RadiationFundamentals

{
  "reference": {
    "notes": "source_ref: GasChem.jl@8c12c048482b515fb8eb2110bf8ab4b4f4e71309:src/radiation_fundamentals.jl:367\n\nUpstream `RadiationFundamentals` is an MTK `@component` that composes the seven radiation-fundamentals components of Seinfeld & Pandis (2006) Chapter 4 (Eqs. 4.1-4.11) into one system. The upstream constructor is a pure aggregation:\n    @named photon              = PhotonEnergy()\n    @named blackbody           = BlackbodyRadiation()\n    @named wien                = WienDisplacement()\n    @named stefan_boltzmann    = StefanBoltzmann()\n    @named energy_balance      = PlanetaryEnergyBalance()\n    @named climate_sensitivity = ClimateSensitivity()\n    @named toa_forcing         = TOARadiativeForcing()\n    eqs = Equation[]            # No additional equations - all physics is in subsystems\n    return System(eqs, t; systems = [photon, blackbody, wien, stefan_boltzmann,\n                                     energy_balance, climate_sensitivity, toa_forcing], name)\n\nThere are NO connecting equations and NO coupling between the seven subsystems (`eqs = Equation[]`): the upstream model is a structural bag of seven independent components that share only the independent variable t. Each subsystem keeps its own namespace, so e.g. `photon.λ` and `blackbody.λ` are distinct parameters, and `blackbody.T`, `wien.T`, `stefan_boltzmann.T` are three independent temperatures.\n\nMigration shape — `models.RadiationFundamentals` with a `subsystems` block (ESM spec §6.2 / §4.7): the seven components are inlined as named child models under `subsystems`, in the upstream `systems = [...]` order. The top-level model carries no variables and no equations (`\"variables\": {}`, `\"equations\": []`), exactly mirroring the upstream `eqs = Equation[]`. No top-level `coupling` block is emitted because the upstream model has no `couple`/`operator_compose`/`variable_map` connections — the migration-tracker `coupling.couple` feature tag classifies this as a composed `@component`, which the ESS schema represents via `subsystems`, not the `coupling` array (the `coupling` array is for ConnectorSystem equations, of which this model has none).\n\nEach subsystem's `variables` and `equations` are copied verbatim from the corresponding already-migrated standalone `.esm` file in this directory — these are the validated, inline-test-gate-passing migrations of the same seven components:\n  photon              <- components/gaschem/radiation/photon_energy.esm        (PhotonEnergy,        src/radiation_fundamentals.jl:25,  esm-om23)\n  blackbody           <- components/gaschem/radiation/blackbody.esm            (BlackbodyRadiation,  src/radiation_fundamentals.jl:73,  esm-4gsh)\n  wien                <- components/gaschem/radiation/wien.esm                 (WienDisplacement,    src/radiation_fundamentals.jl:121, esm-3e2g)\n  stefan_boltzmann    <- components/gaschem/radiation/stefan_boltzmann.esm     (StefanBoltzmann,     src/radiation_fundamentals.jl:164, esm-mbfz)\n  energy_balance      <- components/gaschem/radiation/planetary_energy_balance.esm (PlanetaryEnergyBalance, src/radiation_fundamentals.jl:211, esm-8b1g)\n  climate_sensitivity <- components/gaschem/radiation/climate_sensitivity.esm  (ClimateSensitivity,  src/radiation_fundamentals.jl:268)\n  toa_forcing         <- components/gaschem/radiation/toa_radiative_forcing.esm (TOARadiativeForcing, src/radiation_fundamentals.jl:327, esm-pbbo)\nInlining (rather than `{\"ref\": \"./photon_energy.esm\"}`) keeps the file fully self-contained per ESM spec §6 (\"All models must be fully specified ... every equation, variable, and parameter must be present in the .esm file\") and avoids the inline-test walker double-processing the referenced standalone files.\n\nStructural fidelity to the upstream tests (GasChem.jl test/radiation_fundamentals_test.jl):\n  - `Structural: RadiationFundamentals composed system` (lines 12-28) asserts exactly 7 subsystems named photon/blackbody/wien/stefan_boltzmann/energy_balance/climate_sensitivity/toa_forcing — reproduced here by the 7 keys of the `subsystems` block.\n  - `Analytical: RadiationFundamentals composed system solves` (lines 473-496) asserts the pre-compiled system has `length(equations(radiation)) == 14` (= 2 photon + 1 blackbody + 1 wien + 1 stefan_boltzmann + 3 energy_balance + 4 climate_sensitivity + 2 toa_forcing) and that `radiation.energy_balance.T_e` solves to ~255 K. The migrated file preserves the 14-equation count across the 7 subsystems (stefan_boltzmann contributes its 1 equation as the `observed` variable F_B, which flattens to one algebraic equation) and the `upstream_analytical_composed_solves` test below pins energy_balance.T_e.\n\nenergy_balance subsystem — the upstream `PlanetaryEnergyBalance` is a closed nonlinear system (F_S ~ S_0/4*(1-R_p); F_L ~ sigma*T_e^4; F_S ~ F_L) that MTK solves with a `NonlinearProblem`. The inlined `energy_balance` subsystem carries the closed-form algebraic rewrite from planetary_energy_balance.esm (F_S ~ S_0/4*(1-R_p); T_e ~ (F_S/sigma)^(1/4); F_L ~ sigma*T_e^4) so the Python ESS runner, which integrates a DAE rather than solving a true nonlinear problem, recovers the unique positive-real root without an initial guess. This keeps the 3-equation / 3-state shape of the upstream `length(equations(balance)) == 3` invariant.\n\nParameter overrides on this composed model must be FULLY namespaced (`RadiationFundamentals.<subsystem>.<param>`, e.g. `RadiationFundamentals.energy_balance.R_p`). A bare name (`R_p`) would set every subsystem that has a parameter of that name (R_p exists in both energy_balance and toa_forcing; T in blackbody/wien/stefan_boltzmann; λ in photon/blackbody; S_0 in energy_balance/toa_forcing; F_L in toa_forcing) and a subsystem-relative name (`energy_balance.R_p`) resolves to nothing. Every `parameter_overrides` key in the tests below uses the fully-qualified form; several tests additionally assert that a sibling subsystem's output is UNCHANGED to pin the namespace-isolation contract that the upstream MTK `@named` composition provides.\n\nNo `examples` block: `tools/render_example_plots.py` builds its sweep-resolution plan from a model's own top-level `equations` only and does not recurse into `subsystems`, so it cannot evaluate a pure-aggregation model whose equations all live in child systems. Because RadiationFundamentals has no emergent behavior (zero coupling), every figure it could produce is already produced by the seven standalone subsystem `.esm` files, each of which carries its own `examples` block. Adding a syntactically-present `examples` block here that the renderer can only skip would itself be a migration gap (migration-guide §7.4), so the scientific-figure coverage (§6.2) is delegated to the seven standalone files.\n\nTolerance rationale (model-level rel=1.0e-9): every one of the 14 equations is algebraic (no time derivative); the ESS runner resolves them by topological substitution into closed form, so each output is correctly-rounded to within a few ULP of the exact real-arithmetic value. rel=1.0e-9 leaves >6 orders of magnitude of headroom above the ~1e-16 ULP floor and matches the looser of the seven standalone subsystem tolerances (blackbody.esm and planetary_energy_balance.esm both use rel=1e-9). Per-assertion `abs=1.0e-12` overrides guard the outputs that are exactly zero by construction (toa_forcing.F_net at radiative equilibrium; climate_sensitivity.ΔF_net / ΔT_e at zero forcing) where a relative tolerance is undefined. The `upstream_analytical_composed_solves` test additionally asserts energy_balance.T_e against the Seinfeld & Pandis book value 255 K at rel=1.0e-2, reproducing the upstream test's `rtol = 1.0e-2` bound.\n\nExpected values were obtained by running the canonical Python ESS runner (`earthsci_ast.simulation.simulate`, rtol=1e-10, atol=1e-12, cse=False) — the same path the inline-test gate `tools/run_esm_inline_tests.py` uses — on the flattened composed system, and cross-checked against the pinned values in the seven standalone subsystem `.esm` files (agreement to within last-ULP across all subsystems)."
  },
  "tolerance": {
    "rel": 1e-09
  },
  "variables": {},
  "equations": [],
  "subsystems": {
    "photon": {
      "variables": {
        "h": {
          "type": "parameter",
          "units": "J*s",
          "default": 6.626e-34,
          "description": "Planck's constant (S&P Page 99, 4-digit-rounded CODATA value). The fundamental quantum of action that links energy and frequency in the photon picture Δε = hν. The upstream default 6.626e-34 J·s is the historical 4-digit-rounded value; the modern CODATA-2019 exact definition is h = 6.62607015e-34 J·s (the SI redefinition of the kilogram fixes h to this value exactly). The two differ by ~1e-5 relative — within the rtol=1e-3 upstream test gate but resolvable at the rel=1e-10 .esm gate, which is why this constant is encoded as a parameter rather than a literal in the equation RHS (so downstream consumers can override h to the modern CODATA value for precision applications without forking the component)."
        },
        "c": {
          "type": "parameter",
          "units": "m/s",
          "default": 299790000.0,
          "description": "Speed of light in vacuum (S&P Page 99, 5-digit-rounded value). The fundamental electromagnetic propagation speed that links frequency and wavelength in the photon picture ν = c/λ. The upstream default 2.9979e8 m/s is the historical 5-digit-rounded value; the modern CODATA-1983 exact definition is c = 2.99792458e8 m/s (the SI redefinition of the meter fixes c to this value exactly via the meter being defined as the distance light travels in 1/299792458 s). The two differ by ~8e-7 relative — well within the rtol=1e-3 upstream test gate but resolvable at the rel=1e-10 .esm gate, encoded as a parameter to support CODATA-precision overrides without forking the component."
        },
        "λ": {
          "type": "parameter",
          "units": "m",
          "default": 5e-07,
          "description": "Wavelength of the photon (S&P Page 99, visible-green canonical default). The upstream default 5.0e-7 m = 500 nm is the yellow-green visible peak that matches Wien's law applied to T_sun ≈ 5800 K and anchors the solar-peak photon used in actinic-flux calculations. Other canonical wavelengths used in atmospheric radiative-transfer applications: 200-300 nm (UV-B/UV-C, the Hartley-Huggins ozone-photolysis bands O3 + hν → O + O2), 300-400 nm (UV-A, the O3 + hν → O(1D) + O2 channel and NO2-photolysis band), 400-700 nm (visible, solar-energy-balance photometric range), 700-1000 nm (near-IR, plant-photosynthesis quantum-yield cutoff), 1-10 μm (thermal-IR, the Earth-radiation longwave range), 1 mm (microwave, the cosmic-microwave-background Wien peak)."
        },
        "Δε": {
          "type": "unknown",
          "units": "J",
          "description": "Photon energy in joules (S&P Eq. 4.1a). Δε = hν is the quantum energy of a single photon at frequency ν — the discrete energy package that gets absorbed or emitted in a photon-matter interaction. The 500-nm visible-green default gives Δε ≈ 3.97e-19 J ≈ 2.48 eV, the canonical visible photon energy that anchors photoelectric-effect work-function and photosynthetic quantum-yield calculations. The full atmospheric photon-energy range spans ~12 orders of magnitude: from ~2e-31 J at the longest radio waves (~1 km) through ~2e-22 J at the microwave CMB peak (~1 mm), ~2e-20 J at the thermal-IR Earth-emission peak (~10 μm), ~4e-19 J at the visible solar peak (~500 nm), ~7e-19 J at the UV-B ozone-photolysis range (~300 nm), up to ~2e-16 J at the soft X-ray solar corona emission (~1 nm)."
        },
        "ν": {
          "type": "unknown",
          "units": "Hz",
          "description": "Photon frequency in hertz (S&P Eq. 4.1b). ν = c/λ is the electromagnetic wave frequency — the inverse-wavelength characterization of monochromatic light. The 500-nm visible-green default gives ν ≈ 600 THz, the canonical visible solar peak frequency. Frequency is the natural unit for radio-frequency atmospheric remote-sensing applications (passive microwave radiometry uses frequencies in GHz, e.g., the 22 GHz water-vapor line and 60 GHz oxygen complex used in the AMSU/ATMS sounders) and for spectroscopy (the rotational-line spacing in mm-wave spectra of atmospheric trace gases is the natural frequency-unit observable). The full atmospheric photon-frequency range spans ~12 orders of magnitude inversely correlated with the wavelength range: from ~3e5 Hz at the longest radio waves through ~3e11 Hz at the CMB peak, ~3e13 Hz at the thermal-IR peak, ~6e14 Hz at the visible peak, ~1e15 Hz at the UV-B range, up to ~3e17 Hz at the soft X-ray range."
        }
      },
      "equations": [
        {
          "lhs": "ν",
          "rhs": {
            "op": "/",
            "args": [
              "c",
              "λ"
            ]
          }
        },
        {
          "lhs": "Δε",
          "rhs": {
            "op": "*",
            "args": [
              "h",
              "ν"
            ]
          }
        }
      ]
    },
    "blackbody": {
      "variables": {
        "h": {
          "type": "parameter",
          "units": "J*s",
          "default": 6.626e-34,
          "description": "Planck's constant (S&P Page 99, 4-digit-rounded CODATA value). The fundamental quantum of action that anchors the discrete photon picture and the Bose-Einstein occupation factor in Planck's law. The upstream default 6.626e-34 J·s is the historical 4-digit-rounded value; the modern CODATA-2019 exact definition is h = 6.62607015e-34 J·s (the SI redefinition of the kilogram fixes h to this value exactly). The two differ by ~1e-5 relative — well within the rtol=5e-2 upstream test gate, encoded as a parameter so downstream consumers can override h to the modern CODATA value for precision applications without forking the component."
        },
        "c": {
          "type": "parameter",
          "units": "m/s",
          "default": 299790000.0,
          "description": "Speed of light in vacuum (S&P Page 99, 5-digit-rounded value). The upstream default 2.9979e8 m/s is the historical 5-digit-rounded value; the modern CODATA-1983 exact definition is c = 2.99792458e8 m/s (the SI redefinition of the meter fixes c to this value exactly via the meter being defined as the distance light travels in 1/299792458 s). The two differ by ~8e-7 relative — well within the rtol=5e-2 upstream test gate, encoded as a parameter to support CODATA-precision overrides."
        },
        "k_B": {
          "type": "parameter",
          "units": "J/K",
          "default": 1.381e-23,
          "description": "Boltzmann constant (S&P Page 99, 4-digit-rounded CODATA value). The fundamental quantity linking thermal-statistical mechanics (mean energy per degree of freedom = (1/2)k_B·T) and macroscopic thermodynamics; appears in the Bose-Einstein occupation factor exp(hν/kT) - 1 of Planck's law. The upstream default 1.381e-23 J/K is the historical 4-digit-rounded value; the modern CODATA-2019 exact definition is k_B = 1.380649e-23 J/K (the SI redefinition of the kelvin fixes k_B to this value exactly via the Boltzmann constant becoming a defining constant). The two differ by ~3e-4 relative — within the rtol=5e-2 upstream test gate, encoded as a parameter to support precision overrides."
        },
        "π_val": {
          "type": "parameter",
          "units": "1",
          "default": 3.141592653589793,
          "description": "Mathematical pi as a Float64 constant (Float64(π) in Julia, ~3.141592653589793). Encoded explicitly as a fixed-default parameter because the upstream Julia source declares `π_val = Float64(π)` as a `@constants` — the conversion to Float64 is required to avoid Julia's automatic Irrational→BigFloat promotion inside MTK's symbolic expressions. The upstream default value is the IEEE-754 double-precision representation of π (3.141592653589793 = the round-to-nearest-even of the exact mathematical π); this exact bit pattern is preserved here. Downstream consumers needing extended precision (e.g., quad-precision sensitivity studies) can override π_val, but the default matches Julia's `Float64(π)` exactly."
        },
        "T": {
          "type": "parameter",
          "units": "K",
          "default": 5800.0,
          "description": "Temperature of the emitting blackbody (S&P Page 99). The upstream default 5800.0 K is the Sun's effective surface temperature — sometimes given as 5778 K (the modern IAU 2015 value derived from the Sun's total luminosity and radius) but the upstream uses the classic 5800 K round figure. At this temperature paired with the default λ=500 nm wavelength, Planck's law gives F_B_λ ≈ 8.46e13 W/m³ — the canonical solar-peak spectral irradiance per unit wavelength that anchors the Sun's irradiance at Earth's distance and the solar-driven photochemistry of the atmosphere. Other canonical temperatures: 300 K (Earth surface) gives a thermal-IR peak at ~9.66 μm with F_B_λ at 10 μm ≈ 3.12e7 W/m³, 3 K (CMB) gives a microwave peak at ~0.97 mm, 1e4 K (cool-star photosphere or stellar corona) gives a UV/X-ray peak shifted by Wien's law."
        },
        "λ": {
          "type": "parameter",
          "units": "m",
          "default": 5e-07,
          "description": "Wavelength of the emitted photon (S&P Page 99, visible-green canonical default). The upstream default 5.0e-7 m = 500 nm is the yellow-green visible peak that matches Wien's law applied to T_sun ≈ 5800 K and anchors the solar-peak photon used in actinic-flux and spectral-irradiance calculations. Other canonical wavelengths used in atmospheric radiative-transfer applications: 200-300 nm (UV-B/UV-C, the Hartley-Huggins ozone-photolysis bands O3 + hν → O + O2), 300-400 nm (UV-A, the O3 + hν → O(1D) + O2 channel and NO2-photolysis band), 400-700 nm (visible, solar-energy-balance photometric range), 700-3000 nm (near-IR, solar-IR component), 3-50 μm (thermal-IR, the Earth-radiation longwave range), 1 mm (microwave, the cosmic-microwave-background Wien peak)."
        },
        "F_B_λ": {
          "type": "unknown",
          "units": "W/m^3",
          "description": "Monochromatic blackbody emissive power in watts per cubic meter (W·m⁻³ = W·m⁻²·m⁻¹, i.e., emitted power per unit area per unit wavelength). Equivalently called the spectral radiance per unit wavelength integrated over the outward 2π hemisphere. F_B_λ(λ, T) gives the wavelength-resolved emission of a thermal source: integrating over all wavelengths recovers the total emissive power F_B = ∫₀^∞ F_B_λ dλ = σT⁴ (Stefan-Boltzmann; see stefan_boltzmann.esm), and the wavelength where F_B_λ is maximized is λ_max = b/T (Wien's law; see wien.esm). At the default solar-peak (T=5800, λ=500 nm), F_B_λ ≈ 8.46e13 W/m³ — the canonical solar-peak spectral irradiance per unit wavelength used in radiative-transfer codes to bin solar energy across the visible band. At the Earth-thermal peak (T=300, λ=10 μm), F_B_λ ≈ 3.12e7 W/m³ — the canonical longwave outgoing radiation peak driving the planetary energy balance (S&P Eq. 4.6 / planetary_energy_balance.esm)."
        }
      },
      "equations": [
        {
          "lhs": "F_B_λ",
          "rhs": {
            "op": "/",
            "args": [
              {
                "op": "*",
                "args": [
                  2,
                  "π_val",
                  {
                    "op": "^",
                    "args": [
                      "c",
                      2
                    ]
                  },
                  "h",
                  {
                    "op": "^",
                    "args": [
                      "λ",
                      -5
                    ]
                  }
                ]
              },
              {
                "op": "-",
                "args": [
                  {
                    "op": "exp",
                    "args": [
                      {
                        "op": "/",
                        "args": [
                          {
                            "op": "*",
                            "args": [
                              "c",
                              "h"
                            ]
                          },
                          {
                            "op": "*",
                            "args": [
                              "k_B",
                              "λ",
                              "T"
                            ]
                          }
                        ]
                      }
                    ]
                  },
                  1
                ]
              }
            ]
          }
        }
      ]
    },
    "wien": {
      "variables": {
        "b": {
          "type": "parameter",
          "units": "m*K",
          "default": 0.002897,
          "description": "Wien's displacement constant (S&P Page 100, 4-digit-rounded CODATA). The proportionality between blackbody temperature and peak emission wavelength in λ_max = b/T. The upstream default 2.897e-3 m·K is the historical 4-digit-rounded value; the modern CODATA-2018 value is 2.897771955e-3 m·K which round-trips to 2.898e-3 at four-digit precision (the upstream choice of 2.897 reflects the pre-2014 CODATA value before the latest least-squares adjustment). The constant follows analytically from the transcendental equation x = 5(1-e^(-x)) where x = hc/(kλT) gives x ≈ 4.965114, so b = hc/(k·x) — anchored by the fundamental constants h (Planck), c (speed of light), k_B (Boltzmann)."
        },
        "T": {
          "type": "parameter",
          "units": "K",
          "default": 5800.0,
          "description": "Temperature of the emitting blackbody (S&P Page 100). The upstream default 5800.0 K is the Sun's effective surface temperature (the temperature of an ideal blackbody emitting the same total radiative flux as the Sun) — sometimes given as 5778 K (the modern IAU 2015 value) but the upstream uses the classic 5800 K round figure. At this temperature, Wien's law gives λ_max = 2.897e-3/5800 = 499.5 nm, the yellow-green visible peak that anchors the human visual system's evolved sensitivity range. Other canonical temperatures: 300 K (Earth surface) → 9.66 μm thermal-IR, 3 K (CMB) → 0.97 mm microwave, 1e6 K (stellar corona/X-ray emission line region) → 2.9 nm soft X-ray."
        },
        "λ_max": {
          "type": "unknown",
          "units": "m",
          "description": "Peak emission wavelength of the blackbody at temperature T (S&P Eq. 4.3). λ_max is the wavelength at which the Planck spectral function dF_Bλ/dλ = 0 — the maximum of the spectral emission curve. The temperature-inverse scaling λ_max ∝ 1/T means hotter sources emit at shorter wavelengths: the canonical fact behind the visible spectrum of stars (red giants vs blue dwarfs), the color of a heated metal as it warms from red-hot to white-hot, and the separation of solar (shortwave) from terrestrial (longwave) radiation that anchors the planetary energy balance in S&P Chapter 4. The peak wavelength is one of three derived quantities from the Planck function (peak λ_max from Wien, total flux F_B from Stefan-Boltzmann, spectral shape F_Bλ from Planck itself) that together characterize blackbody emission."
        }
      },
      "equations": [
        {
          "lhs": "λ_max",
          "rhs": {
            "op": "/",
            "args": [
              "b",
              "T"
            ]
          }
        }
      ]
    },
    "stefan_boltzmann": {
      "variables": {
        "T": {
          "type": "parameter",
          "units": "K",
          "default": 255.0,
          "description": "Temperature (input parameter; default 255 K is Earth's equilibrium temperature per S&P Page 101)"
        },
        "σ": {
          "type": "parameter",
          "units": "W/(m^2*K^4)",
          "default": 5.671e-08,
          "description": "Stefan-Boltzmann constant (upstream `@constants` value 5.671×10⁻⁸ W·m⁻²·K⁻⁴ from S&P Page 101; encoded as a fixed-default parameter per rig convention)"
        },
        "F_B": {
          "type": "unknown",
          "units": "W/m^2",
          "description": "Total blackbody emissive power (Eq. 4.4): F_B = σ·T^4 integrated over all wavelengths."
        }
      },
      "equations": [
        {
          "lhs": "F_B",
          "rhs": {
            "op": "*",
            "args": [
              "σ",
              {
                "op": "^",
                "args": [
                  "T",
                  4
                ]
              }
            ]
          }
        }
      ]
    },
    "energy_balance": {
      "variables": {
        "sigma": {
          "type": "parameter",
          "units": "W/(m^2*K^4)",
          "default": 5.671e-08,
          "description": "Stefan-Boltzmann constant (Seinfeld & Pandis 2006 Eq. 4.4 / Ch. 4 §4.1) — upstream `@constants` sigma; the proportionality constant in the Stefan-Boltzmann law for emissive power of a blackbody. Default 5.671e-8 W/(m^2*K^4) matches the upstream Julia source verbatim; CODATA 2018 value is 5.670374419e-8 W/(m^2*K^4), within ~1e-4 relative of the upstream rounded value."
        },
        "S_0": {
          "type": "parameter",
          "units": "W/m^2",
          "default": 1370.0,
          "description": "Solar constant — total radiative flux per unit area at the top of Earth's atmosphere measured normal to the Sun's direction at 1 AU. Default 1370 W/m^2 matches the upstream Julia source and Seinfeld & Pandis 2006 p. 101; modern observation-derived total solar irradiance is ~1361 W/m^2 (Kopp & Lean 2011). The factor of 4 in Eq. 4.5 (`S_0/4 * (1 - R_p)`) is the ratio of Earth's geometric cross-section (pi*R^2) to its surface area (4*pi*R^2) — averages the per-area solar flux from the cross-section that intercepts the beam onto the full surface area."
        },
        "R_p": {
          "type": "parameter",
          "units": "1",
          "default": 0.3,
          "description": "Planetary albedo (dimensionless) — fraction of incident solar radiation reflected back to space by clouds, atmosphere, and surface. Default 0.3 matches the upstream Julia source and Seinfeld & Pandis 2006 p. 101 (the standard Earth-with-clouds value). The same upstream test family exercises R_p = 0.15 (Earth without clouds, T_e ~ 268 K), R_p = 0 (perfect absorber, T_e ~ 278.77 K), and R_p = 0.99 (near-perfect reflector, T_e ~ 88.16 K)."
        },
        "F_S": {
          "type": "unknown",
          "units": "W/m^2",
          "default": 240.0,
          "description": "Absorbed solar flux at the top of atmosphere averaged over Earth's surface (Seinfeld & Pandis Eq. 4.5): F_S = S_0/4 * (1 - R_p). Default initial value 240 W/m^2 matches the upstream Julia source `F_S(t) = 240.0` — the convergence target near 239.75 W/m^2 at the canonical defaults (S_0 = 1370, R_p = 0.3). At equilibrium F_S = F_L (Eq. 4.7)."
        },
        "F_L": {
          "type": "unknown",
          "units": "W/m^2",
          "default": 240.0,
          "description": "Emitted longwave (terrestrial) radiative flux at the top of atmosphere (Seinfeld & Pandis Eq. 4.6, Stefan-Boltzmann law): F_L = sigma * T_e^4. Default initial value 240 W/m^2 matches the upstream Julia source `F_L(t) = 240.0`. At equilibrium F_L = F_S (Eq. 4.7); the migrated algebraic chain enforces this by composition through T_e."
        },
        "T_e": {
          "type": "unknown",
          "units": "K",
          "default": 255.0,
          "description": "Planetary equilibrium temperature (Seinfeld & Pandis Eq. 4.7): the temperature at which the emitted longwave flux F_L = sigma * T_e^4 balances the absorbed solar flux F_S = S_0/4 * (1 - R_p). Closed-form: T_e = (S_0/4 * (1 - R_p) / sigma)^(1/4). Default initial value 255 K matches the upstream Julia source `T_e(t) = 255.0` — the convergence target at the canonical defaults (S_0 = 1370, R_p = 0.3); upstream Julia `NonlinearProblem` uses 250 K as the initial guess and converges to ~254.99 K (book value 255 K)."
        }
      },
      "equations": [
        {
          "lhs": "F_S",
          "rhs": {
            "op": "*",
            "args": [
              {
                "op": "/",
                "args": [
                  "S_0",
                  4.0
                ]
              },
              {
                "op": "-",
                "args": [
                  1.0,
                  "R_p"
                ]
              }
            ]
          }
        },
        {
          "lhs": "T_e",
          "rhs": {
            "op": "^",
            "args": [
              {
                "op": "/",
                "args": [
                  "F_S",
                  "sigma"
                ]
              },
              0.25
            ]
          }
        },
        {
          "lhs": "F_L",
          "rhs": {
            "op": "*",
            "args": [
              "sigma",
              {
                "op": "^",
                "args": [
                  "T_e",
                  4.0
                ]
              }
            ]
          }
        }
      ]
    },
    "climate_sensitivity": {
      "variables": {
        "σ": {
          "type": "parameter",
          "units": "W/(m^2*K^4)",
          "default": 5.671e-08,
          "description": "Stefan-Boltzmann constant (S&P Page 101). The proportionality between blackbody temperature and total emitted radiative power per unit area. The upstream default 5.671e-8 W/(m^2·K^4) is the CODATA value rounded to four significant figures (the modern CODATA-2018 value is 5.670374...e-8, which round-trips to 5.671e-8 at four-digit precision)."
        },
        "T_e": {
          "type": "parameter",
          "units": "K",
          "default": 255.0,
          "description": "Reference equilibrium temperature for the climate-sensitivity expansion (S&P Page 104). 255 K is Earth's no-greenhouse effective radiating temperature — the temperature a perfect blackbody planet receiving Earth's net solar flux F_S = (1-R_p)·S_0/4 ≈ 240 W/m^2 would have. The actual Earth's surface temperature (~288 K) exceeds T_e by the greenhouse-effect warming of ~33 K. Climate-sensitivity diagnostics are conventionally evaluated at T_e (the planetary radiative balance temperature) rather than at the surface — F_L = σ·T_e^4 must match F_S at radiative equilibrium."
        },
        "ΔF_S": {
          "type": "parameter",
          "units": "W/m^2",
          "default": 4.0,
          "description": "Perturbation to the absorbed solar flux (S&P Eq. 4.8). Positive ΔF_S means more solar energy absorbed (e.g., reduced cloud albedo, reduced ice cover, increased solar luminosity). The upstream default 4.0 W/m^2 is a representative CO2-doubling-equivalent forcing — close to but slightly smaller than the often-cited 4.6 W/m^2 CO2-doubling estimate the upstream test uses for the secondary canonical case."
        },
        "ΔF_L": {
          "type": "parameter",
          "units": "W/m^2",
          "default": 0.0,
          "description": "Perturbation to the emitted longwave flux (S&P Eq. 4.8). Positive ΔF_L means more longwave radiation escaping to space (e.g., reduced opacity of the atmosphere). The default ΔF_L = 0.0 places the full forcing on the solar side, isolating the temperature response to a pure ΔF_S perturbation."
        },
        "ΔF_net": {
          "type": "unknown",
          "units": "W/m^2",
          "description": "Net radiative-forcing perturbation, ΔF_net = ΔF_S - ΔF_L (S&P Eq. 4.8). Positive ΔF_net means the planet receives more net incoming energy than the reference state and must warm to restore balance. This is the input to the linear climate-sensitivity relation ΔT_e = λ_0·ΔF_net."
        },
        "ΔT_e": {
          "type": "unknown",
          "units": "K",
          "description": "Change in equilibrium temperature responding to the net radiative forcing (S&P Eq. 4.9). ΔT_e = λ_0·ΔF_net is the linear-response approximation of the (small-perturbation) temperature change. At Earth's T_e = 255 K, λ_0 ≈ 0.27 K·m^2/W, so a 4 W/m^2 forcing (≈ CO2 doubling) gives ΔT_e ≈ 1.06 K — the no-feedback Planck response, against which feedback-amplified ΔT_e estimates (~1.5-4.5 K for CO2 doubling per IPCC) are conventionally reported."
        },
        "λ_0": {
          "type": "unknown",
          "units": "K*m^2/W",
          "description": "Climate-sensitivity factor in the no-feedback (Planck) limit (S&P Eq. 4.10). λ_0 = 1 / (4·σ·T_e^3) is the analytic inverse of dF_L/dT_e at the reference state — the temperature change per unit radiative forcing that holds when no feedbacks amplify or damp the response. Equivalently λ_0 = T_e / (4·F_L), where F_L is the reference longwave flux. At Earth's T_e = 255 K, λ_0 ≈ 0.27 K·m^2/W; a 1 K cooler T_e would raise λ_0 by ~1% (∂λ_0/∂T_e = -3·λ_0/T_e). The factor is the baseline against which feedback-amplified sensitivities are reported — IPCC equilibrium climate sensitivity ECS = λ·ΔF_2xCO2 where λ ≈ 2-6 × λ_0 captures water vapor, lapse rate, albedo, and cloud feedbacks."
        },
        "F_L": {
          "type": "unknown",
          "units": "W/m^2",
          "description": "Reference longwave flux at the reference temperature, F_L = σ·T_e^4 (Stefan-Boltzmann law applied at T_e). At Earth's T_e = 255 K, F_L ≈ 239.78 W/m^2 — matches (within rounding) the absorbed solar flux F_S ≈ 239.75 W/m^2 (S&P p. 101: F_S = (1-R_p)·S_0/4 at R_p=0.3, S_0=1370 W/m^2). Exposed as a state variable so the alternative form λ_0 = T_e / (4·F_L) can be verified directly against λ_0 = 1 / (4·σ·T_e^3) — they are algebraically identical (multiply numerator and denominator of the second form by T_e to get the first)."
        }
      },
      "equations": [
        {
          "lhs": "ΔF_net",
          "rhs": {
            "op": "-",
            "args": [
              "ΔF_S",
              "ΔF_L"
            ]
          }
        },
        {
          "lhs": "λ_0",
          "rhs": {
            "op": "/",
            "args": [
              1,
              {
                "op": "*",
                "args": [
                  4,
                  "σ",
                  {
                    "op": "^",
                    "args": [
                      "T_e",
                      3
                    ]
                  }
                ]
              }
            ]
          }
        },
        {
          "lhs": "ΔT_e",
          "rhs": {
            "op": "*",
            "args": [
              "λ_0",
              "ΔF_net"
            ]
          }
        },
        {
          "lhs": "F_L",
          "rhs": {
            "op": "*",
            "args": [
              "σ",
              {
                "op": "^",
                "args": [
                  "T_e",
                  4
                ]
              }
            ]
          }
        }
      ]
    },
    "toa_forcing": {
      "variables": {
        "S_0": {
          "type": "parameter",
          "units": "W/m^2",
          "default": 1370.0,
          "description": "Solar constant — the time-averaged solar irradiance at the top of Earth's atmosphere measured perpendicular to the Sun-Earth line (Seinfeld & Pandis 2006 Page 100, IPCC TAR canonical value). Modern accepted value from CODATA / TIM satellite measurements is ~1361 W/m²; the upstream uses the round 1370 W/m² for textbook consistency. Drives the absorbed solar flux F_S via the planetary-cross-section factor 1/4."
        },
        "R_p": {
          "type": "parameter",
          "units": "1",
          "default": 0.3,
          "description": "Planetary albedo (dimensionless) — the fraction of incoming solar flux reflected back to space by clouds (~2/3), ice/snow, ocean, and land surfaces. Default 0.3 is Earth's Bond albedo including clouds (S&P Page 101). Removing clouds gives R_p ≈ 0.15 (T_e ≈ 268 K, S&P Page 102); the no-cloud / no-ice limit gives R_p ≈ 0.07 (just ocean / land surface reflection); the all-ice snowball-Earth limit gives R_p ≈ 0.6+ (T_e ≈ 220 K). The (1-R_p) factor in F_S is the fraction of incoming solar absorbed by the planet."
        },
        "F_L": {
          "type": "parameter",
          "units": "W/m^2",
          "default": 239.75,
          "description": "Emitted longwave flux at TOA (W/m²) — the outgoing thermal radiation the planet emits, treated here as an input parameter. Default 239.75 W/m² is chosen to exactly balance F_S at the default solar constant and albedo (radiative equilibrium F_net = 0). In a coupled system, F_L would be computed by the sibling StefanBoltzmann component as σT_e^4 with T_e ≈ 255 K (5.671e-8 · 255^4 ≈ 239.75 W/m²). A consumer studying a forcing scenario can override F_L: e.g. doubling CO₂ raises F_L by ~4-5 W/m² instantaneously before the surface temperature responds (S&P Page 105 quotes 4.6 W/m² for CO₂ doubling), producing a transient negative F_net ≈ -4 W/m² that drives subsequent warming."
        },
        "F_net": {
          "type": "unknown",
          "units": "W/m^2",
          "description": "Net radiative flux at TOA (W/m²) — F_net = F_S - F_L. Positive: planet gaining energy (warming). Negative: planet losing energy (cooling). At Earth's default radiative-balance parameters F_net = 0 exactly. The IPCC AR6 estimate of the present-day Earth-system energy imbalance is +0.79 W/m² (2006-2018, Forster et al. 2021), consistent with ongoing greenhouse-driven warming."
        },
        "F_S": {
          "type": "unknown",
          "units": "W/m^2",
          "description": "Absorbed solar flux at TOA (W/m²) — F_S = S_0/4 · (1 - R_p). The factor 1/4 is the planetary geometric correction (planet intercepts solar flux over πR² but emits over 4πR²); the factor (1 - R_p) is the fraction of incoming solar absorbed (1 minus reflected). At Earth's defaults: F_S = 1370/4 · 0.7 = 239.75 W/m²."
        }
      },
      "equations": [
        {
          "lhs": "F_S",
          "rhs": {
            "op": "*",
            "args": [
              {
                "op": "/",
                "args": [
                  "S_0",
                  4.0
                ]
              },
              {
                "op": "-",
                "args": [
                  1.0,
                  "R_p"
                ]
              }
            ]
          }
        },
        {
          "lhs": "F_net",
          "rhs": {
            "op": "-",
            "args": [
              "F_S",
              "F_L"
            ]
          }
        }
      ]
    }
  },
  "tests": [
    {
      "id": "composed_default_canonical_all_subsystems",
      "description": "Canonical default-parameter run of the composed system. Reproduces the intent of the upstream `Structural: RadiationFundamentals composed system` test (test/radiation_fundamentals_test.jl:12-28, which asserts the 7 named subsystems photon/blackbody/wien/stefan_boltzmann/energy_balance/climate_sensitivity/toa_forcing) by exercising one canonical output of every one of the 7 subsystems through the dot-namespaced flattened system: photon at the 500 nm visible-green default (ν, Δε), blackbody at T=5800 K / λ=500 nm (F_B_λ), wien at T=5800 K (λ_max), stefan_boltzmann at T=255 K (F_B), energy_balance at S_0=1370 / R_p=0.3 (F_S, T_e, F_L), climate_sensitivity at ΔF_S=4.0 (ΔF_net, λ_0, ΔT_e, F_L), toa_forcing at the radiative-equilibrium defaults (F_S, F_net≈0). Every value is cross-checked against the pinned values in the standalone subsystem .esm files (agreement to last-ULP).",
      "parameter_overrides": {},
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.photon.ν",
          "time": 0.0,
          "expected": 599580000000000.0
        },
        {
          "variable": "RadiationFundamentals.photon.Δε",
          "time": 0.0,
          "expected": 3.97281708e-19
        },
        {
          "variable": "RadiationFundamentals.blackbody.F_B_λ",
          "time": 0.0,
          "expected": 84565887378394.64
        },
        {
          "variable": "RadiationFundamentals.wien.λ_max",
          "time": 0.0,
          "expected": 4.994827586206896e-07
        },
        {
          "variable": "RadiationFundamentals.stefan_boltzmann.F_B",
          "time": 0.0,
          "expected": 239.78409294375
        },
        {
          "variable": "RadiationFundamentals.energy_balance.F_S",
          "time": 0.0,
          "expected": 239.74999999999997
        },
        {
          "variable": "RadiationFundamentals.energy_balance.T_e",
          "time": 0.0,
          "expected": 254.99093542432257
        },
        {
          "variable": "RadiationFundamentals.energy_balance.F_L",
          "time": 0.0,
          "expected": 239.74999999999997
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.ΔF_net",
          "time": 0.0,
          "expected": 4.0
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.λ_0",
          "time": 0.0,
          "expected": 0.2658641747972617
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.ΔT_e",
          "time": 0.0,
          "expected": 1.0634566991890468
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.F_L",
          "time": 0.0,
          "expected": 239.78409294375
        },
        {
          "variable": "RadiationFundamentals.toa_forcing.F_S",
          "time": 0.0,
          "expected": 239.74999999999997
        },
        {
          "variable": "RadiationFundamentals.toa_forcing.F_net",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-12
          }
        }
      ]
    },
    {
      "id": "upstream_analytical_composed_solves",
      "description": "Reproduces the upstream `Analytical: RadiationFundamentals composed system solves` test (test/radiation_fundamentals_test.jl:473-496). The upstream test compiles the composed system, solves it with the initial guess `radiation.energy_balance.T_e => 250.0`, and asserts `isapprox(sol[radiation.energy_balance.T_e], 255.0, rtol = 1.0e-2)` (Eq. 4.7, S&P p. 101). The migrated energy_balance subsystem uses the closed-form algebraic chain so no initial guess is needed; energy_balance.T_e is pinned both to the exact computed value 254.9909354243226 K (rel=1e-9) and to the upstream book value 255 K at the upstream rel=1.0e-2 bound.",
      "parameter_overrides": {},
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.energy_balance.T_e",
          "time": 0.0,
          "expected": 254.99093542432257
        },
        {
          "variable": "RadiationFundamentals.energy_balance.T_e",
          "time": 0.0,
          "expected": 255.0,
          "tolerance": {
            "rel": 0.01
          }
        }
      ]
    },
    {
      "id": "photon_uv_300nm_namespace_isolation",
      "description": "Overrides RadiationFundamentals.photon.λ to 3.0e-7 m (UV-B, the Hartley-Huggins ozone-photolysis band). Reproduces the UV case of the upstream `Equation: PhotonEnergy (Eq. 4.1)` test (test/radiation_fundamentals_test.jl:113-118; upstream asserts ν≈9.993e14 Hz and Δε≈6.622e-19 J at rtol=1e-3) and additionally pins blackbody.F_B_λ UNCHANGED at its λ=5.0e-7 m default value — the photon and blackbody subsystems each carry their own independent `λ` parameter, and the fully-namespaced override must not leak across the subsystem boundary.",
      "parameter_overrides": {
        "RadiationFundamentals.photon.λ": 3e-07
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.photon.ν",
          "time": 0.0,
          "expected": 999300000000000.0
        },
        {
          "variable": "RadiationFundamentals.photon.Δε",
          "time": 0.0,
          "expected": 6.6213618e-19
        },
        {
          "variable": "RadiationFundamentals.blackbody.F_B_λ",
          "time": 0.0,
          "expected": 84565887378394.64
        }
      ]
    },
    {
      "id": "blackbody_earth_thermal_10um",
      "description": "Overrides blackbody.T to 300 K (Earth surface) and blackbody.λ to 1.0e-5 m (10 μm, the thermal-IR Earth-emission peak). Reproduces the Earth case of the upstream `Equation: BlackbodyRadiation (Eq. 4.2)` test (test/radiation_fundamentals_test.jl:161-164; upstream asserts F_B_λ≈3.13e7 W/m^3 at rtol=5e-2). Pinned here at rel=1e-9 to the exact value 31217606.963872716 W/m^3.",
      "parameter_overrides": {
        "RadiationFundamentals.blackbody.T": 300.0,
        "RadiationFundamentals.blackbody.λ": 1e-05
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.blackbody.F_B_λ",
          "time": 0.0,
          "expected": 31217606.963872716
        }
      ]
    },
    {
      "id": "blackbody_temperature_namespace_isolation",
      "description": "Overrides only blackbody.T to 300 K (leaving blackbody.λ at the 5.0e-7 m default, where a 300 K body emits negligibly — F_B_λ ≈ 2.7e-26 W/m^3, the deep Wien tail). Pins wien.λ_max and stefan_boltzmann.F_B UNCHANGED at their respective T=5800 K and T=255 K defaults: blackbody, wien, and stefan_boltzmann each carry an independent `T` parameter, and the fully-namespaced override on blackbody.T must not perturb the sibling subsystems.",
      "parameter_overrides": {
        "RadiationFundamentals.blackbody.T": 300.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.blackbody.F_B_λ",
          "time": 0.0,
          "expected": 2.708496908180942e-26
        },
        {
          "variable": "RadiationFundamentals.wien.λ_max",
          "time": 0.0,
          "expected": 4.994827586206896e-07
        },
        {
          "variable": "RadiationFundamentals.stefan_boltzmann.F_B",
          "time": 0.0,
          "expected": 239.78409294375
        }
      ]
    },
    {
      "id": "wien_terrestrial_peak_300K",
      "description": "Overrides wien.T to 300 K (Earth surface). Reproduces the Earth case of the upstream `Equation: WienDisplacement (Eq. 4.3)` test (test/radiation_fundamentals_test.jl:130-133; upstream asserts λ_max≈10 μm at rtol=5e-2). Pinned at rel=1e-9 to b/T = 2.897e-3/300 = 9.656666666666667e-6 m — the thermal-IR peak that, paired with the 5800 K solar peak at ~500 nm, anchors the shortwave/longwave separation underpinning the planetary energy balance.",
      "parameter_overrides": {
        "RadiationFundamentals.wien.T": 300.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.wien.λ_max",
          "time": 0.0,
          "expected": 9.656666666666667e-06
        }
      ]
    },
    {
      "id": "wien_extreme_hot_xray_1e6K",
      "description": "Overrides wien.T to 1.0e6 K (stellar-corona / X-ray emission regime). Reproduces the hot case of the upstream `Limiting: Wien's law at extreme temperatures` test (test/radiation_fundamentals_test.jl:274-277; upstream asserts λ_max < 1.0e-8 m). Pinned at rel=1e-9 to b/T = 2.897e-3/1e6 = 2.897e-9 m, in the soft X-ray band.",
      "parameter_overrides": {
        "RadiationFundamentals.wien.T": 1000000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.wien.λ_max",
          "time": 0.0,
          "expected": 2.897e-09
        }
      ]
    },
    {
      "id": "wien_extreme_cold_cmb_3K",
      "description": "Overrides wien.T to 3.0 K (cosmic-microwave-background temperature). Reproduces the cold case of the upstream `Limiting: Wien's law at extreme temperatures` test (test/radiation_fundamentals_test.jl:280-283; upstream asserts λ_max > 1.0e-4 m and λ_max≈9.66e-4 m at rtol=1e-2). Pinned at rel=1e-9 to b/T = 2.897e-3/3 = 9.656666666666666e-4 m, in the microwave band.",
      "parameter_overrides": {
        "RadiationFundamentals.wien.T": 3.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.wien.λ_max",
          "time": 0.0,
          "expected": 0.0009656666666666666
        }
      ]
    },
    {
      "id": "stefan_boltzmann_solar_temperature_5800K",
      "description": "Overrides stefan_boltzmann.T to 5800 K (the Sun's effective surface temperature). Reproduces the solar case of the upstream `Equation: StefanBoltzmann (Eq. 4.4)` test (test/radiation_fundamentals_test.jl:145-148; upstream asserts F_B≈6.42e7 W/m^2 at rtol=1e-2). Pinned at rel=1e-9 to σ·T^4 = 5.671e-8 · 5800^4 = 64175848.816 W/m^2.",
      "parameter_overrides": {
        "RadiationFundamentals.stefan_boltzmann.T": 5800.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.stefan_boltzmann.F_B",
          "time": 0.0,
          "expected": 64175848.816
        }
      ]
    },
    {
      "id": "energy_balance_no_clouds_R_p_0_15",
      "description": "Overrides energy_balance.R_p to 0.15 (Earth without clouds — surface and atmosphere albedo only). Reproduces the second case of the upstream `Equation: PlanetaryEnergyBalance (Eqs. 4.5-4.7)` test (test/radiation_fundamentals_test.jl:178-181; upstream asserts T_e≈268 K at rtol=1e-2). Pins F_S = 1370/4·0.85 = 291.125 W/m^2, T_e = (291.125/5.671e-8)^(1/4) = 267.673 K, F_L = 291.125 W/m^2 (= F_S at equilibrium), and toa_forcing.F_S UNCHANGED at the R_p=0.3 default — energy_balance and toa_forcing carry independent `R_p` parameters.",
      "parameter_overrides": {
        "RadiationFundamentals.energy_balance.R_p": 0.15
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.energy_balance.F_S",
          "time": 0.0,
          "expected": 291.125
        },
        {
          "variable": "RadiationFundamentals.energy_balance.T_e",
          "time": 0.0,
          "expected": 267.67324479035756
        },
        {
          "variable": "RadiationFundamentals.energy_balance.F_L",
          "time": 0.0,
          "expected": 291.125
        },
        {
          "variable": "RadiationFundamentals.toa_forcing.F_S",
          "time": 0.0,
          "expected": 239.74999999999997
        }
      ]
    },
    {
      "id": "energy_balance_zero_albedo_R_p_0_0",
      "description": "Overrides energy_balance.R_p to 0.0 (perfect absorber — no reflection). Reproduces the zero-albedo case of the upstream `Limiting: Equilibrium temperature at extreme albedo` test (test/radiation_fundamentals_test.jl:290-295; upstream asserts T_e > 270 K). Pins F_S = 1370/4·1.0 = 342.5 W/m^2 and T_e = (342.5/5.671e-8)^(1/4) = 278.773 K — the upper bound on equilibrium temperature at the canonical solar constant.",
      "parameter_overrides": {
        "RadiationFundamentals.energy_balance.R_p": 0.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.energy_balance.F_S",
          "time": 0.0,
          "expected": 342.5
        },
        {
          "variable": "RadiationFundamentals.energy_balance.T_e",
          "time": 0.0,
          "expected": 278.7726940675581
        }
      ]
    },
    {
      "id": "energy_balance_high_solar_constant_1800",
      "description": "Overrides energy_balance.S_0 to 1800 W/m^2 (the upper end of the upstream `Qualitative: T_e increases with increasing solar constant` sweep, test/radiation_fundamentals_test.jl:355-374). Pins F_S = 1800/4·0.7 = 315.0 W/m^2 and T_e = (315/5.671e-8)^(1/4) = 273.000 K — substantially warmer than the canonical 255 K, anchoring the T_e ∝ S_0^(1/4) scaling.",
      "parameter_overrides": {
        "RadiationFundamentals.energy_balance.S_0": 1800.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.energy_balance.F_S",
          "time": 0.0,
          "expected": 315.0
        },
        {
          "variable": "RadiationFundamentals.energy_balance.T_e",
          "time": 0.0,
          "expected": 273.0000500276826
        }
      ]
    },
    {
      "id": "climate_sensitivity_co2_doubling_4_6",
      "description": "Overrides climate_sensitivity.ΔF_S to 4.6 W/m^2 (the S&P p. 105 CO2-doubling radiative forcing). Reproduces the CO2-doubling case of the upstream `Equation: ClimateSensitivity (Eqs. 4.8-4.10)` test (test/radiation_fundamentals_test.jl:199-201; upstream asserts ΔT_e≈1.22 K at rtol=0.05). Pins ΔF_net = 4.6 W/m^2, λ_0 = 1/(4σT_e^3) = 0.26586 K·m^2/W (unchanged from default — λ_0 depends only on T_e), and ΔT_e = λ_0·ΔF_net = 1.22298 K — the no-feedback Planck temperature response.",
      "parameter_overrides": {
        "RadiationFundamentals.climate_sensitivity.ΔF_S": 4.6
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.climate_sensitivity.ΔF_net",
          "time": 0.0,
          "expected": 4.6
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.λ_0",
          "time": 0.0,
          "expected": 0.2658641747972617
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.ΔT_e",
          "time": 0.0,
          "expected": 1.2229752040674038
        }
      ]
    },
    {
      "id": "climate_sensitivity_zero_forcing",
      "description": "Overrides climate_sensitivity.ΔF_S and ΔF_L both to 0.0 W/m^2. Reproduces the upstream `Steady-State: ClimateSensitivity zero forcing gives zero response` test (test/radiation_fundamentals_test.jl:252-262; upstream asserts ΔT_e≈0 and ΔF_net≈0 at atol=1e-10). With no net radiative forcing the temperature response is exactly zero; asserted with abs=1e-12 since a relative tolerance is undefined at zero.",
      "parameter_overrides": {
        "RadiationFundamentals.climate_sensitivity.ΔF_S": 0.0,
        "RadiationFundamentals.climate_sensitivity.ΔF_L": 0.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.climate_sensitivity.ΔF_net",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-12
          }
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.ΔT_e",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-12
          }
        }
      ]
    },
    {
      "id": "climate_sensitivity_alt_form_T_e_300",
      "description": "Overrides climate_sensitivity.T_e to 300 K. Reproduces the T_e=300 K case of the upstream `Analytical: Climate sensitivity factor alternative form (Eq. 4.10)` test (test/radiation_fundamentals_test.jl:455-470), which verifies λ_0 = 1/(4σT_e^3) equals T_e/(4·F_L). Pins λ_0 = 0.16327383634736833 K·m^2/W and the reference longwave flux F_L = σ·T_e^4 = 459.351 W/m^2; the identity λ_0 = T_e/(4·F_L) = 300/(4·459.351) holds by construction.",
      "parameter_overrides": {
        "RadiationFundamentals.climate_sensitivity.T_e": 300.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.climate_sensitivity.λ_0",
          "time": 0.0,
          "expected": 0.16327383634736833
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.F_L",
          "time": 0.0,
          "expected": 459.351
        }
      ]
    },
    {
      "id": "climate_sensitivity_alt_form_T_e_200",
      "description": "Overrides climate_sensitivity.T_e to 200 K. Reproduces the T_e=200 K case of the upstream `Analytical: Climate sensitivity factor alternative form (Eq. 4.10)` test (test/radiation_fundamentals_test.jl:455-470). Pins λ_0 = 0.5510491976723682 K·m^2/W and F_L = σ·T_e^4 = 90.736 W/m^2; the alternative form λ_0 = T_e/(4·F_L) = 200/(4·90.736) holds by construction. A colder reference temperature gives a larger climate-sensitivity factor (∂λ_0/∂T_e = -3λ_0/T_e < 0).",
      "parameter_overrides": {
        "RadiationFundamentals.climate_sensitivity.T_e": 200.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.climate_sensitivity.λ_0",
          "time": 0.0,
          "expected": 0.5510491976723682
        },
        {
          "variable": "RadiationFundamentals.climate_sensitivity.F_L",
          "time": 0.0,
          "expected": 90.736
        }
      ]
    },
    {
      "id": "toa_forcing_enhanced_greenhouse_F_L_250",
      "description": "Overrides toa_forcing.F_L to 250.0 W/m^2 (enhanced greenhouse — more longwave trapped below, but here F_L is treated as the outgoing flux input so a larger F_L drives F_net negative). Reproduces the upstream `Equation: TOARadiativeForcing (Eq. 4.11)` test's second case (test/radiation_fundamentals_test.jl:214-217; upstream asserts F_net < 0). Pins F_S = 239.75 W/m^2 (unchanged) and F_net = F_S - F_L = 239.75 - 250.0 = -10.25 W/m^2 — the planet losing more energy than it absorbs.",
      "parameter_overrides": {
        "RadiationFundamentals.toa_forcing.F_L": 250.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.toa_forcing.F_S",
          "time": 0.0,
          "expected": 239.74999999999997
        },
        {
          "variable": "RadiationFundamentals.toa_forcing.F_net",
          "time": 0.0,
          "expected": -10.250000000000028
        }
      ]
    },
    {
      "id": "toa_forcing_high_solar_namespace_isolation",
      "description": "Overrides toa_forcing.S_0 to 1800 W/m^2. Pins toa_forcing.F_S = 1800/4·0.7 = 315.0 W/m^2, toa_forcing.F_net = F_S - F_L = 315.0 - 239.75 = 75.25 W/m^2 (strong positive imbalance — planet gaining energy), and energy_balance.F_S UNCHANGED at 239.75 W/m^2 — energy_balance and toa_forcing carry independent `S_0` parameters and the fully-namespaced override must not leak across the subsystem boundary.",
      "parameter_overrides": {
        "RadiationFundamentals.toa_forcing.S_0": 1800.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.toa_forcing.F_S",
          "time": 0.0,
          "expected": 315.0
        },
        {
          "variable": "RadiationFundamentals.toa_forcing.F_net",
          "time": 0.0,
          "expected": 75.25
        },
        {
          "variable": "RadiationFundamentals.energy_balance.F_S",
          "time": 0.0,
          "expected": 239.74999999999997
        }
      ]
    },
    {
      "id": "toa_forcing_zero_albedo_R_p_0_0",
      "description": "Overrides toa_forcing.R_p to 0.0 (perfect absorber). Pins toa_forcing.F_S = 1370/4·1.0 = 342.5 W/m^2 and toa_forcing.F_net = F_S - F_L = 342.5 - 239.75 = 102.75 W/m^2 — the maximum top-of-atmosphere energy gain at the canonical solar constant and equilibrium longwave flux.",
      "parameter_overrides": {
        "RadiationFundamentals.toa_forcing.R_p": 0.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "RadiationFundamentals.toa_forcing.F_S",
          "time": 0.0,
          "expected": 342.5
        },
        {
          "variable": "RadiationFundamentals.toa_forcing.F_net",
          "time": 0.0,
          "expected": 102.75
        }
      ]
    }
  ]
}