Robustness

Which conclusions survive a change of mind?

Temporal aggregation, baseline period, variable and dataset, which orbital terms are allowed, detrending, spectral resolution, resampling, smoothing and chronology error. Some results do not move at all; others move a lot, and the paper is scoped to match.

Smoothing manufactures orbital peaks, unless the null knows about it

Pure AR(1) noise, φ = 0.942 (matched to LR04 at 2 ka), n = 401, 100 replicates

100-kyr band

naive null
smoothing-aware null

41-kyr band

naive null
smoothing-aware null

False-positive rate at α = 0.05 after a running mean. The naive test fits an AR(1) to the smoothed series; the aware test fits it to the raw series and passes every surrogate through the same smoother. The Slutsky–Yule effect in numbers.

A counterfactual orbit can fit better than the real one

R² of the admissible one-pole model, Berkeley Earth

real forcing
circular orbit (obliquity only)
eccentricity only (no tilt)

Real forcing against two counterfactuals with the same model and constraints. In the SH ocean an eccentricity-only forcing fits as well as the real one; in tropical land a circular orbit fits far better. Shape-based fits cannot tell the orbital terms apart, so a good fit is not evidence of cause.

Coarser aggregation inflates everything

Eccentricity detectability ratio by temporal resolution (NCEP)

monthly (9 residual dof)
bimonthly (3)
seasonal (1)

With seasonal means only one residual degree of freedom remains: R² reaches 1.000 and the ratio's denominator collapses, so values above 1 there are artefacts. The paper states the identifiability result at monthly resolution.

Precession coherence needs an accurate clock

Median coherence at 23 kyr under random age-model error (40 draws each)

LR04
EPICA Dome C
Cheng 2016

A smooth, stationary age error (correlation length 20 ka) is added to each chronology. Coherence at the observed level survives only if age errors are well under ~2 ka, so a record showing it either has an excellent independent chronology or was aligned to the forcing.

Which orbital predictor carries each record?

Cross-validated R² of a one-pole linear response; filled = beats 300 phase-randomised surrogates (p < 0.05)

LR04
EPICA Dome C
Cheng 2016

EPICA's linear orbital signal is carried by obliquity, not precession, and its local summer insolation performs worst. LR04 needs all four elements to reach R² ≈ 0.28. The monsoon record is almost entirely precession. Eccentricity alone explains little anywhere.

Explore every row

2,939 statistics across 14 axes. Pick an axis and a statistic; rows are regions (A) or records (B), columns are settings.

AxisStatistic

baseline_period: r2_ebm
Region	1951-1980	1981-2010	1991-2020	1948-2024
NH extratropics \| land	0.998	0.997	0.997	0.998
NH extratropics \| ocean	0.992	0.991	0.989	0.991
SH extratropics \| land	0.996	0.994	0.994	0.996
SH extratropics \| ocean	0.998	1.000	1.000	1.000
Tropics \| land	0.315	0.183	0.196	0.248
Arctic \| all	0.992	0.989	0.985	0.989
Sahel	0.934	0.973	0.970	0.958
Southern Ocean	0.998	0.999	0.999	0.999
Global \| all	0.000	0.000	0.000	0.000