{
  "title": "CALMET saved vertical-coordinate interpretation and bounded reconstruction",
  "createdUTC": "2026-09-11T15:52:07.794299+00:00",
  "publicReport": "woodfibre-vertical-coordinate-check.md",
  "methodsArchive": "woodfibre-vertical-coordinate-methods.zip",
  "interpretation": "All converted values are model-implied estimates under explicitly declared collocation approximations, not independently validated physical vertical winds.",
  "reportSha256": "21223ea6cd78a4c64529e58acb379ad747df2b846e3e6054c0b15799cd6d8766",
  "protocol": {
    "createdUTC": "2026-09-11T15:40:38.298167+00:00",
    "declarationTiming": "Frozen after read-only source/manual audit and before opening wind/terrain arrays or computing any new coordinate-converted values. Prior published W excursions and prior reconstruction results are known. Parent authorized this bounded reconstruction following exact source/array convention message.",
    "purpose": "Interpret the saved terrain-coordinate W using explicitly separated discrete collocation choices; this is model arithmetic and coordinate interpretation, not physical meteorological validation or transport approval. No model runs/tuning/site changes.",
    "inputs": {
      "work/calmet65-local/build/native-650-150223/calmet.for": "fc7fda7cb7e7932f67eb0ce1fb94f1d81a2084063a1dbf797b3270b460b7ee6f",
      "work/calmet65-local/source/original/CALMET_v6.5.0_L150223/CALMET.FOR": "fc7fda7cb7e7932f67eb0ce1fb94f1d81a2084063a1dbf797b3270b460b7ee6f",
      "work/calmet65-local/build/native-650-150223/build-manifest.json": "24c61fceca63ac055e3e423ce6113fa9e34ad51c8f65fadb08aba19e042b444b",
      "work/buffered-wind-2023/vertical-followup/source-check.json": "45e90ca99d8095950b35131381050175af5ec6a3a375c83f0167c37b399b62d0",
      "work/buffered-wind-2023/vertical-followup/results.json": "84e05b1d4cb35a9191f7fddedbe06af27550210790a23eeeffb6a9e4e4d61668",
      "work/calmet-observation-check-2023/source-review.json": "7c3a37556429457043f2b3e2af130b652e0474d8940c09ff36ec790e32a5412b",
      "work/calmet-vertical-interpretation-2023/private-reference/CALMET_UsersGuide_V5.pdf": "45f98ec385d2ece13cfa7f500d605d58ccb62a397308e6dddd1e0176302867af",
      "work/bc-wrf-access/pilot/format-review/private-reference/CALPUFF_Version6_UserInstructions.pdf": "953b4cb885d67480ad54c8c0d897df5166e68135bb3079c684bfa8c1c00750fe"
    },
    "cases": [
      {
        "id": "wrf-interpolation",
        "runDirectory": "work/buffered-wind-2023/runs/wrf-interpolation",
        "controlSha256": "be5cff439162ad3068807bb5297ff24f07b6dd0da87a7b1cbc96d5dbc1e97930",
        "outputSha256": "87fa4e6c19c1a663efe7211a47fd60bd54aff9bf3d6f38ccd62ba7d4ec59eadc",
        "controls": {
          "IWFCOD": "1",
          "IPROG": "14",
          "NOOBS": "2",
          "NSSTA": "0",
          "NUSTA": "0",
          "NOWSTA": "0",
          "IOBR": "0",
          "IKINE": "0",
          "LCALGRD": "T",
          "LSAVE": "T",
          "NSMTH": "2 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4",
          "IFRADJ": "0",
          "ISLOPE": "0",
          "PMAP": "UTM"
        }
      },
      {
        "id": "terrain-5km",
        "runDirectory": "work/buffered-wind-2023/runs/terrain-5km",
        "controlSha256": "0e614895b605fe38e7817ae0173c33571e5e38244e58497a8fe6e878c7f5330e",
        "outputSha256": "a37c6e4d1de051b0ec8a6f2633def1ee38682b9514bb20941f834c897291e2bb",
        "controls": {
          "IWFCOD": "1",
          "IPROG": "14",
          "NOOBS": "2",
          "NSSTA": "0",
          "NUSTA": "0",
          "NOWSTA": "0",
          "IOBR": "0",
          "IKINE": "0",
          "LCALGRD": "T",
          "LSAVE": "T",
          "NSMTH": "2 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4",
          "IFRADJ": "1",
          "ISLOPE": "1",
          "PMAP": "UTM"
        }
      },
      {
        "id": "terrain-10km",
        "runDirectory": "work/buffered-wind-2023/runs/terrain-10km",
        "controlSha256": "fb4b7bb338b37d0fbc9dadee911e54d4fbf28f44624d316d051afac42901af90",
        "outputSha256": "8bc1b4c5b5da07d6f95bbcb0c7fc5bda08e74670b4f727e398967bdf46b32002",
        "controls": {
          "IWFCOD": "1",
          "IPROG": "14",
          "NOOBS": "2",
          "NSSTA": "0",
          "NUSTA": "0",
          "NOWSTA": "0",
          "IOBR": "0",
          "IKINE": "0",
          "LCALGRD": "T",
          "LSAVE": "T",
          "NSMTH": "2 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4 ,  4",
          "IFRADJ": "1",
          "ISLOPE": "1",
          "PMAP": "UTM"
        }
      }
    ],
    "geometry": {
      "nx": 201,
      "ny": 201,
      "nz": 10,
      "originUTM32610M": [
        464000,
        5485600
      ],
      "dxM": 200,
      "dyM": 200,
      "facesAGLM": [
        0,
        20,
        40,
        80,
        160,
        300,
        600,
        1000,
        1500,
        2200,
        3000
      ],
      "arrayOrder": "[interval0, component U/V/W, verticalIndex0, rowSouth0, columnWest0]; Fortran x-index fastest becomes final NumPy axis. U/V k at layer midpoint; W k is output top face f[k+1].",
      "terrainRole": "Saved static ELEV (sometimes called TERRAIN by analysis code), not native WRF terrain, external DEM, slope-flow HMAX, or AGL face height. DIAGI copies ELEV to HTOPO; OUTHD serializes ELEV.",
      "terrainSlope": "strict interior hx=(h[j,i+1]-h[j,i-1])/(2dx); hy=(h[j+1,i]-h[j-1,i])/(2dy); terrain in m, dx/dy in m. Both the coordinate formula and velocities use CALMET local model axes; no added rotation.",
      "edgeTreatment": "Exclude all original expanded outermost rows/columns. TOPOF2 duplicates missing terrain neighbour with h(i,j) and keeps 2dx divisor (half ordinary one-sided derivative). Saved perimeter W additionally depends on unsaved pre-smoothing U/V ghosts. No edge substitute or broad regridding.",
      "populations": {
        "expandedStrictInterior": "rows/cols1..199 inclusive:39601cells",
        "commonOriginal": "expanded rows/cols50..150 inclusive:10201cells",
        "addedStrictInterior": "strict interior excluding commonOriginal:29400cells"
      }
    },
    "time": {
      "intervals": 24,
      "intervalStartFixedPST": "2023-06-01T00:00:00-08:00 through23:00",
      "intervalEndUTC": "2023-06-01T09:00:00Z through2023-06-02T08:00:00Z",
      "operator": "Preserve saved intervals and normalize hour+seconds. Native horizontal forcing targets end; final diagnostic includes other processing, not a guaranteed instantaneous or hourly mean velocity."
    },
    "methods": {
      "W": "saved terrain-following top-face W, all10faces; separate nine-face common cohort",
      "A": "wA[k]=W[k]+U[k]*hx+V[k]*hy. Source TOPOF2 below-layer-center convention transferred explicitly as a diagnostic approximation to final fields. All10faces; highest top face uses same explicit below-layer convention, never silently extrapolated/interpolated. TOPOF2 was disabled and final W recomputed.",
      "B": "k=0..8 only: Uf[k]=(dz[k+1]*U[k]+dz[k]*U[k+1])/(dz[k]+dz[k+1]); same Vf. wB[k]=W[k]+Uf[k]*hx+Vf[k]*hy. Linear interpolation in AGL height to face bracketed by centers. This is an analyst collocation inference, not a recovered stored CALMET face U/V.",
      "BTopFace": "undefined at3000m, because highest saved U/V center is2600m; no extrapolation.",
      "commonCohort": "W[0:9], A[0:9], B[0:9] on identical cells/times. A\u2212B measures collocation sensitivity; do not compare all10face A max to nineface B as if the same population."
    },
    "checks": [
      "Verify all input/source/output SHA256, original/build source byte identity, all three controls, 24interval records, labeled array lengths, finite values, expected face heights, date normalization, exact equality of static terrain across three cases.",
      "Recompute strict-interior diagnostic continuity from saved U/V with existing absolute5e-5m/s tolerance; this is source consistency only.",
      "Check interpolation weights0..1 and exact at arithmetic hand-selected point; verify A\u2212B equals (U\u2212Uf)hx+(V\u2212Vf)hy to floating tolerance1e-12m/s."
    ],
    "summaries": [
      "For each case/population: W and A all10faces plus W/A/B common9faces; signed min/max/mean, meanabsolute, absolute p50/p90/p95/p99/p99.9/max, historical descriptive counts abs>1,3,5m/s. Perface versions and signed/absolute extreme locations/times.",
      "Same common9face population: A\u2212B, A\u2212W, B\u2212W distributions, signed reversal counts (strict product<0), and counts of abs-conversion less/equal/greater than abs-W; these are descriptive, not acceptance thresholds.",
      "All3cases: preserve prior expanded global/common-original W extreme columns and prior perface extrema from earlier frozen results; include same persistent original-area excursion at prior selected interval. Full10face values in anchor profiles and full24interval\u00d710face profile at persistent location; B top absent.",
      "Find new absolute W/A/B extremes for each population and perface; record W,A,B and terrain slope/collocated wind values at each. Whole-population summaries prevent selected-example cancellation claims."
    ],
    "limits": [
      "Static piecewise terrain and discretized velocities do not uniquely specify continuous physical wind. Coordinate conversion is exact for smooth, collocated fields; these saved-array reconstructions require declared interpolation/slope approximations.",
      "CALMET uses a simple Z=z-h transform and incompressible continuity; no density factor or sigma/top compression is inferred. W can cancel or reinforce terrain advection. Large W alone is neither proven Earth-vertical motion nor proven harmless coordinate artifact.",
      "Model PMAP=UTM imports true-north-like native wind without UTM convergence rotation then uses projected-axis diagnostics; follow source convention consistently, retaining local Cartesian approximation. This audit does not repair that preexisting geometric approximation.",
      "No station physical vertical wind validation, no covariance/flow-resolution validation, no boundary-condition adequacy or atmospheric realism claim, no transport calculation."
    ]
  },
  "sourceEvidence": {
    "createdUTC": "2026-09-11T15:44:18.910210+00:00",
    "sourcePath": "work/calmet65-local/build/native-650-150223/calmet.for",
    "sourceSha256": "fc7fda7cb7e7932f67eb0ce1fb94f1d81a2084063a1dbf797b3270b460b7ee6f",
    "originalProviderSource": "work/calmet65-local/source/original/CALMET_v6.5.0_L150223/CALMET.FOR",
    "originalAndBuildByteIdentical": true,
    "providerArchiveUrl": "https://www.calpuff.org/calpuff/download/Mod7_Files/CALMET_v6.5.0_L150223.zip",
    "sourceLocators": [
      {
        "routine": "DIAGI",
        "oneBasedLines": "5147-5157",
        "finding": "Layer DZ is adjacent ZFACE difference; CELLZC is ZMID and CELLZB is ZFACE, with separate NZ+1 top face."
      },
      {
        "routine": "SETCOM",
        "oneBasedLines": "29764-29767",
        "finding": "ZMID is the arithmetic midpoint of adjacent face heights."
      },
      {
        "routine": "DIAGI",
        "oneBasedLines": "5220-5224",
        "finding": "Copies ELEV directly into HTOPO."
      },
      {
        "routine": "READGE",
        "oneBasedLines": "28186-28208",
        "finding": "Reads terrain and applies HTFAC only to convert height to metres."
      },
      {
        "routine": "OUTHD",
        "oneBasedLines": "12480-12486;12522-12525",
        "finding": "Writes ZFACE heights and ELEV terrain as static records."
      },
      {
        "routine": "DIAGNO",
        "oneBasedLines": "5503-5511;5550-5577",
        "finding": "IPROG14 invokes native RDMM5 for UPROG/VPROG and first-guess horizontal fields."
      },
      {
        "routine": "RDMM5",
        "oneBasedLines": "20613-20615;20973-21000;21446-21540",
        "finding": "Prognostic vertical velocity token is read into local scalar w for relevant input formats; no output W argument/array is provided. All executable whole-token w occurrences within RDMM5 are these read statements."
      },
      {
        "routine": "DIAGNO",
        "oneBasedLines": "5613-5629",
        "finding": "Initial W zero; IKINE1 alone invokes TOPOF2 and initial MINIM. Exercised IKINE0 skips both."
      },
      {
        "routine": "DIAGNO",
        "oneBasedLines": "5745-5763",
        "finding": "No observations copies processed UG/VG into U/V then goes directly to smoothing."
      },
      {
        "routine": "DIAGNO",
        "oneBasedLines": "6117-6148",
        "finding": "After SMOOTH, reset all W to zero, calculate layer divergence, integrate upward as W(k+1)=W(k)-DZ(k)DIV(k). Boundary U/V refresh occurs after divergence calculation."
      },
      {
        "routine": "DIAGNO",
        "oneBasedLines": "6153-6159;6177-6180",
        "finding": "IOBR1 would enforce terrain-coordinate zero top W then adjust U/V; exercised IOBR0 bypasses both."
      },
      {
        "routine": "DIVCEL",
        "oneBasedLines": "6246-6303",
        "finding": "Uses center-neighbor U/V derivatives and top-minus-bottom W over DZ. HTOP=1 hardcoded: no density or sigma compression Jacobian. Coordinate slopes are absent because W is the transformed coordinate flux."
      },
      {
        "routine": "TOPOF2",
        "oneBasedLines": "31999-32012",
        "finding": "Centered HTOPO gradient divided by2DX/2DY. Missing edge neighbour replaced by same central terrain value; divisor unchanged."
      },
      {
        "routine": "TOPOF2",
        "oneBasedLines": "32014-32049",
        "finding": "Creates terrain-forced Cartesian W then subtracts terrain advection. At top face K+1 uses below-layer U(K),V(K); no face interpolation. Not exercised and not a hidden output transform."
      },
      {
        "routine": "SMOOTH",
        "oneBasedLines": "30636-30679",
        "finding": "In-place U/V updates retain passed UB/VB; no refresh inside routine."
      },
      {
        "routine": "WINDBC",
        "oneBasedLines": "36404-36442",
        "finding": "UB/VB copy current perimeter normal U/V values. No W copy; earlier pre-smoothing boundary state is absent from CALMET.DAT."
      },
      {
        "routine": "OUTHR",
        "oneBasedLines": "13148-13165",
        "finding": "U/V output layer I; WFACE I is W(I+1), explicitly top face. No transform."
      },
      {
        "routine": "WRTR2D",
        "oneBasedLines": "36829-36879",
        "finding": "Serializes 2D field directly or contiguous copy, x index fastest."
      },
      {
        "routine": "RDMM5",
        "oneBasedLines": "21674-21705",
        "finding": "Only LCC/LPS branches rotate native direction; UTM uses direct components. Source convention retains an approximate local Cartesian interpretation."
      },
      {
        "routine": "RDMM5",
        "oneBasedLines": "22330-22358;22381-22386",
        "finding": "Native horizontal wind temporal interpolation targets interval-end; retained previous source audit explains final diagnostic time limits."
      }
    ],
    "manuals": [
      {
        "title": "A User\u2019s Guide for the CALMET Meteorological Model (Version5)",
        "date": "January2000",
        "role": "Explicit base coordinate theory, checked against exercised6.5source; not mislabeled as a6.5manual",
        "url": "https://calpuff.org/calpuff/download/CALMET_UsersGuide.pdf",
        "retainedPDF": "work/calmet-vertical-interpretation-2023/private-reference/CALMET_UsersGuide_V5.pdf",
        "sha256": "45f98ec385d2ece13cfa7f500d605d58ccb62a397308e6dddd1e0176302867af",
        "locators": [
          {
            "PDFPageOneBased": 23,
            "printedPage": "2-1",
            "item": "Eq2-1 Z=z-h; U/V grid-center and W vertical-face definition; local Cartesian projection assumption",
            "visualChecked": true
          },
          {
            "PDFPageOneBased": 25,
            "printedPage": "2-3",
            "item": "Eq2-2 W=w-u h_x-v h_y",
            "visualChecked": true
          },
          {
            "PDFPageOneBased": 37,
            "printedPage": "2-15",
            "item": "Eq2-27 incompressible continuity from smoothed horizontal winds",
            "visualChecked": false
          },
          {
            "PDFPageOneBased": 38,
            "printedPage": "2-16",
            "item": "Eq2-28 top correction and Eq2-30 staggered discrete divergence; text cautions unconstrained top W can be large",
            "visualChecked": true
          }
        ]
      },
      {
        "title": "CALPUFF Modeling System Version6 User Instructions",
        "date": "April2011",
        "role": "Retained V6 interface/grid and output corroboration",
        "retainedPDF": "work/bc-wrf-access/pilot/format-review/private-reference/CALPUFF_Version6_UserInstructions.pdf",
        "sha256": "953b4cb885d67480ad54c8c0d897df5166e68135bb3079c684bfa8c1c00750fe",
        "locators": [
          {
            "PDFPageOneBased": 191,
            "printedPage": "7-5",
            "item": "CALMET horizontal non-staggering; MM5 sigma grid distinction"
          },
          {
            "PDFPageOneBased": 279,
            "printedPage": "8-14",
            "item": "W at top cell face"
          },
          {
            "textLinesOneBased": "17761 onward",
            "item": "8.11.1 CALMET.DAT output specification"
          }
        ]
      }
    ],
    "mathematicalInterpretation": {
      "coordinate": "Z=z-h(x,y); time-independent terrain and local Cartesian x,y. dZ/dt=W; it is not vertical pressure velocity, density-weighted mass flux, or unit-normal speed.",
      "normalComponent": "For smooth terrain, normal velocity to a constant-Z surface is W/sqrt(1+h_x^2+h_y^2); W itself is an unnormalized normal flux / coordinate rate.",
      "continuityDerivation": "At fixed physical z: u_x|z=u_x|Z-h_x u_Z and v_y|z=v_y|Z-h_y v_Z. For w=W+u h_x+v h_y with h independent of Z, w_z=W_Z+h_x u_Z+h_y v_Z. The shear/slope terms cancel, yielding incompressible u_x|Z+v_y|Z+W_Z=0 with unit Jacobian. This explains DIVCEL, rather than adding an extra metric factor.",
      "staggeringLimit": "Continuous chain rule is exact at collocated smooth fields. Saved U/V centers and W faces require declared reconstruction. A transfers TOPOF2 below-layer convention; B linearly interpolates horizontal wind to interior bracketed faces. Neither recovers an independently stored physical w.",
      "optionalCentreEstimate": "At center c_k, an alternative declared approximation is Wcenter=(Wbottom+Wtop)/2 with missing ground W=0, followed by wcenter=Wcenter+U_k hx+V_k hy. W linear within layer follows treating computed layer divergence as constant; not a saved center W. This option is not used in the authorized numeric comparison.",
      "transportConsequence": "A terrain-height transport coordinate would use dZ/dt=W with consistent x/y and terrain interpolation. An absolute-height trajectory needs a collocated reconstructed w. Adding terrain advection then also moving terrain coordinates double-counts it; treating W alone as dz/dt drops it. Separate transport solver/model-option semantics need review before use."
    },
    "auditScope": "No model runs, tuning, site edits or vertical-observation validation. Numerical coordinate diagnostic separately frozen in protocol.json."
  },
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        "headerGeometryPassed": true,
        "continuityMaximumAbsoluteResidualMs": 5.451962348246298e-07,
        "continuityCountAbove5eMinus5Ms": 0,
        "collocationDifferenceIdentityMaxResidualMs": 2.6645352591003757e-15,
        "separatePointInterpolationCheckPassed": true,
        "terrainEqualityAcrossCasesPassed": true,
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        "terrainEqualityAcrossCasesPassed": true,
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    "allChecksPassed": true,
    "protocolSha256": "02e8819eb84fc9e475f8e28357bdf017bf3c51ea122f5c548cec39bb601494d1",
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  "independentScalarChecks": {
    "purpose": "Independent scalar extraction and alternate linear-interpolation algebra at retained prior and newly selected extrema; not full independent physical validation.",
    "allPassed": true,
    "checks": [
      {
        "case": "wrf-interpolation",
        "hourPST": 22,
        "faceAGLM": 3000.0,
        "rowSouth0": 90,
        "columnWest0": 94,
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