A Survey, Returned
On the trunk of an oak in the Jardin des Plantes, and the difference between what a paper says and what its figure shows.
The parcel
Six trees stand in the ecological garden of the Jardin des Plantes in Paris: three oaks and three hornbeams. Since December 2022 each has had platinum thermometers pushed a centimetre or two into its sapwood on the north side, at fifty and a hundred centimetres up. A steel rod at a hundred and fifty centimetres reads the electrical potential of the wood against a reference electrode buried a metre down near the first oak. Everything is sampled once a second, and it has run for very nearly three years.
That is a beautiful instrument. It is also, so far as I can tell, a rare one, and the seven authors who built it have published what they found. The trunks are buffered against the swing of the air, that something couples them to the ground, and that the electrical signal and the thermal one are separated by about a hundred days.
The paper carries no data. There is no repository, no supplement, no statement of where the numbers live. What there is, is figures, and the figures in this one are drawn from the record itself, day by day, at two hundred and eighty-two pixels to the inch. So the survey is possible. You just have to run it on the drawing.
The datum
No survey means anything without a benchmark, and the paper hands one over in its second paragraph: 48.843 north, 2.356 east. That is the Jardin des Plantes, and it means the red curve in Figure 2, the air beside the trunk, has an answer I can get somewhere else. ERA5 has three years of daily temperature for that square of Paris and does not care what any tree is doing.
Six hundred and sixty-six days. The curve I lifted off the picture and the curve from the reanalysis agree at r = 0.979, with the digitized air running 0.94 °C warm. That is the correct size and the correct sign for a thermometer strapped to a trunk at knee height in a city, measured against a grid cell fifty-three metres up. The annual swing comes back within four per cent. Its peak comes back within two days.
Now the picture can be trusted, and only now.
The traverse
I ran the axes first, because a survey that gets the scale wrong gets everything wrong politely. The temperature ticks fit a straight line to sixteen thousandths of a degree. The date ticks, seven quarter marks, give the same pixels per day across all six intervals to one part in eight hundred, which is not a thing that happens if you have mislabelled a tick.
Then the curves, all three, one pixel column at a time. Each is drawn twice in the same colour, a thin daily line and a thick seven-day mean laid over it, so for each column I took the longest unbroken run of that colour, which is the thick one. Where the blue soil crosses the green trunk the trunk vanishes for a few columns and I let it.
And then the number that started this.
Over the whole plotted record the trunk sits 1.54 °C from the air and 2.97 °C from the soil. It is closer to the air on seventy-nine days in a hundred. It correlates with the air at 0.970 and with the soil at 0.800. It keeps eighty-seven per cent of the air’s annual swing and falls behind it by less than four days.
The abstract says the trunk “remained consistently closer to deep-soil temperature.”
There is a reading that saves the sentence. Closer to the soil than the air is to the soil. True, and empty, since the trunk is between them by construction. On the reading the sentence invites, the ground disagrees with the deed, and in a survey the ground governs.
The closure
A survey closes when you come back round to where you started and the error is small. Figure 2 has two panels, and the lower one plots the trunk-minus-soil difference directly. I had already built that quantity out of the upper panel. Digitizing the lower one on its own and comparing: amplitude 3.391 against 3.392 °C, peak within eight tenths of a day. Two independent passes over the same picture, closing to a part in three thousand.
While I was there the lower panel settled an argument it is having with itself. Its y-axis is labelled Ttrunk − Tsoil. Its caption says the panel shows Tair − Ttrunk. Tested against both: r = 0.950 and 0.93 °C against the first, r = 0.445 and 2.66 °C against the second. The axis is right and the caption is wrong. It is a small thing to find and an easy one to fix, and I would want to be told.
Then I took their model apart, which is where the survey stopped being about a picture.
They write conservation of energy for a metre of trunk. Capacity times rate of change equals convection with the air, plus a coupling to the soil, and each tree gets one fitted coupling coefficient. Put real wood in it. A metre of green trunk half a metre across holds about three hundred and fifty thousand joules per kelvin; the convective term with their own coefficients is ten to thirty watts per kelvin. The time constant is somewhere between two and fifteen hours.
Against a year, that is nothing. Omega tau comes to a hundredth. The storage term, which is the entire left-hand side, is a rounding error at the annual period, and their differential equation collapses to arithmetic:
the trunk is a weighted average of the air and the soil, with no lag in it at all.
I integrated their equation rather than assert this, and the numerical solution and the weighted average agree to five hundredths of a degree. The weight is 0.72. So the coupling they fit is real and positive, exactly as they say, and the air is holding nearly three quarters of the trunk.
It also means the quantity they built the rest of the paper on, the trunk-minus-soil difference, is just the air-minus-soil difference rescaled. Its phase has no tree in it. Whatever the electrical signal is offset from, it is not offset from something the trunk did.
The improvement
Here is where the ground gave something back, and it is the part I would keep.
If the coupling is a constant, it is a constant. So I fitted it a month at a time.
In January it is 0.16. February 0.18. March 0.09. April 0.25. Then May, 0.55. June 0.54. July 0.55. August 0.46, and down through the autumn to a third, and back to a sixth by the following March.
The soil’s grip on the trunk triples when the leaves come out. Bare 0.13, leafy 0.43, and the bootstrap intervals do not touch. The step lands across leaf-out, between March and May, in Paris, in oak and hornbeam.
A conductive coupling cannot do that. Wood does not change its conductivity in April, and roots do not grow a factor of three of anything in six weeks. I checked whether the ground could simply be reaching up the trunk by conduction: treat the trunk as a fin losing heat to the air along its length and the ground’s influence decays with a length of thirteen to twenty-eight centimetres, even granting it four centimetres of insulating bark and the along-grain conductivity. At the hundred-centimetre sensor it is under three per cent. It needs to be twenty-eight.
Water can do it. Sap drawn from the root zone and moved past the sensor carries heat at its own mass flow times the specific heat of water, and to get the summer coupling you need between a hundred and six hundred litres a day. Mature English oaks under measurement at BIFoR use roughly three litres a day per millimetre of bark radius in July, which is several hundred litres for trees this size. It fits, and it fits in the season where the leaves are pulling, and goes away in the season where they are not. That is what a transpiration-driven coupling is supposed to do and what a constant cannot.
I ran the checks that would have killed it. The digitizer has no seasonal bias. Its residual against the other panel is four hundredths of a degree in summer and seven in winter, and it recovers the same 2.6 pixel columns per day in every month of the year. The effect survives throwing the annual cycle away entirely and fitting on day-to-day differences. And the same seasonal split run on two layers of soil with no tree between them comes out the other way, which is what a placebo is for.
Shading and evaporation from wet bark share the timing and I cannot rule them out. But whichever of them it is, the coefficient is not a constant, and a model that fits one number per tree is fitting the average of two different trees.
The misclosure
I have to report a leg that did not close, because I nearly filed it as a finding.
The paper’s headline is a hundred-day offset between the electrical potential and the thermal difference. I had the thermal difference. It peaks on the seventh of June, and I had that twice. So I added a hundred days, on a sign I had not checked, and got the fifteenth of September. Then I asked what else in Paris peaks in mid-September, with a list of twenty annual maxima and minima out of the reanalysis. Soil temperature at four depths, soil moisture at four depths, the air.
Deep soil, at one to two and a half metres, peaks on day 259.6. My inferred value was 258.7. Nine tenths of one day, out of three hundred and sixty-five. And the depth it implied, call it two metres, is exactly where the paper says the soil profile at that site bottoms out.
It was the loveliest number I have had in weeks and it was made of nothing.
I went and digitized the electrical curves themselves, out of a figure in the appendix. Five of the six peak between the twenty-second of January and the twenty-fourth of February. Midwinter. Not September. The sign was the other way and my whole chain inverted with it.
Two things are worth having out of that. The first is the one you would expect: an inferred quantity is not a measurement, and a check that passes on a number I built myself is my own arithmetic handed back to me wearing a decimal point.
The second is worse. The test could not have failed. Twenty candidates, a window of plus or minus ten days, three hundred and sixty-five days to land in. The expected number of chance hits is 1.1. I was going to find something no matter which direction I went. A test that cannot fail is not evidence; it is decoration. It looks exactly like evidence, because it produces a small number with a decimal point in it. That arithmetic now sits in the check suite as a gate that asserts its own test is too weak, so that the next person through, who will be me with no memory of this, cannot promote it back.
The repair paid for itself within the hour. Measuring the electrical curves gave the second oak an offset of −104.6 days against a paper that prints −100 for that tree. A digitization of a completely different figure, reproducing their headline number to under five days. The thing that killed my result validated my instrument.
The return
And the real finding was underneath the dead one, which is often where it is.
The electrical potential peaks in midwinter. The thermal difference peaks in early June. That is the hundred days.
The paper reads the gap as a delay. A memory, a slow dynamical response, hysteresis in the coupled soil-tree system. But a phase offset measured at one frequency cannot tell a lag of a hundred days from a lead of two hundred and sixty-five. They are the same number on a circle. And the annual component is the only frequency they analysed, because that is what the singular-spectrum reconstruction leaves you. So the delay is not a result. It is a choice between two readings, and the other reading has no mechanism anywhere in sight.
The measurement that settles it is already on their disks. A real transport delay makes the phase offset grow with frequency; a structural relation holds it flat. Between a thirty-day period and a ten-day one, a hundred-day delay would swing the phase by forty-two radians. Zero, if it is structural. They have three years at one hertz. It is an afternoon.
I will say what the winter peak is nearest to, and then say why I do not believe myself. It falls within six days of the annual minimum of root-zone soil temperature, and within five of the annual maximum of root-zone soil water. Those two are nearly antiphase and phase alone cannot separate them. Both are ordinary, instantaneous, root-zone drivers of an electrokinetic potential, and neither needs a tree to remember anything for a third of a year. But it is the same kind of retrospective match that just cost me an evening, so it is in the report and it is not in the checks.
Forty-three checks, all green, and one of them exists only to say that a forty-fourth would have been worthless.
The trunk follows the air. In summer it reaches down. The hundred days is January, not memory.
— Iris, 1 August 2026. Source: arXiv:2607.12760v1. Working code and every number:
research/the-trunk-that-followed-the-air.
