Temperature Data: Sufficient to Make
the Case for Global Warming?

In general, the case that global climate change is now occurring is based on the Preponderance of Evidence (see next lecture) that exists. In particular, the procedure one would use to establish the most credible case is simply to find measurable indicators of climate change. But this is hard as it requires:

• robust definition of what constitutes a climate
  
  
• set of procedures for measuring change
  
  
• instrumental precision sufficient to measure change

Because of these reasons, there is no one indicator (smoking gun) for global climate change. An aggregate of all forms of climate data then provides the preponderance of evidence as we will see.

However, for most arguments, the case of Global Warming rests on just one represenation of the data and this is a scientifically absurd thing to do.

By way of example we will use a form of the "hockey stick diagram" of a few years ago. For purposes of the argument here, it is not necessary to use the most modern version - that version will be shown later on.

Here we use a presentation of 2007 - not the largest spike occurs in 1998. After that spike failed to increase over the next couple of years, there was a wave stating that Global warming had reached its peak and is now over. This is another example of a scientifically illterate public. Climate data is subject to short term flucutations, and none of thse flucations can be used to predice future behavior.

Without deciding yet whether or not these kinds of data make a convincing case that global warming is occurring, we need to ask some important scientific questions:

• Is the global annual average temperature of the Earth a meaningful number? What does it represent?
  
  
• How does one measure it? How many thermometers should be used? Where should those thermometers be located?
  
  
• Are the thermometers used in 1860 the same as those used in 2007?
  
  
• Have the 20^th century data been properly corrected for the effects or urbanization. In many cases, the location of the thermometer has not changed for 80 years, but in those 80 years, the cow pasture that the thermometer used to be located in is now a parking lot or is now surrounded by buildings.
  
  For example, the image below shows the environment an official thermometer which is located in Lampass, Texas:
  
  
  
  
  

  So there are significant issues of data reliability over the period of record when it comes to using only the global mean temperature of the Earth as an indicator of climate change.

  Now, concerning the top hockey stick figure - what is typically plotted on the Y-axis is not the actual mean global temperature but instead a deviation from the average value that is determined by some baseline. While this form of data presentation is scientifically valid, the amplitude of the deviations does depend upon how the baseline is chosen.
  
  In the diagram above, a baseline period of 1961-1990 was used. (in most climate studies, 30 years is taken to be the time period for establishing average behavior) as the baseline. Therefore, the mean global temperature of the Earth over the period 1961-1990 is subtracted from each yearly data point. The problem with this approach is that is no guarantee that this period is representative – furthermore, if this period was characterized by either general cooling or general warming, then it doesn’t represent a flat baseline.
  
  What you choose as your baseline period does effect the data. In the example below, we compare the 1961-1990 baseline subtracted data against that using the period 1885-1915 for the baseline:

  

  Clearly, by 2007, the amplitude of the warming (value of the Y-axis) is larger in the case of the 1885-1915 baseline – the overall shape of the curve doesn't change, of course, because you're just shifting it up or down in Y by a constant, where that constant is the average global temperature within the baseline period.

  
  
  This is the set of generic arguments that can be made from just using global average temperature as the principle measure of climate change and those same arguments can certainly to all forms of the hockey stick. Here we show the 2015 version:
  
  
  
  Recently, a slightly better version of global temperature data is now provided by NASA Goddard which now uses a combined land+ocean data set, and once an be sure that the ocean signal is not contaminated very much by urbanization. The use of this combined data set also, physically correclty, lowers the overall amplitude a bit of the temperature anamoly.
  
  
  
  At this point, you should read this blog article about all of this. The points in that blog are:
  
  
  • The temperature data is not linear and therefore a non-linear fit is required.
  • The last 4 years of temperature data should have the most weight as they clearly indicate that non-linearity is present:
  
  
  
  
  One of the problems with data representations like this is the use of annual average temperature. Weather is not an annual phenomena; it is primarily a seasonal feature. The following represents a new approach to this by considering monthly data rather than annual data (so now there are 12 data points per year). An example, done by the author, is shown below.

  Raw Data

  

  The overall trend is more easily revealed when the data is smoothed; in this case smoothed on a time scale similar to the occurences between El Ninos.

  

  Recent down turn most likely just part of the short term El Nino/La Nino cycle. No evidence from this wave form that global warming has stopped. This approach is more extensively discussed in in this blog article . This article was done in response to the claims that global warming had stopped ...
  
  A good representation of the hockey stick diagram, but one that is rarely seen is shown below. In this case, the +/- 2 standard deviation errors are indicated (labeled as 5-95% decadal error bars), and the data has been averaged over a long enough window to suppress much of the inherent noise. The 4 colored lines indicate the linear slopes that are obtained in different time periods, in units of degrees C per decade. Presented in this way, the data reveal an increasing slope when the most recent data is used. This is another way to indicate non-linarity.

  
  
  Next we can make use of statistics to understand if the rise is significant or not. We can now also apply the Z-test to this global data. For instance, we can ask the question, is the average mean temperature of the Earth over the period 1980 – 2007 significantly different than the period of 1900-1980?

  The actual global data is here – but here is a table of the results:

  Time Period	Avg. Temp	Deviation	Error in Mean
  1900 – 1980	58.2	0.37	.04
  1980 - 2007	59.4	0.31	.06
  Z-statistic			16.7 (!)

  So yes, a highly significant difference exists if one wanted to present the data in this manner. But is that difference due to urbanization and thermometer location or is it indicative of a real change in the climate system?
  
  
  The bottom line scientifically is that collapsing all the data down to a one dimensional measure of global average temperature is an ambiguous and unreliable measure of global warming.

  A far more convincing case arises when the actual location of the temperature measurements are used. Simple models easily show that heat flows from the equator to the poles. Since there is much less surface area at the poles of a sphere, then the heat flux per unit area in the Earth’s polar region will be higher than in the equatorial regions.
  
  

  
  
  

  This leads to a simple prediction Warming should be higher in the high latitude regions of the Earth. Here is some data that strongly supports this:

  

  
  
  Here the temperature data is sliced into 4 different time periods for analysis. Panel (c) clearly shows what is known as the mid-century cooling period (seen in the hockey stick diagram over the period 1940-1965). However, the alarming trends appear in panel (d) – throughout the northern hemisphere, there are significant temperature trends as high as increases of 1 degree C per decade! It is this form of data slicing and representation that is, by far, the most scientifically convincing evidence that global warming is now seen in the actual land temperature data.

  Further slicing of the data shows that this high latitude signal is strongest in the winter months – this has grave implications with respect to permafrost melting and methane releases which we will discuss later:

  

  
  
  
  The above illustrations were used to make the basic point about how to represent temperature trends as 2D. Below are some more examples using more recent data, which serves to maintain the trends already seen but makes them worse:
  
  

  
  
  
  
  Note that you can make your own maps like this using the interactive form located HERE (you will do some exercises on Sections on Friday using this interface)
  
  
  Finally, a new regional climate record has been analyzed in seasonal terms that have revealed fairly significant summer time warming in Central Europe:
  

  Conceptually increasing climate volatility can be represented as follows:

  

  Panel (a) shows the expectation if there is simply if the new climate simply is a direct shift in average quality from the old climate but the variation around the average is the same. This is likely to be too simplified of notion.

  Panel (b) shows the case where the new climate simply shows more extreme variations around the same average values as the old climate.

  Panel (c) shows the case where there is both a shift in the average and an increase in the volatility (i.e., variance around the average). That situation would predict the most amount of record heat.

  The observed data is mostly consistent with Panel c.