A reproducible research study
How much seasonal-climate variability does orbital forcing explain?
Most monthly temperature variance on Earth is the seasonal cycle, and a physical response to orbital sunlight with one timescale per surface reproduces nearly all of it. That is the easy half. The hard half is what such a fit licenses you to say, and on every time scale tested here the answer is less than it first appears.
What the study found
- 01
The seasonal cycle is a physical response to sunlight, in the extratropics
One relaxation time per surface does it: median τ of 27 days over land and 126 over ocean. With one τ and one gain shared across NH land, the model predicts the seasonal cycle of latitude bands it never saw at R² = 0.992, against 0.913 for a forcing-free description.
- 02
A better fit is not a better explanation
Global-mean temperature is anti-correlated (r = −0.95) with the global-mean insolation cycle, which is purely eccentricity-driven. An unconstrained fit “explains” it with R² = 0.999 using a negative gain: more sunlight, colder. In tropical land a circular-orbit forcing fits better (R² 0.966) than the real one (0.291).
- 03
Eccentricity shapes the seasonal forcing but cannot be identified in the response
At monthly resolution, the most R² eccentricity could add is smaller than the model's own misfit in every one of the 29 admissible regions, in both datasets (largest ratio 0.91; identifiable needs more than 1). A free gain and lag absorb it.
- 04
Modern shifts in the timing of the seasons are not orbital
Precession moves the annual insolation cycle by at most 0.04 days per decade. Measured against insolation, so that Gregorian calendar drift cancels, observed shifts are larger, change sign between windows, and disagree between NCEP and Berkeley.
- 05
On orbital time scales, precession survives an untuned clock; the 100-kyr cycle does not
The U-Th dated speleothem record is coherent with precession at 23 kyr (MSC 0.98, p = 0.002), and the ice core with obliquity. LR04's 100-kyr coherence with eccentricity fails its surrogate test (p = 0.054), and a linear insolation response reproduces 0.1% of LR04's variance in that band against the 21% observed.
- 06
Tuning and smoothing manufacture the evidence they are used to find
Red noise with LR04's spectrum, tuned with ±10 ka of freedom, reaches a median precession coherence of 0.85 against LR04's published 0.83. On smoothed pure noise, a naive red-noise test finds a 100-kyr peak 44% of the time; a smoothing-aware null, 0%.
Regime A · the seasonal cycle, 1948–2024
Present-day orbital geometry gives the daily and monthly insolation at every latitude. Monthly gridded temperature from a reanalysis and an independent observational product is compared with it cell by cell, row by row and region by region, with a model that can only lag and damp the real forcing.
Regime B · the orbital cycles, 0–2000 ka
The La2004 solution drives an ice-volume stack, an Antarctic ice core and a Chinese cave record. Because the most-used chronology was tuned to the forcing, every test is repeated on a record dated by uranium–thorium, and against a null that measures how much coherence tuning itself creates.
What this study does not show
- Causation. There is no intervention and no climate model; attribution statements rest on the physics of the forcing and on counterfactual forcings, and are scoped accordingly.
- Nonlinear responses. The orbital-scale tests are linear; ice-sheet dynamics that could turn eccentricity pacing into a 100-kyr cycle are outside scope.
- Ground truth at the surface. NCEP 2 m temperature is model-influenced and its surface shortwave is model-only; Berkeley Earth is the observational check.
- Exact tuning. The tuning null uses dynamic time warping, which is more aggressive than LR04's procedure, so its numbers are upper bounds for a given age freedom.
Data
- IMCCE La2004orbital elements, 1 kyr, 0–3 Ma
- NCEP/NCAR Reanalysis 12 m temperature and surface shortwave, monthly, 1948–2024
- Berkeley Earthland and ocean temperature, monthly, 1°
- LR04 benthic stackδ¹⁸O, 0–2 Ma (orbitally tuned)
- EPICA Dome Ctemperature, 0–800 ka (partly tuned)
- Cheng et al. 2016speleothem δ¹⁸O, 0–640 ka (U-Th dated, untuned)