Why can I not see the pressure or the regime?

Because no observatory can. Every number on the screen is synthesized from the hidden state and then corrupted — Poisson counts, log-normal amplitudes, instrument noise, dead batteries, telemetry gaps in the rain. That gap between the state and the record is the whole job.

What is the Brier score?

The standard way of scoring a probabilistic forecast. Every day your stated probability of an eruption in the next seven days is banked; a week later it is compared with what happened and the squared difference is added up. Always saying 50% scores 0.25. Saying 5% every day at a volcano that does not erupt scores about 0.0025. Saying 95% the day before it goes scores almost nothing.

The alert was at Warning for a month and nothing happened. Why did my credibility fall?

Because that is what happens. Compliance with an evacuation order is not a constant — it is the memory of how often you have been right. The model ties the fraction of a town that actually leaves to a credibility number that falls while you hold a high alert on a quiet volcano and rises slowly when you do not.

Why did my field team die?

You sent them up to service a station during an ascent or an eruption. Maintenance visits have a real casualty rate in exactly the conditions that make the data most valuable. Deciding not to go is also a decision.

Observatory — The mountain will not tell you. The instruments only hint.

You are the duty scientist. You are the duty scientist at a volcano observatory. Somewhere under the summit a magma reservoir is filling, or emptying, or doing nothing at all — and you cannot see it. What you have is a handful of instruments you paid for out of a fixed budget, a town or five in the valleys, an alert level, and a public that stops believing you the third time you are wrong. Call it too late and people die. Call it too early, too often, and nobody leaves when it matters.

Timescale: 6–12 months. Model: Hidden-Markov magma system with an elastic reservoir, Mogi point-source deformation, Poisson/Gutenberg–Richter seismicity, an energy-cone PDC and an advecting Gaussian ash plume.

What you will learn

Why seismicity tracks the rate of pressurisation and not the pressure — and why a quiet volcano can still be dangerous.
What ground deformation actually measures, and how a Mogi source turns centimetres of uplift into a magma volume.
Why a failed eruption looks exactly like a real one until the moment it stops.
What a false alarm costs, in a currency that is not money.

Scenarios

Sandbox — Nine months, every dial, nothing scored.
Escalation — A stratovolcano with clear precursors. Get the town out in time.
Quiet Mountain — Nine months of unrest that never becomes an eruption. Hold your nerve.
Lahar Season — The eruption is over. The rains are not.
Shield Effusion — Lava, a village, and months to think about it.

What you control

Type — Sets the shape of the edifice, the eruption-size distribution, and therefore which hazards you have to worry about.
Magma supply (×) — How fast the reservoir fills during unrest, as a multiple of the base rate. Higher means shorter fuses.
Wall strength (MPa) — The excess pressure at which a dike leaves the reservoir. A strong wall means longer, larger build-ups and bigger eruptions when they come.
Regime persistence — How long the system stays in one state. Low persistence means short bursts of unrest that die away — the false alarms.
Chance a dike stalls — The fraction of ascending dikes that freeze before they reach the surface. Every one of them is a swarm that escalates and then stops.
Instrument noise — Scales the scatter on every measurement: hypocentre location, tilt drift, RSAM. The difficulty dial.
Automatic alert rule — Raise the alert to Watch automatically when RSAM crosses the threshold below. It reacts faster than you do and it has no judgement at all.
RSAM threshold (units) — The trigger for the automatic rule. Set it low and the wind will evacuate a town.

Questions

Why can I not see the pressure or the regime?: Because no observatory can. Every number on the screen is synthesized from the hidden state and then corrupted — Poisson counts, log-normal amplitudes, instrument noise, dead batteries, telemetry gaps in the rain. That gap between the state and the record is the whole job.
What is the Brier score?: The standard way of scoring a probabilistic forecast. Every day your stated probability of an eruption in the next seven days is banked; a week later it is compared with what happened and the squared difference is added up. Always saying 50% scores 0.25. Saying 5% every day at a volcano that does not erupt scores about 0.0025. Saying 95% the day before it goes scores almost nothing.
The alert was at Warning for a month and nothing happened. Why did my credibility fall?: Because that is what happens. Compliance with an evacuation order is not a constant — it is the memory of how often you have been right. The model ties the fraction of a town that actually leaves to a credibility number that falls while you hold a high alert on a quiet volcano and rises slowly when you do not.
Why did my field team die?: You sent them up to service a station during an ascent or an eruption. Maintenance visits have a real casualty rate in exactly the conditions that make the data most valuable. Deciding not to go is also a decision.

What this model cannot do

The reservoir is a single point source with one pressure. Real systems have several, connected, at different depths, and much of the interesting behaviour lives in the plumbing between them.
The regimes are a Markov chain fitted to nothing. Real unrest has memory, and the sequence of precursors at one volcano is a poor guide to the next.
Deformation is elastic and instantaneous. Real edifices creep, and much of the observed signal at long-lived unrest is viscoelastic relaxation rather than fresh magma.
The hazard footprints are first-order sketches, not simulations. An energy cone knows nothing about topographic channelling, a Gaussian plume nothing about wind shear with height, and the lahar router nothing about erosion or bulking.
Nobody has ever forecast an eruption this cleanly. The precursors here are more legible and better behaved than the real thing, because a sim in which the answer is genuinely unknowable is not a game.

Sources

Mogi, K. (1958) Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them — Bulletin of the Earthquake Research Institute 36, 99–134. The point source.
Sheridan, M. F. (1979) Emplacement of pyroclastic flows: a review — The energy-cone construction still used for first-order PDC hazard maps.
Mastin, L. G. et al. (2009) A multidisciplinary effort to assign realistic source parameters to models of volcanic ash-cloud transport — Journal of Volcanology and Geothermal Research 186, 10–21. The H = 0.24·Q^0.25 scaling.
Sparks, R. S. J. (2003) Forecasting volcanic eruptions — Earth and Planetary Science Letters 210, 1–15. Why precursors are ambiguous.
Newhall, C. & Hoblitt, R. (2002) Constructing event trees for volcanic crises — Bulletin of Volcanology 64, 3–20. Where probabilistic forecasting at observatories comes from.
Brier, G. W. (1950) Verification of forecasts expressed in terms of probability — Monthly Weather Review 78, 1–3.