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## Comments

The natural climate is not chaotic, or to put it a better way, it's as chaotic as the daily cycle, the annual cycle, or the tidal cycle.

`The natural climate is not chaotic, or to put it a better way, it's as chaotic as the daily cycle, the annual cycle, or the tidal cycle.`

Large problems may require large solutions. See ‘Space bubbles’ between Earth, sun possibly could reverse destructive climate change.

`Large problems may require large solutions. See [‘Space bubbles’ between Earth, sun possibly could reverse destructive climate change](https://www.oregonlive.com/environment/2022/06/space-bubbles-between-earth-sun-possibly-could-reverse-destructive-climate-change-mit-researchers-say.html).`

The Indian Ocean Dipole temperature index over the years

What everyone is concerned about : The upward trend

What scientists wished they could predict : All the erratic cycles

`The Indian Ocean Dipole temperature index over the years ![](https://imagizer.imageshack.com/img923/8442/VdpJom.gif) What everyone is concerned about : The upward trend What scientists wished they could predict : All the erratic cycles`

Since it's been 10 years since this forum has engaged in modeling of climate, I wrote up this blog post from my perspective. Remember that the original goal of the Azimuth Code Project was to be able to model El Nino cycles well enough for prediction purposes. Deferring to chaos as a mechanism is essentially the same as punting, and it took a lot of effort to get to the simple model described at the following link:

https://geoenergymath.com/2022/08/23/what-happened-to-simple-models/

`Since it's been 10 years since this forum has engaged in modeling of climate, I wrote up this blog post from my perspective. Remember that the original goal of the Azimuth Code Project was to be able to model El Nino cycles well enough for prediction purposes. Deferring to chaos as a mechanism is essentially the same as punting, and it took a lot of effort to get to the simple model described at the following link: https://geoenergymath.com/2022/08/23/what-happened-to-simple-models/`

One of the V8 moments in studying the math of fluid dynamics is that streamflow variables that are at most linear in time (or weakly non-linear) enable Navier-Stokes, Euler, or Laplace's Tidal Equations to be more analytically tractable. What the linear terms do is eliminate the 2nd-order factors from the DiffEq, allowing solutions of the wave equation with novel formulations, and these can be nonlinear!

I've been looking at the NINO4 region (in the western Pacific) as an El Nino index since a recent paper says the time-series shows a greater sample entropy

See the other thread on Negative Entropy here https://forum.azimuthproject.org/discussion/2561/negative-entropy

I have had success cross-validating the NINO4 time-series using the calibrated tidal forcing as input. The key is the staircase nature of the forcing with at most linear risers on the step plateaus. The step transitions occur on a semi-annual basis where the thermocline is metastable. The training exclusion area is highlighted in yellow and is the result of fitting the time-series outside the interval.

`> "“Nonlinear aspects plays a major role in the understanding of fluid flows. The distinctive fact that in nonlinear problems cause and effect are not proportional opens up the possibility that a small variation in an input quantity causes a considerable change in the response of the system. Often this type of complication causes nonlinear problems to elude exact treatment. “ https://doi.org/10.1029/2012JC007879 One of the V8 moments in studying the math of fluid dynamics is that streamflow variables that are at most linear in time (or weakly non-linear) enable Navier-Stokes, Euler, or Laplace's Tidal Equations to be more analytically tractable. What the linear terms do is eliminate the 2nd-order factors from the DiffEq, allowing solutions of the wave equation with novel formulations, and these can be nonlinear! I've been looking at the NINO4 region (in the western Pacific) as an El Nino index since a [recent paper](https://d197for5662m48.cloudfront.net/documents/publicationstatus/96301/preprint_pdf/8b1ed053f271d2322cadb0c682a8386f.pdf) says the time-series shows a greater sample entropy ![](https://imagizer.imageshack.com/img922/2009/jcNWOY.png) See the other thread on Negative Entropy here https://forum.azimuthproject.org/discussion/2561/negative-entropy I have had success cross-validating the NINO4 time-series using the calibrated tidal forcing as input. The key is the staircase nature of the forcing with at most linear risers on the step plateaus. The step transitions occur on a semi-annual basis where the thermocline is metastable. The training exclusion area is highlighted in yellow and is the result of fitting the time-series outside the interval. ![](https://user-images.githubusercontent.com/2855758/214451485-26010dd8-1dc9-4e7b-b98f-1c046ee6d500.png)`

One of John's former students co-authored this paper:

"A topological perspective on weather regimes" https://link.springer.com/content/pdf/10.1007/s00382-022-06395-x.pdf

Misguided to look at mid-latitudes before the lower-dimensional equatorial regions have been understood as a consensus.

They clearly bit off more than they can chew according to concluding remarks:

Climate is not even close to chaotic. All the major climate indices such as ENSO, AMO, QBO are straight-forward responses to tidal forcing subject to the standing-wave boundary conditions of the region under consideration. Take it to PubPeer.com if disagreements arise.

`One of John's former students co-authored this paper: "A topological perspective on weather regimes" https://link.springer.com/content/pdf/10.1007/s00382-022-06395-x.pdf Misguided to look at mid-latitudes before the lower-dimensional equatorial regions have been understood as a consensus. They clearly bit off more than they can chew according to concluding remarks: > "The apparent subtlety of regime structure gleaned from low-dimensional projections of the atmospheric circulation has been a longstanding source of uncertainty and ambiguity. The topological perspective we present here does not add further insight into such near-Gaussian data sets, as these would be classifed as being just a single connected component with no further structure. Instead, if taken at face value, our perspective suggests that the varied approaches to characterising Euro-Atlantic weather regimes are indicative of non-trivial topological structure in the associated region of the climate attractor. In fact, there are tantalising clues in the literature that genuinely non-trivial loops in the attractor might be detectable when taking into account sufciently many variables, and that such loops relate to the regime behaviour of the Euro-Atlantic sector (cf. Novak et al. 2017, Figures 4 and 5). It is the hope of these authors that persistent homology may be a tool capable of detecting such topological features in the atmosphere using unprocessed, but very high-dimensional, observational data." Climate is not even close to chaotic. All the major climate indices such as ENSO, AMO, QBO are straight-forward responses to tidal forcing subject to the standing-wave boundary conditions of the region under consideration. Take it to PubPeer.com if disagreements arise.`