Likely impossible to create a model for predicting magnitude 9 earthquakes -- because they are so rare. But predicting magnitude 6 via models may be a more likely way to make progress, see YouTube
Using the same approach on the other major climate index, the PDO, a pattern is starting to emerge. The PDO has a significant LTE sin() modulation that is the same as ENSO, but also has a strong factor with a wavenumber that is 5 times as rapid. I…
Finding this common-mode forcing between ENSO and AMO is either the correct scientific interpretation or the most unlikely rabbit hole to fall into. There is always a concern with regards to over-fitting. The ENSO fit could be fortuitous, based on …
A recent climate science review paper covers "Inferring causation from time series in Earth system sciences", Runge et al 2019, Nature Communications
Unfortunately they do not describe common-mode factor causation. I took one of their figures and…
This opinion piece by Hossenfelder in the NYT makes the claim that "Only Supercomputers Can Do the Math" of modeling the global climate:
https://www.nytimes.com/2019/06/12/opinion/climate-change-supercomputers.html
I recall that Hossenfelder wrote…
Interesting data from this paper on the equatorial-only Semi-Annual Oscillation (SAO) of the upper stratosphere and lower mesosphere wind pattern.
[1] T. Hirooka, T. Ohata, and N. Eguchi, “Modulation of the Semiannual Oscillation Induced by Sudden…
Jim said:
"Re your 2005 observation: NPL accepted the original paper so an update to their model must fit their T&C scope. If not, I bet the authors would want to know."
The scientific discussion is fascinating as is -- I have my model pub…
Lots of the fluid dynamics is done through OpenFOAM and VisualCFD
https://www.openfoam.com/products/visualcfd.php
As for solid geometry simulations, I would also consider something like PTC Creo. https://en.wikipedia.org/wiki/PTC_Creo_Elements/Pro…
Jim, thanks. I burned my bridges at PRL when I tried submitting something earlier. Wish I could find the response, but it was something to the effect that PRL is mainly looking for models that improve the fundamental understanding of physics and t…
It's newsworthy when a climate science paper appears in the prestigious Physical Review Letters. This paper concerns the anomaly observed in the QBO in 2016
Synopsis:A Missing Beat in Earth’s Oscillating Wind Patterns
https://physics.aps.or…
From the outset, the forcing to the modeled behaviors of ENSO and QBO were split into a few categories. There is the declination of the lunar cycles, the proximity of the lunar cycles, and the sun's orbit. Each of these categories has similar comple…
Here is a recent update to the quantitative QBO model. The telling point about these kinds of alignments based on known fixed inputs is that they either work or they don't -- there is no middle ground. For example, two sine waves that have slightl…
the last several comments captured in 2 blog posts:
https://geoenergymath.com/2019/05/20/applying-wavelet-scalograms/
https://geoenergymath.com/2019/05/22/characterizing-spatial-standing-waves-of-enso/
Getting to the point that I may be able to p…
This is also a good ref on Hovmoller diagrams
Fedorov, Alexey V, and Jaclyn N Brown. “Equatorial Waves.” In Ocean Currents, Ed. J. H. Steele, S. A. Thorpe, and K. K. Turekian. Elsevier Science, 2010. http://people.earth.yale.edu/sites/default/files…
One aspect of ENSO that I haven't analyzed too deeply is the spatial part of the standing wave dipole. In solving Laplace's Tidal Equations, the separation of the partial diffEq leads to a family of terms
sin(a f(t)) sin(k a x) + sin(b f(t)) sin(…
Thanks
(a) Looks good, capturing zero crossings is something I've been thinking about, having used a simple metric that compares sign changes between two time series. SiZer should be similarly useful as well.
(b) That looks interesting in terms o…
This is my last use of Mathematica before my license expires
In addition to applying the modeling steps to ENSO, we can apply the same procedure to QBO. This is more straightforward because the arcsin transformation for QBO is very mild in compari…
The last model forcing to arcsin comparison had low resolution. This is with a shorter Gabor window in the wavelet. The y-axis scaling is in octaves (each unit is a period doubling based on the fundamental unit, in months or days)
Here you can …
Thanks Pierre, I should have known the R library has some good wavelet algorithms. I was looking for a good wavelet correlation for awhile so this biwavelet approach should be useful
Since I had a few days left on my evaluation copy of Mathematica, here are a few wavelet transform comparisons of ENSO model and data.
Result :
The wavelet scalogram doesn't show much order yet the model fits well.
The model forcing for the dai…
Thanks, I see that there are wrapper functions called Monitor and EvaluationMonitor, which may be useful.
As for a gold standard, this is the kind of dynamic monitoring that Eureqa provided before it disappeared. One could move the cursor to any e…
I didn't see any options for progress, just for time out and max iterations.
Example of an evaluation
The NonlinearModelFit works well but FindFormula looks hopeless for this case. As I recall, Eureqa would try much harder than this.
I downloaded an evaluation version of Mathematica, and FindFormula was able to find an exact solution to Sin(3 * Sin(x)) after around 30 seconds of computation. That probably explains why it's not available on Alpha -- way too computation intensive…
I looked at the recent online documentation for the Mathematica symbolic regression function called FindFormula. It seems a bit more free-form now than I recall. I should be able to do FindFormula with a set of paired data points and it now appe…
Jan, Yes, I experimented with the symbolic reasoning of Mathematica a bit a few years ago. I could not get it to converge to a solution as easily as it seemed to get hung up on local minima. There also weren't a lot of options for objective funct…
New blog post here:
https://geoenergymath.com/2019/05/02/implicit-interpolating-cross-validation-of-enso/
What's unnerving about the model is that although the results are excellent, there may be a few minor factors that are missing. I kind of mis…
For #265, I reviewed an adjoint approach to unwinding a model from the data. In a related context, here is a recent paper based on the methods of Errico(1997).
Wang, Qiang, Mu Mu, and Guodong Sun. “A Useful Approach to Sensitivity and Predictabi…
If anyone is interested in this paper:
"Manifestation of the topological index formula in quantum waves and geophysical waves" https://arxiv.org/pdf/1901.10592.pdf
"Abstract: Using semi-classical analysis in R^n we present a quite general mode…