Guest Post by Willis Eschenbach

The fundamental and to me incorrect assumption at the core of the modern view of climate is that changes in temperature are a linear function of changes in forcing. Forcing is defined as the net downwelling radiation at the top of the atmosphere (TOA). According to this theory, in order to figure out what the change in global temperature will be between now and the year 2050, you just estimate the change in net forcing between now and then, multiply it by the magic number, et voilá—the change in temperature pops out!

I find this theory very doubtful for a number of reasons. I went over the problems with the mathematics underlying the claim in a post called “The Cold Equations“, for those interested. However, I’m not talking theory today, what I want to look at is some empirical data.

The CERES dataset contains measurements of upwelling radiation at the top of the atmosphere. It also has various other subsidiary datasets which are calculated from both the CERES data, other satellite data, and ground measurements. These include the upwelling thermal (IR) radiation from the surface. I apply the Stefan-Boltzmann equation to that upwelling IR data in order to calculate the surface data. I’ve checked this data against the HadCRUT surface temperature data, and they agree very closely with the exception of certain areas around the poles. I ascribe this to the very poor coverage of ground weather stations around the poles. This has forced the ground datasets to infill these areas based on the nearest stations. Even with that polar difference, however, the standard deviation of difference between the CERES and the HadCRUT monthly data is only 0.08°C, extremely small. the CERES data is more complete than the HADcrut data, so I use it for the surface temperature.

Now, this lets us compare changes in the net TOA forcing imbalance with the changes in the surface temperature. For this kind of study we need to remove the effects of the seasons. We do this by subtracting the full-dataset average for each month from the data for that month. For each month, this leaves the “anomaly”—how much warmer or colder it is that month compared to the average.

For example, here’s the temperature data, with the top panel showing the raw data, the middle panel showing the annually repeated seasonal variations, and the bottom panel showing the “anomaly”, how much warmer or cooler the globe is compared to average.

Figure 1. Raw data, seasonal changes, and anomaly of the CERES surface temperature dataset. Note the upswing at the end from the latest El Nino. The temperature has dropped since, but the CERES data has not been updated past February 2016.

According to the incorrect paradigm that says that changes in surface temperatures follow the changes in forcing, we should be able to see the relationship between the two in the CERES data—when the TOA forcing takes a big jump, the temperatures should take a big jump as well, and vice-versa. However, it turns out that that is not the case:

Figure 2. Changes in TOA radiation (forcing) ∆F versus changes in surface temperature ∆T. Delta (∆) is the standard abbreviation meaning “change in”. In this case they are the month-to-month changes. The background is a hurricane from space. I added it because I got tired of plain old white

As you can see, in the CERES dataset there is no statistically significant relationship between the changes in TOA forcing ∆F and the changes in surface temperature ∆T. Go figure.

Now, I can already hear some folks thinking something like “But, but, that’s far too short a time period for that small a change to have an effect … I mean, one watt per square metre over a month? The Earth has thermal inertia, it wouldn’t respond to that …”

So lets take a look at a different scatterplot. This time we’ll look at change in total surface energy absorption (shortwave plus longwave) versus change in temperature.

Figure 3. Changes in surface energy absorption versus changes in surface temperature ∆T.

So the objection that the time span is too short is nullified. A change of one watt per square metre over a month is indeed able to change the surface temperature, by about a tenth of a degree.

Finally, is this just an artifact because we’re using CERES data for both surface temperature and total surface energy absorption? We can check that by repeating the analysis, but this time we’ll use the HadCRUT surface temperature data instead of the CERES data …

Figure 4. As in Figure 3, but this time using HadCRUT surface temperature data.

While as we’d expect there are differences when we use the different surface temperature datasets, in both of them the surface clearly is able to change temperature from a difference of one watt per square metre over a month.

So we are left at the end of the day with Figure 2, showing that there is no significant relationship between changes in TOA forcing and surface temperatures.

Note that I am NOT claiming that this method can determine the so-called “climate sensitivity”. I am merely pointing out that the CERES data does not show the expected relationship between changes in net TOA radiation imbalance and changes in surface temperature.

Best to all,

w.

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