Guest Post by Willis Eschenbach
Over at Dr. Curry’s excellent website, she’s discussing the Red and Blue Team approach. If I ran the zoo and could re-examine the climate question, I’d want to look at what I see as the central misunderstanding in the current theory of climate.
This is the mistaken idea that changes in global temperature are a linear function of changes in the top-of-atmosphere (TOA) radiation balance (usually called “forcing”).
As evidence of the centrality of this misunderstanding, I offer the fact that the climate model output global surface temperature can be emulated to great accuracy as a lagged linear transformation of the forcings. This means that in the models, everything but the forcing cancels out and the temperature is a function of the forcings and very little else. In addition, the paper laying out those claimed mathematical underpinnings is one of the more highly-cited papers in the field.
To me, this idea that the hugely complex climate system has a secret control knob with a linear and predictable response is hugely improbable on the face of it. Complex natural systems have a whole host of internal feedbacks and mechanisms that make them act in unpredictable ways. I know of no complex natural system which has anything equivalent to that.
But that’s just one of the objections to the idea that temperature slavishly follows forcing. In my post called “The Cold Equations” I discussed the rickety mathematical underpinnings of this idea. And in “The TAO That Can Be Spoken” I showed that there are times when TOA forcing increases, but the temperature decreases.
Recently I’ve been looking at what the CERES data can tell us about the question of forcing and temperature. We can look at the relationship in a couple of ways, as a time series or a long-term average. I’ll look at both. Let me start by showing how the top-of-atmosphere (TOA) radiation imbalance varies over time. Figure 1 shows three things—the raw TOA forcing data, the seasonal component of the data, and the “residual”, what remains once we remove the seasonal component.
Figure 1. Time series, TOA radiative forcing. The top panel shows the CERES data. The middle panel shows the seasonal component, which is caused by the earth being different distances from the sun at different times of the year. The bottom panel shows the residual, what is left over after the seasonal component is subtracted from the data.
And here is the corresponding view of the surface temperature.
Figure 2. Time series, global average surface temperature. The top panel shows the data. The middle panel shows the seasonal component. The bottom panel shows the residual, what is left over after the seasonal component is subtracted from the data. Note the El Nino-related warming at the end of 2015.
Now, the question of interest involves the residuals. If there is a month with unusually high TOA radiation, does it correspond with a surface warming that month? For that, we can use a scatterplot of the residuals.
Figure 3. Scatterplot of TOA radiation anomaly (data minus seasonal) versus temperature anomaly (data minus seasonal). Monthly data, N = 192. P-value adjusted for autocorrelation.
From that scatterplot, we’d have to conclude that there’s little short-term correlation between months with excess forcing and months with high temperature.
Now, this doesn’t exhaust the possibilities. There could be a correlation with a time lag between cause and effect. For this, we need to look at the “cross-correlation”. This measures the correlation at a variety of lags. Since we are investigating the question of whether TOA forcing roolz or not, we need to look at the conditions where the temperature lags the TOA forcing (positive lags). Figure 4 shows the cross-correlation.
Figure 4. Cross-correlation, TOA forcing and temperature. Temperature lagging TOA is shown as positive. In no case are the correlations even approaching significance.
OK, so on average there’s very little correlation between TOA forcing and temperature. There’s another way we can look at the question. This is the temporal trend of TOA forcing and temperature on a 1° latitude by 1° longitude gridcell basis. Figure 5 shows that result:
Figure 5. Correlation of TOA forcing and temperature anomalies, 1° latitude by 1° longitude gridcells. Seasonal components removed in all cases.
There are some interesting results there. First, correlation over the land is slightly positive, and over the ocean, it is slightly negative. Half the gridcells are in the range ±0.15, very poorly correlated. Nowhere is there a strong positive correlation. On the other hand, Antarctica is strongly negatively correlated. I have no idea why.
Now, I said at the onset that there were a couple of ways to look at this relationship between surface temperature and TOA radiative balance—how it evolves over time, and how it is reflected in long-term averages. Above we’ve looked at it over time, seeing in a variety of ways if monthly changes or annual in one are reflected in the other. Now let’s look at the averages. First, here’s a map of the average TOA radiation imbalances.
Figure 6. Long-term average TOA net forcing. CERES data, Mar 2000 – Feb 2016
And here is the corresponding map for the temperature, from the same dataset.
Figure 7. Long-term average surface temperature. CERES data, Mar 2000 – Feb 2016
Clearly, in the long-term average we can see that there is a relationship between TOA imbalance and surface temperature. To investigate the relationship, Figure 8 shows a scatterplot of gridcell temperature versus gridcell TOA imbalance.
Figure 8. Scatterplot, temperature versus TOA radiation imbalance. Note that there are very few gridcells warmer than 30°C. N = 64,800 gridcells.
Whoa … can you say “non-linear”?
Obviously, the situation on the land is much more varied than over the ocean, due to differences in things like water availability and altitude. To view things more clearly, here’s a look at just the situation over the ocean.
Figure 9. As in Figure 8, but showing just the ocean. Note that almost none of the ocean is over 30°C. N = 43,350 gridcells.
Now, the interesting thing about Figure 8 is the red line. This line shows the variation in radiation we’d expect if we calculate the radiation using the standard Stefan-Boltzmann equation that relates temperature and radiation. (See end notes for the math details.) And as you can see, the Stefan-Boltzmann equation explains most of the variation in the ocean data.
So where does this leave us? It seems that short-term variations in TOA radiation are very poorly correlated with temperature. On the other hand, there is a long-term correlation. This long-term correlation is well-described by the Stefan-Boltzmann relationship, with the exception of the hot end of the scale. At the hot end, other mechanisms obviously come into play which are limiting the maximum ocean and land temperatures.
Figure 9 also indicates that other than the Stefan-Boltzmann relationship, the net feedback is about zero. This is what we would expect in a governed, thermally regulated system. In such a system, sometimes the feedback acts to warm the surface, and other times the feedback acts to cool the surface. Overall, we’d expect them to cancel out.
Is this relationship how we can expect the globe to respond to long-term changes in forcing? Unknown. However, if it is the case, it indicates that other things being equal (which they never are), a doubling of CO2 to 800 ppmv would warm the earth by about two-thirds of a degree …
However, there’s another under-appreciated factor. This is that we we’re extremely unlikely to ever double the atmospheric CO2 to eight hundred ppmv from the current value of about four hundred ppmv. In a post called Apocalypse Cancelled, Sorry, No Ticket Refunds. I discussed sixteen different supply-driven estimates of future CO2 levels over the 21st century. These peak value estimates ranged from 440 to 630 ppmv, with a median value of 530 ppmv … a long ways from doubling.
So, IF in fact the net feedback is zero and the relationship between TOA forcing and surface temperature is thus governed by the Stefan-Boltzmann equation as Figure 9 indicates, the worst-case scenario of 630 ppmv would give us a temperature increase of a bit under half a degree …
And if I ran the Red Team, that’s what I’d be looking at.
Here, it’s after midnight and the fog has come in from the ocean. The redwood trees are half-visible in the bright moonglow. There’s no wind, and the fog is blanketing the sound. Normally there’s not much noise here in the forest, but tonight it’s sensory-deprivation quiet … what a world.
My best regards to everyone, there are always more questions than answers,
PS—if you comment please QUOTE THE EXACT WORDS YOU ARE DISCUSSING, so we can all understand your subject.
THE MATH: The Stefan-Boltzmann equation is usually written as
W = sigma epsilon T^4
where W is the radiation, sigma is the Stefan-Boltzmann constant 5.67e-8, epsilon is emissivity (usually taken as 1) and T is temperature in kelvin.
Differentiating, we get
dT/dW = (W / (sigma epsilon))^(1/4) / (4 * W)
This is the equation used to calculate the area-weighted mean slope shown in Figure 9. The radiation imbalance was taken around the area-weighted mean oceanic thermal radiation of 405 W/m2.