FuelModelLookup

{
  "reference": {
    "citation": "Anderson, H.E. (1982). Aids to determining fuel models for estimating fire behavior. USDA Forest Service Gen. Tech. Rep. INT-122.",
    "notes": "source_ref: WildlandFire.jl@126976f2508ceacca6c486b21ae6da5b168c6f46:src/coupling.jl:155\n\nUpstream `FuelModelLookup` is an MTK `@mtkmodel` whose single input is `code` (`@parameters code=1`) and whose six outputs are `@variables sigma(t), w_0(t), delta(t), M_x(t), h(t), T_f(t)` defined by `@observed` equations that call the six `@register_symbolic` fuel functions:\n\n  sigma ~ fuel_savr(code)\n  w_0   ~ fuel_load(code)\n  delta ~ fuel_depth(code)\n  M_x   ~ fuel_mce(code)\n  h     ~ fuel_heat(code)\n  T_f   ~ fuel_weight(code)\n\nEach fuel_* registered function maps the integer Anderson code to a physical property in SI units, falling back to the fuel-model-1 default for out-of-range codes. The sole exception is fuel_heat, which maps codes 1–13 to the shared value 18,608,000 J/kg and all other codes (including LANDFIRE non-burnable 91–99) to 0 J/kg.\n\nSI unit conversions (applied in the registered function ESMs, preserved here):\n  sigma  (σ): 1/ft → 1/m via ÷ 0.3048\n  w_0 (w₀): upstream mixed units → kg/m² via × (0.45359237 / 0.09290304)\n  delta (δ): ft → m via × 0.3048\n  M_x:  already dimensionless fraction in source\n  h:    BTU/lb → J/kg via × 2326 (8000 BTU/lb for all Anderson models)\n  T_f:  s (weight / 0.8514 where weight is the source time constant)\n\ngt-p3ep resolution: each property except h is expressed as\n  ifelse(AND(code>=1, code<=13), interp.linear(values, [1..13], code), default)\nwhere interp.linear on integer-valued code returns the exact table value.\nh uses the degenerate form ifelse(AND(code>=1, code<=13), 18608000.0, 0.0)\nbecause all 13 Anderson models share the same heat content.\n\nAnderson fuel model parameter table (SI units):\n  code |  sigma (m⁻¹) |  w_0 (kg/m²) | delta (m) |  M_x  |  h (J/kg) |  T_f (s)\n  1    | 11482.939633 | 0.166002540  | 0.3048    | 0.12  | 18608000  | 8.221752\n  2    |  9842.519685 | 0.449183343  | 0.3048    | 0.15  | 18608000  | 8.221752\n  3    |  4921.259843 | 0.673775014  | 0.762     | 0.25  | 18608000  | 8.221752\n  4    |  5705.380577 | 1.122958356  | 1.8288    | 0.20  | 18608000  | 211.41649\n  5    |  5521.653543 | 0.224591671  | 0.6096    | 0.20  | 18608000  | 29.36340\n  6    |  5131.233596 | 0.336887507  | 0.762     | 0.25  | 18608000  | 29.36340\n  7    |  5124.671916 | 0.253886237  | 0.762     | 0.40  | 18608000  | 29.36340\n  8    |  6197.506562 | 0.336887507  | 0.06096   | 0.30  | 18608000  | 1057.08245\n  9    |  8149.606299 | 0.654245303  | 0.06096   | 0.25  | 18608000  | 1057.08245\n  10   |  5787.401575 | 0.673775014  | 0.3048    | 0.25  | 18608000  | 1057.08245\n  11   |  3877.952756 | 0.336887507  | 0.3048    | 0.15  | 18608000  | 1057.08245\n  12   |  3756.561680 | 0.898366685  | 0.70104   | 0.20  | 18608000  | 1057.08245\n  13   |  3802.493438 | 1.572141699  | 0.9144    | 0.25  | 18608000  | 1057.08245\n  other| 11482.939633 | 0.166002540  | 0.3048    | 0.12  | 0         | 8.221752\n\nTolerance rationale (model-level rel=1e-12): all six outputs are computed\nvia ifelse + interp.linear at integer-valued code inputs, which returns\nexact table values at grid knots. 1e-12 covers the one-ULP float64\nrounding without admitting any physical imprecision."
  },
  "tolerance": {
    "rel": 1e-12
  },
  "variables": {
    "code": {
      "type": "parameter",
      "units": "1",
      "default": 1.0,
      "description": "Anderson 13 fuel model code (integer 1–13). Values outside this range (including LANDFIRE non-burnable codes 91–99) return fuel-model-1 defaults for all properties except h, which returns 0 J/kg for out-of-range codes."
    },
    "sigma": {
      "type": "unknown",
      "units": "1/m",
      "description": "Surface-area-to-volume ratio σ of the fuel particle (m⁻¹). Anderson model 1 (short grass): 11482.94 m⁻¹ through model 13 (heavy slash): 3802.49 m⁻¹. Out-of-range codes return 11482.94 m⁻¹ (fuel model 1 default). Sourced from fuel_savr registered function."
    },
    "w_0": {
      "type": "unknown",
      "units": "kg/m^2",
      "description": "Oven-dry fuel load per unit area w₀ (kg/m²). Anderson model 1: 0.1660 kg/m² (light short-grass fuel); model 13 (heavy slash): 1.5721 kg/m². Out-of-range codes return 0.1660 kg/m² (fuel model 1 default). Sourced from fuel_load registered function."
    },
    "delta": {
      "type": "unknown",
      "units": "m",
      "description": "Fuel bed depth δ (m). Anderson model 1: 0.3048 m (1 ft, short grass); model 4 (chaparral): 1.8288 m (6 ft). Models 8 and 9 (closed/open timber litter): 0.06096 m (0.2 ft). Out-of-range codes return 0.3048 m (fuel model 1 default). Sourced from fuel_depth registered function."
    },
    "M_x": {
      "type": "unknown",
      "units": "1",
      "description": "Dead fuel moisture content of extinction Mₓ (dimensionless dry-weight-basis fraction). Ranges from 0.12 (model 1, short grass) to 0.40 (model 7, southern rough). Out-of-range codes return 0.12 (fuel model 1 default). Sourced from fuel_mce registered function."
    },
    "h": {
      "type": "unknown",
      "units": "J/kg",
      "description": "Low heat content of combustion h (J/kg). All 13 Anderson fuel models share h = 8000 BTU/lb = 18,608,000 J/kg (using 1 BTU/lb = 2326 J/kg). LANDFIRE non-burnable codes (91–99) and other out-of-range codes return 0 J/kg (no combustion). Sourced from fuel_heat registered function."
    },
    "T_f": {
      "type": "unknown",
      "units": "s",
      "description": "Fuel particle residence time Tᶠ (s), computed as the WRF-SFIRE weight constant divided by 0.8514. Codes 1–3 (grass): ≈ 8.22 s; code 4 (chaparral): ≈ 211.4 s; codes 5–7 (shrub): ≈ 29.4 s; codes 8–13 (timber/slash): ≈ 1057 s. Out-of-range codes return ≈ 8.22 s (fuel model 1 default). Sourced from fuel_weight registered function."
    },
    "wind_reduction": {
      "type": "unknown",
      "units": "1",
      "description": "Midflame wind adjustment factor (unsheltered fuel; Baughman & Albini 1980, Andrews 2012 RMRS-GTR-266): WAF = 1.83 / ln((6.096 + 0.36·δ)/(0.13·δ)), with δ the fuel-bed depth in METRES and 6.096 m = 20 ft (the reference wind height). This is the feet-form 1.83/ln((20+0.36·δ_ft)/(0.13·δ_ft)) rewritten in SI (multiply num & den by 0.3048) so it is dimensionally consistent. It is the ratio of the midflame wind to the 10 m (≈20 ft) wind: grass (δ=1 ft=0.305 m)→≈0.36, brush/chaparral (δ=6 ft=1.83 m)→≈0.55. Coupled to MidflameWind.wind_reduction to replace the former fixed 0.4, making the reduction fuel-dependent. δ floored at 0.01 m so the log stays finite for non-burnable codes (which carry h=0 → R0=0 anyway)."
    }
  },
  "equations": [
    {
      "lhs": "sigma",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">=",
                "args": [
                  "code",
                  1.0
                ]
              },
              {
                "op": "<=",
                "args": [
                  "code",
                  13.0
                ]
              }
            ]
          },
          {
            "op": "fn",
            "name": "interp.linear",
            "args": [
              {
                "op": "const",
                "value": [
                  11482.939632545931,
                  9842.51968503937,
                  4921.259842519685,
                  5705.380577427822,
                  5521.653543307087,
                  5131.233595800525,
                  5124.6719160104985,
                  6197.50656167979,
                  8149.606299212598,
                  5787.40157480315,
                  3877.952755905512,
                  3756.561679790026,
                  3802.49343832021
                ],
                "args": []
              },
              {
                "op": "const",
                "value": [
                  1.0,
                  2.0,
                  3.0,
                  4.0,
                  5.0,
                  6.0,
                  7.0,
                  8.0,
                  9.0,
                  10.0,
                  11.0,
                  12.0,
                  13.0
                ],
                "args": []
              },
              "code"
            ]
          },
          11482.939632545931
        ]
      }
    },
    {
      "lhs": "w_0",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">=",
                "args": [
                  "code",
                  1.0
                ]
              },
              {
                "op": "<=",
                "args": [
                  "code",
                  13.0
                ]
              }
            ]
          },
          {
            "op": "fn",
            "name": "interp.linear",
            "args": [
              {
                "op": "const",
                "value": [
                  0.16600253963702372,
                  0.4491833425472406,
                  0.673775013820861,
                  1.1229583563681016,
                  0.2245916712736203,
                  0.3368875069104305,
                  0.2538862370919186,
                  0.3368875069104305,
                  0.6542453032753287,
                  0.673775013820861,
                  0.3368875069104305,
                  0.8983666850944813,
                  1.5721416989153423
                ],
                "args": []
              },
              {
                "op": "const",
                "value": [
                  1.0,
                  2.0,
                  3.0,
                  4.0,
                  5.0,
                  6.0,
                  7.0,
                  8.0,
                  9.0,
                  10.0,
                  11.0,
                  12.0,
                  13.0
                ],
                "args": []
              },
              "code"
            ]
          },
          0.16600253963702372
        ]
      }
    },
    {
      "lhs": "delta",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">=",
                "args": [
                  "code",
                  1.0
                ]
              },
              {
                "op": "<=",
                "args": [
                  "code",
                  13.0
                ]
              }
            ]
          },
          {
            "op": "fn",
            "name": "interp.linear",
            "args": [
              {
                "op": "const",
                "value": [
                  0.3048,
                  0.3048,
                  0.762,
                  1.8288,
                  0.6096,
                  0.762,
                  0.762,
                  0.06096,
                  0.06096,
                  0.3048,
                  0.3048,
                  0.70104,
                  0.9144
                ],
                "args": []
              },
              {
                "op": "const",
                "value": [
                  1.0,
                  2.0,
                  3.0,
                  4.0,
                  5.0,
                  6.0,
                  7.0,
                  8.0,
                  9.0,
                  10.0,
                  11.0,
                  12.0,
                  13.0
                ],
                "args": []
              },
              "code"
            ]
          },
          0.3048
        ]
      }
    },
    {
      "lhs": "M_x",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">=",
                "args": [
                  "code",
                  1.0
                ]
              },
              {
                "op": "<=",
                "args": [
                  "code",
                  13.0
                ]
              }
            ]
          },
          {
            "op": "fn",
            "name": "interp.linear",
            "args": [
              {
                "op": "const",
                "value": [
                  0.12,
                  0.15,
                  0.25,
                  0.2,
                  0.2,
                  0.25,
                  0.4,
                  0.3,
                  0.25,
                  0.25,
                  0.15,
                  0.2,
                  0.25
                ],
                "args": []
              },
              {
                "op": "const",
                "value": [
                  1.0,
                  2.0,
                  3.0,
                  4.0,
                  5.0,
                  6.0,
                  7.0,
                  8.0,
                  9.0,
                  10.0,
                  11.0,
                  12.0,
                  13.0
                ],
                "args": []
              },
              "code"
            ]
          },
          0.12
        ]
      }
    },
    {
      "lhs": "h",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">=",
                "args": [
                  "code",
                  1.0
                ]
              },
              {
                "op": "<=",
                "args": [
                  "code",
                  13.0
                ]
              }
            ]
          },
          18608000.0,
          0.0
        ]
      }
    },
    {
      "lhs": "T_f",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": "and",
            "args": [
              {
                "op": ">=",
                "args": [
                  "code",
                  1.0
                ]
              },
              {
                "op": "<=",
                "args": [
                  "code",
                  13.0
                ]
              }
            ]
          },
          {
            "op": "fn",
            "name": "interp.linear",
            "args": [
              {
                "op": "const",
                "value": [
                  8.221752407798919,
                  8.221752407798919,
                  8.221752407798919,
                  211.4164904862579,
                  29.36340145642471,
                  29.36340145642471,
                  29.36340145642471,
                  1057.0824524312895,
                  1057.0824524312895,
                  1057.0824524312895,
                  1057.0824524312895,
                  1057.0824524312895,
                  1057.0824524312895
                ],
                "args": []
              },
              {
                "op": "const",
                "value": [
                  1.0,
                  2.0,
                  3.0,
                  4.0,
                  5.0,
                  6.0,
                  7.0,
                  8.0,
                  9.0,
                  10.0,
                  11.0,
                  12.0,
                  13.0
                ],
                "args": []
              },
              "code"
            ]
          },
          8.221752407798919
        ]
      }
    },
    {
      "lhs": "wind_reduction",
      "rhs": {
        "op": "/",
        "args": [
          1.83,
          {
            "op": "log",
            "args": [
              {
                "op": "/",
                "args": [
                  {
                    "op": "+",
                    "args": [
                      6.096,
                      {
                        "op": "*",
                        "args": [
                          0.36,
                          {
                            "op": "max",
                            "args": [
                              "delta",
                              0.01
                            ]
                          }
                        ]
                      }
                    ]
                  },
                  {
                    "op": "*",
                    "args": [
                      0.13,
                      {
                        "op": "max",
                        "args": [
                          "delta",
                          0.01
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "code_1_short_grass_all_properties",
      "description": "Anderson fuel model 1 (short grass): code=1 → verify all six Rothermel fuel properties. This is the lowest-numbered Anderson model and the default for out-of-range codes (except h).",
      "parameter_overrides": {
        "code": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 11482.939632545931,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "w_0",
          "time": 0.0,
          "expected": 0.16600253963702372,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "delta",
          "time": 0.0,
          "expected": 0.3048,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.12,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "h",
          "time": 0.0,
          "expected": 18608000.0,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 8.221752407798919,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        }
      ]
    },
    {
      "id": "code_2_timber_grass",
      "description": "Anderson fuel model 2 (timber/grass/shrub understory): code=2 → verify σ and T_f (same T_f as model 1 but different σ and w₀).",
      "parameter_overrides": {
        "code": 2.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 9842.51968503937,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "w_0",
          "time": 0.0,
          "expected": 0.4491833425472406,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.15,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 8.221752407798919,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        }
      ]
    },
    {
      "id": "code_4_chaparral_all_properties",
      "description": "Anderson fuel model 4 (chaparral): code=4 → verify all six properties. Model 4 has the deepest fuel bed (1.8288 m) and the longest residence time (≈211.4 s) of the shrub/brush group.",
      "parameter_overrides": {
        "code": 4.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 5705.380577427822,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "w_0",
          "time": 0.0,
          "expected": 1.1229583563681016,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "delta",
          "time": 0.0,
          "expected": 1.8288,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.2,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "h",
          "time": 0.0,
          "expected": 18608000.0,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 211.4164904862579,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        }
      ]
    },
    {
      "id": "code_7_southern_rough",
      "description": "Anderson fuel model 7 (southern rough): code=7 → highest Mₓ (0.40) in the Anderson table; T_f in the shrub group (≈29.4 s).",
      "parameter_overrides": {
        "code": 7.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 5124.6719160104985,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "w_0",
          "time": 0.0,
          "expected": 0.2538862370919186,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "delta",
          "time": 0.0,
          "expected": 0.762,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.4,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "h",
          "time": 0.0,
          "expected": 18608000.0,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 29.36340145642471,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        }
      ]
    },
    {
      "id": "code_8_closed_timber_litter",
      "description": "Anderson fuel model 8 (closed timber litter): code=8 → transitions to the timber/slash group with T_f≈1057 s and very shallow fuel bed (0.06096 m = 0.2 ft).",
      "parameter_overrides": {
        "code": 8.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 6197.50656167979,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "delta",
          "time": 0.0,
          "expected": 0.06096,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.3,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 1057.0824524312895,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        }
      ]
    },
    {
      "id": "code_13_heavy_slash_all_properties",
      "description": "Anderson fuel model 13 (heavy logging slash): code=13 → highest-numbered valid model; highest w₀ (1.5721 kg/m²) and long residence time (≈1057 s).",
      "parameter_overrides": {
        "code": 13.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 3802.49343832021,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "w_0",
          "time": 0.0,
          "expected": 1.5721416989153423,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "delta",
          "time": 0.0,
          "expected": 0.9144,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.25,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "h",
          "time": 0.0,
          "expected": 18608000.0,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 1057.0824524312895,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        }
      ]
    },
    {
      "id": "code_0_below_range",
      "description": "Code 0 (below valid range 1–13): all five non-h properties return fuel-model-1 defaults; h returns 0.0 J/kg (no combustion for non-burnable codes).",
      "parameter_overrides": {
        "code": 0.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 11482.939632545931,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "w_0",
          "time": 0.0,
          "expected": 0.16600253963702372,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "delta",
          "time": 0.0,
          "expected": 0.3048,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.12,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "h",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-12
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 8.221752407798919,
          "tolerance": {
            "rel": 1e-12
          }
        }
      ]
    },
    {
      "id": "code_14_above_range",
      "description": "Code 14 (above valid range 1–13): same default behavior as code 0. Confirms upper boundary of the guard.",
      "parameter_overrides": {
        "code": 14.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 11482.939632545931,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "h",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-12
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 8.221752407798919,
          "tolerance": {
            "rel": 1e-12
          }
        }
      ]
    },
    {
      "id": "code_91_nonburnable_urban",
      "description": "LANDFIRE non-burnable code 91 (urban): h returns 0 J/kg (fire spread suppressed via zero heat content); other five properties return fuel-model-1 defaults.",
      "parameter_overrides": {
        "code": 91.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 11482.939632545931,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "w_0",
          "time": 0.0,
          "expected": 0.16600253963702372,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "delta",
          "time": 0.0,
          "expected": 0.3048,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.12,
          "tolerance": {
            "rel": 1e-12
          }
        },
        {
          "variable": "h",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-12
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 8.221752407798919,
          "tolerance": {
            "rel": 1e-12
          }
        }
      ]
    },
    {
      "id": "code_11_light_logging_slash",
      "description": "Anderson fuel model 11 (light logging slash): code=11 → lowest σ of the three slash models (3877.95 m⁻¹); M_x drops back to 0.15 (same as model 2).",
      "parameter_overrides": {
        "code": 11.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "assertions": [
        {
          "variable": "sigma",
          "time": 0.0,
          "expected": 3877.952755905512,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "w_0",
          "time": 0.0,
          "expected": 0.3368875069104305,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "delta",
          "time": 0.0,
          "expected": 0.3048,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "M_x",
          "time": 0.0,
          "expected": 0.15,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        },
        {
          "variable": "T_f",
          "time": 0.0,
          "expected": 1057.0824524312895,
          "tolerance": {
            "abs": 0.0,
            "rel": 0.0
          }
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "fuel_properties_vs_code",
      "description": "Sweep fuel model codes 0–14 to visualise all six Rothermel fuel properties across the 13 Anderson models. Code 0 and 14 return the out-of-range defaults (fuel-model-1 for σ, w₀, δ, Mₓ, Tᶠ; 0 for h). The plots show the piecewise-constant lookup structure and the discontinuity in h at the boundary between burnable (codes 1–13) and non-burnable codes.",
      "initial_state": {},
      "parameters": {
        "code": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "code",
            "range": {
              "start": 0.0,
              "stop": 14.0,
              "count": 15,
              "scale": "linear"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "sigma_vs_code",
          "type": "line",
          "description": "Surface-area-to-volume ratio σ (m⁻¹) across fuel model codes. Short grass (1) and hardwood litter (9) have the highest σ; heavy slash (12–13) the lowest.",
          "x": {
            "variable": "code",
            "label": "fuel model code"
          },
          "y": {
            "variable": "sigma",
            "label": "σ (m⁻¹)"
          }
        },
        {
          "id": "w0_vs_code",
          "type": "line",
          "description": "Oven-dry fuel load w₀ (kg/m²) across fuel model codes. Chaparral (4) and heavy slash (13) have the heaviest fuel loads.",
          "x": {
            "variable": "code",
            "label": "fuel model code"
          },
          "y": {
            "variable": "w_0",
            "label": "w₀ (kg/m²)"
          }
        },
        {
          "id": "h_vs_code",
          "type": "line",
          "description": "Heat content h (J/kg) across fuel model codes. Codes 1–13 share the Anderson 8000 BTU/lb value; codes outside 1–13 return 0 (non-burnable).",
          "x": {
            "variable": "code",
            "label": "fuel model code"
          },
          "y": {
            "variable": "h",
            "label": "h (J/kg)"
          }
        },
        {
          "id": "Tf_vs_code",
          "type": "line",
          "description": "Fuel particle residence time Tᶠ (s) across fuel model codes. Grass models (1–3) have the shortest Tᶠ (≈8 s); timber/slash models (8–13) the longest (≈1057 s).",
          "x": {
            "variable": "code",
            "label": "fuel model code"
          },
          "y": {
            "variable": "T_f",
            "label": "Tᶠ (s)"
          }
        }
      ]
    }
  ]
}