1 Introduction

More than 1300 volcanoes have erupted during the last 10,000 years (Simkin et al. 1994). They produced direct immediate destruction and death as well as long-term consequences, such as some climate modulation. Regarding the former, the volcanic eruption is one of the most serious natural disasters in the world, with huge and devastating power. As an example, we remind the eruption of Vesuvius volcano that destroyed the Pompeii city on the 24 August, 79 CE (Lomax et al. 2001). About 12% of the world’s population is living on or nearby about 550 active and dangerous volcanic complexes (McGuire and Kilburn 1997; Small and Naumann 2001). Volcanic activities have been so frequent in recent years that we should pay more attention to the eruptions, which may bring serious damages to the social security, especially for the volcanoes in Japan and the super volcano in the Yellowstone Park of the United States (Yamaoka et al. 2014; Farrell et al. 2009). Nowadays, also in Italy there is a very hi-risk hazard due to Vesuvio and Campi Flegrei volcano and caldera (Mastrolorenzo et al. 2017; De Natale et al. 2017).

Volcanic eruptions are one of the most dramatic manifestations of the dynamics of the Earth’s interior as a prominent proof that the Earth is an active planet. Despite this, the volcanoes remain quiescent for most of time and the eruptive activity represents only a small portion of their life. The study of inter-eruption periods is fundamental to understand what changes in the system and what phenomena occur in preparation of the volcanic eruption. It is known that magma flews toward reservoir. Magma itself changes its physical and/or chemical properties. Studying such type of perturbations of the reservoir is fundamental to understand how they drive the volcano to a new eruption (Brenguier et al. 2008).

Studies carried out by means sensitive seismographs networks confirmed that volcanic eruptions had a detectable short-term seismic precursor with times between 15 min and 13 days, although for several events occurred, where magma movements were detected by their seismicity and crustal deformation signals, did not result in eruptions (Einarsson 2018).

Scientists usually use repeated Δg (differential gravity) and Δh (differential deformation) observations measured by a network of stations in and around the active craters or calderas to monitor volcanic activity (Rymer 1994; Rymer et al. 1998; Rymer and Williams-Jones 2000).

The conventional micro-gravity monitoring at active volcanoes threatens even the life safety of volcanologists seriously (Baxter and Gresham 1997; Fujii and Nakada 1999).

Recently, repeated seismic tomography (Patanè et al. 2006) has been used to detect changes in seismic velocity within Etna for periods of a few years. The method revealed changes in the internal volcanic structure before and after an eruption. However, repetitive tomographic imaging requires long periods of seismicity observation and cannot be easily performed continuously.

Satellite remote sensing has been exploited in the past, for volcano activity monitoring. In particular using the short wave infrared (SWIR) radiation for monitoring the high-temperature activity within the active crater (Wooster and Rothery 1997); thermal infrared (TIR) radiation for automated detection of thermal features of active volcanoes (Pergola et al. 2004; Marchese et al. 2010) and for monitoring any precursory activity for predicting eruptions (Reath et al. 2016).

More recently, both satellite and ground-based data, such as Global Navigation Satellite System (GNSS) data, Synthetic Aperture Radar Interferometry (InSAR) images, etc., are used to estimate the information of gravity and ground deformation near the volcano of interest. The areas near volcanic vent usually uplift or subside with the rate of 2–3 cm per year before the volcanic eruption (Pritchard and Simons 2004a, b; Yu et al. 2015). Because of low time resolution of InSAR image, this method is suitable to medium-term prediction of the volcanic eruption rather than the impending volcanic eruption.

The lithosphere–atmosphere–ionosphere coupling (LAIC) model (Pulinets and Ouzounov 2011) suggests that, in the earthquake preparation phase (driven by the tectonic stress), a variety of precursory phenomena occurs, due to some exchange of energy or particles from the lithosphere to the above atmosphere and then up to the ionosphere. The methodology is based on the integrated analysis of more atmospheric and environmental parameters, whose abnormal variations can be possibly associated with the impending earthquake. These observations are mainly: thermal infrared radiation (TIR); electromagnetic (EM) variations; radon/ion activity; air temperature and humidity, and the electron density (Ne) in the ionosphere (e.g. De Santis et al. 2015). Recently ionospheric disturbances recorded by DEMETER satellite over active volcanoes have been observed indicating that the amount of anomalies seems related to the powerfulness of the eruptions (Zlotnicki et al. 2010, 2013).

Volcanic eruptions are preceded by magma pressure increasing, leading to the inflation of volcanic edifices (Patanè et al. 2003). Ground deformation resulting from inflation can be monitored by different techniques, among these the satellite remote sensing (Massonnet et al. 2001).

We can briefly depict a possible scenario that explains the chain of processes. Increasing of magmatic camera activity can cause a raise of temperature whose evidence could be appreciated at the surface (Slezin 2003). One of the possible pre-eruption effects could be the appearance of some thermal anomalies in the crater area, weeks/months before explosive volcanic eruptions. At the same time, the rising of fluids in the magma chamber can lead to the release of substances that can alter the atmospheric chemical composition and opacity.

Similarly, the water vapour could be used as an indicator of the volcanic eruption preparation phase since an increasing of its concentration is expected to be due to fluids rising and evaporation induced by heat flux. For example, Brenguier et al. (2008) monitored the inflation volcanic edifices as a consequence of magma pressures. This effect increases the seismic noise starting around 20 days before the eruption.

According to the lithosphere-atmosphere effect, thermal anomalies could be observed several days before some dramatic geophysical activities (Occhipinti et al. 2006; Pulinets and Davidenko 2014; Piscini et al. 2017), which may be useful to recognize for a possible impending volcanic eruption with a more anticipated time. Therefore, in the next sections we will investigate the thermal and water vapour anomalous variations before the volcanic eruptions from 2002 to 2017 using the CAPRI algorithm (Piscini et al. 2017). Furthermore, AOT (Aerosol Optical Thickness), SO2 and DMS (Dymethilsulphyde), obtained from NASA MERRA-2 Global Modeling and Assimilation data archive, are also analyzed. These parameters have been selected to investigate the possible changes of the physical/chemical composition of the atmosphere. In particular, AOT is predicted by LAIC model to be altered before seismic/lithospheric events (Pulinets and Ouzounov 2011).

2 Data and Method

Twelve volcanic eruptions have been investigated in this work. In particular, nine VEI4 volcanic events through 2002–2015, one VEI5 and one VEI3 in 2014 are selected from Smithsonian Institution “Global Volcanic Program” database (https://volcano.si.edu/) and one eruption without (at present time) VAI4+ explosion by Agung Volcano in 2017 has been selected (VEI2). Among them, there are ten stratovolcanoes and two calderas; the information about eruptive events and their location is listed in Table 1.

Table 1 Information about volcanic eruptions occurred from 2002 to 2017 analyzed in this work

For each eruption, it was checked if a strong earthquake (M6+) had occurred both in the same area and time window of the analysis, extracting earthquake data from worldwide USGS (United States Geological Survey) catalogue (https://earthquake.usgs.gov). This close earthquake-eruption simultaneity occurred for two case studies: in the case of Merapi 2010 eruption, a M7.8 earthquake occurred on 25 October 2010 at 14:42:22 (UTC), located at 3.487°S 100.082°E, Kepulauan Mentawai region, Indonesia; for Kelud 2014 eruption, a M6.1 earthquake occurred on 25 January 2014 at 05:14:18 (UTC), located at 7.986°S 109.265°E, 38 km SSE of Adipala, Indonesia. Both considered eruptions are located inside the area defined by Dobrovolsky et al. (1979), which approximates the large-scale areas where seismic precursors are usually expected around the impending faults.

2.1 ECMWF Climatological Data

The European Centre for Medium-range Weather Forecasts (ECMWF) is a meteorological European centre that provides meteo-climatological observations and forecasts.

Some studies have been carried out to validate ECMWF operational analyses data. Different parameters were deeply investigated, as temperature, specific humidity, and others, showing a good agreement especially at mid-latitudes, but lower in the south Polar Regions (Lambert 1988; Gobiet et al. 2005).

ERA-Interim is a global atmospheric reanalysis that uses satellite data (European Remote Sensing Satellite, EUMETSAT and others) input observations prepared for ERA-40 and data from ECMWF’s operational archive. It covers dates from 1 January 1979 to present, continuously updated in real time (Dee et al. 2011).

For the year that includes the volcanic eruption under investigation, we use the ECMWF skin temperature (skt) and total column water vapour (tcwv) data analysis (i.e. operational archive), in an interval preceding 90 days the volcanic eruption and compared with the same period of ERA-Interim of the previous years since 1979.

ERA-Interim data are provided four times a day, i.e. at 00:00, 06:00, 12:00 and 18:00 UTC. In order to distinguish possible volcano-induced temperature enhancements from the normal weather phenomenon, only the data close to the local night-time were used, because thermal anomalies related to normal weather variations are seldom at night-time, without solar radiation.

The data have been extracted with a spatial resolution of 0.0625° corresponding to a spatial resolution of around 7 km. The operational archive reaches this level of resolution, while the ERA-Interim data have a lower resolution, but for homogeneity we extract the latter with the same resolution of the former ones.

2.2 MERRA-2 Chemical Data

MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, Version 2) is a climatological atmospheric model developed by NASA that provides data beginning in 1980 and continuous in present time with a delay of one-two months (Gelaro et al. 2017). MERRA-2 input data come from conventional observations, aircraft, meteo satellite (the second version of MERRA takes advantage from the modern hyperspectral radiance and microwave observations, along with GPS-Radio Occultation datasets). MERRA-2 assimilates space-based observations of aerosols and it represents their interactions with other physical processes in the climate system. Spatial resolution is about 50 km in the latitudinal direction.

In this paper M2T1NXAER version: 5.12.4, a subset of MERRA-2, has been analyzed. M2T1NXAER is a time-averaged, single-level (vertically integrated), aerosol and chemical model of atmosphere with 1-hourly values provided in NetCDF version 4 format. Spatial resolution is 0.5o in latitude and 0.625o in longitude. Three parameters are extracted from this database: DMSSMASS, SO2CMASS and TOTEXTTAU that are dimethylsulphide surface mass concentration in kg/m3, sulphur dioxide (SO2) column mass density in kg/m2 and total aerosol extinction (AOT) at wavelength of 550 nm, respectively. The choice of the former parameter was intended to introduce in the analysis a chemical compound that we would not expect to change significantly before a volcanic eruption. The atmospheric DiMethylSulphide (DMS) has been identified as the major volatile sulfur compound in surface seawater (Lovelock et al. 1972; Andreae and Raemdonck 1983).

2.3 CAPRI Algorithm

The Climatological Analysis for seismic PRecursor Identification (CAPRI) algorithm was developed for the study of possible climatological anomalies before earthquakes by using a statistical analysis applied to climatological time series (Piscini et al. 2017). In principle, as this algorithm has been developed, it could also be used for detection of volcanic eruption precursors.

Before being processed, the data (T that is the parameter under investigation, i.e. skt or tcwv) are spatially averaged using only those over the land:

$$T_{ERA} \left( d \right)_{y} = <T_{ERA} \left( {d,\lambda ,\varphi } \right)>_{y\lambda ,\varphi }$$
(1)

where \(T_{ERA} \left( d \right)_{y}\) is the mean value of T for the specific day in the year in the year y between 1979 and the year before the eruption) in the ERA-interim data; \(\lambda ,\varphi\) are the latitude and longitude, respectively; triangular brackets stand for spatial average.

To remove an eventual long-term trend (for example the so called “global warming” effect), the slope of a linear trend is computed and subtracted from the date. This operation could be important as for example underlined by Brohan et al. (2006).

The formula applied to remove the trend is:

$${\text{T}}^{\prime } \left( {\text{d}} \right)_{\text{y}} = {T}_{\text{ERA}} \left( {\text{d}} \right)_{\text{y}} - {\text{m}}\left( {\text{d}} \right) \times \left( {{\text{y}} - {\text{y}}_{0} } \right)$$
(2)

where m(d) is the fit slope, \(\Delta T\left( d \right)={\text{m}}\left( {\text{d}} \right) \times \left( {{\text{y}} - {\text{y}}_{0} } \right)\) is the variation of temperature for the same day d, between the considered year, \(y\) and the first year of time series \(y_{0}\), i.e. 1979, which is used as a “reference”.

Finally, for each day d, the data of the time series are averaged over all the years, thus obtaining the average temperature, \({\text{T}}_{\text{h}} \left( {\text{d}} \right)\), of that particular day in the years that preceded the eruption:

$${\text{T}}_{\text{h}} \left( {\text{d}} \right) = \frac{1}{{{\text{N}}_{\text{y}} }}\mathop \sum \limits_{{{\text{y}} = 1979}}^{{y_{eru} - 1}} {\text{T}}^{\prime } \left( {\text{d}} \right)_{\text{y}}$$
(3)

where \({\text{N}}_{\text{y}}\) is the total number of the averaged years (for example 36 years for a 2015 eruption), yeru is the year of the eruption. In addition, the standard deviation, σ is also calculated for each day. The variable behaviour of the year in analysis (\({\tilde{\text{y}}}\)) is then compared with the historical series (3). To make this comparison feasible, we impose the (ECMWF operational archive) average value in the period analyzed to coincide with the average of the historical (ERA-interim) time series:

$${\text{T}}\left( {\text{d}} \right)_{{{\tilde{\text{y}}}}} = {\text{T}}^{\prime } \left( {\text{d}} \right)_{{{\tilde{\text{y}}}}} - \left( {\left\langle {{\text{T}}^{\prime }_{{{\tilde{\text{y}}}}} } \right\rangle_{\text{d}} - \left\langle {{\text{T}}_{\text{h}} } \right\rangle_{\text{d}} } \right)$$
(4)

In this paper, we apply the same algorithm to volcanic eruptions, mainly of explosive type. The novelty of the method consists in the way in which the complete time series is processed, where even the possible effect of global warming is adequately removed.

The values of skt and tcwv in a square area of one-degree side, centred on the volcano, are taken into account. First of all, the algorithm calculates the spatial averages only on the land pixels of the investigated parameter, for all the considered days and years.

For both climatological parameters and for all the analyzed volcanoes, the time series was built for each of the 90 days before the event. The mean and standard deviation were calculated for each analyzed day. The algorithm shows for each parameter the historical mean together with a band at ± 2 standard deviations. The values of the year with the eruption that overpass this threshold are then tagged as anomalous.

The CAPRI algorithm searches for the more anomalous days and produces for those days some maps to deeply investigate the geographical distribution of the anomalies.

2.4 MEANS Algorithm

From the original dataset we extracted some other parameters of interest: SO2, DMS and AOT. The data are available from 1980 to present (with some delay for the elaboration of the model, updated one time a month).

The “MErra-2 ANalysis to search Seismic precursors” (MEANS) algorithm selects an NxN square area centered on the volcano of a 3° × 3° size and time starting 90 days before the event (eruption). If the start of the period is before 1 January then the first year is 1981 to have a complete time series of each year.

Using the longitude \(\lambda\) of the event (i.e. volcano’s longitude) the local time LT is computed by the usual conversion of the universal time UT:

$$LT = UT + \lambda \cdot \frac{12}{180^\circ }$$

The closest value to local midnight is selected by the algorithm for the whole investigated area.

The MEANS algorithm computes the spatial mean of the parameter P over the studied area day (d) by day at the hour closest local midnight:

$$P_{d,y} = <P\left( {\lambda ,\varphi ,d,y} \right)>_{\lambda ,\varphi }$$

where y is the year, λ is latitude and ϕ is longitude. For each day the mean \(m_{d}\) and the standard deviation \(\sigma_{d}\) are computed from 1980 to 2017 excluding the year with the eruption.

Some years present high value of some parameters due often to other events (also other eruptions of the same volcano). To detect these years, and to neglect them from the statistical analysis, the median \(m_{m}\) and the standard deviation \(m_{\sigma }\) of the mean value \(m_{d}\) are computed, respectively. If in a year a parameter has a value equal to or greater than \(m_{m} + 10 \cdot m_{\sigma }\), then that year is automatically excluded from the historical time series.

So the historical mean \(P_{h} \left( d \right)\) is now computed and the standard deviation \(\sigma_{d}\) is re-computed on the “standard” remaining years (its total number is \({\text{N}}_{\text{y}}\)):

$$P_{h} \left( d \right) = \frac{1}{{{\text{N}}_{\text{y}} }}\mathop \sum \limits_{{{\text{y}} = 1980}}^{2017} P_{d,y}$$

Also in this case the eruption year is not taken into account in the historical time series \(P_{h}\).

Finally, the MEANS algorithm produces a graph with the historical mean \(P_{h}\) ± 1.0, ± 1.5 and ± 2.0 standard deviations. The year with the eruption event is superposed and so it is possible to know if in the investigated period the analyzed parameter has one or more anomalous days (i.e. the parameter that exceeds the mean by 2.0 standard deviations). Although the analyzed quantities are different and even with different units, we define the anomaly with respect to two times the standard deviation of the same quantity. To compare the different parameters, we take into account the number of the anomalies that is a comparable number as it is defined over the common 2σ criterion.

Note that as the mean and standard deviation are individually evaluated for each day, some typically seasonal behaviors do not affect the anomaly threshold.

3 Results and Discussion

Table 2 summarizes the occurrences of climatological anomalies for each analyzed parameter associated with each volcano. Volcanoes are grouped in relation to their geographical location. The first two volcanoes, Grimsvotn and Eyjafjallajokull, reside in Iceland, than we find the Nyiragongo African volcano and Okmok in the Aleutian Islands, while Reventador, Puyehe, Calbuco and Chaiten lie in South America. Reventador volcano lies in the eastern Andes of Ecuador, while Calbuco, Chaiten and Puyehe lie in the Andes of Chile. Merapi and Kelud volcanoes are located on the border between Central Java, East Java, Indonesia and Agung is a volcano in Bali Island, Indonesia. Finally, Ontake volcano is located in Japan.

Table 2 Notation of anomalous days for all investigated eruptions and for all parameters

As preliminary result, we notice that, for most of the volcanoes, SO2 confirms its role as the best proxy for impending explosive eruptions, since anomalies for this parameter occur some days before the eruption starts. Anomalies are present in all cases, for all parameters, with the quasi-exception of Agung volcano. In this case, no VEI4+ explosive eruption was yet occurred. Concerning the latter volcano, we notice that only skt reveals some anomalous days, probably related to the ongoing magmatic camera activity. For this volcano, we present also a SO2 map in Fig. 1 of the surrounding area for 27 November 2017 at 5 UTC as extracted from MERRA-2. This could be compared to the map published by ESA by TROPOSOMI instrument onboard Sentinel 5-precursor satellite (see ESA/DLR 2017). It is possible to see that the pixel in which lies the volcano reveals a clear high value of SO2 concentration in atmosphere.

Fig. 1
figure 1

SO2 map example of the Indonesian region for 27 November 2017 at 5 UTC as extracted from MERRA-2. The Agung volcano location is highlighted by a white star. It represents an example map of a quantity extracted from MERRA-2 archive (SO2 in this case) with the aim to indicate the level of confidence of the dataset. The map indicates some sulfide gas emission due to ongoing eruption

Kelud volcano has only one anomalous day for climatological data (only skt on day 22) while the MERRA-2 parameters reveal anomalies starting 45 days before eruption (SO2 and AOT).

From our results, it seems that the occurrence of this kind of anomalies does not depend from the volcano type, since anomalies are present both for caldera and stratovolcano eruptions. Furthermore, neither the geographical location of the volcano seems to produce differences in the anomalies occurrences.

Now we will show a specific case as example among all the analysed cases, both in the case of the year of concern and in the confutation case of another year when no eruption occurred. As typical example, we consider 2014 Ontake eruption.

Figures 2, 3, 4, 5, and 6 describe the results obtained from the above case study. These figures represent the comparison of time-series between the investigated year and the historical time series, for all parameters (Figs. 2, 3, 4, 6). Figure 5 shows the distribution map of a parameter in an anomalous day giving also an indication on the spatial dimension of the area of study. Figure 7 depicts the same map for all analyzed parameters. It would have been difficult to represent all results using the same figures. Nevertheless, the results for all cases are condensed in Fig. 8, which resumes the description of all anomalies detected for each parameter and for each volcano.

Fig. 2
figure 2

Case study for 2014 Ontake ECMWF skt at 12:00 UTC (i.e. about 21 LT). The 2014 time series (red line) is compared with the historical time series (1979–2016, blue line). The circle puts in evidence two anomalous consecutive days. Colored stripes indicate 1.0 (cyan), 1.5 (green) and 2.0 (yellow) standard deviation from the mean of the historical time series, respectively. The eruption occurred at the end of period analysed (91th day)

Fig. 3
figure 3

2008 Ontake ECMWF skt at 12:00 UTC (i.e. about 21 LT). The 2008 time series (red line) is compared with the historical time series (1979–2013, blue line). Colored stripes indicate 1.0 (cyan), 1.5 (green) and 2.0 (yellow) standard deviation from the mean of the historical time series, respectively. No anomalies are present for this year when no eruptions occurred. The eruption occurred at the end of period analysed (91th day)

Fig. 4
figure 4

Ontake 2014 ECMWF tcwv at 12:00 UTC. The 2014 time series (red line) is compared with the historical time series (1979–2013, blue line). Colored stripes indicate 1.0 (cyan), 1.5 (green) and 2.0 (yellow) standard deviation from the mean of the historical time series, respectively. Some anomalies are present but without multiday persistence. The eruption occurred at the end of period analysed (91th day)

Fig. 5
figure 5

Ontake skt map of the difference between the ΔT (skt) for 27 September, 2014 and the historical mean with the values on 5 July subtracted. ΔT represents the difference pixel by pixel between the skt for that day and the historical mean

Fig. 6
figure 6

Ontake 2014 MERRA-2 SO2, DMS and AOT at 550 nm. The 2014 time series (red line) is compared with the historical time series (1979–2016). Colored stripes indicate 1.0 (cyan), 1.5 (green) and 2.0 (yellow) standard deviations from the mean of the historical time series, respectively. The eruption occurred at the end of period analysed (91th day)

Fig. 7
figure 7

Maps of a particular day for some of analyzed volcanoes, considering both skt and tcwv parameters

Fig. 8
figure 8

Cumulative number of atmospheric two-day persistent anomalies since 90 days before the explosion/eruption for the twelve analyzed volcanoes, for each parameter; a skt, b tcwv, c SO2, d DMS, e AOT, f all parameters. The red dashed line represents the mean cumulative curve. Agung volcano has been excluded from the mean

Figure 2 shows Ontake 2014 ECMWF skt at 12:00 UTC (i.e. about 21 LT). The time series comparison shows one anomaly on 25 July which persisted for two days. It deviates from historical mean by 1.54 K over two standard deviations.

For confutation, a computational test in order to establish the goodness of the algorithms has been carried out analyzing, for a specific volcano, the same interval of the year, but for another year without eruption. Figure 3 shows ECMWF skt for Ontake in the same period and time (12:00 UTC) but another year, i.e. 2008. The latter analysis does not reveal any anomaly.

Figure 4 shows ECMWF tcwv for the case study Ontake 2014 at 12:00 UTC. Time series comparison shows a few anomalies, one in the same day as skt anomaly and another in the next days, but none is persistent for more than a day.

Figure 5 describes the map of the difference between the skt for 27 September, 2014 and the historical mean with the values on 5 July subtracted. ΔT represents the difference pixel by pixel between the skt for that day and the historical mean and ΔT = 0.30 K is the amount of skt over two standard deviation. The results indicate that the occurrence of the thermal anomaly before volcanic eruption depends on its position with respect to the volcano. This behavior characterizes also the location of thermal anomalies for the other volcanic eruptions.

Figure 6 shows Ontake 2014 MERRA-2 SO2, DMS and AOT at 550 nm. These analyses show one anomaly for sulphur dioxide and DMS, almost concomitant with those for skt and tcwv. Further anomalies are present at around the fortieth day. No AOT anomaly is present.

Comparing the precursor time in our anomalies (Fig. 7) with that found by Brenguier et al. (2008), i.e. 20 days before the eruption, our approach provides a greater anticipation time alert. This could be very useful to better organize the activities and protect the involved people.

CAPRI algorithm produces also the map of the most anomalous days for each investigated parameter. Figure 7 presents a selection of some interesting concentration of skt and tcwv around the volcanoes. These maps can help in the classification of the anomalous values obtained by the comparison with the historical mean showing which are geographical related with the volcano area and which are probably related to other phenomena.

Figure 7 collects a selection of maps related to the analyzed events with peculiar geographical characteristics around the volcano. This selection takes into account the events that show some lobes of the investigate parameters close or just around the volcanoes.

The use of the maps allows, in some cases, to confirm, at least spatially, the peaks in the time series analyses with the volcano under study. In any case, it is necessary to pay particular attention to the weather conditions that can easily alter these maps, especially for the parameters that are more closely linked to the atmosphere, which can have some variability even on hour basis. As regards the skin temperature, it must be taken into account that the thickness of the volcanic cone could make it more difficult to observe the increasing of temperature due to the magma rising, which could therefore be easier to observe around the volcanic cone where the magma finds a lower crust thickness. For example, Eyjafjallajokull 2010 presents a clear skt anomaly located at the western part of the caldera in the same day of the explosion, but about 6 h before. Nyiragongo (2002) presents a well centered anomaly, little covered by Kivu Lake south-west placed with respect to the volcano. The anomaly has a circular shape with a diameter approximately of 60 km. A very similar shape anomaly is shown by Reventador (2002) volcano. Both anomalies not only are clearly centred on the volcano but also they exceed two standard deviations with respect to the mean of the historical time series. This latter volcano presents also a circular anomaly in tcwv that precedes of about 1 month the skt anomaly. Calbuco (2015) presents a very wide anomaly, with the most intense one just in northern part of the volcano. In addition, the amount of the value is well above two standard deviations (1.81 K). Kelud (2014) presents a particular anomaly in tcwv as an increase of the water vapour in south-eastern part and a decrease in north-eastern part with respect to the volcano. It is interesting to note a tcwv pattern with two lobes shape, one more positive (12 kg/m2) and the less positive (5 kg/m2), and we suggest that it could be due to the volcanic alteration of the atmosphere above the interested region.

The graphs of the Fig. 8 are useful to visually search for a possible acceleration in number of anomalies toward the explosive eruption and to quickly compare each other the different case studies and also to determine a mean behavior of the time shape increase of the cumulative number of anomalies (red dashed line). The figure describes the cumulative number of two-day persistent atmospheric anomalies for all volcanoes since 90 days before the explosion/eruption, for each parameter (a,b,c,d,e) and considering all together (f). The graph is obtained by increasing by one unit the curve of each studied volcano when the analyzed parameter reveals an anomaly (i.e. a value over two standard deviations) for at least two consecutive days. If in the same day there is more than one anomaly, the curve of Fig. 8 is increased by the same number of anomalous parameters in that day.

Looking at the curves for each single parameter in Fig. 8a–e, we notice that, as expected, among all parameters SO2 shows more anomalies. The parameter skt does not show a significant number of persistent anomalies: this is probably due to the short (3 months) shown period, in fact in next paragraph about confutation analysis skt parameter shows a consistent number of anomalies in 1 year before the explosive eruptions. The fact that the other minor anomalous parameters, such as, twvc, AOT have comparable anomalies with DMS is interesting, with a twofold alternative explanation: 1) their changes are not significant in the analysed time period; or 2) the role of DMS is more important than previously expected. However, the latter possible interpretation would need more case studies to be validated.

Moreover, from Fig. 8a–e it is possible to estimate the precursor time of explosive eruption, in particular for MERRA-2 dataset. The cumulative graphs put in evidence how the first anomaly increasing is for AOT, then DMS followed by SO2 (Calbuco, Chaiten, Puyehue).

Analyzing the total cumulative graph (Fig. 8f), it is possible to note an activation that starts from 80 days to 10 days before the explosive eruption. Interesting enough is also the possible chain of processes that happens: tcwv and skt appear usually first (although the latter appears clearly only in three volcanic eruptions), then they are followed, in order, by DMS, AOT and SO2. Another interesting result is that AOT is the parameter that changes anomalously in more cases.

Regarding the single case studies, we notice the following characteristics. The case studies of Grismvotn 2011 and Agung 2017 do not present significant influence in atmosphere. For the Agung volcano this could be due to the fact that it has not been characterized by a VEI4+ explosive eruption, as confirmed by the anomalies described in Table 2. Eyjafjallajokull 2010 presents the higher slope, due mainly to significant sulphur dioxide emission, confirming the role of this parameter as a proxy for the eruptive activity that starts on 20 March 2010. Also the cumulative curve of Nyrangongo 2002 eruption presents a very high number of anomalies mainly due to an emission of DMS from 50 to 30 days prior the explosive eruption.

On Fig. 8, we superpose to the single curves also the mean cumulative curve (red dashed line) to see the behaviour of the specific volcano activity. The Agung volcano has been excluded from the mean since it has not actually reached a VEI4, so it is not comparable to the other volcano eruptions.

It is possible to note in Fig. 8f that seven volcanoes (Agung 2017, Grismvotn 2011, Okmok 2008, Puyehue 2011, Chaiten 2008, Kelud 2014 and Ontake 2014) are at the end under the mean curve and only the Okmok 2008, and Ontake 2014 present a part of their curves above the mean cumulative curve. Merapi 2010 and Calbuco 2015 reach a very close end value to the mean curve. In any case, Merapi 2010 overpasses the mean curve little more than 30 days before the explosion. The data regarding two volcanoes eruptions, Nyrangongo 2002 and Reventador 2002, are always above the mean cumulative curve, so we can hypothesize that their activity is very intense and it anticipated the mean behaviour of the studied volcanoes. On the other hand, Calbuco 2015 started with a high intense activity but it stopped to produce anomalies about 50 days before the explosion. The mean cumulative curve can also be used to see if a volcano increases rapidly its activity, as the Eyjafjallajokull 2010, about 20 days before the explosion, overpasses the mean curve and continues its rapidly increase toward the explosion. In general, the volcano anomalies activity seems to start from 75 days and 20 days before the eruption, showing a strong dependence with the event (or the volcano). Unfortunately the used dataset covers a time too short to see if a behaviour is typical of a particular volcano as such so “explosive” (VEI4+) eruptions are not so frequently.

4 Confutation Analysis

Starting from a peculiar behavior represented by the persistence of anomalies by some parameters for all strong volcanic eruptions, a confutation analysis has been carried out comparing the eruption year (i.e. the “active year”) with a quiet one (i.e. the “calm year”) for a period of 1 year before eruption.

In this analysis the November, 25th 2017 Agung eruption has been excluded as it did not reach the VEI4.

Table 3 describes the analyzed eruption and year of comparison highlighting the main characteristics of occurred eruption and other interesting eruptive events in the investigated area.

Table 3 Analyzed eruption and year of comparison for each volcano highlighting the main characteristics of the occurred eruption

The “calm year” was selected generally taking into account from one to 2 years after the eruption in order to be sure that volcanic activity was over. To define a “calm year” we check the absence of eruptive activity (all VEI) in the area during and following (for at least one year) this period. The selected calm years for all case studies have reported in Table 3. Note, that the comparison period is at the same day and month of the eruption (but obviously in a different year), in this way eventual seasonal effects act in the same behavior for the pre-eruption year and for the calm year.

In order to appreciate the reliability of the method we performed a test to compare the number of persistent anomalies detected for both “active” and “calm” years. Then we considered the test successful, indicated by 1, if the number of anomalies for year investigated was higher than the confutation year, otherwise indicated by 0 (i.e. the number of anomalies of the “calm year” was higher than those of the “active year”). Finally, a Hit Rate (the fraction of successful cases with respect to the total number of cases) was calculated, in order to establish the accuracy of method for each investigated parameter (i.e. skt, tcwv, AOT, SO2 and DMS).

Table 4 summarizes the results obtained considering the anomaly persistence (at least 2 days) for all volcanoes. Blue columns represent the number of anomalies for each parameter estimated in the eruption year; the green columns list the number of anomalies detected in corresponding calm years; the last (orange) columns describe the result of comparison as 1 and 0 and summarize them in term of accuracy.

Table 4 Summary of the results obtained considering the anomaly persistence (at least 2 days) for all volcanoes

It is worth noting that the method gives an accuracy of 100% for both AOT and DMS, a little lower accuracy (91%) for skt, tcwv and SO2 (only one volcano that is preceded by less anomalies than in the comparison year). The test confirms that the year with eruption (i.e. the “active year”) is characterized by a consistent number of persistent anomalies for the analyzed parameters and such a high accuracy confirms that the selected parameters are systematically increased above 2 standard deviations for at least two consecutive days in the year that precedes the VEI4+ explosive volcanic eruption.

5 Conclusions

We used ECMWF and MERRA-2 climatological data to analyze the variations before VEI4+ volcanic eruptions from 2002 to 2017 with two kinds of algorithms, both based on a standard deviation threshold range method.

The results suggest that the occurrence rate of skt, tcwv, SO2, AOT and DMS anomalies before great volcanic eruptions is likely related with the volcanic type and geographical settings. For most of the volcanoes, SO2 confirms its leading role as proxy for impending explosive eruptions since anomalies occur some days before the eruption starts (Thomas and Prata, 2011; Sears et al. 2013).

Simultaneous analysis of several climatological parameters showed that in the case of strong eruptions (VEI4+) the anomalies are present more or less for all the observed quantities. These anomalies are probably caused by the underground magma uplift flows that precede the eruption in the quiescent inter-eruption phase. The spatial location of skt, tcwv, SO2, AOT and DMS anomalies before great volcanic eruptions is related with the geographical settings. All positive anomalies are taken into account for the expected interaction with the atmosphere by the just mentioned underground physical process. The use of the maps improves, in some cases, the time series analysis. Furthermore, it helps also to better understand the phenomena, i.e. the perturbations induced by the preparation activity of the volcanic explosion.

We found a general agreement between the amount of anomaly and the entity of the volcanic explosion, for example, the strong activity of Puyehue (2011) is well compatible as it is a VEI5 volcanic eruption.

Unfortunately, in the cases of Merapi (2010) and Kelud (2014) eruptions, we are not able to confirm the role of the thermal anomalies as precursor for volcanic eruption since both events had occurred soon after a strong seismic event which defines the large-scale areas around the impending faults where seismic precursor usually occurs.

In the case of the Agung eruption (VEI2/3), no one can say the same thing because only the skt reveals some anomalies. This reinforces the concept that the simultaneous analysis of climatological quantities is fundamental to affirm with a certain margin of confidence the beginning of the preparatory phase of a strong explosive eruption.

A confutation analysis confirms with a very high accuracy (91–100%) that skin temperature, total column water vapor, aerosol optical thickness, sulphur dioxide and dimethylsulphide are systematically above 2 standard deviations with a persistence of at least two consecutive days during the year that precedes the eruptions with volcanic explosive index VEI4+ . This confirms the reliability of the method and of the used climatological datasets, suggesting its use as potential technique for volcanic eruption prediction and/or monitor purpose.

This is further corroborated by the fact that the here considered physical and chemical anomalies precede by many days also the seismic noise variations, caused by the inflation of the volcanic edifice (Brenguier et al. 2008), making this technique powerful and reliable method to predict the evolution of volcanic activity with large anticipation time.

Future enhancements will include the simultaneous use of multi satellite and ground datasets in order to better assess and reinforce the operational performance of such as geophysical indicators as volcanic eruption precursors.