# Analysis of Volcanic Thermohaline Fluctuations of Tagoro Submarine Volcano (El Hierro Island, Canary Islands, Spain)

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

_{c}and θ parameters, between a time length from 9 to 13 min, with the exceptions of CTDs 41, 43 and 47, as a result of discarding some periods of fluctuations because the rosette was not static one meter above the seafloor (Table 1). Thus, each CTD time series was sampled with a frequency of 24 Hz or 0.0417 s distance between two consecutive measurements maintaining the rosette sampler, through the altimeter sensor, at approximately 1 m above the seabed. At the same time, the ship remained stationary on the surface through its Dynamic Positioning System. Data were acquired using an SBE 911-plus CTD equipped with dual temperature and conductivity sensors, calibrated at the SeaBird laboratory before and after the cruise, with accuracies of 0.001 °C and 0.0003 S/m, respectively.

_{c}) recorded at each location inside the grid are subject to fluctuations and have been analysed as the result of stochastic processes. In this sense, an initial evaluation of the dynamics of the hydrothermal emissions fluctuations driven by the activity of the volcano, $x\left(t\right)$, can be made by examining the time dependence of its variance, $W\left(t\right)=\langle {x}^{2}\left(t\right)\rangle -\langle x{\left(t\right)\rangle}^{2}$. If the process, $x\left(t\right)$, corresponds to uncorrelated random events (normal distribution), then the variance of $x\left(t\right)$ grows linearly in time (Gaussian behaviour). Any departure from linearity, i.e., anomalous behaviour, might indicate the existence of anti-correlated/correlated events and/or systems where the environment fluctuates at similar time scales as the random variable $x\left(t\right)$ [29]. In the anomalous regime, the behaviour is sub-normal/super-normal for growth slower/faster than linear, and the variance reads [30]:

^{2}s

^{−γ}, and Γ () is the Gamma function. According to the exponent γ, the stochastic processes can be classified as sub-normal (anti-persistent process) for values from 0 < γ < 1, Brownian or normal for γ = 1, super-normal (persistent process) for 1 < γ < 2, ballistic for γ = 2, and stationary for γ = 0. It is worth mentioning that Equation (1) does not apply to instantaneous changes of enormous amplitude (Lévy flights) where the first moment diverges. For discrete time series, Equation (1) is expressed as time average and reads:

_{c}.

- Construction of N/10 new time series each of length $T-\Delta $. The new time series, ${y}_{n}(\Delta )$, contains the absolute change between two values of the original series that are set apart by Δ, so that ${y}_{n}(\Delta )=\left|x\left(n\tau +\Delta \right)-x\left(n\tau \right)\right|$ for $n=1,2,\dots ,\left(\left(T-\Delta \right)/\tau \right)$ and for $\Delta =m\tau $ with m = 1, 2, ..., N/10 where $\tau $ and $N\tau /10$ define the minimum and maximum time lags.
- Estimation of the statistical moments, order of q, for each one of the new time series, ${y}_{n}(\Delta )$, is carried out according to:$$\rho \left(q,\Delta \right)=\frac{1}{T-\Delta}{\displaystyle \sum}_{n=1}^{T-\Delta}{\left({y}_{n}(\Delta )\right)}^{q}$$
- The moments will scale according to:$${\rho}_{m}\left(q,\Delta \right)\approx {\Delta}^{z\left(q\right)}$$$$z\left(q\right)=Hq-\frac{C}{a-1}\left({q}^{a}-q\right)$$

## 3. Results

_{c}(mS/cm) measured simultaneously on the submarine volcano surroundings (see Figure 1c), we obtained the average temperature and conductivity reference profiles and their standard deviation down to 127 m (shown in Figure 2). The high variations of both properties during the whole time series over the seabed, concerning the reference profile’s standard deviation, confirm the significance of the fluctuations due to the continuous release of hydrothermal emissions. These fluctuations as a function of time and their correlations for the randomly selected CTD30, one of the 21 time series collected with a time interval of 11 min and 21 s, are illustrated in detail in Figure 3.

^{γ}, obtaining the early (small lag times) and the long-time (all lag times) behaviour for θ and E

_{c}. For small lag times, $0.042<\Delta \le 3.5\mathrm{s}$, temperature and conductivity pose similar weak sub-normal behaviour, with scaling exponents 0.84 and 0.85, respectively. For the long-time behaviour, the whole lag times range has been considered. Again, both θ and E

_{c}scale similarly, with values of exponents γ = 0.75 and γ = 0.77, respectively. For both small and large times, temperature and conductivity follow sub-normal behaviour, anti-persistent variations, which become stronger for longer times and lesser when scaling exponents. The absence of stationary behaviour (γ = 0) in temperature confirms the presence of a mechanism that causes the alterations (see also below), suggesting the existence of a remarkable hydrothermal vent field, consistent with what has been described so far in the area [8,21].

_{c}, each moment shows dependence on the time lags.

_{c}, respectively. Considering the structure functions obtained for all the CTD time series for the first regime ($a$ = 2), listed in Table 2, the H exponent is varied between 0.540 and 0.695, implying super-normal processes if the intermittency parameter, parameter C, were zero. However, the latter is not true, and the non-zero intermittent effects establish conductivity and temperature mean fields as non-conservative. In the long-time limit, the structure-function of CTD30 provides values of H and C of 0.424 and 0.059 for θ and 0.434 and 0.060, for E

_{c}, respectively. For long times, the Hurst exponents are lower than 0.5, implying stronger sub-normal processes and an increasing complexity reflected in the value of the alpha-stable index, which is different now for temperature and conductivity. For short times, the structure functions of both temperature and conductivity have a high similarity indicating a strong correlation of one another. Indeed, the normalised cross-correlation coefficient of the two, r

_{θ,Ec}, is higher than 0.95 for short times and decreases as the time increases (Figure 3c). Strong correlation does not necessarily imply the existence of causality between temperature and conductivity since this is the result of a broader mechanism affecting both properties equally and simultaneously, as the hydrothermal field does. Actually, by differentiating, with respect to time, the time series of temperature, Δθ, and conductivity, ΔE

_{c}, (Figure 3d,e), respectively, the normalised cross-correlation coefficient of the two, r

_{Δθ, ΔEc}, goes rapidly to zero (it is not exactly delta correlated) and the crossing of the abscissa is at 0.6 s. After that point and for a short window, before fluctuations start around zero (see Figure 3f), Δθ and ΔE

_{c}are anticorrelated to one another. These findings support the argument that the hydrothermal field is the reason for the strong correlation between temperature and conductivity since it operates as a vehicle carrying material to a sampling point.

^{−9}m

^{2}/s for ions moving in water during our observations results only in a displacement of ~1.3 mm) and to create a homogeneous one in such a reduced time of observation. Dynamic drifting is always present in open oceans, and its contributions might differ at different sampling points, thus mirroring the structure of the submarine volcano. The existence of drift is compatible with the variations of the temperature field. At sampling points where intermittency is almost zero for the conductivity field, its corresponding value for the temperature field is high indicating a strong mixing process. Certainly, there are points where intermittency takes high values for both fields mirroring strong mixing/competition of various random processes at these locations.

## 4. Discussion

_{2}[11], in nutrient enrichment [27], and also in biological changes in terms of species composition [11,16,26], mainly related with bacterial and planktonic groups [20,22]. In agreement with the high fluctuations observed in the CTD profiles and the emerging gasses and particles documented by ROV videos, our results show that the system is far from both equilibrium and homogeneity.

## 5. Conclusions

_{c}time series have been analysed by the GMM method in a short window of observation, delivering a wealth of findings. GMM returns structure functions with convex shapes indicating that both temperature and conductivity fluctuations correspond to multiplicative processes. This behaviour indicates the direct competition between the overlying marine short-term circulation and the degassing material of the volcano leading to long-lived non-equilibrium states. The nonstationary nature of the temperature field points to an open system that releases energy continuously to the environment. The estimated H and C parameters showed that the risk of eruption is low at the corresponding time window. However, continuous monitoring of the volcanic activity is necessary to further compare and classify the future volcano activity. The latter can be done by using the metrics (moments) analysed in the present work, which can be part of a machine learning approach aiming at forecasting the future activity of the Tagoro volcano.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Map of El Hierro Island with the triple rift system marked (dashed line) and the location of Tagoro submarine volcano (red triangle). (

**b**) Location of El Hierro Island (red square box) in the Canary Islands Archipelago. (

**c**) High-resolution bathymetric map of the Tagoro submarine volcano with the location of the main crater of 15 m in diameter (red dot), the reference profiles (grey dots) and (

**d**) the distribution of the 21 CTD time series recorded along the crest of the seamount.

**Figure 2.**Mean vertical profile of (

**a**) temperature, θ, and (

**b**) conductivity, E

_{c,}with their standard deviation used as a reference from outlying stations not affected by the submarine volcano emissions. The time series fluctuations measured around and over the main crater, in orange for temperature and dark green for conductivity, are located close to 127 m depth.

**Figure 3.**(

**a**) Temperature, θ, and (

**b**) conductivity, E

_{c,}time series of CTD30 collected as part of the high-resolution grid. The similarity between both variable fluctuation patterns as well as the occasional distinct peaks is remarkable, and (

**c**) their normalised cross-correlation coefficient r

_{θ,Εc}showing a strong correlation for short times (t < 3.5 s), which remains large even for long times. (

**d**) The differentiation with respect to time of the temperature time series, Δθ, (

**e**) the differentiation with respect to time of the conductivity time series, ΔE

_{c}, and (

**f**) the normalised cross-correlation coefficient r

_{Δθ,ΔEc}of the differentiation with respect to time of temperature and conductivity time series going rapidly to zero, at the crossing point 0.6 s. In grey is indicated the 95% confidence bounds, where the time series are uncorrelated.

**Figure 4.**Logarithmic plots of the variance for (

**a**) temperature, θ, (orange dots) and (

**b**) conductivity, E

_{c}, (dark green dots) with respect to the lag time for the CTD30 time series. The variance for both temperature and conductivity has been fitted by Equation (1). In each figure, the short black solid line represents the best fit for short times (first regime), and the long one the best fit for long times (whole regime). Notice that Δ (s) refers to the unit of time in seconds.

**Figure 5.**Generalised moments of CTD30 for (

**a**) temperature, θ, and (

**b**) conductivity, E

_{c}, as function of the lag time, Δ, for different moment orders, $q$, ranging from 0.25 to 4 with steps of 0.25. The line represents the turning point where the convex shape of the short lag times ends. Notice that Δ (s) refers to the unit of time in seconds.

**Figure 6.**The structure function $z\left(q\right)$ versus the order of the moment, $q$, for (

**a**) the first regime (short times) and (

**b**) the whole regime (long times) for temperature, θ, and conductivity, E

_{c}, time series and for the CTD30 data.

**Figure 7.**High-resolution grid distribution of (

**a**) temperature, θ, and (

**b**) conductivity, E

_{c}, measurements above of the main crater. The black dots indicate the position where the CTD time series were registered over the seafloor. The filled contours represent the C parameter, while the white contours show the values of the Hurst parameter. The main crater (dashed orange line) is located over the CTDs 30, 34, 35, and 36.

**Table 1.**The location, duration and date of the 21 CTD time series recorded during the multidisciplinary cruise VULCANO-II-1016. The initial and final times correspond to the entire time in which the oceanographic rosette sampler remained in the water. The duration at the seabed (in minutes and seconds) corresponds to the length of the CTD time series fluctuations without the descending and ascending track. All the minutes until the oceanographic rosette reach the volcano edifice and remain steady one meter above the seafloor were discarded, resulting in significatively shorter time series for CTDs 41, 43 and 47.

Nº CTD | Latitude | Longitude | Initial Time | Final Time | Duration |
---|---|---|---|---|---|

CTD30 | 27°37.1788′ N | 17°59.5831′ W | 28 October 2016 12:59 | 28 October 2016 13:17 | 11 min. 21 s |

CTD31 | 27°37.1793′ N | 17°59.5893′ W | 28 October 2016 13:38 | 28 October 2016 13:56 | 12 min. 20 s |

CTD32 | 27°37.1793′ N | 17°59.5944′ W | 28 October 2016 14:36 | 28 October 2016 14:54 | 9 min. 37 s |

CTD33 | 27°37.1788′ N | 17°59.6008′ W | 28 October 2016 15:14 | 28 October 2016 15:32 | 10 min. 44 s |

CTD34 | 27°37.1795′ N | 17°59.5775′ W | 28 October 2016 15:57 | 28 October 2016 16:15 | 11 min. 40 s |

CTD35 | 27°37.1725′ N | 17°59.5773′ W | 28 October 2016 16:36 | 28 October 2016 16:55 | 11 min. 49 s |

CTD36 | 27°37.1732′ N | 17°59.5836′ W | 28 October 2016 17:18 | 28 October 2016 17:37 | 12 min. 32 s |

CTD37 | 27°37.1729′ N | 17°59.5895′ W | 28 October 2016 17:57 | 28 October 2016 18:16 | 12 min. 17 s |

CTD38 | 27°37.1729′ N | 17°59.5257′ W | 28 October 2016 18:28 | 28 October 2016 18:47 | 13 min. 19 s |

CTD39 | 27°37.1731′ N | 17°59.6008′ W | 28 October 2016 19:42 | 28 October 2016 19:59 | 11 min. 25 s |

CTD40 | 27°37.1849′ N | 17°59.5878′ W | 28 October 2016 20:16 | 28 October 2016 20:34 | 12 min. 1 s |

CTD41 | 27°37.1670′ N | 17°59.5904′ W | 28 October 2016 20:55 | 28 October 2016 21:13 | 5 min. 0 s |

CTD42 | 27°37.1848′ N | 17°59.5949′ W | 29 October 2016 07:10 | 29 October 2016 07:28 | 11 min. 35 s |

CTD43 | 27°37.1849′ N | 17°59.5936′ W | 29 October 2016 07:56 | 29 October 2016 08:13 | 6 min. 6 s |

CTD44 | 27°37.1674′ N | 17°59.5948′ W | 29 October 2016 08:42 | 29 October 2016 08:59 | 11 min. 28 s |

CTD45 | 27°37.1680′ N | 17°59.5792′ W | 29 October 2016 09:33 | 29 October 2016 09:50 | 10 min. 45 s |

CTD46 | 27°37.1704′ N | 17°59.5822′ W | 29 October 2016 10:51 | 29 October 2016 11:11 | 11 min. 25 s |

CTD47 | 27°37.1701′ N | 17°59.5895′ W | 29 October 2016 11:33 | 29 October 2016 11:52 | 6 min. 38 s |

CTD48 | 27°37.1616′ N | 17°59.5887′ W | 29 October 2016 12:23 | 29 October 2016 12:40 | 11 min. 28 s |

CTD49 | 27°37.1674′ N | 17°59.6005′ W | 29 October 2016 13:01 | 29 October 2016 13:18 | 9 min. 53 s |

CTD50 | 27°37.1909′ N | 17°59.5891′ W | 29 October 2016 13:48 | 29 October 2016 14:06 | 10 min. 46 s |

**Table 2.**γ, α, H, and C parameters of the temperature and conductivity for both first and whole regimes (short and long times) and for each one of the recorded CTD time series. Notice that for short times the alpha index is 2.

Temperature θ | Conductivity E_{c} | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

First Regime | Whole Regime | First Regime | Whole Regime | |||||||||||||

γ | α | H | C | γ | α | H | C | γ | α | H | C | γ | α | H | C | |

CTD30 | 0.84 | 2 | 0.662 | 0.055 | 0.75 | 1.610 | 0.424 | 0.059 | 0.85 | 2 | 0.669 | 0.054 | 0.77 | 1.578 | 0.434 | 0.060 |

CTD31 | 0.80 | 2 | 0.620 | 0.041 | 0.50 | 1.045 | 0.352 | 0.099 | 0.81 | 2 | 0.628 | 0.045 | 0.51 | 1.078 | 0.360 | 0.100 |

CTD32 | 0.91 | 2 | 0.738 | 0.046 | 0.55 | 1.159 | 0.316 | 0.085 | 0.99 | 2 | 0.730 | 0.052 | 0.61 | 1.428 | 0.330 | 0.068 |

CTD33 | 0.78 | 2 | 0.598 | 0.032 | 0.85 | 1.79 | 0.403 | 0.053 | 0.90 | 2 | 0.620 | 0.033 | 0.87 | 1.793 | 0.391 | 0.052 |

CTD34 | 0.78 | 2 | 0.557 | 0.046 | 0.44 | 1.076 | 0.316 | 0.065 | 0.90 | 2 | 0.571 | 0.048 | 0.46 | 1.104 | 0.324 | 0.063 |

CTD35 | 0.74 | 2 | 0.564 | 0.025 | 0.42 | 1.136 | 0.382 | 0.124 | 0.75 | 2 | 0.578 | 0.028 | 0.42 | 1.188 | 0.384 | 0.117 |

CTD36 | 0.80 | 2 | 0.601 | 0.028 | 0.57 | 1.115 | 0.446 | 0.180 | 0.75 | 2 | 0.593 | 0.019 | 0.62 | 1.208 | 0.456 | 0.168 |

CTD37 | 0.96 | 2 | 0.619 | 0.056 | 0.74 | 1.622 | 0.405 | 0.048 | 0.82 | 2 | 0.631 | 0.061 | 0.79 | 1.633 | 0.422 | 0.047 |

CTD38 | 0.96 | 2 | 0.622 | 0.047 | 0.55 | 1.190 | 0.390 | 0.067 | 0.96 | 2 | 0.644 | 0.055 | 0.66 | 1.171 | 0.406 | 0.065 |

CTD39 | 0.73 | 2 | 0.568 | 0.021 | 0.80 | 1.199 | 0.469 | 0.109 | 0.86 | 2 | 0.588 | 0.024 | 0.83 | 1.244 | 0.483 | 0.110 |

CTD40 | 0.83 | 2 | 0.564 | 0.004 | 0.39 | 1.395 | 0.295 | 0.105 | 1.01 | 2 | 0.589 | 0.018 | 0.42 | 1.480 | 0.306 | 0.105 |

CTD41 | 0.85 | 2 | 0.604 | 0.058 | 0.26 | 1.275 | 0.307 | 0.102 | 0.84 | 2 | 0.627 | 0.058 | 0.29 | 1.314 | 0.324 | 0.100 |

CTD42 | 0.93 | 2 | 0.614 | 0.021 | 0.59 | 1.796 | 0.430 | 0.047 | 0.94 | 2 | 0.631 | 0.017 | 0.71 | 1.821 | 0.446 | 0.055 |

CTD43 | 0.85 | 2 | 0.623 | 0.05 | 0.62 | 1.367 | 0.426 | 0.126 | 0.84 | 2 | 0.642 | 0.056 | 0.63 | 1.391 | 0.438 | 0.123 |

CTD44 | 0.77 | 2 | 0.598 | 0.064 | 0.61 | 1.210 | 0.356 | 0.051 | 0.85 | 2 | 0.623 | 0.075 | 0.53 | 1.223 | 0.368 | 0.055 |

CTD45 | 0.88 | 2 | 0.620 | 0.013 | 0.88 | 1.902 | 0.416 | 0.051 | 0.90 | 2 | 0.646 | 0.022 | 0.90 | 1.847 | 0.430 | 0.056 |

CTD46 | 0.77 | 2 | 0.540 | 0.039 | 0.52 | 2.000 | 0.345 | 0.017 | 0.82 | 2 | 0.573 | 0.048 | 0.77 | 2.000 | 0.358 | 0.018 |

CTD47 | 0.73 | 2 | 0.559 | 0.032 | 0.57 | 1.547 | 0.356 | 0.055 | 0.77 | 2 | 0.599 | 0.039 | 0.59 | 1.540 | 0.377 | 0.061 |

CTD48 | 0.88 | 2 | 0.619 | 0.034 | 0.43 | 1.431 | 0.393 | 0.162 | 0.99 | 2 | 0.652 | 0.045 | 0.21 | 1.445 | 0.405 | 0.163 |

CTD49 | 0.77 | 2 | 0.584 | 0.036 | 0.59 | 1.000 | 0.536 | 0.130 | 0.79 | 2 | 0.600 | 0.043 | 0.62 | 1.000 | 0.545 | 0.134 |

CTD50 | 0.97 | 2 | 0.662 | 0.037 | 0.15 | 0.941 | 0.237 | 0.122 | 1.07 | 2 | 0.695 | 0.044 | 0.14 | 0.928 | 0.283 | 0.131 |

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Olivé Abelló, A.; Vinha, B.; Machín, F.; Zerbetto, F.; Bakalis, E.; Fraile-Nuez, E.
Analysis of Volcanic Thermohaline Fluctuations of Tagoro Submarine Volcano (El Hierro Island, Canary Islands, Spain). *Geosciences* **2021**, *11*, 374.
https://doi.org/10.3390/geosciences11090374

**AMA Style**

Olivé Abelló A, Vinha B, Machín F, Zerbetto F, Bakalis E, Fraile-Nuez E.
Analysis of Volcanic Thermohaline Fluctuations of Tagoro Submarine Volcano (El Hierro Island, Canary Islands, Spain). *Geosciences*. 2021; 11(9):374.
https://doi.org/10.3390/geosciences11090374

**Chicago/Turabian Style**

Olivé Abelló, Anna, Beatriz Vinha, Francisco Machín, Francesco Zerbetto, Evangelos Bakalis, and Eugenio Fraile-Nuez.
2021. "Analysis of Volcanic Thermohaline Fluctuations of Tagoro Submarine Volcano (El Hierro Island, Canary Islands, Spain)" *Geosciences* 11, no. 9: 374.
https://doi.org/10.3390/geosciences11090374