CAPE Estimator (simplified) mechanism

Model scope

The concept is suitable only as an explicitly approximate educational estimator. Before implementation, specify the parcel ascent algorithm, virtual-temperature and mixing-ratio equations, saturation-vapor-pressure convention and interpolation, pressure-to-height treatment, positive-buoyancy clipping, LFC/EL rules, required level inputs, and category thresholds. The current honest label is appropriate, but the missing definitions require review before the instrument can produce a uniquely verifiable CAPE or instability category.

• Standard CAPE integrates only positive buoyancy: CAPE = g·∫max(0,(Tv_parcel−Tv_env)/Tv_env) dz. The stated summation omits max(0,...), so negatively buoyant layers could incorrectly reduce CAPE.
• The parcel virtual-temperature path is unspecified: the algorithm must define dry-adiabatic lifting below the LCL and moist-adiabatic lifting above the LCL, including how the moist lapse-rate table is applied.
• Pressure-level environmental temperatures cannot be integrated in height without specified geopotential heights or a hypsometric pressure-to-height conversion using temperature and moisture.
• The handling of entrainment, condensate loading, virtual-temperature correction, LFC, and equilibrium level is unspecified. A standard CAPE calculation normally integrates from the parcel's LFC to its EL and not over arbitrary layers.
• The instability-category thresholds are not supplied, so the requested category output is not uniquely defined. Test-vector categories below use a clearly labeled provisional convention only: weak <100 J/kg, moderate 100–250 J/kg, strong 250–2000 J/kg, extreme >=2000 J/kg.
• The supplied test vectors use precomputed parcel and environmental virtual temperatures so that the stated integration can be tested independently of the missing parcel-path and saturation-vapor-pressure algorithms.

Units and conventions

• g = 9.80665 m/s^2, the standard acceleration of gravity.
• Virtual temperatures are in kelvin; temperature differences in the buoyancy ratio are therefore dimensionless.
• Layer thicknesses are converted to metres before multiplication by g.
• CAPE has units m^2/s^2, numerically equal to J/kg.
• The provisional category thresholds are not standard universal thresholds and must not be presented as authoritative without product approval.
• Saturation vapor pressures are represented in kPa in the lookup checks; if used in mixing-ratio calculations, parcel pressure must use the same pressure unit.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "layers": [
      {
        "z_bottom_m": 0,
        "z_top_m": 1000,
        "Tv_parcel_K": 301,
        "Tv_env_K": 300
      },
      {
        "z_bottom_m": 1000,
        "z_top_m": 2000,
        "Tv_parcel_K": 300,
        "Tv_env_K": 300
      }
    ],
    "height_unit": "m",
    "category_convention": "provisional: weak <100, moderate 100-250, strong 250-2000, extreme >=2000",
    "saturation_vapor_pressure_lookup": {
      "temperature_C": 0
    }
  },
  "expected_outputs": {
    "cape_J_per_kg": 32.688833,
    "instability_category": "weak",
    "saturation_vapor_pressure_kPa": 0.6113
  },
  "reference_data": {
    "standard_gravity_m_s2": 9.80665,
    "standard_gravity_source_convention": "widely tabulated standard value (CGPM standard gravity)",
    "saturation_vapor_pressure_0C_kPa": 0.6113,
    "saturation_vapor_pressure_source_convention": "widely tabulated standard value (IAPWS/CRC convention)"
  },
  "working": "Layer 1 buoyancy ratio = (301−300)/300 = 1/300. Layer 1 contribution = 9.80665 × (1/300) × (1000−0) = 32.688833 J/kg. Layer 2 ratio = (300−300)/300 = 0, so its contribution is 0. CAPE = 32.688833 + 0 = 32.688833 J/kg. This is below 100 J/kg, hence provisional category weak. The lookup fragment gives e_s(0 °C) = 0.6113 kPa exactly."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The zero-environment-virtual-temperature vector makes the required denominator vanish, so an implementation that accepts it without validation produces an undefined result. The specification also leaves positive-buoyancy clipping, height sign, and temperature-unit conventions insufficiently explicit.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json