How to read a warming trend
A warming trend is the slope of a line fitted by linear regression to a series of annual means; it should only be asserted when the accompanying statistical test shows it cannot reasonably be explained by chance.
The slope: degrees per decade
Take the annual mean of each year in the period, and you have a scatter of points. Find the line that passes closest to all of them — in the least-squares sense, minimising the sum of squared deviations. The slope of that line is the trend.
It is usually expressed in degrees per decade, which makes it comparable between places. Multiplied by the length of the period, it gives the total delta: cumulative warming across the whole window.
One important remark about choosing the period: the shorter the window, the more unstable the slope. Over five years, two remarkable summers are enough to produce a spectacular slope that describes nothing. This is why the trends on this site are computed over the long window.
r²: how closely the points follow the line
The coefficient of determination, written r², runs from 0 to 1. It measures the share of year-to-year variation that the line accounts for.
An r² of 0.6 means the trend explains 60 % of what moves from one year to the next; the rest is variability — a mild winter, a washed-out summer, an ocean oscillation. On annual climate series, modest r² values are normal and do not disqualify the trend: meteorological noise is large, and a real slope can perfectly well coexist with a lot of scatter.
So r² does not tell you whether the trend is real. It tells you how regular it is.
The p-value: could the trend be chance?
That is the question r² does not answer, and the only one that decides whether anything may be asserted.
The p-value answers: "if there were in fact no trend at all, what is the probability of seeing, by pure chance, a slope at least as pronounced as this one?". A p-value of 0.03 means three chances in a hundred. A p-value of 0.4 means forty — that is, the result would be entirely unremarkable with no underlying warming whatsoever.
The conventional threshold is 0.05. Below it, the trend is called statistically significant. Above it, the data do not support a conclusion — which does not mean there is no trend, only that this series is not enough to establish one.
Why this site sometimes says "no clear trend"
When the p-value exceeds 0.05, Climate Memory does not display the slope: the page states that no clear trend emerges.
That is not missing data, and it is the most important point in this article. It is a result. It means that at this place and over this period, variability dominates the signal.
The refusal is deliberate because the consequences are asymmetric. Publishing "+2.1 °C" with a p-value of 0.4 produces a false and perfectly quotable claim: it will be repeated, copied, possibly ingested by a language model, and nothing downstream will carry the caveat. A page that says "we cannot conclude" cannot be misquoted.
If you are reading this because a city page showed that wording: it does not have a gap in its data. It has an answer, and the answer is that we do not know.
Local warming and global warming
A local trend is not the planetary trend, and it is almost always noisier. Global warming is an average over the entire surface of the globe, where most regional variability cancels out; over a single grid cell, nothing cancels.
Land warms faster than ocean, and high latitudes faster than the tropics. A northern city can therefore show a slope well above the global mean without that being a measurement anomaly.