Bulletin of Volcanology

, Volume 72, Issue 2, pp 185–204

Towards real-time eruption forecasting in the Auckland Volcanic Field: application of BET_EF during the New Zealand National Disaster Exercise ‘Ruaumoko’


    • School of Geography, Geology and Environmental ScienceThe University of Auckland
    • Institute of Earth Science and EngineeringThe University of Auckland
  • Warner Marzocchi
    • Istituto Nazionale di Geofisica e Vulcanologia
  • Gill Jolly
    • GNS Science, Wairakei Research Centre
  • Robert Constantinescu
    • Institute of Earth Science and EngineeringThe University of Auckland
  • Jacopo Selva
    • Istituto Nazionale di Geofisica e Vulcanologia
  • Laura Sandri
    • Istituto Nazionale di Geofisica e Vulcanologia
Research Article

DOI: 10.1007/s00445-009-0311-9

Cite this article as:
Lindsay, J., Marzocchi, W., Jolly, G. et al. Bull Volcanol (2010) 72: 185. doi:10.1007/s00445-009-0311-9


The Auckland Volcanic Field (AVF) is a young basaltic field that lies beneath the urban area of Auckland, New Zealand’s largest city. Over the past 250,000 years the AVF has produced at least 49 basaltic centers; the last eruption was only 600 years ago. In recognition of the high risk associated with a possible future eruption in Auckland, the New Zealand government ran Exercise Ruaumoko in March 2008, a test of New Zealand’s nation-wide preparedness for responding to a major disaster resulting from a volcanic eruption in Auckland City. The exercise scenario was developed in secret, and covered the period of precursory activity up until the eruption. During Exercise Ruaumoko we adapted a recently developed statistical code for eruption forecasting, namely BET_EF (Bayesian Event Tree for Eruption Forecasting), to independently track the unrest evolution and to forecast the most likely onset time, location and style of the initial phase of the simulated eruption. The code was set up before the start of the exercise by entering reliable information on the past history of the AVF as well as the monitoring signals expected in the event of magmatic unrest and an impending eruption. The average probabilities calculated by BET_EF during Exercise Ruaumoko corresponded well to the probabilities subjectively (and independently) estimated by the advising scientists (differences of few percentage units), and provided a sound forecast of the timing (before the event, the eruption probability reached 90%) and location of the eruption. This application of BET_EF to a volcanic field that has experienced no historical activity and for which otherwise limited prior information is available shows its versatility and potential usefulness as a tool to aid decision-making for a wide range of volcano types. Our near real-time application of BET_EF during Exercise Ruaumoko highlighted its potential to clarify and possibly optimize decision-making procedures in a future AVF eruption crisis, and as a rational starting point for discussions in a scientific advisory group. It also stimulated valuable scientific discussion around how a future AVF eruption might progress, and highlighted areas of future volcanological research that would reduce epistemic uncertainties through the development of better input models.


Auckland Volcanic FieldEruption forecastingBayesian Event TreeRuaumokoDisaster exercise


In a volcanic crisis scientists and civil authorities are expected to make decisions under extreme pressure and in very short time-frames. Decisions on when and which areas to evacuate will affect the safety of human lives, property, and infrastructure, and should ideally be made objectively using sound volcanological data, monitoring parameters, and pre-defined thresholds of probability based on cost-benefit analysis (e.g. Marzocchi and Woo 2007, 2009; Woo 2008). Nonetheless, quantitative volcanic risk metrics have been proposed only very recently (Marzocchi and Woo 2009), and thus quantitative strategies for risk mitigation are yet to be widely used. To achieve this goal, a strong foundation is required, and thus a primary aim of modern volcanology is to feed volcanological information and quantitative short-term eruption forecasting into risk-based decision-making in emergency management.

In recent years, important advances have been made in the development of probabilistic approaches to eruption forecasting (e.g. Newhall and Hoblitt 2002; Aspinall et al. 2003; Marzocchi et al. 2004, 2006 and 2008; Connor et al. 2006; Marzocchi and Zaccarelli 2006; Jaquet et al. 2006, 2008). One method that has been gaining prominence since it was introduced by Newhall and Hoblitt (2002) is the use of event trees for determining risks during volcanic crises. An event tree is essentially a representation of events in which branches are logical steps from a general prior event through increasingly specific subsequent events to final outcomes (Newhall and Hoblitt 2002). Carefully constructed event trees enable us to improve our understanding of the likelihood of possible outcomes of escalating volcanic unrest, and thus have huge potential for optimizing and clarifying decision-making procedures.

In order for an event tree to successfully contribute to the decision-making process during volcanic unrest, it needs to provide outcome probabilities in near real time, as well as be user-friendly enough to be incorporated into actual volcanic risk management. Bayesian Event Tree for Eruption Forecasting (BET_EF) is an example of a recently developed probabilistic eruption forecasting tool (Marzocchi et al. 2004, 2008) that fulfils both these requirements. It permits the user to compute long-term and short-term probabilities for eruption outcomes by using past data and monitoring data for a specific volcano (Marzocchi et al. 2008). BET_EF is currently being set up or refined for several live volcanoes around the world (e.g. Etna, Vesuvius, Campi Flegrei, Marapi and Cotopaxi), and has been applied retrospectively to at least two real volcanic crises, namely the 1982–1984 unrest at Campi Flegrei caldera and, using historical chronicles, the 1631 eruption of Vesuvius (Sandri et al. 2009).

An excellent way to facilitate the application of, and to test, probabilistic eruption forecasting tools such as BET_EF is through simulated disaster exercises involving volcanic eruptions. Application of BET_EF during Exercise MESIMEX (Major Emergency SIMulation EXercise) at Vesuvius in 2006 facilitated an important step towards the capacity for quantitative eruption forecasting at Vesuvius. Good correlation was observed between probabilities independently determined by the code and the qualitative opinions of scientists (Marzocchi et al. 2008). In March 2008, the New Zealand government ran Exercise Ruaumoko1, a test of New Zealand’s nation-wide arrangements for responding to a major disaster resulting from a volcanic eruption in Auckland City. We used BET_EF during Exercise Ruaumoko to track the unrest evolution and to forecast the most likely onset time, location, and style of the initial phase of the simulated eruption. Our application provides a significant contrast to that carried out during MESIMEX in that: 1) far more historical eruption and monitoring data are available for Vesuvius than for the AVF; 2) many more scientists are involved in monitoring Vesuvius; and 3) the vent area was known in the MESIMEX exercise, whereas the vent area of a future eruption in the AVF is unknown.

In this paper, we outline the set up of BET_EF for the AVF. We highlight the difficulties arising from essentially all volcanological inputs being based on the interpretation of deposits rather than observations of historical activity. Notably, our approach highlights gaps and limitations in our current knowledge. We also compare the probabilities calculated by BET_EF during Exercise Ruaumoko with those independently estimated by the advising scientists to evaluate the potential for BET_EF to be used in the future for decision-making during volcano crisis management in New Zealand. Our study illustrates how our existing knowledge of a volcanic field can be applied directly to mitigate the human impact of volcanoes.

Auckland Volcanic Field

Volcanic setting

The AVF is a young basaltic field on which the urban area of New Zealand’s largest city, Auckland, is built (Fig. 1). The AVF covers an area of 360 km2 and comprises a minimum of 49 scattered volcanic centers (Searle 1964, Kermode 1992). The estimated erupted magma volume is ~3 km3 (Allen and Smith 1994). The earliest activity may date back to 250,000 years BP (Shane and Sandiford 2003) and the youngest and largest eruption, forming Rangitoto Island, occurred about 600 years ago and was witnessed by early Maori living on nearby islands (Brothers and Golson 1959). Past eruptions in the AVF have ranged in style from phreatomagmatic (forming maars and tuff rings) to magmatic (producing scoria cones and lava flows). Single vents commonly displayed several different eruption styles (Allen 1992; Smith and Allen 1993; Allen and Smith 1994; Houghton et al. 1996).
Fig. 1

Map of the Auckland region showing the Auckland Volcanic Field (AVF) centers (black dots) and deposits (after Kermode 1992). Inset shows the position of the AVF relative to other major volcanic centers, Egmont and the Taupo Volcanic Zone (TVZ), in the North Island of New Zealand. This map is also the area used for node 4, ‘vent location’. A uniform prior probability distribution is assigned to the whole area. Details of the grid cell size and coverage are given in the text. Box indicates the existing AVF and is the area shown in Figs. 3 and 5

A general lack of reliable numeric ages, together with intense urban development obscuring surface outcrop, has limited studies of patterns of past activity in the AVF. The volcanoes in the AVF exhibit no obvious spatio-temporal patterns that might indicate structural controls on vent locations, although the limited age data do indicate that eruption frequency and magnitude have been variable during the life of the field, and overall eruption magnitude has increased with time (Allen and Smith 1994; Cassidy et al. 2007).

Recent investigations of tephra layers interbedded with laminated lake sediments in maars have revealed at least 24 eruptions in the last 80,000 yrs (Sandiford et al. 2001; Shane and Hoverd 2002; Molloy et al. 2009) at an average frequency of 1 per 3,500 yrs, similar to long-lived basaltic volcanic fields elsewhere (Molloy et al. 2009). However, the past activity has been episodic, and has waxed and waned. A major ‘flare-up’ in volcanism at 32 ± 2 ka revealed by tephra layers (Molloy et al. 2009) is also recorded in combined paleomagnetic and Ar-Ar age data, which indicate that five of the volcanoes in the AVF appear to have captured the Mono Lake geomagnetic excursion 30 kyrs ago, possibly forming within a period of only 50–100 years or less (Cassidy 2006; Cassata et al. 2008).

The youngest volcano, Rangitoto (Fig. 1), is about 10 times larger than any of the older volcanic centers, and appears to have been produced during two different eruptive phases separated by a time break of maybe several decades (Needham 2009). The most recent eruptive phase (which produced the extensive lava flow field) involved magma of different composition from the rest of the AVF, signaling a possible change in its evolution. This, together with poor age control and the strong evidence for time clustering of past activity in the AVF, makes probabilistic hazard assessment challenging. Comparison with life spans of analogue volcanic fields (e.g. Sherburn et al. 2007) and the presence of a mantle anomaly at depths of about 70–90 km beneath Auckland that has been interpreted as a zone of partial melting (Horspool et al. 2006) suggest the field will erupt again. Thus, having a procedure for determining volcanic risk in a more rigorous and quantitative manner is important for long-term planning and volcanic hazard mitigation in the Auckland region.

Volcano monitoring

All volcanoes in New Zealand are monitored by GNS Science through the GeoNet project (www.geonet.org.nz). At the time of Exercise Ruaumoko, the Auckland Volcano-Seismic Network (AVSN) consisted of five telemetered seismographs, comprising three single-component, short-period (1 Hz) seismographs, one broadband three-component station and one short-period three-component seismograph. Subsequent to the exercise, two short-period (2 Hz), three-component borehole seismographs and a further surface three-component, short-period seismograph have been added to the network. With the constitution of the AVSN in March 2008, some earthquakes down to about ML = 1.5 would have been reliably detected. For events with ML < 2.5, the locations would have been poor, having accuracy in the order of 10–20 km. For ML > ca. 2.5, the uncertainty in location reduces to 5–10 km. During Exercise Ruaumoko, it was assumed that the AVSN was fully functional.

Given the large area covered by the field and its state of repose, there is no routine monitoring of other parameters such as gas, thermal or deformation indicators, although Interferometric Synthetic Aperture Radar (InSAR) data are available once every 35-day orbit period and are routinely checked for field-wide deformation that may indicate magma intrusion (e.g. Stevens et al. 2004). In the event of increased seismicity beneath the AVF, GeoNet is likely to install additional seismometers, initiate soil-gas measurements, collect additional InSAR data, and possibly take rapid static GPS measurements (e.g. Miller et al. 2001).

Historically, there has been a low level of seismicity in the AVF. From 1960 to 1983, 81 earthquakes with a depth <40 km and of ML ≥ 4 (ML ≥ 3.7 since 1982) occurred within 100 km of Auckland (Cassidy et al. 1986). Most were located in the Hunua Range southeast of Auckland or east near the Coromandel Peninsula, and only one was recorded close to the AVF. Prior to 1995, the AVSN comprised just two short-period, single-component stations. From 1995 onwards, the AVSN was gradually expanded, and GeoNet started upgrading the network further in early 2007. As the network expanded, the ability to detect and locate smaller events was enhanced. Between 1995 and 2005, 24 earthquakes were located in the Auckland region (Sherburn et al. 2007); all were <15 km deep, but only one occurred within the AVF. Magnitudes ranged from ML 1.6 to 3.3, and five earthquakes of ML ≥ 2.4 were felt. In early 2007, a swarm of earthquakes, some felt, occurred several kilometres north of the AVF. Although precursory earthquake swarms may occur away from the eventual vent (e.g. Aspinall et al. 1998), in this particular case, the earthquakes are thought to be related to faulting on the adjacent Hauraki rift (not related to the AVF). All the above earthquakes were of high-frequency, tectonic type; no low-frequency volcanic earthquakes have been recorded (Sherburn et al. 2007). All historical Auckland earthquakes represent normal background seismicity rather than eruption precursors (Sherburn et al. 2007).

Exercise Ruaumoko

Although the volcanoes in Auckland are small and their eruptions have been infrequent, the risk associated with future activity is very high given the high physical and economic vulnerability of Auckland, which has a population of 1.3 million (2006 census). In recognition of this, the New Zealand government ran Exercise Ruaumoko in March 2008, a test of New Zealand’s nation-wide arrangements for responding to a major disaster resulting from a volcanic eruption in Auckland. Planning for Exercise Ruaumoko was led by the Department of the Prime Minister and Cabinet, the Ministry of Civil Defence & Emergency Management (MCDEM), and the Auckland Civil Defence Emergency Management (CDEM) Group. Also playing in the exercise were the Northland, Waikato, and Bay of Plenty CDEM Groups, central government departments, emergency services, lifeline utilities, hospitals, airports, universities and GNS Science.

Exercise Ruaumoko provided an excellent and rare opportunity to test a large number of mitigation, scientific and technical procedures. The core objectives of Exercise Ruaumoko were to: 1) understand, develop and practice the respective roles of agencies in response; 2) embed the National CDEM Plan in standard processes for all participating agencies; and 3) confirm the connections between local, regional, national and international agencies. A supporting objective was to test plans for: 1) the evacuation of affected communities; 2) the continuance of essential services, including local government, lifeline utilities, emergency services, and national government agencies; 3) management of potential economic impacts; 4) co-ordination of science aspects; and 5) management of public information and education.

The exercise scenario was based on a possible volcanic eruption somewhere in the AVF and was developed in secret by a volcano seismologist from GNS Science (known as ‘the volcano’). ‘The volcano’ did not participate in any of the scientific deliberations during the exercise, and thus did not influence the advice provided by the advising scientists.

The exercise scenario covered the period of precursory activity up until the eruption, and commenced with seismicity in the Auckland region in November 2007. After a quiet period of several months, seismicity resumed in early March 2008, and was sustained until the eventual eruption on 14 March. The simulated seismicity was presented by ‘the volcano’ as daily, sometimes more frequent, ‘injects’ (information feeds) to scientists at GNS Science, who then prepared Science Alert Bulletins, (SABs) based on their interpretation of the monitoring data. The bulletins were distributed via email to a list of exercise participants and also mounted on a dedicated public website. These SABs provided civil defence authorities with initial advice on matters such as likelihood, timing, location and style of the impending eruption. Authorities obtained further scientific information by consulting a wider scientific group, the Auckland Volcano Science Advisory Group (AVSAG), which was convened shortly after the onset of unusual seismicity.

All the rules required to set up BET_EF were defined before Exercise Ruaumoko by a group of 8 scientists with different areas of expertise. In particular, the rules were defined by reaching a consensus among the scientists, which is considered a powerful way to estimate sound intersubjective probabilities in terms of degrees of belief (e.g. Gillies 2000). Given the small number of scientists working on the monitoring aspects of the AVF, it was difficult to keep the set-up and application of the code completely separate from Ruaumoko, as almost all volcano scientists and seismologists in New Zealand were involved in Ruaumoko. For example, during the set up of the seismic parameters in nodes 1–3 of the code (which was largely based on Sherburn et al. 2007), occasional clarification about this past work was sought from Sherburn, who also had the role of the ‘volcano’ in the exercise. In providing this clarification, Sherburn (‘the volcano’) made every attempt to remain general in his comments, purposely not suggesting any rules that may have directly related to the Ruaumoko exercise scenario.

We did, however, make every effort to keep the set-up and application of the code separate from the exercise. We waited until the end of the exercise to distribute the BET_EF probabilities, so that the present authors who were on the Science Advisory Group (Jolly, Lindsay) were in no way influenced by BET_EF results. To further strengthen the independence of the two processes, Lindsay and Jolly abstained from any discussions around probability during AVSAG deliberations. In this way, we did not create a feedback between official scientific judgment and BET_EF output, thus keeping them independent from each other.

This procedure enabled us to carry out near real-time eruption forecasting during the exercise by using BET_EF to track the unrest evolution and to forecast the most likely onset time, location and style of the initial phase of the eruption. The forecast was intentionally done independently of the exercise, i.e. the BET_EF results were not used to assist scientific deliberations or decision making during the exercise. By not using the BET_EF results during the exercise, we are now able to make valuable comparisons between the average probabilities calculated by BET_EF during Exercise Ruaumoko and the probabilities estimated (somewhat subjectively) by the advising scientists. Hence we can evaluate the potential for BET_EF to be used in the future to assist decision-making during volcano crisis management in New Zealand.

Bayesian event tree for eruption forecasting (BET_EF)

Bayesian Event Tree for Eruption Forecasting (BET_EF) is a statistical code that provides probabilities for specific events of interest (e.g. an eruption, an eruption at a given location, an eruption of a specific size/style, etc.) by merging all relevant available information such as theoretical models, a priori beliefs, monitoring measurements, and past data. The BET_EF model and software package are based on the event tree philosophy and method discussed in Marzocchi et al. (2004) and Newhall and Hoblitt (2002) and are described in detail by Marzocchi et al. (2008). The software and a comprehensive user manual are available free at: http://www.bo.ingv.it/bet.

An event tree is essentially a branching graphical representation of events in which single branches are alternative steps from a general prior event, state, or condition, and which evolve into increasingly specific subsequent events (Fig. 2; Marzocchi et al. 2008). Eventually the branches terminate at specific hazardous outcomes that may materialize in the future. In this way, an event tree attempts to graphically display all relevant possible outcomes of volcanic unrest in progressively greater detail. The points on the graph where new branches are created are referred to as nodes (Newhall and Hoblitt 2002; Marzocchi et al. 2004, 2008). In BET_EF the nodes are as follows (Fig. 2):
  1. Node 1:

    there is either unrest, or no unrest, in the time interval (t0, t0 + τ), where t0 is the present time, and τ is the time window considered (unless specified otherwise, τ = 1 month);

  2. Node 2:

    the unrest is due to magma, or due to other causes (e.g., hydrothermal or tectonic activity), given that unrest is detected;

  3. Node 3:

    the magma will reach the surface (i.e. it will erupt), or it will not erupt, in the time interval (t0, t0 + τ), provided that the unrest has a magmatic origin;

  4. Node 4:

    the eruption will occur in a specific location, provided that there is an eruption;

  5. Node 5:

    the eruption will be of a certain size/style (e.g. VEI), provided that there is an eruption in a certain location.

Fig. 2

Schematic representation of the Bayesian Event Tree used here. The probability of the selected path is the product of conditional probability θi at all selected branches: [θ]path = [θ1] • [θ2] • [θ3] • [θ4] • [θ5]. Any branch that terminates with “clone” is identical to that which follows the top branch for that node. For example, in Node 4, “vent”, the vent clones are identical to the top branch, “location 1”

BET_EF provides quantitative estimations of probabilities of certain eruption-related outcomes through the evaluation of the probability density functions of the above five nodes by merging all available relevant information. The BET_EF code is set up by entering reliable information on the past history of the volcano in question, as well as the monitoring signals expected in the event of magmatic unrest and an impending eruption. In general, the BET_EF code comprises a non-monitoring and a monitoring component. Both components, in turn, comprise a prior distribution as well as a likelihood. For the non-monitoring component, the prior distribution at each node describes general knowledge about that specific node, for instance, expert opinion, and/or general behaviour recorded for other volcanoes. In general, the prior distribution usually represents a ‘best guess’ probability, estimated without using data. This ‘best guess’ probability is assigned an ‘equivalent number of data’ (Λ) that reflects the weighting of the guess. A guess with a low equivalent number of data has a very low reliability; in contrast, if there is a significant convergence of expert opinion on the best guess provided, the equivalent number of data is high. Both the ‘best guess’ and ‘equivalent number of data’ are transformed by the code into an average and standard deviation of a Beta distribution that is used during calculations. The likelihood is shaped by past data that represent any actual data from past eruptions that are relevant to that node from the volcano in question. In essence, the past data modify the prior distribution through Bayesian theory to obtain a posterior distribution that represents a final estimation. In general, if the number of past data is larger than the ‘equivalent number of data’ of the prior distribution, then it has a larger influence on the final posterior distribution. If the number of past data is comparable to the ‘equivalent number of data’, the posterior distribution reflects a weighted merging of both components.

The prior distribution of the monitoring component is derived by using parameters routinely measured during volcano surveillance. These parameters are assigned upper and lower thresholds by experts, and the fuzzy approach is used to manage the data (Marzocchi et al. 2008). A weight may be assigned to each parameter for nodes 2 and 3; a weight of 2 implies the parameter is a strong indicator for the node, and in calculations is the equivalent of 2 parameters with weight equal to 1. No weights are assigned to parameters at node 1, as a positive result for any one of the parameters would indicate unrest, regardless of its weight. The prior distribution is then modified by the likelihood function if past data from actual monitored unrest or eruptive episodes are available. In the case of the AVF, where there has been no historical unrest, such data are not available and the prior therefore equals the posterior distribution.

Set up of the BET_EF code (version 2.0) for the Auckland Volcanic Field

The AVF comprises spatially separate, typically short-lived volcanoes and is located in a coastal environment which leads to some inherent differences between it and the stratovolcanoes (e.g. Vesuvius) and calderas (e.g. Campi Flegrei) to which BET_EF has been applied in the past. In particular, a future vent could appear anywhere within or adjacent to the existing field, and the style of the initial stages of the eruption will be strongly dependent on the water (seawater or groundwater) available for interaction with the magma. To take this into account, some changes were made to BET_EF, and the set up of the adapted code, referred to as BET_EF V2, is described below.

In general, any model and input data used to set up the BET_EF code are selected by following the basic principles of simplicity and acceptance by a wide scientific community. In practice, the starting point is always a state of maximum ignorance (i.e. no possibility is excluded). Probabilities are then revised (in a Bayesian framework) based on the availability of robust and widely accepted models and data. In using this strategy, some published models for the AVF were excluded from the set up of the code. This does not mean that these models are “unreliable”, rather that we believe they have not yet been properly tested due to a lack of past data, or not fully accepted by the wider scientific community (determined during expert elicitation). Although the inclusion of sophisticated (yet not properly tested) models would increase the precision of our estimates, it may introduce biases that make the probability assessment inaccurate (and therefore useless).

Monitoring parameters are of particular importance in this application. Relevant parameters and thresholds were established before Exercise Ruaumoko during discussions with the GeoNet scientists responsible for monitoring activity in the AVF. All parameters at each node must provide a consistent volcanological picture; in other words, if some parameters are “anomalous” at a given node, there must be anomalous parameters at all previous nodes. If not specified, the probability of an event is considered per month and the time window for collecting data is one month. The rules for the AVF are not fixed in stone; rather we believe that they represent an accurate picture of our present knowledge of the AVF. Obviously, they must be revised periodically, whenever new information emerges from future studies. The description provided here illustrates the philosophy adopted, and may be helpful to other researchers undertaking a similar approach elsewhere.

Node 1: unrest/no unrest

Non-monitoring component

Prior distribution

The AVF comprises 49 volcanic centers that have erupted over the last 250,000 years. We define a prior BETA distribution with average = B / A, where B is the frequency of eruption per month, and A is the expected ratio of eruption to unrest. Here we set B = 49/(250,000*12), and A = 0.2 (i.e., about 1 out of 5 episodes of unrest ends with an eruption). This ratio represents a lower limit of the frequency of eruption relative to unrest episode observed in volcanic fields, and accounts for the fact that not all episodes of unrest end with an eruption (unrest can be non-magmatic in origin, and magmatic unrests can end with an intrusion rather than an eruption). This figure is in agreement with what is reported for the following two nodes, and it only affects long-term forecasting, as during an unrest episode like Exercise Ruaumoko, the probability at this node is set to 1. The number of equivalent data (Λ) for this distribution is 1 (indicating a rough estimate with large uncertainty).

Past data

There has been no confirmed volcanic unrest in the AVF since seismic monitoring of the area began in 1960 (Sherburn et al. 2007), therefore n = 47(years) * 12(months), and no unrest. Note, however, that the small simulated earthquake swarm recorded on one day in November 2007 as part of Exercise Ruaumoko is treated as an episode of unrest (i.e. a failed eruption) in subsequent calculations.

Monitoring component

For this node we consider 6 parameters (Table 1).
Table 1

Summary of the volcanological and monitoring BET_EF input information for the Auckland Volcanic Field. Upper and lower thresholds as well as units are given for monitoring parameters

Input Parameter



NODE 1: Unrest/no unrest

Non-monitoring component

Prior distribution

BETA dist. B/A (see text)


Past data

n1 = 564 months; y1 = 1c


Monitoring component

1. Number of Long Period (LP) earthquakes

> 0; 1 month−1


2. Number of Volcano-Tectonic (VT) earthquakes

> 1; 3 month−1


3. “Significant” ground deformation

= 1


4. Presence of SO2 gas

= 1


5. Presence of CO2 gas

= 1


6. Changes in ground water reservoirs

= 1


NODE 2: Magma/no magma

Non-monitoring component

Prior distribution

No info (uniform dist.)


Past data

No data


Monitoring component

1. Number of LP earthquakes

> 0; 1 month−1


2. Max. magnitude of VT earthquakes

> M3.5; M4.5 month−1


3. Dispersion in depth of hypocenters

> 5; 10 km month−1


4. Acceleration of seismicity (LP or VT)

= 1


5. “Significant” ground deformation

= 1


6. Presence of SO2 gas

= 1


7. Presence of CO2 gas

= 1


NODE 3: Eruption/no eruption

Non-monitoring component

Prior distribution

BETA dist. 0.5


Past data

No data


Monitoring component

1. Seismic tremor

= 1


2. Depth of earthquakes if dispersion is > 5 km

<15; 5 km month−1


3. Acceleration of seismicity

= 1


4. Acceleration of deformation

= 1


5. Sudden reversals of ground deformation and/or seismicity pattern and/or gas concentrations

= 1


6. Significant increase in gas concentrations

= 1


NODE 4: Vent location

Non-monitoring component

Prior distribution

Uniform distribution


Past data

No data


NODE 5: Eruption size/style

Non-monitoring component

Prior distribution (three scenarios: Typical phreatomagmatic, TP, Large phreatomagmatic, LP, and Effusive, E; and WET or DRY)

WET: TP/LP/E = 0.70/0.30/0.00


DRY: TP/LP/E = 0.70/0.25/0.05

Past data

WET: TP/LP/E = 0.00/1.00/0.00


DRY: TP/LP/E = 0.70/0.10/0.20

a weight of monitoring parameter; b the number of equivalent data for non-monitoring parameters; c The one unrest episode here refers to the simulated earthquake swarm in November. See text for details

Parameter 1

Given the low level of seismicity in the AVF, in particular the complete lack of historical low-frequency events, it is considered that just one long period (LP) event (or more) would represent an anomaly and be indicative of unrest.

Parameter 2

One volcanotectonic (VT) event would not be considered anomalous, given the occasional tectonic events close to or within the AVF, however >1 event would be anomalous and 3 or more certainly anomalous.

Parameter 3

In recent years, ENVISAT ASAR scene captures over Auckland have revealed small, localised deformation in the region (between −0.4 and + 0.4 cm per year), possibly due to variations in groundwater level (Samsonov et al. 2008). Here we use the qualifier significant to indicate any deformation that is clearly different from these small fluctuations observed in the past.

Parameters 4 and 5

Gases are not routinely monitored in the AVF at the present time, but we consider that the high population density in the area would ensure that any anomalous emissions would be detected. Hence we infer that there is currently no significant emission of SO2 (a typical magmatic gas) or CO2 (typically released during basaltic eruptions, e.g. Chiodini et al. 1998, Aiuppa et al. 2006) and any emission of these gases would therefore be considered anomalous. Based on measurements at other New Zealand volcanoes, detection limits for soil gas CO2 and airborne SO2 are ca. 10 g/m2/day and >ca. 10 tonnes/day, respectively. Future monitoring strategies may include annual surveys of soil gas or other technologies such as eddy covariance to provide background levels of volcanic gases specific to the AVF (e.g. Lewicki et al. 2008).

Parameter 6

Any detectable and unusual variation in water wells, aquifers and reservoirs would be considered anomalous. For parameters 3 to 6, the threshold is set to = 1, indicating that any changes in these parameters would be considered anomalous and an indicator of unrest.

Node 2: magma/no magma

Non-monitoring component

In the past there have been no episodes of magmatic unrest in the AVF, hence there is no non-monitoring data that can be used for this node. The prior distribution is considered uniform (maximum ignorance) and no past data are used.

Monitoring component

For this node we consider 7 parameters (Table 1). The weight of the parameters is 1 by default; a value of 2 is given for those parameters considered particularly indicative.

Parameter 1

Shallow swarms of LP events beneath a volcano are sometimes attributed to the movement of hydrothermal fluids (e.g. at Campi Flegrei, or Guadeloupe in the French Antilles; Jousset and Chouet 2008). In such cases, the depth of LP events is critical, and LP hypocenters >10–15 km are considered more likely to indicate magma than shallower events, given the presence of shallow water tables and hydrothermal systems. In the AVF, however, there is no shallow hydrothermal system and no evidence for a crustal magma chamber. Furthermore, it is unknown how LP events will migrate in a future eruption; in the 1992 eruption of Mt. Spurr, the LP hypocenters were initially quite shallow but deeper LP events (probably related to magma depressurisation) were recorded after the initial explosions (Power et al. 2002). Therefore, we believe any LP events, regardless of depth, may be indicative of magma in the AVF.

Parameter 2

One of the features that distinguishes seismic swarms related to simple unrest from those that culminate in an eruption is the energy involved (Sandri et al. 2004; Blake et al. 2006). The magnitude of VT events can be a good proxy for energy. Based on the limited seismic activity recorded in the Auckland region, an anomalously large magnitude earthquake in the AVF would be M = 4.5. We make the gradual transition from normal (M < 3.5) to anomalous (M ≥ 4.5) using thresholds similar to those suggested by Sherburn et al. (2007) for seismicity during magmatic unrest in the AVF based on analogous eruptions (e.g. Parícutin). In BET_EF, the gradual transition between two states is modeled using a fuzzy procedure (Marzocchi et al. 2008).

Parameters 3 and 4

A clear upward migration of seismicity is very rarely observed before eruptions. A large dispersion of hypocenters (e.g. a spread >10 km) is, however, typical for dike intrusion and/or migrating magma (e.g. Mt. Spurr 1992, Power et al. 2002; Pinatubo 1991, Harlow et al. 1996). The error in hypocentral location in the AVF is approximately 5 km, thus a 5 km dispersion would be considered just within error, assuming a best case scenario that the network is fully operational and the events are >ML = 2.5. We consider that dispersion >10 km would be a strong indicator of magma causing the unrest, and make the gradual transition from normal (5 km) to anomalous (10 km) dispersion and assign a strong weight (2) to this parameter. Acceleration of seismicity is often indicative of magma migration and eventual eruption (e.g. Kilburn 2003) and this is reflected in Parameter 4.

Parameter 5

Another indicator of magma intrusion is strong localized deformation that is usually (but not always) detectable by the human eye (e.g. Campi Flegrei; Mt. St. Helens 1980, Lipman et al. 1981). During an episode of unrest, we would consider any deformation (uplift, subsidence, ground fractures) that clearly deviates from background activity in the AVF to be strongly indicative of magma involvement (weight 2).

Parameters 6 and 7

SO2 gas is typically magmatic in origin and is therefore a strong indicator of magma driving the unrest (weight 2). Rising basaltic magma may release CO2; in fact CO2 may be the first magmatic gas detected in the lead up to a future AVF eruption (e.g. Aiuppa et al. 2006; Gerlach et al. 2002). However, CO2 release is also common during unrest with no direct involvement of magma through, for example, interaction of hydrothermal fluids with calcareous sediments (Chiodini and Frondini 2001; Carapezza and Tarchini 2007). CO2 is considered less indicative of magma than SO2 and is therefore given a weight of 1.

Node 3: eruption/no eruption

Non-monitoring component

Prior distribution

There have been no episodes of historical magmatic unrest in the AVF and there are very few historical eruptions at analogous volcanic fields. It is therefore not possible to say much about the prior distribution of this node. A prior Beta distribution is assumed, with an average of 0.5 (Newhall written comm. 2008) and a number of equivalent data Λ = 5. This figure derives from what is usually observed at basaltic volcanoes (Newhall and Hoblitt 2002) and means that, on average, 50% of episodes of unrest that are clearly magmatic in origin culminate in an eruption.

Past data

No past data are used.

Monitoring component

Parameter 1

Low-frequency (1–5 Hz) seismic tremor may indicate a coalescence of LP events and is typically observed during or immediately (a few hours) before an eruption. We consider the presence of seismic tremor strongly indicative of magmatic unrest leading to an eruption (weight 2).

Parameter 2

A shallowing combined with a dispersion in earthquake hypocenters is strongly indicative of magma migrating towards the surface. We consider these parameters together as, in isolation, they may indicate other outcomes; e.g. isolated shallow earthquakes may occur without an eruption, and magma migrating at depth causing deep dispersion may in fact stall and not reach the surface. We consider the dispersion in hypocenters larger than 5–10 km a strong indicator of an eruption if the shallowest earthquake within the dispersion (i.e. we exclude outliers) is   ≤ 5 km deep. We make the gradual transition from normal (15 km) to anomalous (5 km) depth for the dispersion and assign a strong weight (2) to this parameter.

Parameter 3

Acceleration of seismicity is considered a typical eruption precursor (e.g. Kilburn 2003). It has a clear physical explanation and typically manifests a few hours to days prior to the eruption (Kilburn 2003).

Parameter 4

Acceleration of deformation is considered strongly indicative of an eruption (weight 2).

Parameter 5

Before an eruption it is not uncommon for there to be a sudden reversal of activity. Seismicity or gas release may slow or even stop (e.g. Pinatubo; Daag et al. 1996) or subsidence may occur where previously ground was uplifting, such as in the last eruption at Campi Flegrei.

Parameter 6

A significant increase in gas concentrations is considered indicative of an eruption. For other New Zealand volcanoes, a sudden order-of-magnitude increase in airborne gas emissions to ca. >2000 tonnes/day for CO2 and ca. >1000 tonnes/day for SO2 would be significant.

Node 4: location of the vent

Non-monitoring component

Prior distribution

For this node we provide a base map that covers an area significantly larger than the existing AVF (Fig. 1) to account for the possibility that future eruptions may occur outside the margins of the current field (e.g. Magill et al. 2005). The AVF is monogenetic in nature, and the paucity of reliable age determinations makes it very difficult to identify any clear space-time patterns. Reliable ages are available for less than one quarter of AVF centers; minimum ages based on tephrochronology are available for 8 centers, and 20 centers are as yet undated. In the case of the undated centers, some age estimates have been made based on morphology and field relations (e.g. Allen and Smith 1994), although these only give very tentative relative ages at best. Combined paleomagnetic and Ar-Ar radiometric data led Cassidy (2006) and Cassata et al. (2008) to suggest that several volcanoes in different parts of the field may have been active simultaneously or near simultaneously (within 100 years), thus the location of the last vent may not be indicative of the next opening, as was suggested for example by Magill et al. (2005).

The presence of very few reliable ages led us to exclude a spatio-temporal model from the prior distribution, which we instead consider to be uniform over the whole area. We do not rule out that there may be a spatio-temporal pattern to past eruptive activity at AVF (seen for example at other monogenetic volcanic fields; e.g., Connor and Hill 1995; Condit and Connor 1996; Conway et al. 1998), only that the few data available do not permit the use of a single robust model. Our choice of a uniform distribution (representing maximum ignorance) is conservative and accurate, even though of low precision. The inclusion of any spatio-temporal pattern not strongly supported by past data or widely accepted by the scientific community would increase the precision, but it may also introduce bias. Although prior distribution is important for long-term assessment, during a well-localised volcanic unrest, like the one observed during Exercise Ruaumoko, the vent location probability is dominated by the location of monitored anomalies. In other words, our final results for vent location are not sensitive to the choice of different non-monitoring prior distributions in this case.

The basemap for node 4 covers the area within 17 km to the north, 10 km to the south, 3 km to the east and 7 km to the west of the existing AVF (Fig. 1). The reason for the greater extension to the north and south reflects the continuity of the underlying geology in these areas. This area was then subdivided into a regular grid of uniform probability (average probability of 0.0005556). The grid contained 30 × 60 cells, each with dimensions 1 km × 1 km. The lower left corner has coordinates longitude = 288000 and latitude = 5887000 in UTM (zone 60 south). The coordinates of the center are: longitude = 303000 and latitude = 5917000 in UTM (174.78976°, −36.87238°).

Past data

No past data are used.

Monitoring component

The localization of anomalous monitoring parameters is indicative of the next vent opening (Marzocchi et al. 2008). In this case, we localize the number of observations (for instance, the number of earthquakes observed) into the grid. We consider shallower earthquakes more indicative of vent opening than deep ones, and therefore assign weights to earthquake locations that are inversely proportionate to earthquake depths. We then applied a Gaussian filter using 2.5 km of (1σ) standard deviation, which mimics the possible errors in earthquake locations. This procedure modifies the probability of vent opening as described in Marzocchi et al. (2008). Although the localization of monitoring observations does not necessarily completely overrule the non-monitoring information in BET_EF, in our case, given that the monitoring anomalies are strongly localized and the prior distribution is uniform, the spatial probabilities are a function of the monitoring data alone.

Node 5: size/style of the initial phase of the eruption

Non-monitoring component

Prior distribution

For this node, we only use non-monitoring information as monitoring parameters do not provide useful insight into the size and style of the impending eruption (e.g. Sandri et al. 2004). The eruption styles of past activity in the AVF have been described in detail by Allen (1992), Smith and Allen (1993) and Allen and Smith (1994). In total, 71% of the volcanoes in the AVF show evidence of phreatomagmatic activity, 77% have evidence of Hawaiian to Strombolian activity and 61% have produced lava flows (Allen 1992; Allen and Smith 1994). Phreatomagmatism typically occurs early in the eruption sequence, and dominates activity until the water source has been depleted or the magma supply exhausted (Allen and Smith 1994). At some centers, deposits from an early phreatomagmatic phase may now be buried under later erupted lavas (Allen 1992), implying that up to 81% of previous eruptions may have had a phreatomagmatic phase (Magill and Blong 2005). Given that sea levels during most of the lifespan of the AVF were much lower than those today (Lambeck and Chappell 2001), the main sources of water for this phreatomagmatic activity are thought to be rivers, aquifers and wet surficial sediments rather than sea water (Allen and Smith 1994). The only volcano in Auckland known to have initially erupted below sea level is Rangitoto (Allen and Smith 1994). Low-density deposits beneath the lava and scoria from this center identified in geophysical studies by Milligan (1977) may represent a tuff ring produced during an early phreatomagmatic phase.

Given the present-day relatively high sea level, together with the presence of significant aquifers and wet Miocene sediments throughout Auckland, there is a high likelihood that a future eruption will begin with a phreatomagmatic phase. Nowhere within the AVF is the water depth >30 m, indicating that a future eruption initiated at sea is likely to encounter shallow water and thus has the potential to be explosive. Hydrostatic pressures are nowhere likely to be high enough to suppress explosivity, and too little is currently known about magma supply rates in the AVF to evaluate their potential for suppressing (or encouraging) an early phreatomagmatic phase.

With this in mind, we distinguish three styles: 1) a phreatomagmatic eruption similar to the majority of past phreatomagmatic events forming existing AVF maars 2) a large-magnitude phreatomagmatic eruption, to account for the possibility of a large magma volume combined with optimum magma:water ratios, and 3) a purely effusive eruption, to account for the possibility that the eruption will be initiated with lava extrusion or fire fountains.

Note that this distinction is not based on the actual expected dominant size and style of the entire eruption. We focus on the style of the initial phase of the eruption, as this phase is more relevant for risk mitigation in the early stages of a crisis. Because the presence of water is important in assigning a probability for a phreatomagmatic eruption, we assign a WET or DRY feature to each cell based on the presence of surface water (Fig. 3). Blue cells are WET, and yellow ones are DRY. In BET_EF, we assume that the propensity for a phreatomagmatic eruption is somewhat higher for WET cells than for DRY ones, and that an initial effusive eruption is only possible in DRY cells.
Fig. 3

Map of the existing Auckland Volcanic Field showing the WET (blue) and DRY (yellow) cells used for node 5: size/style. An initial effusive eruption is only considered possible in the DRY cells

We assign slightly different prior distributions for WET and DRY locations. For WET, we assume that the probability of an effusive eruption is negligible (0), and that the probabilities of typical and large phreatomagmatic eruptions occur according to a classical power-law distribution, i.e., 0.70 and 0.30 for a typical and large size, respectively. For a DRY location, we are unsure of the availability of water at depth but we assume it is high. Expert elicitation of 6 colleagues working on the AVF was used to determine probabilities of 0.95 and 0.05 for a phreatomagmatic and effusive eruption in a DRY location, respectively. The phreatomagmatic group is then split into typical and large according to a power-law distribution, assigning 0.70 for a typical and 0.25 for a large phreatomagmatic event. The number of equivalent data (Λ) for this information is 1.

Past data

The work by Allen and Smith (1994) implies that up to 81% of all previous eruptions were initially phreatomagmatic, and 19% were initially magmatic. Of these eruptions, all but one are thought to have occurred subaerially, i.e. in a DRY location, during periods of lowered sea level. Rangitoto is the only volcano in the AVF known to have erupted through the sea, and in this case an initial phreatomagmatic phase was inferred by Milligan (1977). Therefore, using past data we consider 80/20 and 100/0 for initial phreatomagmatic/magmatic activity in DRY and WET locations, respectively.

AVF tuff rings are typically <50 × 104 m2 in size (Allen and Smith 1994). Exceptions are Pupuke, Three Kings and Motukorea (ca. 100 × 104 m2) and Rangitoto (>900 × 104 m2). These exceptions correspond to 13% of tuff rings in past DRY locations and 100% of tuff rings in past WET locations, respectively. We use this information to further divide the phreatomagmatic component of DRY and WET locations based on past data, resulting in the following probabilities for typical/large/effusive: 0.7/0.1/0.2 (DRY) and 0.0/1.0/0.0 (WET). Note that the possibility of accounting for the coupling between size/style and vent location is the main difference between BET_EF version 1 and the version of the code adopted here (BET_EF V2).


Exercise Ruaumoko probabilities: nodes 1-3

Data from exercise injects and Science Alert Bulletins, and calculated median and average probabilities per month for nodes 1 to 3 (Table 2, Fig. 4) are discussed below. We refer to average probabilities per month. The choice of whether to consider average instead of median probabilities is partially subjective, and may depend on the intended use of the data.
Table 2

Summary of Exercise Ruaumoko information relevant to BET_EF as derived from Science Alert Bulletins (labelled AK--/--), and associated BET_EF probabilities for nodes 2 and 3, and relevant decisions made by scientists

Date (SAB no.)

Ruaumoko exercise ‘injects’ used to run the BET_EF code

Node 2: magma Av. (median)

Node 3: eruption Av. (median)

Scientists’ output

Nov 6

16 LP earthquakes (M1.8–2.2)

83% (99%)

25% (15%)

SAL raised to 1(apparent unrest); 70% probability that unrest is magmatic in origin

(AK 07/01)

Depth: 36–45 km

Nov 16

No activity since swarm on Nov 6


SAL lowered to 0(usual quiescent state)

(AK 07/05)

Dec. 9


0.1% (0.07%)

0.05% (0.03%)


March 1

15 LP earthquakes (M1.8–2.2)

86% (99%)

23% (12%)


(AK 08/01)

Depth: 38–46 km

March 2

20 LP earthquakes (M1.8–2.2)

88% (>99%)

26% (16%)


(AK 08/01)

Depth: 36–51 km

March 3

25 LP earthquakes (M1.8–2.2)

87% (>99%)

24% (14%)

SAL raised to 1(apparent unrest)

(AK 08/01)

Depth: 35–47 km

March 4

30 LP earthquakes (M1.8–2.2)

88% (>99%)

24% (14%)


(AK 08/02)

Depth: 30–41 km

March 5

25 LP earthquakes (M1.8–2.2)

88% (> 99%)

24% (14%)


(AK 08/03)

Depth: 28–38 km

March 6

10 LP earthquakes (M1.8–2.2)

87% (> 99%)

24% (14%)


(AK 08/04)

Depth: 30–40 km

March 7

No activity

87% (> 99%)

24% (14%)

Unrest now considered to be caused by a magmatic intrusion

(AK 08/05)

March 8

3 VT earthquakes (largest M2.5)

87% (> 99%)

25% (16%)

Increased threat of magma intrusion leading to a possible eruption, as VTs suggest magma has passed into lower crust; SAL raised to 2(confirmation of volcano unrest)

(AK 08/06)

Depth: 24–28 km

March 9

8 VT earthquakes (largest M2.5; felt)

88% (> 99%)

25% (16%)

Threat of eruption in days to weeks

(AK 08/07)

Depth: 18–26 km

March 10 (AK 08/08)

40 VT earthquakes (largest M3.0; felt)Depth: 14–26 km

88% (> 99%)

27% (18%)

Increased threat of an eruption over a period of days to weeks; probability of unrest leading to an eruption remains low, about 50/50

March 11

12 VT earthquakes (largest M3.0; felt)

89% (> 99%)

54% (56%)

Threat of an eruption in the next 2–3 days

(AK 08/09)

Depth: 11–17 km

March 12

100 VT earthquakes (largest M4.0; felt)

92% (> 99%)

77% (91%)

25–50% probability of an eruption within next 24 hours increasing to 75–90% within the next 48 hours; SAL raised to 3(Real possibility of hazardous eruptions)

(AK 08/11)

Depth: 5–19 km

Anomalous CO2 concentrations 2 cm uplift

March 13 am

300 VT earthquakes (largest M4.5; felt)

94% (> 99%)

82% (98%) (with accel. 86%)

Probability of an eruption is 90%

(AK 08/14; AK 08/15)

Depth: 1–13 kmIncreased flux of CO2 Continued uplift

March 13 pm (AK 08/17, AK 08/18)

Drop in earthquake numbers since 1200 hr 20 VT events; depth: 1–7 km

95% (> 99%)

87% (>99%)

Probability of an eruption within the next 24 hours is at least 90%


Near continuous volcanic tremor Gradual uplift continues

March 14 am

Volcanic tremor amplitude increasing Continuous accelerating ground uplift

96% (> 99%)

90% (> 99%)


(AK 08/19)

March 14 pm

Steam and ash eruption


SAL raised to 4 (hazardous local eruption in progress)

(AK 08/23)

Fig. 4

Time evolution of BET_EF magmatic unrest and eruption forecasting during Exercise Ruaumoko. The probability of eruption given by expert scientists is indicated by an asterix (dotted line indicates a probability range), and the days when SAL changes were made are indicated by boxed numbers. The eruption occurred on March 14. A = average probabilities, B = median probabilities (see text for more details)

On 6 November 2007, 16 LP earthquakes were detected by the AVSN, resulting in a BET_EF probability of unrest of 100%. The probability that magma was driving the unrest (Pm) was calculated at 83%, and the probability of eruption (Pe) 25% (Table 2). After one month of no further activity, the probability of magma and eruption dropped to <0.1%. On 1 March 2008, activity resumed with deep LP earthquakes, which continued until 6 March, decreasing in average depth from about 42 to 35 km over this time (Table 2). Activity paused for a day, resuming on 8 March with VT earthquakes at about 26 km depth, replacing the LP events as the dominant type of seismicity. VT activity occurred until 14 March, with earthquakes shallowing over this time. Anomalous CO2, ground deformation and seismic tremor were observed on 12 and 13 March, intensifying until the eruption commenced on 14 March at 13:00 h (Table 2).

Right from the onset of anomalous activity in March, the BET_EF probability of unrest was 100%. Pm and Pe stayed around 87% and 24%, respectively, from 1 March to 11 March, when there was a jump in Pe to 54% (Fig. 4) as the depth of dispersed earthquake hypocenters entered the critical depth threshold range (<15 km). On 12 March, Pm and Pe increased to 92% and 77%, respectively, reflecting CO2 detected in soil gas, uplift, and the shallowest earthquakes passing the lower depth threshold value of 5 km. Between 11 and 13 March, there was a marked jump in number of VT events recorded, from 12 (11 March) to 100 (12 March) to 300 per day on 13 March. Despite this jump, a clear trend was not seen on a plot of inverse event rate (e.g. Kilburn 2003), and we therefore did not treat this as an ‘acceleration’. On 13 March, an increase in CO2 soil gas flux and a M = 4.5 earthquake resulted in an increase in Pe to 82%. (Note that a positive result for ‘acceleration in seismicity’ here would have increased Pe to 86%; Table 1). The sudden drop in VT seismicity and onset of tremor on 13 March and the accelerating ground uplift on 14 March led to a probability of eruption of 90% on 14 March, the morning of the eruption (Fig. 4).

Exercise Ruaumoko probabilities: nodes 4 and 5

By plotting earthquake epicenters and weighting them according to depth, we generated maps showing relative probabilities of the vent occurring at particular locations (Fig. 5). Note that the eventual point of outbreak fell consistently within the highest probability (darkest) zone on all maps from 8 March. The probabilities at Node 5 (i.e. style/size) do not change with time as they are independent of the monitoring data. As they are extremely similar regardless of location (Table 1), we did not calculate probabilities for this node for single locations, although this calculation can easily be done by multiplying the probability of a given location in Node 4 by the probabilities of the different styles.
Fig. 5

Maps showing probability of vent opening on selected days. Purple ellipses indicate likely vent areas proposed by advising scientists in Science Alert Bulletins for the same days. The dashed purple line indicates a map released on March 11. Arrow points to the actual point of outbreak


Comparison with scientists’ probabilities

During Exercise Ruaumoko, the advising scientists periodically reported probabilities of a particular event occurring to civil authorities to assist their decision making (Table 2; Fig. 4). We emphasise that this advice was given completely independently of the BET_EF probabilities, which were not distributed until the last day of the exercise. In addition, the Scientific Alert Level (SAL) was raised or lowered depending on the scientists’ interpretation of the incoming data (Table 2; Fig. 4). Operationally, GeoNet scientists assessed the current and past data and then discussed likely mechanisms to explain the observations, based on previous activity at the AVF and at other similar volcanoes. After this discussion, a vote was taken on whether the SAL should change, based on the interpretation of the activity compared to the definition of each SAL. The SAL was changed if a majority favoured a change. The scientists also estimated the probability of future eruption through expert judgment. This estimate was again achieved by round-table discussion among the scientists and then individual estimates of probabilities were simply averaged. The scientists raised the SAL to 1 (apparent unrest) upon receipt of the first ‘inject’ in November 2007. Based on the LP seismicity observed in November, scientists announced a 70% probability that magma was involved. This compares with a Pm of 83% calculated by BET_EF at this time. On 16 November, scientists dropped the SAL to 0, whereas the BET_EF probability of unrest only became negligible after the time window of one month had passed (Table 2). It should, however, be noted that the monitoring group lowered the SAL partly because of exercise constraints rather than a realistic assessment of risk: it was felt that the initial phase of the exercise, designed to coincide with a series of co-ordination meetings, was over and therefore the monitoring group could stand down.

Upon resumption of activity in March 2008, scientists again raised the SAL to 1, and BET_EF probabilities for unrest again reached 100%. From 1–10 March, the BET_EF probability of magma and eruption remained fairly stable at 87% and 24%, respectively (Fig. 4). Interestingly, during this time, the scientists declared the unrest likely to be caused by a magmatic intrusion (on 7 March), raised the SAL to 2 (on 8 March) and declared a 50% chance of unrest leading to eruption (10 March). The scientists’ probability refers to an unspecified forecasting time interval, whereas BET_EF output always refers to a time interval of one month. For this reason, a rigorous comparison between the two cannot be made, although general comparisons are possible.

It is interesting to note that the reason for the scientists’ increased concern during 7–10 March was the fact that seismicity paused for a day on 7 March, resuming on 8 March with the onset of VT events at <30 km depth (replacing the deep LP events). The scientists interpreted these signals as indications of magma pausing briefly at the 30-km-deep crust-mantle boundary, then passing from the mantle into the lower crust, thus decreasing any chance of magma stalling. Seismicity passing through the assumed 30-km-deep crust-mantle boundary was clearly an important threshold for the scientists as an indicator for Node 3, yet this threshold was not articulated during the development of the monitoring thresholds for this node before the exercise. From 11 March, BET_EF probabilities corresponded well to probabilities determined by the scientists and were consistent with SAL changes (Table 2; Fig 4).

Four times during the lead-in to the eruption, the advising scientists produced maps showing likely vent locations. These were essentially ellipses enclosing the majority of earthquake epicenters superimposed on a map of the AVF (Fig. 5). Typically a probability statement was given with the map, e.g. on 12 March the scientists estimated that, within the ellipse, there was a 25–50% probability of an eruption within the next 24 h increasing to 75–90% within the next 48 h (Fig. 5). In one case (13 March), epicenters from two different time periods were shown on the map and the last day’s epicenters were highlighted. Instead of using the ‘recentness’ of earthquakes to assign probabilities to vent locations, we chose to use their depth (with shallower earthquakes corresponding to higher probabilities; Fig. 5). In general, the BET_EF maps corresponded well with the scientists’ maps, and may in fact be somewhat more useful, if it is assumed that shallow earthquakes indicate proximity to the rising magma, as they were able to indicate higher levels of probability of vent opening in a certain location.

A brief discussion about the time window for observations is appropriate here. The time window used for BET_EF probabilities is set to one month. The use of a constant forecasting window makes it easier to interpret the evolution of probability through time, and it does not pose any problem when used as a basis for decision-making (Marzocchi and Woo 2007, 2009). As the Exercise Ruaumoko eruption drew closer, the probabilities provided by scientists typically referred to a much shorter time interval, e.g. the next 24 or 48 h (Table 2). Despite this difference in the forecasting window length, we argue that a general comparison between BET_EF probabilities and those given by the scientists is still possible. In fact, as a volcanic crisis escalates towards actual outbreak, monitoring parameters are changing rapidly, so that probabilities of eruption also change rapidly. In particular, anomalies in the parameters at node 3 (usually considered the ‘precursors’ of an eruption) indicate that an eruption may occur in a few hours or days at most (Marzocchi et al. 2004). In other words, during the first stage of the unrest, when monitoring parameters are changing slowly, the probability per month of an eruption means that eruption can occur at any time during the forecasting period. In contrast, when the probability of eruption is increasing rapidly, it is much more likely that the eruption will occur in the next few days, rather than at the end of the forecasting window. In practice, this means that when anomalies are detected at node 3 (i.e., when the probability of eruption becomes high), the probability per month can be considered comparable to the probability in the next few days.

BET_EF as a decision-making tool

In a review of provision of scientific advice during Exercise Ruaumoko (Cronin 2008), it was pointed out that there were often long time delays (hours) in transferring information (e.g. probabilities) between scientists and the civil authorities. One reason for this was the way in which the scientific deliberations were conducted, generally by conference calls between scientists from different organizations in different parts of the country. Another reason was the time it took time for the scientists to process information from ‘the volcano’, compare it with their knowledge of past data from the AVF and analogue volcanic fields, share their expert opinions with other scientists, and come up with a single statement upon which everyone agreed. Clearly, if a scientific advisory group can collectively agree on a set of quantitative and transparent rules for eruption forecasting before a crisis, then the decision-making process can be optimized during an actual crisis.

If properly configured, BET_EF should quantify the expert opinions of an advisory group in an appropriate way. During a crisis, a good strategy could be to use the current BET_EF output as a starting point for a discussion of the day’s events. Most of the time, BET_EF output will facilitate and speed up the achievement of a consensus opinion within a scientific advisory group. Furthermore, pre-defined thresholds can be set to ease decision making. For example, in the lead up to the simulated evacuation during Exercise Ruaumoko, civil authorities wanted to know when the 48 h ‘time window’ before outbreak had been entered, because 48 h was thought to be the time required for evacuation. In this case, overcoming a pre-defined threshold (e.g. a particular probability of an eruption in a given location in the next 48 h) based on cost-benefit analysis could act as a transparent and acceptable basis for providing this critical information to the authorities. Marzocchi and Woo (2007, 2009) give more information on how thresholds in BET_EF can be used to assist evacuation calls.

Experts who make decisions under pressure (e.g. nurses, intensive care units, firefighters etc) do not logically and systematically compare all available options, rather they draw on their experience and intuition and a rough mental simulation of a decision tree to come to their rapid decisions (e.g. Klein 1998). When a crisis only lasts for a short period of time, and the expert can make decisions as an individual rather than having to discuss possible decisions with colleagues, the decision-making is fast, even though not necessarily rational or optimal (e.g., Viscusi 1992). In the case of volcanic unrest, crises are often long, sometimes over weeks to months, requiring scientists to make decisions while under extreme pressure and exhausted. Furthermore, it is rare that a single scientist is expected to make these decisions. Typically, some degree of consultation with other scientific experts is expected or even required, which slows down response times and may even reduce the scientists’ ability to make sensible rapid intuitive decisions. Computer-based decision trees can be extremely useful in optimizing and clarifying decision-making procedures under these conditions, as demonstrated in applications outside volcanology (e.g. Reilly et al. 2002).

BET_EF as research-focusing tool

In the lead up to and during Exercise Ruaumoko, our work with BET_EF stimulated valuable scientific discussion around how a future AVF eruption might progress. The process of identifying and quantifying past data, existing models and monitoring parameters and thresholds that would be indicative of magma unrest, the presence of magma and an impending eruption in a particular location and of a particular style had the effect of encouraging scientists to filter out all extraneous information and focus on the data and knowledge that directly informs on these events. This process also highlighted gaps in our understanding of the AVF. Thus, in order to reduce epistemic uncertainties through the development of better input models for tools such as BET_EF, future volcanological research in the AVF will include determining: the effect of shallow groundwater and <30 m deep seawater on the initial stages of an eruption; relationships between morphology of past centers and eruption size/style; better ages for existing centers to test existing spatio-temporal models of vent opening, or to propose new ones; the nature of the crust beneath Auckland and its thickness (and thus the influence on magma behaviour and eruption probability of the crust-mantle boundary); and appropriate methods for developing hazard maps for monogenetic fields where precursory seismicity is likely to at best provide a wide zone of possible outbreak sites rather than a point source.


In this paper, we have illustrated the set up and application of a recently developed technique for eruption forecasting (BET_EF) for the AVF during a simulated volcanic eruption, Exercise Ruaumoko. As a special experiment in critical evaluation and decision-making, Exercise Ruaumoko proved to be a very instructive exercise that has allowed a large number of scientific and technical procedures to be tested. Such testing is of paramount importance in maximising preparedness for a possible future eruption in the long-dormant, high-risk AVF.

We have explained how we defined BET_EF rules for the AVF, and suggest that the focus should not be on the specific values of the rules adopted, rather on the philosophy and procedure embraced to define them.

The average probabilities calculated by BET_EF during Exercise Ruaumoko corresponded well to the probabilities estimated by the advising scientists, and provided a sound forecast of the timing, location and style of the eruption. Prior to our application, it was unclear how useful BET_EF would be in a monogenetic field where there has been no historical activity and for which very little prior information is available. The results suggest that BET_EF can in fact be applied to such a field. Our experience during Exercise Ruaumoko further suggests that the main advantages of the use of BET_EF are:
  1. 1.

    BET_EF uses a set of quantitative and transparent ‘rules’ for eruption forecasting that can be established by scientists in an advisory group before a crisis, and thus has huge potential for optimizing and clarifying decision-making procedures.

  2. 2.

    It is always possible to trace back and explain how a given probability was derived; subjective and qualitative estimates given by scientists are much less transparent.

  3. 3.

    If prepared through consensus by a science advisory group, BET_EF will rapidly recount (in near real-time) the group’s opinions as probabilities as information about the unrest comes to hand, and may therefore be useful as a rational starting point for the group’s further discussions.

  4. 4.

    Establishing the BET_EF code for a particular volcano will focus scientific discussion on how a future eruption might progress, as well as help guide future research by highlighting gaps in understanding of the volcano.


As a final remark, we emphasize that the BET_EF code as defined here may not necessarily successfully forecast a future real eruption at the AVF. What we have shown, however, is that, in this artificial exercise, the code was able to independently capture quantitatively and transparently what the scientists thought might happen in the lead up to an eruption. In other words, the code is able to give a coherent picture of the degrees of belief of researchers. Thus, the success of any application relies on the quality of the input provided by researchers.


In Maori mythology, Ruaumoko is the god of earthquakes and volcanoes



This research was carried out through support from the New Zealand Earthquake Commission (EQC) and the Foundation for Science and Technology grant to GNS Science under contract CO5X0402. We thank Brad Scott, Ian Smith, Colin Wilson and Steve Sherburn for helpful discussions during the process of setting up the code. Graham Leonard provided valuable assistance with map generation. We also thank Phil Shane for providing constructive comments on an earlier draft. Reviewers Christina Magill, Chris Newhall and two anonymous reviewers provided many constructive comments and greatly improved the quality of the manuscript. We are grateful to Jocelyn McPhie for her thoroughness in editorial handling.

Copyright information

© Springer-Verlag 2009