One Spin, Written Across Every Latitude

1 · Three models make three different pictures

What makes this decisive rather than merely consistent is that the competing models don't disagree by a little. They predict qualitatively different figures, and the difference is visible without any statistics at all.

Take the local Coriolis parameter, f, which sets both the rate and the handedness of the loops. It is twice the component of the planet's rotation along your local vertical:

• — A stationary Earth. Nothing rotates, so f = 0 everywhere. There are no inertial loops at any latitude. Drifters follow the current and nothing else.
• — A flat turntable spinning about an axis through the pole. The rotation axis is perpendicular to the surface everywhere on the disc, so f = 2Ω at every location: loops of identical period, roughly 12 hours, turning the same way from the centre to the rim. Nothing distinguishes one circle of latitude from another, and nothing at all happens at the equator. Worth saying plainly: nobody defends this model. It is here as a logical bracket, because it is the only way a flat Earth can rotate at all. The position actually taken in the book is the stationary disc under a turning sky — which is the first panel, f = 0, no loops anywhere.
• — A spinning sphere. Only the vertical component of the rotation counts, so f = 2Ω sin φ. Loops are fastest at the poles, slow to nothing at the equator, and reverse handedness across it, because the local vertical points the opposite way relative to the spin.

2 · Nobody deployed these buoys to prove anything

This is the part that matters most, and it is easy to skim past. These buoys are not instruments for measuring the Earth. A Global Drifter Program float is a plastic sphere with a satellite transmitter and a drogue hanging fifteen metres below it, released into the ocean by people who want to know about currents and sea-surface temperature. It has no sensitive axis. It is not aimed at anything. It does not measure rotation, or latitude, or the shape of the planet.

All it does is report where it is.

The rotation isn't in what the buoys measure. It's in how they move.

The signature is a property of the trajectory — something nobody has to record, because it emerges from a list of positions when someone else, later, asks a different question. The oceanographers who collected this data were not testing anything about Earth's spin. Many of them actively did not want these loops: near-inertial motion is routinely filtered out of circulation studies because it obscures the mean flow that the study is actually about. The part of the record that demonstrates the rotation is the part the original users throw away.

That provenance closes a door that is otherwise always open. The standard objection to any rotation experiment is an objection about the instrument: it drifts, it was calibrated on a rotating-Earth assumption, it is responding to some other medium or effect. Those objections need an instrument to attach themselves to. A float has no bias term, no calibration chain to Earth's rotation, no sensitive axis to misalign, and nothing inside it that could plausibly be responding to something other than the water it is sitting in. It is a lump of plastic going where the sea takes it, and the sea takes it in circles whose direction reverses at the equator.

3 · The measurements

One buoy per latitude rung, January to April 2019, each analysed independently. “Confidence” is the ratio of clockwise to counter-clockwise energy in the search band — how cleanly one handedness dominates. Rows shaded red fall outside 10% of prediction.

Predicted period is 11.967 h ÷ sin φ, computed from the buoy's own mean latitude with no fitted parameters.

4 · The buoys measure the length of the day

The relationship has exactly one constant in it. Write the law as T = A ÷ sin φ and ask what value of A the fifteen buoys actually imply, rather than assuming it:

That is roughly the accuracy Arthur Compton got in 1915 from a ring of water on a bench, built for the purpose. These fifteen were built to track ocean currents. The point was never that drifters are a precision clock — a ring laser does this ten million times better — it is that the number falls out of data collected for something else entirely, by instruments that cannot see the sky, and lands on the right answer.

One further consistency point, raised before anyone else does. The 25.4°N buoy is excluded from the handedness count but its 29.7-hour period is still in this fit — a defensible split, because a peak was found in the search band whether or not one rotational sense dominated it, and period and handedness are separate measurements. It is worth showing that the choice does not flatter the answer: dropping that buoy entirely moves the unweighted mean from 12.02 h to 11.97 h, a shift of 0.4% — toward the true value, not away. Keeping it in makes the headline slightly worse.

One methodological note, since the weighting is doing visible work. The confidence figure is the ratio of clockwise to counter-clockwise energy in the search band, computed per buoy before any of this and with no knowledge of the answer — and every weighting scheme moves the result toward the truth rather than away from it, which is how an honest quality metric behaves and is not how a fudge factor behaves. Discarding the two weakest buoys outright makes the answer worse (12.04 h), so the good number is not coming from dropping inconvenient data.

5 · Method, in enough detail to repeat

Everything here comes from a public archive and can be reproduced from scratch.

• 1 Source. NOAA AOML Global Drifter Program, hourly drifter product, served over ERDDAP — dataset drifter_hourly_qc on the AOML server at erddap.aoml.noaa.gov/gdp/erddap. Public domain. The product is documented in Elipot et al. (2016). Fields used: ID, time, latitude, longitude, ve, vn.
• 2 Per buoy, pull hourly eastward and northward velocity across a multi-month window — about 2,880 hourly samples for a full run.
• 3 Form the complex velocity w = (ve − mean) + i(vn − mean). Removing the mean strips out the background current so the loops stand clear of the drift.
• 4 Rotary spectrum by FFT. Negative frequency is clockwise, positive is counter-clockwise. The sign of the dominant peak is the handedness — it is read off the data, not assigned.
• 5 Locate the peak within an adaptive band of 0.6 to 1.7 times the predicted frequency. In-band energy ratio between the two senses of rotation gives the confidence figure.

6 · What could be wrong with this

Stated before anyone else has to.

Fifteen buoys is a ladder, not a distribution. The airtight version of this claim is statistical — hemisphere energy asymmetry across hundreds of drifters, binned by latitude, crossing zero at the equator. One buoy per rung demonstrates the effect and traces the curve; it does not yet pin down the scatter. That larger run has in fact been done, by Elipot & Lumpkin (2008) across the whole array, and it returns the sin φ law and the hemisphere asymmetry — but it is their work, not this page's.

The selection rule matters more than the disclaimer, so here it is. Latitude rungs were fixed first, roughly every 5–10°. For each rung, the first buoy in the January–April 2019 window with a continuous track long enough to hold several loop periods was taken, and analysed. No buoy was analysed and then discarded. Three rows carry short windows (887, 951 and 1,029 samples against 2,881 for a full window) because those tracks ended or were interrupted — not because they were trimmed. Anyone can pull a different fifteen; the interesting reply would be a set that does not reverse at the equator.

Several periods are a few percent off, and one is about 20% off. That is the buoy at 22.7°S, and the discrepancy is real physics rather than noise. Two effects push measured periods off f. Near-inertial waves are intrinsically super-inertial — their dispersion relation puts them slightly above f — which is the generic reason measured periods skew short. And the background flow shifts the effective frequency to roughly f + ζ/2: cyclonic vorticity raises it and shortens the loop, anticyclonic vorticity lowers it and lengthens the loop, which is why near-inertial energy pools in anticyclones in the first place. So the fast buoy at 22.7°S wants cyclonic vorticity or wave propagation; the slow one at 9.9°N is the one that fits the anticyclonic story. These periods are deliberately left uncorrected. Correcting them would tighten the fit and would also be the single easiest place to hide a thumb on the scale.

“These are tides, not inertial loops.” Worth raising because the 63.1°N buoy invites it: 12.4 h sits close to the M2 semidiurnal tide at 12.42 h, and northern shelf seas have strong tidal currents, so that row may well be partly tidal — treat it as the weakest in the table. But it cannot be the general explanation. Tidal periods are fixed — 12.42, 12.00, 23.93, 25.82 hours — and do not scale with sin φ; tidal ellipses put energy into both rotary senses rather than one; and most of the table sits at periods (17 to 80 hours) with no tidal line anywhere near. A tide that reversed handedness at the equator and stretched toward infinity approaching it would not be a tide.

“The fixes assume a globe, so the loops are a coordinate artefact.” Satellite positioning does use a WGS-84 ellipsoid, so the objection is worth stating. It does not work: coordinate transformations are smooth and cannot manufacture a 12-to-80-hour oscillation whose period tracks latitude and whose handedness flips at a line. The loops are kilometres across in raw latitude and longitude, before any projection.

“The loops are wind-driven, not rotation-driven.” Half right, and the half that is right does not help. Wind is what excites an inertial oscillation — that is why loop amplitude is erratic and is not plotted here. The frequency is set by f alone, and frequency is what this page tests.

Velocities are a derived product. The ve/vn fields are computed by interpolating satellite position fixes and differentiating them, with quality control applied. The inertial signal is present in the raw fixes too, but anyone who wants to argue “interpolation artifact” is entitled to, and the clean answer is to redo one buoy from raw fixes. Also not done here.

The band-pass is for display, not for manufacturing the result. The unfiltered rotary spectrum already shows the hemisphere asymmetry at roughly ten to one. Filtering makes the loops legible on a chart; it does not create them.

7 · Why the equator is the null and not the maximum

The natural objection: if Coriolis comes from the Earth's spin, and the spin is fastest at the equator — a thousand miles an hour — shouldn't the effect be strongest there rather than absent?

The acceleration is a = −2Ω × v, and everything follows from which way that cross product points. For horizontal deflection only the vertical component of Ω contributes, giving f = 2Ω sin φ — the same for any heading at a given latitude, and zero at the equator. At the equator the rotation axis lies flat in the local horizontal plane: motion north or south is parallel to it, so the cross product vanishes, and motion east or west produces a force that is vertical rather than sideways.

That vertical part does not disappear — it goes as cos φ and is maximal at the equator. It is the Eötvös effect: travel east and you weigh very slightly less, travel west and slightly more. One cross product, two projections, opposite latitude dependence. The horizontal one dies at the equator; the vertical one peaks there.

And this is not an exotic prediction that only shows up in buoy data. The same sign flip is the reason hurricanes spin counter-clockwise north of the equator and clockwise south of it — and the reason none form within about five degrees of the line, where f is too small to organise a rotating storm at all. Most readers already believe that one. The drifters are the same fact, measured rather than watched.

Sources & further reading

• NOAA AOML Global Drifter Program — roughly 1,300 active satellite-tracked surface buoys; data released to the public domain.
• ERDDAP tabledap, dataset drifter_hourly_qc, erddap.aoml.noaa.gov/gdp/erddap. Analysis window January–April 2019.
• S. Elipot, R. Lumpkin, R. C. Perez, J. M. Lilly, J. J. Early & A. M. Sykulski, “A global surface drifter data set at hourly resolution,” J. Geophys. Res. Oceans 121, 2937–2966 (2016) — the dataset paper.
• S. Elipot & R. Lumpkin, “Spectral description of oceanic near-surface variability,” Geophys. Res. Lett. 35, L05606 (2008) — the large-n version of §6's “not done here”: near-inertial energy from the whole drifter array, binned by latitude, showing the sin φ law and the hemisphere asymmetry.
• E. Kunze, “Near-inertial wave propagation in geostrophic shear,” J. Phys. Oceanogr. 15, 544 (1985) — the f + ζ/2 effective frequency used in §6.
• J. Gonella, “A rotary-component method for analysing meteorological and oceanographic vector time series,” Deep-Sea Res. 19, 833 (1972) — origin of the rotary-spectrum method, and the standard treatment of tidal ellipses versus inertial motion.
• A. H. Compton, “A Laboratory Method of Demonstrating the Earth's Rotation,” Science 37, 803 (1913) — the water-ring apparatus referenced in §3.
• Companion page: gyroscopes and Earth's rotation — why ring-laser and fibre-optic instruments detect the same rotation by an entirely different route.