Every Trend You Could Draw

The answer before the apparatus

Two claims enter. Only one leaves intact.

“Global warming stopped” cannot survive this surface. “Warming slowed for a while” can. The latter is a description of short-run pace, not a claim about the long run.

Each cell is compared with its own record’s 1970-onward rate, computed under the same El Niño treatment as the cell. Adjusting the window and leaving the comparator raw would build in a bias the reader could not see.

The operable surface

Move one choice. Watch the headline move.

Loading the shipped records…

Two honest colour scales, one rhetorical choice. Centre on the long-run rate and the surface asks whether warming slowed. Centre on zero and it asks whether warming stopped. The data do not change. The visual argument does.

Fyfe et al. 2016’s named position: the early-2000s slowdown was a real feature worth explaining. That claim lives in the blue cells under the long-run-centred view. It does not require, or imply, zero long-run warming.

All choices at once

The specification curve

… valid combinations enter this curve. … are undefined. Another … combinations are crossed out before the run because their windows are shorter than ten years.

Waiting for the full grid.

Plot disclosure will appear here.

The highlighted grid point uses NOAA v4’s July 2019 monthly snapshot because the multiverse needs monthly data. The exact anchor above uses the September 2017 annual snapshot that reproduces the paper. The record moved between them, so the page refuses to collapse the two vintages.

Depth layer one

What actually moved the line?

The argument was about the ocean data. The arithmetic says the argument should have been about where to stop the line.

The main effects leave an interaction remainder of …. Because the ten-year rule makes start and end years unbalanced, the page labels these shares descriptive rather than pretending they are an exact orthogonal partition.

Which choices are honestly inert

A main-effects table can call a choice irrelevant by construction. The honest test is that a factor’s main effect and all of its pairwise interactions are small, so the page runs that test rather than eyeballing the bars.

Inert on both counts: …. Inert only on the main effect: ….

The El Niño result is the interesting one and it is a trap the grid was built to catch. Removing Niño3.4 barely moves the pooled variance, because Niño3.4 has almost no trend of its own inside 1998–2012. It has a large trend either side of that window, so what the adjustment is worth depends on where you stop the line. A page that reported only the main effect would have told you El Niño does not matter here, which is not true and is not what the argument was about.

The control offered here is Niño3.4 alone. The fuller adjustment of Foster and Rahmstorf (2011) also removes volcanic aerosol and the solar cycle, and is worth appreciably more than El Niño by itself. This page does not ship those two forcing series, so it does not offer that adjustment and does not report a number for it.

An estimator this page refuses to offer

Reading a trend off the two endpoints is what a person with a ruler does, and in isolation it is defensible. Crossed with a free choice of window it stops being an estimator and becomes a comparison of two El Niño years. Over the same … windows, on …, the endpoint difference ranges … °C per decade while ordinary least squares ranges …. It is not on the control panel, and this is the measurement that says why.

Depth layer two

The choice that is not on the grid

Every cell above answers “how fast was it warming in this window”. Almost nobody arguing about the hiatus was asking that. They were asking “was it slower than before”, and that question needs a second number the grid never asks for: the reference period.

Hold the window at 1998–2012, hold the record and the method fixed, and change only what you compare it against.

On NOAA v6.0.0 that single choice moves the answer by … °C per decade and flips its sign, from … against Karl’s 1950–1999 to … against the 1972–2001 period Fyfe et al. used. The trend itself never moves. Karl chose the reference most favourable to his conclusion; Fyfe et al. chose one among the least. Neither is wrong, which is the point.

The vacuous row is shown on purpose. A reference period that contains the window is a legal setting and an empty one. Take 1998–2012 as its own reference and the difference is exactly zero and the ratio is exactly 1.000 for every record: nothing has been measured. The 1880–2014 row is the milder version of the same defect. A 135-year comparator still contains the window, and most of what it averages is a period nobody was arguing about, so it flatters the recent window for reasons that have nothing to do with the hiatus.

This axis is deliberately not one of the six controls above, because it changes what is being estimated rather than how. For scale: the raw span of this choice on one record and one window, …, is smaller than the span of the window axis at fixed everything else, …. It is not the largest number on the page. It is the only one that changes the sign of the answer without changing the data.

Depth layer three

The record moved under the argument

Same window, same method, same agencies. Only the release of the record changes. Four successive NOAA products and both coverage variants of HadCRUT5 are shipped so this can be watched rather than asserted.

Karl et al.’s published correction was the whole controversy: 0.039 to 0.086, a change of +0.047 °C per decade, both figures printed in their Table S1. The unheadlined reissues of NOAA’s own record since then have moved the same number by a further …. Against the 0.05 that AR5 printed from HadCRUT4, today’s infilled HadCRUT5 gives … more.

And the largest single steps are coverage, not the sea-surface correction the argument was about. NOAA v5.0.0 to v5.1.0, which is NOAA implementing full spatial coverage, is worth …. HadCRUT5 non-infilled to infilled, which is the same choice made statistically, is worth …. Filling in the Arctic moves this number more than the ship-and-buoy correction did.

Vintage also beats the thing everyone treats as the real disagreement. Across the four NOAA releases the answer moves …, and across the two HadCRUT5 coverage variants …. Across three different agencies at their current release it moves …. Which agency you cite barely matters. Which release of it you cite matters several times more.

Karl’s headline verdict, evaluated on each release

The sentence the paper is remembered for is that the rate of warming over 2000–2014 was at least as great as over 1950–1999. It was true on his own data by four thousandths of a degree per decade. Here it is on everything shipped.

…

That does not make any release fraudulent. It makes vintage part of the measurement, and it means a verdict quoted without its release date is not a verdict.

Depth layer four

Would steady warming make a hiatus anyway?

Fit an AR(1) noise process to NOAA v6.0.0 annual values from 1970 onward, taken about a quadratic so the curvature of the real record is not counted as noise. That gives residual standard deviation … °C and lag-one correlation …. Then build 20,000 seeded 55-year records of a world whose warming rate is constant at 0.18 °C per decade, faster than anything anybody claimed for the hiatus era, and look for hiatuses in it.

… of these steadily-warming records contain a 15-year window whose trend is not significantly positive at 90%. And the median lowest 15-year trend available anywhere in such a record is … °C per decade.

That last number is the finding. AR5 printed 0.05 for 1998–2012. The lowest 15-year trend you should expect to be able to find in a record that never slowed down at all is about the same value, before any data problem, any estimator choice and any El Niño. Choosing the start year is not a small liberty.

Waiting for the multiverse.

What the search costs a p-value

Take the null to be steady warming at the observed 1970–1997 rate of … °C per decade. A p-value that ignores the search asks how often one prespecified window comes in this low. A p-value that prices in the search asks how often the lowest of the 41 available windows does. 1998 is not a prespecified start year: it is the start year that minimises the 15-year trend in several of these records, and it was chosen after the fact.

The noise model is allowed to fail

A simulation that under-states real variability would inflate every number above. So the same simulated records are asked how far apart their highest and lowest 15-year trends are, and the answer is compared with the real records: … simulated against … observed. …

A second check the simulator has to pass: the standard deviation of a 15-year trend in these worlds is … °C per decade, against … from the closed-form variance of an ordinary least squares slope under AR(1) errors. If the generator were wrong, these would not agree.

Depth layer five

Could a 15-year window have found a real slowdown?

This is the other half, and it decides whether “no significant slowdown” means anything at all. Same noise, same method. Give the world a genuinely slower window and ask how often a 15-year trend test notices: the test is that the 90% interval sits entirely below the long-run rate of 0.18.

A 15-year window has … power against a halving of the warming rate. If the world really had slowed from 0.18 to 0.09 °C per decade and stayed there for fifteen years, a 15-year trend test would have missed it more often than it caught it. And in … of these windows the 90% interval contains zero and the full long-run rate at once: formally compatible with “no warming” and “warming at the full rate” in the same breath.

Karl et al. wrote that the data “do not support the notion” of a slowdown, and that wording is exactly right. The data also could not have ruled one out. Both poles of this argument were entitled to far less than they claimed, and the asymmetry the public fight assumed, that one side needed evidence and the other needed only the absence of it, was never there.

Waiting for the power run.

Depth layer six

Why the shortest windows are refused

The controls above will not let you take a window shorter than ten years, and a refusal is only honest if it can be shown. Here is what happens to windows starting in 1998 as they get shorter: how many of the seven records still have a 90% interval containing zero, which is the state in which a comparison between records conveys nothing at all.

…

Note the non-monotonicity at the long end rather than reading the table as “longer is always better”. Past a certain length the window swallows 2015 onward and stops being about the hiatus at all.