Starting the S&B story at the beginning, as did Steve McIntyre, with Dessler 2010 in Science, I’ll put a new spin on the satellite data uploaded by Steve, using the accumulation theory. Although I am not familiar with the data, it turns out to be easily interpretable.
In black is the replication of Steve’s Figure 1 and Dessler’s 2010 Figure 2A, the scatter plot of monthly average values of ∆R_cloud (eradr) versus ∆T_s (erats) using CERES and ECMWF interim data. There is extremely little correlation as noted by Steve. In fact, it is not statistically significant in the conventional sense, Science apparently adopting the new IPCC-speak qualitative standard of ‘likely’.
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.01751 0.04599 0.381 0.704
X 0.54351 0.36184 1.502 0.136
Residual standard error: 0.5036 on 118 degrees of freedom Multiple R-squared: 0.01876, Adjusted R-squared: 0.01045 F-statistic: 2.256 on 1 and 118 DF, p-value: 0.1358
The points in red are the sequential difference of temperature against the cloud radiance. While these have a lower slope, unlike the former, they are conventionally significant, almost to the 99%CL.
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.01269 0.04524 0.280 0.7796
dX 1.07071 0.42782 2.503 0.0137 * ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.4954 on 118 degrees of freedom Multiple R-squared: 0.0504, Adjusted R-squared: 0.04236 F-statistic: 6.263 on 1 and 118 DF, p-value: 0.01369
So why plot the sequential temperature differences and not the temperature directly? Firstly, while the autoregression coefficient (AR) of atmospheric temperature, erats (using arima(dess[,5],order=c(1,0,0))), is AR=0.65, for eradr its AR=0.16. This tells you that the two are different types of processes. The low AR is like a bunch of random numbers. The high AR is like a sequential accumulation of random numbers. Using different terminology, they do not cointegrate, as one can trend strongly (non-stationary) and the other stays around its mean (is stationary). Nor do they necessarily correlate. Though they can causally determine each other.
Differencing temperature is explained in accumulation theory, which pays close attention to heat accumulating in the ocean. Overlooking this basic physical model of the system causes many problems. Interpreting the data in terms of the physical model clears a lot of things up, as shown by the significant result above.
Above is the time-series plot of cloud radiance (black) and differenced global temperature (red) showing the relationship.
What does this say about cloud dynamics? The way to get intuition of dynamic relationships is to imagine the output from three types of input: impulse, step and periodic.
On an impulse of radiation, the surface (and lower atmosphere) warm and then revert. The differenced variable (like the first derivative) surges positive while temperature is rising, then surges negative while temperature is falling.
Electrical engineering buffs will appreciate this as the current-opposing behavior of an inductor. Clouds, in this view, could be compared with the electromagnetic field set up by the changing current. (The ocean heat capacity is comparable to capacitance).
The peak of the differenced pulse will lead the peak of the forcing. This shows it that lag/lead relationships are not reliable indicators of the direction of causation in dynamic systems.
On a step increase in radiation, the surface (and lower atmosphere) will ramp up as long as the forcing persists in accumulating heat in the ocean. The differenced variable will step-up and remain constant while temperature is rising at a constant rate.
This is a fundamentally different view of climate sensitivity, with different units. From the results above, the positive feedback from clouds is 1.1 W/m^2/K^2 and not 0.54 W/m^2/K. This means that clouds provide back-radiation (feedback is positive) while temperature is rising, but when the temperature stops rising, the back-radiation stops too. The number is part of the process.
I do not see how it is possible to interpret this in terms of a particular climate sensitivity. In the alternative view, cloud feedback is twice as strong as the conventional view while temperature is rising, but drops to zero when temperature is stable.
Finally, a periodic forcing is phase shifted 90 degrees (as shown by the impulse example). By simple calculus, the derivative of a sine function is a cosine function.
Could this explain the approximately 4 month lag in terms of an annual cycle (12/4 = 3 months)? Possible? It may explain the negative correlation achieved by Steve McIntyre at 4 month lag, as a 90 degree lead in a peak, produces a 90 degree lag between peak and trough.
Here is my code (you need to download the data from link above).
plot(0,0,cex=1,col=2,xlab="Global Temp (black) and diffTemp (red)",ylab="Clouds R",type="p",xlim=c(-0.4,0.4),ylim=c(-2,2))
plot(Y,col=1,ylab="Cloud R and diff(Temp)")