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Pennsylvania PRISM · EOF/SVD · 1981–2025

Dante's Weather Raccoon Inferno

A guided descent through the statewide precipitation EOF experiment: the deceptively simple all-season result, the Modes 6–8 geometry, exact monthly contributions, and the seasonal split that made winter and summer look like relatives who stopped speaking years ago.

0

The vestibule: how we got here

The point of this page is not merely to display output. It preserves the logic of the experiment so the maps remain attached to what the SVD actually did.

1. The matrix

Each row is one monthly Pennsylvania precipitation field. Each column is one of 7,165 PRISM 4-km cell centers. The original all-season matrix has 540 months.

2. The anomaly/correlation basis

We remove each cell's calendar-month climatology, then standardize cells for a correlation-basis SVD. That strips out the obvious seasonal mean and prevents high-variance locations from automatically owning the decomposition.

3. One fixed loading map, changing score

For a given EOF, the loading map is fixed within that decomposition. A month's exact contribution is temporal score × spatial loading. Positive and negative scores express opposite orientations of the same mode.

All-season Neff robustness

The effective rank stays near two under raw, square-root, anomaly, and z-score treatments. That was the first clue that the low dimensionality was not merely the annual cycle wearing a fake mustache.

Working interpretation of the saved all-season modes

These are geometric descriptions, not proven storm regimes.
I

The seasonal split: the first major fracture

Four independent SVDs, each with 135 monthly fields. Same Pennsylvania grid, same anomaly treatment, same correlation basis. The loading maps are allowed to change by season.

Effective dimensionality

Mode 1's share of variance

II

The spectral staircase

Winter pours most of its variance into the first few steps. Summer keeps spilling variance farther down the staircase. Use the controls to inspect the complete 134-mode seasonal spectrum.

First ten variance shares

III

The ten-mode gallery

Choose a season and one of its first ten EOFs. This is the actual seasonal loading field from the uploaded ZIP, drawn directly from the 7,165 loading values.

negative loading0positive loading

Strongest months for this seasonal mode

EOF sign is arbitrary. A negative score is not a weak month; it can be a very strong expression of the inverse loading pattern.
IV

Same mode number, four seasons

This is where the polite fiction that “Mode 6 is Mode 6” starts to fail. Select a mode number and compare its seasonal loading fields with a common color scale.

How stable is the same mode number across seasons?

V

The identity crisis: modes swap, rotate, and rematch

A seasonal EOF number is a rank within that season, not a universal identity card. The heatmap compares every top-10 mode in one season with every top-10 mode in another.

Cell color is signed Pearson spatial correlation. Click a cell to compare the two loading maps.

Best one-to-one assignment

Subspace similarity

This is the important nuance: the leading low-order subspace can remain very similar even while variance is redistributed and the higher individual modes become unstable or reorder.
VI

Seasonal monthly explorer: exact mode contribution

The seasonal ZIP saved all 134 temporal scores. That lets us calculate a mode's exact share of the complete seasonal anomaly energy for any one of the 135 months, not merely its share among the first ten.

score × loading
negative contribution0positive contribution

This month's first-ten energy budget

VII

The all-season Modes 6–8 laboratory

This preserves the experiment we did before the seasonal split. Pick any of the 540 months and inspect the exact all-season contributions of Modes 6, 7, and 8. The table below is sortable and filterable; clicking a row updates the maps.

For the old all-season run, only the first eight temporal scores were saved. “Share of first 8” is therefore exact within those eight, not a whole-539-mode monthly fraction.
VIII

The 27-class geometry: useful picture, dangerous temptation

Each all-season cell gets negative / neutral / positive labels for Modes 6, 7, and 8. Three states cubed gives 27 combinations. The three-panel map avoids a 27-color act of violence by splitting on Mode 6 and coloring Mode 7 × Mode 8.

Mode 7 × Mode 8 color key

27 combination frequencies

Null-model warning: smooth EOF loading fields will naturally create contiguous sign regions when thresholded. This figure visualizes joint EOF geometry; it does not, by itself, prove 27 physical precipitation regimes.
IX

What the descent actually tells us

The seasonal ZIP changed the story, but not in the simplistic “winter and summer share nothing” way. The strongest conclusion is more interesting.

Supported by this experiment

Season changes the variance allocation dramatically.
Winter concentrates variance in Mode 1; summer spreads it much farther into higher modes.
Summer is much more effectively multidimensional.
The seasonal Neff rises from about 1.80 in DJF to 3.42 in JJA.
The first few spatial directions are still related.
Low-order seasonal subspaces remain strongly aligned, especially Modes 1–5. The planets share geology even if the weather systems run different governments.
Mode numbering becomes unreliable higher up.
From roughly Mode 6 onward, same-number spatial correlations collapse and better matches often occur at different ranks.

Not yet established

EOFs are not storm types.
A Mode 6 shape that resembles a Miller-B precipitation field is a hypothesis, not an identification.
Smooth regions are not automatically physical regimes.
We still need matched spatial-autocorrelation null fields to know how much of the geometry is generic EOF behavior.
Individual higher EOFs need stability testing.
Bootstrap resampling should tell us whether Modes 6–10 recur as recognizable directions or rotate within a stable subspace.
Physical attribution comes after stability.
Then we can test terrain, physiographic provinces, cyclone classes, tropical remnants, and daily-event projections.
Current research sentence: Pennsylvania's precipitation covariance structure has a strongly shared low-order spatial backbone, but the seasonal allocation of variance and the higher-order EOF geometry change substantially, with summer exhibiting markedly greater effective dimensionality and weaker higher-mode correspondence to winter.
Built entirely from the uploaded seasonal EOF ZIP plus the earlier all-season anomaly/correlation outputs generated in this conversation. No external data are used in this explorer. Maps show PRISM cell centers; they are analytical loading/contribution fields, not administrative climate regions.
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