Regime A · the modern seasonal cycle

How much of the seasonal cycle is a response to the orbit?

The annual cycle of sunlight is orbital forcing. The informative questions are how the climate responds to it (lag, damping, land against ocean), whether the forcing's finer structure survives into temperature, and where a good fit stops meaning what it appears to mean.

Dataset (scopes everything below)

Baseline 1981–2010 · fits constrained to k ≥ 0, τ ≤ 365 d

Seasonal share of monthly variance83.1%land 91% · ocean 80% (area-weighted)

Explained by insolation through a one-pole model78.1%of all monthly variance; 91% of the seasonal cycle

Median relaxation time27 d · 126 dland · ocean: heat capacity, not forcing

Eccentricity term identifiable0 of 29admissible regions; median detectability 0.18 (needs > 1)

Where the seasonal cycle behaves like a response to sunlight

Berkeley Earth, cell by cell

Loading map…

Each grid cell's 1981–2010 monthly climatology is fitted with T = T₀ + k·(insolation filtered by 1/(1 + iωτ)). High R² in the extratropics, failure in the tropics and monsoon regions where circulation and hydrology set the seasonal cycle. Hover or use the arrow keys for values; the table gives 10° band means.

Zonal profiles, land against ocean

R² one-pole model

Land
Ocean

Zonal means of the cell climatology per Gaussian or 1° latitude row. The one-pole τ separates land (weeks) from ocean (months) at every latitude.

Global mean: the textbook trap

Insolation peaks at perihelion; temperature near aphelion

Global-mean TOA insolation anomaly (W m⁻²)

Global-mean temperature anomaly (K)

With a circular orbit, global-mean insolation would be constant (the obliquity terms cancel between hemispheres). The real one swings 22.0 W m⁻² and peaks on 3 Jan; temperature peaks on 22 Jul, r = −0.95. A free fit “explains” it with k = −0.17 K per W m⁻² (R² 0.999): more sun, colder. The admissible fit explains R² = 0.000. Predictive association, not attribution.

Who sets the global cycle

Area-weighted annual amplitude and peak month

NH | land2.18 K · peaks Jul
NH | ocean1.00 K · peaks Aug
SH | land0.58 K · peaks Jan
SH | ocean0.84 K · peaks Feb

Northern-hemisphere land, a fifth of the globe with a small heat capacity, dominates the annual harmonic of global-mean temperature and pins its peak to July, near aphelion.

Is the eccentricity term identifiable anywhere?

29 physically admissible regions, Berkeley Earth

Perfect-model test: the largest R² that eccentricity could add (a circular-orbit model fitted to the noise-free real-forcing response) divided by the misfit of the real-forcing model to the data. Below 1, eccentricity's contribution is smaller than what the model already gets wrong. A free gain and lag absorb the eccentricity term, which is an annual harmonic peaking near perihelion.

Has the timing of the seasons changed, and could the orbit explain it?

Annual-cycle phase trend relative to insolation, days per decade (+ later)

full record
1954–2007
1979 onward
precession-only prediction

Measured against calendar-anchored insolation so Gregorian leap-year drift (about −0.07 d per decade) cancels. Whiskers are 95% HAC intervals. The precession-only prediction (diamond) is at most 0.04 d per decade; observed shifts change sign between windows and between datasets.

All regions

Bootstrap 95% intervals resample baseline years (B = 500). “Free fit” is the unconstrained model; where it needs k < 0 or τ > 365 d the region is marked inadmissible and excluded from attribution statements.

Regional fits
Region	Seasonal share	R² one-pole [95%]	R² 1 harmonic	R² zero lag	τ (d) [95%]	k (K/W m⁻²)	Lag (d)	A₂/A₁: T · model · Q	Free fit
Global \| all	0.974	0.000 [0.000, 0.000]	1.000	0.910	0 [0, 0]	0.000	-164.8	0.01 · — · 0.02	inadmissible (k −0.17, τ 18 d)
Global \| land	0.990	0.994 [0.993, 0.995]	0.999	0.690	38 [38, 39]	0.130	33.9	0.02 · 0.06 · 0.08	admissible
Global \| ocean	0.614	0.000 [0.000, 0.000]	0.979	0.834	0 [0, 0]	0.000	—	0.09 · — · 0.04	inadmissible (k −0.01, τ 24 d)
NH \| all	0.995	0.999 [0.999, 0.999]	0.999	0.626	45 [45, 45]	0.064	38.2	0.03 · 0.02 · 0.03	admissible
NH \| land	0.996	0.999 [0.998, 0.999]	0.998	0.769	32 [31, 32]	0.088	29.0	0.04 · 0.01 · 0.02	admissible
NH \| ocean	0.989	0.998 [0.997, 0.998]	0.999	0.289	90 [90, 93]	0.055	58.3	0.01 · 0.03 · 0.05	admissible
SH \| all	0.992	0.996 [0.995, 0.997]	0.995	0.516	55 [55, 57]	0.025	44.7	0.07 · 0.02 · 0.03	admissible
SH \| land	0.989	0.994 [0.992, 0.995]	0.979	0.904	18 [17, 19]	0.045	18.3	0.14 · 0.11 · 0.12	admissible
SH \| ocean	0.993	1.000 [0.999, 1.000]	1.000	0.225	106 [106, 110]	0.030	62.6	0.01 · 0.01 · 0.01	admissible
Tropics \| all	0.718	0.720 [0.655, 0.763]	0.441	0.015	354 [354, 354]	0.167	—	1.12 · 0.57 · 1.13	inadmissible (k +1.75, τ 3650 d)
Tropics \| land	0.811	0.291 [0.255, 0.323]	0.214	0.119	23 [21, 24]	0.038	—	1.92 · 1.53 · 1.81	admissible
Tropics \| ocean	0.723	0.971 [0.944, 0.980]	0.727	0.002	354 [354, 354]	0.163	—	0.61 · 0.51 · 1.00	inadmissible (k +1.68, τ 3650 d)
NH extratropics \| all	0.996	0.998 [0.997, 0.998]	0.998	0.626	45 [44, 45]	0.065	38.2	0.05 · 0.02 · 0.03	admissible
NH extratropics \| land	0.996	0.998 [0.998, 0.999]	0.998	0.767	32 [31, 32]	0.088	29.2	0.04 · 0.01 · 0.01	admissible
NH extratropics \| ocean	0.993	0.986 [0.986, 0.987]	0.990	0.168	131 [126, 131]	0.066	66.7	0.09 · 0.02 · 0.04	admissible
SH extratropics \| all	0.996	0.998 [0.998, 0.999]	0.997	0.324	84 [84, 84]	0.024	56.0	0.06 · 0.02 · 0.04	admissible
SH extratropics \| land	0.991	0.996 [0.994, 0.997]	0.994	0.815	27 [26, 28]	0.047	25.6	0.08 · 0.02 · 0.02	admissible
SH extratropics \| ocean	0.995	0.998 [0.998, 0.999]	0.996	0.206	114 [110, 114]	0.026	63.8	0.06 · 0.02 · 0.04	admissible
Arctic \| all	0.988	0.990 [0.988, 0.991]	0.988	0.606	45 [45, 47]	0.076	38.5	0.09 · 0.17 · 0.25	admissible
Arctic \| land	0.992	0.996 [0.995, 0.997]	0.988	0.689	38 [37, 39]	0.093	33.3	0.10 · 0.15 · 0.20	admissible
Arctic \| ocean	0.981	0.982 [0.979, 0.984]	0.986	0.538	54 [52, 55]	0.069	42.7	0.10 · 0.17 · 0.27	admissible
Antarctic \| all	0.983	0.987 [0.984, 0.990]	0.903	0.908	16 [15, 17]	0.042	18.3	0.32 · 0.27 · 0.30	admissible
Antarctic \| land	0.980	0.987 [0.983, 0.989]	0.862	0.933	12 [11, 13]	0.046	14.6	0.39 · 0.31 · 0.33	admissible
Antarctic \| ocean	0.981	0.975 [0.970, 0.979]	0.979	0.775	30 [29, 31]	0.037	28.4	0.14 · 0.19 · 0.24	admissible
North America	0.988	0.999 [0.997, 0.999]	0.999	0.719	37 [35, 37]	0.086	32.3	0.03 · 0.01 · 0.01	admissible
Europe	0.967	0.998 [0.996, 0.999]	0.998	0.708	37 [35, 39]	0.056	33.0	0.02 · 0.01 · 0.01	admissible
Siberia	0.983	0.992 [0.989, 0.994]	0.997	0.788	30 [29, 31]	0.107	27.1	0.04 · 0.05 · 0.06	admissible
East Asia monsoon	0.988	0.997 [0.996, 0.998]	0.995	0.786	30 [29, 31]	0.102	27.9	0.07 · 0.07 · 0.09	admissible
Sahel	0.965	0.991 [0.987, 0.993]	0.903	0.847	20 [19, 22]	0.098	19.2	0.32 · 0.27 · 0.31	admissible
Amazon	0.763	0.932 [0.904, 0.951]	0.730	0.731	23 [19, 27]	0.027	19.5	0.59 · 0.36 · 0.42	admissible
Australia	0.978	0.997 [0.995, 0.998]	0.990	0.829	26 [24, 27]	0.060	24.6	0.10 · 0.05 · 0.06	admissible
North Atlantic	0.962	0.960 [0.954, 0.965]	0.961	0.155	131 [126, 140]	0.044	67.3	0.19 · 0.00 · 0.01	admissible
Tropical Pacific	0.309	0.675 [0.520, 0.736]	0.869	0.056	354 [354, 354]	0.165	—	0.39 · 0.60 · 1.18	inadmissible (k +1.81, τ 3650 d)
Southern Ocean	0.985	0.992 [0.990, 0.994]	0.986	0.152	135 [131, 140]	0.020	67.8	0.11 · 0.03 · 0.06	admissible