Presentation and analysis of a worldwide database for lava dome collapse events: the Global Archive of Dome Instabilities (GLADIS)

Lava dome collapses generate hazardous pyroclastic flows, rockfalls and debris avalanches. Despite advances in understanding lava dome collapses and their resultant products, the conditions that occur prior to collapse are still poorly understood. Here, we introduce the Global Archive of Dome Instabilities (GLADIS), a database that compiles worldwide historical dome collapses and their reported properties, including original dome volume (at the time of collapse), dome morphology, emplacement conditions, precursory activity, dome geometry and deposit characteristics. We determine the collapse magnitude for events where possible, using both absolute deposit volumes and relative collapse volume ratios (this being deposit volume as a proportion of original dome volume). We use statistical analysis to explore whether relationships exist between collapse magnitude and extrusion rate, dome growth style, original dome volume and causal mechanism of collapse. We find that relative collapse magnitude is independent of both the extrusion rate and the original dome volume. Relative collapse volume ratio is dependent on dome growth style, where endogenous growth is found to precede the largest collapses (~ 75% original volume). Collapses that comprise a higher proportion (> 50%) of original dome volume are particularly attributed to both gravitational loading and the development of gas overpressure, whilst collapses comprising a small proportion (< 10%) of original dome volume are associated with the topography surrounding the dome, and variations in extrusion direction. By providing validation and/or source data, we intend these data on various dome growth and collapse events, and their associated mechanisms, to be the focus of future numerical modelling efforts, whilst the identified relationships with relative collapse volume ratios can inform collapse hazard assessment based on observations of a growing dome.


Introduction
Lava domes and spines form when viscous magma is extruded but is not able to flow far from the volcanic vent . Instability of lava domes results in pyroclastic flows, rockfalls and sometimes debris avalanches, all of which can pose a significant hazard to areas surrounding the edifice (Voight 2000;Wadge 2009). Despite the threat posed by dome collapse, we still know relatively little about the interplay between dome growth conditions and the collapse mechanisms of lava domes. A broad variety of mechanisms, and triggers, have already been identified for individual collapse events. These include gravitational collapse (Ui et al. 1999), rainfall (Matthews et al. 2002) and gas overpressure (Voight and Elsworth 2000). However, the general conditions that determine which collapse mechanism is dominant are still not clear.
Various modelling strategies have been used to investigate lava dome stability, although many focus on the resultant pyroclastic flows (e.g. Hooper and Mattioli 2001;Saucedo et al. 2005;Wadge et al. 1998) or initial dome emplacement (e.g. Hale 2008;Hale et al. 2009aHale et al. , 2009b. Perturbation factors Editorial responsibility: J. Dufek Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00445-019-1276-y) contains supplementary material, which is available to authorized users. likely to cause instability have been considered particularly in numerical models, for example calculation of diffusion of gas pressurisation across a dome (Voight and Elsworth 2000), limit equilibrium (LE) analysis of slope height/stability relationships (Simmons et al. 2005) or a revised LE analysis incorporating rainfall (Taron et al. 2007). Discrete element models have also been designed to test the impact of external triggers on a dome's stability, such as development of gas overpressure or variation in extrusion direction (Harnett et al. 2018).
Understanding previous dome collapse behaviour is an important tool for helping to develop forecasts for future activity (cf. Ogburn et al. 2015;Sheldrake et al. 2016;Wolpert et al. 2016). To improve our ability to respond to volcanic crises involving dome extrusion, it is vital for volcanologists, particularly those advising decision makers, to have access to records from previous dome-forming eruptions that have undergone collapse. If lava dome extrusion begins at a volcano that has not shown dome growth in recorded history, it is important for observatories and the wider volcanological community to have access to a database that details potential trends in behaviour, by examining historical records from similar volcanic systems. This was the case for Soufrière Hills in Montserrat, where dome growth began in 1995 after~350 years of no extrusion (Branney and Kokelaar 2002).
Many previous studies have highlighted the importance of global databases in volcanology (e.g. Crisp 1984;Crosweller et al. 2012;Donne et al. 2010;Ebmeier et al. 2018;Geyer and Martí 2008;Hédervári 1963;Ogburn et al. 2015;Witham 2005;Wright et al. 2004). However, only a few studies have focussed particularly on dome-building episodes (DomeHaz) and pyroclastic flows (FlowDat) (Ogburn 2012;Ogburn and Calder 2017). Of these two databases, the DomeHaz database of Ogburn et al. (2012) contains information about domeforming eruptions and explosions, which has allowed probabilistic analysis of eruptions and their link to explosive activity (VEI > 4) (Ogburn et al. 2015) as well as analysis of eruption longevity (Wolpert et al. 2016). Instead, FlowDat (Ogburn 2012) is a collection of mass flow (e.g., block-and-ash flows, debris avalanches, pumice flows) parameters and mobility metrics, and has been used for probabilistic analysis of metrics such as height/length data and planimetric areas ). However, a complete inventory of individual dome collapse events for different volcanoes is not currently incorporated into existing databases.
From previous literature (Voight 2000), it is clear that a single volcano can exhibit various collapse styles associated with different dome growth styles and different eruptive phases, ranging from small-scale persistent rockfalls, to large-scale explosive collapse. This provides the main rationale behind this study, as it is important to assess the nature of each collapse, rather than to attribute a single collapse style to an individual volcano.
In this study we thus collate data about dome collapse events in a Global Archive of Dome Instabilities (GLADIS). Dome collapses present a hazard to surrounding regions (e.g. Genareau et al. 2015;Mercado et al. 1988;Sato et al. 1992) and can influence the behaviour of the remaining dome and future dome growth (Voight and Elsworth 2000). We estimate first-order statistics of global trends, focussing primarily on dome growth style, extrusion rate and collapse trigger, with the aim of identifying correlations between these and dome collapse magnitude. We also use one way analysis of variance (ANOVA) to undertake statistical analysis on data currently in GLADIS. We discuss how these results alongside examples of collapse events from GLADIS may influence our understanding of dome collapse processes.

Database design and structure
To analyse the relationships between dome collapse events and their mechanisms, we have compiled an open-access database that includes 293 individual collapse events from 35 different volcanoes (Table 1). The full flat-file database is accessible by joining the GLADIS group on VHub (http:// vhub.org/groups/domecollapse). Here, we summarise the content of GLADIS and report relationships between collapse properties and pre-collapse conditions. The database was initially designed using the list of dome-forming volcanoes in DomeHaz (Ogburn et al. 2015). Volcanoes that had experienced lava dome collapse were identified and details of those events were compiled. This was achieved using peerreviewed literature, the Smithsonian Institution Global Volcanism Program (GVP) (Venzke et al. 1968 to present), the Bulletin of the Global Volcanism Network (https:// volcano.si.edu) and FlowDat. A complete reference list for all entries into the database can be found within GLADIS, and is also provided in Online Resource 1.
Dome collapses are included in the database if they (a) have a known source volcano; (b) have a known year of occurrence; and (c) appear from related literature to be a significant event in the dome growth chronology. The definition of significant event is relative and largely qualitative due to lack of volume data. Where quantitative data are unavailable, an event is considered significant enough for database inclusion if it is explicitly documented within literature as a collapse, or where there is reference to Merapi-type pyroclastic flows, as these refer specifically to dome collapse products (Bardintzeff 1984).
For each collapse event, the major database fields (see Table 2) focus primarily on dome morphology, lava dome emplacement conditions, precursory activity, dome geometry and description of the collapse deposit (usually a blockand-ash deposit). The nature of each database field is indicated in Fig. 1, and a further explanation of each data field can be found in Table 2, where we also define the way in which observations were parameterised. As shown in Table 2, certain database fields are open fields for qualitative or quantitative entries (e.g. human impact, deposit volume), whereas other fields are restricted to the entry of multiple choice and therefore termed closed fields (e.g. dome growth style must have one of the following entries: exogenous, endogenous or combination). These metrics are not exhaustive but do allow us to capture the principal characteristics of the well-documented collapses, as well as the fundamental characteristics of those that are more poorly documented. We note that all data recorded in GLADIS are taken directly from the associated source (Online Resource 1) with no reinterpretation.

Overview of dome collapse regimes in GLADIS
The magnitude and frequency of dome collapses, and the longevity of dome growth can vary at a single volcano (Wolpert et al. 2016). Previous work has documented phases of dome growth and associated pauses (Ogburn et al. 2015;Sheldrake et al. 2016). In this study, we add the relationship  Population % is shown for the whole dataset, the post-1950 dataset and the classified dataset. Population % is calculated by using the number of fields that are filled as a proportion of the number of possible fields (i.e. for each parameter, for each collapse) Sheldrake et al. (2016) identify patterns in volcanic behaviour, defining two distinct eruptive regimes: (1) episodic activity, where duration of repose intervals exceeds the eruption duration; and (2) persistent activity, where the duration of the eruptive phases and reposes are comparable. We examine collapse activity in a similar way by showing the collapses at a volcano, binned in number of collapses per year, alongside periods of extrusion (Fig. 2). We identify three regimes of collapse activity: (1) frequent activity, where collapses are persistently seen during extrusion (for example at Merapi, Indonesia); (2) infrequent activity, where the duration of extrusion without collapse exceeds the duration of extrusion with collapse (for example at Bezymianny, Russia); and (3) time-declining activity, where the number of collapses per year decreases through time (for example at Soufrière Hills volcano, Montserrat). From this dataset, we are unable to determine if these regimes of collapse activity are mutually exclusive, and hence suggest that time-declining activity could be considered a possible sub-regime of both frequent and infrequent collapse styles. We note that small collapses (e.g. constant rockfalls) may not be accurately represented here, due to underreporting and observation bias towards larger events. We therefore expect an underestimation of total volume of material shed.

Data completeness and bias
Investigations of global catalogues of explosive eruptions have demonstrated that under-recording of events becomes more significant with increasing time from present, and decreasing eruption magnitude (Furlan 2010;Brown et al. 2014). We assume such a bias also exists within our dataset; this bias is also highly location dependent, and depends on the level of monitoring in place at a volcano. There is no cut-off before which collapse events are excluded from the database,   (Venzke et?al. 1968 to present), white boxes show qualitative data, filled boxes show quantitative data or data that have a multiple choice option (i.?e. yes or no) and boxes with a thick outline show data that are derived using GLADIS. Dotted black lines show conceptual links between processes although we expect there may be a problem of underrecording prior to about 1950. In Fig. 2, we plot collapse events since 1900 from volcanoes where dome collapses are common. For example, Merapi exhibits persistent collapse behaviour and if we make the assumption that this is not time dependent, it is likely there are more collapse events before 1950 than those that have been observed and recorded in GLADIS. We note that the 28 events (< 10% of database events) from before 1950 contribute very little to the global event catalogue (< 1% of overall data population).
We define data population here as the number of possible fields that are filled as a proportion of all possible database fields. Overall, for 28 parameters and 293 events, there is a possible 8204 entries; 4514 are populated giving an overall data population of 55%. This is a general degree of population (i.e. this considers all database fields equally) and individual events or parameters (e.g. composition) have a higher degree of population than others (e.g. collapse mechanism). In Table 2, population percentage is shown per database field for the whole dataset, the post-1950 dataset and the dataset for which collapse volume as a percentage of dome volume is known, here called the classified dataset. An empty database field does not necessarily mean lack of activity, e.g. if the field <seismic activity> is not recorded in the database, it simply shows that no data are documented in GLADIS, rather than that no seismic activity occurred.
We expect that observatory reporting culture and capacity will influence data availability. For example, Soufrière Hills volcano is one of 35 volcanoes for which we have dome collapse information, but populates 27% of the database, due to quality of recording during the intensely studied 1995-2010 eruption. Of the 78 events where volume information is available, 37 are from SHV. Our analysis is therefore likely to be skewed towards the events from Montserrat, but as more data are added to GLADIS in years to come, the impact of its current dominance is likely to decrease.
Extrusion rate is another parameter affected by recording in the database. Extrusion rates are taken from the original literature, and we do not recalculate rates within this study. This data field is however subject to variations in the time period over which the extrusion rate is recorded (ranging from daily estimates from the day of collapse, to rates averaged over the whole eruptive period). Where possible, daily estimates of extrusion rate are used for the statistical analysis within this study, although often only time-averaged rates are available. All available data are used for the statistical analysis, but this likely introduces bias to the results and alludes to the importance of shorter term flux estimates at growing domes.

Metastable domes
GLADIS also includes data on domes that were emplaced and remain stable at the time of reporting. It is difficult to define what constitutes a stable dome over time, and so we define these here as metastable domes, as weathering and alteration over time could still result in instabilities (Ball et al. 2013). In order to be included in the database, these must be domes that (a) have a citable source of information and (b) have not been completely destroyed by large explosive eruptions or collapses. Unlike the portion of the database recording collapse events, the metastable domes are not required to have a known emplacement date to be included in the database. We record available composition data for 90% of the metastable domes (references for which can be found in GLADIS). Of the domes with known composition, 37% (n = 31) are basaltic-andesite to andesite, 35% (n = 29) dacite and 28% (n = 23) rhyolite.
We include these domes in GLADIS for completeness because structures that have remained stable over a long time could eventually collapse and therefore potentially provide insight into dome collapse processes. However, analysis of these domes is not considered further in this study due to the relative paucity of related data in the associated literature. We note also that if a dome has remained stable for a long period of time (on the order of hundreds of years), the documentation of a later collapse may be reported in the context of landsides or debris avalanches, rather than explicitly named as a dome collapse. If we consider all database fields, only 18% of the metastable dome portion of the database is populated, making any in-depth analysis very difficult.

Defining collapse
The term collapse is used to describe a variety of processes and products resulting from dome instability. In order to build the database, we must more clearly define collapse. Collapse processes range from small-scale rockfalls to larger scale pyroclastic density currents and even debris avalanches. As one end member, rockfalls are defined as abrupt movements of rocks or boulders that detach from a slope and roll, bounce and slide downslope under the influence of gravity (Hungr et al. 2014). When associated with lava domes, rockfalls are generated by disaggregation of cooled lava from the dome surface Hale et al. 2009b) and typically have short runouts of < 0.5 km with volumes on the order of magnitude of 10 3 m 3 (Wadge et al. 2014). Hundreds of smallscale rockfalls can occur daily during active dome growth periods . Pyroclastic density currents are considered as the large end member of collapse products and are defined as density-driven mixtures of volcanic particles and gases (Cole et al. 2002). They are generally larger in volume (> 10 4 m 3 )  and longer in runout (> 0.5 km) than rockfalls. Pyroclastic density currents are the most common deposit type in GLADIS, ranging in volume from 10 4 m 3 to 300 × 10 6 m 3 .
Collapses at Soufrière Hills volcano have been quantified and differentiated using the terms large (1-4 × 10 6 m 3 ) and major (> 4 × 10 6 m 3 ) by Calder et al. (2002). This is a useful classification at an individual volcano, where successive domes and collapses tend to be of similar magnitudes. A definition based on an absolute volume for one volcano is however not necessarily effective and does not facilitate comparison on a global scale where initial dome volumes range over two orders of magnitude.
Therefore, we present a global dome collapse analysis and examine relationships between observed variables and absolute collapse volume (ΔV) and relative collapse volume ratio (ΔV/V, volume of material shed during a collapse event, expressed as a percentage of original pre-collapse dome volume, V). We consider it likely that collapse mechanisms and processes are related to proportion of dome removal rather than absolute dome or collapse volumes, and so using relative collapse volume ratios facilitates comparison of the global dataset.
One challenge in this study is that absolute collapse volumes are not routinely estimated within the literature. Deposit volumes are more commonly reported and relate directly to the collapse volume (Siebert 1984). We therefore use deposit volume as a proxy for collapse volume. Reported volumes are often a combination of both dense rock equivalent (DRE) and bulk volumes. Where available, we record both in GLADIS and specify the measurement type for each volume entry. When calculating relative collapse volume ratio, we use two of the same measurement types (e.g. both deposit and original dome volume are DRE, or both are bulk); the measurement types in each case are shown in Fig. 3. To maximise the sample size for statistical analysis, we assume in this study that these different volume measurements are comparable. Where relative collapse volume ratio is explicitly reported within the associated literature, we directly take this value and do not recalculate a percentage.

Defining attributed collapse mechanisms
One database field we focus on in this study is that of <causal mechanism> (Fig. 1). We define causal mechanisms to be processes that occur to change the equilibrium state of the dome and therefore lead to collapse. Causal mechanisms are defined as processes associated with the growth of the dome, e.g. the generation of gas overpressure within the dome (Voight and Elsworth 2000). Instead, we define a triggering mechanism as an external event where the consequence of the event is a change in dome stability, e.g. intense rainfall (Taron et al. 2007). Although the nuance of each term is different, both causes and triggers are treated equally as collapse-driving mechanisms in the remainder of this work.
For the purpose of quantitative data analysis, GLADIS currently lists one dominant mechanism for each event based on the conditions and causes for collapse as reported in the associated literature. We recognise that in the majority of cases, multiple processes may be at work and therefore also list full descriptions of mechanisms attributed to each collapse event as qualitative information within GLADIS. This information is stored in the <mechanism source> field of the database, where quotations are given from relevant literature to show determination of the dominant collapse mechanism. We also Fig. 3 a Original dome volume versus deposit volume, shown by type of volume measurement (bulk-triangle, DRE-square, combination of both-diamond). All red markers are collapses at Soufrière Hills volcano. See Fig. 2 for volcano labelling, with the addition of KAR (Karangetang), Shiveluch (SHI), Sisters Dome (SIS), Wahanga (WAH) and Ruawahia (RUA). b As in (a) but highlighting smaller absolute original volumes by zooming in on a portion of (a)shown by grey shading acknowledge that characterisation of only the dominant mechanism may create bias in analysis of collapse mechanisms, but this limitation comes from the primary literature, rather than re-interpretation in this study.
Interrogating GLADIS allows us to identify the most commonly cited mechanisms attributed to collapse. We show the number (n) of occurrences in each case, and we find these mechanisms to be: (i) Gravitational loading (n = 57)-this focuses on addition of material, through continued extrusion, to the dome system. Where possible, volume and height are recorded as quantitative information in the database. High extrusion rates are not essential for inclusion in this category. We include here over-steepening (i.e. dome flank angle) due to endogenous (Swanson et al. 1987) or exogenous (Ui et al. 1999) growth. (ii) Internal gas overpressures (n = 19) have been implicated in collapses after observations of explosive eruptions following major dome collapses ).
Overpressures exist within gas bubbles and lead to dome expansion. Pressurised gas trapped within the dome can weaken the bulk strength of the lava, leading to a decrease in overall dome stability (Voight and Elsworth 2000). This includes collapses where dome removal is cited in association with explosive activity. (iii) Topography-controlled (n = 15) collapses, defined here as collapses that occur when the size of a dome exceeds the crater size and overtops the crater walls, likely due to dome and/or crater morphology . This includes perched domes where the dome is emplaced onto a slope and the collapse is attributed to the effect of the slope itself. (iv) Intense rainfall (n = 14) has been attributed to several collapses as a triggering mechanism, with varying physical models associated. Rainwater can contribute to erosion of the slope toe, leading to undercutting and dome destabilisation (Carn et al. 2004). Percolation of rainwater into a dome through fracture networks and interaction of rainwater with hot gases may create steam that pressurises existing potential failure surfaces (Matthews and Barclay 2004;Taron et al. 2007). We also consider the influence on local stresses within the dome by rainfall-induced thermal contraction (Simmons et al. 2004;Yamasato et al. 1998).
(v) A switch in extrusion direction (n = 5) is commonly observed immediately before collapse (e.g. Loughlin et al. 2010;Luckett et al. 2008;Stinton et al. 2014a). This is most likely attributed to thrust forces associated with emergence of a new lobe on older, cooled dome material where the new material is able to exert a force onto the adjacent older material , leading to collapse.
We note that some of these collapse mechanisms depend on the same fundamental physical processes. For example, collapses defined here as topography-controlled collapses are ultimately gravitational in nature. To be categorised as topography-controlled in the database, they must be collapse events that are dependent on the topography, e.g. growing within a crater, and therefore would not have collapsed gravitationally if they had been emplaced onto a horizontal surface.
In the following sections, these mechanisms are grouped into a category called 'other' within the field <causal mecha-nism>, as they are cited in only 11% of cases with listed mechanisms.

Statistical analysis of the database
GLADIS contains information about 293 individual collapses from 35 different volcanoes. We find evidence for statistical dependence of absolute collapse volume on collapse mechanism, and of relative collapse volume ratio on both dome growth style and collapse mechanism. We show that the largest (≥ 50%) relative collapse volume ratios occur when collapses are attributed to gas overpressures or gravitational loading. Instead, small (< 10%) relative collapse volume ratios occur in topography-controlled collapses or those attributed to a switch in extrusion direction. We find no correlation or statistical dependence between the following parameters: absolute collapse volume and extrusion rate (albeit on varied timescales, as defined within GLADIS and discussed later); relative collapse volume ratio and extrusion rate, absolute collapse volume and dome growth style, collapse mechanism and original dome volume.

Overview of data within GLADIS
Of these 293 events, 76% (n = 222) occurred at andesitic or basaltic-andesite volcanoes, 21% (n = 60) at dacitic volcanoes, 3% (n = 9) at rhyolitic volcanoes and < 1% (n = 1) at a basaltic volcano. We do not attempt to draw relationships between collapse and dome composition due to the dominance of andesitic/basaltic-andesite domes within the database. Deposit volume and original dome volume data are available for 27% of events in the database (n = 78), and we focus on these events in the majority of our analysis as the collapse magnitude (absolute and relative) is one of the parameters that would be most useful to forecast for the purpose of hazard assessment. The overall spread of relative collapse volume ratios within GLADIS are shown in Fig. 4.
For the events at Colima and Merapi, it is likely that the percentage falsely exceeds 100% due to the time resolution of the original dome volume calculations. For example, the collapse at Colima on 10 July 2015 was after the final dome volume measurement, and so original dome volume is extrapolated from the data reported in Thiele et al. (2017). We assume that both Merapi and Colima collapses removed significant dome portions, and so these are approximated as 100% collapses in all quantitative analysis. The 14 March 1990 Redoubt event had a deposit volume of 3.5 × 10 6 m 3 , and an original dome volume of 1-5 × 10 6 m 3 . For the purpose of quantitative analysis, we assume a volume of 3 × 10 6 m 3 , which results in a relative collapse volume ratio exceeding 100%. The dataset for the Montserrat 2006 event has the highest time resolution, and likely the most reliable volume calculations of these four events due to close monitoring of this eruption. We suggest therefore that the 114% collapse stems from entrainment of material during the pyroclastic flow process so as to bulk up the volume (Siebert 1984;Bernard et al. 2014) but truly represents complete dome collapse. Thus, for cases where addition of material to the deposit volume through entrainment of non-dome material can cause the collapse percentage to exceed 100%, we assume that 100% of the original dome volume has contributed to the collapse. Despite the uncertainties, we can thus be confident in each case that these are large events that involve complete dome removal. Therefore, for all calculations within this study, events for which the collapse percentage exceeds 100% are considered as having a relative collapse volume ratio of one (or 100%).

Method of statistical analysis
We use statistical tests to examine the relationship between collapse magnitude and observed parameters: extrusion rate, collapse mechanism and dome growth style. Collapse magnitude here refers both to absolute collapse volume (ΔV) and relative collapse volume ratio (ΔV/V). Extrusion rate is an example of a continuous variable (i.e. one where any value is possible) and we analyse this using a regression line, where goodness of fit is expressed as an R 2 value. Dome growth style and causal mechanism are both categorical variables (i.e. where only certain values are possible), and for these we use one-way analysis of variance (ANOVA) to determine if they are statistically correlated with collapse magnitude.
ANOVA is a technique used to test if there is statistical dependence between groups, by accepting or rejecting a null hypothesis. By using ANOVA, we determine an F value which can be summarised as the variation between sample means, divided by variation within the samples. A critical F value (F crit ) is identified from the degrees of freedom in the test, and if the calculated F value exceeds F crit , we conclude a dependent relationship exists between the two variables. A measure of statistical significance (a p value) is also obtained from an ANOVA test, whereby this value is compared to a given significance level (generally α = 0.05). The null hypothesis is accepted (i.e. statistical independence) if the calculated p value falls below the chosen α value.

Correlation between extrusion rate and collapse magnitude
We first test whether collapse size can be associated with extrusion rate prior to collapse. This analysis is carried out using collapse events where values are contained in GLADIS for original dome volume (V), collapse volume (ΔV) and extrusion rate. All three data fields are populated for 23% of the database (n = 68).
We examine the relationship first between relative collapse volume ratio (ΔV/V) and extrusion rate (Fig. 5a), and then between absolute collapse volume (ΔV) and extrusion rate (Fig. 5b), showing a regression line and 95% confidence intervals in both cases. We find very low R 2 values for the correlation between extrusion rate and relative collapse volume ratio (R 2 < 0.10) and absolute collapse volume (R 2 < 0.13). This shows that there is no apparent correlation between extrusion rate and collapse volume; however, we note that this

Correlation between dome growth style and collapse magnitude
To test the relationship between collapse size and dome growth style, we use the entries in GLADIS where there are data for original dome volume (V), collapse volume (ΔV) and dome growth style. All three data fields are populated for 25% (n = 72) of database entries (Fig. 6).
We first propose a null hypothesis that collapse size is independent of dome growth style. Dome growth is a categorical variable within GLADIS and can be (1) exogenous, where magma can reach the surface and extrude as new lobes or spines; (2) endogenous, where new magma is intruded into the base of the dome causing inflation; or (3) combination, where pulses of both exogenous and endogenous growth are observed. We test whether relative collapse volume ratio (ΔV/V) varies according to dome growth style and find an F value of 14.1, which means we can reject the null hypothesis (F crit = 3.1, p = 7.5 × 10 −6 ). This suggests a significant effect of dome growth style on relative collapse volume ratio at a significance level of α = 0.05. The average relative collapse volume ratio for this dataset (where n = 72) is 0.34, and the average relative collapse volume ratios for each dome growth group are shown in Table 3. The most significant deviation from this mean is for domes that grow endogenously, where the average ΔV/V is 0.76. We can confirm this significance with a post hoc analysis using the Bonferroni procedure where we determine that the most statistically significant difference in ΔV/V between the groups shown in Table 3 is between exogenous and endogenous growth (with p = 5 × 10 −5 ). Of the 13 endogenous domes with available volume data, 12 of these are domes from the 1989-90 eruption of Redoubt. It therefore seems likely that our analysis is heavily biased by the data from Redoubt and so the conclusion that relative collapse volume ratio is dependent on dome growth style may not be reliable on a global scale.
We also test the null hypothesis that absolute collapse volume (ΔV) is independent of dome growth style. We find an F value of 1.9 (F crit = 3.1, p = 0.16), demonstrating statistical independence. This suggests an insignificant effect of dome growth style on absolute collapse volume, and that growth style has greater effect on proportion of collapse, rather than absolute volume. Average absolute collapse volumes for each dome growth group are given in Table 3.

Correlation between collapse mechanism and collapse magnitude
To test the relationship between collapse magnitude and causal mechanism, we use the entries in GLADIS where we have values for original dome volume (V), collapse volume (ΔV) and causal mechanism. All three of these data fields are populated in 18% of events (n = 54). We test the null hypothesis that collapse triggers are independent of original dome volume. This test gives an F value of 0.4 (F crit = 2.4, p = 0.84), so we accept the null hypothesis and conclude that original dome size does not have a major impact on the causal mechanism of collapse.
We next propose the null hypothesis that relative collapse volume ratio (ΔV/V) is independent of the causal mechanism for collapse. We find an F value of 5.6 (F crit = 2.4, p = 4 × 10 −4 ), therefore we reject the null hypothesis and show statistical dependence. This indicates a significant effect of causal mechanism on collapse proportion. The average relative collapse volume ratios for each causal mechanism are shown in Table 4.
We again use a Bonferroni post hoc analysis to find the most significant statistical difference. To do this, we add the one event with a causal mechanism of rain to the other category, as the Bonferroni analysis requires more than one event per group. We find the largest statistical significance lies between causal mechanisms of gravitational loading and topography (p = 9 × 10 −3 ). The average relative collapse volume ratio (ΔV/V) for this dataset (n = 54) is 0.41, so we can see that both gravitational loading and topography are outside of this group average. This suggests that collapses caused by topography or a switch in extrusion direction involve, on average, small (~10%) proportions of original dome volume, whereas collapses caused by gravitational loading on average involve more substantial (~50%) dome volume fractions. Bonferroni analysis also shows that there is a large statistical significance (p = 4 × 10 −3 ) between the resultant ΔV/V values for collapses caused by gas pressurisation and those caused by a switch in extrusion direction, with average ΔV/V values at 0.68 and 0.05, respectively. The collapse mechanism that leads to the largest relative volume collapses is gas pressurisation and rainfall interaction, showing that pore fluid pressure plays an important role in dome stability.
We follow up this result by testing the null hypothesis that absolute collapse volume (ΔV) is independent of collapse mechanism. We find an F value of 7.8 (F crit = 2.4, p = 1.9 × 10 −5 ), showing statistical dependence. This shows a very significant effect of causal mechanism on absolute collapse volume, and average absolute volumes for each causal mechanism are given in Table 4.
The 23 cases of gravitational loading as a causal mechanism are spread across eight volcanoes (Soufrière Hills, Unzen, Mt. St. Helens, Merapi, Redoubt, Chaitén, Santiaguito and Colima) so we can be confident that these results are not skewed by the prevalence of Soufrière Hills and Redoubt data within the database. However, the data for both switch in extrusion direction and topographic collapse come wholly from Soufrière Hills. This is due to the quality and frequency of observations during this eruption, particularly when considering that the definitive parameters can be hard to detect in real time (especially those that can be more subtle such as switch in extrusion direction). Although not Table 4 Average relative collapse (ΔV/V) and absolute collapse volume (ΔV) for the following causal mechanisms: gravitational, rain, gas overpressures, switch in extrusion direction, topography, other

Causal mechanism
Average relative collapse volume ratio (ΔV/V) Average absolute collapse volume (ΔV, 10 6 m 3 ) Gravitational 0.50 (n = 24) 4.58 (n = 24) Gas 0.68 (n = 10) 6.37 (n = 10) Topography 0.08 (n = 10) 4.0 (n = 10) Rain 1.0 (n = 1) 97.0 (n = 1) Extrusion direction switch 0.05 (n = 5) 2.92 (n = 5) Other 0.36 (n = 4) 52.95 (n = 4) Number in brackets is the number (n) of entries considered for each mean calculation considered here due to availability of volume data, these collapse mechanisms have been observed elsewhere, for example extrusion direction at Mt. St. Helens (Vallance et al. 2008) and topography-controlled collapse at Volcán de Colima (Hutchison et al. 2013). Therefore, we suggest this result is still globally applicable. This analysis does not consider instances when the mechanism has been observed but has not been followed by collapse, and therefore, these statistics are relevant only given that a collapse has taken place. This, though, allows us to predict that if gravitational loading and change in extrusion direction were to cause collapses, an event triggered by loading is likely to be larger. From the group average (n = 293, ΔV/V = 0.37), there is some suggestion that the subset for which causal mechanism is known is slightly biased towards higher values of relative collapse volume ratio. This could be a reporting bias as causal mechanisms are more commonly observed/ reported for collapses that remove a more noticeable portion of the dome.
This analysis does not consider collapses with an interpreted causal mechanism but where volume information has not been reported (n = 77). Of these 131 (54 with volume data, 77 without) events with listed causal mechanisms, 43% (n = 56) are gravitational, 11% (n = 14) are rainfall related, 20% (n = 26) are attributed to gas overpressures or explosive behaviour, 4% (n = 5) to a switch in extrusion direction, 12% (n = 16) to topography and 11% (n = 14) to various other causes (e.g. weathering, earthquakes or collapse of a crater wall). This suggests that rainfall is particularly underrepresented in the dataset with available volume data (n = 1 with volume data, n = 14 in whole database).

Database uncertainties and reporting bias
We find that relative collapse volume ratio shows a statistically significant dependence on both the reported causal mechanisms, and dome growth styles. These parameters are not always routinely recorded and depend largely on independent observatory culture and also the observation opportunity during an eruption. We suggest therefore that for this type of study looking at forecasting dome collapse, the most important observations to be recorded during dome-forming eruptions that would aid further global statistical analysis are (a) original dome volume; (b) collapse volume (calculated from the missing dome volume where possible); (c) dome growth style and (d) cause of collapse.
An ideal analysis would be one where these mechanisms are recorded both when they exist as precursors to collapse and when they exist during baseline activity of volcanic unrest at dome-forming volcanoes. This would allow a more probabilistic analysis of conditions leading to dome collapse, and will be enabled by increases in the frequency of satellite measurements of deformation, topography and dome surface changes (e.g. Arnold et al. 2016;Ebmeier et al. 2018;Walter et al. 2019;Wang et al. 2015) as well as technical advances in field methods such as Structure from Motion and terrestrial laser scanning (de Zeeuw-van Dalfsen et al. 2017;James and Varley 2012;Thiele et al. 2017).
The largest data uncertainties in GLADIS arise from original dome volume estimates at Redoubt. Following the destruction of the February 1990 dome, 11 domes were emplaced and destroyed, all of which have individual volume estimates between 1 and 5 × 10 6 m 3 (Miller 1994). For all analyses so far in this study, we follow the example of Miller (1994) and take an arbitrary average of 3 × 10 6 m 3 , however this inevitably introduces an uncertainty to collapse volume calculations at Redoubt, and therefore our ANOVA tests throughout.
To test the effect of this uncertainty on our results, we retest independence of collapse volume and causal mechanism/ dome growth style (Table 5) using the range of original dome volumes, and present this alongside the original analysis using a dome volume of 3 × 10 6 m 3 . The reality is likely that some domes at Redoubt were nearer to 1 × 10 6 m 3 , and some nearer to 5 × 10 6 m 3 in original volume. We assume each extreme and run ANOVA with all 11 original volumes at 1 × 10 6 m 3 and then all 11 original dome volumes at 5 × 10 6 m 3 .
We retest the null hypothesis that causal mechanism and relative collapse volume ratio are independent, using a range of original dome volumes at Redoubt (and maintaining the condition that any event with a ΔV/V > 1 is given a ΔV/V of 1). All F values exceed F crit of 2.4 (Table 5), showing statistical dependence. We also retest the null hypothesis that dome growth style and relative collapse volume ratio are independent, finding again that all F values exceed the F crit of 3.1 (Table 5). It therefore seems that our result that relative collapse volume ratio is dependent on both causal mechanism Table 5 F value from ANOVA test, and p value showing significance. Calculated from running ANOVA on causal mechanism and relative collapse volume ratio (ΔV/V), and dome growth style and relative collapse volume ratio (ΔV/V)

Implications for understanding lava dome collapse
Using ANOVA has allowed us to propose null hypotheses and reject or accept these based on data currently in GLADIS. We discuss how these results alongside examples of collapse events from GLADIS may influence our understanding of dome collapse processes. It could be expected that high extrusion rates lead to higher collapse magnitudes (Husain et al. 2014;Zorn et al. 2018). We find that there is no apparent link between extrusion rate and collapse volumes (both absolute and relative). Of the highest recorded extrusion rates in GLADIS, we find a range in collapse magnitudes. For example, an extrusion rate of 25 m 3 /s preceded a 100% collapse at Merapi on 5 November 2010 (Pallister et al. 2013b), and a rate of 25.5 m 3 /s preceded an 80% collapse at Redoubt on 2 January 1990 (Brantley 1990). However, we also find that a 10% collapse at Chaitén on 19 February 2009 was preceded by a 45 m 3 /s extrusion rate (Pallister et al. 2013a), and an 18% collapse at Soufrière Hills volcano on 11 February 2010 was preceded by a 35 m 3 /s extrusion rate Stinton et al. 2014b). Both the Merapi and Redoubt events with relative collapse volume ratios > 80% have attributed collapse mechanisms of gas pressurisation, whereas the smaller relative events at Chaitén and Soufrière Hills volcano are attributed to gravitational loading. We infer from this that collapse mechanism has a more significant effect on the resultant collapse than extrusion rate. Therefore, qualitative observations designed to indicate the processes behind the collapse mechanisms listed in this study are extremely important, e.g. observed inflation of the dome suggests presence of gas pressure or qualitative description of added material to the dome surface in one preferred extrusion direction.
We do however note that our analysis of this correlation is affected by the variations in time period over which the extrusion rate is recorded (ranging from daily estimates from the day of collapse, to rates averaged over the whole eruptive period), and so a higher time resolution would aid this. We speculate that extrusion rate may be linked to triggering collapse in a way that is not currently determinable using this dataset. For example, a faster magma ascent rate limits the timescale over which magma outgassing occurs (Zorn et al. 2018), which can contribute to gas pressurisation of the dome (Sparks 1997). Therefore, whilst extrusion rate can be linked to explosivity or conceptually to the other collapse mechanisms discussed in this study, we identify no explicit causal link between extrusion rate and collapse magnitude. We suggest instead that the effect of extrusion rate on overall dome stability depends on dome conditions prior to collapse, and the time period over which a high extrusion rate occurs.
In this study, we also found that dome growth style (e.g. exogenous, endogenous, combination) influences relative collapse volume ratio but not absolute collapse volume. We suggest this may be due to limited mass wastage at a dome which is emplaced endogenously. For example, the seismological record from the endogenously emplaced 1989-1990 dome at Redoubt shows very few minor rockfalls (Cornelius and Voight 1994), whereas the exogenous domes at Mt. Unzen and Soufrière Hills volcano experienced a large number of minor rockfalls and pyroclastic flows due to crumbling of the dome carapace and shedding of material during growth Sato et al. 1992).
Although this proposed mechanism of limited mass wastage during endogenous growth could explain why endogenous domes are more prone to larger relative collapses, we suggest that this dataset is biased by the endogenous domes at Redoubt. The exogenous domes in GLADIS have a huge range in relative collapse volume ratios, for example 0.6% at SHV (5 June 1997) (Calder et al. 1999;Sparks et al. 1998) and 96% at Merapi (11 November 1994) (Voight et al. 2000a(Voight et al. , 2000b. The same applies to absolute collapse volumes where we have a range of 10 4 m 3 at Unzen (25 February 1992) (Ui et al. 1999) to 164 × 10 6 m 3 at Soufrière Hills volcano (12 July 2003) (Herd et al. 2005). Therefore, to accept the statistical dependence of relative collapse magnitude on growth style, and the independence of absolute collapse volume from growth style, we suggest more data would be required to remove the Redoubt bias. This analysis particularly benefits from using relative collapse volume ratio. This reinforces the importance of original dome volume measurements in global dome stability analyses, particularly those with high temporal resolution.
We also show that original dome size cannot be used as a predictor of the cause of collapse. For example, two domes emplaced during the 1989-1990 eruption at Redoubt were both clearly linked to explosive collapse (Miller 1994), but the 2 January 1990 collapse was of a 25 × 10 6 m 3 dome, whereas the 21 April 1990 collapse was of a dome with a volume of 1-5 × 10 6 m 3 . Miller et al. (Miller 1994) suggest that explosive collapse was caused due to circulation of water caused by the ice-filled summit crater at Redoubt. We observe therefore that the explosive fragmentation caused by groundwater vaporisation is scale-insensitive, and suggest that this conclusion of scale independence holds true for the other collapse mechanisms listed.
In this study, we demonstrate that collapse mechanism has a significant impact on both absolute and relative collapse volume ratios. We show that the largest difference in collapse magnitude lies between collapses attributed to gravitational loading and those controlled by topography. For example, collapses at Soufrière Hills volcano on 2 and 3 September 1996 had absolute volumes of 1.5 × 10 6 m 3 and 3 × 10 6 m 3 , and relative collapse volume ratios of 6% and 9%, respectively. Both occurred due to overspilling after new lobes had filled up previous collapse scars . At Redoubt however, a series of gravitational failures (Bull and Buurman 2013;Miller 1994) all exceeded 66% in relative volume.
The processes of collapse due to gravitational loading and topographical constraint were modelled by Harnett et al. (2018), where it was shown that larger relative volumes during gravitational collapse arose from development of a failure plane much deeper within the dome, whereas topographycontrolled collapses involved only surface material and development of small-scale rockfalls, agreeing with the statistical analysis presented here. Resultant relative collapse volume ratios were also shown to be significantly different between collapses caused by gas pressurisation and those caused by a switch in extrusion direction. Similar physical processes are found to be the cause of this difference by Harnett et al. (2018), where a preferred extrusion direction results in much more superficial failures than gas pressurisation, and therefore this leads to a much smaller relative volume loss.

Conclusions
By statistically analysing a global and historical database of individual dome collapse events, we are able to examine relationships between collapse magnitude (both absolute and relative) and extrusion rate, dome growth style and collapse mechanism.
We find that: 1. Short-term extrusion rate does not affect relative collapse volume ratio (ΔV/V) or absolute collapse volume (ΔV). 2. Dome growth style impacts relative collapse volume ratio, but does not influence absolute collapse volume. We see that endogenous dome growth is most likely to precede larger relative collapse volume ratios (average ΔV/V = 0.76), and exogenous dome growth is most likely to precede smaller relative collapse volume ratios (average ΔV/V = 0.24). 3. Dome volume at the time of collapse does not influence the mechanism of collapse. 4. The mechanism attributed to collapse significantly effects both relative collapse volume ratio (ΔV/V) and absolute collapse volume (ΔV). The most significant statistical difference shows particularly that collapses attributed to gravitational loading (average ΔV/V = 0.50) or gas pressurisation (average ΔV/V = 0.68) involve larger dome proportions and topography-controlled collapses (average ΔV/V = 0.08) or those caused by a switch in extrusion direction (average ΔV/V = 0.05) involve smaller dome proportions.
In this study, we identify five key causal mechanisms for collapse: increased gravitational loading associated with dome growth; intense rainfall; increased gas overpressure leading to explosive activity; thrust forces associated with lava lobe extrusion and changing extrusion direction; and the relative size of the dome compared to the crater in which it sits (or the underlying slope). The strongest statistical link found through the analysis in this study exists between collapse size (both relative and absolute) and causal mechanism. We suggest therefore that these mechanisms should be the focus of future lava dome modelling efforts.
Although the GLADIS database is not exhaustive in its data collation, it allows us to examine historical and global trends in dome collapse and determine the parameters needed to inform short-term forecasting and hazard assessment at dome-forming volcanoes. Observatories play a key role in monitoring dome-building eruptions and feeding that information into the published literature which has been compiled in GLADIS. By adding more detailed recordings of real-time volume estimates of the dome and collapse volumes to GLADIS, an even more detailed picture of dynamic dome processes will emerge.