GlobalWarmingPotential

{
  "reference": {
    "notes": "source_ref: GasChem.jl@280ee50fbc8fb6d8bdf4b12c9ef1c506fe890551:src/climate_forcing.jl:182\n\nUpstream `GlobalWarmingPotential` is an MTK `@component` declaring two `@constants` (`τ_CO2` = 150·yr·s ≈ 4.7336e9 s, the effective CO₂ atmospheric lifetime per S&P p. 1043 assumed value, and `a_CO2` = 1.0, the reference radiative efficiency of CO₂ — normalized so the GWP ratio is dimensionless), three `@parameters` (`τ_A` with no upstream default — the atmospheric lifetime of species A, `a_A` with no upstream default — the radiative efficiency of species A relative to CO₂, and `t_f` = 100·yr·s ≈ 3.1558e9 s, the time horizon for the GWP integration), five time-indexed `@variables` (`GWP` the global warming potential ratio, `AGWP_A` and `AGWP_CO2` the absolute GWPs of species A and CO₂, `decay_integral_A` and `decay_integral_CO2` the exponential-decay time integrals — all algebraic with no derivative), and five algebraic equations (`decay_integral_A ~ τ_A · (1 - exp(-t_f/τ_A))`, `decay_integral_CO2 ~ τ_CO2 · (1 - exp(-t_f/τ_CO2))`, `AGWP_A ~ a_A · decay_integral_A`, `AGWP_CO2 ~ a_CO2 · decay_integral_CO2`, `GWP ~ AGWP_A / AGWP_CO2`). Identical structure preserved here. Upstream structural test (`GlobalWarmingPotential structural verification`, test/climate_forcing_test.jl:148-158) asserts `length(equations(sys)) == 5` and that `GWP` and `AGWP_A` are in the unknowns list — matched here by the five entries in `equations` and the GWP / AGWP_A entries typed as `state` in `variables`.\n\nThe two upstream `@constants` (`τ_CO2`, `a_CO2`) are encoded here as `type: parameter` with the upstream default values, matching the rig-wide convention used by sibling .esm migrations (wien.esm at components/gaschem/radiation/wien.esm encodes its `b` `@constants` the same way; chapman.esm at components/gaschem/stratospheric/chapman.esm encodes its four `@constants` k2_A/k4_A/C_k4/T_ref the same way). This makes the CO₂-reference values overridable from a downstream consumer's `parameter_overrides` block — useful for sensitivity studies that probe the assumed CO₂ lifetime (the 150-yr value is a simplification — the actual CO₂ removal involves multiple coupled reservoir timescales from ~5 yr to >1000 yr, not a single first-order decay, so the upstream choice is an effective-lifetime stand-in noted on S&P p. 1043). The three upstream `@parameters` (`τ_A`, `a_A`, `t_f`) are also `type: parameter` with the canonical CO₂ self-reference defaults: τ_A = 150·yr·s = τ_CO2 and a_A = 1.0 = a_CO2 so that the default-parameter run gives GWP = 1.0 exactly (the CO₂ self-reference scenario from the upstream test at test/climate_forcing_test.jl:160-179). This default choice differs from the upstream MTK model (which leaves τ_A and a_A unbound), but is the natural way to make the component runnable without overrides; downstream consumers will always override τ_A and a_A to the species-specific values (CH₄ at τ=12 yr / a=140, N₂O at τ=114 yr / a=326, SF₆ at τ≈3200 yr / a≈22000, etc.).\n\nObservability classification: this component is observed-only — every output variable is given by a single algebraic equation in the inputs (no time derivative, the `(t)` time index has no role since there is no `D(·)` operator in any of the five equations). Test scenarios use `time_span: [0.0, 1.0]` and sample at t=0 to mirror the convention used by sibling observed-only ESM files in this rig (wien.esm at components/gaschem/radiation/wien.esm, typical.esm at components/gaschem/combined/typical.esm, slip.esm at components/aerosol/particle_dyn/slip.esm) — algebraic identities have no time dependence and converge to the same fixed-point in one nonlinear-solver step regardless of the sampling time.\n\nPhysics structure: the GWP framework (S&P §23.3) defines AGWP_A = ∫₀^{tf} a_A(t)·`[A](t)` dt where `[A](t)` is the time-evolving concentration perturbation from a 1 kg pulse emission and a_A is the instantaneous radiative efficiency. For species with first-order exponential decay `[A](t)` ∝ exp(-t/τ_A) and constant radiative efficiency a_A, the integral collapses analytically to AGWP_A = a_A · τ_A · (1 - exp(-t_f/τ_A)) — the τ·(1-exp(-tf/τ)) factor is the time-integrated exponential-decay normalization that appears in both the species-A and CO₂-reference paths. The GWP ratio (Problem 23.3 closed form) is the dimensionless ratio AGWP_A / AGWP_CO2, designed so that GWP_CO2 ≡ 1 by construction (independent of t_f) — anchoring the upstream CO2 self-reference test which asserts GWP = 1 at any time horizon when τ_A = τ_CO2 and a_A = a_CO2.\n\nNumerical defaults (S&P Ch. 23 IPCC AR4 baseline, with CO₂ self-reference for τ_A and a_A):\n  τ_CO2 = 150·yr·s = 4733640000.0 s   (Effective CO₂ atmospheric lifetime, S&P p. 1043)\n  a_CO2 = 1.0                          (Reference radiative efficiency, normalized)\n  τ_A   = 150·yr·s = 4733640000.0 s   (Species lifetime, defaults to τ_CO2 → CO₂ self-reference)\n  a_A   = 1.0                          (Radiative efficiency relative to CO₂, defaults to a_CO2 → CO₂ self-reference)\n  t_f   = 100·yr·s = 3155760000.0 s   (Time horizon, S&P canonical 100-yr default)\nNote yr_to_s = 365.25 · 24 · 3600 = 31557600.0 s is the IUPAC Julian year used throughout the upstream Julia code and reproduced exactly here.\nAt these defaults:\n  decay_integral_A   = 4733640000.0 · (1 - exp(-100/150)) = 4733640000.0 · 0.4865829442... = 2303308188.662561 s\n  decay_integral_CO2 = (same — τ_A = τ_CO2)                                              = 2303308188.662561 s\n  AGWP_A             = 1.0 · 2303308188.662561                                            = 2303308188.662561 s\n  AGWP_CO2           = 1.0 · 2303308188.662561                                            = 2303308188.662561 s\n  GWP                = 2303308188.662561 / 2303308188.662561                              = 1.0\nThis matches the upstream `GlobalWarmingPotential CO2 self-reference` test (test/climate_forcing_test.jl:160-179) which asserts GWP = 1.0 at rtol=1e-6 for τ_A=150yr, a_A=1, across t_f ∈ {20, 100, 500} years.\n\nUpstream test reproduction:\n- The upstream `GlobalWarmingPotential structural verification` test (test/climate_forcing_test.jl:148-158) asserts the system has 5 equations and both GWP and AGWP_A are unknowns — reproduced by the .esm structural shape (5 entries in `equations`, GWP and AGWP_A typed as `state` along with AGWP_CO2, decay_integral_A, decay_integral_CO2).\n- The upstream `GlobalWarmingPotential CO2 self-reference` test (test/climate_forcing_test.jl:160-179) asserts GWP = 1.0 at rtol=1e-6 for τ_A=150·yr·s, a_A=1, at three time horizons t_f ∈ {20, 100, 500}·yr·s. Reproduced by `co2_self_reference_t_f_20yr`, `co2_self_reference_t_f_100yr`, `co2_self_reference_t_f_500yr` — three .esm tests pinning GWP = 1.0 at rel=1e-10 (tighter than upstream rtol=1e-6 because the algebra of the @component is a closed-form division of two identical floating-point values, exact to within 0 ULP — IEEE-754 floating-point division of x/x is exactly 1.0 for any finite non-zero x).\n- The upstream `GlobalWarmingPotential CH4 estimate` test (test/climate_forcing_test.jl:181-194) asserts the pure helper function `GWP_exponential(12, 140, 100)` ≈ 23 at rtol=0.1 (within 10% of IPCC tabulated GWP₁₀₀ for CH₄). The pure helper is a Julia-only artifact (the .esm spec has no helper functions), so the CH₄ scenario is reproduced via the @component by binding τ_A=12·yr·s, a_A=140, t_f=100·yr·s in `ch4_100yr_gwp` and pinning GWP = 23.012128662648355 at rel=1e-10. (The exact pinned value vs the IPCC AR4 tabulated 23 reflects the difference between the upstream 4-digit-rounded τ_CO2 = 150 yr / a_CO2 = 1 closed-form and the IPCC TAR atmospheric-chemistry model used for the AR4 table — within the upstream's stated 10% policy bound.)\n- The upstream `GlobalWarmingPotential time horizon dependence` test (test/climate_forcing_test.jl:196-221) asserts that for short-lived species (τ=2 yr) the GWP decreases with increasing t_f and for long-lived species (τ=10000 yr) the GWP increases with t_f. The .esm runner does not directly support cross-test monotonicity assertions; reproduced here by pinning all six absolute GWP values at rel=1e-10 across the (τ ∈ {2, 10000} yr) × (t_f ∈ {20, 100, 500} yr) Cartesian grid in `short_lived_tau_2yr_t_f_{20,100,500}yr` and `long_lived_tau_10000yr_t_f_{20,100,500}yr` — by the analytic monotonicity of τ·(1-exp(-tf/τ))/τ_CO2·(1-exp(-tf/τ_CO2)) in t_f (the function is strictly monotone decreasing in t_f when τ < τ_CO2 and strictly increasing when τ > τ_CO2), the cross-test inequalities are exact under the closed-form division.\n- The upstream `GWP_exponential function` test (test/climate_forcing_test.jl:223-237) asserts (i) GWP_exponential(150, 1, 100) = 1.0 at rtol=1e-10 (already covered by `co2_self_reference_t_f_100yr`); (ii) GWP_exponential(0.001, 1, 100) < 0.01 (very short-lived → GWP → 0); (iii) GWP_exponential(1e6, 1, 100) ≈ 100/(150·(1-exp(-100/150))) at rtol=0.01 (very long-lived → GWP → asymptotic limit a_A·t_f/AGWP_CO2). Reproduced via the @component by binding τ_A to the limit values in `very_short_lived_tau_0p001yr` (pins GWP = 1.3700988932064815e-05 at rel=1e-10) and `very_long_lived_tau_1e6yr` (pins GWP = 1.3700303905452804 at rel=1e-10).\n- The upstream `N2O GWP estimate` test (test/climate_forcing_test.jl:239-249) asserts GWP_exponential(114, 326, 100) ≈ 296 at rtol=0.1 (within 10% of IPCC tabulated GWP₁₀₀ for N₂O). Reproduced via the @component by binding τ_A=114·yr·s, a_A=326, t_f=100·yr·s in `n2o_100yr_gwp` and pinning GWP = 297.3892393811234 at rel=1e-10. (The exact pinned value matches the IPCC AR4 tabulated 296 ± 10%.)\n\nTolerance rationale (model-level rel=1e-10): observed-only algebraic system with a small number of arithmetic operations per equation. Each equation evaluates one of {division, multiplication, subtraction, exp()}; the worst-case error path is the exp() in the decay-integral equation, which is IEEE-754 correctly-rounded to within ~1 ULP ≈ 1e-16 relative at any of the tested magnitudes (decay_integrals range from ~3e4 s at τ_A=0.001·yr to ~5e9 s at τ_A=500·yr, with GWPs spanning 1e-5 to 3e2). 1e-10 leaves 6 orders of magnitude of headroom over the IEEE-754 floor and matches the convention used by sibling algebraic .esm files in this rig (wien.esm at rel=1e-10, typical.esm at rel=1e-10, slip.esm at rel=1e-9). The upstream Julia tests use rtol=1e-6 (CO₂ self-reference structural check), rtol=0.1 (CH₄ and N₂O policy-tolerance bound), rtol=1e-10 (GWP_exponential self-consistency identity), and rtol=0.01 (very-long-lived asymptotic limit) — re-asserted here at the uniform model-level rel=1e-10 which is tighter than upstream for the structural and policy-bound tests and matches upstream for the identity/asymptotic tests.\n\nUnit balance (verified): all five equations balance dimensionally.\n  `decay_integral_A ~ τ_A · (1 - exp(-t_f/τ_A))`: s · (1 - exp(s/s)) = s · dimensionless = s ✓\n  `decay_integral_CO2 ~ τ_CO2 · (1 - exp(-t_f/τ_CO2))`: s · dimensionless = s ✓\n  `AGWP_A ~ a_A · decay_integral_A`: dimensionless · s = s ✓ (matches AGWP_A unit `u\"s\"`)\n  `AGWP_CO2 ~ a_CO2 · decay_integral_CO2`: dimensionless · s = s ✓\n  `GWP ~ AGWP_A / AGWP_CO2`: s / s = dimensionless ✓ (matches GWP unit `u\"1\"`)\nThe migrated `.esm` preserves the upstream units verbatim — all timescales (τ_A, τ_CO2, t_f, decay_integrals, AGWPs) in SI seconds, all radiative-efficiency ratios (a_A, a_CO2, GWP) dimensionless. SI throughout; no unit conversion at parse or runtime."
  },
  "tolerance": {
    "rel": 1e-10
  },
  "variables": {
    "τ_CO2": {
      "type": "parameter",
      "units": "s",
      "default": 4733640000.0,
      "description": "Effective CO₂ atmospheric lifetime for GWP calculations (S&P p. 1043, assumed value). The upstream default 150·yr·s = 150 · 31557600 = 4733640000.0 s is the simplified single-timescale stand-in for the actual CO₂ removal process, which involves multiple coupled reservoir timescales spanning ~5 yr (ocean mixed-layer uptake) to >1000 yr (deep-ocean / lithospheric uptake) and cannot be exactly captured by a first-order exponential decay. The 150-yr value is the conventional choice from IPCC TAR (2001) that the closed-form GWP formula uses; modern impulse-response analyses (Joos et al. 2013) characterize the CO₂ airborne fraction as a sum of three to four exponentials plus a long-lived constant term. The upstream component is overridable at this parameter to support sensitivity studies that probe the τ_CO2 assumption — a downstream consumer can bind τ_CO2 to its preferred effective lifetime (e.g., 50 yr for short-horizon analysis, 1000 yr for long-horizon analysis) without forking the component."
    },
    "a_CO2": {
      "type": "parameter",
      "units": "1",
      "default": 1.0,
      "description": "Reference radiative efficiency of CO₂ (S&P §23.3, normalized). The upstream default 1.0 normalizes the GWP ratio to be dimensionless and pins GWP_CO2 ≡ 1 by construction (any species with τ_A = τ_CO2 and a_A = 1 will have GWP = 1 exactly). The actual instantaneous radiative efficiency of CO₂ is ~1.4e-15 W/m²/molec (IPCC AR4 Ch. 2 Table 2.14), but the GWP framework absorbs this absolute scale into the ratio, leaving only the lifetime-and-efficiency ratios that determine the relative climate impact of species A vs CO₂. Overridable to support cross-framework comparisons (e.g., the IPCC AR5 update introduced different efficacy parameters Eᵢ that effectively scale a_CO2 by species)."
    },
    "τ_A": {
      "type": "parameter",
      "units": "s",
      "default": 4733640000.0,
      "description": "Atmospheric lifetime of species A (S&P §23.3). The upstream MTK component leaves τ_A unbound (no default); the .esm migration defaults it to τ_CO2 = 150·yr·s = 4733640000.0 s so the default-parameter run gives the CO₂ self-reference scenario (GWP = 1.0) — a sentinel default that makes the regression-detection signal obvious if the GWP equation is accidentally rewired (any GWP ≠ 1 at the defaults flags a structural break). Canonical species-specific values for the IPCC AR4 GWP table (S&P p. 1042): CH₄ at ~12·yr·s = 3.787e8 s (perturbation lifetime including OH-feedback amplification factor), N₂O at ~114·yr·s = 3.598e9 s, SF₆ at ~3200·yr·s = 1.010e11 s, CO₂ at 150·yr·s = 4.734e9 s (effective single-timescale assumed value, matches τ_CO2 default)."
    },
    "a_A": {
      "type": "parameter",
      "units": "1",
      "default": 1.0,
      "description": "Radiative efficiency of species A relative to CO₂ (S&P §23.3, dimensionless). The upstream MTK component leaves a_A unbound (no default); the .esm migration defaults it to 1.0 = a_CO2 so the default-parameter run gives the CO₂ self-reference scenario. Canonical species-specific values back-calculated from the IPCC AR4 GWP table (S&P p. 1042) at the upstream τ_CO2 = 150 yr / t_f = 100 yr defaults: CH₄ at a_A ≈ 140 (to give GWP₁₀₀ ≈ 23), N₂O at a_A ≈ 326 (to give GWP₁₀₀ ≈ 296), SF₆ at a_A ≈ 22800 (to give GWP₁₀₀ ≈ 22800 — for long-lived species the ratio limit τ_A·1/(τ_CO2·(1-exp(-t_f/τ_CO2))) approaches a_A/(1-exp(-t_f/τ_CO2)) · τ_A/τ_CO2 which simplifies further as τ_A → ∞). The dimensionless scaling reflects the design choice that radiative efficiency is reported as a per-molecule (or per-mass) instantaneous forcing relative to the reference CO₂ value — the absolute W/m²/molec scale of CO₂ is absorbed by the GWP ratio."
    },
    "t_f": {
      "type": "parameter",
      "units": "s",
      "default": 3155760000.0,
      "description": "Time horizon for the GWP calculation (S&P §23.3). The upstream default 100·yr·s = 100 · 31557600 = 3155760000.0 s is the IPCC AR4 canonical 100-year reporting horizon for the GWP₁₀₀ values published in policy frameworks (Kyoto Protocol, Paris Agreement Annex B). Three time horizons are commonly reported: 20-yr (short-term policy / methane emphasis), 100-yr (canonical reporting / Kyoto), 500-yr (long-term policy / N₂O emphasis). The choice of t_f has a large effect on the GWP for species whose lifetime is dissimilar from τ_CO2: short-lived species (CH₄ at τ ≈ 12 yr) have larger GWP at shorter t_f because their integrated forcing is concentrated in the first decade while CO₂'s is spread over centuries (CH₄ GWP₂₀ ≈ 72 vs GWP₁₀₀ ≈ 23 vs GWP₅₀₀ ≈ 7); long-lived species (SF₆ at τ ≈ 3200 yr) have larger GWP at longer t_f because their integrated forcing keeps accumulating after CO₂'s has saturated."
    },
    "decay_integral_A": {
      "type": "unknown",
      "units": "s",
      "description": "Time integral of the exponential-decay impulse-response function for species A (S&P §23.3, exponential-decay closed form). Equals τ_A · (1 - exp(-t_f/τ_A)) which is the analytic closed form for ∫₀^{tf} exp(-t/τ_A) dt — the dimensional factor that converts the instantaneous radiative efficiency a_A into the integrated absolute GWP. Limiting behavior: as t_f → ∞ the integral approaches τ_A (the species reaches its full atmospheric inventory); as t_f → 0 the integral approaches t_f (the species hasn't decayed yet); for t_f = τ_A the integral equals τ_A · (1 - 1/e) ≈ 0.632 · τ_A. The integrand exp(-t/τ_A) is the normalized impulse response of a pure first-order decay process — accurate for species with a single dominant removal mechanism (CH₄ via OH oxidation, N₂O via stratospheric photolysis, halocarbons via stratospheric photolysis + OH), inaccurate for species with multiple competing removal timescales (CO₂'s ocean-uptake / land-uptake / deep-ocean-uptake cascade — handled by the effective-lifetime stand-in)."
    },
    "decay_integral_CO2": {
      "type": "unknown",
      "units": "s",
      "description": "Time integral of the exponential-decay impulse-response function for CO₂ (S&P §23.3, exponential-decay closed form). Equals τ_CO2 · (1 - exp(-t_f/τ_CO2)) which is the analytic closed form for ∫₀^{tf} exp(-t/τ_CO2) dt — the CO₂-reference denominator of the GWP ratio. At the upstream τ_CO2 = 150·yr·s default, decay_integral_CO2 saturates slowly with t_f: at t_f=20 yr the integral is 590884570.0455421 s (about 12.5% of τ_CO2 — only the first 13 years of CO₂'s integrated forcing have accumulated), at t_f=100 yr it is 2303308188.662561 s (about 49% of τ_CO2), at t_f=500 yr it is 4564772158.131712 s (about 96% of τ_CO2 — nearly saturated)."
    },
    "AGWP_A": {
      "type": "unknown",
      "units": "s",
      "description": "Absolute Global Warming Potential of species A (S&P Eq. 23.6). Equals a_A · decay_integral_A = a_A · τ_A · (1 - exp(-t_f/τ_A)). The units (s) reflect the time-integration; the dimensionless a_A and the seconds τ_A multiply to give an integrated forcing with units of (a_A_units · s) which the GWP ratio then cancels against AGWP_CO2 to produce the dimensionless GWP. The 'absolute' qualifier distinguishes AGWP from the normalized GWP ratio: AGWP carries the absolute integrated radiative forcing magnitude (which can be scaled to physical W/m²·yr by multiplying by the absolute CO₂ radiative efficiency of ~1.4e-15 W/m²/molec), while GWP is a dimensionless comparison ratio that abstracts away the absolute scale."
    },
    "AGWP_CO2": {
      "type": "unknown",
      "units": "s",
      "description": "Absolute Global Warming Potential of CO₂ (S&P Eq. 23.6). Equals a_CO2 · decay_integral_CO2 = a_CO2 · τ_CO2 · (1 - exp(-t_f/τ_CO2)). At the upstream defaults (a_CO2 = 1, τ_CO2 = 150·yr·s, t_f = 100·yr·s), AGWP_CO2 = 2303308188.662561 s. AGWP_CO2 is the CO₂-reference denominator of the GWP ratio — its magnitude alone has no physical interpretation (the absolute CO₂ scale is set to 1 by convention), but its variation with t_f and τ_CO2 directly determines how the GWP ratio responds to those parameters."
    },
    "GWP": {
      "type": "unknown",
      "units": "1",
      "description": "Global Warming Potential of species A relative to CO₂ (S&P Eq. 23.5 / Problem 23.3). Equals AGWP_A / AGWP_CO2 = a_A · τ_A · (1 - exp(-t_f/τ_A)) / [a_CO2 · τ_CO2 · (1 - exp(-t_f/τ_CO2))]. Dimensionless by construction. The canonical GWP₁₀₀ table from IPCC AR4 (S&P p. 1042) reports CH₄ ≈ 23 (medium-lived, OH-removed), N₂O ≈ 296 (long-lived, stratospheric photolysis-removed), SF₆ ≈ 22800 (very-long-lived, only stratospheric photolysis removal), HFC-23 ≈ 14800, CFC-12 ≈ 10900. The three-order-of-magnitude span anchors the policy design choice of representing GWP as a derived ratio rather than a hardcoded table — different t_f horizons or different τ_CO2 assumptions give different GWP values for the same species, and the ratio expression makes those sensitivities explicit. By construction GWP_CO2 = 1 at any (t_f, τ_CO2) when τ_A = τ_CO2 and a_A = 1."
    }
  },
  "equations": [
    {
      "lhs": "decay_integral_A",
      "rhs": {
        "op": "*",
        "args": [
          "τ_A",
          {
            "op": "-",
            "args": [
              1.0,
              {
                "op": "exp",
                "args": [
                  {
                    "op": "/",
                    "args": [
                      {
                        "op": "*",
                        "args": [
                          -1,
                          "t_f"
                        ]
                      },
                      "τ_A"
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "decay_integral_CO2",
      "rhs": {
        "op": "*",
        "args": [
          "τ_CO2",
          {
            "op": "-",
            "args": [
              1.0,
              {
                "op": "exp",
                "args": [
                  {
                    "op": "/",
                    "args": [
                      {
                        "op": "*",
                        "args": [
                          -1,
                          "t_f"
                        ]
                      },
                      "τ_CO2"
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "AGWP_A",
      "rhs": {
        "op": "*",
        "args": [
          "a_A",
          "decay_integral_A"
        ]
      }
    },
    {
      "lhs": "AGWP_CO2",
      "rhs": {
        "op": "*",
        "args": [
          "a_CO2",
          "decay_integral_CO2"
        ]
      }
    },
    {
      "lhs": "GWP",
      "rhs": {
        "op": "/",
        "args": [
          "AGWP_A",
          "AGWP_CO2"
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "co2_self_reference_t_f_100yr",
      "description": "Default scenario: CO₂ self-reference at the upstream t_f = 100·yr·s canonical reporting horizon. With τ_A = τ_CO2 = 4733640000.0 s and a_A = a_CO2 = 1.0, the GWP equation simplifies to AGWP_A / AGWP_CO2 = (1·τ_CO2·X) / (1·τ_CO2·X) = 1.0 exactly where X = 1 - exp(-100/150) ≈ 0.4865829442 is the common decay-integral factor. Reproduces the upstream `GlobalWarmingPotential CO2 self-reference` test (GasChem.jl test/climate_forcing_test.jl:160-179) middle case (t_f = 100 yr): upstream asserts GWP ≈ 1.0 at rtol=1e-6, this one pins GWP = 1.0 (exact IEEE-754 1.0 from x/x division at rel=1e-10) along with the intermediate-state values that anchor the structural regression-detection signal at all five state variables.",
      "parameter_overrides": {},
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 1.0,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "co2_self_reference_t_f_20yr",
      "description": "CO₂ self-reference at the 20·yr·s short-horizon: τ_A = τ_CO2 and a_A = a_CO2 = 1.0, t_f = 20·yr·s = 631152000.0 s. GWP = 1.0 exactly (as in the 100·yr case — the GWP_CO2 ≡ 1 identity is independent of t_f when τ_A = τ_CO2 and a_A = 1 — anchoring the principle that the CO₂-vs-CO₂ ratio is unity at any reporting horizon). decay_integral_A and decay_integral_CO2 both equal τ_CO2 · (1 - exp(-20/150)) · = 4733640000.0 · 0.124836... = 590884570.0455421 s. Reproduces the upstream `GlobalWarmingPotential CO2 self-reference` test (GasChem.jl test/climate_forcing_test.jl:160-179) short-horizon case (t_f = 20 yr).",
      "parameter_overrides": {
        "t_f": 631152000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 1.0,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 590884570.0455421,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_CO2",
          "time": 0.0,
          "expected": 590884570.0455421,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 590884570.0455421,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 590884570.0455421,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "co2_self_reference_t_f_500yr",
      "description": "CO₂ self-reference at the 500·yr·s long-horizon: τ_A = τ_CO2 and a_A = a_CO2 = 1.0, t_f = 500·yr·s = 15778800000.0 s. GWP = 1.0 exactly. decay_integral_A and decay_integral_CO2 both equal τ_CO2 · (1 - exp(-500/150)) · = 4733640000.0 · 0.96435... = 4564772158.131712 s — saturated at ~96% of τ_CO2 because t_f >> τ_CO2 (the species has had 3.33 lifetimes to decay). Reproduces the upstream `GlobalWarmingPotential CO2 self-reference` test (GasChem.jl test/climate_forcing_test.jl:160-179) long-horizon case (t_f = 500 yr).",
      "parameter_overrides": {
        "t_f": 15778800000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 1.0,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 4564772158.131712,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_CO2",
          "time": 0.0,
          "expected": 4564772158.131712,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 4564772158.131712,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 4564772158.131712,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "ch4_100yr_gwp",
      "description": "CH₄ GWP₁₀₀ scenario: τ_A = 12·yr·s = 378691200.0 s (CH₄ perturbation lifetime including OH-feedback amplification, IPCC TAR Ch. 4), a_A = 140 (radiative efficiency relative to CO₂ back-calculated from the IPCC TAR GWP table value 23), t_f = 100·yr·s. Result: GWP = 23.012128662648355 — closed-form analytic value at rel=1e-10. Reproduces the upstream `GlobalWarmingPotential CH4 estimate` test (GasChem.jl test/climate_forcing_test.jl:181-194) which tests the pure helper function `GWP_exponential(12, 140, 100, τ_CO2=150)` against the IPCC tabulated GWP₁₀₀ ≈ 23 at rtol=0.1 (within 10% policy bound). The .esm migration cannot reproduce the pure function (no helper functions in spec), so the @component is bound to the equivalent parameter set; the resulting GWP matches the upstream pure-function output to within IEEE-754 precision because the @component and the pure function evaluate the same closed-form expression. Pins all five state variables to anchor the decay_integral_A = 378600174.1945313 s (96% of τ_A — CH₄ has decayed nearly completely over 100 yr) and AGWP_A = 53004024387.23438 s = 140 · decay_integral_A.",
      "parameter_overrides": {
        "τ_A": 378691200.0,
        "a_A": 140.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 23.012128662648355,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 53004024387.23438,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 378600174.1945313,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "n2o_100yr_gwp",
      "description": "N₂O GWP₁₀₀ scenario: τ_A = 114·yr·s = 3597566400.0 s (N₂O atmospheric lifetime, stratospheric photolysis + reaction with O(¹D)), a_A = 326 (radiative efficiency relative to CO₂ back-calculated from the IPCC TAR GWP table value 296), t_f = 100·yr·s. Result: GWP = 297.3892393811234 — closed-form analytic value at rel=1e-10. Reproduces the upstream `N2O GWP estimate` test (GasChem.jl test/climate_forcing_test.jl:239-249) which tests the pure helper function `GWP_exponential(114, 326, 100, τ_CO2=150)` against the IPCC tabulated GWP₁₀₀ ≈ 296 at rtol=0.1 (within 10% policy bound). decay_integral_A = 2101162792.290405 s = τ_A · (1 - exp(-100/114)) · = 3597566400 · 0.58404... — N₂O has not fully decayed at 100 yr because its lifetime is comparable to the reporting horizon (~88% lifetime fraction utilized).",
      "parameter_overrides": {
        "τ_A": 3597566400.0,
        "a_A": 326.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 297.3892393811234,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 684979070286.672,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 2101162792.290405,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "short_lived_tau_2yr_t_f_20yr",
      "description": "First entry in the short-lived `short_lived_tau_2yr_t_f_*` series (t_f = 20 / 100 / 500 yr) that reproduces the upstream `GlobalWarmingPotential time horizon dependence` test (GasChem.jl test/climate_forcing_test.jl:196-209) short-lived case which asserts strict monotonic decrease of GWP across t_f ∈ [20, 100, 500] yr at τ_A = 2 yr, a_A = 100. The .esm runner does not directly support cross-test monotonicity assertions; reproduced by pinning all three absolute GWP values at rel=1e-10 — by the analytic monotonicity of τ_A·(1-exp(-tf/τ_A))/τ_CO2·(1-exp(-tf/τ_CO2)) in t_f when τ_A < τ_CO2, the cross-test inequalities GWP_20 > GWP_100 > GWP_500 are exact. At t_f = 20·yr·s, τ_A = 2·yr·s = 63115200.0 s, a_A = 100: GWP = 10.680992155454103. The CH₄-like profile (short τ, moderate a) at the short-horizon — short-lived species are amplified at short t_f because their integrated forcing concentrates in the first few years while CO₂'s spreads over the full 150-yr decay.",
      "parameter_overrides": {
        "τ_A": 63115200.0,
        "a_A": 100.0,
        "t_f": 631152000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 10.680992155454103,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 6311233457.435306,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 63112334.574353054,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 590884570.0455421,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "short_lived_tau_2yr_t_f_100yr",
      "description": "Second entry in the `short_lived_tau_2yr_t_f_*` series. At t_f = 100·yr·s, τ_A = 2·yr·s, a_A = 100: GWP = 2.7401977864129625. The decay_integral_A is fully saturated at decay_integral_A ≈ τ_A = 63115200.0 s (the species has decayed >99% over 100 yr = 50 lifetimes, so 1 - exp(-50) ≈ 1 - 2e-22 = 1.0 exactly at IEEE-754 precision) while decay_integral_CO2 is at 49% of τ_CO2. The 4× drop from GWP_20 ≈ 10.68 to GWP_100 ≈ 2.74 reflects the short-lived species' inability to keep contributing forcing past its ~10-yr saturation point while CO₂ continues accumulating.",
      "parameter_overrides": {
        "τ_A": 63115200.0,
        "a_A": 100.0,
        "t_f": 3155760000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 2.7401977864129625,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 6311520000.0,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 63115200.0,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "short_lived_tau_2yr_t_f_500yr",
      "description": "Third entry in the `short_lived_tau_2yr_t_f_*` series (largest t_f). At t_f = 500·yr·s, τ_A = 2·yr·s, a_A = 100: GWP = 1.3826582754533807. decay_integral_A = 63115200.0 s (still saturated at τ_A — short species cannot decay further once they're gone), decay_integral_CO2 = 4564772158.131712 s (saturated at 96% of τ_CO2). The continued drop from GWP_100 ≈ 2.74 to GWP_500 ≈ 1.38 reflects CO₂'s ongoing accumulation past the species' saturation point. By construction, in the τ_A → 0 limit GWP → 0 (species disappears immediately, contributes zero integrated forcing) at any t_f; in the τ_A << τ_CO2 with t_f >> τ_A regime, GWP → a_A · τ_A / decay_integral_CO2(t_f) which is the asymptotic short-lived-species formula.",
      "parameter_overrides": {
        "τ_A": 63115200.0,
        "a_A": 100.0,
        "t_f": 15778800000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 1.3826582754533807,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 6311520000.0,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 63115200.0,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 4564772158.131712,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "long_lived_tau_10000yr_t_f_20yr",
      "description": "First entry in the long-lived `long_lived_tau_10000yr_t_f_*` series that reproduces the upstream `GlobalWarmingPotential time horizon dependence` test (GasChem.jl test/climate_forcing_test.jl:211-220) long-lived case which asserts strict monotonic increase of GWP across t_f ∈ [20, 100, 500] yr at τ_A = 10000 yr, a_A = 100. The .esm runner does not directly support cross-test monotonicity assertions; reproduced by pinning all three absolute GWP values at rel=1e-10 — by the analytic monotonicity of τ_A·(1-exp(-tf/τ_A))/τ_CO2·(1-exp(-tf/τ_CO2)) in t_f when τ_A > τ_CO2, the cross-test inequalities GWP_20 < GWP_100 < GWP_500 are exact. At t_f = 20·yr·s, τ_A = 10000·yr·s = 315576000000.0 s, a_A = 100: GWP = 106.7080273409575. The SF₆-like profile (very long τ, moderate a) at the short-horizon — long-lived species are dampened at short t_f because their integrated forcing only just begins to accumulate in the first 20 years while CO₂ already has 13% of its full integration accumulated.",
      "parameter_overrides": {
        "τ_A": 315576000000.0,
        "a_A": 100.0,
        "t_f": 631152000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 106.7080273409575,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 63052126855.76962,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 630521268.5576962,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 590884570.0455421,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "long_lived_tau_10000yr_t_f_100yr",
      "description": "Second entry in the `long_lived_tau_10000yr_t_f_*` series. At t_f = 100·yr·s, τ_A = 10000·yr·s, a_A = 100: GWP = 136.32711767485262. decay_integral_A = 3140033664.772526 s (still ~1% of τ_A — the long-lived species has barely begun to decay over 100 yr) while decay_integral_CO2 = 2303308188.662561 s (49% saturated). The increase from GWP_20 ≈ 106.7 to GWP_100 ≈ 136.3 reflects the long-lived species continuing to accumulate integrated forcing while CO₂'s accumulation rate slows — the asymptotic regime where CO₂'s decay-integral is bounded by τ_CO2 while the long-lived species' is bounded only by t_f.",
      "parameter_overrides": {
        "τ_A": 315576000000.0,
        "a_A": 100.0,
        "t_f": 3155760000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 136.32711767485262,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 314003366477.25256,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 3140033664.772526,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "long_lived_tau_10000yr_t_f_500yr",
      "description": "Third entry in the `long_lived_tau_10000yr_t_f_*` series (largest t_f). At t_f = 500·yr·s, τ_A = 10000·yr·s, a_A = 100: GWP = 337.1651990635583. decay_integral_A = 15390823133.762674 s (still ~4.9% of τ_A) while decay_integral_CO2 = 4564772158.131712 s (saturated at 96% of τ_CO2). The continued increase from GWP_100 ≈ 136.3 to GWP_500 ≈ 337.2 reflects the long-lived species' near-linear accumulation regime (when t_f << τ_A, decay_integral_A ≈ t_f · 1 = t_f) versus CO₂'s saturation regime — the GWP ratio grows roughly as t_f / decay_integral_CO2_saturated which is the long-lived asymptotic limit a_A · t_f / [τ_CO2 · (1 - exp(-t_f/τ_CO2))].",
      "parameter_overrides": {
        "τ_A": 315576000000.0,
        "a_A": 100.0,
        "t_f": 15778800000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 337.1651990635583,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 1539082313376.2673,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 15390823133.762674,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 4564772158.131712,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "very_short_lived_tau_0p001yr",
      "description": "Very short-lived asymptotic limit: τ_A = 0.001·yr·s = 31557.6 s (~9 hours), a_A = 1.0, t_f = 100·yr·s. Result: GWP = 1.3700988932064815e-05 (~14 ppm of CO₂'s impact). decay_integral_A = 31557.600000000002 s (saturated at τ_A — the 0.001-yr species decays in <1 day so 100-yr integration is effectively τ_A · 1). Reproduces the upstream `GWP_exponential function` test (GasChem.jl test/climate_forcing_test.jl:223-237) very-short-lived case which asserts GWP_exponential(0.001, 1, 100) < 0.01 (qualitative bound, GWP → 0 in the τ → 0 limit because the species disappears before contributing any integrated forcing). The .esm migration tightens the assertion to rel=1e-10 on the closed-form value 1.37e-05 — the asymptotic limit a_A · τ_A / [τ_CO2 · (1 - exp(-t_f/τ_CO2))] = 1 · 31557.6 / 2303308188.66 = 1.370e-5 is reproduced to within 0.001% (the difference comes from the saturated 1 - exp(-100/0.001) ≈ 1 having no correction term).",
      "parameter_overrides": {
        "τ_A": 31557.6,
        "a_A": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 1.3700988932064815e-05,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 31557.600000000002,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 31557.600000000002,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "very_long_lived_tau_1e6yr",
      "description": "Very long-lived asymptotic limit: τ_A = 1e6·yr·s = 31557600000000.0 s (~1 million years, beyond any real GHG), a_A = 1.0, t_f = 100·yr·s. Result: GWP = 1.3700303905452804 (~37% above CO₂'s impact — the asymptotic limit a_A · t_f / decay_integral_CO2). decay_integral_A = 3155602217.259511 s (≈ t_f since 100·yr << 1e6·yr means the species has barely decayed) while decay_integral_CO2 = 2303308188.662561 s (49% of τ_CO2). Reproduces the upstream `GWP_exponential function` test (GasChem.jl test/climate_forcing_test.jl:223-237) very-long-lived case which asserts GWP_exponential(1e6, 1, 100) ≈ 100/(150·(1-exp(-100/150))) = 100/72.987... = 1.3700... at rtol=0.01 (within 1% of the asymptotic τ_A → ∞ limit a_A · t_f / [τ_CO2 · (1 - exp(-t_f/τ_CO2))]). The .esm migration tightens the assertion to rel=1e-10 on the closed-form value 1.37003... — the 0.001% deviation from the exact asymptotic limit 100/72.987 = 1.37005... reflects the exp(-100/1e6) ≈ 1 - 1e-4 first-order Taylor correction term that keeps decay_integral_A slightly below t_f.",
      "parameter_overrides": {
        "τ_A": 31557600000000.0,
        "a_A": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 1.3700303905452804,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 3155602217.259511,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 3155602217.259511,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "a_co2_override_halves_gwp",
      "description": "Override the upstream `@constants` a_CO2 to 2.0 (vs the upstream default 1.0) at the CO₂ self-reference defaults (τ_A=τ_CO2, a_A=1, t_f=100yr). Result: GWP = AGWP_A / AGWP_CO2 = 2303308188.66 / 4606616377.33 = 0.5 exactly. Anchors the design choice that a_CO2 behaves as a parameter (not a hardcoded constant) at the .esm boundary — a downstream consumer can re-base the GWP ratio against a different CO₂ reference (e.g., for cross-framework comparison with IPCC AR5's efficacy-weighted forcing values where Eᵢ = λᵢ/λ_CO2 effectively scales a_CO2 by species). Catches a regression where a_CO2 is accidentally fixed at 1.0 instead of being a tunable parameter.",
      "parameter_overrides": {
        "a_CO2": 2.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 0.5,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 2303308188.662561,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_CO2",
          "time": 0.0,
          "expected": 4606616377.325122,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "tau_co2_override_ch4_sensitivity",
      "description": "Override the upstream `@constants` τ_CO2 to 50·yr·s = 1577880000.0 s (vs the upstream default 150·yr·s) at the CH₄ scenario (τ_A=12yr, a_A=140, t_f=100yr). Result: GWP = 38.84965228063611 (~69% above the default-τ_CO2 GWP of 23.01 — because the shorter CO₂ lifetime means CO₂'s integrated forcing saturates faster, reducing AGWP_CO2 and increasing the GWP ratio). decay_integral_CO2 = 1364337163.2866135 s (saturated at 86% of τ_CO2 = 50 yr vs the default's 49% of 150 yr). Anchors the design choice that τ_CO2 behaves as a parameter (not a hardcoded constant), supporting sensitivity studies that probe the assumed CO₂ effective lifetime (the 150-yr value is a TAR convention; AR5 and AR6 use different impulse-response models that effectively shorten the early-time CO₂ removal).",
      "parameter_overrides": {
        "τ_A": 378691200.0,
        "a_A": 140.0,
        "τ_CO2": 1577880000.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "GWP",
          "time": 0.0,
          "expected": 38.84965228063611,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_A",
          "time": 0.0,
          "expected": 53004024387.23438,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "AGWP_CO2",
          "time": 0.0,
          "expected": 1364337163.2866135,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_A",
          "time": 0.0,
          "expected": 378600174.1945313,
          "tolerance": {
            "rel": 1e-10
          }
        },
        {
          "variable": "decay_integral_CO2",
          "time": 0.0,
          "expected": 1364337163.2866135,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "ch4_time_horizon_sweep",
      "description": "CH₄ GWP across the canonical 20/100/500-yr policy reporting horizons and intermediate values: τ_A = 12·yr·s = 378691200.0 s (perturbation lifetime), a_A = 140 fixed, t_f swept from 5 to 1000 yr on a log scale. Surfaces the canonical short-lived-species GWP-vs-t_f curve from S&P Figure 23.15: at t_f << τ_A the GWP is large (high amplification), at t_f ~ τ_A the GWP transitions through ~τ_A·a_A/τ_CO2, at t_f >> τ_A the GWP decays as ~τ_A·a_A/decay_integral_CO2(t_f). The three canonical reporting horizons (20/100/500 yr) bracket the policy-relevant range — methane's GWP₂₀ ≈ 72 vs GWP₁₀₀ ≈ 23 vs GWP₅₀₀ ≈ 7 illustrates the order-of-magnitude time-horizon sensitivity that makes the choice of reporting horizon a policy lever in its own right.",
      "initial_state": {},
      "parameters": {
        "τ_A": 378691200.0,
        "a_A": 140.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "t_f",
            "range": {
              "start": 157788000.0,
              "stop": 31557600000.0,
              "count": 30,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "ch4_gwp_vs_tf_loglog",
          "type": "line",
          "description": "CH₄ GWP as a function of time horizon t_f on a log-log plot, swept from 5·yr (short policy emphasis) to 1000·yr (multi-millennium horizon) at τ_A = 12·yr fixed. Strictly decreasing curve passing through the canonical IPCC values: GWP₂₀ ≈ 72 at t_f = 20·yr, GWP₁₀₀ ≈ 23 at t_f = 100·yr, GWP₅₀₀ ≈ 7 at t_f = 500·yr. The shape illustrates the short-lived-species GWP-vs-t_f decay: as t_f grows, the species' contribution saturates at τ_A while CO₂'s keeps growing, so the ratio decreases monotonically.",
          "x": {
            "variable": "t_f",
            "label": "t_f (s)"
          },
          "y": {
            "variable": "GWP",
            "label": "GWP (dimensionless)"
          }
        }
      ]
    },
    {
      "id": "species_lifetime_sweep_at_gwp100",
      "description": "Sweep species lifetime τ_A across 6 orders of magnitude [1·day, 100000·yr] at the GWP₁₀₀ reporting horizon (t_f = 100·yr fixed) and a_A = 100 fixed. Surfaces the canonical GWP-vs-τ_A monotonicity from S&P Figure 23.15 (alternate cut): GWP rises sharply from near-zero at τ_A → 0 (species disappears too fast to contribute), transitions through ~a_A · τ_A / decay_integral_CO2 (saturated species contributes a fixed amount), and asymptotes to ~a_A · t_f / decay_integral_CO2 in the τ_A → ∞ limit. The crossover region is around τ_A ~ τ_CO2 = 150 yr where the species and CO₂ have similar integration behaviors. Anchors the design observation that very-short-lived species have low GWP regardless of their radiative efficiency, while very-long-lived species saturate at the asymptotic a_A · t_f / decay_integral_CO2 limit independent of τ_A.",
      "initial_state": {},
      "parameters": {
        "a_A": 100.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "τ_A",
            "range": {
              "start": 86400.0,
              "stop": 3155760000000.0,
              "count": 50,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "gwp_vs_tau_a_loglog",
          "type": "line",
          "description": "GWP as a function of species lifetime τ_A on a log-log plot at fixed t_f=100·yr and a_A=100. Strictly increasing curve from near-zero at τ_A=1·day (GWP ≈ a_A · τ_A / decay_integral_CO2 ≈ 100 · 86400 / 2.30e9 ≈ 3.8e-6) through ~100 at τ_A=τ_CO2 (CO₂-self-reference inflection) to the asymptotic τ_A → ∞ limit a_A · t_f / decay_integral_CO2 ≈ 100 · 100·yr / 2.30e9 = 136.3 at τ_A=100000·yr. The two log-decade-wide transition near τ_A ~ τ_CO2 visualizes the time-integration crossover from CO₂-bounded (τ_A < τ_CO2 → species saturates first) to species-bounded (τ_A > τ_CO2 → CO₂ saturates first) regimes.",
          "x": {
            "variable": "τ_A",
            "label": "τ_A (s)"
          },
          "y": {
            "variable": "GWP",
            "label": "GWP (dimensionless)"
          }
        }
      ]
    },
    {
      "id": "lifetime_horizon_joint_sweep",
      "description": "Joint 2D sweep over the (τ_A, t_f) policy-design space at a_A = 100 fixed: τ_A from 1·yr to 10000·yr (covering CH₄/N₂O/SF₆/CFC range) and t_f from 20·yr to 500·yr (the canonical policy reporting horizons). Surfaces the full GWP(τ_A, t_f) policy-relevant surface that policy-makers implicitly choose from by picking a reporting horizon: at fixed a_A = 100, the GWP varies by ~factor-of-100 across this (τ_A, t_f) plane (from 0.7 at τ_A=1yr/t_f=500yr where the short species saturates and CO₂ does too, to 337 at τ_A=10000yr/t_f=500yr where the long species accumulates linearly while CO₂ saturates). The 2D heatmap is the canonical 'GWP-policy-design diagram' showing both the species-property axis (τ_A) and the policy-choice axis (t_f) simultaneously.",
      "initial_state": {},
      "parameters": {
        "a_A": 100.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "τ_A",
            "range": {
              "start": 31557600.0,
              "stop": 315576000000.0,
              "count": 20,
              "scale": "log"
            }
          },
          {
            "parameter": "t_f",
            "range": {
              "start": 631152000.0,
              "stop": 15778800000.0,
              "count": 20,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "gwp_heatmap_tau_a_tf",
          "type": "heatmap",
          "description": "GWP as a function of (τ_A, t_f) on a log-log plot at a_A=100 fixed: heatmap surface showing the bivariate dependence. The lower-right corner (τ_A=1yr, t_f=500yr) is the short-species / long-horizon limit where GWP is small (CO₂ has overtaken the saturated species); the upper-left corner (τ_A=10000yr, t_f=20yr) is the long-species / short-horizon limit where GWP is moderate (~107 — both species and CO₂ are still in their linear-accumulation regimes); the upper-right corner (τ_A=10000yr, t_f=500yr) is the long-species / long-horizon limit where GWP is large (~337 — species accumulates linearly while CO₂ saturates). The diagonal CO₂-self-reference line τ_A=τ_CO2=150yr is implicit (GWP=1 there at a_A=1, not at a_A=100 used here so the line is at GWP=100 here).",
          "x": {
            "variable": "τ_A",
            "label": "τ_A (s)"
          },
          "y": {
            "variable": "t_f",
            "label": "t_f (s)"
          },
          "value": {
            "variable": "GWP",
            "reduce": "final"
          }
        }
      ]
    }
  ]
}