Many of the standard volcanic gas flux measurement approaches involve absorption spectroscopy in combination with wind speed measurements. Here, we present a new method using video images of volcanic plumes to measure the speed of convective structures combined with classical plume theory to estimate volcanic fluxes. We apply the method to a nearly vertical gas plume at Villarrica Volcano, Chile, and a wind-blown gas plume at Mount Etna, Italy. Our estimates of the gas fluxes are consistent in magnitude with previous reported fluxes obtained by spectroscopy and electrochemical sensors for these volcanoes. Compared to conventional gas flux measurement techniques focusing on SO_{2}, our new model also has the potential to be used for sulfur-poor plumes in hydrothermal systems because it estimates the H_{2}O flux.

Monitoring the flux of gas from volcanoes is a fundamental component of volcano monitoring programs and is used as a basis for eruption forecasting. Here, the authors present a new method using video images of volcanic gas plumes to measure the speed of convective structures and to estimate volcanic fluxes.

Volcanic gas plumes are composed of water vapour, CO_{2}, SO_{2} and a range of other gases, with the dominant gas typically being H_{2}O (70–99%). The volcanic gas typically forms a buoyant plume, which is either carried downwind (Fig.

The methods by which volcanic gases are typically measured include Fourier transform infrared spectroscopy (FTIR), Ultraviolet camera (UV camera) and Differential Optical Absorption Spectroscopy (DOAS).

A number of different approaches exist to measure the gas flux issuing from the volcano, many of which involve absorption spectroscopy in the mid-infrared or ultraviolet region, whereby the gas column amounts from a specific plume cross-section are integrated and recorded in time^{1–5}. The flux of the gas can be then calculated by combining the mass in the cross-section with the plume speed (often the wind speed). The measurement of volcanic fluxes has largely focused on SO_{2} because of its low ambient concentrations and strong absorption signature in the UV region^{6,7}, which make it easy to measure by remote sensing techniques^{8}. The wind speed is estimated using the closest meteorological station^{9,10}; alternatively, an anemometer can be used on the volcanic crater rim to measure the wind directly^{11}. Another approach to measure the gas flux issuing from a volcanic vent is the cross-correlation method, which is used to estimate the mean speed of the plume by tracking features of the plume^{5,12} or by motion-tracking algorithms^{13–15}. The SO_{2} flux data can be combined with data on the concentration of different volatile species measured in the vent of the volcano using integrated gas sensors^{16,17} (MultiGAS) or Fourier transform infrared spectroscopy (FTIR) instruments^{18,19} (see Fig.

In this paper, we take a complementary approach to calculate gas fluxes by using models of turbulent buoyant plumes to analyse video records of a nearly vertical gas plume at Villarrica Volcano, Chile, taken in 2012^{20} and a wind-blown gas plume at Mount Etna, Italy, taken in 2015^{21}. In particular, we describe the speed of the intermittent convective structures in these plumes as a function of the distance from the vent. We show that these measurements are consistent with classical plume theory for both vertical and wind-blown plumes. We then combine these measurements with some analogue laboratory experiments and historical plume data, to show how these measurements can provide an estimate of the gas flux in the plume. We compare these estimates with published measurements of typical gas fluxes at these volcanoes, and find they are of the same magnitude.

In the case of a very low wind speed compared to the speed of the plume, a source of hot buoyant gas will lead to a near-vertical plume. In this situation, provided the ambient is unstratified, the classical theory of turbulent buoyant plumes^{22} suggests that the vertical speed, _{0} is the virtual origin of the plume, corresponding to the distance behind the actual source at which a point source with zero mass flux would produce the same plume^{22,23}. We expect turbulent structures in the plume to move with speed proportional to _{1} is the initial position of the structure at time _{1} and

Bhamidipati and Woods^{24} reported experiments of a turbulent plume produced by the continuous release of salt water at the top of a tank filled with fresh water. By periodically injecting pulses of black dye into the saline source fluid and recording the descent of the dye front through the plume, they measured the speed of some of the turbulent structures in the plume. Figure ^{25}.

We now analyse the speed of turbulent structures in a visual video from a gas plume issuing from Villarrica Volcano in February 2012^{20}. In Fig. ^{23,26}. This simplification should apply to the Villarrica gas plume as it rises through the first 600–800 m above the vent, and hence is not impacted by the ambient stratification.

To test the model, for each height in the image (Fig. ^{4 }s^{−3}, corresponding to an uncertainty of about 28%, using the empirical value _{0} which is estimated to be 50 m below the rim of the vent. The length scales in the video have been estimated using images of the summit crater, which has a diameter 250 m^{27}. We now use this buoyancy flux to estimate the gas mass flux associated with the plume.

To convert the buoyancy flux to a gas flux, we account for the flux of heat _{V} and the mass flux _{V} much higher than the ambient temperature

To calculate the buoyancy flux, we note that as air is entrained, heat conservation requires that the mixture temperature _{A} is given in terms of the mass flux of entrained air, _{A}_{V} and _{A} are the density of the volcanic gas and the air mixed into the plume respectively, each of which may be calculated using the ideal gas law^{−1} K^{−1} for air and 461 J kg^{−1} K^{−1} for water vapour^{28}. For the volcanic gas, we use the mass-averaged value of ^{29}, this average is approximately given by the value for water vapour. The buoyancy of the mixture is given by^{−2} is the acceleration of gravity and _{0} is the ambient density of the air. Combining these results, we estimate that after a mass flux _{A} of air has been entrained into the plume, the buoyancy flux,

In Fig.

Using the buoyancy flux estimated from the speed of convective structures rising through the plume, which corresponds to the asymptotic buoyancy flux following the entrainment of air (Fig. _{V}/_{V}. Note that in these calculations we assume the volcanic gas is primarily composed of water vapour.

For the Villarrica plume, we assume that the erupting gas has a temperature comparable to the magma; although there is no documented measurement for this eruption, magma at Villarrica has been measured to have a temperature of 1134 °C^{30}, and so we assume a temperature of 1134 ± 50 °C herein. Based on Fig. _{2}O flux of 7.5%, and hence we estimate that the H_{2}O flux has value 18.6 ± 6.8 kg s^{−1}. Although there is no estimate of the H_{2}O flux for the actual time when the video was recorded, published estimates of the SO_{2} flux at Villarrica Volcano are 1.5 kg s^{−1}^{17} and 3.7 kg s^{−1}^{31}. Given that the molar ratio of H_{2}O to SO_{2} in the gas issuing from Villarrica is between 35^{31} and 65^{17}, and the molar mass ratio of H_{2}O to SO_{2} is 18:64, these published SO_{2} fluxes imply a H_{2}O flux of 27–36 kg s^{−1}, which is a little higher than, but of similar magnitude to the range we estimate from the plume dynamics. The main source of uncertainty in our estimate lies in the range of estimates of

A number of models of wind-blown plumes have been developed based on pioneering laboratory experiments^{32}. Many adopt a Lagrangian approach, in which the model follows the ascent of the fluid in the plume^{32–34}. These models have shown that provided the source momentum is not too large^{34–37}, then over a relatively short distance after leaving the source, the flow adjusts so that the downwind speed in the plume matches the wind speed, and the subsequent motion of the plume fluid relative to the ambient is dominantly in the vertical direction owing to the buoyancy of the plume fluid. If the buoyancy flux in the plume is ^{22,23}_{o} is the virtual origin of the source. If we move with the fluid, then the height of the plume increases with time, _{0} is the time of release from the source, while the distance downwind increases with time according to the relation_{0} is the horizontal position of virtual origin which accounts for the acceleration of the flow to the wind speed. Combining Eqs. (^{32–34} and has been shown to be consistent with small-scale laboratory experiments^{34}. In the next section, we report some new experiments of such plumes, in which we examine the ensemble average of a video recording of the plumes for several values of the wind speed, and thereby estimate the value of

We have carried out a series of experiments in a flume tank filled with water; the experimental tank was 245 cm long, 60 cm wide and 50 cm deep (see Fig. ^{−1}. The source volume flux of 5.27 cm^{3} s^{−1} was supplied using a Watson Marlow 520 N peristaltic pump. The tank was backlit with a uniform light sheet and the experiments were recorded using a Nikon D5300 camera with a frame rate of 50 Hz.

A nozzle is located at the top of the tank and moves at a constant speed from the right to the left side of the tank during an experiment. Six experiments were carried out, with nozzle speeds of 0.104, 0.092, 0.087, 0.075, 0.056 and 0.037 ms^{−1}.

In Fig. _{0}, _{0} and _{0}/_{0}/

We have analysed a movie of the gas plume venting from Etna’s north east crater (NEC) recorded in the UV range of light in September 2015. In Fig. ^{−1}. We note that when we applied the same technique for estimating ^{4} s^{−3}, corresponding to an uncertainty of about 11%.

^{−1}, corresponding to an error of about 4%.

We now use the calibration curve in Fig. ^{38}, and so we assume it lies in the range 1080 ± 50 °C. This leads to an uncertainty in the conversion from buoyancy flux to H_{2}O flux of about 7.5%, and using the buoyancy flux estimated above, we predict that the volcanic gas flux, _{V}, lies in the range 87 ± 16 kg s^{−1}. Here, the main source of uncertainty lies in the use of plume theory to model the shape of the plume, combined with the estimate of the local wind speed experienced by the plume. Although there is no estimate of the H_{2}O flux for the actual time when the video was recorded, the SO_{2} fluxes reported in previous studies from Etna are 18 kg s^{−1}^{15}. From this, we estimate the H_{2}O flux to be 186 kg s^{−1} by using the measured molar H_{2}O/SO_{2} ratio from the NEC crater of 36^{39} and combining this with the molar mass ratio of 18:64 for H_{2}O to SO_{2}, which is of comparable size, although a little larger than our estimate. The length scale in the images was estimated by reference to the length scale of the northeast crater (NEC), which has a diameter of about 200 m^{40}.

Turbulent buoyant plumes develop convective eddy-type structures, which are carried upwards in the plume, and their speed provides information about the underlying buoyancy flux of the plume. The ascent speed of the turbulent structures in the vertical volcanic gas plume at Villarrica Volcano analysed in this paper is consistent with this model and provides an estimate of the buoyancy flux. We have then developed a simple model to convert this to a mass flux of gas issuing from the volcano. We have also considered the shape of a wind-blown gas plume at Mount Etna, and shown this is consistent with the classical models and experiments of the shape of a wind-blown turbulent buoyant plume far downwind. By comparing the shape of the Etna plume with the model, we estimate the buoyancy flux of that plume, and again using our model, we convert this to the source gas mass flux. The gas flux values we find are comparable to the typical estimates of gas fluxes at these volcanoes derived from spectroscopy combined with electrochemical sensors.

This study paves the way to using high-quality video images of gas plumes to quantify total volatile mass fluxes. If the plume gas composition is known via the measurement of the chemical gas composition at the crater rim with sensor packages or FTIR, the flux of individual species may be estimated. This new method gets around the difficulties of estimating fluxes using spectroscopy when plumes are vertical and not in an ideal configuration for traverses. Furthermore, this method could also be used to estimate fluxes in sulfur-poor plumes, which are difficult to characterise by spectroscopy (e.g., plumes at hydrothermal systems at Yellowstone or White Island).

There is also some uncertainty associated with the use of plume theory to derive the estimates of the buoyancy flux, especially since the trajectories of the plumes depend on the fractional powers of the source buoyancy flux. For the vertical plume the turbulent fluctuations lead to an uncertainty of about 28%, while for the horizontal plume they combine to give an uncertainty of about 24%. Measurement of the magma temperature at the surface would remove some uncertainty in the conversion from buoyancy flux to mass flux. Nonetheless, the approach provides an independent estimate of the gas flux and hence complements the other approaches mentioned in the introduction.

We thank Tehnuka Ilanko, Nial Peter, Yves Moussallam, Kayla Iacovino and Kelby Hicks for providing the Villarrica plume video. We also thank Neeraja Bhamidipiti for providing us with the data for Fig.

A.W.W. conceived this study, N.M. carried out the wind-blown plume experiments. J.W., N.M. and A.W.W. analysed the plume videos using plume theory. A.W.W. and J.W. wrote the manuscript. M.E. helped with the discussion and writing.

The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

The authors declare no competing interests.

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