Gamma-index: evaluating displaced irradiance forecasts

Cyril Voyant · Updated 2026-10-18

Research question

Pointwise errors can penalize a forecast structure that is displaced in time or space. The gamma-index asks whether a forecast value agrees with a nearby observation within explicitly chosen spatial, temporal and intensity tolerances.

Quantities and units

The index minimizes a joint normalized distance over a search neighbourhood. Gamma ≤ 1 marks agreement within the combined tolerance criterion. The Gamma Pass Rate is the percentage of evaluated points meeting that criterion; mean and maximum gamma complement it.

Reproduce the public example

The repository provides main.m with synthetic maps and the function computeGammaMetrics.m. Follow its MATLAB and toolbox requirements. Synthetic examples demonstrate the workflow and do not reproduce access-restricted satellite observations.

% From the downloaded repository directory:
main

Check physical pixel size, time-step units, temporal window and field alignment before using real data. Consult the function reference for the full signature.

Tolerances are part of the result

Choose tolerances from the application before comparing methods and report sensitivity. Looser tolerances increase acceptance; a high pass rate alone does not prove a useful forecast. The repository's example thresholds are not universal validation standards. Report pointwise errors alongside gamma and document edge effects and resampling.

Publication status and citation

The companion article, “A tolerance-based framework for spatiotemporal forecast validation using the γ-index”, is published in International Journal of Forecasting, 42(4), 1207–1214 (2026). Read the published article. The repository README retains an older review-status notice. Software DOI · Source, current citation and licence. Full MATLAB numerical execution was not performed during this documentation update.

Research explained

Read the findings, evidence and limits in these first-author research stories.