Principal Component Analysis of Doppler Radar Data. Part I: Geometric Connections between Eigenvectors and the Core Region of Atmospheric Vortices
Bibliographic record
Abstract
Abstract This is the first in a three-part series of papers that present the first applications of principal component analysis (PCA) to Doppler radar data. Although this novel approach has potential applications to many types of atmospheric phenomena, the specific goal of this series is to describe and verify a methodology that establishes the position and radial extent of the core region of atmospheric vortices. The underlying assumption in the current application is that the streamlines of the nondivergent component of the horizontal wind are predominantly circular, which is a characteristic often observed in intense vortices such as tropical cyclones. The method employs an S2-mode PCA on the Doppler velocity data taken from a single surveillance scan and arranged sequentially in a matrix according to the range and azimuth coordinates. Part I begins the series by examining the eigenvectors obtained from such a PCA applied to a Doppler velocity model for a modified, Rankine-combined vortex, where the ratio of the radius of maximum wind to the range from the radar to the circulation center is varied over a wide range of values typically encountered in the field. Results show that the first two eigenvectors within the eigenspace of range coordinates represent over 99% of the total variance in the data. It is also demonstrated that the coordinates of particular cusps in the curves of the eigenvector coefficients plotted against their indices are geometrically related to both the position of circulation center and the radius of maximum wind.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".