Pennsylvania precipitation regimes: a pilot for historical daily reconstruction

Technical summary

The data support your central concern: a grid cell cannot be assigned an independent daily percentile without changing the entire field's geometry. A useful reconstruction should first choose a statewide activity/coverage tier, then choose a coherent spatial-shape regime, and only then generate one joint precipitation field whose cells move together. The best initial temporal unit is a 3-day block: it preserves most storm structure while reducing the false precision and instability of individual daily 4-km/800-m values. Five-day blocks are defensible for sensitivity tests; weekly blocks are too likely to merge unrelated convective systems.

Season changes the spatial regime, not just the amount

Among wet station days, east/southeast focus rises from 45.1%Source for 45.1%Source: Pennsylvania climate daily parquet - measured reportsTables: pa_climate_daily_2000_2004, pa_climate_daily_2005_2009, pa_climate_daily_2010_2014, pa_climate_daily_2020_2026 in winter to 66.7%Source for 66.7%Source: Pennsylvania climate daily parquet - measured reportsTables: pa_climate_daily_2000_2004, pa_climate_daily_2005_2009, pa_climate_daily_2010_2014, pa_climate_daily_2020_2026 in summer, while west/northwest focus rises from 26.1%Source for 26.1%Source: Pennsylvania climate daily parquet - measured reportsTables: pa_climate_daily_2000_2004, pa_climate_daily_2005_2009, pa_climate_daily_2010_2014, pa_climate_daily_2020_2026 in summer to 49.1%Source for 49.1%Source: Pennsylvania climate daily parquet - measured reportsTables: pa_climate_daily_2000_2004, pa_climate_daily_2005_2009, pa_climate_daily_2010_2014, pa_climate_daily_2020_2026 in winter. Spring is transitional but remains east-weighted. That is strong evidence for conditioning the spatial regime on season before drawing any local amount.

Intensity and coverage are a separate first-stage decision

An unconstrained model primarily discovers three intensity/coverage tiers: scattered-light, ordinary wet, and widespread-heavy. In the station panel their mean statewide amounts are 1.31, 2.57, and 15.78 mm/day. In PRISM they are 0.91, 5.37, and 25.41 mm/day. These tiers are operationally useful, but they do not by themselves describe storm placement or angle.

The 4Source for 4Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features-km field preserves statewide amount but shaves the local tail

Matched daily statewide means agree very well, but agreement weakens as the statistic becomes more local and extreme. Mean correlation is 0.966Source for 0.966Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features, p95 correlation is 0.907Source for 0.907Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features, and daily-maximum correlation is 0.778Source for 0.778Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features. Stations exceed the 4Source for 4Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features-km grid by 6.29 mm on average at the daily maximum, with a 16.09 mm mean absolute difference. This is direct evidence of smoothing at 4 km, even when statewide water mass is credible.

Spatial fields remain high-dimensional after intensity normalization

The first 10Source for 10Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids principal components explain only 71.9%Source for 71.9%Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids of normalized PRISM field variance; 15Source for 15Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids explain 81.7%Source for 81.7%Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids. This is why independent cell percentiles fail: displacement, orientation, fragmentation, regional gradient, and intensity footprint vary jointly. A compact classifier can select a regime, but the generated object must still be a complete correlated field.

Weekly results are useful for seasonality, not as the primary storm unit

The four-year station sample shows episodic peaks around ISO weeks 13, 16, 32, 36, and 40, but each week has only about 28 day observations. Use weekly summaries to modulate prior probabilities through the year; do not force every historical event into a seven-day bucket.

One daily and one wet-spell example for each broad sector

The tables identify concrete 4-km fields for prototype testing. The regions are broad geometric sectors, not Pennsylvania physiographic provinces. Replace them with physiographic or watershed polygons before a production model.

What was measured and how the classifier works

The station evidence uses measured-only precipitation from 2000, 2005, 2011, and 2020, with 132-242 reporting stations per day. The PRISM evidence uses 129 D2 4-km fields from four Julys/late August/September samples. Daily features include statewide and regional amount distributions, wet-area coverage, connected wet components, precipitation-weighted centroid, covariance-ellipse angle/eccentricity, effective wet area, and top-decile mass concentration. Intensity clusters use these raw features. Shape clusters remove overall amount using regional log contrasts and wet-fraction contrasts, then cluster robustly scaled geometry features. Three shape families were retained because they had the best combination of interpretability and bootstrap stability.

Limits and uncertainty that matter

The PRISM grid sample is warm-season weighted, so winter and spring spatial conclusions are station-driven rather than grid-validated. The station network changes over time and is not area-uniform. Consecutive wet days can merge separate systems, especially in convective summer periods; true storm segmentation needs radar or reanalysis-assisted object tracking. The three-family shape result is stable (bootstrap ARI about 0.87 for station fields and 0.80 for grids), but silhouettes are modest, confirming that regimes overlap rather than form hard natural boxes.

Recommended reconstruction architecture

1. Use monthly precipitation as the hard mass constraint, with explicit uncertainty around the chosen monthly product.
2. Allocate the month into 3-day event blocks; repeat with 5-day blocks as a sensitivity ensemble.
3. For each block, draw a season-conditioned activity/coverage tier and spatial-shape regime jointly.
4. Select or generate a complete correlated field from regime-conditioned PRISM analogs or a covariance model; never draw grid-cell percentiles independently.
5. Disaggregate within the block only after its spatial field is fixed, and reconcile all daily values back to the block and monthly totals.
6. Add full-year PRISM D2 samples and circulation predictors before freezing winter/spring regimes.

Further questions

The next decisive tests are whether physiographic-region boundaries outperform the six geometric sectors, whether 3-day blocks retain enough sequencing for flood applications, and whether a true storm-object tracker splits long wet spells into meteorologically coherent systems. A complete D2 year plus the station inventory by product/month would answer all three much more cleanly.