What is Normal?

I titled my very first climate video "What is Normal," alluding to the fact that climate doomsayers argue that we have shifted aspects of the climate (temperature, hurricanes, etc.) from "normal" without us even having enough historical perspective to say what "normal" is.

A more sophisticated way to restate this same point would be to say that natural phenomenon tend to show various periodicities, and without observing nature through the whole of these cycles, it is easy to mistake short term cyclical variations for long-term trends.

A paper in the journal Water Resources Research makes just this point using over 200 years of precipitation data:

We analyze long-term fluctuations of rainfall extremes in 268 years of daily observations (Padova, Italy, 1725-2006), to our knowledge the longest existing instrumental time series of its kind. We identify multidecadal oscillations in extremes estimated by fitting the GEV distribution, with approximate periodicities of about 17-21 years, 30-38 years, 49-68 years, 85-94 years, and 145-172 years. The amplitudes of these oscillations far exceed the changes associated with the observed trend in intensity. This finding implies that, even if climatic trends are absent or negligible, rainfall and its extremes exhibit an apparent non-stationarity if analyzed over time intervals shorter than the longest periodicity in the data (about 170 years for the case analyzed here). These results suggest that, because long-term periodicities may likely be present elsewhere, in the absence of observational time series with length comparable to such periodicities (possibly exceeding one century), past observations cannot be considered to be representative of future extremes. We also find that observed fluctuations in extreme events in Padova are linked to the North Atlantic Oscillation: increases in the NAO Index are on average associated with an intensification of daily extreme rainfall events. This link with the NAO global pattern is highly suggestive of implications of general relevance: long-term fluctuations in rainfall extremes connected with large-scale oscillating atmospheric patterns are likely to be widely present, and undermine the very basic idea of using a single stationary distribution to infer future extremes from past observations.

Trying to work with data series that are too short is simply a fact of life -- everyone in climate would love a 1000-year detailed data set, but we don't have it.  We use what we have, but it is important to understand the limitations.  There is less excuse for the media that likes to use single data points, e.g. one storm, to "prove" long term climate trends.

A good example of why this is relevant is the global temperature trend.  This chart is a year or so old and has not been updated in that time, but it shows the global temperature trend using the most popular surface temperature data set.  The global warming movement really got fired up around 1998, at the end of the twenty year temperature trend circled in red.

click to enlarge


They then took the trends from these 20 years and extrapolated them into the future:

click to enlarge

But what if that 20 years was merely the upward leg of a 40-60 year cyclic variation?  Ignoring the cyclic functions would cause one to overestimate the long term trend.  This is exactly what climate models do, ignoring important cyclic functions like the AMO and PDO.

In fact, you can get a very good fit with actual temperature by modeling them as three functions:  A 63-year sine wave, a 0.4C per century long-term linear trend  (e.g. recovery from the little ice age) and a new trend starting in 1945 of an additional 0.35C, possibly from manmade CO2.Slide52

In this case, a long-term trend still appears to exist but it is exaggerated by only trying to measure it in the upward part of the cycle (e.g. from 1978-1998).



  1. dirk:

    Nice, would you mind giving the parameters of the fitted sine curve (e.g. phase and length or the functional form) and/or a plot of predictions for the next 20 years or so. Thanks

  2. Dan Pangburn:

    I would like to know what R^2 this produces. (Wikipedia shows how to calculate the coefficient of determination between calculated and measured for other than straight line correlations)

    I got 0.9+ using the time-integral of sunspot number anomalies combined with a saw-tooth approximation for annual average effective surface temperature oscillations resulting from ocean oscillations.

  3. Zachriel:

    Eppur si riscalda.

  4. Dan Pangburn:

    According to the average of the five agencies that report average global temperatures it isn't true in Italian either. Their reported average global temperatures are graphed at http://endofgw.blogspot.com

  5. Zachriel:

    The first ten months of 2014 (January–October) were the warmest such period since record keeping began.

    The 12-month period, November 2013–October 2014, broke the record (just set in the previous month) for the all-time warmest 12-month period.

    The combined global land and ocean average surface temperature for the year-to-date (January–November 2014) was the warmest such period on record.


  6. Dan Pangburn:

    Five agencies report average global temperature. I track them all. NOAA is an outlier on the high side. This is shown on the co-plot of all of them through 2013 at http://endofgw.blogspot.com. I have them graphed through Nov. 2014 on my computer and will make this graph public after all through Dec. are reported. NOAA remains an outlier on the high side.

    Part of the story is that records of temperature measurement began in 1850 as the planet was emerging from the Little Ice Age. According to proxy measurements, both the Roman Warm Period and the Medieval Warm Period were warmer than the present.

    Temperatures increased from the depths of the LIA (around 1700) until significant increase stopped in about 2005 (reported measurement trend has been flat since 2001). Random uncertainty in reported measurements is s.d 0.09 K.

    As the NOAA site reports, the average global temperature anomaly (AGT) in Nov. 2014 is 0.65 K. The average of values reported by NOAA 2001-2013 is 0.55 K. The fact that the reported number for Nov. 2014 is higher by 1.1 s.d. is well within the range of random uncertainty. The number is further discounted because NOAA reported anomalies are demonstrated to be outlier.

    Thus the fact that the latest value reported by NOAA is a new high means nothing with respect to the current average global temperature trend. Further, the fact that the average of measurements at the end of a warming period is the highest over the warming period also means nothing with respect to the current average global temperature trend.

  7. Zachriel:

    Here's the longer trend. Note the stratospheric cooling, indicative of greenhouse warming.

  8. Dan Pangburn:

    Looks like the stratosphere trend has been flat since before the warming stopped in 2001 (average of reported temperatures).

    Look closely at the surface and near surface data. The times in common are plots of the same data. How these fit into much longer period is shown at http://agwunveiled.blogspot.com

    Are you aware that the huge effective thermal capacitance of the planet (mostly oceans) absolutely prohibits the rapid fluctuations in reported average global temperatures? The reported values contain a lot of random 'noise' which means that trends are more credible (less uncertainty) while individual reported values are not.

  9. CB:

    No, Dan Pangburn. Your blog is nowhere near as credible a resource as NOAA, especially given your failure to understand even the simplest concepts of both logic and scientific endeavour:

    "The first ten months of 2014 were the warmest such period on record."


    If you think 2014 wasn't the warmest year on record, which year was and how do you know?

    If you know your sources of information are misleading you, why would you continue to rely on them?

  10. CB:

    "would you mind giving... predictions for the next 20 years or so"

    How about making your own prediction?

    Arctic sea ice has declined 59% in the last 36 years:

    "Monthly averaged ice volume for September 2014 was 6,970 km3... 59% lower than the maximum in 1979"


    If it won't be completely gone in a few more decades at this rate, how long will it take?

    If you understand this sea ice stabilises temperatures throughout the northern hemisphere, don't you think this is information you should know?

  11. Zachriel:

    Dan Pangburn: Are you aware that the huge effective thermal capacitance of the planet (mostly oceans) absolutely prohibits the rapid fluctuations in reported average global temperatures?

    And as the oceans are warming while the surface temperatures are edging upwards, that means total heat content is increasing. Meanwhile the stratosphere has cooled.

  12. dirk:

    and if we include the antarctic total ice volume is expanding despite climate models predicting otherwise. Make your own conclusion about falsification/verification of the models.

    The point is that climate modelers told us that there is proof of manmade/Co2-induced global warming because no other factor they can think of could explain the rapid warming from 80s and beginning of 90s. This was already in itself BS because there periods with comparable warming rates in the past, but now they admit that natural effects such as PDO are sttrong enough to hide the warming from end of 90es to now. Draw your own conclusion about what this tells about the "proof" of manmade global warming

  13. policygeek:

    Blah blah blah. If you can prove the mountain of scientific evidence for man made climate change wrong, then do it and win yourself a Nobel Prize. Otherwise you're just a long winded blowhard.

  14. Dan Pangburn:

    NOAA is one of the sources that I use.

    Because the random uncertainty in reported measurements is s.d. 0.09 K, no one really knows when the warmest year was, The high year of the average of the five reporting agencies was 2010. The average for 2014 looks to be about 0.06 K cooler than 2010.

    If you cherry pick NOAA and ignore GISS, HADcrut, UAH, and RSS, then 2014 is higher than 2010 by about 0.05 K while the uncertainty in each of the reported values is s.d. 0.09 K. Considering all this, the assertion that 2014 is the warmest year is not justified.

  15. Scottar:

    When BO got the prize it showed how corrupt and ridiculous NPP has become, along with Algore.

  16. policygeek:

    When you can't disprove the science, attack the institution.

  17. Dan Pangburn:

    Apparently some people are still gullible enough to believe that increasing the atmospheric CO2 from 3 parts in 10,000 to 4 parts in 10,000 drastically changed the way that the oceans absorb sunlight.

  18. Zachriel:

    Dan Pangburn: CO2 from 3 parts in 10,000 to 4 parts in 10,000 drastically changed the way that the oceans absorb sunlight.

    Most of the atmosphere is transparent to heat radiation. CO2 represents about 20% of the greenhouse effect. An increase in the greenhouse effect will result in more heat being absorbed by the surface than is emitted.

  19. Scottar:

    You Know Dirk, climate alarmists like to overlooks the previous 30~40 years from the past 36 years because climate scientists and meteorologists know that the Artic basin goes through a 60 year cycle of expansion and melting due to what is known as the PDO- AMO cycle which is part of the Earths climate moderation cycle.


    Arctic Temperatures and Ice – Why it is Natural Variability


    Multidecadal Ocean Cycles and Greenland and the Arctic

    Climate change can't be trended by jacked up climate models nor 30~100 years of dubious, contrived data by what have become science bureaucracies run by bureaucrats, not scientists for the money gravy train:


    Climate Money


    Climate Bullies

  20. CB:

    "antarctic total ice volume is expanding"

    NASA says you're incorrect. The volume of Antarctic ice is decreasing by 100 km³ per year:

    "The continent of Antarctica has been losing more than 100 cubic kilometers (24 cubic miles) of ice per year since 2002."


    Which space agency informs you otherwise?

  21. Dan Pangburn:

    You have been hoodwinked by mob-think. CO2 has no significant effect on climate. The absorption opportunities of terrestrial radiation for water vapor out number the absorption opportunities for CO2 by about 60,000 to 1.

    Paraphrasing Richard Feynman: Regardless of how many experts believe it or how many organizations concur, if it doesn’t agree with observation, it’s wrong.

    The Intergovernmental Panel on Climate Change (IPCC), some politicians and many others mislead the gullible public by stubbornly continuing to proclaim that increased atmospheric carbon dioxide is a primary cause of global warming.

    Measurements demonstrate that they are wrong.

    CO2 increase from 1800 to 2001 was 89.5 ppmv (parts per million by volume). The atmospheric carbon dioxide level has now (through November, 2014) increased since 2001 by 28.17 ppmv (an amount equal to 31.5% of the increase that took place from 1800 to 2001) (1800, 281.6 ppmv; 2001, 371.13 ppmv; November, 2014, 399.3 ppmv).

    The average global temperature trend since before 2001 is flat (average of the 5 reporting agencies, http://endofgw.blogspot.com ). Current measurements are well within the range of random uncertainty with respect to the trend.

    That is the observation. No amount of spin can rationalize that the temperature increase to 2001 was caused by a CO2 increase of 89.5 ppmv but that 28.17 ppmv additional CO2 increase had no effect on the average global temperature trend after 2001.

  22. Scottar:

    When the institution is corrupt, you have to go outside of it for the truth.


    Climate Money


    Climate Bullies

    And the biggest institution is the government and all that operates under it is tainted.

  23. Zachriel:

    Dan Pangburn: CO2 has no significant effect on climate. The absorption opportunities of terrestrial radiation for water vapor out number the absorption opportunities for CO2 by about 60,000 to 1.

    CO2 and H2O do not have the same infrared spectrum. Basic physics indicates that if CO2 increases, the surface will warm. This has been known for over a century. The only question is how much warming due to the positive feedback of increased water vapor.

  24. Dan Pangburn:

    The basic physics that has been known for over a century is that CO2 absorbs terrestrial radiation which makes it a greenhouse gas. The basic physics that has been learned since then is that CO2 absorbs terrestrial radiation only at 15 microns while water vapor absorbs terrestrial radiation at more than 400 different wave lengths. There are about 15,000 ppmv water vapor compared to the 100 ppmv increase in CO2 which results in the 1 part in 60,000 increase in absorption 'opportunities' which is insignificant.

    Another factor that has been ignored (or not realized) is that at least part of the energy that is absorbed by the CO2 is thermalized. That is, the energy is conducted to non-greenhouse gases N2 and O2. This energy is eventually reverse-thermalized back to ghg (mostly water vapor) and radiated to space.

    The equation in "agwunveiled" results from a valid application of the first law of thermodynamics (conservation of energy). The fact that R2 is not significantly different whether CO2 change is included or not demonstrates that CO2 change has no significant effect on climate.

    Take the blinders off. The GCMs that the consensus have been scaring you with did not predict the flat temperature trend since before 2001. On average, they predicted that current average global temperatures would be 0.3 K warmer than reported measurements say they are. Then they rationalize this failure with the silly idea that the added heat suddenly started going into the ocean.

    Some graphs that I have seen (at Skepticalscience) didn't even know the difference between rate-of-change of energy (TSI) and energy (temperature).

    The cause of climate change, at least for the period 1610-2015, has been discovered. Near future (decades) climate will depend on sunspots and ocean cycles and "agwunveiled" shows possible trends to 2037. Long term (millennia) on Milankovitch cycles (which include glaciation).

  25. CB:

    "CO2 has no significant effect on climate"

    If there's a stronger driver of planetary temperature than CO₂ over long time scales, point to a single moment in Earth's history when this driver caused polar ice caps to form with CO₂ as high as we have today.

    If what you say were true, this should be happening all the time, right?

    ...so why doesn't it?

  26. dirk:

    you have to look at the sea ice extent. Continental extent is (1) in large parts driven by precipitation rather than temperatures and (2) varies much slower. It is the sea ice which goes through the annual cycle where one should quickly discover a warming signal.

  27. Dan Pangburn:

    Still showing these old charts . . .

    Not that it matters, because CO2 change is demonstrated to have no significant effect on climate, but to put things in perspective, 1000 gigatons on Antarctica amounts to 2.8 inches on an ice pack that averages 7870 feet thick.

  28. Zachriel:

    Dan Pangburn: The equation in "agwunveiled" results from a valid application of the first law of thermodynamics (conservation of energy).

    The valid application of conservation of energy is to note that the heat energy of the Earth's surface (atmosphere, hydrosphere, cryosphere) is increasing. As energy is conserved, that means excess heat has to come from somewhere. Solar output is relatively stable. The excess heat, however, is consistent with greenhouse warming.

  29. CB:

    "you have to look at the sea ice extent"

    ...and why would you be doing that?

    Extent is a measurement of area, not volume.

    Is area the way we measure the amount of ice?

  30. CB:

    "NOAA is one of the sources that I use."

    ...so state which year was the hottest and cite NOAA supporting your claim. It'll look like this:

    "The first 11 months of 2014 (January–November) was the warmest such period on record across the world's land and ocean surfaces"


  31. S Graves:

    You are fond of arguing "what satellites tell you otherwise?". So what do the satellites tell us about 2014 temps?
    So, CB, if you know how much warmer 2014 appears on the chart you cite and you know what the error bars are then you know you don't really know that 2014 was actually the warmest in history...just the warmest on the chart, don't you?

  32. CB:

    "So what do the satellites tell us about 2014 temps?"

    I dunno, Babs. It's not relevant to this conversation.

    If you think NOAA's incorrect about 2014 being the hottest year on record, state which year was and cite your sources.

    If you understand NOAA is correct, please state that NOAA's correct:

    "The first 11 months of 2014 (January–November) was the warmest such period on record across the world's land and ocean surfaces"


    Because you have a habit of attempting to hijack threads about climate science with non sequitur and unsupported claims, you have one opportunity to meet this incredibly simple challenge.

    If you cannot comport yourself like an adult, you will be ignored.

  33. S Graves:

    So you don't think that satellite temp data is of any value? But you claim that satellite ice data is the gold standard? Why the difference? Or are you just making stuff up as you go to attempt to seem relevant?
    You are citing a statistical analysis, aren't you? Do you know the temps of the other warmest years? Do you know the error bars? So then you know that you only know which years is the warmest on the CHART...not necessarily the ACTUAL warmest. Or do you think that chart tells you something it doesn't?

  34. Kevin:

    I've updated your chart based on 2015 HadCRUT data. Your approach is now well outside the error bars for 2015:

    Perhaps there's a more accurate model? Say, including CO2?