Milan from 1940 to today

Annual anomaly · 1961-1990 baseline

How far the mean has moved

Each bar is the difference between that year's mean temperature and the mean over the 30-year period 1961-1990, the standard reference period of the World Meteorological Organization.

A single year tells you nothing. 1947 was scorching and 1956 was bitter, and that was happening well before anyone talked about emissions. What matters is where the centre of the distribution sits, and whether it moves.

The values appear here once the series has been read.

Ordinary linear regression assumes errors that are independent and normally distributed, an assumption never quite true of a climate series. Beside it sits the Theil-Sen estimator, taking the median of the slopes between every pair of years and needing no normality in the residuals, and beside that the Mann-Kendall test, non-parametric, answering one question: how likely a run this consistently one-directional would be if there were no trend at all. On independence neither of them helps. Autocorrelation between consecutive years inflates significance, and the intervals shown here carry no correction for it, so read the p value as indicative.

The Mann-Kendall verdict on the period the series covers appears here once the data have been read.

Daily maxima · two 30-year periods compared

What used to be rare is now ordinary

The same days, counted. On the left the first 30-year period of the series, on the right the last. Same city, same grid cell, same model.

The curve keeps its shape. It slides. The slide tells most in the right tail, where the extreme days sit: a modest shift of the bell changes how many of those days there are by a good deal.

The values appear here once the series has been read.

SU30 · TR20 · FD · fixed-threshold counts

Counting the days

Annual means invite argument. The number of nights that never dropped below 20 degrees invites a lot less: either that night happened or it did not.

These are counts of days against a fixed threshold, of the same family as the indices set out by the Expert Team on Climate Change Detection and Indices at the World Meteorological Organization. FD follows the ETCCDI definition. SU30 and SU35 raise the summer-day threshold, which ETCCDI puts at 25 °C, and TR20 counts a night whose minimum lands exactly on 20 degrees. The thresholds used here are written out in the method table, so the count can be redone under the same rule.

The line is the Theil-Sen estimator. Each index uses the threshold declared in the method table.

The values appear here once the series has been read.

Daily records by decade

Which way the records fall

For every day in the calendar there is a year in which that day was the warmest on record, and a year in which it was the coldest. Here they are counted by decade.

In a stable climate the two colours come out even, and records grow rarer as time passes, because beating an ever longer archive takes an ever more extreme value.

The values appear here once the series has been read.

Rainfall · annual total and Rx1day

Where the data prove nothing

Two rainfall indicators: the annual total and the highest total in a single day.

Rainfall behaves differently from temperature: it swings a great deal from one year to the next, and pulling a signal out of it takes a longer series than the thermometer needs. The verdict below comes from the same Mann-Kendall test used on temperature.

The statistical verdict on rainfall is computed in the browser and appears here alongside the charts.

Cross-checks

The objections

Four are reasonable and deserve an answer from the numbers on this page. One makes no sense and gets said anyway.

Data, method, limits

Where these numbers come from

The exact request that produced this series, the methods applied to it and the limits of the data. The full series can be downloaded below.

The source

The values appear here once the series has been read.

The query

The models=era5 parameter is not optional. Without it the API picks the best model available and from 2017 switches to ECMWF IFS at 9 km. Changing model halfway through a series introduces an artificial step in exactly the recent years that are under discussion.

The exact query that produced this series appears here once the data have been read.

The statistical methods

Anomaly baseline

1961-1990

Regression

ordinary least squares, 95% CI from Student's t

Robust estimator

Theil-Sen, median of the slopes across every pair

Trend test

two-sided Mann-Kendall with a correction for ties

SU30

days with a maximum temperature ≥ 30 °C

TR20

nights with a minimum temperature ≥ 20 °C

FD

days with a minimum temperature < 0 °C

Rx1day

highest daily rainfall of the year

Colour scale

ColorBrewer RdBu reversed, diverging and safe for colour blindness

Where the maths runs

in your browser, on the raw daily values

The limits

A reanalysis is a model constrained by observations, not a direct measurement. The grid cell is about 25 kilometres on a side and takes in the hinterland as well as the city, so absolute values can sit apart from those of an urban station. Far fewer observations were assimilated in 1940 than are assimilated today, which leaves the early decades less constrained by the data and more dependent on the model. None of these limits works in a way that would manufacture a rising trend out of nothing.

What to cite

The values appear here once the series has been read.