by J Storrs Hall

In my previous post, I argued that sea-surface temperatures hadn’t shown an inflection in the mid-twentieth century, and that the post-50’s rise was essently a land-based phenomenon. To take the analysis further, I thought I could try to find just what the climate signal from CO2 was. The method is to find a fit to the temperature record that included the CO2 forcing signature as a component, and see how big its contribution was compared to the other components of the fit.

First, the CO2. To get a curve since 1850, I got the estimated emissions from here, integrated for accumulation, scaled by matching to the Mauna Loa measured CO2 (red), and took the log for forcing. (No arguments, please; this is the bog-standard story. Let’s assume it’s true for the sake of argument.)

There’s clearly a knee in the curve ca. 1960. Also note that it’s been essentially straight since the 70’s — it’s the log of an exponential.

For components of the fit function, I used a cosine to capture the cyclicity we already know is in the record, a quadratic, and the forcing curve. I had used a second cosine before, and we know it produced two inflections in the result. The quadratic can only produce one, so the forcing curve has a better chance of matching the other one.

The idea is to find the overall best match and then look at the components to see how big the signal from the forcing is in comparison with the other components, which we will assume represent natural variability. We’ll plot each curve with the amplitude the optimizer gives it. Here’s what we get:

The blue line is the overall fit. Cyan is the 61-year oscillation, as before. No surprises here. Magenta is the quadratic, looking a lot like the sinusoid of the previous fit. Red is the CO2 forcing.

The CO2 forcing is upside down.

I gave the optimizer an initial guess for the forcing coefficient of 1; it came back with -1.67. This was, frankly, unexpected. I had seriously thought I would find some warming contribution from the forcing component.

So what on earth is going on? Here’s what we get if we add just the quadratic and the forcing curve:

For comparison, I’ve also plotted the second sinusoid from last time (green). It seems that the secular trend that the optimizer really, really wants is the shape of a Nike swoosh. If given only a quadratic to work with, it has to subtract the forcing curve to straighten out the twentieth-century rise. And it really, really wants the knee of the curve to be in 1890.

Does this mean that CO2 is actually producing a cooling effect? Absolutely not. It simply means that the secular rise in the twentieth century was a straight line, and the fit would do whatever it took to produce that shape. (This is why Pat Frank’s linear fit worked so well. As he noted, the linearity of sea-level rise would tend to confirm this.) What it does mean, though, is that there is no discernable CO2 warming signal in the HadSST temperature record. The (very real) twentieth century warming trend appears to have started about the time Sherlock Holmes was investigating the Red-Headed League.

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