The methodology
A transparent look at the probabilistic model behind our eruption forecasts โ how a long-term base rate, official alert levels and live seismic precursors combine into a single, honest probability.
Data sources
4
GVP ยท PHIVOLCS ยท seismic
Precursors analysed
5
seismic signal families
Alert levels
0โ5
PHIVOLCS scale
Forecast windows
2
1-year & 30-day
GVP volcanoes
1,215
11,089 eruptions
References
9
peer-reviewed
Overview
We do not predict that a volcano will erupt on a given day. No one can. Instead the model estimates a probability โ the chance of at least one eruption within a window of time โ and shows the evidence behind it.
Every forecast starts from how often a volcano has actually erupted, measured from the Smithsonian GVP record. This is the long-run anchor.
Short-term precursors โ the official alert level and live seismicity โ raise or lower that rate to reflect current unrest.
A Poisson event model converts the resulting rate into a clear 1-year and 30-day probability, with a stated confidence level.
This is an evidence-based statistical model, not a physics simulation of the magma system. It is designed to be honest about uncertainty: it caps every probability at 98% and reports lower confidence when the underlying data is thin.
Data sources
The model only combines authoritative, openly published data. Nothing is invented.
0
GVP volcanoes in the catalog
0
Confirmed eruptions on record
0โ5
PHIVOLCS alert level scale
Long-term base rates
Confirmed-eruption frequencies for 1,215 volcanoes (11,089 eruptions). The base rate is each volcano's eruption count divided by its documented record length โ the empirical anchor of every forecast.
Visit source โAlert levels & sub-M3 seismicity
The Philippine Institute of Volcanology and Seismology issues the official Volcano Alert Level (0โ5) and monitoring bulletins โ the strongest near-term unrest signal we use. It also runs the national seismic network, the only catalog that resolves Philippine earthquakes down to ~M1; those sub-M3 micro-earthquakes (which USGS and EMSC miss in-region) anchor the completeness magnitude and feed the b-value and swarm analyses.
Visit source โLive seismicity
Earthquake catalogs (magnitude, depth, location, time) feed the short-term precursor analyses โ b-value, hypocenter depth migration, accelerating seismicity, large-quake triggering and swarms.
Visit source โSub-M4 micro-seismicity
The European-Mediterranean Seismological Centre aggregates regional network solutions (PHIVOLCS, BMKG and others), cataloguing Philippine earthquakes down to ~M2โ3 โ the small events USGS doesn't resolve in the region. These fill the low-magnitude band that the b-value, completeness-magnitude and swarm analyses depend on.
Visit source โThe math, simply
Eruptions are treated as random events arriving at an average rate. The probability of seeing at least one in a given window follows the Poisson distribution.
A homogeneous Poisson process: if eruptions arrive randomly at an average rate ฮป per year, this is the chance of seeing at least one within a window of t years. The model caps the output at 98% โ a statistical estimate should never claim certainty.
ฮป (lambda)
The effective annual eruption rate โ the long-run base rate after it is scaled by precursors, the alert level and the repose adjustment.
t (time)
The forecast window, in years. We report two: t = 1 (one year) and t = 30/365.25 (the next 30 days).
Long-term base rate
The base rate ฮปโ is the simplest possible estimate of how active a volcano is: its number of confirmed eruptions divided by how long its record covers.
For example, a volcano with 20 confirmed eruptions since 1750 has a base rate of 20 / 276 โ 0.072/yr, or roughly one eruption every 14 years. Because eruptions before ~1500ย CE are heavily under-recorded, we measure frequency over the complete-record era rather than diluting it with an ancient first-eruption date โ otherwise a frequently-active volcano like Etna or Kฤซlauea looks far quieter than it is.
When a volcano's own record is sparse, the model leans on a data-derived prior that already encodes where it is and how large it is โ both calibrated from the 1,215-volcano Smithsonian catalog, not guessed (see the next panel).
Rates are clamped between ~1 per 1,250 years and ~1 per 2 years, and a single global correction ties the model to reality: the sum of every volcano's annual rate reproduces the observed ~50 volcanoes erupting worldwide each year.
Base rate formula
Size & uncertainty
A forecast is not just whether a volcano will erupt, but how large it might be, and how trustworthy its recorded history is. We treat both as explicit variables.
Eruptions span the Volcanic Explosivity Index from gentle VEIย 0โ1 lava effusion to catastrophic VEIย 6+ events. Globally, each step up the scale is roughly 5ร rarer โ a power-law sizeโfrequency relation. We characterise each volcano by its typical VEI (its most common size) and its maximum recorded VEI, then estimate the chance of a large (VEIย โฅย 4) eruption by scaling the base rate down for each step above typical:
A volcano whose eruptions are usually VEIย 2 produces a VEIย โฅย 4 event only ~1 in 25 times โ rarer, but far more hazardous. One that has never exceeded VEIย 3 is treated as not large-capable.
The eruptive record is systematically incomplete: small eruptions โ and almost everything before ~1500ย CE or in remote regions โ went unrecorded. Treating a sparse record as ground truth would underestimatethe true rate, so we blend a volcano's own observed frequency with a volcano-type prior (calderas, stratovolcanoes, shieldsโฆ each have a characteristic rate and size), weighted by how complete the record is:
Every volcano page surfaces these directly: a typical & maximum VEI, the chance of a large eruption, a record-completeness grade (comprehensive โ sparse), and a 1-year probability range that widens when the history is uncertain.
Repose & 'overdue'
A pure Poisson process is memoryless โ but real volcanoes show quasi-periodic repose. We apply a bounded, renewal-inspired adjustment that compares the time since the last eruption to the average recurrence interval.
Recently active
ratio < 0.3
ร0.90
Erupted recently relative to its average โ repose adds no near-term risk.
Within window
0.3 โ 1.3
ร0.95 โ 1.0
Inside its typical repose window; the rate is essentially unchanged.
Overdue
1.3 โ 2.5
ร1.25
Past its average repose โ the conditional probability is elevated.
Long overdue
ratio โฅ 2.5
ร1.45
Well beyond its average repose โ markedly elevated conditional probability.
The repose ratio is (years since last eruption) รท (mean recurrence interval). We only apply this adjustment when a data-derived recurrence exists โ never from an uncertain prior. The effect is deliberately bounded (0.9โ1.45ร) so it nudges, rather than dominates, the forecast.
Short-term precursors
For volcanoes with live seismic monitoring (Philippine volcanoes), the model analyzes the local earthquake catalog for five families of precursor. Each multiplies the base rate; their product is capped at ร10.
What it means: The slope of the magnitudeโfrequency distribution. A low b-value (<0.7) means relatively more large quakes โ a sign of high differential stress. A high b-value (>1.3) means many small, similar events โ a fluid/swarm signature common at volcanoes.
In the model: analyzeBValue() estimates b by maximum likelihood (Aki 1965) above a data-driven completeness magnitude Mc (Wiemer & Wyss 2000, maximum curvature). A low or high anomaly raises the rate (ร1.3 / ร1.2).
GutenbergโRichter (1944); Aki (1965); Wiemer & Wyss (2000)
What it means: Earthquakes that get systematically shallower over days to weeks can trace magma ascending toward the surface โ one of the clearest mechanical precursors to an eruption.
In the model: analyzeDepthMigration() fits hypocenter depth against time. Coherent shallowing โฅ0.5 km/day (with Rยฒโฅ0.3) is flagged; rapid shallowing โฅ2 km/day is critical and multiplies the rate up to ร2.5.
Roman & Cashman (2006)
What it means: As rock approaches failure, events speed up. The Failure Forecast Method projects a possible failure time from the inverse event rate trending toward zero.
In the model: analyzeAcceleration() fits the daily event rate; a positive, well-fit trend is classed as linear / exponential / power-law (ร1.3 โ ร2.0). A power-law inverse-rate fit can project a tentative peak date.
Voight (1988); Kilburn (2003)
What it means: A large nearby earthquake can perturb a magma or hydrothermal system through static (Coulomb) stress transfer and dynamic (seismic-wave) shaking, modestly raising eruption odds for years afterward.
In the model: analyzeTriggeringEvents() tests each quake against Nishimura (M7.5+, โค200 km, 5 yr), Jenkins (M7.0+, โค750 km, 4 yr) and Manga & Brodsky (M8.0+, โค5000 km, 1 yr). The effect decays linearly over its window.
Coulomb (1785) / King et al. (1994); Nishimura (2017); Jenkins et al. (2024); Manga & Brodsky (2006)
What it means: Bursts of similar-sized quakes with no clear mainshock โ swarms โ indicate fluid migration or stress concentration beneath the edifice. Clusters on opposite sides ('bracketing') can mark a pressurizing source.
In the model: identifyClusters() groups near-field events by direction and time. Swarms, shallowing clusters and bracketing geometry each add a multiplier (capped at ร3 combined).
Seismic cluster analysis; McNutt (1996)
When a volcano has little or no live monitoring data, these precursors simply return a neutral ร1 โ the forecast falls back to the base rate and repose, and its confidence is reported as lower.
PHIVOLCS alert levels
The alert level (0โ5) is the authoritative, expert-assessed measure of unrest. It scales the rate, and โ crucially โ sets a probability floor that encodes PHIVOLCS's near-term judgement. The final probability is the larger of the model output and that floor.
| Level | Meaning | Rate factor | 1-yr floor |
|---|---|---|---|
| 0Normal | No significant unrest; eruption not expected in the near term. | ร1 | โ |
| 1Low-level unrest | Abnormal but low-level activity; slightly elevated chance of steam-driven events. | ร1.5 | 8% |
| 2Increasing unrest | Probable magmatic unrest; heightened chance of eruption. | ร4 | 30% |
| 3Magma at shallow depth | Hazardous eruption possible within days to weeks. | ร12 | 70% |
| 4Intense unrest | Hazardous eruption imminent (within days). | ร40 | 92% |
| 5Eruption in progress | Hazardous eruption underway. | ร150 | 99% |
The multipliers are deliberately modest so a frequently-erupting volcano at a low alert level isn't pushed to extreme risk by the alert factor alone โ the floors carry the alert-implied minimum. For example, Alert Level 3 guarantees at least a 70% one-year (35% 30-day) probability, matching PHIVOLCS's "hazardous eruption possible within weeks" assessment.
Putting it together
Every factor multiplies the previous one to build the effective annual rate ฮป, which the Poisson model turns into the probabilities you see on a volcano page.
Base rate
ฮปโ
GVP eruption frequency: count รท record length.
ร Precursors
ร1โ10
Seismic signals: b-value, depth, acceleration, triggering, swarms.
ร Alert level
ร1โ150
PHIVOLCS alert level 0โ5 โ the dominant near-term signal.
ร Repose
ร0.9โ1.45
Renewal 'overdue' adjustment from time since last eruption.
Poisson
1 โ e^(โฮปt)
Effective rate ฮป โ probability over window t.
Output
P + level
1-year & 30-day probability, risk level & confidence.
ฮป = base rate ร precursor product ร alert factor ร repose factor ร recent-episode factor. Then P(โฅ1 eruption in t) = 1 โ e^(โฮปt), with the PHIVOLCS alert-level floor applied as a minimum.
Confidence
HIGH
Dense monitoring network (10+ stations) and ample local seismicity (50+ events). Precursors are well constrained.
Confidence
MEDIUM
A monitoring network and a multi-eruption GVP history, but with meaningful uncertainty in the short-term signals.
Confidence
LOW
Sparse monitoring or few local earthquakes. The forecast leans on the base rate and repose, with wide uncertainty.
How to read a forecast
What each figure on a volcano page actually means.
The chance of at least one eruption in the next 12 months. A 20% figure means roughly a 1-in-5 chance over the year โ not that an eruption is due.
The same idea over the next month. It is always smaller than the 1-year figure, and most useful when a volcano is in active unrest.
A plain-language band (Background โ Critical) derived purely from the 1-year probability โ e.g. โฅ20% is HIGH, โฅ50% is CRITICAL.
1 รท base rate: the typical interval between eruptions from history. Context for the base rate, not a countdown.
How much data constrains the estimate. LOW confidence means treat the number as a rough order of magnitude.
Whether active unrest is currently pushing risk above the long-run baseline (rising), at it (steady), or below it (easing).
Volcanic eruptions are inherently uncertain. Volcanoes can erupt with little warning, or show strong precursors and never erupt. This model produces statistical estimates, not predictions.
FAQ
Eruptions are forecast probabilistically, not predicted exactly. QuakeGlobe uses a Poisson event model: a long-term base rate from the volcano's eruption history is adjusted by short-term signals โ seismic precursors, the official alert level, and time since the last eruption โ to give a 1-year and 30-day eruption probability.
No. Eruptions are inherently uncertain. Models estimate the probability of an eruption over a time window and flag rising unrest; they cannot give an exact date. Always follow official agencies such as PHIVOLCS or the USGS for warnings.
The base rate is how often a volcano erupts on average โ its confirmed-eruption count divided by the length of its documented record, from the Smithsonian Global Volcanism Program. It is the long-run anchor that short-term signals adjust up or down.
Key precursors are a shifting b-value (changing stress), earthquakes migrating shallower (magma ascent), accelerating seismicity (rock approaching failure), triggering by large nearby earthquakes, and earthquake swarms beneath the volcano.
References
The peer-reviewed research and authoritative data sources the model is built on.
Statistical analysis of New Zealand volcanic occurrence data โ renewal models of repose.
Probabilistic eruption forecasting at short and long time scales. Bull. Volcanol.
Minimum magnitude of completeness in earthquake catalogs (maximum-curvature Mc). BSSA.
A method for prediction of volcanic eruptions โ the Failure Forecast Method. Nature.
Multiscale fracturing as a key to forecasting volcanic eruptions. JVGR.
The origin of volcano-tectonic earthquake swarms โ depth migration of seismicity. Geology.
Triggering of volcanic eruptions by large earthquakes. Geophys. Res. Lett.
Volcanoes of the World database โ confirmed-eruption frequencies.
Volcano Alert Level System and monitoring bulletins.