Islands across the sciences · climate · real data

Ice-age flips

During the last ice age, Greenland's climate jumped between a cold state and a warm one again and again, each warming taking only decades. Did those states end at random, or on a clock?

Sense of island: basin-island Data: NGRIP ice core, GICC05 timescale Tests computed once, 30 September 2026

Snow that fell on Greenland over the last hundred thousand years is still there, pressed into ice layer by layer. The ratio of heavy to light oxygen in each layer records how cold it was when the snow fell: the lower the number, the colder. Read down the ice, and the last ice age turns out not to have been steadily cold. The climate kept jumping into warm spells, within a few decades each time, stayed for centuries or millennia, slid back, and waited in the cold again. These are the Dansgaard-Oeschger events, named for the two scientists who found them.

Which sense of island. Each state, cold and warm, is a basin-island: a state the climate stayed in until something moved it out. That is the sense proposition 3 is stated in, and this is the first page on the site where it meets real measurements rather than a model.

The record

The record holds 6,113 measurements, one for every 20 years from 30 to 122,270 years before 2000. The frozen event rule finds 35 warmings and 34 coolings in the published list of events, counting the start of the present warm period and the separately numbered spells that some interstadials are split into.

The NGRIP oxygen-isotope ratio (per mil, higher is warmer) in 20-year means, oldest on the left. Green ticks mark each warming as defined by the frozen event rule, numbered as the Greenland interstadials are. Shaded bands are the cold periods between a cooling and the next warming. The last warming on the right is the start of the present warm period, the Holocene.

What the tests asked

Both tests were frozen before any age, duration or isotope value had been computed from these files, then deposited with a date and computed once. They replicate a known question under rules fixed in advance: the published readings disagree, and the author and Claude know them.

survives

C1. Are the cold spells memoryless?

If the warmings came at random, a cold spell that had already lasted a long time was no closer to ending than a fresh one. The test fits how the chance of ending changes with a cold spell's age. With about 30 cold spells it can see a strong pattern, not a mild one, and its thresholds say so.

no clock

C2. A 1,470-year clock?

One well-known reading found the warmings keeping time with a 1,470-year beat. If they did, their ages cluster at one phase of that cycle. The test checks exactly that period, declared in advance, with a strict threshold.

Warning signs before each warming, rising variability or memory in the last 400 years of each cold spell, are reported as a table without a verdict: with one measurement every 20 years there are too few points before each warming for a fair test, and finer data have been read both ways.

Results

The two tests were computed once, on 30 September 2026, after the frozen rules were deposited as 10.5281/zenodo.23066235. They draw no random numbers, and both verdicts follow the deposited rules.

Test	Bears on	Verdict	What was found
C1. Are the cold spells memoryless?	P3	survives	The Weibull shape of the 34 cold spells' lengths was 0.97 (0.74 to 1.22), where memoryless is 1. Survival needed an interval that holds 1 and lies within 0.6 to 1.6.
C2. A 1,470-year clock?	P3	no clock	At the period declared in advance, the phases of the 35 warmings did not cluster: Rayleigh p = 0.71, where a clock needed less than 0.01.

Reported without a verdict, as the rules require:

Warm spells: the same fit gives a shape of 0.75 (0.58 to 0.94) over 34 spells. Their chance of ending falls with age, the pattern proposition 3 rules out for islands of the same depth. These warm spells lasted from 100 to 13,900 years, and without a measure of depth a mix of shallow and deep warm states cannot be told apart from real aging. That is why it carries no verdict.
Drift: the correlation between a cold spell's length and its starting age is -0.22 (p = 0.22).
Other periods: none of 101 trial periods from 1,000 to 2,000 years reached p below 0.01. The lowest was 0.016, at 1,590 years.
Warning signs: before the 24 warmings with enough measurements, variance rose before 11, autocorrelation before 11, and both before 5.

Every trial period

Period, years	Rayleigh r	p
1,000	0.078	0.809
1,010	0.135	0.534
1,020	0.153	0.442
1,030	0.200	0.246
1,040	0.141	0.501
1,050	0.068	0.852
1,060	0.269	0.078
1,070	0.071	0.838
1,080	0.111	0.653
1,090	0.023	0.982
1,100	0.035	0.959
1,110	0.145	0.485
1,120	0.208	0.222
1,130	0.276	0.069
1,140	0.273	0.072
1,150	0.082	0.794
1,160	0.131	0.550
1,170	0.186	0.301
1,180	0.072	0.837
1,190	0.069	0.850
1,200	0.155	0.434
1,210	0.141	0.504
1,220	0.257	0.099
1,230	0.140	0.505
1,240	0.077	0.815
1,250	0.157	0.426
1,260	0.070	0.846
1,270	0.214	0.201
1,280	0.318	0.028
1,290	0.174	0.351
1,300	0.056	0.897
1,310	0.052	0.912
1,320	0.084	0.783
1,330	0.123	0.591
1,340	0.099	0.714
1,350	0.037	0.955
1,360	0.034	0.960
1,370	0.160	0.411
1,380	0.217	0.194
1,390	0.188	0.292
1,400	0.277	0.067
1,410	0.127	0.571
1,420	0.116	0.630
1,430	0.170	0.366
1,440	0.259	0.095
1,450	0.102	0.700
1,460	0.159	0.416
1,470	0.100	0.707
1,480	0.171	0.362
1,490	0.243	0.127
1,500	0.208	0.223
1,510	0.248	0.117
1,520	0.218	0.189
1,530	0.149	0.462
1,540	0.170	0.368
1,550	0.221	0.181
1,560	0.235	0.144
1,570	0.207	0.224
1,580	0.248	0.115
1,590	0.342	0.016
1,600	0.321	0.026
1,610	0.191	0.279
1,620	0.069	0.847
1,630	0.017	0.990
1,640	0.048	0.922
1,650	0.037	0.954
1,660	0.102	0.699
1,670	0.150	0.460
1,680	0.106	0.680
1,690	0.137	0.521
1,700	0.222	0.179
1,710	0.208	0.222
1,720	0.125	0.580
1,730	0.068	0.851
1,740	0.089	0.759
1,750	0.156	0.431
1,760	0.171	0.360
1,770	0.082	0.793
1,780	0.083	0.788
1,790	0.238	0.138
1,800	0.305	0.037
1,810	0.261	0.091
1,820	0.141	0.500
1,830	0.093	0.741
1,840	0.193	0.274
1,850	0.239	0.136
1,860	0.200	0.248
1,870	0.118	0.619
1,880	0.101	0.704
1,890	0.130	0.557
1,900	0.109	0.665
1,910	0.051	0.916
1,920	0.065	0.866
1,930	0.098	0.719
1,940	0.082	0.791
1,950	0.035	0.958
1,960	0.058	0.890
1,970	0.102	0.699
1,980	0.108	0.669
1,990	0.071	0.839
2,000	0.022	0.983

Warning signs, warming by warming

Warming	Measurements	Log variance ratio	Change in autocorrelation
GI-24.2	118	1.62	0.58
GI-23.2	46	-0.16	0.32
GI-21.2	127	0.06	0.71
GI-20c	66	-0.26	0.79
GI-19.2	88	-0.28	-0.48
GI-19.1	38	0.33	0.22
GI-18	265	0.30	0.53
GI-17.2	220	0.04	-0.05
GI-15.2	35	1.21	-0.75
GI-14e	34	-0.20	-0.43
GI-12c	74	-0.06	-1.02
GI-11	47	0.75	-0.08
GI-10	39	-0.17	-0.65
GI-9	32	0.23	-0.11
GI-8c	84	-1.27	-0.15
GI-7c	55	0.69	-0.27
GI-6	50	-0.06	-0.33
GI-5.2	43	0.00	-0.63
GI-5.1	60	-0.05	0.22
GI-4	85	-0.57	0.52
GI-3	41	-0.16	-0.04
GI-2.2	210	-0.18	0.42
GI-1e	410	-0.50	0.70
Holocene	60	0.05	0.19

Cost line and fragility line

Cost line. The warm state is thought to be held by the Atlantic's overturning circulation, which carries heat north continuously. If that is right, the warm island is paid for by a flow, as proposition 4 describes. This is the leading explanation, not a settled one.

Fragility line. Fresh water from melting ice can weaken that circulation, and the cold states that followed large releases of icebergs were among the longest. What pushed the climate back into the warm state is less clear.

How the propositions meet the record

Proposition	On the record	Status
P3 Exit statistics	Tested by C1 (memory) and C2 (a clock). The background climate also changed over the period, so proposition 3's condition of a steady disturbance may not hold. The analysis reports whether the cold spells' lengths drift with age.	C1 survives, C2 no clock
P2 The evidence rule	The warning-sign table is a passive reading of the record, reported without a verdict.	description
P4 Cost	If the warm state was held by the ocean's heat transport, it was a paid-for island. Illustration of a hypothesis, not a test.	illustration
P1, P5, P6	Not applied here.	not applied

Source and method

Isotopes: the NGRIP record in 20-year means on the GICC05modelext timescale, from Seierstad and colleagues (Quaternary Science Reviews 106, 2014), with the measurements of the North Greenland Ice Core Project members (Nature 431, 2004). Events: Table 2 of Rasmussen and colleagues (Quaternary Science Reviews 106, 2014). Both distributed by the Centre for Ice and Climate, University of Copenhagen. Their checksums are in the deposited bundle, and the code refuses any other file. The event rule, the tests and their thresholds are in the pre-registration (r1, 10.5281/zenodo.23066235), frozen with the code in lock.json. The chart is drawn from the same record by code that computes none of the tests' statistics. The two readings the tests weigh: Rahmstorf, Geophysical Research Letters 30, 2003 (a 1,470-year clock), and Ditlevsen, Andersen and Svensson, Climate of the Past 3, 2007 (noise-driven). On warning signs, Ditlevsen and Johnsen, Geophysical Research Letters 37, 2010, and Boers, Nature Communications 9, 2018.