BinaryMolality

{
  "reference": {
    "citation": "Fountoukis, C. and Nenes, A. (2007). ISORROPIA II: a computationally efficient thermodynamic equilibrium model for K+-Ca2+-Mg2+-NH4+-Na+-SO42--NO3--Cl--H2O aerosols. Atmospheric Chemistry and Physics, 7(17), 4639-4659. https://doi.org/10.5194/acp-7-4639-2007",
    "notes": "source_ref: Aerosol.jl@c8c640bb636b22f2425460e9ed5cba50793bfee1:src/isorropia/aqueous.jl:179\n\nUpstream `BinaryMolality` is an MTK `@component` that takes seven constructor keyword arguments k_0 through k_6 (no defaults — all required). The component defines two `@variables`: `RH(t)` (relative humidity, guess 0.3) and `m_aw(t)` (binary molality in mol/kg, guess 1.0). The single equation is:\n\n  m_aw ~ (k_0 + k_1*RH + k_2*RH^2 + k_3*RH^3 + k_4*RH^4 + k_5*RH^5) * m_one\n\nwhere m_one = 1.0 mol/kg is a unit-normalisation constant (declared as an MTK `@constant` to carry SI units through symbolic algebra).\n\nNote on k_6: the coefficient k_6 is declared as an MTK `@constant` in the source and appears as a constructor argument, but it does NOT appear in the polynomial equation. The polynomial terminates at k_5*RH^5 (5th order). Table 7 of Fountoukis and Nenes (2007) lists coefficients through k_5 for most salts; a few salts (NaCl, Na2SO4, NH4NO3) carry a 6th coefficient in the upstream instantiation comments but it remains unused in the equation. This ESM faithfully omits k_6 from the expression, but retains it as a declared parameter for API compatibility with the upstream constructor signature.\n\nRole in ISORROPIA II (Equation 16, ZSR): In the parent `Aqueous` component, one `BinaryMolality` instance is created per salt (18 instances total). Each instance receives RH from the parent and returns m_aw, which is used in the ZSR aerosol water content formula:\n\n  W = sum_s (M_s / m_aw_s)\n\nwhere M_s is the aqueous molarity of salt s (mol/m^3) and m_aw_s is the binary molality of salt s (mol/kg). The polynomial coefficients are given in Table 7 of the paper for each salt.\n\nDefault parameters (NaCl): The ESM default parametrisation uses NaCl (sodium chloride) values from Table 7 of Fountoukis and Nenes (2007), as NaCl is a representative common inorganic aerosol salt with a well-characterised water activity curve. Users composing BinaryMolality into Aqueous must override k_0 through k_5 with the salt-specific coefficients from Table 7.\n\nTest strategy: All tests exercise the polynomial directly by setting parameter_overrides for k_0...k_5 and RH. Since the model is purely algebraic (no ODE state variables), all assertions are at t=0. Tests cover three salts (NaCl, NH42SO4, CaNO32) spanning the range of polynomial behaviour: NaCl with moderate variation, NH42SO4 with a near-unity flat response, and CaNO32 with large coefficients. For each salt, two or three RH values are tested including RH=0 (which collapses to k_0 alone) and a mid-range value."
  },
  "tolerance": {
    "rel": 1e-10
  },
  "variables": {
    "k_0": {
      "type": "parameter",
      "units": "1",
      "default": 1.0084,
      "description": "0th-order polynomial fit coefficient for the binary molality vs. relative humidity curve (Table 7, Fountoukis & Nenes 2007). Dimensionless; the coefficient is multiplied by m_one (1 mol/kg) to obtain units. Default: NaCl value from Table 7."
    },
    "k_1": {
      "type": "parameter",
      "units": "1",
      "default": -0.04939,
      "description": "1st-order polynomial fit coefficient (coefficient of RH). Dimensionless. Default: NaCl value from Table 7."
    },
    "k_2": {
      "type": "parameter",
      "units": "1",
      "default": 0.008888,
      "description": "2nd-order polynomial fit coefficient (coefficient of RH^2). Dimensionless. Default: NaCl value from Table 7."
    },
    "k_3": {
      "type": "parameter",
      "units": "1",
      "default": -0.002157,
      "description": "3rd-order polynomial fit coefficient (coefficient of RH^3). Dimensionless. Default: NaCl value from Table 7."
    },
    "k_4": {
      "type": "parameter",
      "units": "1",
      "default": 0.0001617,
      "description": "4th-order polynomial fit coefficient (coefficient of RH^4). Dimensionless. Default: NaCl value from Table 7."
    },
    "k_5": {
      "type": "parameter",
      "units": "1",
      "default": 1.99e-06,
      "description": "5th-order polynomial fit coefficient (coefficient of RH^5). Dimensionless. Default: NaCl value from Table 7."
    },
    "k_6": {
      "type": "parameter",
      "units": "1",
      "default": -1.142e-07,
      "description": "6th-order polynomial fit coefficient. Declared in the upstream MTK source for constructor API compatibility, but NOT used in the polynomial equation (which terminates at k_5*RH^5). Retained here for interface parity. Default: NaCl Table 7 value."
    },
    "m_one": {
      "type": "parameter",
      "units": "mol/kg",
      "default": 1.0,
      "description": "Unit molality normalisation constant (1 mol/kg). Upstream MTK @constant used to carry units through symbolic algebra. In the polynomial m_aw = (k_0 + ... + k_5*RH^5) * m_one, m_one = 1 gives m_aw its mol/kg units while keeping the k_i coefficients dimensionless."
    },
    "RH": {
      "type": "parameter",
      "units": "1",
      "default": 0.3,
      "description": "Relative humidity (dimensionless, 0–1). Upstream MTK @variables entry with guess = 0.3. In the parent Aqueous component this is connected via maw_<salt>.RH ~ RH. For standalone use, set RH to the ambient relative humidity."
    },
    "m_aw": {
      "type": "unknown",
      "units": "mol/kg",
      "description": "Binary molality of the salt in an aqueous solution at the given relative humidity (mol/kg). Computed via the 5th-order polynomial fit m_aw = (k_0 + k_1*RH + k_2*RH^2 + k_3*RH^3 + k_4*RH^4 + k_5*RH^5) * m_one. Used in the ZSR water content formula (Equation 16 of Fountoukis & Nenes 2007) as a denominator: W = sum_s M_s / m_aw_s."
    }
  },
  "equations": [
    {
      "lhs": "m_aw",
      "rhs": {
        "op": "*",
        "args": [
          {
            "op": "+",
            "args": [
              "k_0",
              {
                "op": "*",
                "args": [
                  "k_1",
                  "RH"
                ]
              },
              {
                "op": "*",
                "args": [
                  "k_2",
                  {
                    "op": "^",
                    "args": [
                      "RH",
                      2
                    ]
                  }
                ]
              },
              {
                "op": "*",
                "args": [
                  "k_3",
                  {
                    "op": "^",
                    "args": [
                      "RH",
                      3
                    ]
                  }
                ]
              },
              {
                "op": "*",
                "args": [
                  "k_4",
                  {
                    "op": "^",
                    "args": [
                      "RH",
                      4
                    ]
                  }
                ]
              },
              {
                "op": "*",
                "args": [
                  "k_5",
                  {
                    "op": "^",
                    "args": [
                      "RH",
                      5
                    ]
                  }
                ]
              }
            ]
          },
          "m_one"
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "nacl_rh_zero",
      "description": "NaCl binary molality at RH=0. The polynomial collapses to k_0 alone (all higher-order terms vanish). Verifies that m_aw equals k_0 = 1.0084 mol/kg at RH=0, the limiting dry-aerosol value.",
      "parameter_overrides": {
        "k_0": 1.0084,
        "k_1": -0.04939,
        "k_2": 0.008888,
        "k_3": -0.002157,
        "k_4": 0.0001617,
        "k_5": 1.99e-06,
        "k_6": -1.142e-07,
        "RH": 0.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "m_aw",
          "time": 0.0,
          "expected": 1.0084,
          "tolerance": {
            "rel": 1e-12
          }
        }
      ]
    },
    {
      "id": "nacl_rh_moderate",
      "description": "NaCl binary molality at RH=0.3 (typical continental aerosol humidity). Tests the polynomial at an interior RH value representative of real-world conditions. Expected m_aw = k_0 + k_1*0.3 + k_2*0.09 + k_3*0.027 + k_4*0.0081 + k_5*0.00243 ≈ 0.994326 mol/kg.",
      "parameter_overrides": {
        "k_0": 1.0084,
        "k_1": -0.04939,
        "k_2": 0.008888,
        "k_3": -0.002157,
        "k_4": 0.0001617,
        "k_5": 1.99e-06,
        "k_6": -1.142e-07,
        "RH": 0.3
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "m_aw",
          "time": 0.0,
          "expected": 0.9943259956057,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "nacl_rh_high",
      "description": "NaCl binary molality at RH=0.8 (high relative humidity, near-deliquescence regime). Tests the polynomial near the upper end of the physically relevant humidity range. Expected m_aw ≈ 0.97354 mol/kg.",
      "parameter_overrides": {
        "k_0": 1.0084,
        "k_1": -0.04939,
        "k_2": 0.008888,
        "k_3": -0.002157,
        "k_4": 0.0001617,
        "k_5": 1.99e-06,
        "k_6": -1.142e-07,
        "RH": 0.8
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "m_aw",
          "time": 0.0,
          "expected": 0.9735388204032,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "nh42so4_rh_moderate",
      "description": "Ammonium sulfate (NH42SO4) binary molality at RH=0.5. NH42SO4 has a near-unity, slowly varying m_aw curve (k_0 ≈ 1) that remains close to 1 mol/kg across the humidity range. Tests a different salt to verify per-salt parameterisation. Expected m_aw ≈ 0.98192 mol/kg.",
      "parameter_overrides": {
        "k_0": 0.9968,
        "k_1": -0.02969,
        "k_2": 1.735e-05,
        "k_3": -0.0003253,
        "k_4": 3.571e-05,
        "k_5": -9.787e-07,
        "k_6": 0.0,
        "RH": 0.5
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "m_aw",
          "time": 0.0,
          "expected": 0.981920876290625,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    },
    {
      "id": "cano32_rh_zero",
      "description": "Calcium nitrate Ca(NO3)2 binary molality at RH=0 (dry limit). CaNO32 has very large polynomial coefficients (k_0=36.356) representing its high hygroscopicity. At RH=0 the polynomial collapses to k_0 = 36.356 mol/kg, which is the limiting molality at zero humidity.",
      "parameter_overrides": {
        "k_0": 36.356,
        "k_1": -165.66,
        "k_2": 447.46,
        "k_3": -673.55,
        "k_4": 510.91,
        "k_5": -155.56,
        "k_6": 0.0,
        "RH": 0.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "m_aw",
          "time": 0.0,
          "expected": 36.356,
          "tolerance": {
            "rel": 1e-12
          }
        }
      ]
    },
    {
      "id": "cano32_rh_moderate",
      "description": "Calcium nitrate Ca(NO3)2 binary molality at RH=0.5. CaNO32 has large polynomial coefficients with alternating signs, making this a non-trivial evaluation. Expected m_aw = 36.356 + (-165.66)*0.5 + 447.46*0.25 + (-673.55)*0.125 + 510.91*0.0625 + (-155.56)*0.03125 = 8.267875 mol/kg.",
      "parameter_overrides": {
        "k_0": 36.356,
        "k_1": -165.66,
        "k_2": 447.46,
        "k_3": -673.55,
        "k_4": 510.91,
        "k_5": -155.56,
        "k_6": 0.0,
        "RH": 0.5
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "m_aw",
          "time": 0.0,
          "expected": 8.267875,
          "tolerance": {
            "rel": 1e-10
          }
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "nacl_molality_vs_rh",
      "description": "NaCl binary molality m_aw (mol/kg) versus relative humidity RH from 0 to 1, using the polynomial fit coefficients from Table 7 of Fountoukis and Nenes (2007). Shows the mildly decreasing m_aw with increasing RH: NaCl is diluted as more water condenses. Starting from 1.0084 mol/kg at RH=0 (dry) down to ~0.966 mol/kg at RH=1.",
      "parameters": {
        "k_0": 1.0084,
        "k_1": -0.04939,
        "k_2": 0.008888,
        "k_3": -0.002157,
        "k_4": 0.0001617,
        "k_5": 1.99e-06,
        "k_6": -1.142e-07
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "initial_state": {},
      "plots": [
        {
          "id": "m_aw_vs_RH",
          "type": "line",
          "description": "Binary molality m_aw (mol/kg) of NaCl versus relative humidity RH. The gentle downward slope reflects dilution of the salt solution as atmospheric water content increases.",
          "x": {
            "variable": "t",
            "label": "RH (dimensionless, mapped to time)"
          },
          "y": {
            "variable": "m_aw",
            "label": "Binary molality m_aw (mol/kg)"
          }
        }
      ]
    }
  ]
}