FuelDepth
Anderson (1982) 13-fuel-model fuel-bed depth lookup: maps integer fuel model code (1–13) to fuel bed depth δ in metres, converted from the upstream ft values in ANDERSON_FUEL_DATA via δ_m = depth_ft × 0.3048. Out-of-range codes (including LANDFIRE non-burnable codes 91–99) return the fuel-model-1 default 1.0 × 0.3048 = 0.3048 m. Migrated from WildlandFire.jl src/coupling.jl:125 (`@register_symbolic fuel_depth`). Resolves the gt-p3ep blocking gap via ifelse + interp.linear over the integer axis [1..13].
Description
Anderson (1982) 13-fuel-model fuel-bed depth lookup: maps integer fuel model code (1–13) to fuel bed depth δ in metres, converted from the upstream ft values in ANDERSON_FUEL_DATA via δ_m = depth_ft × 0.3048. Out-of-range codes (including LANDFIRE non-burnable codes 91–99) return the fuel-model-1 default 1.0 × 0.3048 = 0.3048 m. Migrated from WildlandFire.jl src/coupling.jl:125 (@register_symbolic fuel_depth). Resolves the gt-p3ep blocking gap via ifelse + interp.linear over the integer axis [1..13].
Reference
Anderson, H.E. (1982). Aids to determining fuel models for estimating fire behavior. USDA Forest Service Gen. Tech. Rep. INT-122.
_source_ref: WildlandFire.jl@126976f2508ceacca6c486b21ae6da5b168c6f46:src/coupling.jl:125
Upstream fuel_depth(code) is a @register_symbolic Julia function:
const _FUEL_DEPTH = Dict(k => v.depth * 0.3048 for (k, v) in ANDERSON_FUEL_DATA)
fuel_depth(code) = _lookup_fuel(_FUEL_DEPTH, code, 1.0 * 0.3048)
@register_symbolic fuel_depth(code)
where ANDERSON_FUEL_DATA.depth values (in ft) are (from Anderson 1982 / Mandel et al. 2011 Table 1): codes 1, 2: 1.0 ft → 0.3048 m code 3: 2.5 ft → 0.762 m code 4: 6.0 ft → 1.8288 m code 5: 2.0 ft → 0.6096 m codes 6, 7: 2.5 ft → 0.762 m codes 8, 9: 0.2 ft → 0.06096 m codes 10, 11: 1.0 ft → 0.3048 m code 12: 2.3 ft → 0.70104 m code 13: 3.0 ft → 0.9144 m
Default for out-of-range codes: 1.0 ft * 0.3048 = 0.3048 m (fuel model 1). This matches the upstream _lookup_fuel fallback (default argument = 1.0 * 0.3048).
Non-burnable LANDFIRE codes (91, 92, 93, 98, 99) are outside [1, 13] and return 0.3048 m. In practice, fire spread is zero for non-burnable codes regardless of depth because fuel_heat returns 0 for those codes, zeroing Rothermel Reaction Intensity and Rate of Spread.
gt-p3ep resolution: ESM 0.4.0 §9.5 interp.linear supports continuous-axis interpolation. For discrete integer-keyed lookup with separate default, we compose ifelse(AND(code>=1, code<=13), interp.linear(…), default). interp.linear at an exact integer grid knot returns the stored value (blend weight 0 or 1 at the endpoints). Out-of-range codes return the default 0.3048 m exactly.
Tolerance: observed-only algebraic model (no ODE); tolerance={rel:1e-12} — interp.linear on float64 hardware at grid knots is exact for the default branch (literal constant); 1e-12 covers the one-ULP float64 rounding without admitting any physical imprecision._
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
code | 1 | 1.0 | Anderson 13 fuel model code (dimensionless integer 1–13). Values outside this range return the fuel-model-1 default depth. |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
fuel_depth | m | Fuel bed depth δ (m). Encodes the Anderson (1982) depth parameter for the given fuel model code. Used by FuelModelLookup to set the δ input for the Rothermel spread-rate equations. |
Observed expressions
$$ fuel_{depth} = \mathrm{ifelse}\left(\mathrm{and}\left(\mathrm{>=}\left(code, 1.0\right), \mathrm{<=}\left(code, 13.0\right)\right), \mathrm{fn}\left(\mathrm{const}\left(\right), \mathrm{const}\left(\right), code\right), 0.3048\right) $$Fuel bed depth δ (m). Encodes the Anderson (1982) depth parameter for the given fuel model code. Used by FuelModelLookup to set the δ input for the Rothermel spread-rate equations.
Analyses
fuel_depth_by_code
Fuel bed depth δ (m) for each Anderson 13 fuel model code, showing the range from shallow timber litter (0.06 m) to deep chaparral (1.83 m). Compare with Table 1 of Mandel et al. (2011).
Time span: 0.0 → 1.0
Swept over: code
default_for_nonburnable_codes
Out-of-range inputs (including LANDFIRE non-burnable codes 91-99) return the FM1 default 0.3048 m.
Time span: 0.0 → 1.0
Swept over: code
Raw .esm
Raw .esm JSON (this component)
{
"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:125\n\nUpstream `fuel_depth(code)` is a @register_symbolic Julia function:\n const _FUEL_DEPTH = Dict(k => v.depth * 0.3048 for (k, v) in ANDERSON_FUEL_DATA)\n fuel_depth(code) = _lookup_fuel(_FUEL_DEPTH, code, 1.0 * 0.3048)\n @register_symbolic fuel_depth(code)\n\nwhere ANDERSON_FUEL_DATA.depth values (in ft) are (from Anderson 1982 / Mandel et al. 2011 Table 1):\n codes 1, 2: 1.0 ft → 0.3048 m\n code 3: 2.5 ft → 0.762 m\n code 4: 6.0 ft → 1.8288 m\n code 5: 2.0 ft → 0.6096 m\n codes 6, 7: 2.5 ft → 0.762 m\n codes 8, 9: 0.2 ft → 0.06096 m\n codes 10, 11: 1.0 ft → 0.3048 m\n code 12: 2.3 ft → 0.70104 m\n code 13: 3.0 ft → 0.9144 m\n\nDefault for out-of-range codes: 1.0 ft * 0.3048 = 0.3048 m (fuel model 1). This matches the upstream _lookup_fuel fallback (default argument = 1.0 * 0.3048).\n\nNon-burnable LANDFIRE codes (91, 92, 93, 98, 99) are outside [1, 13] and return 0.3048 m. In practice, fire spread is zero for non-burnable codes regardless of depth because fuel_heat returns 0 for those codes, zeroing Rothermel Reaction Intensity and Rate of Spread.\n\ngt-p3ep resolution: ESM 0.4.0 §9.5 interp.linear supports continuous-axis interpolation. For discrete integer-keyed lookup with separate default, we compose ifelse(AND(code>=1, code<=13), interp.linear(...), default). interp.linear at an exact integer grid knot returns the stored value (blend weight 0 or 1 at the endpoints). Out-of-range codes return the default 0.3048 m exactly.\n\nTolerance: observed-only algebraic model (no ODE); tolerance={rel:1e-12} — interp.linear on float64 hardware at grid knots is exact for the default branch (literal constant); 1e-12 covers the one-ULP float64 rounding without admitting any physical imprecision."
},
"tolerance": {
"rel": 1e-12
},
"variables": {
"code": {
"type": "parameter",
"units": "1",
"default": 1.0,
"description": "Anderson 13 fuel model code (dimensionless integer 1–13). Values outside this range return the fuel-model-1 default depth."
},
"fuel_depth": {
"type": "unknown",
"units": "m",
"description": "Fuel bed depth δ (m). Encodes the Anderson (1982) depth parameter for the given fuel model code. Used by FuelModelLookup to set the δ input for the Rothermel spread-rate equations."
}
},
"equations": [
{
"lhs": "fuel_depth",
"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
]
}
}
],
"tests": [
{
"id": "fm1_short_grass",
"description": "Fuel model 1 (short grass): depth=1.0 ft → δ=0.3048 m. Lowest-numbered valid Anderson model.",
"parameter_overrides": {
"code": 1.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.3048,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "fm2_timber_grass",
"description": "Fuel model 2 (timber/grass): depth=1.0 ft → same δ as FM1.",
"parameter_overrides": {
"code": 2.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.3048,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "fm3_tall_grass",
"description": "Fuel model 3 (tall grass): depth=2.5 ft → δ=0.762 m.",
"parameter_overrides": {
"code": 3.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.762,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "fm4_chaparral",
"description": "Fuel model 4 (chaparral): depth=6.0 ft → δ=1.8288 m. Deepest fuel bed among Anderson 13 models.",
"parameter_overrides": {
"code": 4.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 1.8288,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "fm5_brush",
"description": "Fuel model 5 (brush): depth=2.0 ft → δ=0.6096 m.",
"parameter_overrides": {
"code": 5.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.6096,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "fm8_closed_timber",
"description": "Fuel model 8 (closed timber litter): depth=0.2 ft → δ=0.06096 m. Shallowest fuel bed among Anderson 13 models.",
"parameter_overrides": {
"code": 8.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.06096,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "fm13_heavy_logging_slash",
"description": "Fuel model 13 (heavy logging slash): depth=3.0 ft → δ=0.9144 m. Upper boundary of valid range.",
"parameter_overrides": {
"code": 13.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.9144,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "nonburnable_urban_code91",
"description": "LANDFIRE non-burnable code 91 (urban): outside [1, 13] → returns FM1 default 0.3048 m.",
"parameter_overrides": {
"code": 91.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.3048,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "nonburnable_water_code98",
"description": "LANDFIRE non-burnable code 98 (water): outside [1, 13] → returns FM1 default 0.3048 m.",
"parameter_overrides": {
"code": 98.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.3048,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "unrecognized_code0",
"description": "Unrecognized code 0 (below lower bound): returns FM1 default 0.3048 m.",
"parameter_overrides": {
"code": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.3048,
"tolerance": {
"rel": 1e-12
}
}
]
},
{
"id": "unrecognized_code999",
"description": "Unrecognized code 999 (far above upper bound): returns FM1 default 0.3048 m.",
"parameter_overrides": {
"code": 999.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "fuel_depth",
"time": 0.0,
"expected": 0.3048,
"tolerance": {
"rel": 1e-12
}
}
]
}
],
"analyses": [
{
"id": "fuel_depth_by_code",
"description": "Fuel bed depth δ (m) for each Anderson 13 fuel model code, showing the range from shallow timber litter (0.06 m) to deep chaparral (1.83 m). Compare with Table 1 of Mandel et al. (2011).",
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "code",
"values": [
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
]
}
]
},
"plots": [
{
"id": "depth_by_code",
"type": "scatter",
"x": {
"variable": "code",
"label": "Fuel model code (1-13)"
},
"y": {
"variable": "fuel_depth",
"label": "δ (m)"
}
}
]
},
{
"id": "default_for_nonburnable_codes",
"description": "Out-of-range inputs (including LANDFIRE non-burnable codes 91-99) return the FM1 default 0.3048 m.",
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "code",
"values": [
0.0,
14.0,
91.0,
92.0,
93.0,
98.0,
99.0,
999.0
]
}
]
},
"plots": [
{
"id": "depth_nonburnable",
"type": "scatter",
"x": {
"variable": "code",
"label": "Code (out-of-range)"
},
"y": {
"variable": "fuel_depth",
"label": "δ (m)"
}
}
]
}
]
}