Working under the hypothesis that clouds are a regulating feedback in the tropics seems like a slam dunk. Warmer oceans would increase the probability of cloud formation. In the tropics, cloud shortwave reflection amounts to about 20 Wm-2 more of CRF as compared to cloud OLR retention. Just compare cloud cover to SST done, right?
In any case, a warming tropical SST would increase SH and possibly RH up to a point close to saturation. Well, 1998 might be a point close to saturation but there isn't very much data. With the large divergence at the start of the records plus the limited data, any correlation would be questionable. The correlated peaks around 1945 are contrasted by anti-correlated peaks around 1910 and 1998 has no peaks. There isn't a clear explanation. If I shorten the data set, well that would be cherry picking.
Tropical RH and SH have different trends, likely due to the short time period starting year. If anything in climate should be stable it would be tropical marine air RH and SH. So even with more data there would not be much of a reliable variation to play with. Quite likely a reason for the limited data.
Tropical clouds versus the tropical lower troposphere though is a bit more interesting.
There are in and out of phase situations like what I would expect during regulation. Thanks to the absolute temperature provided by RSS there is something to scale cloud anomaly to.
In any case, a little more than half of the increase in cloud cover happened prior to 1950 and the "Year CO2 Took Control". That would be an indication of a continuous increase in water vapor, that other green house gas. 30S-30N is not the whole globe, but right at half of the area and the majority of the energy, especially energy that produces the most water vapor.
Climate science has an odd way of defining forcing and feedback. If water vapor increases due to CO2 equivalent gas "forcing" then it would be a feedback to that forcing. That assumes everything is "normal" prior to the additional GHGs. This leads to models being a "boundary" value problem because the initial conditions are assumed to be "normal". That is a major assumption. Anyone that disagrees or points out behavior inconsistent with something being a "feedback" as narrowly defined catches flack. However, if there are initial value issues, the assumed "normal" isn't, then what would be a feedback response could be a forcing in it's own right. So to humor me, consider water vapor pre-1950 as being a forcing.
Under the assumption that WV is only a feedback to other changes in forcing, the impact is approximately 2 times no-feedback sensitivity of 3.7 Wm-2. Using the cloud data as a proxy for water vapor I can have something like this.
28C is a bit misleading in the tropics though. Only small regions hit the warm pool status and they tend to move around. NINO220.127.116.11, IPWP WPWP, etc. have pseudo-oscillations with respect to one another because of the shifting. Those shifts lead to other weather oscillations which are great for longer term weather forecasting but not so great for "climate" forecasting. Some of the oscillation could last for centuries and there just isn't enough data, maybe.
Moving Right Along.
The lower troposphere temperatures provide one energy reference and the absolute SST another.
A lot of this would be much easier if the variance in the data sets were reliable. You really only have three options, increased variance leading to unstable operation, decreasing variance indicating acquisition of the controller to a better control point and rock solid stable which is pretty much unheard of. The variance though in the data sets, mainly global data sets so increasing variance, but that appears to be related to the inclusion of south pole data circa 1955. Adding the much more variable poles to the natural smoothed SST data creates some issues including the constantly shifting "adjustment" baselines.
There is nothing wrong with trying to compile a "global" anomaly, but then there is nothing wrong with avoiding a "global" anomaly depending on the focus of your evaluation. Approaching this from a control theory perspective would mean isolating more critical "inputs" to reduce noise. My approach would be to start at the primary heat source, tropical oceans and primary control mechanism, tropical clouds and work towards a "global" response instead of dealing with all the noise and constant changes.
As far as CO2 equivalent gas forcing and tropical clouds, there appears to be close to zero evidence that cloud directly respond to GHG but could indirectly respond to GHG forcing of tropical SST by increasing regulation at an easier to maintain set point, a control "sweet spot" if you will.
A control "sweet spot" is a point where the control function and response function are equally matched. There, they are able to track more smoothly reducing the time required to "settle out" after a perturbation or the system is more efficiently damped resulting in less variance. However you like to look at the situation.
This basic control observation can lead to a variety of "novel" approaches. Fluctuations in seemingly random tend to change variance relationship leading to "strange attractors" in Chaos theory which are analogous to control "sweet spots". These "sweet spots" generally require non-linear relationships so you could think of them as "hyperbolic" functions. There are plenty of ways to skin this cat and the different jargon gets in the way of communicating a fairly simple and common relationship between functions. So if you don't like my "sweet spot" create your own terminology.
A weakly damped response like the above using the Oppo 2009 detrended is very common. The fit is less than perfect which is also very common. But as you can seem the amplitude decreases with time as the system approaches its "sweet spot". The differences are likely cause by erratic volcanic forcing timing. That volcanic forcing could be related to orbital influences or could be more random, but the system seeking control will respond with some damped function provided it has potential to be stable.
The oscillatory response curve though will change depending on if the system is above or below set point. There is no reason to expect a continuing stable oscillation, instead you should expect changing oscillatory behavior.
You can compare the entire Oppo et al. 2009 reconstruction with the Stienhilber TSI reconstruction and see that nature is full of pseudo-cyclic oscillations. A "control" oscillation would be different than a cooling response oscillation which would be different than a warming response oscillation. In phase a relatively weak "forcing" can have much more influence than out of phase. You can jump on the "Cyclomania" bus and declare victory, but real systems are a bit more interesting.
You can also jump on the magic bullet bus. Assume there is only one significant driver, CO2 equivalent gases for example and ignore the inconvenient "divergences" like tropical clouds for example.