Regime B · spectral analysis, 0–2000 ka

Real orbital periodicities, or artefacts of tuning and smoothing?

The 100, 41 and 23 kyr bands sit close together, every record is red, and the most-used chronology was built by aligning the record to the forcing it is tested against. Each claim here is judged against a null that knows all three.

Window (scopes everything below)

321 samples · multitaper NW = 2.5 · 23/19-kyr lines resolved

The records on their own chronologies

Signed so up = warmer / less ice / stronger monsoon; each in its own units

LR04 benthic stack (tuned)

EPICA Dome C (partly tuned)

Cheng 2016 speleothems (U-Th, untuned)

Age (ka BP)

Bin-averaged onto a regular 2 ka grid (2.5 ka before the MPT). LR04 is tuned to 65°N insolation, EPICA's EDC3 chronology is glaciological with some orbital tie points, and Cheng 2016 is U-Th dated with no orbital assumption.

Spectra against a red-noise background

Multitaper power (log scale) and the 95% level of a fitted AR(1)

LR04 benthic stack (tuned)

spectrum
AR(1) 95%

EPICA Dome C (partly tuned)

spectrum
AR(1) 95%

Cheng 2016 speleothems (U-Th, untuned)

spectrum
AR(1) 95%

Frequency (cycles per kyr); labels give the period in kyr

A peak must clear the AR(1) 95% level to count; orbital periods marked. Band enrichment is the observed share of power in a band divided by the AR(1) median share, tested against 1000 AR(1) surrogates.

Coherence with the forcing, tested against the record's own surrogates

Filled: significant after Benjamini–Hochberg · tick: 95th percentile of 500 record surrogates

LR04 benthic stack (tuned)
EPICA Dome C (partly tuned)
Cheng 2016 speleothems (U-Th, untuned)
hollow = not significant

Phase-randomising the record keeps its spectral lines, so coherence must reflect the forcing's modulation pattern, not just a shared period. The analytic multitaper level would be anti-conservative here. Positive lag: the record lags the forcing.

How much coherence does tuning manufacture?

Red noise with LR04's spectrum, aligned to a 65°N-insolation target by slope-limited dynamic time warping

23 kyr, against precession

tuned noise, median
tuned noise, 95th pct.
Cheng 2016 re-tuned

41 kyr, against obliquity

tuned noise, median
tuned noise, 95th pct.
Cheng 2016 re-tuned

With ±10 ka of freedom, tuned noise reaches a median coherence of 0.85 at 23 kyr against LR04's published 0.83. Re-tuning the untuned Cheng record by ±6 ka lifts its 41-kyr coherence from 0.57 to 0.95. DTW is more aggressive than LR04's tie-point tuning, so these are upper bounds for a given age freedom.

LR04 through the mid-Pleistocene transition

Morlet wavelet power; outlined cells exceed AR(1) 95%; faded cells lie in the edge-effect zone

Loading wavelet…

The 100/41-kyr power ratio is 4.29 over 0–700 ka and 0.15 over 1250–2000 ka. The forcing did not change character across the transition, but the response did.

Linear responses to orbital forcing

τ is chosen by blocked cross-validation (5 blocks, 10 ka embargo). The surrogate p re-fits every τ for each of 500 phase-randomised copies of the record, so the freedom to pick τ is paid for.

Linear response models
Record	Model	τ (ka)	R²	CV R²	Null R² p95	p	100-kyr fit / obs
LR04 benthic stack (tuned)	one_pole_Q65N	13	0.232	0.218	0.115	0.002	0.001 / 0.271
LR04 benthic stack (tuned)	one_pole_local	13	0.232	0.218	0.115	0.002	0.001 / 0.271
LR04 benthic stack (tuned)	orbital_regression	7	0.348	0.224	0.242	0.004	0.026 / 0.271
EPICA Dome C (partly tuned)	one_pole_Q65N	10	0.201	0.167	0.117	0.002	0.000 / 0.218
EPICA Dome C (partly tuned)	one_pole_local	16	0.020	-0.005	0.118	0.854	0.000 / 0.218
EPICA Dome C (partly tuned)	orbital_regression	7	0.277	0.107	0.237	0.014	0.009 / 0.218
Cheng 2016 speleothems (U-Th, untuned)	one_pole_Q65N	3	0.520	0.517	0.270	0.002	0.000 / 0.027
Cheng 2016 speleothems (U-Th, untuned)	one_pole_local	5	0.542	0.539	0.301	0.002	0.001 / 0.027
Cheng 2016 speleothems (U-Th, untuned)	orbital_regression	3	0.572	0.552	0.381	0.002	0.001 / 0.027