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Rise dynamics and relative ash distribution in vulcanian eruption plumes at Santiaguito Volcano, Guatemala, revealed using an ultraviolet imaging camera

[1] Santiaguito Volcano, Guatemala, regularly produces small vulcanian eruption plumes which rise to heights of up to 2 km. A combined study using a novel UV camera coupled with classical analysis of the fluid dynamics of finite-volume buoyant releases (thermals) has been used to develop a detection algorithm for ground-based volcanic ash monitoring. Analysis of plume rise dynamics shows that vulcanian eruption plumes at Santiaguito behave as axisymmetric buoyant thermals, and this behaviour is consistent with eruption of volcanic gas and particle mixtures whose initial momentum is dissipated by flow through a porous capping layer. The UV imager has been adapted to detect relative ash burdens through the use of a single filter, centred on 307 nm, an edge detection and background fitting procedure and normalising to a simple theoretical model. The method provides the capability to observe and measure the internal structure of the plume, and processes occurring during plume rise, including concentration of ash over time into the thermal ‘head’, increased ash at the plume edges during early formation of the thermal and dilution at the top of the plume head as entrainment occurs.

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[2] Vulcanian eruptions are short-lived volcanic explosions thought to result from rapid decompression of a conduit containing pressurized magma [Self et al., 1979; Woods et al., 1995; Sparks, 1997]. They typically have a duration of tens of seconds and erupt less than 0.1 km^{3} of magma [Morrissey and Mastin, 2000], suggesting that only a portion of the magma in the conduit is fragmented and evacuated. They can result from repeated pressurisation of intermediate composition lava domes, in the absence of any more explosive activity. Vulcanian activity can persist for years, occurring regularly at several volcanoes around the world, potentially representing a large cumulative erupted mass (∼10^{10}–10^{13} kg) [Morrissey and Mastin, 2000].

[3] Santiaguito Volcano, Guatemala, (2520 m) is a dacitic lava-dome complex that began growing in 1922 inside the crater left by the 1902 eruption of its parent Santa María Volcano (3720 m). Small vulcanian eruptive events take place at intervals of between 30 minutes and 2 hours, with each event producing a plume of ash and steam for 30–60 seconds [Bluth and Rose, 2004]. In this paper, we describe direct observations of vulcanian activity at Santiaguito, Guatemala, made using an UV imaging camera [Bluth et al., 2007] designed to detect SO_{2} emissions from volcanoes at high temporal resolution in real time. We show, by combining constraints from the observed plume dynamics, and transmitted light intensity measurements from the UV imaging camera, how a novel ground-based volcanic ash detection algorithm can be developed for small scale volcanic eruption plumes and smaller buoyant releases. The ash detection method can provide direct measurements of use in the study of fundamental dynamics of short-duration volcanic events and for testing associated numerical models of such events [Clarke et al., 2002], and represents an initial quantitative step towards measuring near-source ash concentrations.

2. Methods

[4] The observations presented in this paper were collected on 27th March 2006 from a ridge line 4.12 km SE of the dome, capturing two eruption sequences at a regular frame rate of 0.13 frames per second, using a UV camera [Bluth et al., 2007] and a single bandpass filter centred at 307 nm. At the time of the eruptions, the atmosphere approximated to a state of neutral stability, i.e., no strong vertical updrafts, and there was no significant atmospheric crosswind.

[5] Operation of UV imaging camera has been detailed elsewhere [Bluth et al., 2007], so what follows is a brief summary. The camera operates on the principle of difference imaging, deriving a proxy for the amount of radiation leaving the source (in this context the sky) either using a single narrow (10 nm FWHM) filter, or more robustly, multiple filters, and then solving the Beer-Lambert Law [Bluth et al., 2007]. This yields absorbance, which can then be converted, using the camera in conventional mode, to SO_{2} line-of-sight burden using calibration curves generated by insertion of calibration cells in the field of view. The fundamental assumption in this work is that the absorbance by ash overwhelms any signal from SO_{2} and that absorbances can be attributed to the presence of ash alone. This is easily verified by comparing ash-laden vs SO_{2}-laden transmittances from both the UV camera and DOAS instruments; ash is responsible for >95% of attenuation during explosions.

[6] The camera is capable (in single filter mode) of taking a measurement approximately every eight seconds which represents an order of magnitude improvement in temporal resolution when compared to SO_{2} emission rate measurement using current technologies (e.g., DOAS) [Edmonds et al., 2003]. This improvement is significant for many facets of volcanic gas measurement, and critical in studying plume rise dynamics.

[7] The timescale of vulcanian eruption duration is short compared to the rise time of the resulting eruption plume [Sparks et al., 1997], and is on the order of a few seconds at Santiaguito, compared to several tens of seconds of rise. Therefore, as a first approximation we can consider the vulcanian eruption plumes as finite volume releases, unlike at Soufriere Hills, Montserrat where explosions lasted much longer [Formenti et al., 2003]. We expect that momentum effects will be important in the initial stages of plume rise, and that subsequently the plume will decelerate and buoyancy effects will dominate [Sparks et al., 1997]. Observations of smaller volume volcanic plumes suggest that the transition between these phases may be characterised by deceleration of the thermal to velocities less than 15 m s^{−1} [Patrick, 2007]. Thus we first investigate the plume dynamics by analogy to steady finite volume releases of buoyant fluid, or thermals.

[8] For a thermal rising by buoyancy only and through a static atmosphere, the conservation equations for mass, momentum and buoyancy have been derived by Morton et al. [1956], and solutions for the variation of horizontal radius, r, vertical rise velocity, w, and buoyancy (or reduced gravity), g′ with height, z, have the following forms

where ɛ is the entrainment constant and the subscript 0 denotes the initial value of the parameter. The buoyancy g' depends on the difference between the bulk density of the plume and the atmosphere,

where g is the acceleration due to gravity, and ρ_{p} and ρ_{a} are the bulk density of the plume and the density of the atmosphere, respectively. The entrainment constant has an empirically-determined value of about 0.25 [Scorer, 1957; Turner, 1979]. Equation (3) can be integrated subject to the initial condition w = 0 at z = 0 to give the dependence of thermal propagation with height,

The radius of the thermal can be related to the volume of the thermal, V, by a shape factor, m, defined such that

A value of m = 3 defines the shape of the thermal as being an oblate spheroid [Turner, 1979], and equation (5) can be rewritten

Equation (7) is appropriate for axisymmetric thermals released from a source which approximates to a point source of buoyancy, with a time-averaged cross-section that is circular. Comparing observations of the propagation of the flow front of vulcanian eruption plumes with the form of equation (7) provides a robust test for whether the plume cross-section is circular. Furthermore, the time dependence of the plume front propagation also provides an indication of the cross-sectional shape. Dimensional analysis of plume rise dynamics from a point source of buoyancy, suggests immediately that z ∼ t^{1/2}, as shown by equation (7). For a two-dimensional line source of buoyancy, dimensional analysis suggests that z ∼ t^{2/3}, so the form of the rise propagation can also be used to constrain the cross-sectional shape of the thermal.

3. Observations of Plume Dynamics at Santiaguito

[9] The dynamics of vulcanian eruption plumes at Santiaguito were determined from analysis of conventional digital video (30 frames per second) and UV camera images (1 frame approximately every 8 seconds). Analysis of the plume propagation shows that the plume front position varies as t^{1/2} (Figure 1). Using equation (7) and estimating the volume of the thermal close to the vent, we determined the entrainment constant to have the value ɛ = 0.22, close to the value ɛ = 0.25 determined in laboratory experiments [Scorer, 1957; Turner, 1979]. Based on these observations, we infer that the eruption plume is propagating as a buoyant thermal. Typical plume front rise velocities were about 10 m s^{−1}, further suggesting that the motion was controlled by buoyancy [Patrick, 2007]. Measurements of the rise dynamics at two positions can be used to estimate the source buoyancy, g_{0}′, which had the value g_{0}′ ≈ 5 m s^{−2} for both eruptions described here. Assuming an atmospheric density of approximately 1.2 kg m^{−3}, using equation (4) yields the source bulk density of the Santiaguito plumes to be approximately 0.6 kg m^{−3}.

[10] Direct measurements of the shape of the vulcanian eruption plumes at Santiaguito show that these have the form of an oblate spheroidal front with a tapering tail. An important consequence of these observations of the plume front propagation and the value of the shape factor is that these eruption plumes can be approximated as being circular in cross-section.

4. Volcanic Ash Detection Algorithm

[11] Observations of the plume rise dynamics can be combined with measured absorbances, obtained using the UV imaging camera, to develop an algorithm for ground-based detection of ash within an erupting plume. The basis of this algorithm is a comparison of the absorbances obtained from the UV imaging measurements with the theoretical absorbance that would be expected through the plume cross-section if the absorbing materials were homogeneously distributed.

[12] The observation position at Santiaguito is 4.12 km from the eruption plumes, whose maximum width is less than approximately 200 m (for our range of observations) so the light path through the plume can be adequately represented by parallel chord lengths given the assumption that single scattering dominates. The edge of the plume is defined using a transmittance threshold as follows: the UV imaging camera's field-of-view was wider than the plume width, and the transmittance was measured for each horizontal line across each image, with pixels at the edge of the image giving values of the transmittance of the atmosphere (regions where no ash is present). A polynomial was fitted to the transmittance across each horizontal line, using only the edges of the image, and the edge of the plume was defined as the position at which the transmittance deviates significantly from the fitted curve, as determined by goodness-of-fit analysis (see Figure 2). The transmittance threshold was set empirically at 0.95 of the fitted curve which was the maximum useable value without triggering an unacceptable (<0.1%) level of false positives.

[13] The theoretical absorbance of the plume was then calculated assuming that ash was homogeneously distributed across the plume cross-section (Figure 3 (top)). For circular cross-section plumes, such as those at Santiaguito, the theoretical absorbance profile will be symmetrical about the plume centreline with a central peak, based on the path length of transmitted light, single scattering, and homogeneous ash distribution within the plume. We define the relative absorbance γ as the ratio of the measured absorbance to the theoretical absorbance, such that values γ > 1 indicate regions where the ash concentration is greater than the theoretical homogeneous concentration of ash across the plume cross-section (Figure 3 (bottom)).

[14]Figure 4 shows the relative ash concentration for three successive UV imaging camera images of a Santiaguito plume. Several things are worthy of note; (1) over time mass concentrates in the head of the thermal. (2) The top of the thermal has a significantly lower relative absorbance, indicative of dilution due to direct interaction with the atmosphere. (3) The edges of the thermal have significantly higher ash concentration than the centre, particularly in the early stages of the development of the thermal. These direct observations of the interior of a small volcanic ash plume are consistent with the fluid dynamical structure of buoyant flows [Turner, 1979].

[15] The rise dynamics of the eruption plume can also be used to estimate the mass of ash within the plume as follows: for vulcanian eruptions at Santiaguito, we estimate the source bulk density of the plume to be approximately 0.6 kg m^{−3}. The volume fraction of volcanic ash in the plume, V_{a}, can be determined from the bulk density of the plume

where ρ_{ash} and ρ_{gas} are the densities of volcanic ash and gas in the eruption plume, respectively. Assuming the state behaviour of volcanic gases can be adequately described by the perfect gas law [Sparks et al., 1997], we estimate that the volcanic gas density at Santiaguito can range between approximately 0.15–0.30 kg m^{−3}, taking water vapour to be the volatile component, eruption temperatures from 800–1400 K and decompression to atmospheric pressure appropriate for vulcanian eruptions at Santiaguito where shock waves are not observed [Bluth and Rose, 2004].

[16] For typical values of the density of dacitic volcanic ash (ρ_{ash} = 650 kg m^{−3}) [Bonadonna and Phillips, 2003], equation (8) suggests the volume fraction of ash within the Santiaguito plumes is approximately 4.5 × 10^{−4} to 7.0 × 10^{−4}.

[17] Combining the estimate of the ash volume fraction for the Santiaguito plumes with the relative ash concentration measurements using the UV imaging camera (Figure 4) enables the ash mass distribution within the plume to be estimated. Figure 4 (right) shows the plume with a radius of ∼150m, for which equation (6) suggests a plume volume of 7 × 10^{7} m^{3}. Using the volume fraction and density above, this suggests the mass of a single thermal episode to be on the order of 2 × 10^{4} tonnes of ash. The ash volume fraction estimates can also be used to convert the relative ash concentration to a mass distribution, as shown in Figure 4.

5. Discussion

[18] Added value obtained from combining field monitoring measurements and analysis of the fundamental dynamics of eruption plumes can provide a new monitoring tool for ground-based volcanic ash detection. Eruption plume dynamics at Santiaguito are simplified by the observation that plume rise is only dependent on the source buoyancy, although it is possible to also constrain the plume geometry when both source momentum and buoyancy control the plume rise dynamics. The absence of any influence of the momentum of the plume near its source is consistent with the observation that the initial release occurs through a system of annular cracks [Bluth and Rose, 2004].This is the expected configuration for eruption plumes except for those from strongly two-dimensional source geometries, such as elongated fissures.

[19] Field measurements of ash distribution show that for small, finite-volume eruptions, the ash becomes concentrated in the plume head during its rise. There is only a relatively low concentration of ash in the flow that follows the plume front, consistent with the observation that the plume rises as discrete thermal, with the trailing region not contributing to the rise dynamics. Even at the low rise velocities of Santiaguito plumes (less than 20 m s^{−1} for the images shown in Figure 4), the ash remains fully suspended within the main plume front and there is little evidence of significant ash settling or dispersion from the plume as it rises close to its source. High relative concentrations of ash at the edges of the rising plume are consistent with the circular geometry of the source of the thermal. These observations offer the possibility of detailed analysis of the meter-length scale structure of volcanic plumes, which could be used to test predictions from multidimensional numerical models [e.g., Clarke et al., 2002].

[20] Measurements of evolution of ash distribution within the rising plume can only be obtained by using absorbance as a proxy for ash distribution to exploit the high temporal resolution of the UV imaging camera (1 measurement every 8 seconds). The primary source of unsystematic error with this method of ash detection is UV scattering from the surface of the plume. This was minimised during the field experiment by controlling the sun-target-camera angle and not having the sun strongly illuminate one side of the plume. An inherent difficulty is that the three-dimensional scattering physics controlling the behaviour of UV radiation as it strikes the plume is extremely complex and time dependent. Whilst we appreciate this can be a major source of unquantifiable variation, this study shows interesting and important possibilities if care is taken to minimise these effects. At present, these effects cannot be fully quantified until more sophisticated methodology becomes available to account for the transient spatial and temporal variations in UV scattering.

6. Conclusions

[21] Through a combination of a novel field monitoring technique and constraints from fundamental plume dynamics, a new ground-based ash detection algorithm has been developed. The UV imaging camera, an imaging system based on an off-the-shelf UV sensitive CCD camera [Bluth et al., 2007] has been used to directly measure the absorbance by the ash in small vulcanian eruption plumes at Santiaguito. An algorithm has been developed to identify ash mass distribution within the plumes, using constraints on plume geometry and density obtained from analysis of the plume rise dynamics. The observations suggest that the eruption plumes at Santiaguito behave as constant volume releases whose dynamics is controlled by buoyancy only, consistent with eruption through a porous system of cracks [Bluth and Rose, 2004]. Ash mass distributions within the plumes are consistent with expectations for buoyant thermal rise, and these measurements offer the possibility for detailed investigation of the structure of volcanic plumes and detailed comparisons with numerical models. The retrieval of the absorbance is simplified, although based on robust assumptions about the relative absorbance of the plume constituents. Future work will include developing a dynamic thresholding algorithm for plume edge detection and improved treatment of UV scattering from the plume surface.