Month: December 2024

Bluesky

/ Paul Pukite (@whut) / Leave a comment

In a #Geophysics feed on Bsky.app, the latest “post” after 2 days is still this:

Instead, this is what they should be discussing [1,2]:

Possible breakthroughs in understanding the inverse energy cascade behavior of fluid dynamics.bpb-us-e1.wpmucdn.com/wp.nyu.edu/d…arxiv.org/pdf/2406.00264www.realclimate.org/index.php/ar…

— Puͣkiͧte̍ (@pukite.com) 2024-12-20T00:39:51.019Z

Also discussed at https://www.realclimate.org/index.php/archives/2024/11/twenty-years-of-blogging-in-hindsight/

yet responses are not on point

Typical response totally ignores the climate science aspect.Always gotchas .. so reciprocated.

— Puͣkiͧte̍ (@pukite.com) 2024-12-24T04:12:35.056Z

CITES

  1. Shavit, Michal, Oliver Bühler, and Jalal Shatah. “Sign-indefinite invariants shape turbulent cascades.” Physical Review Letters 133.1 (2024): 014001. https://bpb-us-e1.wpmucdn.com/wp.nyu.edu/dist/0/18842/files/2024/09/PhysRevLett.133.014001.pdf
  2. Vivanco, Isis, et al. “A synchrotron-like pumped ring resonator for water waves.” arXiv preprint arXiv:2406.00264 (2024). https://arxiv.org/pdf/2406.00264

QBO Metrics

/ Paul Pukite (@whut) / Leave a comment

In addition to the standard correlation coefficient (CC) and RMS error, non-standard metrics that have beneficial cross-validation properties include dynamic time warp (DTW), complexity invariant-distance (CID) see [2], and a CID-modified DTW. The link above describes my implementation of the DTW metric but I have yet to describe the CID metric. It’s essentially the CC multiplied by a factor that empirically adjusts the embedded summed distance between data points (i.e. the stretched length) of the time-series so that the signature or look of two time-series visually match in complexity.

   CID = CC * min(Length(Model, Data))/ max(Length(Model, Data))

The authors of the CID suggest that it’s a metric based on “an invariance that the community seems to have missed”.

And a CID-modified DTW is thus:

CID = DTW * min(Length(Model, Data))/ max(Length(Model, Data))

I have tried this on the QBO model with good cross-validation results featuring up to-data data from https://www.atmohub.kit.edu/data/qbo.dat

These have similar tidal factor compositions and differ mainly in the LTE modulation and phase delay. As discussed earlier, any anomalies in the QBO behavior are likely the outcome of an erratic periodicity caused by incommensurate annual and draconic cycles and exaggerated by LTE.

from https://gist.github.com/pukpr/e562138af3a9da937a3fb6955685c98f

REFERENCES

[1] Batista, Gustavo EAPA, et al. “CID: an efficient complexity-invariant distance for time series.” Data Mining and Knowledge Discovery 28 (2014): 634-669.R
https://link.springer.com/article/10.1007/s10618-013-0312-3

Low Dimensions

/ Paul Pukite (@whut) / Leave a comment

“A key enabling assumption, sometimes called the manifold hypothesis [14], is that the data lie on or near a low-dimensional manifold; for physical systems with dissipation, such manifolds can often be rigorously shown to exist [15–18]. These manifolds enable a low-dimensional latent state representation, and hence, low-dimensional dynamical models. Linear manifold learning techniques, such as principal component analysis, cannot learn the nonlinear manifolds that represent most systems in nature. To do so, we require nonlinear methods, some of which are developed in [19–25] and reviewed in [26].“

Floryan, Daniel, and Michael D. Graham. “Data-driven discovery of intrinsic dynamics.” Nature Machine Intelligence 4.12 (2022): 1113-1120.

From <https://www.nature.com/articles/s42256-022-00575-4>

GC22A-04 Can ML beats chaos?

Abstract

“Chaos is typically blamed for the lack of predictability beyond a forecasting time window, which is on the order of 10 days for weather forecasting. However, on the one hand, most turbulent and chaotic systems exhibit strong coherence in the flow, such as synoptic events in weather or coherent structures in turbulence. On the other hand, most physical model might have additional structural errors that limit their capacity to correctly forecast beyond a certain time horizon, independent of chaos.

We will show in this presentation that most chaotic and turbulent flows can be predicted on relatively long range, at least longer than expected with both physical models and standard deep learning, using a combination of a reduced order model (that captures the low-dimensional coherent structures in the flow) and generative AI to obtain the crisp results and details of the flow. We will conclude stating that current AI-based weather models might not have achieved a plateau in performance yet, especially at longer time scales, and that physics-based weather model still have room for improvements. Reduced order models might not be able to beat chaos but can lead to much longer-range prediction than currently expected.“

https://agu.confex.com/agu/agu24/meetingapp.cgi/Paper/1522150