Agree to Disagree
Debate in a non-hostile environment
How warming rates vary
with split date ranges
The purpose of this article, is to answer a question that was asked by Eli Mi, on the website http://www.drroyspencer.com.
Here is a link to Eli Mi’s original post:
Here is a link to Eli Mi’s second post:
I will summarise Eli Mi’s question, and then answer the question, with the help of some graphs. The graphs are a special type of graph, called a “Global Warming Contour Map.
A global warming contour map uses colour to display the warming rates for EVERY possible date range, that lies between 2 dates. In this case, we are looking at UAH Global Lower Troposphere temperature anomalies. We are looking at all temperature anomalies that lie between 1980 and 2018.
Because we are using colour to represent warming rates, the first thing that we need is a Legend, to show what warming rates each colour represents. Please look at the following Legend.
Eli calculated the warming rate for the “big” date range 1980 to 2018, using the UAH Global Lower Troposphere temperature anomalies. He got a warming rate of approximately +1.30 degrees Celsius per century.
He then split the big date range into 2 smaller date ranges, at the year 1998. This gave him 2 smaller date ranges, 1980 to 1998, and 1998 to 2018. The 2 smaller date ranges can be combined, and the result is the original big date range. He calculated the warming rate for each of the smaller date ranges. The warming rates that he got were approximately:
1980 to 1998..=..+0.95 degrees Celsius per century
1998 to 2018..=..+0.79 degrees Celsius per century
Eli was surprised to see that the warming rates for both of the smaller date ranges, were considerably lower than the warming rate of the big date range.
Since the two smaller date ranges can be combined to give the big date range, why don’t the warming rates follow a similar rule. Shouldn’t the warming rate of the big date range be something like an average of the warming rates, of the 2 small date ranges?
You can see what the situation is, very clearly, by looking at a plot of the calculated linear regression lines, for all of the date ranges:
To make the situation even more confusing, another person posted the warming rates when the date range is split at 1999, rather than 1998.
When the big date range is split at 1999, the 2 smaller date ranges have warming rates that are both BIGGER than the warming rate of the big date range. This is the exact opposite of what Eli found, when he split the big date range at 1998.
The warming rates when the big date range is split at 1999, are (approximately):
1980 to 1999..=..+1.66 degrees Celsius per century
1999 to 2018..=..+1.47 degrees Celsius per century
Remember, the warming rate of the big date range is +1.30 degrees Celsius per century.
You can see what the situation is, with the 1999 split, by looking at a plot of the calculated linear regression lines, for all of the date ranges:
Linear regressions are most sensitive to the points near the ends of the date range, and less sensitive to points in the middle of the date range. The points that made splitting at 1998, so different to splitting at 1999, were the points corresponding to the 1998 super El Nino. This can be seen, by looking at the 2 “woodfortrees” graphs. However, we will investigate the reason for the slope differences, using a different type of graph. A “Global Warming Contour Map”. This will give us more information about how warming rates vary, with split date ranges
I have summarised all of the results in the following table. There is also some additional information, that will help us to understand the global warming contour maps.
You can see in the table, that I have listed the data for 5 points, A, B, C, D, and E.
A is the big date range (1980 to 2018)
B is the first small date range, when the big date range is split at 1998 (1980 to 1998)
C is the second small date range, when the big date range is split at 1998 (1998 to 2018)
D is the first small date range, when the big date range is split at 1999 (1980 to 1999)
E is the second small date range, when the big date range is split at 1999 (1999 to 2018)
The table shows the start date, the end date, the middle date, the length of the date range, the warming rate, the colour that corresponds to the warming rate, the colour name, and the warming rate range, that the colour represents.
We are now ready to look at the global warming contour maps. Many people find contour maps confusing, when they first look at them. So don’t worry if things are not totally clear, when you first look at a global warming contour map. I will try to explain how contour maps work, and with a little practice, you will probably be able to understand them.
The first thing to notice, is that the middle date of the date range, is plotted on the X-axis. This is a standard date axis, but it is NOT the start date, or the end date. It is the middle date (many people find this confusing).
The second thing to notice, is that the length of the date range is plotted on the Y-axis. This shouldn’t be confusing. Longer date ranges are plotted near the top, and shorter date ranges are plotted near the bottom.
Have a quick look at the following global warming contour map, and notice that it is made up of small squares. The most important point to understand about a contour map, is that each of those small squares, represents a unique date range. And the colour of the square, represents the warming rate of the unique date range.
So if you want to know the warming rate for a date range (say, 1980 to 2018), you just have to figure out which small square represents the date range that you are interested in, and look at the colour.
An example will help. Assume that we want to know the warming rate for 1980 to 2018.
First, calculate the length of the date range. This is easy, it is just
length of the date range = end date minus start date
= 2018 – 1980
= 38 years
Next, calculate the middle of the date range. Again, this easy, it is just
middle of the date range = (start date + end date) / 2
= (1980 + 2018) / 2
Now, look on the graph, and find the small square at ( X = 1999, Y = 38 )
To make it easy to find a particular year on the X-axis, remember that each small square is 1 year wide (and 1 year high). I sometimes use a “window”, like the window that you get when you run the program “Notepad.exe”, as a “straight edge”, to help me find the right small square. You can use the vertical edge of the window, and the horizontal edge of the window, to show you the right square.
If you try to locate the small square at ( X = 1999, Y = 38 ), you should get the small square labelled “A”, at the top of the triangle. This is the point that corresponds to the big date range (1980 to 2018). Look at the colour, and check the Legend to see what it means.
It is medium-orange, which represents the warming rate range +1.0 to +1.5 degrees Celsius per century. From now on, I am not going to keep writing “degrees Celsius per century”. It takes too long. All of the warming rates that I mention, will be in degrees Celsius per century.
Now, check in the table above, to see what the actual warming rate was for the big date range (point “A”). It was +1.30. Guess what, +1.30 is in the range +1.0 to +1.5, the warming rate range for medium-orange. That is how it works. With a little practice, you will be able to look up any date range that you like.
It is important to realise, that the global warming contour map doesn’t give you the warming rate accurate to several decimal digits. To do that, it would need to use hundreds, or thousands, of colours, and it would be a confusing mess of coloured dots.
The strength of a global warming contour map, is that it summarises what happened to the warming rate, in a way that is easy to understand. Look at the big area of green, blue, and grey, small squares, in the bottom half of the previous contour map, on the right side. Some people won’t like me saying this, but that is the recent slowdown. Remember, you didn’t hear that from me.
Let’s try to answer Eli’s question, using the global warming contour map. I have labelled all of the points on the contour map, with the appropriate letter. The different colours, show you that the warming rates were different. Look at each of the points, and see if you can understand how the global warming contour map works.
The contour map tells you the story of what the warning rate did, for any date range. When the colour is yellow, orange or red, it is warming. Yellow is mild warming. Orange is a medium warming, Red is strong warming.
When the colour is green or blue, it is cooling. Green is mild to medium cooling, blue is medium to strong cooling.
Grey means that the warming rate is very near zero. It is not really warming or cooling.
What are the dark blues and dark reds near the bottom of the triangle? They are powerful short-term climate events (things like El Nino’s and La Nina’s). Have a look at the previous contour map, near the X-axis, at X = 1998. The squares are deep red, and deep blue. Guess what that is. It is the 1998 super El Nino.
I can understand if you are a bit skeptic about the 1998 super El Nino. But it is true. It is hard to make out, because the resolution of this contour map, is only “yearly”. I made it specially to answer Eli’s question. Normally I make contour maps with a resolution of “monthly”. And that makes things look a lot clearer.
Also, I normally don’t have gaps between the small squares. I did that this time, to make it easier for you to see how each unique date range, corresponds to a small square. The following global warming contour map, is the same as the last one, but it has no gaps between the small squares. It looks more like a picture. The small squares of the same colour, join up to make a pattern.
The pattern tells the story of what the warming rate was, for each unique date range. You just have to know how to read it. You can identify major trends (big areas of one colour), and the colour changes tell you whether it is warming faster, or slower.
The answer to Eli’s question, is that the warming rate varies a lot, and where you split a big date range, determines what you get. It is a matter of chance. Eli got 2 lower warming rates, when he split the big date range at 1998. The other person got 2 higher warming rates, when he split the big date range at 1999. It is also possible to get 1 lower warming rate, and 1 higher warming rate. It is a matter of luck.
Linear regressions are most sensitive to the points near the ends of the date range, and less sensitive to points in the middle of the date range. The points that made splitting at 1998, so different to splitting at 1999, were the points corresponding to the 1998 super El Nino.
When the date range was 1980 to 1999, the points corresponding to the 1998 super El Nino “pulled” the RIGHT END of the regression line up, giving it a higher warming rate.
When the date range was 1980 to 1998, the points corresponding to the 1998 super El Nino were NOT “pulling” the RIGHT END of the regression line up, so the other points in the date range dominated the warming rate, and it was lower.
When the date range was 1998 to 2018, the points corresponding to the 1998 super El Nino “pulled” the LEFT END of the regression line up, giving it a lower warming rate.
When the date range was 1999 to 2018, the points corresponding to the 1998 super El Nino were NOT “pulling” the LEFT END of the regression line up, so the other points in the date range dominated the warming rate, and it was higher.
A global warming contour map shows you the range of warming rates, that you are likely to get. The lower on the contour map that you go, the more variability there is. The higher that you go on the contour map, the more that things have been “averaged”, so you get less variability.
I hope that you have enjoyed this brief introduction to global warming contour maps. We have only “brushed the surface”, in this article. If you are interested in learning more about them, then there are a lot of articles on my website. I will list some, at the end of this article.
Anybody who is keen to learn more about contour maps, should read the article called “Robot-Train contour maps”. This article explains how contour maps work, using simple “train trips”, as an analogy for global warming.
I am happy to answer questions about global warming contour maps, and enjoy using contour maps to solve climate questions. You can contact me through the “Comments” page of my website, or through the “Contact” page. You can also leave feedback on the “Comments” page of my website.
[ this article shows how “global warming contour maps” work ]
[ this article shows why Alarmist thinking on slowdowns, in one-dimensional ]
[ this article investigates the Alarmist myth, that the slowdown was caused by the 1998 super El Nino ]
[ this article shows why the slowdown is so special (No, no, no, no, no! It only LOOKS special. It isn’t really special.) ]
[ A guide to the CORRECT way to look for slowdowns. Please try to stay quiet. Slowdowns scare easily, and then they run away and hide. ]
[ this article investigates warming in the USA, using NOAA’s new ClimDiv temperature series ]
[ this article investigates regional warming, by dividing the earth into 8 equal sized areas, by latitude]
[ this weather balloon article has global warming contour maps with very nice colours ]
[ this article uses global warming contour maps to compare GISTEMP and UAH ]