Estimating the sensitivity of the response to forcing is challenging because of the concept of reduced effective gravity across a stratified interface. The smaller the difference of the densities between the stratified layers of the thermocline, the greater the reduction of gravity to forcing perturbations.

![](https://imagizer.imageshack.com/v2/1233x312q90/r/924/aUrd7X.png)

But since density differs by just the temperature differential (or salinity), and this can be exceedingly small, the magnification blows up. So one can show that any forcing can have an effect just by making the differential small enough. This is the basis for making the best wave motion machines -- the manufacturer picks the oil & water combination that has the smallest density difference so that it will show the wildest swings to a nudge, as the inertial response out-competes the restoring force of gravity.

![](https://www.gadgetify.com/wp-content/uploads/2020/10/01/Dolphin-F-X-Wave-Motion-Machine.gif)

Conventional tide analysts have long known about the futility of trying to calculate the strength of tidal effects as no one does that in practice. Instead, predictions of ocean tide changes are calibrated from the measurements.

As far as QBO, they can easily debunk my model. All they have to do is show that the measured periods are incommensurate with the lunar and solar tidal periods I suggest in the submitted paper.

For ENSO, this is more of a mess since the solution to Laplace's Tidal Equations (LTE) is highly nonlinear and all the tidal factors cross-multiply with each other. I'm not going to go through the explanation of this here, because I recently finished up a blog post that describes the generation of the harmonics [on my own blog here](https://geoenergymath.com/2021/01/16/nonlinear-generation-of-power-spectrum-enso/). This has some interesting interactive charting widgets that I would be unable to reproduce here anyways, so worthwhile to take a look.

I should also add that what is challenging about fitting the harmonics is that conventional tidal cross-terms such as Mf‘ (the Mf tropical monthly 27.32 day crossed with the 27.21 day term), the fortnightly anomalistic 13.77 day, the 9 day, and 6 day will conflate with the cross-terms generated by the LTE modulation. So one can easily add these to match a model to the data, but the issue is to avoid overfitting. Or it could be that the conventional tidal cross-terms are at least partially caused by the LTE non-linear modulation. Conventional tidal analysis tables contain several hundred potential cross terms generated by the harmonics of the 4 principal Doodson tidal indices, i.e. the 4th harmonic expansion of 4 terms is 4^4 = 256.

Bottom-line is that surface tides are only slightly non-linear, whereas the subsurface tides (and therefore ENSO) are highly nonlinear and this explains why they have been stumbling over explaining the cycles for years. So most of them punt and say it's chaotic and leave it at that.

![](https://imagizer.imageshack.com/v2/1233x312q90/r/924/aUrd7X.png)

But since density differs by just the temperature differential (or salinity), and this can be exceedingly small, the magnification blows up. So one can show that any forcing can have an effect just by making the differential small enough. This is the basis for making the best wave motion machines -- the manufacturer picks the oil & water combination that has the smallest density difference so that it will show the wildest swings to a nudge, as the inertial response out-competes the restoring force of gravity.

![](https://www.gadgetify.com/wp-content/uploads/2020/10/01/Dolphin-F-X-Wave-Motion-Machine.gif)

Conventional tide analysts have long known about the futility of trying to calculate the strength of tidal effects as no one does that in practice. Instead, predictions of ocean tide changes are calibrated from the measurements.

As far as QBO, they can easily debunk my model. All they have to do is show that the measured periods are incommensurate with the lunar and solar tidal periods I suggest in the submitted paper.

For ENSO, this is more of a mess since the solution to Laplace's Tidal Equations (LTE) is highly nonlinear and all the tidal factors cross-multiply with each other. I'm not going to go through the explanation of this here, because I recently finished up a blog post that describes the generation of the harmonics [on my own blog here](https://geoenergymath.com/2021/01/16/nonlinear-generation-of-power-spectrum-enso/). This has some interesting interactive charting widgets that I would be unable to reproduce here anyways, so worthwhile to take a look.

I should also add that what is challenging about fitting the harmonics is that conventional tidal cross-terms such as Mf‘ (the Mf tropical monthly 27.32 day crossed with the 27.21 day term), the fortnightly anomalistic 13.77 day, the 9 day, and 6 day will conflate with the cross-terms generated by the LTE modulation. So one can easily add these to match a model to the data, but the issue is to avoid overfitting. Or it could be that the conventional tidal cross-terms are at least partially caused by the LTE non-linear modulation. Conventional tidal analysis tables contain several hundred potential cross terms generated by the harmonics of the 4 principal Doodson tidal indices, i.e. the 4th harmonic expansion of 4 terms is 4^4 = 256.

Bottom-line is that surface tides are only slightly non-linear, whereas the subsurface tides (and therefore ENSO) are highly nonlinear and this explains why they have been stumbling over explaining the cycles for years. So most of them punt and say it's chaotic and leave it at that.