{"id":214094,"date":"2022-08-17T17:11:22","date_gmt":"2022-08-17T15:11:22","guid":{"rendered":"https:\/\/climatescience.press\/?p=214094"},"modified":"2022-08-17T17:11:23","modified_gmt":"2022-08-17T15:11:23","slug":"fun-with-trends","status":"publish","type":"post","link":"https:\/\/climatescience.press\/?p=214094","title":{"rendered":"Fun with Trends"},"content":{"rendered":"\n
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Brief Note by Kip Hansen \u2013 17 August 2022<\/p>\n\n\n\n

I have been doing research for other people\u2019s book projects (I do not write books).  One of the topics I looked at recently was the USCRN \u2014 U.S. Surface Climate Observing Reference Networks (noaa.gov)<\/a>;  Self-described as \u201cThe U.S. Climate Reference Network (USCRN) <\/strong>is a systematic and sustained network of climate monitoring stations with sites across the conterminous<\/a> U.S., Alaska, and Hawaii. These stations use high-quality instruments to measure temperature, precipitation, wind speed, soil conditions, and more.\u201d<\/p>\n\n\n\n

A main temperature data product produced by USCRN is\u00a0Average Temperature Anomaly\u00a0<\/em>for the entire network over its full length of about 17 years.\u00a0 It is shown up-to-date here at WUWT in the Reference Pages section as \u201cSurface Temperature, US. Climate Reference Network, 2005 to present<\/a>\u201d where it looks like this:<\/p>\n\n\n\n

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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<\/em> is either \u201cgoing up\u201d or \u201cgoing down\u201d and how quickly it is doing so.<\/p>\n\n\n\n

But let\u2019s start with a more pragmatic approach and ask first:  \u201cWhat do we see here?\u201d <\/p>\n\n\n\n

I suggest the following:<\/p>\n\n\n\n

1.  What is the range over the time period presented (2005-2022)?<\/p>\n\n\n\n

          Highest to lowest, the range<\/a><\/em><\/strong> is about 11 \u00b0F or 6 \u00b0C.  This range represents not a rise of fall of the metric but rather the variability<\/a><\/em><\/strong> (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. <\/p>\n\n\n\n

2.  Is the anomaly visually going up or down?<\/p>\n\n\n\n

          Well, for me, it was hard to say<\/strong>.  Oddly, the anomaly seems to run a bit above \u201c0\u201d \u2013 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 <\/strong>base period for \u201c0\u201d when figuring these anomalies, the base period is not inside the time range of this particular time-series data set. <\/p>\n\n\n\n

We can, however, ask\u00a0Excel<\/em>\u00a0to tell us mathematically, what the trend is over the whole time period.<\/p>\n\n\n\n

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There, now you know.  Or do you?  MS Excel<\/em> says that USCRN Average Temperature Anomaly<\/em> is trending up, quite a bit, about 1 \u00b0F (0.6 \u00b0 C) over 17 years. <\/strong><\/p>\n\n\n\n

~ ~ ~<\/strong><\/p>\n\n\n\n

Now comes the FUN!<\/strong><\/p>\n\n\n\n

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I\u2019ve arbitrarily picked five-year time increments as they are about 1\/3 of the whole period.\u00a0 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.<\/p>\n\n\n\n

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Lessons We Might Learn:<\/p>\n\n\n\n

a.  Don\u2019t use short time periods when determining trends in a time series.  Trends are always sensitive to start and end dates.<\/strong><\/p>\n\n\n\n

b.  This phenomena is somewhat akin<\/em> to Simpson\u2019s Paradox<\/a>: \u201cis 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.\u201d <\/p>\n\n\n\n

\u201cIn his 2022 book Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy and Everything Else<\/a>,<\/em> Jordan Ellenberg<\/a> argues that Simpson\u2019s paradox is misnamed:\u201d<\/p>\n\n\n\n

\u201cParadox\u201d isn\u2019t the right name for it, really, because there\u2019s no constriction involved, just two different ways to think about the same data. \u2026 The lesson of Simpson\u2019s paradox isn\u2019t really to tell us which viewpoint to take but to insist that we keep both the parts and the whole in mind at once.\u201d  <\/sup>[ source<\/a> ]<\/p>\n\n\n\n

c.  It does bring to mind other data sets that change trend (or even trend sign) when looked at in differing time lengths  \u2014 sea level rise comes to mind, with the short satellite record claiming to be double the century-long tide-gauge SLR rate. <\/p>\n\n\n\n

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 \u201creal\u201d I do not mean just mathematically correct \u2013 but physically correct<\/em>.)<\/p>\n\n\n\n

e.  Are we dealing with a Simpson\u2019s-like aberration here?  Is there something important to learn from this?  Both views are valid but seem improbable.<\/p>\n\n\n\n

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 \u2013 when the physical reality is that this rather short data set is better described as simply \u201chighly variable\u201d?<\/p>\n\n\n\n

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Author\u2019s Comment:<\/u><\/strong><\/p>\n\n\n\n

I hope some reader\u2019s will find this Brief Note interesting and that it might lead to some deeper thought than \u201cthe average and its trend have to be correct \u2013 they are simply maths\u201d. <\/p>\n\n\n\n

Many metrics of CliSci are viewed at an artificially assigned time scale of  \u201csince the beginning of the modern Industrial Era\u201d usually interpreted as the late 19th<\/sup> century,  roughly 1860 to 1890.  Judith Curry, in her recent interview at Mind and Matter<\/a> <\/em>suggests that this is literally \u201cshort sighted\u201d and that for many metrics, a much longer time period<\/em> should be considered. <\/p>\n\n\n\n

I hope I have time to keep up with your comments, I try to answer all that are addressed expressly to me. <\/p>\n\n\n\n

Thanks for reading.<\/p>\n\n\n\n

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via Watts Up With That?<\/mark><\/em><\/strong><\/p>\n\n\n\n

August 17, 2022<\/p>\n\n\n\n

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Fun with Trends<\/a><\/blockquote>