# Fun with Trends

Brief Note by Kip Hansen – 17 August 2022

I have been doing research for other people’s book projects (I do not write books).  One of the topics I looked at recently was the USCRN — U.S. Surface Climate Observing Reference Networks (noaa.gov);  Self-described as “The U.S. Climate Reference Network (USCRN) is a systematic and sustained network of climate monitoring stations with sites across the conterminous U.S., Alaska, and Hawaii. These stations use high-quality instruments to measure temperature, precipitation, wind speed, soil conditions, and more.”

A main temperature data product produced by USCRN is Average Temperature Anomaly for the entire network over its full length of about 17 years.  It is shown up-to-date here at WUWT in the Reference Pages section as “Surface Temperature, US. Climate Reference Network, 2005 to present” where it looks like this:

Now, a lot of people would like to jump in and start figuring out trend lines and telling us that the US Average Temperature Anomaly is either “going up” or “going down” and how quickly it is doing so.

I suggest the following:

1.  What is the range over the time period presented (2005-2022)?

Highest to lowest, the range is about 11 °F or 6 °C.  This range represents not a rise of fall of the metric but rather the variability (natural or forced).  Look at the difference between the high in late 2005 and the low in early 2021.  If this graph had been unlabeled, I would have identified it as semi-chaotic.

2.  Is the anomaly visually going up or down?

Well, for me, it was hard to say.  Oddly, the anomaly seems to run a bit above “0” – which tells us that the base period for the anomaly must be from some other time period.   And it is, USCRN uses a 1981-2010 base period for “0” when figuring these anomalies, the base period is not inside the time range of this particular time-series data set.

We can, however, ask Excel to tell us mathematically, what the trend is over the whole time period.

There, now you know.  Or do you?  MS Excel says that USCRN Average Temperature Anomaly is trending up, quite a bit, about 1 °F (0.6 ° C) over 17 years

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Now comes the FUN!

I’ve arbitrarily picked five-year time increments as they are about 1/3 of the whole period.  Three five-year trends (the last one, slightly longer) which are all down-trending, add up to one up-trending graph when placed end to end in date order.

Lessons We Might Learn:

a.  Don’t use short time periods when determining trends in a time series.  Trends are always sensitive to start and end dates.

b.  This phenomena is somewhat akin to Simpson’s Paradox: “is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined.”

“In his 2022 book Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy and Everything Else, Jordan Ellenberg argues that Simpson’s paradox is misnamed:”

“Paradox” isn’t the right name for it, really, because there’s no constriction involved, just two different ways to think about the same data. … The lesson of Simpson’s paradox isn’t really to tell us which viewpoint to take but to insist that we keep both the parts and the whole in mind at once.”  source ]

c.  It does bring to mind other data sets that change trend (or even trend sign) when looked at in differing time lengths  — sea level rise comes to mind, with the short satellite record claiming to be double the century-long tide-gauge SLR rate.

d.  Why look at trends that are obviously not reliable over different time scales?   This is a philosophical question.  Can a longer trend be real if all the shorter components of the trend have the opposite sign?  Can three shorter down-trends add up to a longer up-trend that has applicability in the Real World?  Or is it just an artifact of the time scale chosen?  Or is the opposite true?  Are three shorter down-trends real if they add up to an up-trend? (When I say “real” I do not mean just mathematically correct – but physically correct.)

e.  Are we dealing with a Simpson’s-like aberration here?  Is there something important to learn from this?  Both views are valid but seem improbable.

f.  Or, is what we see here just a matter of attempting to force a short highly variable data set to have a real world trend?   Are we fooling ourselves with the interpretation of the USCRN Average Temperature Anomaly as having an upward trend – when the physical reality is that this rather short data set is better described as simply “highly variable”?

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Author’s Comment:

I hope some reader’s will find this Brief Note interesting and that it might lead to some deeper thought than “the average and its trend have to be correct – they are simply maths”.

Many metrics of CliSci are viewed at an artificially assigned time scale of  “since the beginning of the modern Industrial Era” usually interpreted as the late 19th century,  roughly 1860 to 1890.  Judith Curry, in her recent interview at Mind and Matter suggests that this is literally “short sighted” and that for many metrics, a much longer time period should be considered.