Dave said:

> "QBO and ENSO are obviously hypercomplex multi-chaos cases."

No evidence of this. Regarding linear vs non-linear vs chaotic behaviors in climate models, it’s instructional to consider that even the most subtle non-linear models can wreak havoc on an analysis. And since the number of non-linear formulations is essentially infinite with respect to the number of linear possibilities, this topic of investigation has only begun to be explored. In other words, by punting the football and suggesting that the solutions are chaotic means that one has prematurely eliminated all the non-linear possibilities — and that are only challenging WRT linear models. IOW, they are deterministic and solvable, but with extreme difficulty.

So for solutions to Navier-Stokes, no one really knows what possibilities remain to be explored on a shallow-water 3-D rotating sphere. For my N-S fluid dynamics solution that is analytically similar to Mach-Zehnder modulation. This is good news and bad news — it’s good news because M-Z modulation is a straightforward non-linear formlation, but it’s bad news because M-Z modulation is also used as a highly secure encryption scheme that is very difficult to decode without the nonlinear mapping key.

![](https://www.researchgate.net/profile/Roberto_Torroba/publication/224038950/figure/fig5/AS:668615602892803@1536421790100/Experimental-arrangement-to-encrypt-the-input-object-Object-path-of-the-Mach-Zehnder.png)

This means that the model fitting process is computationally intensive because it is essentially a trial-and-error optimizing process using a gradient descent search, if that even gets close to the solution range.

Now consider the computational intensiveness of GCMs and multiplying that by the complexity of a non-linear fitting/decryption algorithm — one hasn’t even approached the scale of computational power needed to make headway. That's all the problem is -- can either join in or move out of the way.

> "QBO and ENSO are obviously hypercomplex multi-chaos cases."

No evidence of this. Regarding linear vs non-linear vs chaotic behaviors in climate models, it’s instructional to consider that even the most subtle non-linear models can wreak havoc on an analysis. And since the number of non-linear formulations is essentially infinite with respect to the number of linear possibilities, this topic of investigation has only begun to be explored. In other words, by punting the football and suggesting that the solutions are chaotic means that one has prematurely eliminated all the non-linear possibilities — and that are only challenging WRT linear models. IOW, they are deterministic and solvable, but with extreme difficulty.

So for solutions to Navier-Stokes, no one really knows what possibilities remain to be explored on a shallow-water 3-D rotating sphere. For my N-S fluid dynamics solution that is analytically similar to Mach-Zehnder modulation. This is good news and bad news — it’s good news because M-Z modulation is a straightforward non-linear formlation, but it’s bad news because M-Z modulation is also used as a highly secure encryption scheme that is very difficult to decode without the nonlinear mapping key.

![](https://www.researchgate.net/profile/Roberto_Torroba/publication/224038950/figure/fig5/AS:668615602892803@1536421790100/Experimental-arrangement-to-encrypt-the-input-object-Object-path-of-the-Mach-Zehnder.png)

This means that the model fitting process is computationally intensive because it is essentially a trial-and-error optimizing process using a gradient descent search, if that even gets close to the solution range.

Now consider the computational intensiveness of GCMs and multiplying that by the complexity of a non-linear fitting/decryption algorithm — one hasn’t even approached the scale of computational power needed to make headway. That's all the problem is -- can either join in or move out of the way.