Pennsylvania PRISM Precipitation Product Comparison

A reproducible comparison of LT81m, AN M2/M3, D1/D2, resolution filtering, radar-era interpretation, and station residuals for a Pennsylvania daily reconstruction back to 1895.

Bottom line

• Use M2 monthly constraints for 1895-1980 and M3/D2 for 1981 onward for the best-estimate reconstruction, while preserving explicit era flags and overlap adjustments.
• Keep LT81m as a parallel homogeneous-climate baseline, not as a silent substitute for the best-estimate storm product.
• 4 km filtering barely changes Pennsylvania-wide monthly volume, but daily convective sub-cell structure matters: the mean 5×5 sub-cell range is about 20.7% of the daily mean on days above 2 mm.
• M3 equals ΣD2 to storage precision. ΣD1 can miss M2 badly: −12.96 mm (−15.92%) in July 2000, +0.49 mm in July 2005, and +5.07 mm in September 2011.
• Independent daily placement error dominates. Measured-only D2 wet-day RMSE is 122-158% of the mean wet-day amount, and roughly 14-26% of stations prefer a one-day shift.
• Radar alone is not identifiable here. Both D1 and D2 use radar in the central/eastern U.S. starting in 2002, so D2−D1 is not radar-on minus radar-off.

What the PRISM documentation settles

M3 and D2 begin in 1981 and continue to the present. M2 and D1 end in June 2015. In the central/eastern U.S., M3 is forced to equal the sum of D2; D2 apportions non-PRISM-day and multi-day station totals and applies monthly completeness. D1 and M2 used different input rules and were not reconciled. Both daily versions use CAI plus radar from 2002. The radar source changes again in July 2020, when radar-only MRMS replaces ST2un in the weighting process. These are method boundaries, not mere filename trivia.

The daily series can change the monthly result in two distinct ways

For the three complete paired months, the arithmetic identity is:

M3 − M2 = (ΣD1 − M2) + (ΣD2 − ΣD1) − (ΣD2 − M3).

The last term is essentially zero. This separates the old D1/M2 inconsistency from the D2/D1 method change, but neither term is a pure radar effect.

D2−D1 is event-dependent, not a monthly scale factor

ΣD2 exceeds ΣD1 by 9.99 mm in July 2000, 5.70 mm in July 2005, and 2.89 mm in September 2011. Daily spatial MAE peaks at 2.18 mm on July 15, 2000, 2.22 mm on July 9, 2005, and 2.43 mm on September 7, 2011. Differences grow on wet/event days, so a single statewide correction multiplier would erase the very structure the newer method is trying to recover.

What radar changed—and what these data cannot say

The pre-2002 samples establish that M3/D2 can differ materially from M2/D1 even without radar, because station-day apportionment, completeness, networks, QC, and reconciliation changed. Post-2002 contrasts add radar, but also all those other differences. July 2020 is itself a radar-input transition month. A radar-only number requires a matched CAI-only and CAI+radar rerun under identical station, QC, and reconciliation rules; these archives do not contain that counterfactual.

800 m-to-4 km loss is local smoothing, not missing state volume

Across supplied July fields from 1971 through 2020, state-mean bias is −0.185% to +0.092%, while local paired MAE is 1.09-3.79 mm. For the 36 daily 2011 fields, precipitation-weighted within-4 km variance is 0.67%, but the mean 5×5 sub-cell range is 20.7% of the daily mean on days above 2 mm and reaches 67-69% on scattered September days. Daily maxima fall 3.8% on average on those wetter days. Monthly aggregation hides much of this: for September, within-cell variance is 0.35%, local MAE is 3.92 mm, and the maximum falls from 643.47 to 637.45 mm. Treat the loss as regime-dependent sub-grid uncertainty, especially on scattered convection.

Station evidence favors M3/D2 in aggregate, but holdout evidence is thin

For complete measured-only station months, ΣD2 MAE is lower than ΣD1 by 6.69 mm (2000), 1.38 mm (2005), and 1.42 mm (2011). However, most observations helped construct at least one PRISM product. Among stations not listed in either monthly input inventory, D1 and D2 are essentially tied in 2000 and 2005, while D1 is better in 2011; those subsets contain only 12-30 stations. The honest conclusion is that D2 fits the assimilated station field better, while clean out-of-sample superiority is not yet established.

Daily validation changes the priority order

The supplied station-day parquet contains 25,559 rows and daily assimilation flags; 10.3% of its precipitation values are marked estimated, so this report recomputes headline results using measured-only rows. At D2-independent station-days, wet-day RMSE is 122-158% of the mean wet-day total and correlation is 0.34-0.68. D2 skill relative to D1 at stations independent of both is +4.3% in July 2000, −3.2% in July 2005, and +1.8% in September 2011—no consistent post-radar daily advantage. At 25 mm/day, measured-only probability of detection is 0.17-0.59 and false-alarm ratio is 0.36-0.60. Monthly anchoring controls mass and homogeneity; day allocation and timing dominate daily uncertainty.

Observation-time alignment is a first-order daily error

After excluding estimated station values, 13.6-25.9% of D2 stations prefer a one-day-shifted observation series; with all reported values the range is 19.5-25.8%, matching the supplied analysis. The sign depends on whether the shift is described from the grid or gauge perspective, so the report treats it direction-agnostically. Multi-day totals can be accurate while individual days alternate between dry and wet errors. Validate reconstruction amplitude on multi-day/event windows or model each station's observation time before scoring single days.

Product construction dominates resolution uncertainty

Annual M3−M2 is −3.93 mm in 1981, −18.93 mm in 1991, −11.40 mm in 2000, +22.14 mm in 2005, and +36.16 mm in 2011. The sign changes by year and month, while local pixel MAE remains much larger than the state-mean difference. This is spatial redistribution plus network/method change—not a stable bias correction.

Empirical structural uncertainty

The annual mean cellwise range among current AN, stable M2, and block-averaged LT grows from 14.0 mm in 1971 to 63.0 mm in 2005; the 2005 95th-percentile cell range is 136.9 mm. Use this product spread as a structural sensitivity layer, not a probabilistic confidence interval. Calibrate a separate stochastic error model from genuinely held-out gauges where possible.

The practical choice for a 1895-present daily reconstruction

No one of the three candidates exists with the same purpose and method across the full period. A defensible operational design therefore has two products: a best-estimate track that splices monthly anchors with an explicit transition model, and a homogeneous LT track for climate sensitivity. The switch and method flags belong in the data model, not in a footnote discovered years later by an irritated raccoon.

Recommended reconstruction architecture

1. 1895-1980: constrain temporally disaggregated daily estimates to M2 monthly totals. Use station days, weather regimes, and neighboring-day structure for timing; force exact monthly mass closure.
2. 1981-present: use D2 daily totals where available and M3 monthly totals as the closure target. Preserve native 800 m values when local hydrology matters; otherwise attach a 4 km smoothing uncertainty layer.
3. Parallel LT track: maintain LT81m as a homogeneous climate/station baseline for trend and breakpoint sensitivity.
4. Era flags: record at least 1981 (M3/D2 start), 2002 (radar use), July 2015 (M2/D1 availability ends), July 2020 (MRMS radar-input transition), and 2021 (new normals/predictor regime).
5. Transition model: estimate month × physiographic region × elevation × wetness adjustments over overlaps. Never use one statewide multiplier.
6. Daily regimes: give scattered-convective days wider spatial uncertainty than organised storms; a 4 km probability distribution may be more honest than a single value.
7. Observation time: infer per-station day offsets and score amplitude on multi-day windows before using single-day residuals.
8. Uncertainty: keep gauge/measurement error, anchor/product spread, temporal disaggregation error, and 800 m-to-4 km sub-grid smoothing separate.
9. Validation: exclude estimated gauge values for the primary score, use daily inventory flags for true withheld sets, and report sample size and assimilation status.

Scope and validation status

Share with caveats. The workflow validates complete daily coverage, exact 5:1 grid alignment, D2-to-M3 closure below 0.01 mm pixel MAE, and the decomposition identity above. Pennsylvania contains 180,464 native 800 m cell centers and 7,164 4 km centers in this mask; state means use cosine-latitude weights. All 25,559 supplied station-day points fall inside the Pennsylvania polygon; 2,625 estimated values are excluded from the primary daily validation. The archive labeled 1992 contains 1991 grids. The 1981 annual 800 m AN archive is truncated, so only its valid July resolution comparison is used. LT is reduced to 4 km with an area-conserving 5×5 mean for cross-product spread; that does not recreate PRISM's production Gaussian kernel. Remaining limitations are radar causal identification, only one transition-month sample for MRMS, daily inventory matching at 0.02 degrees, and small fully independent monthly-gauge subsets.