Multiscale Variability of Solar Irradiance at Earth: Reference amplitudes from minutes to gigayears

Solar irradiance data from across the literature can't be added together without first fixing a bookkeeping problem that inflates energy budgets by an order of magnitude.

The core issue is that published irradiance amplitudes look like they're measuring the same thing but aren't. A 0.1% solar-cycle variation is a fraction of total solar irradiance at Earth's mean distance. A 13% precessional variation is a fraction of a local seasonal insolation diagnostic at 65°N. These have different denominators and can't be summed. On top of that, some listed "periods" — like the 405,000-year eccentricity cycle — aren't independent oscillators at all; they modulate the amplitude of shorter cycles whose variance is already counted. Adding them as separate sinusoids double-counts the same energy. And many tables don't say whether they're quoting peak-to-peak amplitude or semi-amplitude, an ambiguity of 2× in amplitude and 4× in variance.

This paper fixes the bookkeeping. It builds a reference table spanning minutes to gigayears under explicit conventions: all amplitudes are peak-to-peak, every local insolation entry names the exact diagnostic it summarizes (because "65°N summer insolation" is undefined until you specify what counts as summer), and every percentage is normalized to the present-day value of its own diagnostic. The orbital and local entries are computed from first principles rather than copied from other tables, and the implementation is validated against Huybers (2006) — reproducing four specific insolation values and recovering an eccentricity value (~0.05) that the original source left implicit. A sensitivity sweep shows that fractional amplitudes (obliquity ~5.7%, precession ~13.8%) are stable to 3% across a wide range of summer-window definitions, while the corresponding absolute values in W/m² drift by up to 22%. The fraction is the transferable quantity; the absolute value is not.

For displaying variance across thirteen decades of period, the paper uses variance density per logarithmic period, D(P) = f·S(f), rather than a conventional power spectral density. This weights each decade equally so that area on the plot corresponds to actual variance — and it makes envelope double-counting visible, since a term with no independent variance contributes no area.

The practical payoff connects to WP0202, which studies planetary regulation on a Daisyworld and needs a forcing that is simultaneously stochastic and partially predictable. Solar forcing has exactly that structure for physical reasons: the orbital component (eccentricity, obliquity, precession) is deterministic and computable up to the ~50 Myr Solar System chaos horizon, while the magnetic component (sunspot cycles, grand minima/maxima) is broadband and stochastically driven. This paper supplies the clean forcing specification that WP0202 requires, with the energy budget correctly normalized so the regulation studies don't inherit inflated numbers.