# Periodicity in Volcanic Gas Plumes: A Review and Analysis

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## Abstract

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## 1. Introduction

_{2}O), carbon dioxide (CO

_{2}), and sulfur dioxide (SO

_{2}, or in reduced form, hydrogen sulfide, H

_{2}S), with SO

_{2}being the easiest to resolve against background atmospheric concentrations and therefore, generally the target gas used for emissions measurements [6]. Present generally in trace quantities are halogen compounds such as chlorine, fluorine, bromine, and iodine, the latter of which is highly reactive in the atmosphere forming gaseous species such as bromine monoxide (BrO), and iodine monoxide (IO) [7,8,9].

_{2}, compared to other major gas species, has meant that this gas is often the target for remote sensing. Prior to the development of ultra violet (UV) camera technology [10,11], measurement techniques were constrained by sampling rate and therefore lacked the temporal resolution to detect rapid changes in SO

_{2}flux. For example, Differential Optical Absorption Spectroscopy (DOAS) could at best achieve resolutions of minutes because of the need to traverse or scan gas plumes [12,13,14]. Now, with the advent of UV cameras, which generally acquire at frequencies approaching 1 Hz, periodic components (oscillations) in gas flux are resolvable on timescales of 10 s to 1000 s [6,15,16,17,18,19].

_{2}flux measurements alone, and periodicity can also be identified in timeseries of molar gas ratios [16,24,25,26,27]. Open-Path Fourier Transform Infrared Spectroscopy (OP-FTIR) can capture high temporal resolution datasets of molar gas ratios for a broad range of gases, including trace species such as chlorine [28,29,30,31,32]. In combination with thermodynamic models of volatile solubility, molar gas ratios can be directly related to the pressure (depth) of gas-melt separation and are therefore critical to the identification and tracking of new magma inputs and their subsequent ascent through the shallow magmatic system [33,34,35,36] or to discriminate between redox- and solubility-driven processes [24,37].

## 2. Methods for Detecting Periodicity

#### 2.1. Spectral Analysis

#### 2.2. Autocorrelation

#### 2.3. Fast Fourier Transform

^{n}samples, for integer n (e.g., 256, 512, 1024 samples). For example, if a timeseries of 2048 samples was acquired at 1 Hz and the signal of interest has a period of 80 s, the window length must be long enough to capture several cycles, yet short enough to ensure stationarity over the window duration and therefore reduce spectral leakage (manifest as poorly-defined peaks on the spectrogram): a moving window of 256 samples at 1 Hz would be optimal. A common FFT method employing moving windows is Welch’s method [39] an improvement on the earlier Bartlett’s method [63], because it allows the overlap of moving windows. Welch’s method therefore facilitates investigation of non-stationary periodic components whilst minimising noise within the frequency component, and reduces spectral leakage between windows.

_{2}ratios and by Sweeney et al. [67] for SO

_{2}flux at Erebus. Yet, when the proportion of missing datapoints to overall sample size is low, i.e., with sporadic missing data points of short length, it may be better to employ interpolation to enable use of other FFT methods or the CWT. Lomb-Scargle can also incorporate false alarm probabilities with some codes, a method to interpret the significance of peaks on a periodogram. The false alarm probability represents the probability that a non-periodic signal could generate a peak of a given power. Peaks in the power-frequency plot must exceed a given value to be considered statistically significant, and hence represent a ’real’ periodicity. These levels should be set at p = 0.01 or p = 0.05 as is common statistical practice; any peak in a periodogram below the p = 0.05 threshold is therefore considered as part of background Gaussian noise.

#### 2.4. Continuous Wavelet Transform

#### 2.5. Worked Example

^{®}(Version R2018a). Three sine waves were added to this signal of length 1000 s, such that it contained a stable periodicity of 40 s for 400 s, no periodicity for 200 s, a periodicity of 50 s for the final 400 s, and a stable 200 s periodicity for the length of the signal. Noise was then added to the signal using a normally distributed random number generator, and finally, the entire dataset was squared to more closely resemble a volcanic dataset (i.e., by removing the negative trough from the sine wave), altering the cycle periods to 20 s, 25 s, and 100 s respectively. This example analysis shows that the FFT based Welch’s method provides the clearest assessment of the known periodicities present, producing clearly resolvable peaks at 20, 25, and 100 s (Figure 2d). Lomb-Scargle and the Multitaper method also identify the important peaks (Figure 2e,f), but with a greater degree of spectral leakage leading to a loss of frequency precision. In contrast, the greater temporal resolution of the CWT (Figure 2c) clearly identified the discontinuity from 400–600 s, and also identified where the 20 and 25 s periods began and ended, showing a lack of spectral leakage. This example clearly highlights the value of using the CWT to show the stability of periodicities with time. Interestingly, however, in this example, autocorrelation did not identify all of the present periods (Figure 2b), emphasising the need to use Fourier or CWT analysis for non-stationary timeseries. The periods of 20 and 100 s were present, but the 25 s period was absent (given proximity of the periods in duration, i.e., the 5 s difference), in addition, there were multiple other peaks present which are not key periodicities. Note the position of autocorrelation significance thresholds on Figure 2e; care should be taken when using these, particularly where the sample size is large, given that thresholds (or confidence bounds/intervals) are calculated using sample size. For very large datasets of thousands of datapoints, the threshold approaches a correlative value of 0 whereby no meaningful correlation would exist. In such situations, a scatter plot should be used to investigate dataset associations with and without a lag applied as appropriate.

## 3. Previous Studies on Periodicity within Volcanic Plumes

_{2}) and gas ratios (e.g., CO

_{2}/SO

_{2}). Furthermore, we highlighted several studies on volcanic plumes that have published flux or ratio timeseries at sufficient temporal resolution, but for which periodic degassing was not investigated. These data were extracted using an online data extraction tool, where required [74] (Available at: https://automeris.io/WebPlotDigitizer/) and reprocessed using the techniques described in Section 2. When using this tool, care was taken to extract data accurately and consistently. Although slight deviations (unfortunately unquantifiable) from the original data may have been introduced, the key focus of this study – periodicity – was not affected. Alternatively, in cases where data were provided as supplementary tables, these values were directly. Overview and analyses were split into three sections: (1) lava lakes; (2) basaltic volcanoes; (3) non-basaltic (andesite to rhyolite) volcanoes. These categorizations were selected based on the strong influence of magma rheology on in-conduit fluid dynamics, and thus bubble flow behaviour. Lava lakes, of all compositions, are dealt with separately due to their unique shallow geometry and our ability to directly observe the top of the magmatic column, which aids interpretation of degassing mechanisms.

#### 3.1. Studies of Periodicity at Lava Lakes

_{2}flux ranging from 240–900 s [76,95]. This timescale of periodicity is ascribed to the addition of magma into the shallow portions of the lake by pulses of lower viscosity magma in a bi-directional-flow, with pulses containing a higher proportion of exsolved gas [77,97]. This drives periodicity in degassing and other lake features such as plate movement and lake height [95,98]. Girona et al. [56] identified periodic components in SO

_{2}and H

_{2}O flux, with the latter measured using visible imagery and plume pixel brightness as a proxy for water content. Here, FFT analysis identified ‘fractal degassing’, whereby H

_{2}O emissions followed a well-defined fractal (power law) distribution across a wide range of frequencies (i.e., the timescale of periodicity decreased in tandem with increasing amplitude of the gas pulse). Interestingly, whilst two of the cycles identified at Erebus were shared by both H

_{2}O and SO

_{2}(100–250 s and 500–650 s), a third was only manifest in SO

_{2}(300–450 s). The authors attribute the presence of decoupled cycles in multiple gas species to a thermochemical reaction, whereby exsolved bubbles from higher temperature magma batches contain elevated proportions of SO

_{2}compared to H

_{2}O [30,56,99].

_{2}), thermal, and lake height measurements have been attributed to gas pistoning [82,83,84,85]. Gas pistoning is visually identified by a sustained rising of the lava level followed by a rapid drop, lasting a small fraction of the rise time, during this time SO

_{2}emissions are low prior to the rapid drop, increase rapidly on release of gas during the gas pistoning event and then return to normal [84]. Exact durations varied widely, from seconds to 15.8 hours, with the likely mechanism being the shallow accumulation of gas below the surface crust of the lake. The unique quality of the observations at Kīlauea are a direct result of the distinctly shallow generation mechanism, as modulations in degassing are frequently attributed to changes at deeper sources [85]. For example, at Erta ‘Ale, Bouche et al. [78] identified that large gas bubbles periodically broke the surface of the lake, in a similar location, suggesting that they have passed through the more constrained geometry of a feeding conduit.

_{2}flux timeseries from a remote UV camera. Whilst the shorter-period cycles are temporally linked to discrete audible bubble bursts at the lake surface, the authors suggest that the longer-period cycles are atmospherically-generated through large-scale turbulent organization of the plume as it exits the crater [19]. Notably, in the original study Moussallam et al. [53] used autocorrelation, which, as we highlighted in Section 2, may not identify non-stationary periodic components. On extraction and reprocessing of data using Lomb-Scargle analysis, we also find no dominant periodicities, however, the CWT (Figure 3) shows a weakly stable period at ~300–500 s, which could be related to the 345–714 s period, identified by Liu et al. [19] in SO

_{2}flux data and could also be caused by atmospheric transport phenomena.

_{2}/SO

_{2}ratio prior to the onset of lava lake activity. Here, we used their NOVAC (Network for Observation of Volcanic and Atmospheric Change) data, which spans over the period March 2014 to September 2016 [100], and conducted CWT and Lomb-Scargle analysis to highlight the presence of significant periodic components within the SO

_{2}flux dataset (Figure 4a,b). In the Lomb-Scargle analysis (Figure 4b), the dominant of these has a period of 178.9 days, which we noted is similar to the duration of the solar semiannual tide at 182.6 days (the semiannual tide) [101]. Another cycle has a 23.6 day period, which appears too short to be linked to the lunar 27.6 day cycle [27,101]. Further periodicities at 140, 121, 94, and 46 days could reflect the volcanic influence at Masaya, involving replenishment of magma into storage zones, necessary to feed the observed high degassing rates of Masaya [35,102] which will also reflect changes in surface behaviour of the lava lake [17,93]. Given the large dataset gaps, it was only possible to conduct the CWT over a portion of the dataset between 16/11/2015 and 30/09/2016. The CWT (Figure 4a) shows multiple periodicities (5–7, 12–18, 18–24, 20–25, and 30–50 days) which overlap with Lomb-Scargle values (24 and 36 days) but with none that are present for the entire dataset, which would appear to rule out a dominant effect of tidal forcing, at least over timescales < 50 days. Co-acquired timeseries of SO

_{2}flux, thermal and visible video imagery of the Masaya lava lake over sampling windows of seconds to hours, revealed a periodic component of ~200–300 s in the SO

_{2}flux data, attributed to atmospheric processes given a lack of cyclic behaviour in the other co-acquired datasets [17].

#### 3.2. Studies of Periodicity at Basaltic Volcanoes

_{2}flux timeseries: short-period cycles of 40–250 s (centred on 150 s), and long-period cycles of 500–1200 s (centred on 600 s). The higher frequency periodicities were often sustained on timescales of tens of minutes. Similarly, Pering et al. [16] also identified short-period cycles of ~89 and ~185 s in SO

_{2}flux, but also identified a mid-range period of ~340 s. Importantly, the ~89 s cycle was also observed in the CO

_{2}/SO

_{2}molar ratio (measured using an independent MultiGAS analyser), and therefore, could not be driven by atmospheric processes. Specifically, no plausible mechanism exists for fractionating one gas species from another preferentially during plume transport on the length scales analysed. Finally, Pering et al. [79] identified a similar range of short-period oscillations in SO

_{2}, CO

_{2}, and H

_{2}O flux of ~40–175 s cycles. Intriguingly, the authors discovered stronger links between degassing of SO

_{2}and H

_{2}O than for CO

_{2}with each of these, suggesting that a shared periodicity could be due to similar exsolution depth [103,104] and process operating across this length-scale. Indeed, given that stronger links were found between H

_{2}O and SO

_{2}than CO

_{2}this would suggest a volcanogenic cause, otherwise periodicity would be shared between all three species. Waves of bubbles [105] ascending and bursting at the summit were suggested as a cause by Tamburello et al. [15], whereby bubbles self-organize into layers observed as periodicity at the surface. The detection of longer period components at Etna is often limited by total measurement duration for high-resolution acquisitions.

_{2}and seismicity, however, they did not comment on the presence of shorter-period cycles, which are visible (by eye) in Figure 2c. By extracting this data and using Lomb-Scargle analysis, we indeed highlighted a dominant periodic component of 427 s, with others ranging from 73 to 320 s (see Figure 4d). The CWT (Figure 4c) also highlights stable periods of 200–300 s and 125–175 s. It is plausible that these periodic components are related to the rheological stiffening of the upper conduit, which was posited by Nadeau et al. [80] as a cause of the link between seismicity and gas release. Similarly, reanalysis of timeseries data from Gorely [81] and Pacaya, Guatemala [86] revealed a range of periodicities. At Gorely, a dominant period was discovered at 63 s, with others at 197 and 509 s in Lomb-Scargle analysis (Figure 5b), while the CWT (Figure 5a) shows a period of 350-600 s and 150–250 s which highlights overlap, a further area at 50–120 s was related to transient events in the flux record. At Pacaya, a broad range of 331–3000 s appeared in Lomb-Scargle analysis (Figure 5d), with dominant periods at 3000 s and 1920 s, and less prominent at 1143 s, 353 s, and 331 s. The CWT (Figure 5c) shows that some of these are present for a large proportion of the dataset (900–1400 s and 1500–2500 s) but that spikes between 200–700 s were more transient and likely related to the mild strombolian activity during acquisition [86].

#### 3.3. Studies of Periodicity at Predominantly Non-Basaltic Volcanoes

_{2}/SO

_{2}ratio data and of ~120 s and ~420 s from UV camera SO

_{2}flux data, noting that these two timeseries were not contemporaneous [26]. These measurements were made during a phase of relative eruptive quiescence characterized by continuous passive degassing. The authors noted that such a short-period cycles are unusual for a volcano with a higher viscosity magma. The authors invoked a shallow conduit process involving convection of a gas-rich magma to explain this cyclicity. At Ubinas, Moussallam et al. [26] noted no quantifiable periodicity but did describe ‘puffing’ style activity, where clearly defined gas pulses were released from the summit (similar to observations of Masaya in Pering et al. [17] and Villarrica in Liu et al. [19]). Here, using Lomb-Scargle analyses on extracted data, no significant periods were discovered, although CWT analysis (Figure 6) suggested possible longer term periods between 400–900 s and 900–1200 s which are potentially related to puffing behavior observed by the authors at the time [26].

_{2}on a global scale. Campion et al. [18] discovered distinct periodic components in passive degassing at ~300 s (252 and 328 s), and argued that the thermal buoyancy of the hotter gas released from the vents and the regularity of release mean that the most plausible mechanism was a volcanic origin. Although they did not explicitly ascribe a causal mechanism, Campion et al. [18] did suggest that gas puffing and explosions could be driven by closure of vesicle networks in the melt, which are responsible for high rates of passive degassing. Smaller changes in gas flux through vesicle networks could also be the driver of short-period cycles in passive degassing, and could be a common process at volcanoes with a lava dome or for volcanoes with more evolved magmas, e.g., a ~100-s period was also found in gas flux at Turrialba (Costa Rica) [18,89].

_{2}flux monitoring network has generated a multi-decadal timeseries (2002-present) that is unprecedented in its completeness, thus enabling investigation of periodicity on longer timescales than usual possible in emissions datasets [21,23,110]. Analysing daily flux averages from the interval 2002–2011 (spanning 4 eruptive phases and pauses), revealed dominant cycles evident on both multi-year and multi-week (~50 day) timescales. The short-term cycles persisted through phases of both active extrusion and eruptive pause and broadly correlated to enhanced lava extrusion and elevated seismicity. However, phase offsets of ~4 days were found between the onset of each initial low-frequency seismic pulse and peaks in SO

_{2}flux [21]. Interestingly, the strength of the multi-week cycle appeared to be strongly influenced by the occurrence of explosive activity, being manifest most strongly in the lead-up to such an event; the authors therefore suggested that the amplitude of surface gas flux cycles is modulated by physical conditions within the conduit, a conclusion supported by conduit models [111]. In contrast, the long-term multi-year cycle in SO

_{2}flux is decoupled from magma extrusion and other geophysical parameters [112]. Flower and Carn [66] also highlighted the utility of using satellite thermal and SO

_{2}measurements, identifying longer period cycles of 102, 121, and 159 days which were posited to relate to magma intrusion, whilst a longer period of 238 days was associated with lava dome destabilization.

_{2}O flux data, with the following periods: ~100–500 s (intermittent in strength and duration throughout acquisition), ~600–900 s (stable), ~1200–1600 s (stable), and 2000 s (but just within the detection limit using a CWT). The authors did not posit a causal mechanism, specific to this volcano, although the range of periodicities, the timescales they operate over, and the similarity to those at other volcanoes of similar composition suggests that the drivers may be volcanogenic, particularly for the longer periodicities > 600 s.

_{2}ratios using DOAS (daily averages over a three month dataset) at Cotopaxi (an andesitic/basaltic-andesitic volcano), which they attributed to a fortnightly lunar tidal force, with correlation coefficients of 0.47 and 0.36 (representing links with the North-South and vertical tidal displacements respectively). It is important to note here that the presence of a correlation does not imply causation. The data from Figure 6 in Dinger et al. [27] were extracted and reprocessed, first using Pearson’s correlation to check for matching correlation coefficient of 0.47 and then further processed using regression (conducted in SPSS). The correlations listed in Dinger at al. [27] therefore equate to regression coefficients of 22% (R

^{2}= 0.22, see Figure 7) and 13% (R

^{2}= 0.13) respectively. It is this regression coefficient that we can use to model the change in one variable (the BrO/SO

_{2}ratio) that can be accounted for by another (the tide). The relationship is highlighted in Figure 7 alongside residuals to the linear fit, showing variability. The exact p-value for the 22% regression coefficient is below the p < 0.01 significance level at p = 2.5 × 10

^{−5}. Whilst the North-South tide has a statistically significant relationship with BrO/SO

_{2}there is still a large proportion of unexplained variability; indeed, 78% of the signal can be attributed to other factors (i.e., random fluctuations, error, or a volcanogenic component). The detection of periodicity in BrO/SO

_{2}could reflect a complex process whereby tides preferentially effect degassing of one species relative the other, related to differences in solubility and points of saturation in the melt.

_{2}flux driven by a fortnightly lunar tide, with low correlation coefficients of 0.2–0.3 [65], which give R

^{2}values of 0.04–0.09 (4–9%), hence presenting a weak relationship. Turrialba, also exhibited a 10–14 day period in SO

_{2}flux, which could be tidally induced [90]. Finally, the periods that can be detected are limited by sampling duration and frequency, and this must be considered during data collection if investigation of longer or shorter periodicities is planned.

## 4. Comparison of Volcanoes and Potential Drivers of Periodicity

#### 4.1. Non-Volcanic Periodicity (C1)

_{2}would occur through photochemical reactions. Moreover, atmospherically-driven periodicities are likely to operate towards the high frequency end of the spectrum, on timescales of tens of seconds to minutes. Over minutes, topographic features, such as a caldera or an elevated crater, could facilitate the buildup and periodic release of gases as a result of local pressure differences and wind-fields, e.g., [113], and is probably the case with the 200–300 s periodicity at Masaya [17].

#### 4.2. Periodicities Generated within the Shallow Plumbing System (C2 and C3)

_{2}, OCS, and potentially SO

_{2}) and to shallow exsolution of more soluble species (H

_{2}O, SO

_{2}, HCl, and HF) from fresh magma input to the lava lake [24].

#### 4.3. Periodicity in Magma Storage Region (C4)

_{2}flux (and other geophysical parameters [51]) over timescales of 2–3 years, on which short-term shallow gas periodicities are superposed [21,66,110]. Crucially, these long-term gas cycles are decoupled from phases of magma extrusion or variations in other geophysical parameters, indicating that the underlying periodicity-generating mechanism is intrinsically related to the timescales of volatile-melt separation [112]. In silicic systems, SO

_{2}flux can be used as a first-order indicator of the efficiency and rate of mafic injection at depth [110].

_{2}) can also provide good indications of the onset of volcanic unrest and magma movement at depth [124], although such datasets can also be sensitive to environmental and climatic influences [125,126]; for example, 47% of the soil CO

_{2}flux variations at Fogo, Azores, could be explained by the effect of the soil and air temperature, wind speed, and soil water content [127].

#### 4.4. Synthesis

_{2}flux, such as those of NOVAC [100] are optimized to study cycles with periods of hours to days in SO

_{2}flux, given that scanning can take tens of minutes to complete. Meanwhile, high sampling rate techniques, such as the UV camera, are capable of robustly identifying high frequency periodic components, yet long datasets spanning longer than several hours are rare and limited to permanent networks (e.g., Stromboli [128]; and Etna, [129]). The need to regularly recalibrate the UV camera during campaign field acquisitions (i.e., when using SO

_{2}gas cells) also introduces data gaps, thus precluding the detection of periodic components longer than a calibration window within collected datasets [130]. Similarly, high time resolution measurements of gas composition using MultiGAS or Fourier Transform Infrared (FTIR) instruments are often limited to discrete sampling intervals during field campaigns. Although, there are currently ~25 permanent MultiGAS installations on active volcanoes worldwide, they often only acquire for 4 × 1 h measurement windows each day, thus precluding the detection of intermediate cyclicity on a scale of hours [131]. Finally, it may be possible to improve our long term datasets through the use of satellite observations and methods, which can derive high time resolution SO

_{2}flux measurements, for example, using the method of Queißer et al. [132] or as demonstrated by Flower and Carn [66] for Soufrière Hills Volcano. Spatially, mixing and homogenization of volcanic plumes can occur rapidly on horizontal length scales of <150 m, with varying timescales of periodicity evident at different distances of observation, or obscured, e.g., Liu et al. [19]. The measurement technique, and region of plume targeted, should always be taken into account when directly comparing periodic characteristics between timeseries.

#### 4.5. Future Challenges in Periodicity Analysis

- What are the dominant controls on long-term stability of short-duration periodicity (< an hour)?
- Is there a relationship between total emission fluxes and either the magnitude or timescale of periodicity? If so, how can this help inform our understanding of subsurface processes?
- How do the properties of periodic behaviour change in the time before/after eruptive events, and can these be used to aid in hazard assessment and eruption forecasting?
- Do tidal forces have an effect on volcanoes and, if so, what is the magnitude of oscillation compared to volcanogenic mechanisms? What other external forcings should be considered?
- At multi-vent volcanoes, do the periodic characteristics of outgassing vary between craters? If so, what can this tell us about shallow subsurface plumbing systems?
- Do phase offsets exist between emissions of different gas species, i.e., highlighting a specific source depth for periodicity?

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Example plumes from four volcanoes: (

**a**) Sabancaya, in April 2018, showing a passive plume during intermittent explosive activity, (

**b**) Yasur, in July 2018, with strombolian explosion pulses emanating from the crater approximately every minute, (

**c**) Stromboli, in June 2018, showing passive degassing in between the strombolian explosions, and (

**d**) Fuego, in November 2017, showing clear periodic degassing from Strombolian explosions occurring approximately every 8–10 min.

**Figure 2.**The results of a suite of periodicity techniques on: (

**a**) an artificial signal containing two repeating signals with periods of 20 s and 25 s respectively, briefly discontinued between 400 and 600 s, with blue and red bars indicating their respective positions in time. A further 100 s period is operating across the length of the signal; (

**b**) autocorrelation, where each red line indicates correlation at the given lag on the x axis, the blue lines indicate a significance level whereby points below this line have no statistical significance. Autocorrelation only detects periods at 20 s and 100 s and is difficult to interpret given multiple other peaks above the significance line; (

**c**) the CWT with black boxes showing periodicities, and cone of influence indicated by the white dashed line, areas outside of which are subject to edge effects. Here, all periods are clearly identified along with their operating duration, showing little spectral leakage. Note also the stripes at high frequencies which are associated with dataset noise, highlighting the need to look for coherent and stable periods; (

**d**,

**e**) periodogram of Welch’s and the Multitaper method respectively with peaks indicating dominant periods present; and (

**f**) the Lomb-Scargle technique, with associated false alarm probability at p = 0.01 and p = 0.05, peaks above which can be considered statistically significant. This combined analysis shows the benefit of using multiple techniques to assess periodicity.

**Figure 3.**The results of CWT analysis on SO

_{2}flux data from Villarrica, Moussallam et al. [53]. There was a weakly stable period of 300–500 s for the duration of the dataset, with higher magnitude transient events dominating periods between 50–250 s.

**Figure 4.**CWT and Lomb-Scargle analysis (

**a**,

**b**) for SO

_{2}flux at Masaya (data from Aiuppa et al. [35]); and (

**c**,

**d**) for SO

_{2}flux at Fuego (data from Nadeau et al. [80]. The black boxes highlight points of interest that show stability over intervals longer than the periodicity itself. Masaya highlights a range of periodicities in the CWT (

**a**) of which none are maintained for the length of the dataset, while Lomb-Scargle shows a dominant period of 129 days, and shorter periods of 24 and 46 days which overlap with the CWT. Note that CWT in (

**a**) represents a shorter time period than the Lomb-Scargle analysis in (

**b**). Fuego shows a number of dominant periods in the CWT (

**c**) which are present for a high proportion of the dataset, notably between 200–300 s and 125–175 s. There are a number of commonalities with the Lomb-Scargle analysis (

**d**).

**Figure 5.**CWT and Lomb-Scargle analysis (

**a**,

**b**) for SO

_{2}flux at Gorely (data from Aiuppa et al. [81]); and (

**c**,

**d**) for SO

_{2}flux at Pacaya (data from Battaglia et al. [86]). The black boxes highlight points of interest that show stability for intervals equal to or larger than the periodicity itself. At Gorely, the CWT (

**a**) highlights dominant periods of 350–600 s and 150–250 s which overlap with those in the Lomb-Scargle analysis (

**b**). Shorter periods, 50–120 s in (

**a**) and at 63 s in (

**b**) appear related to frequent transient events. At Pacaya the CWT (

**a**) shows sporadic periods of 200–700 s which are probably related to periods of 353 and 331 s in the Lomb-Scargle analysis (

**b**). Longer periods are also present in both (

**c**) and (

**d**) with those in (

**d**) centering on those discovered in the CWT (

**c**), these also appear more stable for the length of the dataset.

**Figure 6.**CWT analysis of SO

_{2}flux at Ubinas (data from Moussallam et al. [26]). There are potential periods across the ranges 400–900 s, 900–1200 s, and 1500–2500 s, which span high proportions of the dataset, although the latter is only partially visible within the area not effected by edge effects. The black boxes highlight points of interest that show stability for intervals equal to or larger than the periodicity itself.

**Table 1.**A summary of techniques used for identifying periodicity and their ideal usage. FFT refers to the Fast Fourier Transform.

Technique | Ideal Use |
---|---|

Autocorrelation | Stationary periodicity, one clear and dominant period |

Welch’s (FFT) | Non-stationary periodicity, but approx. stationary within window, requires prior knowledge of target periodicity timescale |

Thomson’s Multitaper (FFT) | Stationarity required within an individual analysis window; but, can visualise non-stationary periodicity when employed in the form of the short-term Fourier transform (STFT) moving window method. Requires no prior knowledge of target periodicity timescale |

Lomb-Scargle (FFT) | Non-stationary periodicity, for datasets with missing data points |

Continuous Wavelet Transform | Non-stationary, good for visualizing temporal stability and strength of multiple concurrent periodicities. Requires no prior knowledge on the signal generating process. |

**Table 2.**Papers that investigate periodicity of volcanic degassing. Units: s is seconds, h is hours, d is days. Magma type refers to the dominant magma composition; information sourced from [75].

Volcano | Magma Type | Period (units) | Notes | Key References |
---|---|---|---|---|

Ambrym | Basalt | 100–200, 480 s | Ratio data | [25] |

Cotopaxi | Andesite/Basaltic-Andesite | 13.7 d | Ratio data | [27] |

Erebus | Phonolite | 100–600 s 600 s 10–360 min | Fluxes and Ratio data | [24,56,67,76,77] |

Erta Ale | Basalt | 1 h | Bubble volume | [78] |

Etna | Basalt | 40–340 500–1200 s | SO_{2} flux and ratio data | [15,16,79] |

Fuego | Basalt | 70–430 s | SO_{2} flux | [80], This Study |

Gorely | Basalt | 60–510 s | SO_{2} flux | [81], This Study |

Kīlauea | Basalt | 1–3600 s 1.6–7.8 h 4 m–15.8 h | Gas Pistoning; different ranges represent different time periods. | [82,83,84,85] |

Llaima | Basalt | 14 d | SO_{2} flux | [65] |

Masaya | Basalt | 200–300 s 50–180 d | SO_{2} flux | [17], This Study |

Mayon | Andesite/Basaltic-Andesite | 100–500 s 600–900 s 1200–1600 s 2000 s | H_{2}O flux | [56] |

Soufrière Hills | Andesite/Basaltic-Andesite | 30–50 d 100–340 d | SO_{2} flux | [21,66] |

Pacaya | Basalt | 330–3000 s | SO_{2} flux | [86], This Study |

Popocatépetl | Andesite/Basaltic-Andesite | 250, 330 s | SO_{2} flux | [18] |

Sabancaya | Andesite/Basaltic-Andesite/Dacite | 240 s 120, 420 s | CO_{2}/SO_{2} RatioSO_{2} flux | [26] |

Stromboli | Basalt | ~1–5 s 5–40 m | Strombolian activity | [87,88] |

Turrialba | Andesite/Basaltic-Andesite | 100 s 10–14 d | SO_{2} Flux | [89,90] |

Ubinas | Andesite/Basaltic-Andesite | 400–900 s 900–1200 s 1500–2500 s | SO_{2} Flux | [26], This Study |

Villarrica | Basalt | None 30–50 s 340–710 s 14 d | SO_{2} flux SO_{2} concentration | [19,53,65] |

Yasur | Basalt | ~10 s–10 m | Strombolian activity | [29,91,92] |

Category | Description | Dominant Range |
---|---|---|

C1 | Non-volcanic, atmospheric- or tidal- generated | Variable |

C2 | Gas-driven, shallow process | Seconds to Hours |

C3 | Shallow magma movement, in-conduit or shallow storage | Minutes to Days |

C4 | Deep magmatic processes | Days to Months |

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**MDPI and ACS Style**

Pering, T.D.; Ilanko, T.; Liu, E.J. Periodicity in Volcanic Gas Plumes: A Review and Analysis. *Geosciences* **2019**, *9*, 394.
https://doi.org/10.3390/geosciences9090394

**AMA Style**

Pering TD, Ilanko T, Liu EJ. Periodicity in Volcanic Gas Plumes: A Review and Analysis. *Geosciences*. 2019; 9(9):394.
https://doi.org/10.3390/geosciences9090394

**Chicago/Turabian Style**

Pering, Tom D., Tehnuka Ilanko, and Emma J. Liu. 2019. "Periodicity in Volcanic Gas Plumes: A Review and Analysis" *Geosciences* 9, no. 9: 394.
https://doi.org/10.3390/geosciences9090394