QuasiLaminarResistanceParticle

{
  "reference": {
    "notes": "source_ref: AtmosphericDeposition.jl@e4468c79c8dd4aae88646cd16d6bcf290874742c:src/seinfeld_pandis_ch19.jl:234\nUpstream `QuasiLaminarResistanceParticle` is an MTK `@component` implementing the Zhang et al. (2001) quasi-laminar (boundary-layer) resistance for particle dry deposition, Seinfeld & Pandis (2006) Ch. 19 Eq. 19.27 together with the four collection-mechanism sub-equations 19.21, 19.22 (beta = 2), 19.24, 19.25 and the rebound correction 19.26. It is a flat algebraic component: `System(eqs, t; name)` with seven equations and no subsystems and no differential (D) operator.\n\nVariable typing. Upstream the component declares five input `@parameters` (nu, A, alpha, gamma, D_p), one `@constants` entry (g = G_ACCEL = 9.81 m/s^2), and ten `@variables`: three of those ten — u_star, v_s, D_diff — appear only on equation right-hand sides and have no defining equation, while the other seven — Sc, St, E_B, E_IM, E_IN, R_1, r_b — are each defined by exactly one equation. u_star, v_s and D_diff are externally-supplied inputs: in the `DryDepositionParticle` composite (src line 479) they are connected to the AerodynamicResistance and ParticleSettling subsystems (qlam.u_star ~ u_star, qlam.v_s ~ settling.v_s, qlam.D_diff ~ settling.D_diff). They are declared as `@variables` upstream only so they are connectable in that composite; within the standalone component they carry no equation and no dynamics. This standalone migration therefore types them as `parameter` — there is no defining equation and no D operator that could make them `state`, and a runner needs them as fixed inputs to evaluate the component. This follows the established rig convention for flat algebraic models, where every input is a `parameter` and every equation-defined quantity is a `state`. The closest precedent is the sibling `sp_ch19/surface_resistance.esm` (esm-ug1i), migrated from the same upstream file seinfeld_pandis_ch19.jl, which makes the identical choice for its connected input `@variables` G and T_s; particle_collection_eff.esm and wesley1989/surface_resistance.esm follow the same convention. The upstream `@constants` entry g migrates the same way — a `parameter` carrying its fixed numeric default 9.81 — per the rig convention for translating MTK `@constants` (G_ACCEL is defined at src line 35). The seven equation-defined `@variables` migrate as `type: state`; after `mtkcompile` all seven reduce to observed quantities (the component has zero differential states), so `system_kind` is left unset, consistent with the observed-only sibling particle_collection_eff.esm.\n\nEquations. All seven equations are migrated verbatim from the upstream `eqs` vector in source order (Sc, St, E_B, E_IM, E_IN, R_1, r_b), one .esm equation per upstream line, so the migration is line-checkable. The upstream `Sc^(-gamma)` is encoded as a `^` node whose exponent is a unary-minus `-` node over the parameter gamma (spec §4.2 — `-` is unary or binary); Sc = nu/D_diff is always strictly positive so the power is well-defined. `exp`, `sqrt` and `^` are all spec §4.2 elementary ops, `-sqrt(St)` is a unary minus over `sqrt`, and `St` is always >= 0 (v_s, u_star, g, A all positive) so the square root is real. The component has no `ifelse`, `min`, `max` or `Piecewise` nodes.\n\nDefaults. The upstream `@parameters` and `@variables` carry no defaults, so physically-representative values are supplied here. The three land-use parameters take the Zhang et al. (2001) Table 19.2 `LANDUSE_GRASS` row (A = 2.0e-3 m, alpha = 1.2, gamma = 0.54; src lines 51-58); D_p = 1e-6 m is a 1 um accumulation-mode particle; nu = 1.5e-5 m^2/s is the kinematic viscosity of air near 298 K; g = 9.81 m/s^2 is G_ACCEL; u_star = 0.4 m/s is a representative friction velocity (the value used in upstream test 3.1); v_s = 3.5e-5 m/s and D_diff = 2.7e-11 m^2/s are the Stokes settling velocity and Brownian diffusivity of a 1 um particle (upstream test 2.3 cites v_s ~ 3.5e-5 m/s for a 1 um particle at STP). The deciduous_forest and desert inline tests exercise the other two Table 19.2 rows (`LANDUSE_DECIDUOUS_FOREST` 5.0e-3/0.6/0.56 and `LANDUSE_DESERT` 10.0e-3/50.0/0.54).\n\nTests. Upstream provides only a structural test for this component (`1.4 QuasiLaminarResistanceParticle Structure` — it checks the variable names and that there are seven equations) plus a scalar check of the Eq. 19.26 sticking-fraction formula (`3.3 Sticking Fraction Bounds`); there are no upstream numerical assertions on the assembled component. The seven inline tests here pin exact values for all seven outputs: default_parameters / deciduous_forest / desert sweep the three Table 19.2 land-use categories; ultrafine_particle and coarse_particle exercise the diffusion-controlled (E_B-dominated) and impaction-controlled (E_IM-dominated) limbs of the Zhang et al. deposition curve and the sticking-fraction rebound; high_friction_velocity and low_friction_velocity exercise the r_b ~ 1/u_star turbulent-transport scaling. default_parameters and coarse_particle re-assert r_b at t = 1 to confirm the observed-only system is time-invariant.\n\nTolerance rationale (model-level rel=1e-6, abs=1e-12): observed-only algebraic system, no ODE integration. The seven equations form a triangular chain of +, -, *, /, ^, sqrt and exp on float64; round-off is ~1e-16 per op, so rel=1e-6 leaves wide headroom across the tested ranges (Sc ~ 3e2 to 6e6, r_b ~ 1e1 to 4e3). abs=1e-12 floors the comparison for the smallest collection-efficiency terms — E_IM and E_IN fall to ~1e-11 to ~1e-14 for the ultrafine particle and the high-alpha desert land-use — where a pure relative tolerance on a near-zero physical quantity would be needlessly brittle."
  },
  "tolerance": {
    "rel": 1e-06,
    "abs": 1e-12
  },
  "variables": {
    "nu": {
      "type": "parameter",
      "units": "m^2/s",
      "default": 1.5e-05,
      "description": "Kinematic viscosity of air"
    },
    "A": {
      "type": "parameter",
      "units": "m",
      "default": 0.002,
      "description": "Characteristic radius of surface collectors (Zhang et al. 2001, Table 19.2; default LANDUSE_GRASS)"
    },
    "alpha": {
      "type": "parameter",
      "units": "1",
      "default": 1.2,
      "description": "Impaction efficiency parameter of the land-use category (Zhang et al. 2001, Table 19.2; default LANDUSE_GRASS) (dimensionless)"
    },
    "gamma": {
      "type": "parameter",
      "units": "1",
      "default": 0.54,
      "description": "Brownian diffusion efficiency exponent of the land-use category (Zhang et al. 2001, Table 19.2; default LANDUSE_GRASS) (dimensionless)"
    },
    "D_p": {
      "type": "parameter",
      "units": "m",
      "default": 1e-06,
      "description": "Particle (aerosol) diameter"
    },
    "g": {
      "type": "parameter",
      "units": "m/s^2",
      "default": 9.81,
      "description": "Gravitational acceleration (upstream @constant G_ACCEL)"
    },
    "u_star": {
      "type": "parameter",
      "units": "m/s",
      "default": 0.4,
      "description": "Friction velocity (external input; upstream @variable connected to the AerodynamicResistance subsystem in the DryDepositionParticle composite)"
    },
    "v_s": {
      "type": "parameter",
      "units": "m/s",
      "default": 3.5e-05,
      "description": "Particle gravitational settling velocity (external input; upstream @variable connected to the ParticleSettling subsystem in the DryDepositionParticle composite)"
    },
    "D_diff": {
      "type": "parameter",
      "units": "m^2/s",
      "default": 2.7e-11,
      "description": "Brownian diffusivity of the particle (external input; upstream @variable connected to the ParticleSettling subsystem in the DryDepositionParticle composite)"
    },
    "Sc": {
      "type": "unknown",
      "units": "1",
      "description": "Particle Schmidt number, Sc = nu/D_diff (dimensionless)"
    },
    "St": {
      "type": "unknown",
      "units": "1",
      "description": "Stokes number for vegetated surfaces, St = v_s*u_star/(g*A) (Eq. 19.24) (dimensionless)"
    },
    "E_B": {
      "type": "unknown",
      "units": "1",
      "description": "Brownian diffusion collection efficiency, E_B = Sc^(-gamma) (Eq. 19.21) (dimensionless)"
    },
    "E_IM": {
      "type": "unknown",
      "units": "1",
      "description": "Inertial impaction collection efficiency, E_IM = (St/(alpha+St))^2 (Eq. 19.22, beta = 2) (dimensionless)"
    },
    "E_IN": {
      "type": "unknown",
      "units": "1",
      "description": "Interception collection efficiency, E_IN = 0.5*(D_p/A)^2 (Eq. 19.25) (dimensionless)"
    },
    "R_1": {
      "type": "unknown",
      "units": "1",
      "description": "Sticking (rebound-correction) fraction, R_1 = exp(-sqrt(St)) (Eq. 19.26) (dimensionless)"
    },
    "r_b": {
      "type": "unknown",
      "units": "s/m",
      "description": "Quasi-laminar (boundary-layer) resistance for the particle, Eq. 19.27 (Zhang et al. 2001)"
    }
  },
  "equations": [
    {
      "_comment": "Particle Schmidt number (src line 270): Sc = nu/D_diff",
      "lhs": "Sc",
      "rhs": {
        "op": "/",
        "args": [
          "nu",
          "D_diff"
        ]
      }
    },
    {
      "_comment": "Eq. 19.24 - Stokes number for vegetated surfaces (src line 272): St = v_s*u_star/(g*A)",
      "lhs": "St",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "v_s",
              "u_star"
            ]
          },
          {
            "op": "*",
            "args": [
              "g",
              "A"
            ]
          }
        ]
      }
    },
    {
      "_comment": "Eq. 19.21 - Brownian diffusion collection efficiency (src line 274): E_B = Sc^(-gamma)",
      "lhs": "E_B",
      "rhs": {
        "op": "^",
        "args": [
          "Sc",
          {
            "op": "-",
            "args": [
              "gamma"
            ]
          }
        ]
      }
    },
    {
      "_comment": "Eq. 19.22 - Inertial impaction collection efficiency, beta = 2 (src line 276): E_IM = (St/(alpha+St))^2",
      "lhs": "E_IM",
      "rhs": {
        "op": "^",
        "args": [
          {
            "op": "/",
            "args": [
              "St",
              {
                "op": "+",
                "args": [
                  "alpha",
                  "St"
                ]
              }
            ]
          },
          2
        ]
      }
    },
    {
      "_comment": "Eq. 19.25 - Interception collection efficiency (src line 278): E_IN = 0.5*(D_p/A)^2",
      "lhs": "E_IN",
      "rhs": {
        "op": "*",
        "args": [
          0.5,
          {
            "op": "^",
            "args": [
              {
                "op": "/",
                "args": [
                  "D_p",
                  "A"
                ]
              },
              2
            ]
          }
        ]
      }
    },
    {
      "_comment": "Eq. 19.26 - Sticking fraction / rebound correction (src line 280): R_1 = exp(-sqrt(St))",
      "lhs": "R_1",
      "rhs": {
        "op": "exp",
        "args": [
          {
            "op": "-",
            "args": [
              {
                "op": "sqrt",
                "args": [
                  "St"
                ]
              }
            ]
          }
        ]
      }
    },
    {
      "_comment": "Eq. 19.27 - Quasi-laminar resistance for particles, Zhang et al. (2001) (src line 282): r_b = 1/(3*u_star*(E_B+E_IM+E_IN)*R_1)",
      "lhs": "r_b",
      "rhs": {
        "op": "/",
        "args": [
          1,
          {
            "op": "*",
            "args": [
              3,
              "u_star",
              {
                "op": "+",
                "args": [
                  "E_B",
                  "E_IM",
                  "E_IN"
                ]
              },
              "R_1"
            ]
          }
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "default_parameters",
      "description": "Component defaults: the Zhang et al. (2001) Table 19.2 grassland land-use category (A = 2 mm, alpha = 1.2, gamma = 0.54) collecting a 1 um accumulation-mode particle (v_s = 3.5e-5 m/s, D_diff = 2.7e-11 m^2/s) in a u_star = 0.4 m/s turbulent layer. The 1 um particle sits in the Greenfield gap, where Brownian diffusion has weakened and inertial impaction has not yet switched on: E_B (~7.9e-4) dominates the three collection terms, E_IM and E_IN are ~1e-7, and the resulting quasi-laminar resistance r_b is large (~1.08e3 s/m). The model is observed-only (no differential state), so r_b is re-asserted at t = 1 to confirm time-invariance.",
      "parameter_overrides": {
        "nu": 1.5e-05,
        "A": 0.002,
        "alpha": 1.2,
        "gamma": 0.54,
        "D_p": 1e-06,
        "g": 9.81,
        "u_star": 0.4,
        "v_s": 3.5e-05,
        "D_diff": 2.7e-11
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "Sc",
          "time": 0.0,
          "expected": 555555.5555555555
        },
        {
          "variable": "St",
          "time": 0.0,
          "expected": 0.0007135575942915391
        },
        {
          "variable": "E_B",
          "time": 0.0,
          "expected": 0.0007904004025326843
        },
        {
          "variable": "E_IM",
          "time": 0.0,
          "expected": 3.531662845755827e-07
        },
        {
          "variable": "E_IN",
          "time": 0.0,
          "expected": 1.25e-07
        },
        {
          "variable": "R_1",
          "time": 0.0,
          "expected": 0.9736411242414842
        },
        {
          "variable": "r_b",
          "time": 0.0,
          "expected": 1082.2062495638543
        },
        {
          "variable": "r_b",
          "time": 1.0,
          "expected": 1082.2062495638543
        }
      ]
    },
    {
      "id": "deciduous_forest",
      "description": "The Zhang et al. (2001) Table 19.2 deciduous-forest land-use category (A = 5 mm, alpha = 0.6, gamma = 0.56), same 1 um particle and u_star as default_parameters. The larger collector radius A lowers both the Stokes number St (= v_s*u_star/(g*A)) and the interception term E_IN (= 0.5*(D_p/A)^2) relative to grassland, and the larger Brownian exponent gamma lowers E_B; with all three collection terms reduced, r_b rises above the grassland value.",
      "parameter_overrides": {
        "nu": 1.5e-05,
        "A": 0.005,
        "alpha": 0.6,
        "gamma": 0.56,
        "D_p": 1e-06,
        "g": 9.81,
        "u_star": 0.4,
        "v_s": 3.5e-05,
        "D_diff": 2.7e-11
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "Sc",
          "time": 0.0,
          "expected": 555555.5555555555
        },
        {
          "variable": "St",
          "time": 0.0,
          "expected": 0.0002854230377166157
        },
        {
          "variable": "E_B",
          "time": 0.0,
          "expected": 0.0006066701164541612
        },
        {
          "variable": "E_IM",
          "time": 0.0,
          "expected": 2.2608016071660284e-07
        },
        {
          "variable": "E_IN",
          "time": 0.0,
          "expected": 1.9999999999999997e-08
        },
        {
          "variable": "R_1",
          "time": 0.0,
          "expected": 0.9832474435574972
        },
        {
          "variable": "r_b",
          "time": 0.0,
          "expected": 1396.455820344653
        }
      ]
    },
    {
      "id": "desert",
      "description": "The Zhang et al. (2001) Table 19.2 desert land-use category (A = 10 mm, alpha = 50.0, gamma = 0.54), same 1 um particle and u_star as default_parameters. The very large impaction parameter alpha drives the impaction term E_IM = (St/(alpha+St))^2 to a negligible ~8e-12 (a smooth desert surface barely impacts particles), so collection is carried almost entirely by Brownian diffusion E_B; the gamma value equals grassland's so E_B is unchanged from the default case.",
      "parameter_overrides": {
        "nu": 1.5e-05,
        "A": 0.01,
        "alpha": 50.0,
        "gamma": 0.54,
        "D_p": 1e-06,
        "g": 9.81,
        "u_star": 0.4,
        "v_s": 3.5e-05,
        "D_diff": 2.7e-11
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "Sc",
          "time": 0.0,
          "expected": 555555.5555555555
        },
        {
          "variable": "St",
          "time": 0.0,
          "expected": 0.00014271151885830784
        },
        {
          "variable": "E_B",
          "time": 0.0,
          "expected": 0.0007904004025326843
        },
        {
          "variable": "E_IM",
          "time": 0.0,
          "expected": 8.14658454141356e-12
        },
        {
          "variable": "E_IN",
          "time": 0.0,
          "expected": 4.999999999999999e-09
        },
        {
          "variable": "R_1",
          "time": 0.0,
          "expected": 0.9881248798116502
        },
        {
          "variable": "r_b",
          "time": 0.0,
          "expected": 1066.9818084607048
        }
      ]
    },
    {
      "id": "ultrafine_particle",
      "description": "A 10 nm ultrafine particle over grassland: a small, slowly-settling particle (v_s = 7e-9 m/s) with a large Brownian diffusivity (D_diff = 5e-8 m^2/s). The high diffusivity gives a small Schmidt number Sc = 300, so the Brownian-diffusion efficiency E_B rises to ~0.046 and dominates collection (the diffusion-controlled limb of the deposition curve); the tiny Stokes number leaves E_IM and E_IN negligible. With strong collection the quasi-laminar resistance r_b drops to ~18 s/m.",
      "parameter_overrides": {
        "nu": 1.5e-05,
        "A": 0.002,
        "alpha": 1.2,
        "gamma": 0.54,
        "D_p": 1e-08,
        "g": 9.81,
        "u_star": 0.4,
        "v_s": 7e-09,
        "D_diff": 5e-08
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "Sc",
          "time": 0.0,
          "expected": 300.0
        },
        {
          "variable": "St",
          "time": 0.0,
          "expected": 1.4271151885830784e-07
        },
        {
          "variable": "E_B",
          "time": 0.0,
          "expected": 0.045957301753233475
        },
        {
          "variable": "E_IM",
          "time": 0.0,
          "expected": 1.4143453312919429e-14
        },
        {
          "variable": "E_IN",
          "time": 0.0,
          "expected": 1.2500000000000002e-11
        },
        {
          "variable": "R_1",
          "time": 0.0,
          "expected": 0.999622299565327
        },
        {
          "variable": "r_b",
          "time": 0.0,
          "expected": 18.13962462093789
        }
      ]
    },
    {
      "id": "coarse_particle",
      "description": "A 10 um coarse particle over grassland: a large, fast-settling particle (v_s = 3e-3 m/s) with a small Brownian diffusivity (D_diff = 2.5e-12 m^2/s). The fast settling raises the Stokes number to St ~ 0.061, so inertial impaction E_IM (~2.4e-3) now exceeds the Brownian term E_B (~2.2e-4) — the impaction-controlled limb — while the sticking fraction R_1 falls to ~0.78 as larger Stokes numbers bring particle rebound. r_b is re-asserted at t = 1 to confirm time-invariance.",
      "parameter_overrides": {
        "nu": 1.5e-05,
        "A": 0.002,
        "alpha": 1.2,
        "gamma": 0.54,
        "D_p": 1e-05,
        "g": 9.81,
        "u_star": 0.4,
        "v_s": 0.003,
        "D_diff": 2.5e-12
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "Sc",
          "time": 0.0,
          "expected": 6000000.000000001
        },
        {
          "variable": "St",
          "time": 0.0,
          "expected": 0.06116207951070336
        },
        {
          "variable": "E_B",
          "time": 0.0,
          "expected": 0.00021867459194725388
        },
        {
          "variable": "E_IM",
          "time": 0.0,
          "expected": 0.0023519207195748485
        },
        {
          "variable": "E_IN",
          "time": 0.0,
          "expected": 1.25e-05
        },
        {
          "variable": "R_1",
          "time": 0.0,
          "expected": 0.7808988246673252
        },
        {
          "variable": "r_b",
          "time": 0.0,
          "expected": 413.12697557676404
        },
        {
          "variable": "r_b",
          "time": 1.0,
          "expected": 413.12697557676404
        }
      ]
    },
    {
      "id": "high_friction_velocity",
      "description": "Component defaults but in a strongly turbulent layer, u_star = 0.8 m/s (double the default). A higher friction velocity raises the Stokes number St linearly and strengthens turbulent transport to the surface; the explicit 1/(3*u_star) factor plus the slightly larger collection terms roughly halve r_b relative to default_parameters. Sc, E_B, and E_IN are independent of u_star and stay at their default values.",
      "parameter_overrides": {
        "nu": 1.5e-05,
        "A": 0.002,
        "alpha": 1.2,
        "gamma": 0.54,
        "D_p": 1e-06,
        "g": 9.81,
        "u_star": 0.8,
        "v_s": 3.5e-05,
        "D_diff": 2.7e-11
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "Sc",
          "time": 0.0,
          "expected": 555555.5555555555
        },
        {
          "variable": "St",
          "time": 0.0,
          "expected": 0.0014271151885830783
        },
        {
          "variable": "E_B",
          "time": 0.0,
          "expected": 0.0007904004025326843
        },
        {
          "variable": "E_IM",
          "time": 0.0,
          "expected": 1.4109876023430336e-06
        },
        {
          "variable": "E_IN",
          "time": 0.0,
          "expected": 1.25e-07
        },
        {
          "variable": "R_1",
          "time": 0.0,
          "expected": 0.9629274782756465
        },
        {
          "variable": "r_b",
          "time": 0.0,
          "expected": 546.3926877939356
        }
      ]
    },
    {
      "id": "low_friction_velocity",
      "description": "Component defaults but in a weakly turbulent layer, u_star = 0.1 m/s (a quarter of the default). The low friction velocity weakens turbulent transport to the surface; r_b scales roughly as 1/u_star and climbs to ~4.3e3 s/m. This is the opposite limb of the u_star sensitivity exercised by high_friction_velocity.",
      "parameter_overrides": {
        "nu": 1.5e-05,
        "A": 0.002,
        "alpha": 1.2,
        "gamma": 0.54,
        "D_p": 1e-06,
        "g": 9.81,
        "u_star": 0.1,
        "v_s": 3.5e-05,
        "D_diff": 2.7e-11
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "Sc",
          "time": 0.0,
          "expected": 555555.5555555555
        },
        {
          "variable": "St",
          "time": 0.0,
          "expected": 0.00017838939857288478
        },
        {
          "variable": "E_B",
          "time": 0.0,
          "expected": 0.0007904004025326843
        },
        {
          "variable": "E_IM",
          "time": 0.0,
          "expected": 2.2092582098824823e-08
        },
        {
          "variable": "E_IN",
          "time": 0.0,
          "expected": 1.25e-07
        },
        {
          "variable": "R_1",
          "time": 0.0,
          "expected": 0.9867325494993485
        },
        {
          "variable": "r_b",
          "time": 0.0,
          "expected": 4273.18134505417
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "resistance_vs_friction_velocity",
      "description": "Quasi-laminar particle resistance r_b as a function of friction velocity u_star, for the default 1 um particle over grassland. As u_star rises, turbulent transport across the quasi-laminar sublayer strengthens and r_b falls steeply — roughly as 1/u_star, with a weak additional dependence through the Stokes-number terms E_IM and R_1. Reproduces the friction-velocity control on particle dry deposition discussed in Seinfeld & Pandis (2006) Ch. 19.",
      "initial_state": {},
      "parameters": {
        "nu": 1.5e-05,
        "A": 0.002,
        "alpha": 1.2,
        "gamma": 0.54,
        "D_p": 1e-06,
        "g": 9.81,
        "v_s": 3.5e-05,
        "D_diff": 2.7e-11
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "u_star",
            "range": {
              "start": 0.05,
              "stop": 1.5,
              "count": 30,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "r_b_vs_u_star",
          "type": "line",
          "description": "Quasi-laminar resistance r_b versus friction velocity u_star (log-spaced).",
          "x": {
            "variable": "u_star",
            "label": "Friction velocity (m/s)"
          },
          "y": {
            "variable": "r_b",
            "label": "Quasi-laminar resistance (s/m)"
          }
        }
      ]
    },
    {
      "id": "brownian_term_vs_diffusivity",
      "description": "Brownian-diffusion collection efficiency E_B and quasi-laminar resistance r_b as a function of the particle Brownian diffusivity D_diff, for the default grassland land-use category at u_star = 0.4 m/s. A larger diffusivity (characteristic of smaller particles) lowers the particle Schmidt number Sc = nu/D_diff and raises E_B = Sc^(-gamma), which in turn lowers r_b. This traces the diffusion-controlled limb of the Zhang et al. (2001) particle deposition curve.",
      "initial_state": {},
      "parameters": {
        "nu": 1.5e-05,
        "A": 0.002,
        "alpha": 1.2,
        "gamma": 0.54,
        "D_p": 1e-06,
        "g": 9.81,
        "u_star": 0.4,
        "v_s": 3.5e-05
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "D_diff",
            "range": {
              "start": 1e-12,
              "stop": 1e-07,
              "count": 30,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "E_B_vs_D_diff",
          "type": "line",
          "description": "Brownian-diffusion collection efficiency E_B versus particle diffusivity D_diff (log-spaced).",
          "x": {
            "variable": "D_diff",
            "label": "Brownian diffusivity (m^2/s)"
          },
          "y": {
            "variable": "E_B",
            "label": "Brownian diffusion efficiency (dimensionless)"
          }
        },
        {
          "id": "r_b_vs_D_diff",
          "type": "line",
          "description": "Quasi-laminar resistance r_b versus particle diffusivity D_diff (log-spaced).",
          "x": {
            "variable": "D_diff",
            "label": "Brownian diffusivity (m^2/s)"
          },
          "y": {
            "variable": "r_b",
            "label": "Quasi-laminar resistance (s/m)"
          }
        }
      ]
    },
    {
      "id": "impaction_and_sticking_vs_settling_velocity",
      "description": "Inertial-impaction efficiency E_IM and sticking fraction R_1 as a function of particle settling velocity v_s, for the default grassland land-use category at u_star = 0.4 m/s. The settling velocity sets the Stokes number St = v_s*u_star/(g*A): as v_s rises, E_IM = (St/(alpha+St))^2 increases (faster particles impact more readily) while the sticking fraction R_1 = exp(-sqrt(St)) falls (faster particles rebound more). This traces the impaction-controlled limb of the Zhang et al. (2001) particle deposition curve.",
      "initial_state": {},
      "parameters": {
        "nu": 1.5e-05,
        "A": 0.002,
        "alpha": 1.2,
        "gamma": 0.54,
        "D_p": 1e-06,
        "g": 9.81,
        "u_star": 0.4,
        "D_diff": 2.7e-11
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "v_s",
            "range": {
              "start": 1e-06,
              "stop": 0.01,
              "count": 30,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "E_IM_vs_v_s",
          "type": "line",
          "description": "Inertial-impaction collection efficiency E_IM versus settling velocity v_s (log-spaced).",
          "x": {
            "variable": "v_s",
            "label": "Settling velocity (m/s)"
          },
          "y": {
            "variable": "E_IM",
            "label": "Impaction efficiency (dimensionless)"
          }
        },
        {
          "id": "R_1_vs_v_s",
          "type": "line",
          "description": "Sticking fraction R_1 versus settling velocity v_s (log-spaced).",
          "x": {
            "variable": "v_s",
            "label": "Settling velocity (m/s)"
          },
          "y": {
            "variable": "R_1",
            "label": "Sticking fraction (dimensionless)"
          }
        }
      ]
    }
  ]
}