CO2 vs Temperature
Posted by softestpawn on August 22, 2009
The idea that CO2 levels force temperature changes are key to the claims of global warmers. This post looks at how CO2 changes match temperature changes in the records.
There are lots of ways to find out how well two sets of values correlate, and a relatively simple way is to plot one against the other. If there’s a good positive correlation, we should get a graph something like this:
We can see that as X is higher, so is Y, and when X is lower, Y is lower. More than that, the larger that X is, so Y is larger.
Negative correlations simply swap direction, and might look like this:
The better the correlation, the closer the points are to a straight line.
This approach can help in noisy or chaotic systems, where a ‘by eye’ glance at data can get taken in by apparent but irrelevant patterns. It can also be useful when there are apparent overall similar trends over a long term.
According to the physics, CO2 slows the re-radiation of heat from the earth. So we expect – at the small changes in CO2 that we see from month to month or year to year – that the more CO2 that is added or removed, the more temperature will change. (The relationship is not linear on the larger scale, but we don’t need to worry about that).
We need to allow for time lags, at least between CO2 changing and the temperature of the instruments recording it changing. Mauna Lao is assumed to be ‘well mixed’ CO2, and the repeating patterns imply CO2 mixing on the order of a month is sufficient. CO2 effects tend to be on the whole troposphere, and there is likely to be some delay while the various temperature ‘pressures’ cause the ground to heat up. It’s hard to see, given daily variations, that this would take much longer than a day, but this assumption is definitely ‘iffy’.
Another potential lag is that of the semi-mythical ‘climate sensitivity’ effects. The more enthusiastic climatologists need these to multiply the ordinary not-very-dangerous temperature rises expected from CO2 change (less than 1C for doubled CO2 levels) in order to get to the scary dangerous temperature rises (3-6C). As these may be decoupled by much more than a month, we cannot assume that any correlation seen is accurate.
The system is very noisy, so we shouldn’t expect a good correlation anyway; there are many effects on temperature other than CO2.
We also need to be wary of seasonal effects. Each year the globe’s CO2 levels fluctuate (as you can see in Mauna Lao’s graph of CO2 levels, which has that ripple effect) and the temperatures similarly change over the year. So we might get a correlation that is a result of the earth’s orbit rather than the cause of one value on the other – the classic ‘correlation is not cause’. So we may have to check against annual values too, which may have their own systematic errors due to the rather arbitrary calendar year cutoff.
As an aside: many people have already plotted CO2 levels against temperature. This is not particularly useful; CO2 has risen nearly exponentially since the 1950s, so plotting CO2 levels is almost entirely equivalent to plotting time.
But anyway, using Hadley CRU temperature records, Law Dome ice proxy CO2 records (1850-1978, low resolution thus the stripey effect) and Mauna Lao instrument CO2 records (1959-2008), this is a plot of the month to month (Mauna Lao) or year to year (Law Dome) change in average global temperature against the change in atmospheric CO2 for the same period.
And, rather interestingly, there’s almost no correlation at all. No matter how CO2 changes, the temperature changes in an almost completey independent manner.
With a month lag (ie, comparing the CO2 change with the temperature change of the following month), there’s still none. However if the ordinary CO2/temperature forcing has a lag longer than a week or so (ie, it reaches the same order as the granularity of the records), then this is probably the wrong approach.