 Research
 Open Access
TephraProb: a Matlab package for probabilistic hazard assessments of tephra fallout
 Sébastien Biass^{1, 2}Email authorView ORCID ID profile,
 Costanza Bonadonna^{1},
 Laura Connor^{3} and
 Charles Connor^{3}
https://doi.org/10.1186/s1361701600505
© The Author(s) 2016
 Received: 6 January 2016
 Accepted: 27 July 2016
 Published: 24 August 2016
Abstract
TephraProb is a toolbox of Matlab functions designed to produce scenario–based probabilistic hazard assessments for ground tephra accumulation based on the Tephra2 model. The toolbox includes a series of graphical user interfaces that collect, analyze and pre–process input data, create distributions of eruption source parameters based on a wide range of probabilistic eruption scenarios, run Tephra2 using the generated input scenarios and provide results as exceedence probability maps, probabilistic isomass maps and hazard curves. We illustrate the functionality of TephraProb using the 2011 eruption of Cordón Caulle volcano (Chile) and selected eruptions of La Fossa volcano (Vulcano Island, Italy). The range of eruption styles captured by these two events highlights the potential of TephraProb as an operative tool when rapid hazard assessments are required during volcanic crises.
Keywords
 Probabilistic hazard assessment
 Eruption scenarios
 Tephra
 Ash
 Stochastic
 Operational tool
Introduction
Tephra is the most widespread of all volcanic hazards. Variations in deposit thickness and and grain–size, from proximal (i.e. a few kilometres from the vent) to distal locations (i.e. hundreds of kilometres) result in a wide range of potential impacts, from total loss (e.g. human and livestock casualties, destruction of vegetation and crops, collapse of buildings) to less dramatic but highly problematic consequences (e.g. damage to crops, damage to nonstructural building elements, disruption of water and electricity supplies; Blong 1984; Jenkins et al. 2014; Wilson et al. 2011). Tephra is also responsible for widespread disruption of civil aviation (Biass et al. 2014; Bonadonna et al. 2012; Guffanti et al. 2009; Scaini et al. 2014). Both the dispersal and sedimentation of tephra can generate complex and multifaceted impacts at different spatial and temporal scales, affecting physical, social, economic and systemic aspects of societies. These complex impacts require proactive strategies to effectively increase the level of preparedness and mitigate the risk to exposed communities (Birkmann 2006). In order to develop effective proactive risk mitigation strategies, it is necessary to both develop comprehensive probabilistic hazard assessments for tephra dispersal and sedimentation and communicate the outcomes to decisionmakers and stakeholders.
Our method for quantifying the hazard from tephra fallout begins with the identification of eruption scenarios based on detailed stratigraphic studies. Eruption scenarios reflect the typical eruption styles at a given volcano and are characterized by ranges of eruption source parameters (ESP) such as plume height, erupted mass, mass eruption rate (MER) and total grain–size distribution (TGSD). Eruption scenarios are constrained by the completeness of the eruptive record, as well as an understanding of the range of past activity observed at analogous volcanic systems (Marzocchi et al. 2004; Ogburn et al. 2016). Highly–studied systems result in eruption scenarios describing precise eruptive episodes, whereas poorly–known systems can often only be characterized by generic eruption scenarios based on analogue systems. Some hazard studies have relied on a deterministic approach, defining ESPs as a single set of best guess values, and hazard as expected tephra accumulation (e.g. isomass maps, kg m^{−2}; Barberi et al. 1992). Other strategies rely on a large number of simulations to explore the range of variability in ESPs and atmospheric conditions. In the latter case, the hazard is quantified as a probability to exceed a given tephra accumulation and can be expressed either as conditional to the occurrence of the eruption scenario (e.g. scenario–based hazard assessment; Biass et al. 2016; Bonadonna et al. 2005; Scaini et al. 2014; Volentik and Houghton 2015) or as absolute when the long–term probability of the eruption scenario is also quantified (BearCrozier et al. 2016; Jenkins et al. 2012; Marzocchi and Bebbington 2012; Sandri et al. 2014, 2016; Thompson et al. 2015).
The TephraProb package provides a framework for i) accessing, pre–processing, and analyzing model inputs (e.g. retrieval and probabilistic analysis of Reanalysis wind data), ii) building probabilistic eruption scenarios, iii) running a suitable tephra dispersal model and iv) postprocessing and exporting model results. The package is written in Matlab and released under an open–source GPLv3 license on VHub and GitHub. This paper provides an in–depth review of the possibilities offered by the TephraProb package. The case studies of Cordón Caulle volcano (Chile) and La Fossa volcano (Vulcano Island, Italy) are used to illustrate the flexibility of TephraProb for working with a wide range of probabilistic eruption scenarios and eruptive styles. The user manual provides a technical description of each functionality and each individual Matlab function. The latest version of the package can be found at https://github.com/e5k/TephraProb.
Case studies
Cordón Caulle volcano
The 2011 eruption of Cordón Caulle volcano (Chile), part of the Puyehue–Cordón Caulle system, is considered as an example of a long–lasting sustained sub–Plinian eruption. Cordón Caulle started erupting on the 4th of June 2011 after a month–long seismic swarm (Bonadonna et al. 2015; Collini et al. 2013; Pistolesi et al. 2015). The initial and most vigorous phase (Unit 1; Bonadonna et al. 2015; Pistolesi et al. 2015) was characterized by plume heights varying between 10–14 km asl during a 24–30 h period with a mean MER of 10^{7} kg s^{−1}. The eruption continued until the 15th of June with MER ≥10^{6} kg s^{−1} and was followed by long–lasting, low–intensity activity (Bonadonna et al. 2015; Pistolesi et al. 2015). Modelling details of the 2011 eruption of Cordón Caulle can be found in Elissondo et al. (2016).
La Fossa volcano
During the last 1000 years, La Fossa volcano (Vulcano Island, Italy) experienced two subPlinian eruptions with similar intensities and magnitudes (i.e. plume heights of 7–8 km asl and erupted masses of 2.1–2.4 ×10^{9} kg) and at least 8 long–lasting Vulcanian cycles (Di Traglia et al. 2013). Each of these Vulcanian cycles is characterized by total fallout masses of 0.1–1 ×10^{7} kg over durations of 3 weeks to 3 years. The most recent eruption of La Fossa in 1888–1890, described in detail by Mercalli and Silvestri (1891) and De Fiore (1922), was characterized by explosions occurring every 4 hours to 3 days and associated with plume heights of 1–10 km asl (Di Traglia 2011; Di Traglia et al. 2013; Mercalli and Silvestri 1891). A detailed description of the probabilistic modelling of these eruption scenarios can be found in Biass et al. (2016).
The Tephra2 model
The Tephra2 model (Bonadonna et al. 2005, 2012; Connor and Connor 2006; Volentik et al. 2009) uses an analytical solution of the advection–diffusion equation to compute the tephra mass accumulation depending on eruptive and wind conditions. Main characteristics of the model include: i) grain–sizedependent diffusion and particle density, ii) a vertically stratified wind, iii) particle diffusion within the rising plume and iv) settling velocities that include variations in the Reynolds number depending on whether particles follow a laminar or turbulent flow regime. Tephra2 requires 3 input files: i) a configuration file that specifies the dynamics of the eruption and the surrounding atmosphere, including location of the vent, plume height, erupted mass, TGSD, range of particle sizes and particle densities, and atmospheric and dispersion thresholds, ii) a table of locations where tephra accumulation is calculated, and iii) a table of wind conditions influencing the horizontal dispersion of tephra, including atmospheric level and the wind speed and wind direction at this level. Note that since Tephra2 solves the advection–diffusion equation analytically, the wind is vertically stratified but horizontally and temporally homogeneous, thus limiting the validity of our approach to a few hundred kilometers around the vent. The user is referred to Bonadonna et al. (2005); Connor and Connor (2006) and Volentik et al. (2009) for a complete description of Tephra2 and to Scollo et al. (2008a,b) and Bonadonna et al. (2012) for a comparison with other volcanic ash transport and dispersion models (VATDM).
Tephra2 simplifies atmospheric turbulence by using two different diffusion laws, one for coarse and another for fine particles (Bonadonna 2006; Bonadonna et al. 2005; Connor and Connor 2006; Volentik et al. 2009). These two diffusion regimes of fallout are based on three empirical parameters, namely the fall–time threshold (FTT) acting as a threshold for the modelling of the diffusion of small and large particles (i.e. power law vs. linear diffusion), a diffusion coefficient used for the linear diffusion law and an apparent eddy diffusivity fixed at 0.04 m ^{2} s^{−1} for the power law diffusion (Bonadonna et al. 2005; Suzuki 1983). Secondary atmospheric effects (e.g. topography effects) are neglected. The reader is referred to Bonadonna et al. (2005); Connor and Connor (2006); Volentik et al. (2009) and Volentik et al. (2010) for further information regarding the modeling parameters used by Tephra2. The version of Tephra2 used here was modified to accept an additional input file defining the TGSD, which accounts for aggregation processes (e.g. Biass et al. 2014; Bonadonna et al. 2002a). Aggregation is further discussed in Section “Total grain–size distribution”.
where x is a dimensionless height normalized to the plume height and B(α,β) represents the beta function defined by two parameters, α and β, both greater than 0. Changing the values of α and β changes the shape of the PDF. When α=β=1, the beta function is identical to a uniform random function and the probability of tephra release is equal along the height of the plume. When α>β, the release pattern is shifted towards the top of the plume; when α=β≠1 tephra release is greatest from the middle of the plume; when α<β the release pattern is shifted toward the base of the plume.
The TephraProb package
Input parameters
Calculation points
Tephra2 requires an ASCII file of locations arranged in a threecolumn format containing Easting, Northing, and elevation. Since Tephra2 uses an analytical solution to the advectiondiffusionequation that solves the differential equation using a constant elevation boundary condition, calculations must be performed on flat surfaces and topography is neglected (Lim et al. 2008). Two options are available in TephraProb. The first option is to perform calculations on regularly spaced grids allowing for the compilation of probability maps. Although this is often the preferred option, calculations using large grids is time consuming and might not be achievable in some emergency contexts if computing power is limited. The second option is to perform calculations for user–selected points of interest, which results in a series of hazard curves that require a considerably shorter computation time.
One typical problem arising from the use of UTM coordinates is the shift in Easting coordinates when crossing UTM zones and the shift in Northing coordinates when crossing the equator. In both cases, TephraProb includes a correction to produce grids with contiguous UTM coordinates, where the resulting distortion is assumed negligible compared to the maximum distance deemed valid for the application of Tephra2.
Wind data
Wind velocity is a key input parameter in any tephra dispersal model because it controls the advection of the plume and the sedimentation of tephra. Probabilistic modelling requires access to wind datasets spanning at least one decade in order to capture the variability of wind conditions over a region. Most hazard assessments for tephra dispersal and sedimentation rely on Reanalysis datasets, which provide access to decades of atmospheric observations continuously interpolated in space and time. The two most frequently used datasets are the National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Prediction NCEP/NCAR Reanalysis (i.e. joint project between the National Centers for Environmental Prediction and the National Center for Atmospheric Research; Kalnay et al. 1996) and the European Centre for MediumRange Weather Forecasts (ECMWF) EraInterim datasets (Dee et al. 2011). Both the NOAA NCEP/NCAR and the ECMWF EraInterim datasets can be accessed via GUIs using TephraProb. The TephraProb package downloads the files in the NetCDF format and converts them into three–column ASCII files including altitude, wind direction (i.e. direction the wind blows towards) and wind velocity. Once the files are downloaded and converted, they can be used as an input to any tephra model and/or to explore the wind conditions over a region of interest. Note that Tephra2 uses a single wind profile per simulation extracted for one set of coordinates and one time. Therefore, each simulation is performed in an atmosphere that is vertically stratified but horizontally and temporally homogeneous.
Eruptive history
Hazard assessments are based upon the assumption that future activity will be similar to past activity. In volcanology, this implies a necessity to develop scenarios of future eruptions based on the most complete possible study of the geological record in order to best constrain the eruptive history of a volcano. In practice, assessing the full spectrum of eruptions of a given system is impossible, due firstly to the fact that geological records are not continuously complete through time and secondly because field studies rarely provide a complete picture of the eruptive history (Kiyosugi et al. 2015). In most cases, eruption scenarios are constructed based on a few studied eruptions representing common eruptive styles and/or often relating underlying geologic processes with analogue eruptive events (Sheldrake 2014). Eruption databases such as the Global Volcanism Program of the Smithsonian Institute (GVP; Siebert et al. 2010; Simkin and Siebert 1994) or the Large Magnitude Explosive Volcanic Eruptions (LaMEVE; Crosweller et al. 2012, Ogburn et al. 2016) can prove useful in acquiring a global picture of eruptive history. TephraProb includes a module to access and explore the Holocene eruptive history as recorded in the GVP database. Note that the GVP module does not constitute a source of input in itself but serves as a support tool to identify eruption scenarios and key ESPs.
where t is a forecasting window (years) and λ is the eruption rate (number of eruptions per year) defined over a complete section of the eruptive catalog. As an example, the black line in Fig. 3 d shows the probability of eruption through time for a case where Fig. 3 c represents a complete historical record. In contrast, the colored lines plot probabilities for eruptions of VEI 2 (red line; completeness at around 1880 A.D.), VEI 3 (green line; completeness at around 1920 A.D.) and VEI 5 (orange line; completeness at around 5000 B.C.).
Note that the aim of TephraProb is scenario–based hazard assessments, i.e. based upon the conditional probability that the associated eruption scenario occurs; two caveats should be considered when using the GVP module. First, the GVP database is not a direct input to the probabilistic modelling in TephraProb and should be used as a support tool to develop eruption scenarios and identify critical ESPs with the full knowledge of the limitations and assumptions behind such databases (Biass and Bonadonna 2013; Dzierma and Wehrmann 2010; Jenkins et al. 2012; MendozaRosas and De la CruzReyna 2008; Siebert et al. 2010; Simkin and Siebert 1994). Second assessing the long–term probability of a future eruption is not trivial and should be achieved using a rigorous probabilistic framework in order to quantify and propagate various sources of uncertainties on final estimates (BearCrozier et al. 2016; Connor et al. 2003; Jenkins et al. 2012; Marzocchi and Bebbington 2012; Sandri et al. 2016; Sheldrake 2014; Thompson et al. 2015). Probabilities resulting from a Poisson process should not be viewed as more than a first–order estimate, and only when the hypotheses of stable rate and independent events are satisfied (Borradaile 2003).
Eruption scenarios
Based upon considerations described in Section “Eruptive history”, probabilistic strategies were introduced to account for biases associated with both small and large eruptions. On one hand, they help account for parts of the geological record that are not accessible or that have been removed. On the other hand, they allow for the consideration of larger eruptive events associated with lower probabilities of occurrence that have not taken place during the recent history but cannot be excluded. Probabilistic eruption scenarios rely on a large number of simulated events to explore the uncertainty associated with variable parameters. For tephra hazard, the two main variable parameters are magnitude/style and atmospheric conditions of a future eruption. The variability of a future eruption is commonly described by sets of critical ESPs defined as ranges and/or probability distributions, where the shape of a distribution reflects the degree of certainty for a particular scenario. The maximum degree of uncertainty for a given ESP will be typically described by a uniform distribution, whereas a logarithmic distribution favors the occurrence of smaller values compared to larger ones, and a Gaussian distribution preferentially samples around a central value. Similarly, some regions of the world experience seasonal wind trends, making a seasonal analysis of tephra hazard necessary. Identifying the degree of variability allowed during stochastic sampling requires subjective choices that are influenced by both the degree of knowledge of a volcanic system and the purpose of the hazard assessment.
Total grain–size distribution
Plume height, erupted mass and TGSD are the three most important ESPs for modeling tephra accumulation with Tephra2. In TephraProb, the sampling of plume heights and erupted masses are inherent to the probabilistic eruption scenarios described below, but the stochastic scheme for sampling TGSDs is similar for all scenarios and is therefore described first. TGSDs in TephraProb are assumed Gaussian (in ϕ units) and are defined by ranges of median diameters and sorting coefficients. It is then possible to modify the TGSD to account for aggregation using the empirical approach proposed by Bonadonna et al. (2002a) and Biass et al. (2014) based on observations from Cornell et al. (1983), Bonadonna et al. (2011), and Bonadonna et al. (2002b) by defining a range of values for the empirical aggregation parameter and a maximum diameter affected by aggregation processes.
The empirical aggregation parameter introduced in TephraProb follows Bonadonna et al. (2002a) and Cornell et al. (1983) and represents a weight fraction of particles that form aggregates. In our approach, a fraction of mass equal to the empirical aggregation parameter is removed from all bins equal to or finer than the maximum diameter (Biass et al. 2014; Bonadonna et al. 2002a). The total mass removed is then equally redistributed into bins ≤−1ϕ and >the maximum diameter (where > means coarser than). Although this aggregation scheme is a simple answer to a complex concept (e.g. Brown et al. 2012; Gilbert and Lane 1994; James et al. 2002, 2003; Rose and Durant 2011; Van Eaton et al. 2015) and is based uniquely on observations (Bonadonna et al. 2002b, 2011; Cornell et al. 1983), it is computationally efficient and suitable for hazard assessment purposes (Biass et al. 2014, 2016; Bonadonna et al. 2002a). This scheme has already been validated in previous studies with good agreement with field observations (e.g. Bonadonna et al. 2002a; Bonadonna and Phillips 2003; Cornell et al. 1983). Since no physics is involved in this method, it is not possible to draw a distinction between dry or wet aggregates. Instead, following the nomenclature proposed by Brown et al. (2012), using a maximum diameter of 5 ϕ suggests that particles <63 microns are influenced by aggregation processes (e.g. ash clusters, coated particles and poorlystructured pellets; Bonadonna et al. 2011), whereas a maximum diameter of 4 ϕ extends aggregation up to <125 microns (e.g. pellets with concentric structures (e.g. accretionary lapilli) and liquid pellets (i.e. mud rain); Gilbert and Lane 1994; Van Eaton et al. 2012, 2015).
At each probabilistic run, values of median diameters and sorting coefficients are sampled and used to create a Gaussian distribution. If wanted, the aggregation scheme is applied by randomly sampling an empirical aggregation parameter. The TGSD is then written as a text file and passed as an input to Tephra2.
General eruption scenarios

Eruption Range Scenarios (ERS), designed to assess the probability of accumulation of a critical tephra accumulation based on the statistical distribution of possible eruption source parameters and wind conditions (i.e. stochastic sampling of one set of ESPs and one wind profile at each run);Table 1
Summary of probabilistic eruption scenarios implemented in TephraProb. All Plinian–type scenarios can be modeled as Long–lasting if the eruption duration is longer than the wind sampling interval
Eruption type
Scenario
Acronym
Event ^{a}
ESP
Wind
Single
Multiple
Fixed
Variable
Fixed
Variable
Plinian ^{b}
Eruption range scenario
ERS
✓
✓
✓
One eruption scenario
OES
✓
✓
✓
Wind range scenario
WRS
✓
✓
\(\checkmark ^{\text {c}}\)
Fixed date scenario
FDS
✓
✓
✓
Vulcanian
Eruption range scenario
VERS
✓
✓
✓
LL Eruption range scenario
VLLERS
✓
✓
✓
One eruption scenario
VOES
✓
✓
✓
Wind range scenario
VWRS
✓
✓
\(\checkmark ^{\text {c}}\)
Fixed date scenario
VFDS
✓
✓
✓

One Eruption Scenarios (OES), designed to assess the probability of accumulation of a critical tephra accumulation based on the statistical distribution of wind conditions and a deterministically–defined eruption (i.e. stochastic sampling of one wind profile at each run while ESPs remain constant).

Wind Range Scenarios (WRS) constrain the sampling of wind conditions within pre–defined radial sector around the volcano. Such scenarios are useful to assess the hazard at specific sites considering a specific wind scenario (e.g. Volentik et al. 2009). The probability of occurrence of the wind scenario can itself be assessed using the wind module of TephraProb;

Fixed Date Scenarios (FDS) fix the eruption starting date, thus assessing the probability of tephra accumulation based on the variability of eruption source parameters only. Rather than expressing the hazard of a future eruption, such scenarios are useful to assess the probability of a studied fallout event considering the statistical distribution of wind conditions (e.g. Elissondo et al. 2016). Outcomes of Fixed Date Scenarios can be compared to Eruption Range Scenarios and field–based isomass maps.
Eruptive styles
Different assumptions are made in TephraProb to calculate the erupted mass of sustained sub–Plinian and Plinian eruptions and nonsustained Vulcanian explosions, giving rise to Plinian–type and Vulcanian–type eruptions (Table 1; Figs. 4 and 5). Note that i) in our modelling scheme, sub–Plinian eruptive styles are hereafter considered as a part of Plinian–type eruptions and ii) both Plinian and Vulcanian–type styles can be modeled using the eruption scenarios described in Section“General eruption scenarios ”.
Plinian–type eruptions
where ρ _{ a0} is the reference density of the surrounding atmosphere (kg m^{−3}), g ^{′} the reduced gravity at the source (m s^{−2}), α is the radial entrainment coefficient, \(\bar {N}\) is the average buoyancy frequency (s ^{−1}), H is the plume height (m above the vent), β is the wind entrainment coefficient and \(\bar {v}\) the average wind velocity across the plume height (m s^{−1}). Note that Reanalysis datasets are only used to calculate \(\bar {v}\), and the calculation of other parameters (e.g. \(\bar {N}\), ρ _{ a0}) follows from Degruyter and Bonadonna (2012). The MER is used with the eruption duration to calculate the erupted tephra mass. If the resulting value falls within the user–defined mass range, then the run is sent to the model to be executed, or else the sampling process is re–started. Note that TephraProb also includes an option to sample plume heights and erupted tephra mass independently.
Vulcanian–type eruptions
where H is the plume height (m asl), M is the plume mass (kg) and H _{ V } the vent height (m asl).
Long–lasting eruption scenarios
The hazard associated with long–lasting eruptions is complicated by the fact that wind conditions might vary during the course of an eruption. Long–lasting eruptions can be associated either with sustained plumes (e.g. 2010 eruption of Eyjafjallajökull, Iceland), or with repetitive emissions of limited to moderate amounts of ash (e.g. ongoing eruption of Soufrière Hills volcano, Montserrat, West Indies; ongoing eruption of Sakurajima volcano, Japan). In TephraProb these two eruptive styles are modelled as longlasting Plinian and longlasting Vulcanian eruptions, respectively (Figs. 4 and 5).
Long–lasting Plinian eruptions
Long–lasting Plinian scenarios are constrained by the temporal resolution Δ w of available wind data, which is 6 h for most Reanalysis datasets but can be varied within TephraProb. In cases where the eruption duration defined by the user is longer than the temporal resolution between wind profiles, the eruption is divided into Δ w–duration periods. The corresponding wind profile for each period is retrieved and the Eruption Range Scenario sampling scheme is performed, assuming that ESPs remain steady throughout the duration of the period (Fig. 4). If the sums of the masses of independent periods fall within the initial mass range, each period becomes a separate Tephra2 simulation, and the final accumulation of a long–lasting eruption is the sum of all periods.
Long–lasting Vulcanian eruptions
Long–lasting Vulcanian scenarios describe Vulcanian cycles and require the identification of the total duration of the cycle and the repose interval between explosions in order to apply the workflow shown in Fig. 5. At each run (i.e. each Vulcanian cycle), repose intervals and associated plume heights are constantly sampled until the sum of the repose intervals exceeds the eruption duration. The mass of each explosion is calculated with Eq. 6 and used in a separate Tephra2 simulation. The final accumulation of a Vulcanian cycle is the sum of all explosions. Note that TephraProb does not account for any relationship describing the influence of the repose interval on the corresponding plume height. More details on modeling Vulcanian cycles with TephraProb can be found in Biass et al. (2016).
Seasonality
Because some regions at low latitudes experience significant changes in wind patterns between dry and rainy seasons, a seasonality option is implemented in TephraProb to assess the variability in hazard as a function of the time of year. If the seasonality option is enabled, the user can define start and end dates of the rainy season and three scenarios will be run using winds for i) all months of the year, ii) months of the rainy season and iii) months of the dry season.
Postprocessing
Outputs
ESPs for the Cordón Caulle and the La Fossa case studies
Scenario  

Cordón Caulle  La Fossa  
LLERS  LLFDS  OES  VLLERS  
Plume height (km asl)  10–14 ^{ u }  10–14 ^{ u }  8  1–10 ^{ l }  
Erupted mass (×10^{9} k g)  400–600  400–600  2.3  —  
TGSD range (ϕ)  7–8  7–8  4–8  4–8  
Median diameter (ϕ)  3– 1  3– 1  2–0  1–1  
Sorting (ϕ)  2–3  2–3  1–3  1–3  
Aggregation coefficient  0.1–0.4  0.1–0.4  0.3–0.7  0.3–0.7  
Lithic density (kg m^{−3})  2600  2600  2700  2700  
Pumice density (kg m^{−3})  560  560  600  1000  
Diffusion coefficient (m s ^{−2})  3900  3900  1500  4900  
Falltime threshold (s)  30500  30500  255  5000  
Eruption duration  24–30 h  24–30 h  0.5–6 h  30–1095 d  
Repose interval (hours)  —  —  —  4–72 ^{ l } 
Four variables need to be considered when displaying the probability of exceeding a given tephra accumulation, including geographic coordinates (Easting, Northing or longitude, latitude), a threshold of tephra accumulation and its associated exceedance probability. Since typical maps are limited by three dimensions, it is necessary to fix at least one degree of freedom. TephraProb can produce three main types of outputs.
Probability maps
Figure 6 a–b show probability maps compiled for an accumulation of 10 kg m^{−2} (i.e. critical threshold for crops) for the Long–Lasting Eruption Range Scenario and the Long–Lasting Fixed Date Scenarios of Cordón Caulle based on the climatic phase of the 2011 eruption (i.e. Unit 1 in Bonadonna et al. 2015; Pistolesi et al. 2015, Table 2). These maps show the importance of wind patterns in the hazard assessment of tephra fallout and, put in perspective of Fig. 2, show that the opening phase of the 2011 eruption (i.e. 4–5th of June) occurred in wind conditions of low probability but with high consequences for the town of San Carlos de Bariloche, which experienced accumulations of about 5 kg m^{−2} (Bonadonna et al. 2015; Pistolesi et al. 2015).
Figure 6 c–d show the probabilities of exceeding tephra accumulations of 10 and 100 kg m^{−2} following sub–Plinian OES (Fig. 6 c) and Vulcanian V–LLERS (Fig. 6 d) eruption scenarios at La Fossa volcano, respectively. Note that in the case of long–lasting Vulcanian scenarios, no syn–eruptive erosion between explosions is considered and Fig. 6 d should therefore be regarded as a probability map of the maximum accumulation.
Hazard curves
Probabilistic isomass maps
Discussion and conclusions
The TephraProb package aligns with recent efforts to bridge gaps between academic and operational contexts (Bartolini et al. 2013; BearCrozier et al. 2012; Felpeto et al. 2007). It provides a set of flexible tools for the assessment of tephra hazard and designed to compile comprehensive assessments in a wide range of conditions (e.g. poor constraints on scenarios, rapid assessments), that can be used in the context of probabilistic hazard assessments or separately (e.g. accessing and analyzing wind data or the GVP database). TephraProb integrates various levels of computational requirements and allows hazard assessments to be performed on single CPU computers (i.e. hazard curves only), multi–core personal computers (i.e. grids of moderate resolutions) and computer clusters (i.e. grids of fine resolutions). Resulting hazard assessments are conditional on the occurrence of the associated scenarios, and can serve as direct inputs to probabilistic frameworks such as Bayesian event trees to assess the long–term probability of tephra accumulation (Thompson et al. 2015) or to fit in multi–hazards assessments (Sandri et al. 2014). In order to facilitate the integration of further analyses, each output of TephraProb is saved in a variety of formats (e.g. ASCII columns format, ASCII ArcMap rasters).
The TephraProb package is currently tailored to generate Tephra2–friendly configuration files. However, probabilistic strategies implemented in the package are independent of the adopted model and could be modified to work with any VATDM. For instance, early versions of the macros implemented in TephraProb were applied by Biass et al. (2014) and Scaini et al. (2014) to assess the hazard and the related impact resulting from the eruption of critical Icelandic volcanoes on the European air traffic using the Eulerian model FALL3D (Costa et al. 2006; Folch et al. 2009). Similarly, these probabilistic approaches have already been successfully applied by Bonadonna et al. (2002a); Scollo et al. (2007); Jenkins et al. (2012) and Jenkins et al. (2014) based on both the HAZMAP and ASHFALL models (Armienti et al. 1988; Hurst and Turner 1999; Hurst 1994; Macedonio et al. 2005,1988).
The user manual of TephraProb, submitted as a supplementary file, provides in–depth technical descriptions of all the functions of the package. Each function is thoroughly commented in order to allow customization for more advanced users. In particular, functions to calculate the MER (Eq. 4; Degruyter and Bonadonna 2012) or to calculate the mass of a thermal (Eq. 6; Bonadonna et al. 2002a) contain guidance for modifying all empirical parameters. In addition, all users are free to modify the code for their own needs following the terms and conditions of the GNU GPL3 license.
Intentionally, no default scenario is provided in order to not promote TephraProb as a black box. When volcanoes with little documented history are considered, we encourage the user to rely on a global understanding of eruption processes combined with the use of global databases (Crosweller et al. 2012; Siebert et al. 2010; Simkin and Siebert 1994) to identify analogue eruptions. When eruption scenarios are based upon detailed field studies, the TError code (Biass et al. 2014) can serve as a systematic tool to identify the probability distributions of ESPs. In either case, the user manual of TephraProb provides a list of empirical parameters for Tephra2 for eruptions characterized by the inversion technique of Connor and Connor (2006).
This version of TephraProb is published on GitHub as a basis for further development based on inputs from the scientific community. Identified directios of development include i) the implementation of a variety of models available in the literature to quantify ESPs such as Sparks (1986); Wilson and Walker (1987); Mastin et al. (2009); Woodhouse et al. (2013) and Mastin (2014), ii) probabilistic inversion schemes to systematically assess the likelihood of past events (Elissondo et al. 2016) and iii) better integration of Reanalysis datasets to calculate the required atmospheric parameters (Degruyter and Bonadonna 2012).
Declarations
Acknowledgements
S. Biass and C. Bonadonna were supported by a SNF grant (#200021129997). LJC and CBC were supported by a grant from the U.S. National Science Foundation (ACI 1339768). We thank editor J. Lindsay, reviewers A. van Eaton and A. Folch for helping improving this manuscript, S. Jenkins, L. Pioli and M. Rosi for comments on early versions of the manuscript, A. Parmigiani for his initial ideas, G. Wilson and M.A. Thompson for testing early versions and all contributors to the Matlab File Exchange platform who kindly permitted the use of their functions within TephraProb. All computations were performed on the Baobab cluster of the University of Geneva. NCEP Reanalysis data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at http://www.esrl.noaa.gov/psd/.
Authors’ contributions
SB developed and wrote the TephraProb package and drafted the paper. Probabilistic techniques were developed by CB and CC and further developed by all authors. CB and CC designed the Tephra2 code, which was implemented and further developed by LC. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 Armienti, P, Macedonio G, Pareschi MT. A numerical model for simulation of tephra transport and deposition: Applications to May 18, 1980, Mount St. Helens eruption. J Geophys Res Solid Earth. 1988; 93(B6):6463–76. doi:10.1029/JB093iB06p06463.View ArticleGoogle Scholar
 Barberi, F, Ghigliotti M, Macedonio G, Orellana H, Pareschi MT, Rosi M. Volcanic hazard assessment of Guagua Pichincha (Ecuador) based on past behaviour and numerical models. J Volcanol Geothermal Res. 1992; 49(1–2):53–68. doi:10.1016/03770273(92)90004W.View ArticleGoogle Scholar
 Bartolini, S, Cappello A, Martí J, Del Negro C. QVAST: a new Quantum GIS plugin for estimating volcanic susceptibility. Nat Hazards Earth Syst Sci. 2013; 13(11):3031–42.View ArticleGoogle Scholar
 BearCrozier, AN, Kartadinata N, Heriwaseso A, Nielsen O. Development of pythonFALL3D: a modified procedure for modelling volcanic ash dispersal in the AsiaPacific region. Nat Hazards. 2012; 64(1):821–38. doi:10.1007/s1106901202737.View ArticleGoogle Scholar
 BearCrozier, AN, Miller V, Newey V, Horspool N, Weber R. Probabilistic Volcanic Ash Hazard Analysis (PVAHA) I: development of the VAPAH tool for emulating multiscale volcanic ash fall analysis. J Appl Volcanol. 2016; 5(1):1–20. doi:10.1186/s1361701600434.View ArticleGoogle Scholar
 Bianchi, L. L’eruzione 18881890 di Vulcano (Isole Eolie):Analisi stratigrafica, fisica e composizionale dei prodotti. Unpublished msc thesis, Università di Pisa. 2007.Google Scholar
 Biass, S, Scaini C, Bonadonna C, Folch A, Smith K, Höskuldsson A. A multiscale risk assessment for tephra fallout and airborne concentration from multiple Icelandic volcanoes  Part 1: Hazard assessment. Nat Hazards Earth Syst Sci. 2014; 14(8):2265–287. doi:10.5194/nhess1422652014.View ArticleGoogle Scholar
 Biass, S, Bonadonna C. A fast GISbased risk assessment for tephra fallout: the example of Cotopaxi volcano, EcuadorPart I: probabilistic hazard assessment. Nat Hazards. 2013; 65(1):477–95.View ArticleGoogle Scholar
 Biass, S, Bagheri G, Aeberhard W, Bonadonna C. TError: towards a better quantification of the uncertainty propagated during the characterization of tephra deposits. Stat Volcanol. 2014; 1(2):1–27. doi:10.5038/2163338X.1.2.Google Scholar
 Biass, S, Bonadonna C, Traglia F, Pistolesi M, Rosi M, Lestuzzi P. Probabilistic evaluation of the physical impact of future tephra fallout events for the Island of Vulcano, Italy. Bull Volcanol. 2016; 78(5):1–22. doi:10.1007/s0044501610281.View ArticleGoogle Scholar
 Birkmann, J. Measuring vulnerability to promote disasterresilient societies: conceptual frameworks and definitions. In: Birkmann, J, editor. Measuring Vulnerability to Nat Hazards: Toward Disaster Resilient Societies. Tokyo: United Nations University Press: 2006. p. 9–54.Google Scholar
 Blong, RJ. Volcanic Hazards. A Sourcebook on the Effects of Eruptions. Sydney: Academic Press; 1984, p. 424.Google Scholar
 Bonadonna, C. Probabilistic modelling of tephra dispersion. In: Mader, HM, Coles SG, Connor CB, Connor LJ, editors. Stat Volcanol. London: Geological Society of London: 2006. p. 243–59.Google Scholar
 Bonadonna, C, Macedonio G, Sparks R. Numerical modelling of tephra fallout associated with dome collapses and Vulcanian explosions: application to hazard assessment on Montserrat. In: Druitt, T, Kokelaar B, editors. The Eruption of Soufrière Hills Volcano, Montserrat, from 1995 To 1999 vol. 21. London: Geological Society: 2002a. p. 483–516.Google Scholar
 Bonadonna, C, Mayberry G, Calder E, Sparks R, Choux C, Jackson P, Lejeune A, Loughlin S, Norton G, Rose WI, Ryan G, Young S. Tephra fallout in the eruption of Soufrière Hills Volcano, Montserrat In: Druitt, T, Kokelaar B, editors. The Eruption of Soufrière Hills Volcano, Montserrat, from 1995 To 1999. London: Geological Society: 2002b. p. 483–516.Google Scholar
 Bonadonna, C, Connor CB, Houghton BF, Connor L, Byrne M, Laing A, Hincks TK. Probabilistic modeling of tephra dispersal: Hazard assessment of a multiphase rhyolitic eruption at Tarawera, New Zealand. J Geophys Res. 2005; 110(B3):B03203.View ArticleGoogle Scholar
 Bonadonna, C, Genco R, Gouhier M, Pistolesi M, Cioni R, Alfano F, Hoskuldsson A, Ripepe M. Tephra sedimentation during the 2010 Eyjafjallajökull eruption (Iceland) from deposit, radar, and satellite observations. J Geophys Res. 2011; 116(B12):12202.View ArticleGoogle Scholar
 Bonadonna, C, Phillips JC. Sedimentation from strong volcanic plumes. J Geophys Res Solid Earth. 2003; 108(B7):2340. doi:10.1029/2002JB002034.View ArticleGoogle Scholar
 Bonadonna, C, Folch A, Loughlin S, Puempel H. Future developments in modelling and monitoring of volcanic ash clouds: outcomes from the first IAVCEIWMO workshop on Ash Dispersal Forecast and Civil Aviation. Bull Volcanol. 2012; 74(1):1–10.View ArticleGoogle Scholar
 Bonadonna, C, Cioni R, Pistolesi M, Elissondo M, Baumann V. Sedimentation of longlasting windaffected volcanic plumes: the example of the 2011 rhyolitic Cordón Caulle eruption, Chile. Bull Volcanol. 2015; 77(2):1–19. doi:10.1007/s0044501509008.View ArticleGoogle Scholar
 Borradaile, GJ. Statistics of Earth Science Data: Their Distribution in Time, Space, and Orientation. Berlin: Springer; 2003, p. 321.View ArticleGoogle Scholar
 Brown, R, Bonadonna C, Durant A. A review of volcanic ash aggregation. Phys Chem Earth Parts A/B/C. 2012; 45:65–78.View ArticleGoogle Scholar
 Collini, E, Osores MS, Folch A, Viramonte JG, Villarosa G, Salmuni G. Volcanic ash forecast during the June 2011 Cordón Caulle eruption. Nat Hazards. 2013; 66(2):389–412. doi:10.1007/s110690120492y.View ArticleGoogle Scholar
 Connor, C, Sparks R, Mason R, Bonadonna C, Young S. Exploring links between physical and probabilistic models of volcanic eruptions: The Soufrière Hills Volcano, Montserrat. Geophys Res Lett. 2003; 30(13):1701.View ArticleGoogle Scholar
 Connor, LJ, Connor CB. Inversion is the key to dispersion: understanding eruption dynamics by inverting tephra fallout. In: Mader, HM, Coles SG, Connor CB, Connor LJ, editors. Stat Volcanol. London: Geological Society of London: 2006. p. 231–42.Google Scholar
 Cornell, W, Carey S, Sigurdsson H. Computer simulation of transport and deposition of the Campanian Y5 ash. J Volcanol Geothermal Res. 1983; 17(1):89–109.View ArticleGoogle Scholar
 Costa, A, Macedonio G, Folch A. A threedimensional Eulerian model for transport and deposition of volcanic ashes. Earth Planetary Sci Lett. 2006; 241(3–4):634–47.View ArticleGoogle Scholar
 Crosweller, HS, Arora B, Brown SK, Cottrell E, Deligne NI, Guerrero NO. Global database on large magnitude explosive volcanic eruptions (LaMEVE). J Appl Volcanol. 2012; 1(1):1–13. doi:10.1186/2191504014.View ArticleGoogle Scholar
 De Fiore, O. Vulcano (Isole Eolie) In: Friedlaender, I, editor. Revisita Vulcanologica (Suppl. 3): 1922. p. 1–393.Google Scholar
 Dee, DP, Uppala SM, Simmons AJ, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda MA, Balsamo G, Bauer P, Bechtold P, Beljaars ACM, van de Berg L, Bidlot J, Bormann N, Delsol C, Dragani R, Fuentes M, Geer AJ, Haimberger L, Healy SB, Hersbach H, Hólm EV, Isaksen L, Kållberg P, Köhler M, Matricardi M, McNally AP, MongeSanz BM, Morcrette JJ, Park BK, Peubey C, de Rosnay P, Tavolato C, Thépaut JN, Vitart F. The ERAInterim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorological Soc. 2011; 137(656):553–97. doi:10.1002/qj.828.View ArticleGoogle Scholar
 Degruyter, W, Bonadonna C. Improving on mass flow rate estimates of volcanic eruptions. Geophys Res Lett. 2012; 39:16. doi:10.1029/2012GL052566.View ArticleGoogle Scholar
 Di Traglia, F. The last 1000 years of eruptive activity at the Fossa Cone (Island of Vulcano, Southern Italy). PhD thesis, Università di Pisa. 2011.Google Scholar
 Di Traglia, F, Pistolesi M, Rosi M, Bonadonna C, Fusillo R, Roverato M. Growth and erosion: The volcanic geology and morphological evolution of La Fossa (Island of Vulcano, Southern Italy) in the last 1000 years. Geomorphology. 2013; 194(0):94–107. doi:10.1016/j.geomorph.2013.04.018.View ArticleGoogle Scholar
 Druitt, TH, Young SR, Baptie B, Bonadonna C, Calder ES, Clarke AB, Cole PD, Harford CL, Herd RA, Luckett R, Ryan G, Voight B. Episodes of cyclic Vulcanian explosive activity with fountain collapse at Soufrière Hills Volcano, Montserrat. In: Druitt, T, Kokelaar B, editors. The Eruption of Soufrière Hills Volcano, Montserrat, from 1995 To 1999 vol 21. London: Geological Society: 2002. p. 281–306, doi:10.1144/GSL.MEM.2002.021.01.13.Google Scholar
 Dzierma, Y, Wehrmann H. Eruption time series statistically examined: Probabilities of future eruptions at Villarrica and Llaima Volcanoes, Southern Volcanic Zone, Chile. J Volcanol Geothermal Res. 2010; 193(1–2):82–92.View ArticleGoogle Scholar
 Elissondo, M, Baumann V, Bonadonna C, Pistolesi M, Cioni R, Bertagnini A, Biass S, Herrero JC, Gonzalez R. Chronology and impact of the 2011 Cordón Caulle eruption, Chile. Nat Hazards Earth Syst Sci. 2016; 16(3):675–704. doi:10.5194/nhess166752016.View ArticleGoogle Scholar
 Felpeto, A, Marti J, Ortiz R. Automatic GISbased system for volcanic hazard assessment. J Volcanol Geothermal Res. 2007; 166(2):106–16.View ArticleGoogle Scholar
 Folch, A, Costa A, Macedonio G. FALL3D: A computational model for transport and deposition of volcanic ash. Comput Geosci. 2009; 35(6):1334–42.View ArticleGoogle Scholar
 Gilbert, J, Lane S. The origin of accretionary lapilli. Bull Volcanol. 1994; 56:398–411.View ArticleGoogle Scholar
 Guffanti, M, Mayberry GC, Casadevall TJ, Wunderman R. Volcanic hazards to airports. Nat Hazards. 2009; 51(2):287–302.View ArticleGoogle Scholar
 Hurst, AW, Turner R. Performance of the program ASHFALL for forecasting ashfall during the 1995 and 1996 eruptions of Ruapehu volcano. N Z J Geol Geophys. 1999; 42(4):615–22. doi:10.1080/00288306.1999.9514865.View ArticleGoogle Scholar
 Hurst, A. ASHFALL–A Computer Program for Estimating Volcanic Ash Fallout. 1994. Technical Report 94/23, Institute of Geological & Nuclear Sciences, Wellington, New Zealand.Google Scholar
 James, MR, Gilbert JS, Lane SJ. Experimental investigation of volcanic particle aggregation in the absence of a liquid phase. J Geophys Res Solid Earth. 2002; 107(B9). doi:10.1029/2001JB000950.
 James, MR, Lane SJ, Gilbert JS. Density, construction, and drag coefficient of electrostatic volcanic ash aggregates. J Geophys Res Solid Earth. 2003; 108(B9). doi:10.1029/2002JB002011.
 Jenkins, SF, Spence RJS, Fonseca JFBD, Solidum RU, Wilson TM. Volcanic risk assessment: Quantifying physical vulnerability in the built environment. J Volcanol Geothermal Res. 2014; 276:105–20. doi:10.1016/j.jvolgeores.2014.03.002.View ArticleGoogle Scholar
 Jenkins, S, Magill C, McAneney J, Blong R. Regional ash fall hazard I: a probabilistic assessment methodology. Bull Volcanol. 2012; 74(7):1699–712.View ArticleGoogle Scholar
 Kalnay, EC, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woollen J. The NCEP/NCAR 40year reanalysis project. Bull Am Meteorological Soc. 1996; 77(3):437–71.View ArticleGoogle Scholar
 Kiyosugi, K, Connor C, Sparks RSJ, Crosweller HS, Brown SK, Siebert L, Wang T, Takarada S. How many explosive eruptions are missing from the geologic record? Analysis of the quaternary record of large magnitude explosive eruptions in Japan. J Appl Volcanol. 2015; 4(1):1–15. doi:10.1186/s1361701500359.View ArticleGoogle Scholar
 Lim, LL, Sweatman WL, McKibbin R, Connor CB. Tephra Fallout Models: The Effect of Different Source Shapes on Isomass Maps. Math Geosci. 2008; 40(2):147–57. doi:10.1007/s1100400791344.View ArticleGoogle Scholar
 Macedonio, G, Costa A, Longo A. A computer model for volcanic ash fallout and assessment of subsequent hazard. Comput Geosci. 2005; 31(7):837–45.View ArticleGoogle Scholar
 Macedonio, G, Pareschi MT, Santacroce R. A numerical simulation of the Plinian Fall Phase of 79 A.D. eruption of Vesuvius. J Geophys Res Solid Earth. 1988; 93(B12):14817–27. doi:10.1029/JB093iB12p14817.View ArticleGoogle Scholar
 Marzocchi, W, Sandri L, Gasparini P, Newhall C, Boschi E. Quantifying probabilities of volcanic events: the example of volcanic hazard at Mount Vesuvius. J Geophys Res. 2004; 109(B11201):1–18.Google Scholar
 Marzocchi, W, Bebbington M. Probabilistic eruption forecasting at short and long time scales. Bull Volcanol. 2012; 74(8):1777–805.View ArticleGoogle Scholar
 Mastin, L, Guffanti M, Servranckx R, Webley P, Barsotti S, Dean K, Durant A, Ewert J, Neri A, Rose WI, Schneider D, Siebert L, Stunder B, Swanson G, Tupper A, Volentik A, Waythomas C. A multidisciplinary effort to assign realistic source parameters to models of volcanic ashcloud transport and dispersion during eruptions. J Volcanol Geothermal Res. 2009; 186(1–2):10–21.View ArticleGoogle Scholar
 Mastin, LG. Testing the accuracy of a 1D volcanic plume model in estimating mass eruption rate. J Geophys Res Atmospheres. 2014; 119(5):2474–495. doi:10.1002/2013JD020604.View ArticleGoogle Scholar
 MendozaRosas, AT, De la CruzReyna S. A statistical method linking geological and historical eruption time series for volcanic hazard estimations: Applications to active polygenetic volcanoes. J Volcanol Geothermal Res. 2008; 176(2):277–90.View ArticleGoogle Scholar
 Mercalli, G, Silvestri O. Le eruzioni dell’Isola di Vulcano incominciate il 3 agosto 1888 e terminate il 22 marzo 1890, relazione scientifica. Ann Ufficio Centrale Metereol Geodin Ital. 1891; 10:1–213.Google Scholar
 Ogburn, S, Berger J, Calder E, Lopes D, Patra A, Pitman E, Rutarindwa R, Spiller E, Wolpert R. Pooling strength amongst limited datasets using hierarchical Bayesian analysis, with application to pyroclastic density current mobility metrics. Stat Volcanol. 2016; 2:1–26.View ArticleGoogle Scholar
 Pistolesi, M, Cioni R, Bonadonna C, Elissondo M, Baumann V, Bertagnini A, Chiari L, Gonzales R, Rosi M, Francalanci L. Complex dynamics of smallmoderate volcanic events: the example of the 2011 rhyolitic Cordón Caulle eruption, Chile. Bull Volcanol. 2015; 77(1):1–24. doi:10.1007/s0044501408983.View ArticleGoogle Scholar
 Rose, W, Durant A. Fate of volcanic ash: Aggregation and fallout. Geology. 2011; 39(9):895–6.View ArticleGoogle Scholar
 Sandri, L, Thouret JC, Constantinescu R, Biass S, Tonini R. Longterm multihazard assessment for El Misti volcano (Peru). Bull Volcanol. 2014; 76(2):1–26. doi:10.1007/s0044501307719.View ArticleGoogle Scholar
 Sandri, L, Costa A, Selva J, Tonini R, Macedonio G, Folch A, Sulpizio R. Beyond eruptive scenarios: assessing tephra fallout hazard from Neapolitan volcanoes. Sci Rep. 2016; 6:24271.View ArticleGoogle Scholar
 Scaini, C, Biass S, Galderisi A, Bonadonna C, Folch A, Smith K, Höskuldsson A. A multiscale risk assessment for tephra fallout and airborne concentration from multiple Icelandic volcanoes  Part 2: Vulnerability and impact. Nat Hazards Earth Syst Sci. 2014; 14(8):2289–312. doi:10.5194/nhess1422892014.View ArticleGoogle Scholar
 Scollo, S, Del Carlo P, Coltelli M. Tephra fallout of 2001 Etna flank eruption: Analysis of the deposit and plume dispersion. J Volcanol Geothermal Res. 2007; 160(1–2):147–64.doi:10.1016/j.jvolgeores.2006.09.007.View ArticleGoogle Scholar
 Scollo, S, Folch A, Costa A. A parametric and comparative study of different tephra fallout models. J Volcanol Geothermal Res. 2008a; 176(2):199–211. doi:10.1016/j.jvolgeores.2008.04.002.
 Scollo, S, Tarantola S, Bonadonna C, Coltelli M, Saltelli A. Sensitivity analysis and uncertainty estimation for tephra dispersal models. J Geophys Res Solid Earth. 2008b; 113(B6):06202.Google Scholar
 Sheldrake, T. Longterm forecasting of eruption hazards: A hierarchical approach to merge analogous eruptive histories. J Volcanol Geothermal Res. 2014; 286:15–23. doi:10.1016/j.jvolgeores.2014.08.021.View ArticleGoogle Scholar
 Siebert, L, Simkin T, Kimberly P. Volcanoes of the World. Berkley: University of California Press; 2010, p. 551.Google Scholar
 Simkin, T, Siebert L. Volcanoes of the World. Tucson, AZ: Geoscience Press; 1994, p. 349.Google Scholar
 Sparks, R. The dimensions and dynamics of volcanic eruption columns. Bull Volcanol. 1986; 48(1):3–15.View ArticleGoogle Scholar
 Suzuki, T. A theoretical model for dispersion of tephra. Arc Volcanism Phys Tectonics. 1983; 95:95–113.Google Scholar
 Thompson, M, Lindsay J, Sandri L, Biass S, Bonadonna C, Jolly G, Marzocchi W. Exploring the influence of vent location and eruption style on tephra fall hazard from the Okataina Volcanic Centre, New Zealand. Bull Volcanol. 2015; 77(5):1–23. doi:10.1007/s004450150926y.View ArticleGoogle Scholar
 Van Eaton, AR, Mastin LG, Herzog M, Schwaiger HF, Schneider DJ, Wallace KL, Clarke AB. Hail formation triggers rapid ash aggregation in volcanic plumes. Nat Commun. 2015; 6:7860.View ArticleGoogle Scholar
 Van Eaton, A, Muirhead J, Wilson C, Cimarelli C. Growth of volcanic ash aggregates in the presence of liquid water and ice: an experimental approach. Bull Volcanol. 2012; 74(9):1963–1984.View ArticleGoogle Scholar
 Volentik, ACM, Connor CB, Connor LJ, Bonadonna C. In: Connor C, Chapman NA, Connor L, (eds).Aspects of volcanic hazards assessment for the Bataan nuclear power plant, Luzon Peninsula, Philippines. Cambridge: Cambridge University Press; 2009.Google Scholar
 Volentik, ACM, Bonadonna C, Connor CB, Connor LJ, Rosi M. Modeling tephra dispersal in absence of wind: Insights from the climactic phase of the 2450BP Plinian eruption of Pululagua volcano (Ecuador). J Volcanol Geothermal Res. 2010; 193(1–2):117–36. doi:10.1016/j.jvolgeores.2010.03.011.View ArticleGoogle Scholar
 Volentik, AM, Houghton B. Tephra fallout hazards at Quito International Airport (Ecuador). Bull Volcanol. 2015; 77(6):1–14. doi:10.1007/s0044501509231.View ArticleGoogle Scholar
 Wilson, L, Walker G. Explosive volcanic eruptions  VI. Ejecta dispersal in plinian eruptions: the control of eruption conditions and atmospheric properties. Geophys J R Astr Soc. 1987; 89(2):657–79.View ArticleGoogle Scholar
 Wilson, T, Stewart C, SwordDaniels V. Volcanic ash impacts on critical infrastructure. Phys Chem Earth Pt A/B/C. 2011; 45:5–23.Google Scholar
 Woodhouse, MJ, Hogg AJ, Phillips JC, Sparks RSJ. Interaction between volcanic plumes and wind during the 2010 Eyjafjallajökull eruption, Iceland. J Geophys Res Solid Earth. 2013; 118(1):92–109. doi:10.1029/2012JB009592.View ArticleGoogle Scholar
 Woods, AW, Kienle J. The dynamics and thermodynamics of volcanic clouds: Theory and observations from the April 15 and April 21, 1990 eruptions of redoubt volcano, Alaska. J Volcanol Geothermal Res. 1994; 62(1–4):273–99. doi:10.1016/03770273(94)90037X.View ArticleGoogle Scholar