DRHTemperature

{
  "reference": {
    "citation": "Seinfeld, J. H., and Pandis, S. N. (2006). Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 2nd Edition, John Wiley & Sons, Chapter 10, Equation 10.72 (DRH temperature dependence), Table 10.1 (DRH at 298 K), Table 10.2 (solubility polynomial coefficients), Table 10.3 (enthalpy of solution).",
    "notes": "source_ref: Aerosol.jl@c8c640bb636b22f2425460e9ed5cba50793bfee1:src/seinfeld_pandis_ch10/drh.jl:76\n\nUpstream `DRHTemperature` is an MTK `@component` parameterized by `salt` (Symbol, default :NH4NO3). It declares two `@constants` (`R_gas` = 8.314 J*mol^-1*K^-1, `T_ref` = 298 K), six `@parameters` (`T`, `DRH_298K`, `ΔH_s`, `A_sol`, `B_sol`, `C_sol`) and one `@variables` (`DRH`). The single equation is Eq. 10.72:\n\n  DRH = DRH(298) * exp{ (ΔH_s/R) * [ A*(1/T - 1/298) - B*ln(T/298) - C*(T - 298) ] }\n\nwhere A, B, C are the salt's solubility polynomial coefficients n(T) = A + B*T + C*T^2 (Table 10.2).\n\nsalt fixed to :NH4NO3: the `salt` keyword does not enter the equation — it only selects, at construction time, the numeric defaults of the four salt-specific `@parameters` from the upstream lookup tables (`DRH_298` Table 10.1, `DELTA_HS_298` Table 10.3, `SOLUBILITY_PARAMS` Table 10.2). The .esm encodes one concrete instantiation fixed to the upstream canonical default `DRHTemperature(; name, salt = :NH4NO3)`, giving DRH_298K = 0.618, ΔH_s = 16270 J/mol (the upstream stores 16.27 kJ/mol and multiplies by 1000), A_sol = 4.298, B_sol = -0.03623 K^-1, C_sol = 7.853e-5 K^-2. Because every salt-specific value is a first-class `type: parameter`, the migrated component reproduces any other tabulated salt by overriding the five parameters — the `nacl_*` and `na2so4_*` inline tests exercise exactly this (overriding to the NaCl and Na2SO4 table rows), mirroring the upstream `DRH Temperature Dependence` testitem which checks the same three salts.\n\nConstant->parameter translation: the upstream `@constants` `R_gas` and `T_ref` are encoded as fixed-default `type: parameter` entries carrying their upstream Float64 values bit-for-bit. This mirrors the sibling convention (stefan_boltzmann.esm, critical_ssa.esm, clmu_atmosphere.esm) of translating `@constants` to fixed-default parameters so each named quantity is a first-class symbol in the expression AST rather than a magic literal.\n\nObserved classification: `DRH` is an algebraic function of the eight parameters (`DRH ~ ...`; no time derivative anywhere). After MTK structural_simplify / mtkcompile the compiled system has zero ODE states and `DRH` becomes an observed quantity — the upstream `ModelingToolkit Integration` testitem exercises exactly this compiled form via `mtkcompile(DRHTemperature(salt = :NH4NO3))`. `DRH` is therefore serialized as `type: observed` with an `expression` carrying the Eq. 10.72 right-hand side, and the `equations` array is empty, matching the sibling observed-only Aerosol.jl migrations critical_ssa.esm and zsr.esm.\n\nNot migrated: the file-level helpers `drh_temperature(T, salt)` (a scalar evaluator of the same Eq. 10.72) and `nh4no3_drh(T)` (the empirical Eq. 10.88 correlation for NH4NO3) in drh.jl are plain Julia functions, not MTK components, and are out of scope for this component migration. The upstream tests that call `drh_temperature` directly are reproduced here through the equivalent component-parameter form — the function and the component evaluate the identical Eq. 10.72.\n\nTolerance rationale (model-level rel=1e-8 / abs=1e-12): the model is a small closed-form algebraic expression — one `exp`, one `log`, and a handful of multiplies/divides over fixed Float64 inputs — so evaluation roundoff is at the few-ULP (~1e-15 relative) level; rel=1e-8 leaves ample headroom while still catching a structural regression. abs=1e-12 floors any near-zero DRH cold-limit value. At T = T_ref = 298 K the exponent argument is identically zero (1/T - 1/T_ref, ln(T/T_ref) and T - T_ref each evaluate to exact float 0), so `upstream_reference_T298_NH4NO3` pins DRH = DRH_298K = 0.618 exactly."
  },
  "variables": {
    "T": {
      "type": "parameter",
      "units": "K",
      "default": 298.0,
      "description": "Ambient temperature — the input at which the deliquescence relative humidity is evaluated."
    },
    "DRH_298K": {
      "type": "parameter",
      "units": "1",
      "default": 0.618,
      "description": "Deliquescence relative humidity at the 298 K reference temperature, as a fraction in [0, 1] (Seinfeld & Pandis Table 10.1). Default 0.618 is the NH4NO3 value."
    },
    "ΔH_s": {
      "type": "parameter",
      "units": "J/mol",
      "default": 16270.0,
      "description": "Enthalpy of solution of the salt (Seinfeld & Pandis Table 10.3). Default 16270 J/mol is the NH4NO3 value (16.27 kJ/mol). Salts with ΔH_s > 0 have DRH decreasing with temperature; ΔH_s < 0 reverses the trend."
    },
    "A_sol": {
      "type": "parameter",
      "units": "1",
      "default": 4.298,
      "description": "Solubility polynomial coefficient A in n(T) = A + B*T + C*T^2 (Seinfeld & Pandis Table 10.2; n is moles salt per mole water at saturation, dimensionless). Default 4.298 is the NH4NO3 value."
    },
    "B_sol": {
      "type": "parameter",
      "units": "K^-1",
      "default": -0.03623,
      "description": "Solubility polynomial coefficient B in n(T) = A + B*T + C*T^2 (Seinfeld & Pandis Table 10.2). Default -0.03623 K^-1 is the NH4NO3 value."
    },
    "C_sol": {
      "type": "parameter",
      "units": "K^-2",
      "default": 7.853e-05,
      "description": "Solubility polynomial coefficient C in n(T) = A + B*T + C*T^2 (Seinfeld & Pandis Table 10.2). Default 7.853e-5 K^-2 is the NH4NO3 value."
    },
    "R_gas": {
      "type": "parameter",
      "units": "J/(mol*K)",
      "default": 8.314,
      "description": "Universal gas constant (upstream `@constants` value 8.314 J*mol^-1*K^-1; encoded as a fixed-default parameter per rig convention so it is a named symbol in the expression AST)."
    },
    "T_ref": {
      "type": "parameter",
      "units": "K",
      "default": 298.0,
      "description": "Reference temperature 298 K at which DRH_298K and the solubility-table coefficients are defined (upstream `@constants`; encoded as a fixed-default parameter)."
    },
    "DRH": {
      "type": "unknown",
      "units": "1",
      "description": "Deliquescence relative humidity at temperature T, as a fraction in [0, 1] (Eq. 10.72): DRH = DRH_298K * exp{ (ΔH_s/R_gas) * [ A_sol*(1/T - 1/T_ref) - B_sol*ln(T/T_ref) - C_sol*(T - T_ref) ] }."
    }
  },
  "equations": [
    {
      "lhs": "DRH",
      "rhs": {
        "op": "*",
        "args": [
          "DRH_298K",
          {
            "op": "exp",
            "args": [
              {
                "op": "*",
                "args": [
                  {
                    "op": "/",
                    "args": [
                      "ΔH_s",
                      "R_gas"
                    ]
                  },
                  {
                    "op": "-",
                    "args": [
                      {
                        "op": "-",
                        "args": [
                          {
                            "op": "*",
                            "args": [
                              "A_sol",
                              {
                                "op": "-",
                                "args": [
                                  {
                                    "op": "/",
                                    "args": [
                                      1,
                                      "T"
                                    ]
                                  },
                                  {
                                    "op": "/",
                                    "args": [
                                      1,
                                      "T_ref"
                                    ]
                                  }
                                ]
                              }
                            ]
                          },
                          {
                            "op": "*",
                            "args": [
                              "B_sol",
                              {
                                "op": "log",
                                "args": [
                                  {
                                    "op": "/",
                                    "args": [
                                      "T",
                                      "T_ref"
                                    ]
                                  }
                                ]
                              }
                            ]
                          }
                        ]
                      },
                      {
                        "op": "*",
                        "args": [
                          "C_sol",
                          {
                            "op": "-",
                            "args": [
                              "T",
                              "T_ref"
                            ]
                          }
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    }
  ],
  "tolerance": {
    "rel": 1e-08,
    "abs": 1e-12
  },
  "tests": [
    {
      "id": "upstream_reference_T298_NH4NO3",
      "description": "Reproduces the upstream `DRH Temperature Dependence` testitem reference check `drh_temperature(298.0, :NH4NO3) ≈ 0.618`. At T = T_ref = 298 K the Eq. 10.72 exponent argument is identically zero (1/T - 1/T_ref = 0, ln(T/T_ref) = 0, T - T_ref = 0), so DRH = DRH_298K * exp(0) = 0.618 exactly. Asserted at both ends of the time span to confirm the algebraic model is time-invariant.",
      "parameter_overrides": {
        "T": 298.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.618
        },
        {
          "variable": "DRH",
          "time": 1.0,
          "expected": 0.618
        }
      ]
    },
    {
      "id": "nh4no3_cold_T280",
      "description": "NH4NO3 at T = 280 K. NH4NO3 has ΔH_s = 16.27 kJ/mol > 0, so DRH decreases with increasing temperature; at 280 K (below the 298 K reference) DRH = 0.7276 > DRH(298) = 0.618. Together with `nh4no3_warm_T310` this reproduces the upstream `drh_280 > drh_298 > drh_310` ordering.",
      "parameter_overrides": {
        "T": 280.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.7276339262964759
        }
      ]
    },
    {
      "id": "nh4no3_warm_T310",
      "description": "NH4NO3 at T = 310 K. Above the 298 K reference, the positive-ΔH_s salt's DRH drops to 0.5385 < DRH(298) = 0.618 — the warm half of the upstream `drh_280 > drh_298 > drh_310` monotonic-decrease check.",
      "parameter_overrides": {
        "T": 310.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.5385211858060412
        }
      ]
    },
    {
      "id": "nh4no3_physical_bound_cold_T250",
      "description": "NH4NO3 at T = 250 K — cold end of the upstream physical-bounds loop `for T in [250, 270, 298, 310, 330]: 0 < drh_val < 1`. DRH = 0.8712 lies inside (0, 1).",
      "parameter_overrides": {
        "T": 250.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.871172452231081
        }
      ]
    },
    {
      "id": "nh4no3_physical_bound_hot_T330",
      "description": "NH4NO3 at T = 330 K — hot end of the upstream physical-bounds loop `for T in [250, 270, 298, 310, 330]: 0 < drh_val < 1`. DRH = 0.4049 lies inside (0, 1); the largest temperature excursion still yields a physical DRH.",
      "parameter_overrides": {
        "T": 330.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.40487604425039875
        }
      ]
    },
    {
      "id": "nacl_cold_T280",
      "description": "NaCl at T = 280 K, with all five salt-specific parameters overridden to the NaCl table rows (DRH_298K = 0.753 Table 10.1; ΔH_s = 1880 J/mol Table 10.3; A_sol = 0.1805, B_sol = -5.31e-4, C_sol = 9.965e-7 Table 10.2). NaCl has ΔH_s = 1.88 kJ/mol > 0; with `nacl_warm_T310` this reproduces the upstream `drh_nacl_280 > drh_nacl_310` check.",
      "parameter_overrides": {
        "T": 280.0,
        "DRH_298K": 0.753,
        "ΔH_s": 1880.0,
        "A_sol": 0.1805,
        "B_sol": -0.000531,
        "C_sol": 9.965e-07
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.7570619896210471
        }
      ]
    },
    {
      "id": "nacl_warm_T310",
      "description": "NaCl at T = 310 K (the five salt-specific parameters overridden to the NaCl table rows). DRH = 0.7505 < the 280 K value 0.7571 — the warm half of the upstream `drh_nacl_280 > drh_nacl_310` decrease check for the small-positive-ΔH_s salt.",
      "parameter_overrides": {
        "T": 310.0,
        "DRH_298K": 0.753,
        "ΔH_s": 1880.0,
        "A_sol": 0.1805,
        "B_sol": -0.000531,
        "C_sol": 9.965e-07
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.7505450495320607
        }
      ]
    },
    {
      "id": "na2so4_cold_T280",
      "description": "Na2SO4 at T = 280 K, with all five salt-specific parameters overridden to the Na2SO4 table rows (DRH_298K = 0.842 Table 10.1; ΔH_s = -9760 J/mol Table 10.3; A_sol = 0.3754, B_sol = -1.763e-3, C_sol = 2.424e-6 Table 10.2). Na2SO4 has ΔH_s = -9.76 kJ/mol < 0, which reverses the temperature trend; with `na2so4_warm_T310` this reproduces the upstream `drh_na2so4_280 < drh_na2so4_310` check.",
      "parameter_overrides": {
        "T": 280.0,
        "DRH_298K": 0.842,
        "ΔH_s": -9760.0,
        "A_sol": 0.3754,
        "B_sol": -0.001763,
        "C_sol": 2.424e-06
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.8275236172331673
        }
      ]
    },
    {
      "id": "na2so4_warm_T310",
      "description": "Na2SO4 at T = 310 K (the five salt-specific parameters overridden to the Na2SO4 table rows). DRH = 0.8502 > the 280 K value 0.8275 — confirming that the negative-ΔH_s salt's DRH increases with temperature, the opposite of NH4NO3 and NaCl (upstream `drh_na2so4_280 < drh_na2so4_310`).",
      "parameter_overrides": {
        "T": 310.0,
        "DRH_298K": 0.842,
        "ΔH_s": -9760.0,
        "A_sol": 0.3754,
        "B_sol": -0.001763,
        "C_sol": 2.424e-06
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "DRH",
          "time": 0.0,
          "expected": 0.8501949324719044
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "drh_vs_temperature_NH4NO3",
      "description": "Temperature dependence of NH4NO3 deliquescence relative humidity over a 250-340 K sweep at the upstream default parameterization (Eq. 10.72). Because NH4NO3 has a positive enthalpy of solution (ΔH_s = 16.27 kJ/mol), DRH decreases monotonically with temperature — from ≈ 0.87 at 250 K through the 0.618 reference value at 298 K down to ≈ 0.34 at 340 K.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "T",
            "range": {
              "start": 250.0,
              "stop": 340.0,
              "count": 60,
              "scale": "linear"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "drh_vs_T_nh4no3",
          "type": "line",
          "description": "NH4NO3 deliquescence relative humidity DRH as a function of temperature T — a monotonic decrease for the positive-enthalpy salt.",
          "x": {
            "variable": "T",
            "label": "Temperature T (K)"
          },
          "y": {
            "variable": "DRH",
            "label": "Deliquescence relative humidity DRH"
          }
        }
      ]
    },
    {
      "id": "drh_vs_temperature_na2so4",
      "description": "Temperature dependence of Na2SO4 deliquescence relative humidity over a 250-340 K sweep, with the five salt-specific parameters set to the Na2SO4 table rows. Na2SO4 has a negative enthalpy of solution (ΔH_s = -9.76 kJ/mol), so its DRH increases with temperature — the opposite trend to NH4NO3 in the companion example. The curve rises from ≈ 0.80 at 250 K through 0.842 at 298 K toward ≈ 0.87 at 340 K.",
      "parameters": {
        "DRH_298K": 0.842,
        "ΔH_s": -9760.0,
        "A_sol": 0.3754,
        "B_sol": -0.001763,
        "C_sol": 2.424e-06
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "T",
            "range": {
              "start": 250.0,
              "stop": 340.0,
              "count": 60,
              "scale": "linear"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "drh_vs_T_na2so4",
          "type": "line",
          "description": "Na2SO4 deliquescence relative humidity DRH as a function of temperature T — a monotonic increase for the negative-enthalpy salt.",
          "x": {
            "variable": "T",
            "label": "Temperature T (K)"
          },
          "y": {
            "variable": "DRH",
            "label": "Deliquescence relative humidity DRH"
          }
        }
      ]
    }
  ]
}