Solar Irradiance Analysis
Long-term structure, a strong repeating cycle, and a long interval in the seventeenth century where the cycle is absent.
Key takeaways
- – An approximately eleven-year cycle dominates most of the record.
- – Between roughly 1645 and 1715 the cycle is largely absent — a genuine feature of the data, not a modelling artefact.
- – A model without a changepoint component describes the quiet interval badly and inflates residual noise across the whole series.
- – The long-run level drifts slowly; the drift is small relative to the cycle.
Executive summary
The series is best described by a periodic component with a period near eleven years, modulated by a changepoint structure that switches the cycle off during the Maunder minimum, over a slowly varying baseline.
Dataset
Annual reconstructed total solar irradiance, 1610–2011, 402 observations. Reconstructions before the satellite era carry substantially more uncertainty than later values; this analysis treats the series as observed and does not propagate reconstruction error.
Observed structure
Sunspot-driven cyclic behaviour is visible across most of the record, with amplitude varying between cycles. The seventeenth-century interval is conspicuously flat.
Structural components
| Component | Structure | Interpretation |
|---|---|---|
| 1 | PER | Approximately eleven-year cycle |
| 2 | CP × PER | Cycle suppressed during 1645–1715 |
| 3 | SE | Slow baseline variation |
| 4 | WN | Observation noise |
TABLE 1 — Discovered components
Model criticism and limitations
Fitting a single periodic component without the changepoint produces systematically poor residuals in the quiet interval and understates the amplitude elsewhere, because one variance has to cover both regimes. This is the clearest illustration in the classic examples of why a model needs permission to say that behaviour changed.
The reconstruction itself is a model output, not a direct measurement, for most of the record. Conclusions about absolute levels should be treated accordingly.
Related methods
Periodic kernels, changepoint detection and the treatment of forecast uncertainty.