is the maximum height at which the simulated specific concentration of SO2 reaches or exceeds 0.1 g/kg. The neutral buoyancy height is defined as the height where SO2 reaches a maximum value in the vertical profile. Vertical profiles are calculated for the fully developed plume by horizontal integration over the tracer mass at a constant altitude. This results in a profile of tracer mass per unit altitude as a function of altitude. Ash particles are important for the plume development. However, the details of particle plume interaction are beyond the focus of this study and will be discussed elsewhere.

[10] Fully three-dimensional simulations are shown in detail here. In addition, two-dimensional axisymmetric simulations were performed. The initial atmospheric conditions are horizontally homogeneous and represent a tropical atmosphere with a tropopause (cold point) at 17 km altitude above sea level [McClatchey et al., 1972]. In the following, plume height is always measured in altitude above sea level. The model is run from its initial conditions without additional external forcing for a maximum of one hour of simulated time or until the plume reaches the lateral boundaries of the model domain.

3. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Model Description and Experimental Setup
  5. 3. Results
  6. 4. Conclusions
  7. References
  8. Supporting Information

[11] Figure 1 shows the evolution of the co-ignimbrite plume that is formed from a 1.66 km thick circular layer of hot ash and gases with a radius of 50 km as simulated by the full three-dimensional model. Depicted are the volume concentrations of SO2 after 5 min (Figure 1a), 10 min (Figure 1b), and 30 min (Figure 1c). The plume reaches its maximum height of about 34 km altitude after 10 min into the simulation. This maximum plume height is produced by a pronounced overshooting of the rising plume. In the following minutes the SO2 plume moves back to its neutral buoyancy height where it spreads radially. Most of the SO2 at this later stage of the simulation is found between 15 km and 22 km altitude leading to a NBH that is only about half the maximum plume height.

image

Figure 1. SO2 plumes of the idealized co-ignimbrite with 50 km radius after 5, 10, and 30 minutes are shown in Figures 1a–1c, respectively. Displayed are the volume concentrations of SO2 in [g/m3] as two-dimensional cuts through the model centre of the three-dimensional simulation.

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[12] Towards the end of the simulation the co-ignimbrite plume resembles more and more a plume that also could have formed from a Plinian eruption [see, e.g., Herzog et al., 2003]. However, the co-ignimbrite plume is formed by completely different mechanisms than the Plinian plume. In the Plinian case a single updraft develops above the vent. In the co-ignimbrite case convection always starts within the first minute of simulation at the edges of the hot gas ash layer where horizontal gradients are strongest and where horizontal entrainment of ambient air contributes to the dilution of the gas particle mixture. In the following multiple updrafts develop at the top of the initial hot gas particle layer which is clearly visible from the SO2 plume after 5 min in Figure 1a. From these multiple updrafts one single umbrella cloud is formed (Figures 1b and 1c). The umbrella reaches a radius of more than 200 km already after 30 minutes.

[13] The vertical velocity at 5km altitude after 5min is shown in Figure 2 for the idealized co-ignimbrite with 50 km radius. The updraft velocities typically exceed 50 ms−1 with peak values of over 200 ms−1. Updrafts are surrounded by compensating downdrafts. On average downdrafts are weaker than updrafts with peak values of −120 ms−1. Since the co-ignimbrite is on average an area of updraft it is surrounded by a ring of downdraft. The structure within this ring reflects the mean background wind blowing from the left to the right in Figure 2. Updrafts are randomly distributed over the area covered by the initial ash layer. However, their size has a characteristic spatial scale in the order of few kilometers. The initial temperature perturbation does not determine the number of the structure of the multiple updrafts.

image

Figure 2. Vertical velocity 5 km above ground after 5 min for the idealized co-ignimbrite with 50 km radius simulated in 3d. Updrafts are shown blue, downdrafts in red.

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[14] Figure 3 provides an overview of all the model simulations. The black bars are the results of Baines and Sparks [2005] while the cross-hatched colored bars indicate maximum plume heights and the full colored bars NBH simulated by different versions of ATHAM. In the one-dimensional model the plume height is determined from the height of zero vertical velocity. Since no further height information is available in this model Baines and Sparks [2005] identify this plume height with the NBH for which they find an increase with increased size of the hot pillow. ATHAM simulations, however, produce much reduced NBHs while revealing maximum plume heights for the larger hot pillows comparable to the results of the one-dimensional model. The ATHAM simulations produce NBHs that are very different from the maximum heights. Basically all NBHs are below 20 km, even for the biggest initial hot pillow. Therefore the co-ignimbrite eruptions do not have the potential for climatic impact that the maximum plume height seem to indicate. There is almost no correlation between the maximum and the neutral buoyancy height. Since the injection of SO2 and other trace gases into the atmosphere takes place around the NBH our results suggest much reduced injection heights of SO2 compared with more conventional estimates from one-dimensional models. For the two largest simulated co-ignimbrite plumes the NBH is almost 50% lower than suggested by the one-dimensional model leading to a strong reduction in the atmospheric lifetime and potential climatic effect of the volcanic emissions.

image

Figure 3. Plume Heights: maximum versus neutral buoyancy height. Maximum plume heights from 3d ATHAM simulations agree reasonably well with results from 1d model by Baines and Sparks [2005]. Neutral buoyancy heights are consistent between the 2d and 3d versions of ATHAM and significantly lower than maximum plume heights.

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[15] The tropopause acts as an effective barrier since the stratification changes here from approximately moist adiabatic to extremely stable conditions. For the same increase in plume height much more energy is required above the tropopause than below. Increasing the size of the idealized co-ignimbrite produces more updrafts, however, the strength of each individual updraft remains approximately the same. This behavior cannot be captured by a one-dimensional model. Here only one updraft can be represented. A larger co-ignimbrite will always lead to a stronger updraft leading to an overestimate of the NBH. Hence, stratospheric loading and life time of sulfate compounds (including SO2 and sulfate aerosol forming in the aftermath of a co-ignimbrite eruption) will be much less than one would anticipate from a Plinian eruption with single updraft and similar eruption rate.

[16] Vertical profiles are shown in Figure 4 for the three-dimensional simulations after 30 minutes. The horizontal black line is the tropopause (cold point) height at 17 km. The profiles show that only the biggest initial hot pillows inject substantial amounts of SO2 into the stratosphere, while the smaller co-ignimbrite plumes just reach the tropopause level. The shape of the vertical profiles varies with the size of the initial gas ash layer. An initial radius of 30 km produces a single umbrella cloud with the smallest vertical extent. The umbrella region becomes broader when increasing the initial radius. Decreasing the initial radius produces multi-layered umbrella clouds as indicated by multiple peaks in the vertical profile. Therefore the injection of volcanic emissions into the atmosphere is not simply characterized by a constant emission height but also by a characteristic vertical profile.

image

Figure 4. 3d vertical SO2 profiles after 30 min for idealized co-ignimbrite eruptions with different initial radius. The blue line marks the tropopause (cold point) at 17 km altitude.

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[17] The forcing in our model simulations is axisymmetric and, hence, while there are some differences between the two-dimensional axisymmetric and the full three-dimensional ATHAM simulations in the maximum height of the plume, the NBH agrees quite well between these two model versions.

4. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Model Description and Experimental Setup
  5. 3. Results
  6. 4. Conclusions
  7. References
  8. Supporting Information

[18] We performed a sensitivity analysis of the effects of the size of an idealized pyroclastic flow on co-ignimbrite plumes. Focusing on SO2, results from a three-dimensional numerical model were compared against a standard one-dimensional plume model. Co-ignimbrite eruptions are characterized by multiple updrafts which are less efficient in the vertical transport of tracers and therefore result in reduced neutral buoyancy heights. The plume development is thus very different from that of a Plinian eruption. A regime shift of convection takes place when the initial hot pillow is smaller than about 5 km in radius. Then convection concentrates within one single cell, much like in a Plinian column. A one-dimensional modeling framework is insufficient to capture the relevant dynamics of a co-ignimbrite eruption. The results show that very large co-ignimbrite plumes are not very effective in transporting volcanic gases into the stratosphere. The simulations show that it is necessary to apply at least two-dimensional models to simulate the complex development of a co-ignimbrite plume and to capture correctly the injection heights of material into the atmosphere.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Model Description and Experimental Setup
  5. 3. Results
  6. 4. Conclusions
  7. References
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Model Description and Experimental Setup
  5. 3. Results
  6. 4. Conclusions
  7. References
  8. Supporting Information
FilenameFormatSizeDescription
grl27480-sup-0001-t01.txtplain text document1KTab-delimited Table 1.
grl27480-sup-0002-t02.txtplain text document1KTab-delimited Table 2.

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