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…
As an addendum to comment #249, note that being able to extract the 1-year delay is a consequence of Floquet (math) or Bloch theory (condensed matter physics), concisely expressed as F(t) = exp(-iωt)P(t), whereby a clear periodic function can be ext…
Continuing with the forest & trees analysis of ENSO, there's just an incredible amount of fluctuation detail in the time-series.
If a fit is concentrated on the daily SOI data from 2010 to 2013 (high-resolution training range shown in yellow):
…
from Arbic, Brian K, Matthew H Alford, Joseph K Ansong, Maarten C Buijsman, Robert B Ciotti, J Thomas Farrar, Robert W Hallberg, Christopher E Henze, Christopher N Hill, and Conrad A Luecke. “Primer on Global Internal Tide and Internal Gravity …
From comment #254 above, I was asking about coming up with an adjoint approach to inverting the sin(f(t)) model for ENSO. It's obvious that we can try arcsin to do the inversion, but this generates a solution only on a limited domain. I tried gues…
This is the network model evolution of wave dynamics in the ENSO model. The first response is a damping from the impulse-driven tidal forcing. This response is then constrained according to the solution of Laplace's Tidal Equations as a set of stand…
Thinking about Jan's comment some more, emphasizing the trees and leaves analogy.
"Model the real world as a tree (perhaps but not necessarily a random tree or random forest) with closed-form solutions applicable to tiny bits of physics at each …
From a physics blog thread on public involvement in science: https://andthentheresphysics.wordpress.com/2019/03/20/public-involvement-in-science/
this lecture from a geologist :
"Paul, as we’ve discussed before, there are real-world situations …
Since ENSO is the result of a standing wave dipole and that the SOI measure takes the difference between two SW extremes, then we should see something like \( G(t) = C_1 sin(AF(t)+B_1) + C_2 sin(-AF(t)+B_2) \) as the best fit. And that's exactly …
In red is the input forcing \( F(t) \) which is an annual impulse-driven tidal signal. After each impulse, the signal is integrated into the previous value, thus creating an up-and-down stair-step appearing time series. This approach works well to…
Came across a self-published book "The Deep Pull: A Major Advance in the Science of Tides" by Walter Hayduk, a retired chemical engineer. His claim is that the moon and the sun have major influences on ocean dynamics, and in a way that is outside …
10 Things: What We Learn About Earth by Studying the Moon
By Isabelle Yan, NASA’s Goddard Space Flight Center
"Earth’s magnetic field is our shield, constantly protecting us from harmful solar wind or cosmic ray particles. This importa…
"@WebHubTel, Publish it? If not in a geophysics journal, why not try IOP or a statistics journal like JTSA or even Computational and Graphical Statistics? Or at least put it out there in arXiv?"
Jan, All this is published in the Mathematical Ge…
Here's a very convincing data analysis that shows that ENSO (and El Nino) is far from being chaotic. I ran an auto-correlation of the the Fourier series of an ENSO time-series and found a strongly correlated one-year shift from all spectral compone…