SO2Equilibria

{
  "reference": {
    "notes": "source_ref: Aerosol.jl@c8c640bb:src/aqueous_equilibria.jl:240\nUpstream `SO2Equilibria` is an MTK `@component` where T, H_plus, and p_SO2 are `@variables` driven by a parent `AqueousEquilibria` system. For standalone serialization (and to make the component well-posed in isolation), T, H_plus, and p_SO2 are declared as parameters here — matching the bead's `(S, observed-only)` classification. The eleven algebraic equations are unchanged from upstream.\n\nTolerance rationale (model-level rel=1e-6): observed-only algebraic system (no ODE integration); 1e-6 covers float64 roundoff in the chained exp/multiplications of the van't Hoff K(T) and Henry/dissociation closed-form expressions across the atmospheric T range (273-318 K) and 9-decade [H+] sweep."
  },
  "tolerance": {
    "rel": 1e-06
  },
  "variables": {
    "T": {
      "type": "parameter",
      "units": "K",
      "default": 298.0,
      "description": "Temperature"
    },
    "H_plus": {
      "type": "parameter",
      "units": "mol/m^3",
      "default": 0.0001,
      "description": "Hydrogen ion concentration (1e-4 mol/m³ = pH 7 in pure water at 298 K)"
    },
    "p_SO2": {
      "type": "parameter",
      "units": "Pa",
      "default": 1.0,
      "description": "Partial pressure of SO2"
    },
    "R_gas": {
      "type": "parameter",
      "units": "J/mol/K",
      "default": 8.314,
      "description": "Gas constant"
    },
    "T_ref": {
      "type": "parameter",
      "units": "K",
      "default": 298.0,
      "description": "Reference temperature"
    },
    "H_SO2_298": {
      "type": "parameter",
      "units": "mol/m^3/Pa",
      "default": 0.012139156180606956,
      "description": "Henry's law constant for SO2 at 298 K (1.23 M/atm converted to mol/m³/Pa: 1.23 / 101325.0 * 1000.0)"
    },
    "dH_H_SO2": {
      "type": "parameter",
      "units": "J/mol",
      "default": -26150.0,
      "description": "Heat of dissolution for SO2 (-6.25 kcal/mol converted to J/mol; Seinfeld & Pandis Table 7.4)"
    },
    "K_s1_298": {
      "type": "parameter",
      "units": "mol/m^3",
      "default": 13.0,
      "description": "First dissociation constant at 298 K (1.3e-2 M converted to mol/m³)"
    },
    "K_s2_298": {
      "type": "parameter",
      "units": "mol/m^3",
      "default": 6.6e-05,
      "description": "Second dissociation constant at 298 K (6.6e-8 M converted to mol/m³)"
    },
    "dH_Ks1": {
      "type": "parameter",
      "units": "J/mol",
      "default": -17405.44,
      "description": "Enthalpy for K_s1 (-4.16 kcal/mol converted to J/mol; Seinfeld & Pandis Table 7.4)"
    },
    "dH_Ks2": {
      "type": "parameter",
      "units": "J/mol",
      "default": -9330.32,
      "description": "Enthalpy for K_s2 (-2.23 kcal/mol converted to J/mol; Seinfeld & Pandis Table 7.4)"
    },
    "H_SO2": {
      "type": "unknown",
      "units": "mol/m^3/Pa",
      "description": "Henry's law constant for SO2 at temperature T"
    },
    "K_s1": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "First dissociation constant at temperature T"
    },
    "K_s2": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Second dissociation constant at temperature T"
    },
    "SO2_aq": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Aqueous SO2 concentration [SO2.H2O]"
    },
    "HSO3_minus": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Bisulfite ion concentration [HSO3-]"
    },
    "SO3_2minus": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Sulfite ion concentration [SO3^2-]"
    },
    "S_IV_total": {
      "type": "unknown",
      "units": "mol/m^3",
      "description": "Total S(IV) concentration: [SO2.H2O] + [HSO3-] + [SO3^2-]"
    },
    "H_SO2_eff": {
      "type": "unknown",
      "units": "mol/m^3/Pa",
      "description": "Effective Henry's law constant for SO2 (accounts for dissociation)"
    },
    "alpha_0": {
      "type": "unknown",
      "units": "1",
      "description": "Mole fraction of SO2.H2O in S(IV) (dimensionless)"
    },
    "alpha_1": {
      "type": "unknown",
      "units": "1",
      "description": "Mole fraction of HSO3- in S(IV) (dimensionless)"
    },
    "alpha_2": {
      "type": "unknown",
      "units": "1",
      "description": "Mole fraction of SO3^2- in S(IV) (dimensionless)"
    }
  },
  "equations": [
    {
      "lhs": "H_SO2",
      "rhs": {
        "op": "*",
        "args": [
          "H_SO2_298",
          {
            "op": "exp",
            "args": [
              {
                "op": "*",
                "args": [
                  {
                    "op": "/",
                    "args": [
                      "dH_H_SO2",
                      "R_gas"
                    ]
                  },
                  {
                    "op": "+",
                    "args": [
                      {
                        "op": "/",
                        "args": [
                          1,
                          "T_ref"
                        ]
                      },
                      {
                        "op": "/",
                        "args": [
                          -1,
                          "T"
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "K_s1",
      "rhs": {
        "op": "*",
        "args": [
          "K_s1_298",
          {
            "op": "exp",
            "args": [
              {
                "op": "*",
                "args": [
                  -1,
                  {
                    "op": "/",
                    "args": [
                      "dH_Ks1",
                      "R_gas"
                    ]
                  },
                  {
                    "op": "+",
                    "args": [
                      {
                        "op": "/",
                        "args": [
                          1,
                          "T"
                        ]
                      },
                      {
                        "op": "/",
                        "args": [
                          -1,
                          "T_ref"
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "K_s2",
      "rhs": {
        "op": "*",
        "args": [
          "K_s2_298",
          {
            "op": "exp",
            "args": [
              {
                "op": "*",
                "args": [
                  -1,
                  {
                    "op": "/",
                    "args": [
                      "dH_Ks2",
                      "R_gas"
                    ]
                  },
                  {
                    "op": "+",
                    "args": [
                      {
                        "op": "/",
                        "args": [
                          1,
                          "T"
                        ]
                      },
                      {
                        "op": "/",
                        "args": [
                          -1,
                          "T_ref"
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "SO2_aq",
      "rhs": {
        "op": "*",
        "args": [
          "H_SO2",
          "p_SO2"
        ]
      }
    },
    {
      "lhs": "HSO3_minus",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "K_s1",
              "SO2_aq"
            ]
          },
          "H_plus"
        ]
      }
    },
    {
      "lhs": "SO3_2minus",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "K_s2",
              "HSO3_minus"
            ]
          },
          "H_plus"
        ]
      }
    },
    {
      "lhs": "S_IV_total",
      "rhs": {
        "op": "+",
        "args": [
          "SO2_aq",
          "HSO3_minus",
          "SO3_2minus"
        ]
      }
    },
    {
      "lhs": "H_SO2_eff",
      "rhs": {
        "op": "*",
        "args": [
          "H_SO2",
          {
            "op": "+",
            "args": [
              1,
              {
                "op": "/",
                "args": [
                  "K_s1",
                  "H_plus"
                ]
              },
              {
                "op": "/",
                "args": [
                  {
                    "op": "*",
                    "args": [
                      "K_s1",
                      "K_s2"
                    ]
                  },
                  {
                    "op": "^",
                    "args": [
                      "H_plus",
                      2
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "alpha_0",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "^",
            "args": [
              "H_plus",
              2
            ]
          },
          {
            "op": "+",
            "args": [
              {
                "op": "^",
                "args": [
                  "H_plus",
                  2
                ]
              },
              {
                "op": "*",
                "args": [
                  "K_s1",
                  "H_plus"
                ]
              },
              {
                "op": "*",
                "args": [
                  "K_s1",
                  "K_s2"
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "alpha_1",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "K_s1",
              "H_plus"
            ]
          },
          {
            "op": "+",
            "args": [
              {
                "op": "^",
                "args": [
                  "H_plus",
                  2
                ]
              },
              {
                "op": "*",
                "args": [
                  "K_s1",
                  "H_plus"
                ]
              },
              {
                "op": "*",
                "args": [
                  "K_s1",
                  "K_s2"
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "lhs": "alpha_2",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "K_s1",
              "K_s2"
            ]
          },
          {
            "op": "+",
            "args": [
              {
                "op": "^",
                "args": [
                  "H_plus",
                  2
                ]
              },
              {
                "op": "*",
                "args": [
                  "K_s1",
                  "H_plus"
                ]
              },
              {
                "op": "*",
                "args": [
                  "K_s1",
                  "K_s2"
                ]
              }
            ]
          }
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "baseline_298K_pH7",
      "description": "Reference state at 298 K (T_ref) with neutral water (pH 7) and 1 Pa SO2. At T=T_ref the van't Hoff factors are exp(0)=1, so H_SO2, K_s1, K_s2 take their 298 K values directly. HSO3- dominates the speciation at pH 7 (alpha_1 ≈ 0.60) with significant SO3^2- contribution (alpha_2 ≈ 0.40) due to the high K_s1.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.0001,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_SO2",
          "time": 0.0,
          "expected": 0.012139156180606956
        },
        {
          "variable": "K_s1",
          "time": 0.0,
          "expected": 13.0
        },
        {
          "variable": "K_s2",
          "time": 0.0,
          "expected": 6.599999999999999e-05
        },
        {
          "variable": "SO2_aq",
          "time": 0.0,
          "expected": 0.012139156180606956
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 1578.0903034789042
        },
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 1041.5396002960765
        },
        {
          "variable": "S_IV_total",
          "time": 0.0,
          "expected": 2619.642042931161
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 2619.642042931162
        },
        {
          "variable": "alpha_0",
          "time": 0.0,
          "expected": 4.633898823453088e-06
        },
        {
          "variable": "alpha_1",
          "time": 0.0,
          "expected": 0.6024068470489016
        },
        {
          "variable": "alpha_2",
          "time": 0.0,
          "expected": 0.39758851905227494
        }
      ]
    },
    {
      "id": "cold_273K_pH7",
      "description": "Cold cloud-water reference (273.15 K) at pH 7. SO2 solubility increases at low T (negative ΔH_dissolution) so H_SO2 grows ~2.6×; K_s1 nearly doubles (negative ΔH_Ks1, sign-flipped via -dH); SO3^2- partition increases.",
      "parameter_overrides": {
        "T": 273.15,
        "H_plus": 0.0001,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_SO2",
          "time": 0.0,
          "expected": 0.031710756452134795
        },
        {
          "variable": "K_s1",
          "time": 0.0,
          "expected": 24.63261969180649
        },
        {
          "variable": "K_s2",
          "time": 0.0,
          "expected": 9.296853657124221e-05
        },
        {
          "variable": "SO2_aq",
          "time": 0.0,
          "expected": 0.031710756452134795
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 7811.190038249352
        },
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 7261.949067359078
        },
        {
          "variable": "S_IV_total",
          "time": 0.0,
          "expected": 15073.170816364884
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 15073.17081636488
        }
      ]
    },
    {
      "id": "cold_280K_pH7",
      "description": "Intermediate cold-water reference (280 K).",
      "parameter_overrides": {
        "T": 280.0,
        "H_plus": 0.0001,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_SO2",
          "time": 0.0,
          "expected": 0.023925670142206007
        },
        {
          "variable": "K_s1",
          "time": 0.0,
          "expected": 20.42111446187285
        },
        {
          "variable": "K_s2",
          "time": 0.0,
          "expected": 8.407835263235874e-05
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 4885.888485510025
        }
      ]
    },
    {
      "id": "warm_310K_pH7",
      "description": "Warm-cloud / body-temperature reference (310 K). SO2 solubility falls (negative ΔH_dissolution) and K_s1, K_s2 also decrease. HSO3- partition increases at the expense of SO3^2-.",
      "parameter_overrides": {
        "T": 310.0,
        "H_plus": 0.0001,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_SO2",
          "time": 0.0,
          "expected": 0.008067694063551265
        },
        {
          "variable": "K_s1",
          "time": 0.0,
          "expected": 9.904667524254098
        },
        {
          "variable": "K_s2",
          "time": 0.0,
          "expected": 5.7047113213191966e-05
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 799.0782738687379
        },
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 455.85108755591904
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 1254.9374291187205
        }
      ]
    },
    {
      "id": "hot_318K_pH7",
      "description": "Upper-range reference (318 K, 45 °C) for warm aqueous-phase chemistry.",
      "parameter_overrides": {
        "T": 318.0,
        "H_plus": 0.0001,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_SO2",
          "time": 0.0,
          "expected": 0.006250237148170521
        },
        {
          "variable": "K_s1",
          "time": 0.0,
          "expected": 8.357111469404561
        },
        {
          "variable": "K_s2",
          "time": 0.0,
          "expected": 5.2081243957394926e-05
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 522.3392855747431
        }
      ]
    },
    {
      "id": "acidic_pH4_298K",
      "description": "Acidic cloud water (pH 4, typical polluted rain) at 298 K. Lower [H+] denominator suppresses HSO3- and SO3^2- by 100× and 10000× respectively; alpha_1 dominates (~0.99) since K_s1/[H+] = 130 still drives nearly full dissociation but K_s1*K_s2/[H+]^2 = 8.58e-3.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.1,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "SO2_aq",
          "time": 0.0,
          "expected": 0.012139156180606956
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 1.5780903034789042
        },
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 0.0010415396002960767
        },
        {
          "variable": "S_IV_total",
          "time": 0.0,
          "expected": 1.5912709992598073
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 1.5912709992598075
        },
        {
          "variable": "alpha_0",
          "time": 0.0,
          "expected": 0.007628591350092841
        },
        {
          "variable": "alpha_1",
          "time": 0.0,
          "expected": 0.9917168755120692
        },
        {
          "variable": "alpha_2",
          "time": 0.0,
          "expected": 0.0006545331378379655
        }
      ]
    },
    {
      "id": "acidic_pH2_298K",
      "description": "Strongly acidic regime (pH 2, [H+] = 10 mol/m³) at 298 K. SO2.H2O and HSO3- partition become comparable (K_s1/[H+] = 1.3); SO3^2- vanishes. Stress-tests the [H+]^2 term in alpha_0 and H_SO2_eff at the far-acidic tail.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 10.0,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "SO2_aq",
          "time": 0.0,
          "expected": 0.012139156180606956
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 0.015780903034789042
        },
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 1.0415396002960767e-07
        },
        {
          "variable": "alpha_0",
          "time": 0.0,
          "expected": 0.4347809867735363
        },
        {
          "variable": "alpha_1",
          "time": 0.0,
          "expected": 0.5652152828055972
        },
        {
          "variable": "alpha_2",
          "time": 0.0,
          "expected": 3.7304208665169412e-06
        }
      ]
    },
    {
      "id": "basic_pH9_298K",
      "description": "Mildly basic regime (pH 9) at 298 K. Lower [H+] drives both dissociations; SO3^2- dominates speciation (alpha_2 ≈ 0.985). H_SO2_eff explodes because K_s1*K_s2/[H+]^2 ≈ 8.58e8.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 1e-06,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 157809.03034789042
        },
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 10415396.002960768
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 10573205.045447815
        },
        {
          "variable": "alpha_2",
          "time": 0.0,
          "expected": 0.985074625734702
        }
      ]
    },
    {
      "id": "basic_pH10_298K",
      "description": "Basic regime (pH 10) at 298 K. SO3^2- almost completely dominates speciation (alpha_2 ≈ 0.9985).",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 1e-07,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 1041539600.2960768
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 1043117690.6116949
        },
        {
          "variable": "alpha_2",
          "time": 0.0,
          "expected": 0.9984871406842954
        }
      ]
    },
    {
      "id": "high_pSO2",
      "description": "Henry's-law linearity check: 10× p_SO2 at fixed T, H_plus scales SO2_aq, HSO3-, SO3^2-, S_IV_total by 10× while leaving H_SO2, K_s1, K_s2, H_SO2_eff, and the alpha mole fractions unchanged.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.0001,
        "p_SO2": 10.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "SO2_aq",
          "time": 0.0,
          "expected": 0.12139156180606957
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 15780.903034789044
        },
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 10415.396002960768
        },
        {
          "variable": "S_IV_total",
          "time": 0.0,
          "expected": 26196.42042931162
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 2619.642042931162
        },
        {
          "variable": "alpha_1",
          "time": 0.0,
          "expected": 0.6024068470489016
        }
      ]
    },
    {
      "id": "low_pSO2",
      "description": "Henry's-law linearity check at low partial pressure: p_SO2 = 0.01 Pa scales SO2_aq, HSO3-, SO3^2- by 0.01× from baseline. H_SO2_eff is independent of p_SO2.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.0001,
        "p_SO2": 0.01
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "SO2_aq",
          "time": 0.0,
          "expected": 0.00012139156180606956
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 15.780903034789043
        },
        {
          "variable": "S_IV_total",
          "time": 0.0,
          "expected": 26.196420429311615
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 2619.642042931162
        }
      ]
    },
    {
      "id": "coupled_cold_acidic",
      "description": "Cross-check: cold (273.15 K) AND acidic (pH 4). Combines the van't Hoff temperature shift with the acidic [H+] sweep to exercise both coefficient paths at once.",
      "parameter_overrides": {
        "T": 273.15,
        "H_plus": 0.1,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_SO2",
          "time": 0.0,
          "expected": 0.031710756452134795
        },
        {
          "variable": "K_s1",
          "time": 0.0,
          "expected": 24.63261969180649
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 7.811190038249352
        },
        {
          "variable": "S_IV_total",
          "time": 0.0,
          "expected": 7.850162743768846
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 7.850162743768846
        }
      ]
    },
    {
      "id": "coupled_warm_basic",
      "description": "Cross-check: warm (310 K) AND basic (pH 9). Higher T pushes K(T) down but lower [H+] drives both dissociations; SO3^2- dominates.",
      "parameter_overrides": {
        "T": 310.0,
        "H_plus": 1e-06,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "H_SO2",
          "time": 0.0,
          "expected": 0.008067694063551265
        },
        {
          "variable": "HSO3_minus",
          "time": 0.0,
          "expected": 79907.8273868738
        },
        {
          "variable": "SO3_2minus",
          "time": 0.0,
          "expected": 4558510.875559191
        },
        {
          "variable": "H_SO2_eff",
          "time": 0.0,
          "expected": 4638418.711013759
        },
        {
          "variable": "alpha_2",
          "time": 0.0,
          "expected": 0.9827726127301035
        }
      ]
    },
    {
      "id": "alpha_sum_to_one",
      "description": "Conservation check: alpha_0 + alpha_1 + alpha_2 = 1 by construction (shared denominator). Verified at the baseline state.",
      "parameter_overrides": {
        "T": 298.0,
        "H_plus": 0.0001,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "alpha_0",
          "time": 0.0,
          "expected": 4.633898823453088e-06
        },
        {
          "variable": "alpha_1",
          "time": 0.0,
          "expected": 0.6024068470489016
        },
        {
          "variable": "alpha_2",
          "time": 0.0,
          "expected": 0.39758851905227494
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "H_SO2_eff_vs_pH",
      "description": "Effective Henry's law constant H*_SO2 = H_SO2 * (1 + K_s1/[H+] + K_s1*K_s2/[H+]^2) as a function of [H+] over the atmospheric pH range at 298 K. Demonstrates the steep two-stage enhancement at low [H+] (HSO3- partition adds ~100×, then SO3^2- partition adds ~1e6×) and the asymptotic approach to H_SO2 at very high [H+] (SO2.H2O partition) — Seinfeld & Pandis Eq 7.41.",
      "initial_state": {},
      "parameters": {
        "T": 298.0,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "H_plus",
            "range": {
              "start": 1e-07,
              "stop": 10.0,
              "count": 25,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "Hstar_curve",
          "type": "line",
          "description": "H*_SO2 vs [H+] at 298 K — log-log slope ≈ -2 in the basic regime (K_s1*K_s2/[H+]^2 dominates), -1 in the mid regime (K_s1/[H+] dominates), 0 in the acidic limit.",
          "x": {
            "variable": "H_plus",
            "label": "[H⁺] (mol/m³, log scale)"
          },
          "y": {
            "variable": "H_SO2_eff",
            "label": "H*_SO2 (mol/m³/Pa, log scale)"
          }
        },
        {
          "id": "alpha_curves",
          "type": "line",
          "description": "Mole fractions alpha_0 (SO2.H2O), alpha_1 (HSO3-), alpha_2 (SO3^2-) vs [H+] — the canonical S(IV) speciation diagram crossing at pK_s1 and pK_s2.",
          "x": {
            "variable": "H_plus",
            "label": "[H⁺] (mol/m³, log scale)"
          },
          "y": {
            "variable": "alpha_1",
            "label": "α₁ = HSO3⁻ mole fraction"
          }
        }
      ]
    },
    {
      "id": "H_SO2_vs_temperature",
      "description": "SO2 Henry's law constant vs temperature (van't Hoff with negative ΔH_dissolution). Reproduces the canonical SO2 solubility curve (Seinfeld & Pandis Table 7.4 row for SO2): H_SO2 climbs from ~0.006 mol/m³/Pa at 318 K to ~0.032 mol/m³/Pa at 273 K — a ~5× range over the atmospheric temperature range.",
      "initial_state": {},
      "parameters": {
        "H_plus": 0.0001,
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "T",
            "range": {
              "start": 273.15,
              "stop": 318.0,
              "count": 20,
              "scale": "linear"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "HSO2_curve",
          "type": "line",
          "description": "H_SO2(T) — van't Hoff curve.",
          "x": {
            "variable": "T",
            "label": "Temperature (K)"
          },
          "y": {
            "variable": "H_SO2",
            "label": "H_SO2 (mol/m³/Pa, log scale)"
          }
        },
        {
          "id": "Ks1_curve",
          "type": "line",
          "description": "K_s1(T) — first dissociation constant climbs slightly with T (sign-flipped via -dH; ΔH_Ks1 < 0 means K_s1 actually decreases with increasing T given the upstream sign convention).",
          "x": {
            "variable": "T",
            "label": "Temperature (K)"
          },
          "y": {
            "variable": "K_s1",
            "label": "K_s1 (mol/m³)"
          }
        }
      ]
    },
    {
      "id": "coupled_T_pH_sweep",
      "description": "Two-dimensional sweep over T (freezing-to-warm cloud range) and [H+] (acidic-to-basic). Surfaces the joint dependence of H*_SO2 on temperature and acidity that controls atmospheric SO2 partitioning into cloud and aerosol water.",
      "initial_state": {},
      "parameters": {
        "p_SO2": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "T",
            "range": {
              "start": 273.15,
              "stop": 318.0,
              "count": 10,
              "scale": "linear"
            }
          },
          {
            "parameter": "H_plus",
            "range": {
              "start": 1e-07,
              "stop": 1.0,
              "count": 15,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "Hstar_heatmap",
          "type": "heatmap",
          "description": "H*_SO2 as a function of T and [H+].",
          "x": {
            "variable": "T",
            "label": "Temperature (K)"
          },
          "y": {
            "variable": "H_plus",
            "label": "[H⁺] (mol/m³, log scale)"
          },
          "value": {
            "variable": "H_SO2_eff",
            "reduce": "final"
          }
        }
      ]
    }
  ]
}