A source-first map of every explicit equation found in the supplied 12-PDF PRISM packet, plus fitted regressions, numeric parameters, deterministic prose algorithms, validation statistics, and documented gaps. Paper provenance comes first; cross-paper dependencies come second.
Start here to see which paper contributes which part of the method. Formula/regression counts include source-direct equations and fitted regressions; the larger indexed-item count also includes parameters, deterministic rules, validation statistics, experiments, and documented gaps.
The dependency map below separates the classical climatological engine from modern daily-precipitation operations and downstream PRISM-ELM. Click a box to jump to the relevant ledger entry.
Station observations + target predictor → local linear regression
Distance/physiography/clustering decide who influences a target cell
DEM filtering and effective-terrain logic decide which terrain wavelengths matter
Residuals, probabilistic confidence, observer-bias tests, range/radar/spatial checks
Cross-validation and regression prediction intervals
Short-record station means adjusted to climatological period
Observation-time alignment + daily/monthly reconciliation
Climatology and radar become predictor grids for local PRISM regressions
Local terrain position modifies temperature interpolation and coupling
PRISM climate becomes an input to a separate environmental suitability model
Operational methods / CAI precursor
Existing 1961–1990 mean monthly PRISM grids of Tmin, Tmax, precipitation and dew point are used as predictor grids to interpolate recent monthly observations.
R = P − OPRISM predicts each station with that station withheld; large prediction-observation discrepancies identify suspect observations.
Recent months have fewer finalized station observations; predictor-grid use preserves physiographic detail when station density is sparse.
Core QC methods
R = P − ODifference between PRISM leave-one-out prediction and station observation.
CP = RPOverall observation confidence probability is set to the residual probability in this implementation.
d_R = min(|R − R̄|, |R − 0|)A perfect daily residual of zero should not be penalized because the long-term residual mean is biased. The displayed algebra is a faithful restatement of the prose rule, not a numbered printed formula.
σ* = max(s_r, S, S̄, 1 °C)Replace an unrealistically narrow residual distribution with the largest of residual spread, current regression uncertainty, average regression uncertainty, or 1 °C.
Summary distributions for O, P, R and S use a 30-day moving window centered on the target day inside a 5-year moving window centered on the target year.
For each target station-day, predict with the target withheld; rerun while deleting nearby observations first singly then in pairs; accept the prediction that most closely matches O.
OP, PP, RP, SP = 100 × two-tailed t-test p-valueDaily O, P, R and S are compared with their localized long-term distributions; p-values are expressed as percentages.
Lower-CP observations receive less weight in subsequent PRISM predictions and summary statistics. Iterate until CP changes fall below an equilibrium threshold.
A 1 °C allowance is subtracted from daily-value departures before probability testing to avoid overconfidence beyond observation precision.
Core QC methods / PSQC revision
R = P − OPRISM prediction minus observation.
V = log10(T_o / T_s)Compares a station’s short-term variability with that of surrounding stations; used to detect potential flatliners.
VP = 100 × two-tailed p-value of VV is compared with its localized long-term distribution using the same probabilistic framework as residuals.
CP = min(RP, VP)For potential flatliners, final confidence is limited by whichever is less convincing: spatial residual consistency or temporal variability.
CP = RPOutside special flatliner handling, residual probability is the confidence probability.
d_R = min(|R − R̄|, |R|)Use the smaller departure from the long-term residual mean or from perfect prediction zero.
σ* = max(s_r, S, S̄, 2 °C)2005 raises the practical uncertainty floor from the earlier 1 °C to 2 °C.
σ* = max(s_r, S, S̄, 2 °C, T_s)When observation times differ, surrounding-station temporal variability T_s is also allowed to broaden the uncertainty used for CP.
λ = (CP − CPMIN)/(CPMAX − CPMIN); FINAL = λO + (1−λ)PBetween user-set CP thresholds, output is a linear blend. This algebra is an explicit restatement of the prose description.
2005 uses a 31-day moving window centered on the target day and a 5-year moving window centered on the target year.
score = R + S (as described)Prediction/deletion scenarios are evaluated using the residual and PRISM regression SD; the scenario with the lowest score is retained. The exact algebra/sign convention is described tersely, so this entry should not be treated as a universally specified production formula.
probability = 100 × two-tailed t-test p-valueFive probability statistics characterize unusualness relative to local time-of-year distributions.
Reweight station observations by CP and rerun until current and previous CP values are sufficiently similar.
Evaluation / interpolation framework
Bias = mean(P − O)Bias is the mean signed prediction-observation difference; positive indicates overprediction and negative underprediction.
MAE = mean(|P − O|)Overall unsigned prediction error.
Remove one station, estimate it, replace it, and repeat for every station; then calculate error statistics.
Cross-validation errors should only be compared across methods when interpolation parameters/data are identical; otherwise CV can reward smoothing and mislead.
Direct elevation effects on precipitation do not appear to increase further below about 5–10 km spatial scales.
Cold-air drainage/inversions are typically important at scales below roughly 50 km, although polar regional inversions can be much broader.
Compares full PRISM vs IDW, with all stations vs stations below 1500 m; a stratified holdout of high-elevation stations demonstrates how jackknife CV can conceal extrapolation failure.
Precipitation observation QC / bias diagnostics
R_L = C₆₋₁₀ / C₁₋₅Compares counts of 0.06–0.10-in precipitation observations with counts of 0.01–0.05-in observations.
R = 100 × (P − O)Difference between gamma-predicted and observed frequency in a precipitation bin, scaled by 100.
R̄₁ = (ΣR₁ᵢ)/n₁ ; R̄₅ = (ΣR₅ᵢ)/n₅Average residuals for bins associated with 0.01-in and 0.05-in divisibility patterns.
t = (R̄₁ − R̄₅) / [s²(n₁⁻¹ + n₅⁻¹)]^0.5Tests whether mean residuals differ between frequency-bin groups; s² is pooled variance.
Each of 26 fourteen-day periods in a year must contain at least 12 nonmissing days, and at least 26 years in 1971–2000 must be complete.
Gamma frequency predictions are not made below 0.03 in or above 1 in because of instability/low frequency.
Wet days use at least 0.01 in precipitation.
Daily PRISM application / method extension
Y = β₁X + β₀Moving-window local linear climate-elevation model evaluated at each grid cell.
W = f(W_d, W_z, W_c, W_l, W_t)USSW subset of PRISM weighting functions.
W_t = 1, Δt ≤ Δt_n; W_t = 0, Δt > Δt_x; W_t = 1/(Δt)^z, Δt_n < Δt < Δt_xWeights stations by similarity of local topographic position (valley/midslope/ridge) to the target.
P_s = −0.1667 T_m(pixel) + 0.6667, 0 ≤ P_s ≤ 1Linear snow/rain partition based on daily mean temperature.
T_d = T_t {1 − exp[0.6(1 − B/T_t)/(B − 0.4)]}Relates total horizontal transmittance to diffuse transmittance.
T_d = T_t [1 − exp(1 − 1/T_t)]Eq. 5 with B = 1.0.
M = 3.8253 R_e(UPLMET)^−0.8896Power-law relation for the slope linking site-pair solar-radiation differences to Tmax differences.
C = 0.0174 R_t(UPLMET) + 0.9827Linear correction factor based on observed daily total solar radiation.
T_xr(pixel) = T_x(pixel) + M C [R_t(pixel) − R_e(pixel)]Adjusts interpolated Tmax for local solar-radiation differences.
Find lowest elevation within 15 km, low-pass that base-terrain field to remove features <15 km, then subtract from the original 800-m DEM.
Precipitation DEM was low-pass filtered to remove features <4 km; minimum radius of influence set to about 90 grid cells (~4 km), giving all stations inside that radius equal distance weight.
Two-stream model constants used in this application.
Monthly and annual leave-one-out errors were tabulated for Tmax, Tmin, and precipitation. Annual precipitation bias = 0.20 mm; MAE = 1.51 mm; percent bias = 3.97%; percent MAE = 29.30%.
Core PRISM methods
Y = β₁X + β₀Unique local linear climate-elevation regression for each target grid cell.
W = W_c [F_d W_d² + F_z W_z²]^1/2 W_p W_f W_l W_t W_eCombines cluster, distance, elevation, coastal proximity, facet, vertical-layer, topographic-position, and effective-terrain weights.
W_d = 1 for d − r_m ≤ 0; W_d = 1/(d − r_m)^a for d − r_m > 0Creates a flat distance-weight plateau inside a minimum radius, then inverse-distance decay outside.
x̄ = [Σ(x_i / d_i^a)] / [Σ(1 / d_i^a)]Averages surrounding cells within 8 km with an exponent that varies with field complexity.
a = a_max for Δx̄ ≥ Δx_max; a = a_max(Δx̄/Δx_max) for Δx̄ < Δx_maxUses little smoothing in complex/high-gradient areas and more smoothing in low-gradient areas.
s²{Y_h(new)} = s²{Ŷ_h} + MSE = MSE[1 + 1/(Σw_i) + (X_h − X̄)² / Σ(w_i X_i − X̄)²]Regression prediction variance for a new value at elevation X_h, including model scatter and uncertainty in the expected value.
Ŷ_h ± t_(1−α/2,df) s{Ŷ_h}Two-sided prediction interval around local PRISM prediction.
X̄'_t = X̄_te (X̄_a / X̄_ae)Ratio-adjust short-term target-station mean to the target climatological period using an anchor station.
X̄'_t = X̄_te + (X̄_a − X̄_ae)Difference-adjust short-term Tmax/Tmin target mean using anchor station.
W_c = 1 if S_c = 0; W_c = 1/S_c if S_c > 0Reduces the combined influence of a tight station cluster toward the influence of a single station.
S_c = Σ(h_i v_i), i=1..nCombines horizontal and vertical cluster factors over stations in the regression dataset.
h_i = Σ_j [0 if d_ij > 0.2r; (0.2r − d_ij)/(0.2r) if 0 ≤ d_ij ≤ 0.2r]Clustering influence tapers linearly to zero at 20% of the radius of influence.
v_i = Σ_j [0 if s_ij > p; (p − s_ij)/p if 0 ≤ s_ij ≤ p]Stations close in effective elevation count as more strongly clustered.
s_ij = 0 if |e_i − e_j| < p; s_ij = |e_i − e_j| − p if |e_i − e_j| > pTreats elevation differences within precision p as the same elevation.
I_3c = 1 if h_c ≥ h_3; (h_c−h_2)/(h_3−h_2) if h_2 < h_c < h_3; 0 if h_c ≤ h_2Scales terrain influence from 2D to 3D behavior based on target-cell effective terrain height.
I_3a = 1 if h_a ≥ h_3; (h_a−h_2)/(h_3−h_2) if h_2 < h_a < h_3; 0 if h_a ≤ h_2Same ramp applied to nearby-area effective terrain.
h_a = (Σ w_i h_i) / nDistance-weighted terrain-height aggregation as printed in the paper. Note the denominator is n, not Σw_i.
w_i = 1/d_iInverse-distance weight used in the areal effective-terrain height calculation.
I_3d = max(I_3c, I_3a)Uses the stronger of local target-cell and surrounding-area terrain evidence.
terrain_parameter* = I_3d × terrain_parameter (conceptual linear scaling)As I_3d approaches zero, terrain-related slope parameters (β₁m, β₁x, β₁d) and elevation/facet/layer exponents (b,c,y) are linearly reduced toward zero. The paper states the linear scaling but does not print one generic equation.
Daily-from-hourly requires at least 18/24 nonmissing hourly values; monthly requires 85% nonmissing daily values; a 1971–2000 station-month is long-term with at least 23/30 years.
Precipitation extreme threshold is 115% of state 24-h record; Tmax is 3 °C above state monthly record max; Tmin is 3 °C below state monthly record min.
30-arcsec (~800-m) climate grid; precipitation elevation field suppresses terrain features up to roughly 3.75 arcmin (~7 km); inter-cell filter uses 8-km neighborhood.
Radius expands until a minimum number of stations is available.
W_z, W_p, W_f, W_l, W_t, W_eEq. (2) names these components, but this 12-PDF archive does not contain the complete published formulas for elevation, coastal, facet, and vertical-layer weights. W_t is printed in 2007 JAMC; W_c and effective-terrain machinery are printed in 2008. The omitted formulas are referred back to earlier Daly (2002)/Daly et al. (2002) sources.
Terrain / cold-air-decoupling extension
Slope = 0.003303 + 0.000124(elevation) + 0.005934(topoindex)Multiple linear regression maps how strongly December Tmax responds to the anti-cyclonic minus cyclonic day index.
ΔTmax per +1 A–C day: HILL = +0.36 °C; VALLEY = +0.10 °CExposed HILL is much more coupled to synoptic circulation than cold-pooled VALLEY.
A highly localized topographic index from a 50-m DEM was tested at multiple scales; a 150-m diameter explained the most variance for the December Tmax coupling slope.
R²(elevation, topoindex) = 0.21Elevation and topographic index are related but not strongly collinear.
CAI / extreme-temperature application
local PH statistic ~ linear function of coldest-month Tmin predictorPRISM uses climatologically aided interpolation: the existing gridded coldest-month minimum temperature field serves as predictor for local weighted regressions of annual extreme minimum temperature. The paper describes the regression but does not print a new numbered equation.
Standard deviation of the 1976–2005 hardiness statistic was interpolated using CAI with mean coldest-month minimum temperature because it was more strongly correlated and yielded lower interpolation error than elevation.
Short-record station statistics are adjusted using the Daly et al. (2008) Appendix A procedure.
Single-deletion with replacement; bias and MAE calculated after each station has been withheld once.
PRISM regression prediction intervals are used as a model-based uncertainty measure, with standard weighted-linear-regression methods referenced.
New map depicts 1976–2005 mean annual extreme minimum temperature in half zones.
Downstream PRISM-ELM application
TAW = D_root × AWCTotal available water equals rooting depth times available water capacity.
RAW = p × TAWWater available before stress response.
K_s(t) = [TAW − D_r(t)] / [TAW − RAW]Fractional water-stress coefficient at semi-monthly time step.
D_r(t) = D_r(t−1) + [ET_a(t−1) − P_(t−1)]Time-step water-balance update.
ET_a(t−1) = ET₀(t−1)K_s(t−1)K_c if crop on; K_s(t−1)E_s if crop offDifferent evapotranspiration formulations depending on potential growth period.
C_t = (MaxT − T_t)/(MaxT − OptT); C_t = max(C_t, 0)Normalizes current mean daily temperature between optimum and maximum.
T_r(t) = min[1, C_t^F1 × exp((F1/F2)(Mag − C_t^F2))]Flexible response curve controlled by optimum/maximum temperature and shape parameters.
S_t = K_s(t) × T_r(t)Joint water × temperature suitability for each semi-monthly step.
S_w = mean(highest consecutive M_avg monthly S_m values within M_beg…M_end)The paper specifies this as prose rather than a numbered equation.
If x < Tmin_min or x > Tmin_max: S_c = 0; else S_c = Tmin_mag × exp[Tmin_w1 × ((x−Tmin_opt)/Tmin_w2)^2], 0≤S_c≤100Two-tailed winter cold suitability curve.
S_h = c₀ + c₁x + c₂x² + c₃x³Third-order polynomial fit through user-defined temperature points.
If x < pH_min or x > pH_max: S_p = 0; else S_p = pH_mag × exp[pH_w1 × ((x−pH_opt)/pH_w2)^2], 0≤S_p≤100Two-tailed pH suitability curve.
S_s = c₀ + c₁x + c₂x² + c₃x³Third-order polynomial salinity response.
ESI = min(S_w, S_c, S_h, S_p, S_s, S_d)Liebig-style limiting-factor rule: the least suitable dimension sets final suitability.
y = 0.0501xLeast-squares regression forced through zero between county ESI and reported yield.
y = 0.0508xLeast-squares regression forced through zero between county ESI and reported yield.
y = 0.0505xLeast-squares regression forced through zero between county ESI and reported yield.
y = 0.1057xLeast-squares regression forced through zero between county ESI and reported yield.
y = 0.1039xLeast-squares regression forced through zero between county ESI and reported yield.
y = 0.1048xLeast-squares regression forced through zero between county ESI and reported yield.
These 13 equations are not PRISM interpolation internals. They consume PRISM climate and soil inputs to model crop suitability. They are retained because the user requested every equation in the corpus, but are visually separated from core PRISM.
Validation / terrain-scale experiment
Y = bX + aSeasonal/annual precipitation modeled as a linear function of 7000-m filtered DEM elevation.
Y = 2.63X − 615 mm (reported slope/intercept form)Dense-gauge annual regression using 69 stations and 7000-m filtered DEM.
Y = 1.06X − 259 mmSummer relationship.
Y = 1.58X − 355 mmWinter relationship.
A 10-m DEM was averaged over circular neighborhoods from 100 to 10,000 m; explained variance plateaued near a 7000-m effective wavelength.
Residuals from the P–E regression were interpolated with inverse-distance weighting.
PRISM 70% prediction interval (PI70) from the 2008 regression uncertainty formulation is evaluated against dense independent-like ground truth.
Modern daily precipitation operations
Daily value fails if it exceeds 115% of the published state 24-h record; monthly value fails if it exceeds 115% of the world-record monthly total (9300 mm).
For subdaily stations, >6 missing hours causes the day to fail. If >2 days are missing/invalid in a month, all days in that month fail unless manually excepted.
Day is defined as 1200–1200 UTC. Once-daily observations must fall within ±4 h of 1200 UTC to be on-time.
P*_d = E × G_d / Σ_event G_dInitial grids from on-time stations define relative daily fractions within an event; an off-time or multiday station total E is redistributed according to those fractions while preserving its event total. The formula shown is a direct algebraic restatement of the prose algorithm, not printed in the paper.
East of 105°W, ST4 is compared with the gauge. A false-zero/spike test uses an ~8-km neighborhood and substantial precipitation threshold of 2.5 mm when gauge and radar disagree on zero vs nonzero.
|P − O| > 1.59 × σ_est → candidate failureMonthly precipitation spatial QC uses PRISM leave-one-out estimates and an empirical standard-deviation threshold derived from mean-monthly precipitation relationships.
σ_est = a + b × mean_monthly_precip (family; coefficients not published here)Thirty-year COOP data are used to derive linear relationships between mean monthly precipitation and SD, from which expected variability is estimated for QC.
Remove a station, predict at its location, replace the station, compare observed and predicted, remove failures, and repeat over 3–5 cycles. Model-confidence checks use station density and regression scatter.
Y_daily = local_linear(X_monthly_normal) [conceptual]At each grid cell, station daily/monthly precipitation is regressed locally against PRISM monthly long-term normal values, with physiographic station weighting. The paper does not print coefficients/formula beyond describing a local linear regression.
Y_daily = local_linear(X_radar) [conceptual]24-h ST4 radar–gauge analysis is used as predictor east of the Rockies; ST4 is downscaled from 4 km to 800 m with a modified Barnes Gaussian filter.
Hybrid = blend(CAI, RAI; w_RAI), 0 ≤ w_RAI ≤ 1Pixelwise besting compares local regression correlations from CAI and an independent ST2un-based RAI analysis; a 0–1 RAI weighting-factor grid is then applied when averaging the original ST4 RAI analysis with CAI. The exact correlation-to-weight transform is not published.
D'_d = D_d × M / Σ_d D_dIn the western U.S., all daily grid-cell values are multiplied by the same ratio so the monthly sum equals the separately modeled monthly total. This formula is an algebraic restatement of the prose rule.
M_final = Σ_d D_dWhere monthly interpolation smears precipitation into dry cells, especially pre-2002, the monthly total is adjusted to the sum of daily analyses.
Final daily/monthly grid-cell values below the measurable threshold are set to zero.
If monthly precipitation is ≥0.254 mm but the sum of daily values is nonzero yet below measurable, precipitation is added to days already having nonzero precipitation until the monthly value is reached. If all dailies are exactly zero, monthly is set to zero instead.
SNOTEL precipitation precision can be coarser than standard daily precipitation precision, creating timing issues at low amounts.
Each day receives eight releases: first within ~24 h, second after 5 days, then monthly revisions for six more months; final around six months elapsed.
Native PRISM grids are 30 arc-s (~800 m). AN daily/monthly grids are filtered to 2.5 arc-min (~4 km) for public portal distribution in the 2021 workflow.
LT monthly dataset uses networks with stations having roughly multi-decadal records.
w_RAI = f(r_CAI, r_RAI) — exact f unknownThe paper states that local regression correlation coefficients are compared to create a 0–1 RAI factor, but does not disclose the transform. Do not treat a simple normalized-correlation formula as PRISM unless independently sourced.
The paper says MRMS was being archived since late 2014 and considered as a future replacement for ST4. This corpus cannot establish later operational changes.
Numbers here are tied to the specific historical/application source that stated them. A 2008 setting is not silently promoted to a 2026 production constant.
| Paper | Parameter | Value | Unit | Context | PDF p. |
|---|---|---|---|---|---|
| P2004A | Public monthly grid resolution | 2.5 | arc-min (~4 km) | Recent-month climate maps | 1 |
| P2004A | Coarse delivery grid | 0.5 | degree | Client delivery | 2 |
| P2004B | PSQC spatial grid resolution | 0.8 | km | Climatological predictor/QC development | 3 |
| P2004B | Summary window | 30 days × 5 years | N=150 | Localized long-term distributions | 4 |
| P2004B | Robust sigma floor | 1 | °C | Residual probability | 5 |
| P2004B | Precision allowance | 1 | °C | Probability-departure calculation | 5 |
| P2005 | Summary window | 31 days × 5 years | N=155 | Localized distributions | 5 |
| P2005 | Temporal variability window | 5 | days | T_o and T_s running SD | 6 |
| P2005 | Potential flatliner length | 5–9 | consecutive observations | Use CP=min(RP,VP) | 6 |
| P2005 | Robust sigma floor | 2 | °C | Residual probability | 6 |
| P2005 | CPMIN | 10 | percent | Prediction gets full weight | 5 |
| P2005 | CPMAX | 30 | percent | Observation gets full weight | 5 |
| P2005 | Typical CP iterations | 1–5 | iterations | Convergence | 11 |
| P2006 | Orographic precipitation lower scale | 5–10 | km | Little additional direct elevation effect below this scale | 4 |
| P2006 | Cold-air drainage typical scale | <50 | km | Terrain forcing | 4 |
| P2006 | High-elevation experiment cutoff | 1500 | m | Scenario 3/4 | 10 |
| P2006 | Stratified high-elevation holdout | 9 | stations | Validation experiment | 10 |
| P2007B | Within-year completeness | 12 of 14 | days | Each of 26 periods | 3 |
| P2007B | Period completeness | 26 of 30 | years | 1971–2000 | 3 |
| P2007B | Underreporting threshold R_L | 0.60 | ratio | Final bias test | 4 |
| P2007B | 5/10 t-test alpha | 0.01 | probability | Final threshold | 4 |
| P2007B | Gamma lower prediction bound | 0.03 | in (0.76 mm) | Frequency fit | 3 |
| P2007B | Gamma upper prediction bound | 1.00 | in (25.4 mm) | Frequency fit | 3 |
| P2007B | Wet-day threshold | 0.01 | in (~0.25 mm) | Frequency statistics | 6 |
| P2007J | Topographic-index radius | 15 | km | Local base terrain | 6 |
| P2007J | Topographic Δt_n | 100 | m | Full W_t | 6 |
| P2007J | Topographic Δt_x | 500 | m | Zero W_t | 6 |
| P2007J | Topographic exponent z | 1.0 | dimensionless | W_t middle branch | 6 |
| P2007J | Precipitation terrain/min radius | ~4 | km | Generalized precip field | 8 |
| P2007J | Snow endpoint | −2.5 | °C | Nearly always snow | 8 |
| P2007J | Rain endpoint | 4 | °C | Nearly always rain | 8 |
| P2007J | 50% phase threshold | 1 | °C | Eq. 4 | 8 |
| P2007J | Single-scattering albedo | 0.8 | dimensionless | Solar model | 8 |
| P2007J | Scattering asymmetry | 0.6 | dimensionless | Solar model | 8 |
| P2007J | Surface albedo | 0.15 | dimensionless | Solar model | 8 |
| P2007J | Optical depth | 0.4 | dimensionless | Solar model | 9 |
| P2007J | Bristow–Campbell B | 1.0 | dimensionless | Eq. 5→6 | 10 |
| P2008 | Native grid | 30 | arc-sec (~800 m) | CONUS climatology | 1 |
| P2008 | Daily-from-hourly minimum | 18 of 24 | hours | Completeness | 6 |
| P2008 | Monthly daily-data completeness | 85 | percent | Monthly aggregation | 6 |
| P2008 | Long-term POR criterion | 23 of 30 | years | 1971–2000 | 6 |
| P2008 | Precipitation extreme allowance | 115 | percent of state 24-h record | Range QC | 6 |
| P2008 | Temperature record allowance | ±3 | °C | Range QC | 6 |
| P2008 | Distance exponent a | 2 | dimensionless | Eq. 3 | 8 |
| P2008 | Precipitation r_m | ~7 | km | Eq. 3 | 8 |
| P2008 | Temperature r_m | ~10 | km | Eq. 3 | 8 |
| P2008 | Precipitation terrain smoothing scale | ~7 | km | DEM filtering | 3 |
| P2008 | Inter-cell filter radius | 8 | km | Eq. 4 | 13 |
| P2008 | Filter a_max | 4 | dimensionless | Eq. 5 | 14 |
| P2008 | Filter Δx_max | 4 | percent of center-cell value | Eq. 5 | 14 |
| P2008 | PI confidence level | 70 | percent | Eq. 7 | 17 |
| P2008 | Minimum stations temperature | 15 | stations | Regression search | 17 |
| P2008 | Minimum stations precipitation | 40 | stations | Regression search | 17 |
| P2008 | Cluster distance threshold | 0.2r | radius fraction | Eq. B3 | 32 |
| P2008 | Typical cluster horizontal scale | 6–10 | km | For r=30–50 km | 32 |
| P2008 | Elevation precision p | 50 | m | Eqs. B4–B5 | 32 |
| P2008 | 2D terrain threshold h2 | ~75 | m | Eq. C1/C2 application | 13 |
| P2008 | 3D terrain threshold h3 | ~250 | m | Eq. C1/C2 application | 13 |
| P2008 | Areal effective-terrain radius | 100 | km | Eq. C3 | 33 |
| P2008 | Anchor stations used | 3 | anchors | POR adjustment | 31 |
| P2009 | Topographic-index diameter | 150 | m | Best December Tmax coupling-scale | 5 |
| P2009 | Topoindex-only explained variance | 63 | percent | December slope | 5 |
| P2009 | Combined model explained variance | 82 | percent | December slope | 6 |
| P2009 | Elevation-topoindex R² | 0.21 | R² | Predictor relation | 6 |
| P2012 | Climate normal period | 1976–2005 | years | PH statistic | 1 |
| P2012 | Half-zone width | 5 | °F (2.8 °C) | PHZM categories | 1 |
| P2017G | Default p | 0.5 | dimensionless | Readily available water | 30 |
| P2017G | Simulation time step | semi-monthly | 2 per month | Water balance | 30 |
| P2017G | Spin-up | 1 | year | Water stores equilibrate | 31 |
| P2017G | Typical M_avg | 3 | months | Maximum suitability window | 32 |
| P2017I | Gauge network | 69 | stations | 1951–1958 dense Coweeta network | 1 |
| P2017I | Selected terrain wavelength | 7000 | m | P–E regression predictor | 3 |
| P2017I | Residual IDW neighbors | 12 | stations | Residual interpolation | 4 |
| P2017I | Residual IDW exponent | 1 | dimensionless | Residual interpolation | 4 |
| P2021 | Daily extreme threshold | 115 | percent of state 24-h record | Single-station QC | 4 |
| P2021 | Monthly extreme threshold | 115% × 9300 | mm | World-record monthly QC | 4 |
| P2021 | Subdaily missing limit | >6 | hours/day | Fail day | 4 |
| P2021 | Monthly missing limit | >2 | days | Fail month | 4 |
| P2021 | Standard day | 1200–1200 | UTC | Temporal alignment | 4 |
| P2021 | On-time tolerance | ±4 | hours | Once-daily stations | 4 |
| P2021 | Radar QC longitude | east of 105°W | domain | Radar QC | 5 |
| P2021 | Radar QC neighborhood | ~8 | km | Zero/spike check | 5 |
| P2021 | Radar disagreement threshold | 2.5 | mm | Substantial precipitation | 5 |
| P2021 | Spatial QC threshold | 1.59 | standard deviations | Monthly PRISM jackknife | 6 |
| P2021 | Spatial QC cycles | 3–5 | cycles | Iterative screening | 5 |
| P2021 | ST4 resolution | ~4 | km | RAI predictor | 7 |
| P2021 | Native PRISM resolution | ~800 | m | Operating grid | 7 |
| P2021 | Measurable precipitation | 0.254 | mm | Final zero threshold | 8 |
| P2021 | SNOTEL precision | 2.54 | mm | Timing/precision issue | 8 |
| P2021 | Release count | 8 | versions/day | Operational schedule | 10 |
| P2021 | Second release lag | 5 | days | Operational schedule | 10 |
| P2021 | Final release lag | ~6 | months | Operational schedule | 10 |
| P2021 | LT station POR | ~20–30 | years | Long-term dataset criterion | 9 |
Lower-CP observations receive less weight in subsequent PRISM predictions and summary statistics. Iterate until CP changes fall below an equilibrium threshold.
Open source entryPrediction/deletion scenarios are evaluated using the residual and PRISM regression SD; the scenario with the lowest score is retained. The exact algebra/sign convention is described tersely, so this entry should not be treated as a universally specified production formula.
Open source entryReweight station observations by CP and rerun until current and previous CP values are sufficiently similar.
Open source entryEq. (2) names these components, but this 12-PDF archive does not contain the complete published formulas for elevation, coastal, facet, and vertical-layer weights. W_t is printed in 2007 JAMC; W_c and effective-terrain machinery are printed in 2008. The omitted formulas are referred back to earlier Daly (2002)/Daly et al. (2002) sources.
Open source entryThese 13 equations are not PRISM interpolation internals. They consume PRISM climate and soil inputs to model crop suitability. They are retained because the user requested every equation in the corpus, but are visually separated from core PRISM.
Open source entryThe paper states that local regression correlation coefficients are compared to create a 0–1 RAI factor, but does not disclose the transform. Do not treat a simple normalized-correlation formula as PRISM unless independently sourced.
Open source entryThe paper says MRMS was being archived since late 2014 and considered as a future replacement for ST4. This corpus cannot establish later operational changes.
Open source entry