MixingRatio

{
  "reference": {
    "notes": "source_ref: AtmosphericDynamics.jl@816cc391:src/seinfeld_pandis_ch1.jl:278\nUpstream `MixingRatio` is an MTK `@component` with c_i(t), c_total(t), and xi(t) as `@variables` and the single equation xi ~ c_i / c_total (Seinfeld & Pandis Eq. 1.6). For standalone serialization — and to make the component well-posed in isolation (3 unknowns against 1 equation otherwise) — c_i and c_total are declared as parameters here, with xi the single algebraic state. This matches the bead's `(S, observed-only)` classification in docs/migration-tracker.md and the IdealGasLaw / ScaleHeight / RelativeHumidity serialization pattern in this directory. The upstream `5.5 MixingRatio Compilation` test (test/seinfeld_pandis_ch1_test.jl:485) confirms this input/output split: it compiles the component with `inputs = [mr_nns.c_i, mr_nns.c_total]`, leaving xi as the sole computed unknown. The single algebraic equation is unchanged from upstream.\n\nUpstream provides only structural (`1.5 MixingRatio Structure`) and compilation (`5.5 MixingRatio Compilation`) tests for this component — no numerical-accuracy test. The inline `tests` here therefore anchor on textbook reference values: the total molar concentrations 40.9 mol/m^3 (T = 298 K, p = 101325 Pa) and 44.6 mol/m^3 (STP, T = 273.15 K) given in the chapter's TotalMolarConcentration discussion, and the standard dry-air mole fractions (N2 0.7808, O2 0.2095, Ar 0.0093, CO2 ~4e-4). Each test's c_i is c_i = X * c_total for the named mole fraction X, so xi reproduces X.\n\nTolerance rationale (model-level rel=1e-6): observed-only single-equation algebraic system (no ODE integration); 1e-6 covers float64 roundoff in the single c_i / c_total divide across the full atmospheric mixing-ratio range — xi from 1 (a pure species, c_i = c_total) down to ~1e-12 (parts-per-trillion trace species)."
  },
  "tolerance": {
    "rel": 1e-06
  },
  "variables": {
    "c_i": {
      "type": "parameter",
      "units": "mol/m^3",
      "default": 0.01636,
      "description": "Molar concentration of species i. Default 0.01636 mol/m^3 — a CO2-like trace species at a ~400 ppm mixing ratio in air at 298 K, 1 atm (c_i = 4e-4 * c_total)."
    },
    "c_total": {
      "type": "parameter",
      "units": "mol/m^3",
      "default": 40.9,
      "description": "Total molar concentration of air. Default 40.9 mol/m^3 — the value at T = 298 K, p = 101325 Pa from the ideal-gas law c_total = p / (R * T) (Seinfeld & Pandis Ch 1; 44.6 mol/m^3 at STP)."
    },
    "xi": {
      "type": "unknown",
      "units": "1",
      "description": "Volume (mole) mixing ratio of species i, dimensionless — the fraction c_i / c_total. Conventionally quoted in ppm, ppb, or ppt."
    }
  },
  "equations": [
    {
      "_comment": "Eq. 1.6 - Volume mixing ratio definition: xi = c_i / c_total",
      "lhs": "xi",
      "rhs": {
        "op": "/",
        "args": [
          "c_i",
          "c_total"
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "co2_400ppm_default",
      "description": "Canonical default-parameter run: a CO2-like trace species at a ~400 ppm mixing ratio in air at 298 K, 1 atm (c_i = 0.01636 mol/m^3 = 4e-4 * c_total, c_total = 40.9 mol/m^3). Verifies the defining ratio xi = c_i / c_total of Eq. 1.6. The system is algebraic (xi depends only on the input parameters), so xi is also asserted at t = 1.0 to confirm time-invariance.",
      "parameter_overrides": {
        "c_i": 0.01636,
        "c_total": 40.9
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "xi",
          "time": 0.0,
          "expected": 0.0004
        },
        {
          "variable": "xi",
          "time": 1.0,
          "expected": 0.0004
        }
      ]
    },
    {
      "id": "nitrogen_dominant",
      "description": "Dominant atmospheric gas: molecular nitrogen at its standard dry-air mole fraction 0.7808 (c_i = 31.93472 mol/m^3 = 0.7808 * c_total, c_total = 40.9 mol/m^3). Exercises the high end of the mixing-ratio range — N2 makes up roughly four-fifths of dry air.",
      "parameter_overrides": {
        "c_i": 31.93472,
        "c_total": 40.9
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "xi",
          "time": 0.0,
          "expected": 0.7808
        }
      ]
    },
    {
      "id": "oxygen_major",
      "description": "Second most abundant gas: molecular oxygen at its standard dry-air mole fraction 0.2095 (c_i = 8.56855 mol/m^3 = 0.2095 * c_total, c_total = 40.9 mol/m^3). With nitrogen_dominant this confirms the two major air components; the expected value carries the float64 round-off of the divide.",
      "parameter_overrides": {
        "c_i": 8.56855,
        "c_total": 40.9
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "xi",
          "time": 0.0,
          "expected": 0.20950000000000002
        }
      ]
    },
    {
      "id": "argon_minor",
      "description": "Argon, the third most abundant atmospheric gas, at its standard dry-air mole fraction 0.0093 (c_i = 0.38037 mol/m^3 = 0.0093 * c_total, c_total = 40.9 mol/m^3). A sub-percent minor constituent — bridges the major gases and the trace species.",
      "parameter_overrides": {
        "c_i": 0.38037,
        "c_total": 40.9
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "xi",
          "time": 0.0,
          "expected": 0.0093
        }
      ]
    },
    {
      "id": "ozone_trace_ppb",
      "description": "Trace pollutant regime: ozone at a boundary-layer mole fraction of 50 ppb (c_i = 2.045e-6 mol/m^3 = 5e-8 * c_total, c_total = 40.9 mol/m^3). Exercises the parts-per-billion end of the range, where mixing ratios are conventionally quoted in ppb.",
      "parameter_overrides": {
        "c_i": 2.045e-06,
        "c_total": 40.9
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "xi",
          "time": 0.0,
          "expected": 5e-08
        }
      ]
    },
    {
      "id": "stp_total_concentration",
      "description": "Different total-concentration regime: a 1% mixing ratio evaluated at the STP total molar concentration c_total = 44.6 mol/m^3 (T = 273.15 K, p = 101325 Pa) rather than the 298 K value 40.9 mol/m^3. c_i = 0.446 mol/m^3 = 0.01 * c_total. Confirms xi is set by the ratio, independent of the absolute concentration scale.",
      "parameter_overrides": {
        "c_i": 0.446,
        "c_total": 44.6
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "xi",
          "time": 0.0,
          "expected": 0.01
        }
      ]
    },
    {
      "id": "pure_species",
      "description": "Upper-boundary case: the species fills the entire air sample (c_i = c_total = 40.9 mol/m^3), giving the maximum physical mixing ratio xi = 1. xi is algebraic, so the value is also asserted at t = 1.0 to confirm time-invariance.",
      "parameter_overrides": {
        "c_i": 40.9,
        "c_total": 40.9
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "xi",
          "time": 0.0,
          "expected": 1.0
        },
        {
          "variable": "xi",
          "time": 1.0,
          "expected": 1.0
        }
      ]
    },
    {
      "id": "ultratrace_ppt",
      "description": "Extreme low end: an ultra-trace species at a parts-per-trillion mole fraction ~1e-12 (c_i = 4.09e-11 mol/m^3 = 1e-12 * c_total, c_total = 40.9 mol/m^3). Exercises the bottom of the ~12-order-of-magnitude atmospheric mixing-ratio span; the expected value carries the float64 round-off of the divide.",
      "parameter_overrides": {
        "c_i": 4.09e-11,
        "c_total": 40.9
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "xi",
          "time": 0.0,
          "expected": 1.0000000000000002e-12
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "xi_vs_species_concentration",
      "description": "Volume mixing ratio as a function of the species molar concentration at a fixed total molar concentration (c_total = 40.9 mol/m^3, air at 298 K, 1 atm). Reproduces the linear definition xi = c_i / c_total of Eq. 1.6: c_i is swept from 0 to c_total, so xi covers its full physical range 0 to 1.",
      "initial_state": {},
      "parameters": {
        "c_total": 40.9
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "c_i",
            "range": {
              "start": 0.0,
              "stop": 40.9,
              "count": 25,
              "scale": "linear"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "xi_vs_ci",
          "type": "line",
          "description": "Volume mixing ratio xi as a function of species molar concentration at c_total = 40.9 mol/m^3.",
          "x": {
            "variable": "c_i",
            "label": "Species molar concentration (mol/m^3)"
          },
          "y": {
            "variable": "xi",
            "label": "Volume mixing ratio (dimensionless)"
          }
        }
      ]
    },
    {
      "id": "xi_vs_total_concentration",
      "description": "Volume mixing ratio as a function of the total molar concentration of air at a fixed species concentration (c_i = 0.01636 mol/m^3, a CO2-like trace amount). Reproduces the inverse xi proportional-to 1/c_total dependence: at fixed species content, denser air (larger c_total) dilutes the species to a smaller mixing ratio. c_total is swept from 20 mol/m^3 (mid-troposphere) to 45 mol/m^3 (cold, dense surface air).",
      "initial_state": {},
      "parameters": {
        "c_i": 0.01636
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "c_total",
            "range": {
              "start": 20.0,
              "stop": 45.0,
              "count": 25,
              "scale": "linear"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "xi_vs_ctotal",
          "type": "line",
          "description": "Volume mixing ratio xi as a function of total air molar concentration at c_i = 0.01636 mol/m^3.",
          "x": {
            "variable": "c_total",
            "label": "Total molar concentration of air (mol/m^3)"
          },
          "y": {
            "variable": "xi",
            "label": "Volume mixing ratio (dimensionless)"
          }
        }
      ]
    },
    {
      "id": "xi_concentration_heatmap",
      "description": "Two-dimensional sweep over species concentration and total air concentration. Surfaces the full xi = c_i / c_total response: the mixing ratio rises with c_i and falls with c_total. c_i is swept from 0 to 20 mol/m^3 and c_total from 20 to 45 mol/m^3, so c_i <= c_total throughout and xi stays within its physical range 0 to 1.",
      "initial_state": {},
      "parameters": {},
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "c_i",
            "range": {
              "start": 0.0,
              "stop": 20.0,
              "count": 12,
              "scale": "linear"
            }
          },
          {
            "parameter": "c_total",
            "range": {
              "start": 20.0,
              "stop": 45.0,
              "count": 12,
              "scale": "linear"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "xi_heatmap",
          "type": "heatmap",
          "description": "Volume mixing ratio xi as a function of species molar concentration and total air molar concentration.",
          "x": {
            "variable": "c_i",
            "label": "Species molar concentration (mol/m^3)"
          },
          "y": {
            "variable": "c_total",
            "label": "Total molar concentration of air (mol/m^3)"
          },
          "value": {
            "variable": "xi",
            "reduce": "final"
          }
        }
      ]
    }
  ]
}