Time Predictable Next Eruption Estimator

Fit the time-predictable previous-eruption-volume/subsequent-repose hypothesis and interpolate a last-volume scenario; this historical calibration is not a reliable next-eruption date or an uncertainty interval.

Description

A time-predictable hypothesis links the size of a previous eruption to the subsequent recharge interval.

A time-predictable hypothesis links the size of a previous eruption to the subsequent recharge interval. Regression estimates that historical relationship.

When to use Time Predictable Next Eruption Estimator

Use this tool to fit the time-predictable previous-eruption-volume/subsequent-repose hypothesis and interpolate a last-volume scenario; this historical calibration is not a reliable next-eruption date or an uncertainty interval.

Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.

How to use Time Predictable Next Eruption Estimator and understand its results

Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
Enter previousEruptionDreVolumesM3, subsequentReposeIntervalsYears, lastEruptionDreVolumeM3, lastEruptionYear using the field table and calculation rules, then run the tool.
Read fittedRechargeYearsPerM3, modelNextIntervalYears, modelNextEruptionYear, fitRSquared. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
previousEruptionDreVolumesM3	Previous eruption dre volumes m3	list of number	Required
subsequentReposeIntervalsYears	Subsequent repose intervals years	list of number	Required
lastEruptionDreVolumeM3	Last eruption dre volume m3	number	Required
lastEruptionYear	Last eruption year	number	Required

Enter aligned positive past volumes and subsequent intervals. Fit ordinary least squares, require a positive slope, and evaluate only within the observed volume range. Report slope, interval, next-year scenario and R².^[1]

The least-squares fit needs at least two aligned observations and a varying independent variable; a constant dependent variable has reported R² of 1.

interval = intercept + slope × last DRE volume; year = last year + interval

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
fittedRechargeYearsPerM3	Fitted recharge years per m3	number
modelNextIntervalYears	Model next interval years	number
modelNextEruptionYear	Model next eruption year	number
fitRSquared	Fit r squared	number

json

{
  "input": {
    "previousEruptionDreVolumesM3": [
      1,
      2,
      3
    ],
    "subsequentReposeIntervalsYears": [
      2,
      4,
      6
    ],
    "lastEruptionDreVolumeM3": 2.5,
    "lastEruptionYear": 2000
  },
  "output": {
    "fittedRechargeYearsPerM3": 2,
    "modelNextIntervalYears": 5,
    "modelNextEruptionYear": 2005,
    "fitRSquared": 1
  }
}

Limitations and assumptions

No extrapolation or uncertainty interval. The fitted scenario does not establish an actual next-eruption date.

Numbers and computed results must be finite; overflow produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Repose Interval Recurrence Mean: Summarize complete historical repose intervals separately from right-censored time since last onset; not a survival-corrected mean recurrence estimator or deterministic next-event forecast. For a complementary task, use Weibull Repose Failure Probability: Evaluate conditional Weibull renewal probability given no event through elapsed repose, using supplied fitted parameters and stable hazard increments; model probabilities are not validated volcano-specific eruption risk.

References

Time Predictable Next Eruption Estimator — tool.io

Similar or alternative tools

Repose Interval Recurrence Mean
Summarize complete historical repose intervals separately from right-censored time since last onset; not a survival-corrected mean recurrence estimator or deterministic next-event forecast.
Weibull Repose Failure Probability
Evaluate conditional Weibull renewal probability given no event through elapsed repose, using supplied fitted parameters and stable hazard increments; model probabilities are not validated volcano-specific eruption risk.