This article presents a method for calculating the Earth’s rate of warming, using the existing global temperature series.

Guest essay by Sheldon Walker

It can be difficult to work out the Earth’s rate of warming. There are large variations in temperature from month to month, and different rates can be calculated depending upon the time interval and the end points chosen. A reasonable estimate can be made for long time intervals (100 years for example), but it would be useful if we could calculate the rate of warming for medium or short intervals. This would allow us to determine whether the rate of warming was increasing, decreasing, or staying the same.

The first step in calculating the Earth’s rate of warming is to reduce the large month to month variation in temperature, being careful not to lose any key information. The central moving average (CMA) is a mathematical method that will achieve this. It is important to choose an averaging interval that will meet the objectives. Calculating the average over 121 months (the month being calculated, plus 60 months on either side), gives a good reduction in the variation from month to month, without the loss of any important detail.

Graph 1 shows the GISTEMP temperature series. The blue line shows the raw temperature anomaly, and the green line shows the 121 month central moving average. The central moving average curve has little month to month variation, but clearly shows the medium and long term temperature trend.

The second step in calculating the Earth’s rate of warming is to determine the slope of the central moving average curve, for each month on the time axis. The central moving slope (CMS) is a mathematical method that will achieve this. This is similar to the central moving average, but instead of calculating an average for the points in the interval, a linear regression is done between the points in the interval and the time axis (the x-axis). This gives the slope of the central moving average curve, which is a temperature change per time interval, or rate of warming. In order to avoid dealing with small numbers, all rates of warming in this article will be given in °C per century.

It is important to choose the correct time interval to calculate the slope over. This should make the calculated slope responsive to real changes in the slope of the CMA curve, but not excessively responsive. Calculating the slope over 121 months (the month being calculated plus 60 months on either side), gives a slope with a good degree of sensitivity.

Graph 2 shows the rate of warming curve for the GISTEMP temperature series. The blue line is the 121 month central moving slope (CMS), calculated for the central moving average curve. The y-axis shows the rate of warming in °C per century, and the x-axis shows the year. When the rate of warming curve is in the lower part of the graph ( colored light blue), then it shows cooling (the rate of warming is below zero). When the rate of warming curve is in the upper part of the graph ( colored light orange), then it shows warming (the rate of warming is above zero).

The curve shows 2 major periods of cooling since 1880. Each lasted approximately a decade (1900 to 1910, and 1942 to 1952), and reached cooling rates of about -2.0 °C per century. There is a large interval of continuous warming from 1910 to 1942 (about 32 years). This reached a maximum rate of warming of about +2.8 °C per century around 1937. 1937 is the year with the highest rate of warming since the start of the GISTEMP series in 1880 (more on that later).

There is another large interval of continuous warming from about 1967 to the present day (about 48 years). This interval has 2 peaks at about 1980 and 1998, where the rates of warming were just under +2.4 °C per century. The rate of warming has been falling steadily since the last peak in 1998. In 2015, the rate of warming is between +0.5 and +0.8 °C per century, which is about 30% of the rate in 1998. (Note that all of these rates of warming were calculated AFTER the so‑called “Pause-busting” adjustments were made. More on that later.)

It is important to check that the GISTEMP rate of warming curve is consistent with the curves from the other temperature series (including the satellite series).

Graph 3 shows the rate of warming curves for GISTEMP, NOAA, UAH, and RSS. (Note that the satellite temperature series did not exist before 1979.)

All of the rate of warming curves show good agreement with each other. Peaks and troughs line up, and the numerical values for the rates of warming are similar. Both of the satellite series appear to have a larger change in the rate of warming when compared to the surface series, but both satellite series are in good agreement with each other.

Some points about this method:

1) There is no cherry-picking of start and end times with this method. The entire temperature series is used.

2) The rate of warming curves from different series can be directly compared with each other, no adjustment is needed for the different baseline periods. This is because the rate of warming is based on the change in temperature with time, which is the same regardless of the baseline period.

3) This method can be performed by anybody with a moderate level of skill using a spreadsheet. It only requires the ability to calculate averages, and perform linear regressions.

4) The first and last 5 years of each rate of warming curve has more uncertainty than the rest of the curve. This is due to the lack of data beyond the ends of the curve. It is important to realise that the last 5 years of the curve may change when future temperatures are added.

There is a lot that could be said about these curves. One topic that is “hot” at the moment, is the “Pause” or “Hiatus”.

The rate of warming curves for all 4 major temperature series show that there has been a significant drop in the rate of warming over the last 17 years. In 1998 the rate of warming was between +2.0 and +2.5 °C per century. Now, in 2015, it is between +0.5 and +0.8 °C per century. The rate now is only about 30% of what it was in 1998. Note that these rates of warming were calculated AFTER the so-called “Pause-busting” adjustments were made.

I was originally using the GISTEMP temperature series ending with May 2015, when I was developing the method described here. When I downloaded the series ending with June 2015 and graphed it, I thought that there must be something wrong with my computer program, because the rate of warming curve had changed so dramatically. I eventually traced the “problem” back to the data, and then I read that GISTEMP had adopted the “Pause-busting” adjustments that NOAA had devised.

Graph 4 shows the effect on the rate of warming curve, of the GISTEMP “Pause-busting” adjustments. The blue line shows the rates from the May 2015 data, and the red line shows the rates from the June 2015 data.

One of the strange things about the GISTEMP “Pause-busting” adjustments, is that the year with the highest rate of warming (since 1880) has changed. It used to be around 1998, with a warming rate of about +2.4 °C per century. After the adjustments, it moved to around 1937 (that’s right, 1937, back when the CO2 level was only about 300 ppm), with a warming rate of about +2.8 °C per century.

If you look at the NOAA series, they already had 1937 as the year with the highest rate of warming, so GISTEMP must have picked it up from NOAA when they switched to the new NCEI ERSST.v4 sea surface temperature reconstruction.

So, the next time that you hear somebody claiming that Global Warming is accelerating, show them a graph of the rate of warming. Some climate scientists seem to enjoy telling us that things are worse than predicted. Here is a chance to cheer them up with some good news. Somehow I don’t think that they will want to hear it.

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