↖ CPA Weather Lab

Data Analytics report

Pennsylvania precipitation regimes: a pilot for historical daily reconstruction

Daily and wet-spell precipitation regime analysis using Pennsylvania station observations and PRISM D2 4-km fields.

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.

Station days

1,462Source: 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

Complete daily station feature rows across four selected years.

Complete daily station feature rows across four selected years.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

Measured-only station daily precipitation transformed to statewide distribution and spatial-shape features.

PRISM 4-km days

129Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids

Available 4-km daily fields; the sample is warm-season weighted.

wet-gated 92Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
Available 4-km daily fields; the sample is warm-season weighted.Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids

Area-weighted Pennsylvania extraction of daily PRISM D2 4-km precipitation fields and spatial features.

Mean correlation

0.97Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features

Pearson correlation of matched statewide daily mean precipitation.

Pearson correlation of matched statewide daily mean precipitation.Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features

Date-matched comparison of station distribution statistics with area-weighted PRISM 4-km statistics.

Shape stability

0.87Source: 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

Bootstrap adjusted Rand index for the selected three-family station shape model.

Bootstrap adjusted Rand index for the selected three-family station shape model.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

Measured-only station daily precipitation transformed to statewide distribution and spatial-shape features.

Season changes the spatial regime, not just the amount

Among wet station days, east/southeast focus rises from 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: 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: 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: 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.

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

Measured-only station daily precipitation transformed to statewide distribution and spatial-shape features.

Spatial regime mix by season
Spatial regime mix by season data
SeasonShareSpatial regimeSeason order
winter5.8%compact/localized1
winter45.05%east/southeast focused1
winter49.15%west/northwest focused1
spring3.46%compact/localized2
spring55.02%east/southeast focused2
spring41.52%west/northwest focused2
summer7.22%compact/localized3
summer66.67%east/southeast focused3
summer26.12%west/northwest focused3
autumn8.1%compact/localized4
autumn48.18%east/southeast focused4
autumn43.72%west/northwest focused4

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: 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: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features, p95 correlation is 0.907Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features, and daily-maximum correlation is 0.778Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features. Stations exceed the 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.

Source: Matched station-PRISM daily validationTables: station_daily_features, grid_daily_features

Date-matched comparison of station distribution statistics with area-weighted PRISM 4-km statistics.

Station-grid agreement weakens toward local extremes
Station-grid agreement weakens toward local extremes data
Daily statisticCorrelationStation-grid biasMean absolute differenceMatched days
mean_mm0.970.181.1129
wet_fraction0.96-0.050.09129
p95_mm0.914.345.66129
max_mm0.786.2916.08129

Spatial fields remain high-dimensional after intensity normalization

The first 10Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids principal components explain only 71.9%Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids of normalized PRISM field variance; 15Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids explain 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.

Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids

Area-weighted Pennsylvania extraction of daily PRISM D2 4-km precipitation fields and spatial features.

Normalized PRISM field PCA
Normalized PRISM field PCA data
Principal componentsCumulative varianceIncremental variance
117.7%17.7%
231.74%14.03%
340.09%8.35%
447.76%7.68%
554.12%6.35%
658.94%4.82%
762.98%4.04%
866.77%3.79%
969.48%2.7%
1071.92%2.45%
1174.2%2.28%
1276.39%2.19%
1378.32%1.92%
1480.11%1.79%
1581.74%1.63%

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.

Four-year weekly precipitation profile
Four-year weekly precipitation profile data
ISO weekMean precipitationWidespread-heavy daysDry/trace daysDay observations
14.26mm/day11.54%15.38%26
23.08mm/day10.71%3.57%28
32.14mm/day0%10.71%28
42.2mm/day3.57%17.86%28
51.78mm/day7.14%25%28
61.93mm/day3.57%21.43%28
73.32mm/day10.71%25%28
82.53mm/day7.14%32.14%28
93.41mm/day10.71%35.71%28
104.53mm/day14.29%17.86%28
111.4mm/day3.57%46.43%28
124.59mm/day17.86%10.71%28
135.78mm/day25%17.86%28
143.81mm/day10.71%17.86%28
153.5mm/day14.29%35.71%28
165.27mm/day28.57%7.14%28
173.14mm/day7.14%14.29%28
183.12mm/day14.29%25%28
192.59mm/day3.57%17.86%28
204.43mm/day17.86%14.29%28
213.66mm/day10.71%10.71%28
221.88mm/day0%39.29%28
233.81mm/day14.29%25%28
243.15mm/day14.29%14.29%28
252.36mm/day3.57%28.57%28
262.8mm/day0%25%28
272.89mm/day7.14%21.43%28
283.74mm/day10.71%17.86%28
291.76mm/day0%17.86%28
303.97mm/day10.71%14.29%28
313.96mm/day17.86%14.29%28
325.09mm/day14.29%7.14%28
332.61mm/day3.57%17.86%28
343.56mm/day7.14%42.86%28
354.13mm/day14.29%17.86%28
366.15mm/day17.86%42.86%28
372.92mm/day7.14%21.43%28
382.38mm/day10.71%35.71%28
394.01mm/day21.43%42.86%28
405.52mm/day21.43%32.14%28
412.21mm/day3.57%32.14%28
423.39mm/day17.86%25%28
433.27mm/day14.29%17.86%28
442.15mm/day7.14%50%28
451.58mm/day3.57%57.14%28
463.17mm/day10.71%25%28
473.28mm/day10.71%21.43%28
483.74mm/day10.71%17.86%28
493.32mm/day14.29%14.29%28
503.16mm/day10.71%32.14%28

53 results · Showing first 50

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.

Daily 4-km regional exemplars

Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids

Area-weighted Pennsylvania extraction of daily PRISM D2 4-km precipitation fields and spatial features.

Daily 4-km regional exemplars
RegionDateSeasonPA mean (mm)Region mean (mm)Concentration ratioWet components
NC2005-07-07summer1.53Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids3.35Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids2.12Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids41Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
NE2011-08-29summer5.8Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids21.37Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids3.64Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids5Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
NW2011-09-01autumn2.72Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids10.65Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids3.81Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids4Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
SC2005-07-22summer2.79Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids11.12Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids3.89Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids14Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
SE2000-07-26summer1.41Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids12.83Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids8.56Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids3Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
SW2000-07-11summer2.18Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids12.68Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids5.6Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids4Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids

Wet-spell regional exemplars

Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids

Area-weighted Pennsylvania extraction of daily PRISM D2 4-km precipitation fields and spatial features.

Wet-spell regional exemplars
RegionStartSeasonPA total (mm)Region total (mm)Cell p95 (mm)Concentration ratio
NC2020-07-17summer8.56Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids13.45Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids30.33Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids1.56Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
NE2020-07-01summer1.35Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids6.2Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids8.32Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids4.35Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
NW2011-09-01autumn9.28Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids20.59Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids33.65Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids2.2Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
SC2020-07-22summer21.17Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids36.37Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids55.74Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids1.71Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
SE2011-08-28summer42.41Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids135.19Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids157.22Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids3.18Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids
SW2000-07-10summer8.1Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids17.21Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids22.41Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids2.11Source: PRISM D2 daily 4-km Pennsylvania fieldsTable: PRISM D2 daily 4-km grids

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.

Sources

  1. Pennsylvania climate daily parquet - measured reportsdata/regime/parquet · 2026-08-10T12:00:00Z

    Measured-only station daily precipitation transformed to statewide distribution and spatial-shape features.

    SQL query
    SELECT * FROM read_csv_auto('analysis_output/regimes/station_daily_features.csv')
  2. PRISM D2 daily 4-km Pennsylvania fieldsdata/regime/prism · 2026-08-10T12:00:00Z

    Area-weighted Pennsylvania extraction of daily PRISM D2 4-km precipitation fields and spatial features.

    SQL query
    SELECT * FROM read_csv_auto('analysis_output/regimes/grid_daily_features.csv')
  3. Matched station-PRISM daily validationanalysis_output/regimes/station_grid_validation.csv · 2026-08-10T12:00:00Z

    Date-matched comparison of station distribution statistics with area-weighted PRISM 4-km statistics.

    SQL query
    SELECT * FROM read_csv_auto('analysis_output/regimes/station_grid_validation.csv')
← CPA Weather Lab · Learn