Standardized Precipitation Evapotranspiration Index SPEI Calculator

SPEI standard-normal transform of an independently season/aggregation-matched precipitation-minus-PET CDF calibration. Water balance may be signed; no automatic log-logistic fit or tail extrapolation. Caller independently establishes homogeneous observation coverage and model/reference applicability; not observed future climate, crop suitability or validated drought severity.

Description

A standardized precipitation-evapotranspiration index uses a calibrated water-balance distribution.

A standardized precipitation-evapotranspiration index uses a calibrated water-balance distribution.^[1]

This tool maps supplied probabilities rather than fitting that distribution or calculating evapotranspiration. Use Standardized Precipitation Evapotranspiration Index SPEI Calculator to evaluate the supplied inputs under the model explained below.

When to use Standardized Precipitation Evapotranspiration Index SPEI Calculator

Use Standardized Precipitation Evapotranspiration Index SPEI Calculator to evaluate the supplied inputs under the model explained below. Establish the units, measurement scope and model assumptions before entering values.

How to use Standardized Precipitation Evapotranspiration Index SPEI Calculator and understand its results

Establish the units, measurement scope and model assumptions before entering values.
Enter Independently calibrated water balance coordinates, Independently calibrated water balance cdf, Observed matched water balance using the field table and validation rules below, then run the tool.
Read Conditional standard normal index, Matched cdf probability; interpret the units, signs, ordering and unknown-value placeholders described below.
Correct reported input errors and rerun. Apply successful results according to their specific meanings and check the assumptions before using them in a decision.

Input field	Meaning	Value type	Requirement
independentlyCalibratedWaterBalanceCoordinates	Independently calibrated water balance coordinates	array of number	Required; constraints below
independentlyCalibratedWaterBalanceCdf	Independently calibrated water balance cdf	array of number	Required; constraints below
observedMatchedWaterBalance	Observed matched water balance	number	Required; constraints below

Enter at least two strictly increasing finite water-balance coordinates, aligned nondecreasing CDF values from 0 to 1 and a finite observation within the range. Water-balance coordinates may be negative. Interpolate the CDF and use the inverse-standard-normal approximation; the resulting probability must be strictly between 0 and 1. No rainfall-minus-ET calculation, distribution fitting or accumulation-period choice occurs.

p=interpolatedCalibratedCDF(observedWaterBalance); conditionalIndex=Φ⁻¹(p), requiring 0<p<1

Use the field order, units and branch conditions described above.

Output field	Meaning	Value type
conditionalStandardNormalIndex	Conditional standard normal index	number
matchedCdfProbability	Matched cdf probability	number

json

{
  "input": {
    "independentlyCalibratedWaterBalanceCoordinates": [
      -1,
      0,
      1
    ],
    "independentlyCalibratedWaterBalanceCdf": [
      0.1,
      0.5,
      0.9
    ],
    "observedMatchedWaterBalance": 0
  },
  "output": {
    "conditionalStandardNormalIndex": 0,
    "matchedCdfProbability": 0.5
  }
}

Limitations and assumptions

This tool maps supplied probabilities rather than fitting that distribution or calculating evapotranspiration. Apply the exact scope and assumptions explained above.

All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse arrays fail validation. Domain-specific bounds, alignments and supported tokens are explained above; extremely large inputs or outputs can also be rejected. Input errors differ from successful false results, empty match lists and unknown-evidence placeholders.

Alternative or Complementary methods

Use Standardized Precipitation Index SPI Calculator for a related task: A standardized precipitation index maps a calibrated probability onto a standard-normal scale.

Use Palmer Drought Severity Index Simplified Calculator for a related task: A simplified Palmer recurrence carries a previous state through monthly anomaly inputs.

References

Standardized Precipitation Evapotranspiration Index SPEI Calculator — tool.io

Similar or alternative tools

Standardized Precipitation Index SPI Calculator
A standardized precipitation index maps a calibrated probability onto a standard-normal scale.
Palmer Drought Severity Index Simplified Calculator
A simplified Palmer recurrence carries a previous state through monthly anomaly inputs.