GRID-TDEM-2008PRINTED
Temperature DEM
80-m NED -> 1.3-km Gaussian/Barnes -> 800-m DEM
L: 80-m NED | T: 1.3 km | R: 800-m T DEM
PRISM Visual Puzzle System v0.2
Certified puzzle-piece prototype after the 2002 core and 2008 CONUS closure passes. Individual pieces can be audited alone, then docked into subsystem boards and finally the master decision tree.
GRID-PDEM-2008PRINTED
Precipitation DEM
800-m temperature DEM -> 7-km Gaussian/Barnes -> 800-m precipitation DEM
L: T DEM | T: 7 km | R: P DEM
GRID-FACET-2008PRINTED
Facet ladder
Library: 0.8,12,24,36,48,60 km. Precipitation active in 2008: 12,24,36 km.
L: P DEM | T: scale | R: facet grid
GRID-ET-2008PRINTED
Effective Terrain Height
minimum 22 km -> average 11 km -> subtract -> average 15 km
L: P DEM | T: 22/11/15 | R: h_eff
GRID-PCE-2008PRINTED
Eastern Precip Coastal Grid
Distance from generalized coastline; central/eastern precipitation input.
L: generalized coast | R: PCE
EQ-WD-2008PRINTED
Distance Weight
Wd=1 inside rm; outside, Wd=1/(d-rm)^a. Precip: a=2, rm≈7 km.
L: d | T: a,rm | R: Wd
CTRL-CLUSTERPRINTED
Cluster Geometry
0.2r horizontal threshold; typical r 30-50 km; elevation precision p≈50 m.
L: station geometry | T: r,p | R: Wc
EQ-WCOMB-EASTRESTATED
2008 Eastern-Precip Weight
Source-faithful branch reduction: Wc * sqrt(FdWd²+FzWz²) * Wp * Wf * We
L: weights | T: states | R: W
REG-LOCALPRINTED
Local Weighted P/E Regression
Y = beta1 X + beta0
L: stations+weights | T: bounds | R: beta0,beta1,Yhat
STATE-I3DPRINTED
Effective Terrain State
<75 m: 2-D | 75-250 m: transition | >250 m: 3-D
L: h_c,h_a | T: h2,h3 | R: I3d
CTRL-I3DPRINTED
Terrain Master Controller
I3d linearly rescales beta1m,beta1x,beta1d,b,c,y
L: I3d | R: six parameters
GAP-C3GAP
Areal Effective-Terrain Ambiguity
Printed h_a=sum(w_i h_i)/n with w_i=1/d_i; do not silently normalize denominator.
L: h_i,d_i | R: h_a?
GAP-WEGAP
Effective-Terrain Station Weight Conflict
White-paper formula gives 0.1 at 2D-target/3D-station endpoint; prose says factor-100 downweight.
L: I3dc,I3ds | R: We?
CTRL-ANCHORPRINTED
POR Anchor Ranking
coverage fraction × ASSAY weight; tie-break by ASSAY weight then distance; choose top 3.
L: histories+ASSAY | R: 3 anchors
EQ-A1PRINTED
Precipitation POR Adjustment
X't = Xte × (Xa/Xae), calculated for three anchors then averaged.
L: target+anchor means | R: adjusted target
EQ-PI70PRINTED
Regression Prediction Interval
Eq.6 variance + Eq.7 interval; use 70% interval. Minimum precipitation stations = 40.
L: fit+weights | T: alpha,df | R: PI70
CTRL-NEIGHBORPRINTED
Neighbor Gradient Repair
If final neighbor climate/elevation gradient violates bounds, adjust both pixel values equally until valid.
L: neighbor cells | T: bounds | R: repaired cells
EQ-FILTERPRINTED
Adaptive 8-km Precipitation Filter
Distance-weighted mean; exponent moves 0->4 as local field complexity reaches 4%.
L: 8-km field | T: 4% threshold | R: filtered grid
REVIEW-2008PRINTED
Expert Review / Remodelling
Published human-in-loop stage. Example: East Coast coastal-proximity exponent increased after review.
L: draft maps+expert knowledge | R: revised parameters/grid
PA-ETPA TEST
PA Effective-Terrain State Map
Build exact 22/11/subtract/15 pipeline and map 2-D / transition / 3-D seams.
L: PA DEM | R: state atlas
PA-FACETPA TEST
PA Facet Branch Map
Reconstruct 12/24/36-km precipitation facets; retain selected level, same-facet N, MAE_a/MAE_b.
L: PA P DEM+stations | R: facet state
PA-C3PA TEST
PA C3 Ambiguity Ensemble
Run literal printed C3 versus normalized weighted-mean alternative; map structural spread.
L: h_eff | R: uncertainty
2008 Board A — Pennsylvania terrain lineage
80-m NED
→
1.3-km Gaussian
→
800-m T DEM
→
7-km Gaussian
→
800-m P DEM
Facet lane
12 / 24 / 36 km active precipitation facets
12 / 24 / 36 km active precipitation facets
Effective-terrain lane
min 22 → avg 11 → subtract → avg 15 → h_eff
min 22 → avg 11 → subtract → avg 15 → h_eff
Coastal lane
central/eastern PCE from generalized coastline
central/eastern PCE from generalized coastline
2008 Board B — Eastern precipitation weighting
Wd
Wz
Wc
Wf
Wp
We
→combined W
→weighted local regression
In the 2008 input-grid table, precipitation layer guidance is western-US specific and topographic-position guidance is temperature-specific. Those generic Eq.2 terms are therefore treated as neutral in the 2008 eastern-precipitation application branch unless another source establishes otherwise.
2008 Board C — Effective-terrain controller
h_c
h_a
→
I3d=max(I3c,I3a)
→
beta1m
beta1x
beta1d
b
c
y
RED PIECE: printed C3 uses sum(w_i h_i)/n. Preserve literally; test normalized weighted-mean alternative separately.
RED PIECE: 2002 effective-terrain station-weight formula and prose disagree at the fully 2-D / fully 3-D endpoint.
2008 Board D — After the local regression
local cell predictions
→
neighbor gradient bound repair
→
adaptive 8-km precipitation filter
→
expert review / remodelling
→
final grid
This is why a final grid cell is not guaranteed to equal the raw independent local-regression prediction.
Effective Terrain Board — certified lineage and ambiguity
Developmental grid
~4-km DEM → min 40 → avg 40 → subtract → smooth 20
~4-km DEM → min 40 → avg 40 → subtract → smooth 20
2008 CONUS grid
800-m P DEM → min 22 → avg 11 → subtract → smooth 15
800-m P DEM → min 22 → avg 11 → subtract → smooth 15
h_c → I3c
+
nearby h_i → h_a → I3a
→
I3d = max(I3c,I3a)
→
β1m β1x β1d b c y
target I3d
+
station I3d
→
effective-terrain station weight
Eq. 3: both sources print h_a = Σ(w_i h_i)/n with w_i=1/d_i. Literal and normalized alternatives remain separate.
Eq. 7: literal formula gives 0.1 at the fully-2D-target / fully-3D-station endpoint; prose says factor-100 downweight (0.01).
Asymmetry: the source deliberately penalizes 3-D stations for 2-D targets, but does not penalize 2-D stations merely because the target is 3-D.
Lineage Board — FACET evolves rather than staying fixed
1994
5-point filter
0/8/16/24/32/40 passes
→
5-point filter
0/8/16/24/32/40 passes
2002
6 modified Gaussian/Barnes levels
DEM resolution → lambda_x
→
6 modified Gaussian/Barnes levels
DEM resolution → lambda_x
2008
physical scales 0.8/12/24/36/48/60 km
PPT uses 12/24/36
physical scales 0.8/12/24/36/48/60 km
PPT uses 12/24/36
Same concept, different terrain representation. Treat as versioned pieces, not one immortal FACET box.
Lineage Board — slope repair changes algorithm
1994 influential-outlier repair
Delete candidate causing the largest slope change only if one deletion restores the slope to bounds. Otherwise use DB1.
Delete candidate causing the largest slope change only if one deletion restores the slope to bounds. Otherwise use DB1.
2002 weighted repair
Delete the lowest-weight station, refit, and repeat until slope is valid or the station floor is reached; then beta1d fallback.
Delete the lowest-weight station, refit, and repeat until slope is valid or the station floor is reached; then beta1d fallback.
Historical branch fingerprint: 13% of Willamette regression cells and 13-18% of Northern Oregon regression functions still violated slope bounds after repair attempts.
1994 Regression Fingerprint Board — Northern Oregon
Annual
mean r² 0.70
normalized slope 1.2 km⁻¹
bias 4.5%
MAE 16%
mean r² 0.70
normalized slope 1.2 km⁻¹
bias 4.5%
MAE 16%
Winter tendency
normalized slopes ~1.2-1.3 km⁻¹
r² ~0.61-0.68
normalized slopes ~1.2-1.3 km⁻¹
r² ~0.61-0.68
Summer tendency
normalized slopes ~1.0-1.1 km⁻¹
r² as low as 0.55
MAE up to 27%
normalized slopes ~1.0-1.1 km⁻¹
r² as low as 0.55
MAE up to 27%
Use this as a coefficient ecology template: reproduce the same vector by month and Pennsylvania terrain class instead of chasing one statewide slope.
Lineage Board — post-processing changes
1994 GRADIENT
B1MAXG + MINSLP
increase lower-P cell only
→
B1MAXG + MINSLP
increase lower-P cell only
2008 inter-cell
upper/lower neighbor gradient bounds
adjust both cells equally
+
upper/lower neighbor gradient bounds
adjust both cells equally
2008 adaptive filter
8 km
exponent 0 → 4 by field complexity
8 km
exponent 0 → 4 by field complexity
2003 Board — subsystem ablation is a fingerprint, not just a score contest
Full PRISM precipitation
r² 0.88
b1 0.84
bias 0.5%
MAE 10.8%
RMSE 13.6%
PSE 17%
E 0.85
d 0.96
r² 0.88
b1 0.84
bias 0.5%
MAE 10.8%
RMSE 13.6%
PSE 17%
E 0.85
d 0.96
IDW-like ablation
r² 0.70
b1 0.57
bias 7.1%
MAE 16.2%
RMSE 21.9%
PSE 57%
E 0.68
d 0.88
r² 0.70
b1 0.57
bias 7.1%
MAE 16.2%
RMSE 21.9%
PSE 57%
E 0.68
d 0.88
Forensic lesson: the whole coefficient vector moves when physiographic guidance is removed. Reconstruct hidden state by matching the vector, not one final MAE.
2003 Board — Puerto Rico precipitation guidance branch
unfiltered 15-sec DEM
→
straight-line moisture trajectories
NNE + NE
→
NNE + NE
PI path + terrain penalties
+
coastal CI
→
PI-CI similarity grid
→
station coastal/moisture weight
This application explicitly preferred trajectory guidance over topographic facets for precipitation because of complex terrain and sparse stations.
2003 Board — station metadata can change geometry before PRISM begins
COOP coordinate
precision ~60 arcsec
→
precision ~60 arcsec
search local 60-sec window
→
best DEM-elevation match
→
reassigned station location
→
distance / elevation / regime weights
2003 Board — same MAE can hide the wrong mechanism
July Tmax PRISM
MAE 0.53 C
PSE 12%
b1 0.90
b0 2.97
MAE 0.53 C
PSE 12%
b1 0.90
b0 2.97
July Tmax HYPS
MAE 0.56 C
PSE 34%
b1 0.82
b0 5.56
MAE 0.56 C
PSE 34%
b1 0.82
b0 5.56
The scalar errors look nearly tied. The structural coefficients do not. This is the visual reason our Pennsylvania ladder will retain r², b0, b1, bias, MAE, RMSE, PSE, E, and d together.
2007 Board — match the predictor scale to the station-influence scale
50-m terrain
→
Gaussian/Barnes removes <4-km terrain
→
~4-km precipitation predictor scale
~4-km minimum radius
→
all stations inside plateau get same distance weight
The later 2008 CONUS branch repeats the same architecture at ~7 km. Predictor resolution and station influence are coupled design choices.
Temporal Lineage Board — crude shift becomes event-informed redistribution
2007
0800 COOP total
2/3 previous day + 1/3 current
→
0800 COOP total
2/3 previous day + 1/3 current
wet-day artifact
351433: 183 days >=1 mm
→
351433: 183 days >=1 mm
whole-shift test
157 days >=1 mm
→
157 days >=1 mm
2021
event total redistributed by on-time-grid daily fractions
event total redistributed by on-time-grid daily fractions
QC Board — the station value can change before downstream use
raw observation O
→
target-withheld PRISM prediction P
→
R=P-O
S=regression uncertainty
→
S=regression uncertainty
localized historical distribution
→
CP
CP <=10
prediction
prediction
10 < CP < 30
linear blend
linear blend
CP >=30
observation
observation
The same CP also reweights the observation in the next QC iteration, so confidence changes the model that will generate the next confidence.
QC Feedback Board — recursive confidence
CP
→
station regression weight
→
new PRISM prediction
→
R, S, historical p-values
→
new CP
↺
Gap: 2005 says R and S are combined into a deletion-scenario score, but no complete score equation is printed.
QC State Board — residual confidence changes with context
2004 robust sigma
max(s_r, S, Sbar, 1 C)
max(s_r, S, Sbar, 1 C)
2005 robust sigma
max(s_r, S, Sbar, 2 C)
max(s_r, S, Sbar, 2 C)
time-mismatch state
max(s_r, S, Sbar, 2 C, T_s)
max(s_r, S, Sbar, 2 C, T_s)
flatliner state
V=log10(T_o/T_s)
CP=min(RP,VP) for ambiguous 5-9 day persistence
V=log10(T_o/T_s)
CP=min(RP,VP) for ambiguous 5-9 day persistence
2007 Daily Precipitation Fingerprint — absolute and relative error must travel together
January
MAE 2.05 mm
18.62%
MAE 2.05 mm
18.62%
March
MAE 3.47 mm
32.83%
MAE 3.47 mm
32.83%
July
MAE 0.02 mm
156.82%
MAE 0.02 mm
156.82%
Annual
MAE 1.51 mm
29.30%
MAE 1.51 mm
29.30%
Dry-season relative errors can look apocalyptic while absolute error is tiny. The tree keeps both metrics attached to the same fingerprint piece.