# On the Rainfall Triggering of Phlegraean Fields Volcanic Tremors

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. Methods

_{i}(i = 1, 2, 3, … N) is the timing of consecutive rainy days, and RA(t

_{i}) is the rainfall amount occurring in the day t

_{i}, we propose a time-delayed model, F(t), defined by the following equations:

_{i}(t, t

_{i}) gives the contribution of the single rain event that occurred at time t

_{i}. The parameter τ is a characteristic timescale describing, for example, the water percolation in the soil. The effect is supposed to weaken exponentially following Darcy’s law [32,33], which states that the volumetric flow depends on the pressure difference between the two sides of a sample. The variant proposed in Equation (2) describes how water flows vertically through saturated soil by gravity.

_{0}, a given amount of meteoric water h(t

_{0}) is added to the surface, the solution of the above differential equation is h(t) = h(t

_{0}) exp(−(t − t

_{0})/τ), which is like Equation (2). For large t, h(t) tends towards 0, which indicates that all meteoric water added to the system at time t

_{0}has been absorbed by the soil. Then, the system returns to its stationary state unless it is again perturbed by additional meteoric water. This cumulative process is related to all rainfall events and is indicated by Equation (3), which is herein defined in the units of the rainfall amount (mm) in Naples.

_{i}) on a given day t

_{i}, the longer its ability to trigger tremors lasts.

- (1)
- R = 0.2 mm and τ = 1 day;
- (2)
- R = 0.1 mm and τ = 1 day;
- (3)
- R = 0.2 mm and τ = 2 day;
- (4)
- R = 0.1 mm and τ = 2 day.

- the number of days for each year (DY);
- the number of wet days (WD) as defined by Equation (3) with the threshold R;
- the number of days when earthquakes occur (DE);
- the number of wet days when earthquakes occur (WDE);
- the total number of earthquakes (E);
- the total number of earthquakes that occur during wet days (EWD).

- the probability of having random earthquakes with no relation with wet days (Rand = WD divided by DY), which is our null hypothesis to be tested;
- the measured probability of having a seismic day during a wet day (WEQD = WDE divided by DE);
- the measured probability of having an earthquake during a wet day (WEQ = EWD divided by E).

_{1}, and α = 1 for i > n

_{1}. The meaning of the two equations is the following.

_{1}of obtaining a number of wet days with earthquakes larger than measured n

_{1}, assuming a random distribution of days with seismic activity. Here, n is the number of days with earthquakes, n

_{1}is the number of wet days with earthquakes, d is the total number of days (e.g., 365 or 366 for one year), and d

_{1}is the number of wet days in the same period (e.g., 1 year). The equation assumes that if (d

_{1}− i) < 0, then 1/(d

_{1}− i)! = 0 because x! = Γ(x + 1) and, for negative integers, the gamma function diverges to infinity. In particular, in the extreme cases in which, for example, our proposed model (Equation (3)) would cover the entire year with wet days or, alternatively, earthquakes occur all days of the year, the probabilities P

_{1}and P

_{2}give values equal to 0.5, which means that no relation could be established between rainfalls and seismic activity.

_{2}of obtaining a number of earthquakes in wet days larger than measured (n

_{1}) assuming a random distribution of seismic events. This equation assumes that more than one seismic event could occur on the same day. Here n is the number of earthquakes, n

_{1}is the number of earthquakes that occur on wet days, d is the total number of days, and d

_{1}is the number of wet days.

_{2}(Equation (5)). In fact, even one large seismic swarm, which can occur on a wet day or a dry day, could bias the statistics in one way or the other. Thus, finding an extreme value regarding P

_{2}(e.g., P

_{2}< 0.05 or P

_{2}> 0.95) by using only a single record means that in such a period, an excess of events occurred during wet or dry days, respectively. However, because of the clustering nature of the phenomenon, the finding could have been occasional. Thus, running a single test would be inconclusive.

_{2}< 0.05, which implies that meteoric water could enhance the seismic activity of the area) is found for a significantly large majority of the analyzed years, the working hypothesis cannot be rejected.

## 4. Results

_{1}and P

_{2}reported in the four tables are finally collected in Figure 6.

_{1}< 0.95. One year (scenarios #2 and #4) and 2 years (scenario #1) had P

_{1}≥ 0.95, and one year had P

_{1}≤ 0.05 in all scenarios. Therefore, by considering the 13 analyzed years, no bias in one direction or the other can be established according to the first test.

_{2}reported in Table 1, Table 2, Table 3 and Table 4 suggest that the number of seismic-events could be linked with wet days for most years. That is, seismic swarms are more likely to occur in these conditions. In fact, for each scenario, we found the following statistics:

- Scenario #1: R = 0.2 mm and τ = 1 day. P
_{2}≤ 0.05 for 6 years (2008, 2009, 2012, 2014, 2015, and 2017), 0.05 < P_{2}≤ 0.30 for 3 other years (2018, 2019 and 2020), while P_{2}≥ 0.95 for three years (2010, 2011 and 2016); - Scenario #2: R = 0.1 mm and τ = 1 day. P
_{2}≤ 0.05 for 6 years (2008, 2009, 2012, 2014, 2015, and 2018) while P_{2}≥ 0.95 for just 3 years (2010, 2011 and 2016); - Scenario #3: R = 0.2 mm and τ = 2 day. P
_{2}≤ 0.05 for 9 years (2008, 2009, 2011, 2012, 2013, 2014, 2017, 2018, and 2019), while P_{2}≥ 0.95 for just 2 years (2010, 2016); - Scenario #4: R = 0.1 mm and τ = 2 day. P
_{2}≤ 0.05 for 9 years (2008, 2009, 2010, 2011, 2012, 2013, 2014, 2017, and 2019), 0.05 < P_{2}≤ 0.30 for 2 years (2018 and 2020), while P_{2}≥ 0.95 for just one year (2016).

_{2}, reported in Table 4, suggest that the number of seismic events could be linked with wet days at least for 9 of the 13 analyzed years, that is, in 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2017, and 2019.

_{2}≤ 0.05. Figure 2, Figure 3, Figure 4 and Figure 5 also show that earthquake events tend to cluster. More specifically, seismic swarms are observed and last up to about one hour. For example, on 23 January 2009, there were 143 tremors (without counting those whose magnitude was unknown) in 36 min from 5:15 a.m. to 5:51 a.m. We could not find tremor swarms extending from a day to the following one. Thus, events occurring on different days belong to different clusters. Several seismic events are also isolated; that is, they do not generate any seismic swarm even if their magnitude is relatively high. This result suggests that the seismic properties of the area are not stationary in time. In fact, the physical properties of the soil are expected to be modified by the addition of meteoric water.

_{1}, assuming a random distribution of days with seismic activity.

_{1}fall within each of the five probability ranges for the years 2008–2020. These histograms do not show a significant bias toward wet or dry days. At most, it is possible to observe a slight skewness toward dry days.

_{2}fall within each of the five probability ranges for the years 2008–2020. From scenario #1 to #4, the number of years when P

_{2}≤ 0.05 increases from 6 to 9; the number of years when P

_{2}≥ 0.95 decreases from 3 to 1. Thus, scenario #1 would already support our hypothesis. However, the statistical significance of a positive correlation significantly improves for scenario #4 when the probability that rainfalls could affect seismic events in each given year (P

_{2}≤ 0.05) exceeds the alternative possibility by 9 to 1. Two other years (2018 and 2020) had 0.05 < P

_{2}≤ 0.30; only one year (2015) had 0.70 ≤ P

_{2}< 0.95, and one year (2016) had P

_{2}≥ 0.95.

_{2}≤ 0.05) versus 1 “no” (P

_{2}≥ 0.95) with 10 independent trials (if the other three years are ignored) or for obtaining more than 9 + 2 = 11 “yes” (P

_{2}≤ 0.30 or P

_{2}< 0.50) versus 1 + 1 = 2 “no” (P

_{2}≥ 0.70 or P

_{2}> 0.50) with 13 independent trials (if the leaning years are respectively associated with their correspondent closest hypothesis). We would still get just a probability of 9% for obtaining more than 9 “yes” (P

_{2}≤ 0.05) versus 4 “no” (P

_{2}> 0.05) with 13 independent trials (if the other four cases are considered contrary to our hypothesis).

_{2}≤ 0.05 from 2008 to 2014 and in 2017 and 2019. Thus, we always found (=100% of the trials) P

_{2}≤ 0.05 during the 7 years when the bradyseism was relatively modest (2008-2011, 2013, 2014 and 2017).

## 5. Discussion and Conclusions

_{2}≤ 0.05 also in 2018, which experienced 375 seismic events, and in 2019, with 592 recorded seismic events. Even in 2020, when 766 seismic events were recorded, our statistical approach could still detect a moderate correlation 0.05 < P

_{2}≤ 0.30 between rainfall and seismic events. In 2020 it is possible to visually notice a very large increase in seismic activity from September to December, which was also the most rainy period of the year. In fact, from January to August the rainfall amount was 205.7 mm and there were 339 seismic tremors; from September to December the rainfall amount was 571.4 mm and there were 437 tremors.

_{2}≤ 0.05 (=“yes” to our hypothesis), for 1 year we get P

_{2}≥ 0.95 (=“no” to our hypothesis); two years led toward “yes” (0.05 < P

_{2}≤ 0.30) and one year led toward “no” (0.70 ≤ P

_{2}< 0.95). The probability of getting such a result randomly is less than 1%. However, if the analysis is limited to the 7 years of modest bradyseism (2008, 2009, 2010, 2011, 2013, 2014, 2017: see Appendix A), we found P

_{2}≤ 0.05 for all years (100% of the cases).

^{2}), where a small lake of about 50,000 m

^{2}also exists; by the basin of Agnano (about 3,000,000 m

^{2}), where a large volcanic lake of about 1,000,000 m

^{2}formed in the 11th century and existed until 1870 when it was artificially drained; and by the Solfatara crater itself. The first two large basins and the sea surround the Solfatara crater, which is the area most affected by seismic activity (Figure 1). Other craters and basins are on the Western sides of the Phlegraean area, where Avernus lake is located. Moreover, the underground hot aquifers of the area are very shallow, as demonstrated by the numerous thermal springs of the area and by the boiling mud at Solfatara (Figure 1). Thus, the results of this work envisage the possibility of developing specific rainfall-draining systems or other hydrological strategies to possibly mitigate the seismic activity at the Phlegraean Fields.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Time series of changes in altitude of the RITE station (Pozzuoli-Rione Terra), ACAE (Accademia Aeronautica), SOLO (Solfatara), and STRZ (Pozzuoli-Cemetery) from January 2000 to May 2020 (modified from: INGV-OV Bulletin of Surveillance Phlegraean Area, © CC BY-NC-ND 4.0).

## Appendix B

**Figure A2.**Rainfall time series measured at the Meteorological Observatory of San Marcellino in Naples (blue line) and the Solfatara (red line). The insert represents the calibration of Solfatara on San Marcellino.

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**Figure 1.**(

**Top**) The Phlegraean Fields (PF) area, with the most seismic region highlighted (yellow circle) (modified from Google Earth Pro). The events that occurred in 2020 are shown in the right insert against the digital terrain model of the area (modified from INGV-OV: http://www.ov.ingv.it, © CC BY-NC-ND 4.0). (

**Bottom-left**): The fumarolic field at the Solfatara (https://en.wikipedia.org/wiki/Solfatara_(volcano), © CC BY-SA 3.0). (

**Bottom-rig**

**ht**): Close-up view of a boiling mud pool at the Solfatara (https://en.wikipedia.org/wiki/Solfatara_(volcano), © CC BY-SA 4.0).

**Figure 2.**Scenario #1: R = 0.2 mm and τ = 1 day. Comparison between the empirical water stress-function (Equation (3)) estimated with the rainfall record of the Meteorological Observatory at San Marcellino in Naples (blue) and the seismic events at the Phlegraean Fields from 2008 to 2020 (red). Each panel covers one year. See Table 2.

**Figure 3.**Scenario #2: R = 0.1 mm and τ = 1 day. Comparison between the empirical water stress-function (Equation (3)) estimated with the rainfall record of the Meteorological Observatory at San Marcellino in Naples (blue) and the seismic events at the Phlegraean Fields from 2008 to 2020 (red). Each panel covers one year. See Table 2.

**Figure 4.**Scenario #3: R = 0.2 mm and τ = 2 day. Comparison between the empirical water stress-function (Equation (3)) estimated with the rainfall record of the Meteorological Observatory at San Marcellino in Naples (blue) and the seismic events at the Phlegraean Fields from 2008 to 2020 (red). Each panel covers one year. See Table 3.

**Figure 5.**Scenario #4: R = 0.1 mm and τ = 2 day. Comparison between the empirical water stress-function (Equation (3)) estimated with the rainfall record of the Meteorological Observatory at San Marcellino in Naples (blue) and the seismic events at the Phlegraean Fields from 2008 to 2020 (red). Each panel covers one year. See Table 4.

**Figure 6.**Histograms reporting the number of times the P

_{1}and P

_{2}value ranges occur in Table 1, Table 2, Table 3 and Table 4 from 2008–2020. The upper panel does not show any prevailing tendency, which suggests that the seismic activity exists because of the bradyseism. However, the bottom panel shows a strong prevailing tendency toward P

_{2}≤ 0.05 (blue) that increases from scenario #1 to scenario #4, which suggests that the seismic swarms are mostly linked to rainfalls. The results indicate that wet days enhance the seismic activity in the Phlegraean Fields.

**Table 1.**Scenario #1, rain threshold R = 0.2 mm, memory τ = 1 day. The cases 0 < P ≤ 0.30 are highlighted in bold.

Year | DY | WD | DE | WDE | E | EWD | Rand (%) | WEQD (%) | P_{1} | WEQ (%) | P_{2} |
---|---|---|---|---|---|---|---|---|---|---|---|

2008 | 366 | 195 | 8 | 3 | 53 | 46 | 53 | 38 | (0.70 ≤ p < 0.95) | 87 | (p ≤ 0.05) |

2009 | 365 | 204 | 8 | 3 | 162 | 155 | 56 | 38 | (0.70 ≤ p < 0.95) | 96 | (p ≤ 0.05) |

2010 | 365 | 237 | 10 | 6 | 124 | 19 | 65 | 60 | (0.30 < p < 0.70) | 15 | (p ≥ 0.95) |

2011 | 365 | 187 | 17 | 5 | 59 | 10 | 51 | 29 | (p ≥ 0.95) | 17 | (p ≥ 0.95) |

2012 | 366 | 183 | 47 | 26 | 225 | 186 | 50 | 55 | (0.05 < p ≤ 0.30) | 83 | (p ≤ 0.05) |

2013 | 365 | 212 | 18 | 14 | 47 | 27 | 58 | 78 | (p ≤ 0.05) | 57 | (0.30 < p < 0.70) |

2014 | 365 | 219 | 38 | 22 | 155 | 106 | 60 | 58 | (0.30 < p < 0.70) | 68 | (p ≤ 0.05) |

2015 | 365 | 178 | 44 | 20 | 175 | 108 | 49 | 45 | (0.30 < p < 0.70) | 62 | (p ≤ 0.05) |

2016 | 366 | 208 | 78 | 38 | 288 | 104 | 57 | 49 | (0.70 ≤ p < 0.95) | 36 | (p ≥ 0.95) |

2017 | 365 | 154 | 54 | 25 | 180 | 87 | 42 | 46 | (0.05 < p ≤ 0.30) | 48 | (p ≤ 0.05) |

2018 | 365 | 227 | 107 | 60 | 375 | 241 | 62 | 56 | (0.70 ≤ p < 0.95) | 64 | (0.05 < p ≤ 0.30) |

2019 | 365 | 194 | 180 | 87 | 592 | 322 | 53 | 48 | (p ≥ 0.95) | 54 | (0.05 < p ≤ 0.30) |

2020 | 366 | 165 | 209 | 97 | 776 | 364 | 45 | 46 | (0.05 < p ≤ 0.30) | 47 | (0.05 < p ≤ 0.30) |

all | 4749 | 2563 | 818 | 406 | 3211 | 1775 | 54 | 50 | 55 |

**Table 2.**Scenario #2, rain threshold R = 0.1 mm, memory τ = 1 day. The cases 0 < P ≤ 0.30 are highlighted in bold.

Year | DY | WD | DE | WDE | E | EWD | Rand (%) | WEQD (%) | P_{1} | WEQ (%) | P_{2} |
---|---|---|---|---|---|---|---|---|---|---|---|

2008 | 366 | 211 | 8 | 4 | 53 | 47 | 58 | 50 | (0.30 < p < 0.70) | 89 | (p ≤ 0.05) |

2009 | 365 | 217 | 8 | 3 | 162 | 155 | 59 | 38 | (0.70 ≤ p < 0.95) | 96 | (p ≤ 0.05) |

2010 | 365 | 258 | 10 | 7 | 124 | 20 | 71 | 70 | (0.30 < p < 0.70) | 16 | (p ≥ 0.95) |

2011 | 365 | 205 | 17 | 5 | 59 | 10 | 56 | 29 | (p ≥ 0.95) | 17 | (p ≥ 0.95) |

2012 | 366 | 203 | 47 | 31 | 225 | 195 | 55 | 66 | (0.05 < p ≤ 0.30) | 87 | (p ≤ 0.05) |

2013 | 365 | 225 | 18 | 15 | 47 | 28 | 62 | 83 | (p ≤ 0.05) | 60 | (0.30 < p < 0.70) |

2014 | 365 | 235 | 38 | 25 | 155 | 115 | 64 | 66 | (0.30 < p < 0.70) | 74 | (p ≤ 0.05) |

2015 | 365 | 200 | 44 | 22 | 175 | 112 | 55 | 50 | (0.70 ≤ p < 0.95) | 64 | (p ≤ 0.05) |

2016 | 366 | 228 | 78 | 44 | 288 | 118 | 62 | 56 | (0.70 ≤ p < 0.95) | 41 | (p ≥ 0.95) |

2017 | 365 | 173 | 54 | 26 | 180 | 88 | 47 | 48 | (0.30 < p < 0.70) | 49 | (0.30 < p < 0.70) |

2018 | 365 | 247 | 107 | 66 | 375 | 272 | 68 | 62 | (0.70 ≤ p < 0.95) | 73 | (p ≤ 0.05) |

2019 | 365 | 210 | 180 | 97 | 592 | 345 | 58 | 54 | (0.70 ≤ p < 0.95) | 58 | (0.30 < p < 0.70) |

2020 | 366 | 180 | 209 | 106 | 776 | 381 | 49 | 51 | (0.05 < p ≤ 0.30) | 49 | (0.30 < p < 0.70) |

all | 4749 | 2792 | 818 | 451 | 3211 | 1886 | 59 | 55 | 59 |

**Table 3.**Scenario #3, rain threshold R = 0.2 mm, memory τ = 2 day. The cases 0 < P ≤ 0.30 are highlighted in bold.

Year | DY | WD | DE | WDE | E | EWD | Rand (%) | WEQD (%) | P_{1} | WEQ (%) | P_{2} |
---|---|---|---|---|---|---|---|---|---|---|---|

2008 | 366 | 248 | 8 | 5 | 53 | 49 | 68 | 63 | (0.30 < p < 0.70) | 92 | (p ≤ 0.05) |

2009 | 365 | 260 | 8 | 5 | 162 | 157 | 71 | 63 | (0.70 ≤ p < 0.95) | 97 | (p ≤ 0.05) |

2010 | 365 | 293 | 10 | 7 | 124 | 20 | 80 | 70 | (0.70 ≤ p < 0.95) | 16 | (p ≥ 0.95) |

2011 | 365 | 264 | 17 | 11 | 59 | 51 | 72 | 65 | (0.70 ≤ p < 0.95) | 86 | (p ≤ 0.05) |

2012 | 366 | 255 | 47 | 37 | 225 | 203 | 70 | 79 | (0.05 < p ≤ 0.30) | 90 | (p ≤ 0.05) |

2013 | 365 | 267 | 18 | 17 | 47 | 46 | 73 | 94 | (p ≤ 0.05) | 98 | (p ≤ 0.05) |

2014 | 365 | 292 | 38 | 32 | 155 | 136 | 80 | 84 | (0.05 < p ≤ 0.30) | 88 | (p ≤ 0.05) |

2015 | 365 | 253 | 44 | 26 | 175 | 122 | 69 | 59 | (0.70 ≤ p < 0.95) | 70 | (0.30 < p < 0.70) |

2016 | 366 | 280 | 78 | 56 | 288 | 148 | 77 | 72 | (0.70 ≤ p < 0.95) | 51 | (p ≥ 0.95) |

2017 | 365 | 215 | 54 | 35 | 180 | 122 | 59 | 65 | (0.05 < p ≤ 0.30) | 68 | (p ≤ 0.05) |

2018 | 365 | 293 | 107 | 82 | 375 | 314 | 80 | 77 | (0.70 ≤ p < 0.95) | 84 | (p ≤ 0.05) |

2019 | 365 | 254 | 180 | 122 | 592 | 445 | 70 | 68 | (0.70 ≤ p < 0.95) | 75 | (p ≤ 0.05) |

2020 | 366 | 226 | 209 | 130 | 776 | 490 | 62 | 62 | (0.30 < p < 0.70) | 63 | (0.05 < p ≤ 0.30) |

all | 4749 | 3400 | 818 | 565 | 3211 | 2303 | 72 | 69 | 72 |

**Table 4.**Scenario #4, rain threshold R = 0.1 mm, memory τ = 2 day. The cases 0 < P ≤ 0.30 are highlighted in bold.

Year | DY | WD | DE | WDE | E | EWD | Rand (%) | WEQD (%) | P_{1} | WEQ (%) | P_{2} |
---|---|---|---|---|---|---|---|---|---|---|---|

2008 | 366 | 262 | 8 | 6 | 53 | 50 | 72 | 75 | (0.30 < p < 0.70) | 94 | (p ≤ 0.05) |

2009 | 365 | 270 | 8 | 5 | 162 | 157 | 74 | 63 | (0.70 ≤ p < 0.95) | 97 | (p ≤ 0.05) |

2010 | 365 | 312 | 10 | 8 | 124 | 117 | 85 | 80 | (0.30 < p < 0.70) | 94 | (p ≤ 0.05) |

2011 | 365 | 278 | 17 | 12 | 59 | 52 | 76 | 71 | (0.70 ≤ p < 0.95) | 88 | (p ≤ 0.05) |

2012 | 366 | 274 | 47 | 38 | 225 | 204 | 75 | 81 | (0.05 < p ≤ 0.30) | 91 | (p ≤ 0.05) |

2013 | 365 | 280 | 18 | 17 | 47 | 46 | 77 | 94 | (p ≤ 0.05) | 98 | (p ≤ 0.05) |

2014 | 365 | 302 | 38 | 32 | 155 | 136 | 83 | 84 | (0.30 < p < 0.70) | 88 | (p ≤ 0.05) |

2015 | 365 | 269 | 44 | 28 | 175 | 124 | 74 | 64 | (0.70 ≤ p < 0.95) | 71 | (0.70 ≤ p < 0.95) |

2016 | 366 | 297 | 78 | 57 | 288 | 149 | 81 | 73 | (p ≥ 0.95) | 52 | (p ≥ 0.95) |

2017 | 365 | 234 | 54 | 38 | 180 | 143 | 64 | 70 | (0.05 < p ≤ 0.30) | 79 | (p ≤ 0.05) |

2018 | 365 | 314 | 107 | 87 | 375 | 328 | 86 | 81 | (0.70 ≤ p < 0.95) | 87 | (0.05 < p ≤ 0.30) |

2019 | 365 | 270 | 180 | 131 | 592 | 473 | 74 | 73 | (0.30 < p < 0.70) | 80 | (p ≤ 0.05) |

2020 | 366 | 245 | 209 | 139 | 776 | 531 | 67 | 67 | (0.30 < p < 0.70) | 68 | (0.05 < p ≤ 0.30) |

all | 4749 | 3607 | 818 | 598 | 3211 | 2510 | 76 | 73 | 78 |

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## Share and Cite

**MDPI and ACS Style**

Scafetta, N.; Mazzarella, A.
On the Rainfall Triggering of Phlegraean Fields Volcanic Tremors. *Water* **2021**, *13*, 154.
https://doi.org/10.3390/w13020154

**AMA Style**

Scafetta N, Mazzarella A.
On the Rainfall Triggering of Phlegraean Fields Volcanic Tremors. *Water*. 2021; 13(2):154.
https://doi.org/10.3390/w13020154

**Chicago/Turabian Style**

Scafetta, Nicola, and Adriano Mazzarella.
2021. "On the Rainfall Triggering of Phlegraean Fields Volcanic Tremors" *Water* 13, no. 2: 154.
https://doi.org/10.3390/w13020154