Warm Spell Duration Index WSDI

Calculate warm WSDI maximum-temperature spells against caller independently calibrated day-of-year percentiles with strict exceedance and minimum run; threshold ties excluded, gap-free coverage required.

Description

Warm spell duration measures time spent in sustained unusually warm conditions.

Warm spell duration measures time spent in sustained unusually warm conditions. An exceedance threshold can vary with the day of year; counting whole qualifying runs distinguishes persistent warmth from isolated hot days.^{[1, 2]}

When to use Warm Spell Duration Index WSDI

Use this tool to calculate warm WSDI maximum-temperature spells against caller independently calibrated day-of-year percentiles with strict exceedance and minimum run; threshold ties excluded, gap-free coverage required.

Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.

How to use Warm Spell Duration Index WSDI and understand its results

Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
Enter dailyExtremesC, callerDayOfYearPercentileThresholdsC, callerMinimumSpellDays using the field table and calculation rules, then run the tool.
Read qualifyingSpellStartIndices, qualifyingSpellLengthsDays, spellDurationIndexDays. 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
dailyExtremesC	Daily extremes c	list of number	Required
callerDayOfYearPercentileThresholdsC	Caller day of year percentile thresholds c	list of number	Required
callerMinimumSpellDays	Caller minimum spell days	integer	Required

Enter aligned daily maximum temperatures and caller-supplied daily thresholds in °C, plus a positive integer minimum spell length. A day qualifies only when its temperature is strictly above its matching threshold. The tool finds maximal consecutive qualifying runs, retains those meeting the minimum length, and returns their zero-based start indices, lengths and total days. Empty or unequal-length lists are rejected.

Paired lists must be nonempty and have equal lengths.

warm_i = (Tmax_i > threshold_i); WSDI = Σ length of each warm run with length ≥ minimum spell length

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

Output field	Meaning	Value type
qualifyingSpellStartIndices	Qualifying spell start indices	list of number
qualifyingSpellLengthsDays	Qualifying spell lengths days	list of number
spellDurationIndexDays	Spell duration index days	number

json

{
  "input": {
    "dailyExtremesC": [
      20,
      20,
      5,
      20
    ],
    "callerDayOfYearPercentileThresholdsC": [
      10,
      10,
      10,
      10
    ],
    "callerMinimumSpellDays": 2
  },
  "output": {
    "qualifyingSpellStartIndices": [
      0
    ],
    "qualifyingSpellLengthsDays": [
      2
    ],
    "spellDurationIndexDays": 2
  }
}

Limitations and assumptions

The tool does not calculate percentile thresholds or a reference climatology. Supply a gap-free daily sequence and the appropriate thresholds yourself. Runs at the edges of the supplied window can continue outside it; the reported duration describes only the supplied observations.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value 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 Wet Spell Length Analyzer: Analyze full consecutive wet spell distribution at a caller inclusive precipitation threshold; supplied sequence must have no missing days and zero means no observed qualifying spell. For a complementary task, use Growing Season Length GSL: Locate thermal growing-season onset/end under caller threshold/run and hemisphere-specific cold-end search index; preserve left-censored onset and right-censored end, without assigning dates outside supplied gap-free coverage.

Further background: Climate extreme index definitions.

References

Warm Spell Duration Index WSDI — tool.io
Climate extreme index definitions — Climdex

Similar or alternative tools

Wet Spell Length Analyzer
Analyze full consecutive wet spell distribution at a caller inclusive precipitation threshold; supplied sequence must have no missing days and zero means no observed qualifying spell.
Growing Season Length GSL
Locate thermal growing-season onset/end under caller threshold/run and hemisphere-specific cold-end search index; preserve left-censored onset and right-censored end, without assigning dates outside supplied gap-free coverage.