I've followed Gell-Mann's work on complexity over the years and will now try my hand at using his approach to describe the simplicity of the models developed in this long thread.
Each model fits the data applying a concise algorithm -- the key being its conciseness but not necessarily subjective intuitiveness.
Here's a quick breakdown :
#1. Say I was doing tidal analysis and fitting a model to a SLH tidal gauge time-series. That's essentially an effective complexity of **1** because it just involves fitting known sinusoid amplitudes and phases.
#2. Same effective complexity of **1** for the dLOD, as it is straightforward additive tidal cycles.
#3. The Chandler wobble model that I developed has an effective complexity of **2** because it takes a single monthly tidal forcing and it multiplies it by a semi-annual nodal impulse (one for each nodal pass). Just a bit more complex than #1 or #2 but evidently too difficult for geophysicists to handle in this day and age.
#4. The QBO model that I developed is also estimated at an effective complexity of **2** as it is impulse modulated by nearly the same mechanism as for the Chandler wobble of #3. Instead of a bandpass filter for #3 (Chandler wobble) it uses an integrating filter to create more of a square-wave-like time-series. Again, this is apparently at the breaking point of understanding for the atmospheric physicists
#5. The ENSO model that I developed is an effective complexity of **3** because it adds the nonlinear Laplace's Tidal Equation (LTE) modulation to the square-wave-like fit of #4 (QBO), tempered by being calibrated by the tidal forcing model for #2 (dLOD). Of course this additional level of "complexity" is certain to be above the heads of ocean scientists and climate scientists, who are still scratching their heads over #3 and #4.
By comparison, most GCMs of climate behaviors have effective complexities much more than this because (as Gell-Man defined it) the shortest algorithmic description would require pages and pages of text to express. To climate scientists, perhaps the massive additional complexity of a GCM is preferred over the intuition required for enabling incremental complexity.
Since started with a Gell-Mann citation, may as well stick one here at the end: