A panel test read climate driving tree rings correctly, and our own rule still failed it

Tree rings and summer temperature give a causal-direction test with a known answer: warmth shapes the ring, and the ring has no meaningful effect on the weather. An earlier round on 135 European sites found that a site-by-site transfer entropy estimator could not tell the two directions apart. In this second round we read lagged Granger tests across a panel of 161 held-out ring-width chronologies at or above 55 degrees north, under a plan hash-locked before any ring series was set against climate. On the high-pass series the panel direction index was +1.206 (95% interval +0.871 to +1.591), against a far-pairing 95th percentile of +0.213.c1 Reversing time flipped the index to -0.894.c2 Rings predicted the next summer at 6.8 percent of sites, below the no-coupling world's 7.8 percent and above the 95th percentile of the far-site pairing control, 6.2 percent.c5 Two binding first-difference checks failed by less than 0.02: the planted reverse world was called correctly at 58.4 percent of sites against a bar of 60 percent, and the shared-trend world's reverse rate was 0.117 against a limit of 0.10.c3 The kill condition written before the run therefore fired, and the instrument earned no standing in this round. The real-data asymmetry is reported as an exploratory reading.

Methods that read causal direction from two time series are used across climate science and ecology, and Runge and colleagues [1] set out the conditions under which such readings can be trusted in the Earth sciences. A known-answer testDefinition: known-answer test measurement and method validation A test of a method on a case where the true answer is fixed by physics or by construction, so that any wrong reading is a fault of the method. Excludes agreement with another method, which can share the same fault. full definition asks a method to recover a direction that is fixed in advance. Summer warmth shapes ring width at cold sites, and a ring cannot set the next summer, so annual rings and summer temperature give one such test on public data.

The first round of this study, finding F132questioned, ran a nearest-neighbour transfer entropy estimator site by site on 135 European chronologies and failed: the two directions were detected at similar rates, time reversal made no difference, and a planted direction was misread at about half the sites. Its own account was low power at about 78 years of data and a ring-temperature correlation near 0.2.

This round changes that assumption. It reads the direction across a panelDefinition: panel statistics and econometrics A set of units, here tree-ring sites, each observed over time and analysed together so that one statistic summarises all of them. Excludes a verdict reached site by site, and a pooled regression that treats all years of all sites as one series. full definition of sites at once, where F132questioned asked each site for its own verdict. The tool is the Granger testDefinition: Granger test econometrics and time-series statistics A regression test of whether the past values of one series improve the prediction of another beyond that series' own past. Here an F test on lags 1 and 2. Excludes a test of same-year effects, and proof of a physical cause. full definition, the lagged regression test Granger introduced in 1969. Panel versions exist in econometrics: Dumitrescu and Hurlin [2] average per-unit Wald statistics into one panel test of non-causality. Our index is simpler and was written from that idea, not copied from their statistic: a mean difference of per-site z-scores, with its null drawn from far-site pairings.

Two parts of the literature bear on the design. Preprocessing can create or hide Granger causality. Florin and colleagues [3] reported spurious and missed causalities after filtering, Barnett and Seth [4] showed that Granger causality is unchanged by filtering in theory and that filtering in practice raises both error rates, and Anderson and colleagues [5] gave conditions under which filtering does and does not distort it. That is why the plan ran three preprocessing arms and why their disagreement matters. Second, the lag structure of boreal conifer growth is not simple. Tumajer and Lehejcek [6] found in white spruce a positive effect of summer temperature in the year of ring formation and a negative effect of the summer one year before, and Lloyd and colleagues [7] reported that the previous growing season's temperature and precipitation control growth at most of their interior Alaska sites. Our searches, run on 9 November 2026, found no panel Granger test of ring width against climate with planted worlds of known direction. That is a search result, not proof that none exists.

The plan was written as a preregistrationDefinition: preregistration research method (metascience) A dated written plan for a study, fixed and hash-locked before any result is seen: the question, the data, the statistic, the controls, the forecasts and the kill conditions. Excludes a plan revised after looking at the outcome, and a protocol written only for the record after the run. full definition and hash-locked on 2 November 2026 at 09:42:37 UTC. Before the lock, the only facts read from the new data were outcome-free: the site count, the regions, the blocks, the series lengths, the distance to the nearest climate cell and the species. No ring series had been correlated, regressed or tested against any climate series. The estimator had been tested on synthetic autoregressive series only.

The plan named the assumption it changed from F132questioned and split the instrument's job into two readings scored apart. The first is reverse-route exclusion: past rings carry no lagged route into next year's summer temperature at the strength of the observed same-year coupling. The second is the forward reading: past summers add to next year's ring beyond the ring's own past. The plan forecast that the forward reading would lack power.

The kill conditionDefinition: kill condition research method (our usage, after Popper's falsification) A rule written in the preregistration that, when met, decides against the claim with no room for judgement after the run. Excludes reasons found after the run for setting a result aside. full definition was written without room for judgement: if any binding checkDefinition: binding check research method, our usage A preregistered rule on a synthetic world that the instrument must pass before any reading of the real data counts. Under the kill condition a single failure removes all standing. Excludes power checks and limit checks, which were recorded but could not remove standing. full definition fails, or the reverse-route exclusion fails on real data, the instrument gets no standing and F132questioned's block on direction readings stands. Exclusion status needed every binding check and the exclusion rule to pass. Forward status needed, in addition, the planted forward world at real strength and the forward rule on real data.

One deviation was recorded before any result was seen. The first run stopped on a division by zero inside the precipitation arm, which is descriptive and decides no verdict. CRU precipitation at many of these cells is filled with climatology where stations are absent, and at four sites the June to August total is constant over the whole window. The fix returns a p value of 1 when the target's residual sum of squares is zero. No temperature series can reach that branch: temperature repeats for at most 2 years at any site. The plan, the verdicts and the seed were unchanged.

Rings: standard ring-width chronologies from the International Tree-Ring Data Bank [8], held by NOAA's National Centers for Environmental Information as public data with a request to cite the contributors. The selection rule was fixed in the build script before the lock: standard chronologies with no earlywood, latewood or density keyword, latitude at or above 55 degrees north, outside longitudes 12 W to 45 E so that no site falls in F132questioned's European region, years 1901 to 2025 with at least 5 samples, and a longest gap-free run of at least 60 years. This gave 161 sites: 100 in Canada, 45 in Alaska and 16 in Asia, in 77 two-degree blocks, with series of 60 to 115 years and a median of 89. The species are mostly white spruce, Picea glauca.

Climate: June to August mean temperature of the ring's year from the nearest land cell of CRU TS 4.10 [9] [10], released under the Open Database License 1.0 with attribution to the Climatic Research Unit, University of East Anglia. The nearest cell lay a median of 16.8 km from the site and at most 31 km. June to August precipitation was run as a descriptive secondary target.

For ring width $R_t$ and summer temperature $C_t$ at one site, the climate-to-ring test compares the full regression

with the same regression without the two climate terms, by an F test on the same rows. The ring-to-climate test is the mirror, with the roles of $R$ and $C$ exchanged. Each p value becomes a z-scoreDefinition: z-score of a p value statistics The point of the standard normal distribution that leaves the p value above it, so that a smaller p gives a larger z. Here capped at 6. Excludes a standardised value of the data themselves. full definition, $z=Q(1-p)$, where $Q$ is the quantile function of the standard normal distribution, capped at 6. The site's direction statistic is

where $z_{f,i}$ is the forward (climate to ring) score and $z_{r,i}$ the reverse one.

The panel direction indexDefinition: panel direction index time-series statistics, our usage The mean over sites of d, the z-score of the climate-to-ring Granger test minus that of the ring-to-climate test. Positive values point from summer temperature to ring width. Excludes a test of significance at any one site. full definition is the mean over the $N=161$ sites:

Its 95% interval is a block bootstrapDefinition: block bootstrap statistics An interval made by resampling whole 2 degree blocks of sites with replacement, here 2,000 times, so that neighbouring sites that share climate move together and the interval is not too narrow. Excludes a bootstrap over single sites, and a binomial interval that treats sites as independent. full definition over the 77 two-degree blocks with 2,000 resamples. The detection rateDefinition: detection rate statistics, our usage The share of sites at which the Granger test in one direction gives p 0.05 or below. For synthetic worlds it is averaged over the draws. Excludes a rate corrected for testing 161 sites. full definition in each direction is the share of sites with p 0.05 or below. The same-year correlation between ring and temperature is reported and gives no direction.

Each pair of series was analysed three ways: through a high-pass filterDefinition: high-pass filter signal processing A filter that keeps fast variation and removes slow trends. Here each series minus a Gaussian smooth of width 10 years, then scaled to unit variance. Excludes first differences, which are reported as a separate arm. full definition (the primary arm, as in F132questioned), as first differencesDefinition: first differences time-series statistics Each year's value minus the previous year's, a second way to remove slow trends that weights the fastest changes most. Excludes the high-pass filter, which removes trends by smoothing. full definition, and raw, scaled only. The raw arm is descriptive and shows what a shared trend does.

Each world is built per site from iAAFT surrogatesDefinition: iAAFT surrogate time-series statistics, surrogate data A copy of a series built by repeated rounds of Fourier phase randomisation and rank reordering, so that it keeps both the original spectrum, and with it the autocorrelation, and the original set of values, while its timing against any other series is lost. Excludes a shuffle of single years, which destroys the autocorrelation. full definition of that site's own series, five draws per site. In the planted forward world a surrogate $S_t$ of the ring series receives the site's own climate:

At real strength $a$ is the larger of the site's absolute same-year correlation on the high-pass arm and 0.1. In the planted reverse world a surrogate of the climate series receives the ring:

with the same $a$. The strong worlds use coefficients 0.6 and 0.3. In the no-coupling world both series are independent surrogates. In the common-driver world an autoregressive driver with coefficient 0.5 enters both series in the same year with weight $\sqrt{0.2}$. In the shared-trend world independent surrogates receive a common line and random walk before preprocessing.

For a world with a planted direction, direction accuracyDefinition: direction accuracy method validation, our usage The share of sites at which the sign of d matches the direction planted in a synthetic world. 0.5 is what a coin would give. Excludes whether the test at any site is significant. full definition is

where $m$ is the number of sites whose $d_i$ has the planted sign.

The far-site pairingDefinition: far-site pairing statistics, our usage A control in which each ring series is paired with the summer temperature of a random site at least 1,000 km away, so that real coupling is removed while both series keep their own form. Repeated 199 times. Excludes pairings with nearby sites, which share regional climate. full definition pairs each ring with the summer temperature of a random site at least 1,000 km away, 199 times, on the high-pass and first-difference arms. Every site had at least 65 partners at that distance. Its p value is the share of pairings at or above the real index:

with $n=199$, so the floor is 0.005. That floor sits under 0.0083, the smallest threshold the Benjamini-Hochberg correctionDefinition: Benjamini-Hochberg correction statistics, multiple testing A rule that adjusts a set of p values so that, among the tests called significant, the expected share of false calls stays at or below a chosen rate, here 0.05. The adjusted value is called q. Excludes the stricter Bonferroni rule, which bounds the chance of any false call. full definition at 0.05 over six tests can need, a lesson from F132questioned, where 20 pairings left a floor too high to correct. The six family p values are the two pairing tests, the real reverse rate on each of two arms against a binomial 5 percent, and two sign tests on the planted worlds at real strength.

Every controlDefinition: control statistics and experimental design A version of the data with the structure under test removed (for example shuffled or pooled), scored the same way as the real data, so the real score has something to beat. Excludes a comparison with a different dataset or with a published number. full definition and synthetic world ran in the same run as the real data. The planted checksDefinition: planted check research method; called a positive control in experimental science Data built so that the right answer is known, run through the same analysis before the real data, to show that the analysis can see the effect when it is there. Excludes any check made on the real data, which cannot show what the analysis misses. full definition were split by role in the plan.

Binding checks, any failure fatal:

Power and limit checks, recorded but not binding:

Real-data rules:

The time-reversedDefinition: time reversal time-series analysis The same test run on both series read backwards in time. A method that reads direction from lag order should flip. Excludes a control on coupling strength. full definition real series were reported beside the rules and decide nothing.

Table 1 gives the panel index and both detection rates in every world, and Figure 1 draws the index with its interval on the two binding arms. Synthetic worlds are averaged over five draws per site.

On the high-pass series the panel direction index was +1.206 (95% interval +0.871 to +1.591), against a far-pairing 95th percentile of +0.213.c1 The pairing mean was +0.047 and its 5th percentile -0.099, and no pairing reached the real value, so p is 0.005, the floor at 199 pairings. First differences gave +1.107 against a pairing 95th percentile of +0.186 (p 0.005), and the raw series +1.242 (+0.873 to +1.655). Climate predicted next year's ring at 39.8 percent of sites. Rings predicted the next summer at 6.8 percent of sites, below the no-coupling world's 7.8 percent and above the 95th percentile of the far-site pairing control, 6.2 percent.c5 The mean same-year correlation on the high-pass arm was 0.160, positive at 87.0 percent of sites.

Reversing time flipped the index to -0.894.c2 On first differences it flipped to -1.092 and on the raw series to -1.041. The shared trend pushed the high-pass index negative (-0.317) and the raw index further (-0.744, with rates 0.335 and 0.594), and the common driver gave -0.090 with an interval across zero. Neither confound produced a positive index like the real one.

Figure 2 sets every binding rule against its bar.

Two binding first-difference checks failed by less than 0.02: the planted reverse world was called correctly at 58.4 percent of sites against a bar of 60 percent, and the shared-trend world's reverse rate was 0.117 against a limit of 0.10.c3 Every high-pass binding check passed: the planted reverse world was called at 71.4 percent with its interval upper end at -0.303, and the no-coupling rates were 0.055 and 0.078. Every real-data rule passed, the power checks passed, including the planted forward world at real strength (interval lower end +0.073), and the shared-trend limit on high-pass failed as forecast (0.135 and 0.221). Under the kill condition one binding failure is enough. The instrument gets no standing from this round.

The $p$ values over the six-test family, corrected by Benjamini and Hochberg, rejected both pairing tests (q 0.0086 each), the reverse-world sign test (q 1.6e-7) and the forward-world sign test (q 0.0086). The real reverse rates against 5 percent were not rejected (q 0.22 on high-pass, 0.29 on first differences). The binomial tests treat sites as independent; the block intervals carry the spatial dependence.

Table 3 in Appendix A sets the forecasts written before the run against the outcomes. The forecasts for the forward signal were far off. They leaned on F132questioned's forward rate of 0.089 in its variant without the same-year term, and on synthetic smoke tests (short trial runs that check the code executes) in which a positive planted prior-summer term was absorbed by the ring's own past.

On the high-pass arm the panel test did what F132questioned's estimator could not. It pointed from summer to ring on sites the first round never touched, reversed with time, kept the reverse rate at the no-coupling level, and stayed clear of what a shared trend or a common driver produce. Read alone, that is a working instrument. It is not credited here, because the plan made two first-difference checks binding and both failed. This is an honest nullDefinition: honest null research method (our usage) A working test that found no effect beyond a stated bound, a forecast that failed, or an error of our own found and fixed, reported with the same weight as a positive result. Excludes a void run, and a result left unpublished because it was negative. full definition about the instrument as locked, and the real-data asymmetry stays exploratory.

The failures say something about first differences. Differencing weights the fastest changes, and in the planted reverse world it shrank the index from -0.429 to -0.157 and the accuracy from 0.714 to 0.584. Smoke tests before the lock had already shown the first-difference arm weaker against the reverse world, and the plan made it binding anyway. That is a design error of ours. It agrees in kind with the filtering literature, where preprocessing can raise both error rates of a Granger test [4] [3] [5].

A look after the run, which is exploratory and not a result, explains why the forward signal was so much larger than forecast. Regressing ring on same-year and prior-year summer temperature on the high-pass arm, without the ring's own past, gave a same-year slope with median +0.170, positive at 88.8 percent of sites, and a prior-summer coefficientDefinition: prior-summer coefficient dendroclimatology The slope on the previous year's summer temperature in a regression of this year's ring width on this year's and last year's summer temperature. Excludes the same-year slope, and any effect of the ring's own past unless it is added to the regression. full definition with median -0.127. The planted forward effect carried a positive prior-summer term, and the real prior-summer coefficient was negative at most sites (median -0.127, positive at 21.7 percent).c4 Its size was a median of 0.76 times the same-year term, and with the ring's own past added the median grew to -0.173. The inference, not tested here, is that a negative lag-one term adds to the Granger signal where a positive one is absorbed by the ring's own past. The planted world at real strength was then not at the real lag structure, and the same error sat in F132questioned. A negative effect of the previous summer in white spruce is reported in the literature [6] [7].

The real index (+1.206) sits close to the strong planted forward world (+1.274) and far from the one at real strength (+0.180), which fits that reading.

A third round, finding F676, ran the same day on 145 further held-out sites with the planted prior-summer term fitted to the measured sign and only the high-pass arm binding. It gave a panel index of +1.204 against a pairing 95th percentile of +0.461, passed every binding check but one, and its kill condition did not fire, so the panel method gained a limited direction status at that coupling strength. That later result does not change this round's verdictDefinition: verdict research method (our usage) The pass or fail of one preregistered rule set against the run's numbers, read off by code. Excludes an interpretation written after reading the numbers. full definition.