Guest Post by Willis Eschenbach
Every fall, there’s good news in the world of satellite information, because the CERES satellite folks add one more year’s worth of data to their full dataset. So I went and downloaded the whole 18 years worth, which is close to a full gigabyte of data …
The other good news is that even though I live out in the country, the neighbors all got together a year ago and got a grant from the state to install fiber-optic lines to all of our houses. Last year I was on satellite internet, with a ping time of ~800 msec and about 10 Mbps upload and download. Here’s where I am today, one happy data junkie … go figure.
But I digress … I decided to take a look at the relationship between the top-of-atmosphere (TOA) total radiation imbalance and the surface temperature. Figure 1 shows how the Northern Hemisphere temperature varies with respect to the TOA imbalance.
Figure 1. Scatterplot, monthly Northern Hemisphere surface temperature versus the monthly TOA imbalance. Temperature is in degrees Celsius (°C), and TOA imbalance is in watts per square metre (W/m2).
The oval shape of the relationship indicates that there is a lag between the change in the TOA radiation and the temperature, as we’d expect. Figure 2 shows the same scatterplot after lagging the relationship by one month.
Figure 2. Scatterplot, monthly Northern Hemisphere surface temperature versus the monthly TOA imbalance lagged by one month.
I’ve indicated in the top left the “Instantaneous Climate Sensitivity”. This is the immediate system response to a change in the TOA radiation.
Now, in a post from three years ago called “Lags and Leads” I discussed how to determine the true size of the response if there were no lag between the forcing and the response. A more detailed calculation of the data in Figure 2 shows a lag of 34°. Using the equations given in that post, it gives us the no-lag climate sensitivity shown in the lower right of Figure 2, which is about a tenth of a degree for each additional watt per square meter (W/m2) of TOA radiation.
So far, so good. Here’s where it gets interesting. Suppose we remove the average repeating monthly variations (called the “climatology”) in both datasets, leaving just the anomalies. What would we expect to find?
Well, we’d expect to find that the temperature anomalies would vary as a linear function of the TOA radiation anomaly. In a perfect world, it would look like Figure 3.
Figure 3. Scatterplot, expected value of the Northern Hemisphere temperature anomaly versus the NH TOA imbalance anomaly in a perfect world. The slope is the slope of the data shown in Figure 2.
Of course, however, things are not perfect. So let me add some errors to the expected perfection. I’ve used random normal errors with a standard deviation equal to that of the actual temperature anomaly. Figure 4 shows the result in Figure 3 plus a random error applied to each data point.
Figure 4. Scatterplot, expected value of the NH temperature anomaly versus the NH TOA imbalance anomaly plus random errors.
Note that the addition of the errors doesn’t remove the statistical significance. The p-value is vanishingly small. Nor does adding the errors significantly change the calculated slope of the relationship between the temperature anomaly and the TOA imbalance anomaly.
So … what do we find when we look at the actual data? Curiously, we find no relationship at all between the temperature and the TOA anomaly.
Figure 5. Scatterplot, expected value of the NH temperature anomaly versus the one-month lagged NH TOA imbalance anomaly.
As you can see, there is no relationship between the temperature anomaly and the TOA radiation anomaly.
So … why is there no relationship as we might expect? It’s because of the thermostatic action of the emergent phenomena. Let me explain using a familiar example of a thermostatically regulated system—a house with a thermostat controlling a furnace.
Let’s suppose that it’s cold outside. We go out for a while, so we turn the thermostat down to say 50°F (10°C). After a while, the house cools to that temperature and then remains there. When it gets cooler, the furnace kicks in and heats it up to slightly above the thermostat setting. Then it turns off.
Now, let’s suppose we come home, walk in the door, and kick the thermostat up to say 70°F (21°C). The furnace comes on, and the house starts to heat.
As the house is heating up to the 70°F setting, we can calculate the incoming energy as the amount of heat put out by the furnace per minute. Then we can compare it to the change in temperature per minute. This is the equivalent of comparing the change in global surface temperature to the change in the TOA radiation imbalance. We get an answer showing the amount of temperature change in the house versus a given change in incoming energy.
But once the temperature of the house reaches 70°F, a funny thing happens. The temperature of the house totally decouples from the amount of incoming energy. If the day is cold, the furnace will run a lot to keep the house at that temperature setting … but if the day is warm, the furnace will hardly run at all to keep the temperature at the setting. And as a result, there is no longer a fixed relationship between temperature and incoming energy.
So in the same system, we have some situations where the temperature is related to the incoming energy, and other situations where the temperature is totally decoupled from the incoming energy.
Similarly, when the Northern Hemisphere goes from say the August temperature setting to the September setting, we get a clear, albeit small, relationship between temperature and TOA energy input.
But when we look at what happens when we isolate and just look at say the September setting, we find that there is no relationship between temperature anomaly and TOA energy input anomaly.
Anyhow, that’s what I noticed while looking at the latest CERES data …
Here, we’ve had about four inches (10 cm) of rain in the last two days. This has washed all of the forest fire smoke out of the atmosphere. And last night, we had a wonderful Thanksgiving dinner chez nous, featuring the usual cast of inlaws and outlaws, seventeen in total. No, we didn’t discuss politics, although I’m sure if we had I could have saved big money on Christmas presents … instead, we laughed and told family stories and caught up on what we’ve been doing since last year at this time.
And just like every Thanksgiving,
But what’s a poor boy to do, the food was amazing.
My very best Thanksgiving wishes to all,
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