For the 10th consecutive year, October temperatures in Philadelphia in all likelihood will finish above normal. That might qualify as a mathematical paradox — like all the children being above average.

But it also would qualify as a symptom of worldwide warming. The 2009-18 period saw the warmest 10-year run of Octobers in Philly in records dating to 1874.

That the world has warmed is indisputable, but precisely how much warmer is a far more complicated concept. Taking the world’s temperature isn’t like sticking a meat thermometer into a turkey breast.

In Philadelphia, the fact that temperatures are averaging about 2.5 degrees above normal is the result of readings taken at a single quality-controlled location with a calibrated thermometer at Philadelphia International Airport.

The world? That’s another cosmic matter.

The Earth’s wonderfully varied landmasses alternate among mountains, valleys, and plains, a mix of glaciers, deserts, and rain forests, farmland, and cities. The overwhelming majority of the planetary surface is covered by water or otherwise uninhabited.

So what did the National Centers for Environmental Information (NCEI) mean last week when it said that the September global temperature was 1.71 degrees Fahrenheit above the 20th-century average, or that last year, the planet’s annual average temperature was 1.42 degrees higher?

The calculations involve immense processes, and the people who do this for a living do fret over how the public interprets their results.

If they had their druthers, everyone would focus on anomalies — the difference from baseline temperatures — rather than the so-called absolute temperatures. They hold that those anomalies are more accurate and a far-more useful measure.

That said, what is the Earth’s absolute temperature?

According to the National Centers for Environmental Information, the globally averaged temperature in the 20th century was 57.0 degrees Fahrenheit. In 2018, it was about 58.4.

That is almost identical to the 58.5 degree 2018 estimate by NASA’s Goddard Institute for Space Studies, another of the world’s major global-temperature monitoring agencies.

That would be an estimate of surface temperatures averaged over a one-year period at roughly 6.5 feet above all surfaces — mountain peaks, oceans, and everything else.

Heat is unevenly distributed by month and by hemisphere. In the 20th century, the NCEI temperature estimate was 60.4 Fahrenheit for July and 53.6 for January.

Where are the temperatures measured?

At thousands of stations worldwide.

NCEI receives from 2,000 to 2,500 reports monthly from more than 180 countries, said Deke Arndt, chief of the monitoring branch.

Those monthly averages are based on daily highs and lows from the reporting stations, supplemented by data from ships.

Some nations take their time in reporting temperatures, and then the data have to be analyzed and massaged for gaps in observations.

The annual report is a compilation of the 12 monthly averages, with each month carrying equal weight, including day-challenged February.

Why not use the absolute temperatures instead of the anomalies?

Surface temperatures can vary radically within relatively short distances. For example, on Saturday morning, it got down to 32 at Wings Field in Montgomery County, but only 41 at Philadelphia International, about 30 miles away.

Elevation is a huge factor. Temperatures decrease on average 3.5 degrees Fahrenheit for every 1,000 feet of elevation; thus, a modest 2,000-foot summit would be 7 degrees cooler than the valley.

The anomalies allow for more uniform comparisons, the data keepers say.

“A summer month over an area may be cooler than average, both at a mountaintop and in a nearby valley,” says NCEI, “but the absolute temperatures will be quite different at the two locations. The use of anomalies in this case will show that temperatures for both locations were below average.”

For a variety of reasons, including the sparseness of measuring points in the same areas of the planet — take the Sahara — estimates of that absolute temperature are imprecise.

The anomalies, says NASA’s Gavin A. Schmidt, “shouldn’t be combined with the less accurate mean to try and give an absolute value every year.”

So how accurate are those anomalies?

NCEI’s comprehensive annual and monthly reports published include margins of errors.

In the cases of both the 2018 annual and September 2019 reports, that margin was plus or minus 0.27 degrees Fahrenheit. For September, for example, the range would have been 1.44 and 1.98 degrees.

Those margins, says Arndt, “take into account several types of uncertainties, the two most important types of which are typically areas with sparse or missing data and biases arising from changes in observing conditions or practices and our associated methods of correcting such biases.”

History of global temperature since the mid-19th century through 2018 compared to the 1981-2010 average from four analysis teams: NOAA (red), NASA (tan), University of East Anglia (pink), and the Japan Meteorological Agency (orange). In the background is an image of Earth on Aug. 3, 2018, from NOAA's DSCOVR satellite.
NOAA
History of global temperature since the mid-19th century through 2018 compared to the 1981-2010 average from four analysis teams: NOAA (red), NASA (tan), University of East Anglia (pink), and the Japan Meteorological Agency (orange). In the background is an image of Earth on Aug. 3, 2018, from NOAA's DSCOVR satellite.

NCEI, NASA, and other global databases all use slightly different methods. But year after year, they come to the same conclusion: The world is getting warmer.