What is linked, what is not
Each arc joins two phenomena tested on this site. Green and animated: clear link (correlation significant at 5 % after correcting for autocorrelation, or a response outside chance in an event study). Grey: inconclusive test. A statistical link alone does not establish causation.
- Clear link
- Inconclusive
Arc width from |r| of the stored result; several tests between the same phenomena are drawn as stacked arcs.
What the masses predict and what the pole did, 2002–2026
Result. The rotation pole drifted by 4.7 mas a year towards 11° W; the masses seen by GRACE predict 6.7 mas a year towards 26° W: the right order of magnitude and nearly the right direction (16° apart), but a speed 1.43 times too large. The melting of Greenland alone would push the pole by 2.2 mas a year towards its meridian, 48 % of the observed speed.
Where is the gap? From year to year, trend and seasons removed, both excitations have the same amplitude (slopes 0.99 and 0.96, close to 1): the conversion from gravity coefficients to pole motion is right. The gap is therefore only in the secular trend, where two known effects come in: the post-glacial rebound, which is in the GRACE coefficients but does not follow the elastic relation used here, and the “mean pole” convention of the GRACE processing, which leaks into C21 and S21 (Wahr et al., 2015). We correct neither for lack of a published model we could check; the gap is given as it is.
Show the data as a table
Show the data as a table
| Period | observed (IERS) | predicted by GRACE | Greenland alone (GravIS) |
|---|---|---|---|
| All (258 months) | 4.66 ± 0.16 mas/yr, towards 11° W (± 2°) | 6.65 ± 0.12 mas/yr, towards 26° W (± 1°) | 2.25 ± 0.08 mas/yr, towards 42° W (± 2°) |
| GRACE 2002–2017 (161 months) | 4.96 ± 0.37 mas/yr, towards 6° W (± 4°) | 6.78 ± 0.26 mas/yr, towards 20° W (± 2°) | 2.56 ± 0.10 mas/yr, towards 42° W (± 2°) |
| GRACE-FO 2018– (97 months) | 4.38 ± 0.74 mas/yr, towards 34° W (± 10°) | 6.21 ± 0.62 mas/yr, towards 27° W (± 6°) | 1.72 ± 0.19 mas/yr, towards 42° W (± 6°) |
What the pole did. Daily pole coordinates (IERS C04, continued after its end by the observed days of the USNO finals, predictions left out; the USNO alone if C04 is missing), p = x − i y; geodetic excitation χ = p + (i/σc) dp/dt, which removes the Chandler resonance (period 433.0 days, Q = 179; Wilson and Vicente, 1990), then monthly means.
What the masses predict. C21 and S21 of the monthly GRACE and GRACE-FO solutions (CSR RL06): χ = −k (ΔC21 + iΔS21), k = 1.098 √(5/3) M R² / ((C − A)(1 + k′2)), k′2 = −0.301 (Chen and Wilson, 2008); published conventions differ by about 10 % on this factor. The atmosphere and ocean are removed from the GRACE data, the post-glacial rebound stays. Greenland: mass anomaly of the ice sheet (GravIS, rebound removed) placed at 72° N, 42° W.
Comparison. Least-squares trends with annual and semi-annual terms, standard errors inflated for the autocorrelation of the residuals, over GRACE (2002–2017), GRACE-FO (2018–) and the whole; year-to-year residuals as 13-month running means, correlation with the effective number of independent values, and the slope of one on the other.
Computation parameters
{
"mass": "χ = −k (ΔC21 + iΔS21), k = 1.098 √(5/3) M R² / ((C − A)(1 + k2′)) = 1872.63, k2′ = −0.301 (Chen & Wilson, 2008); CSR RL06 GSM, atmosphere and ocean removed, GIA kept",
"pole": "IERS C04 2002-03-01 to 2025-05-05; USNO finals 2025-05-06 to 2026-10-22",
"trends": "least squares with annual and semi-annual terms, standard errors inflated for lag-1 autocorrelation; GRACE 2002-04 to 2017-06, GRACE-FO 2018-06 onwards, all",
"geodetic": "p + (i/σc) dp/dt = χ, p = x − i y, T = 433.0 days, Q = 179 (Wilson & Vicente, 1990); daily, averaged by calendar month (≥ 25 days)",
"greenland": "GravIS ice mass anomaly at 72° N, 42° W, χ = 1.098 ΔI / (C − A)",
"interannual": "residuals of the whole-record fit, 13-month running means, Pearson r with effective sample size"
}Inputs : grace.c21.monthly (258 pts, run #13100) · grace.s21.monthly (258 pts, run #13100) · iers.pm_x.daily (23,136 pts, run #13098) · iers.pm_y.daily (23,136 pts, run #13098) · usno.pm_x.daily (20,024 pts, run #160) · usno.pm_y.daily (20,024 pts, run #160) · gravis.gis.mass.monthly (259 pts, run #3712)
- GRACE and GRACE-FO degree-2 order-1 gravity coefficients C21 and S21 (CSR RL06, NASA PO.DAAC)
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Save, H. (2020). CSR GRACE and GRACE-FO RL06 Level-2 monthly gravity field solutions. GRACE: doi:10.5067/GRGSM-20C06; GRACE-FO RL06.3: doi:10.5067/GFL20-MC063. Tapley, B. D., et al. (2019). Contributions of GRACE to understanding climate change. Nature Climate Change, 9, 358–369.
· doi:10.1038/s41558-019-0456-2 · source page ↗
Licence : NASA open data, no restriction; Earthdata login required; cite the data DOIs · retrieved on Oct 28, 2026 · SHA-256 a9b6a48309ca… - IERS EOP 20 C04 daily Earth orientation since 1962
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IERS Earth Orientation Centre, EOP 20 C04 (IAU2000A) combined series, 1962–; Bizouard, C., et al. (2019), J. Geod. 93, 621–633.
· doi:10.1007/s00190-018-1186-3 · source page ↗
Licence : IERS data, free use with citation (Bizouard et al., 2019) · retrieved on Oct 28, 2026 · SHA-256 395e94687b8a… - IERS Bulletin A daily Earth orientation (USNO finals2000A.all)
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IERS Rapid Service/Prediction Centre (USNO), Bulletin A: polar motion, UT1−UTC and length of day since 1973, with predictions (finals2000A.all).
· source page ↗
Licence : U.S. Government work, public domain; cite IERS Bulletin A · retrieved on Oct 23, 2026 · SHA-256 95a61292c957… - GravIS mass anomalies from GRACE and GRACE-FO: ice sheets and river-basin water storage (GFZ, COST-G)
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Sasgen, I., Döhne, T., Boergens, E., Horwath, M. (2026): COST-G GravIS RL02 Ice-Mass Change Products, V. 0001, GFZ Data Services, doi:10.5880/COST-G.GRAVIS_02_L3_ICE. Boergens, E., Dobslaw, H., Dill, R. (2025): COST-G GravIS RL02 Terrestrial Water Storage Anomalies, V. 0001, GFZ Data Services, doi:10.5880/COST-G.GRAVIS_02_L3_TWS. Dahle, C., et al. (2025): GravIS: mass anomaly products from satellite gravimetry, Earth Syst. Sci. Data, 17, 611–631.
· doi:10.5194/essd-17-611-2025 · source page ↗
Licence : CC BY 4.0 (GFZ Data Services); cite the data DOIs and Dahle et al. (2025) · retrieved on Oct 25, 2026 · SHA-256 59c02eaae985… - Chen et al. (2013)
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Chen, J. L., Wilson, C. R., Ries, J. C., & Tapley, B. D. (2013). Rapid ice melting drives Earth’s pole to the east. Geophysical Research Letters, 40, 2625–2630.
· doi:10.1002/grl.50552
Licence : Published literature; cited - Adhikari et al. (2016)
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Adhikari, S., & Ivins, E. R. (2016). Climate-driven polar motion: 2003–2015. Science Advances, 2(4), e1501693.
· doi:10.1126/sciadv.1501693
Licence : Published literature; cited - Chen et al. (2008)
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Chen, J. L., & Wilson, C. R. (2008). Low degree gravity changes from GRACE, Earth rotation, geophysical models, and satellite laser ranging. Journal of Geophysical Research: Solid Earth, 113, B06402.
· doi:10.1029/2007JB005397
Licence : Published literature; cited - Wahr et al. (2015)
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Wahr, J., Nerem, R. S., & Bettadpur, S. V. (2015). The pole tide and its effect on GRACE time-variable gravity measurements: implications for estimates of surface mass variations. Journal of Geophysical Research: Solid Earth, 120, 4597–4615.
· doi:10.1002/2015JB011986
Licence : Published literature; cited - Wilson et al. (1990)
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Wilson, C. R., & Vicente, R. O. (1990). Maximum likelihood estimates of polar motion parameters. In Variations in Earth Rotation, Geophysical Monograph 59, 151–155. AGU.
· doi:10.1029/GM059p0151
Licence : Published literature; cited - Gross (2015)
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Gross, R. S. (2015). Earth rotation variations – long period. In Treatise on Geophysics (2nd ed.), vol. 3, 215–261. Elsevier.
· doi:10.1016/B978-0-444-53802-4.00059-2
Licence : Published literature; cited - Deng et al. (2021)
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Deng, S., Liu, S., Mo, X., Jiang, L., & Bauer-Gottwein, P. (2021). Polar drift in the 1990s explained by terrestrial water storage changes. Geophysical Research Letters, 48(7), e2020GL092114.
· doi:10.1029/2020GL092114
Licence : Published literature; cited - A et al. (2013)
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A, G., Wahr, J., & Zhong, S. (2013). Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: an application to glacial isostatic adjustment in Antarctica and Canada. Geophysical Journal International, 192, 557–572.
· doi:10.1093/gji/ggs030
Licence : Published literature; cited - Caron et al. (2018)
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Caron, L., Ivins, E. R., Larour, E., Adhikari, S., Nilsson, J., & Blewitt, G. (2018). GIA model statistics for GRACE hydrology, cryosphere, and ocean science. Geophysical Research Letters, 45, 2203–2212.
· doi:10.1002/2017GL076644
Licence : Published literature; cited - Peltier et al. (2018)
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Peltier, W. R., Argus, D. F., & Drummond, R. (2018). Comment on “An assessment of the ICE-6G_C (VM5a) glacial isostatic adjustment model” by Purcell et al. Journal of Geophysical Research: Solid Earth, 123, 2019–2028.
· doi:10.1002/2016JB013844
Licence : Published literature; cited - Dahle et al. (2025)
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Dahle, C., Boergens, E., Sasgen, I., Döhne, T., Reißland, S., Dobslaw, H., et al. (2025). GravIS: mass anomaly products from satellite gravimetry. Earth System Science Data, 17, 611–631.
· doi:10.5194/essd-17-611-2025
Licence : Published literature; cited