RothermelFireSpread
Rothermel (1972) surface fire spread model — predicts rate of spread (R), fireline intensity (IB), flame length (F_L), and related outputs from fuel-bed properties, fuel moisture, wind speed, and terrain slope. Migrated from WildlandFire.jl@126976f2 src/rothermel.jl:70 (`RothermelFireSpread` @component). Observed-only (algebraic): all 27 unknowns are defined by algebraic equations; no ODE states. Implements Table 3 and Table 7 in Andrews (2018) RMRS-GTR-371 using SI units. All empirical coefficients are converted from US customary. See reference notes for the complete Unicode→ASCII identifier map and the coupling interface (RothermelCoupler couple2 methods).
Description
Rothermel (1972) surface fire spread model — predicts rate of spread (R), fireline intensity (IB), flame length (F_L), and related outputs from fuel-bed properties, fuel moisture, wind speed, and terrain slope. Migrated from WildlandFire.jl@126976f2 src/rothermel.jl:70 (RothermelFireSpread @component). Observed-only (algebraic): all 27 unknowns are defined by algebraic equations; no ODE states. Implements Table 3 and Table 7 in Andrews (2018) RMRS-GTR-371 using SI units. All empirical coefficients are converted from US customary. See reference notes for the complete Unicode→ASCII identifier map and the coupling interface (RothermelCoupler couple2 methods).
Reference
_source_ref: WildlandFire.jl@126976f2508ceacca6c486b21ae6da5b168c6f46:src/rothermel.jl:70
Upstream RothermelFireSpread is an MTK @component with 11 @parameters (fuel-bed and environmental inputs), 35 @constants (empirical coefficients, reference values, and floor guards), and 27 time-indexed @variables defined by 27 purely algebraic equations (no D(x) terms — observed-only system). Structural verification: length(equations(sys)) == 27, length(unknowns(sys)) == 27 (see test_rothermel.jl Structural Verification).
Unicode → ASCII identifier transliteration follows the rig convention (components/wildland_fire/terrain_slope.esm, components/wildland_fire/rothermel/effective_midflame_wind.esm): σ → sigma ρ_p → rho_p tanϕ → tan_phi δ → delta ρb → rhob Γ_max → Gamma_max β → beta β_op → beta_op Γ’ → Gamma_prime β_ratio → beta_ratio η_M → eta_M η_s → eta_s ξ → xi φw → phi_w φs → phi_s φs_coeff → phi_s_coeff ε → epsilon σ_ref → sigma_ref, σ_floor → sigma_floor, δ_floor → delta_floor β_floor → beta_floor, β_ratio_floor → beta_ratio_floor ρb_floor → rhob_floor, ε_floor → epsilon_floor
MTK @constants are unified into ESM parameter declarations (same pattern as wind_limit.esm, live_fuel_moisture_extinction.esm). Both the empirical-coefficient constants and the floor-guard constants are preserved as parameters with their upstream default values.
Floor constants rationale: several equations involve bases raised to non-integer powers and denominators. Floor guards prevent 0^negative or 0/0 when fuel is absent (depletion) or non-burnable (σ=0). Only denominators and negative-power bases are guarded; numerators are unguarded so IR→0 and R→0 naturally when fuel is absent.
SI conversion notes (from US customary, Table 3, Andrews 2018): c_beta_op = 8.858 (from 3.348 * ft_to_m^(-0.8189)) c_A = 340.5 (from 133 * ft_to_m^(-0.7913)) c_C_2 = 0.0692 (from 0.133 * ft_to_m^0.55) c_B = 0.01317 (from 0.02526 * ft_to_m^0.54) c_E_2 = 1.094e-4 (from 3.59e-4 * ft_to_m) c_eps = 452.7 (from 138 / ft_to_m) c_Qig_1 = 581500 J/kg, c_Qig_2 = 2595816 J/kg (from 250 and 1116 Btu/lb) c_tr = 75590.6 s/m (from 384 min / ft_to_m * 60) c_FL = 0.00323 m (from 0.45 ft / (Btu/ft/s → W/m)^0.46) U_ref = 0.3048/60 m/s = 1 ft/min (non-dimensionalizes U for the wind-factor power law)
Coupling interface (RothermelCoupler, coupling.jl): couple2(FuelModelLookupCoupler, RothermelCoupler) promotes sigma, w0, delta, Mx, h from parameters to variables and connects them to FuelModelLookup outputs. couple2(TerrainSlopeCoupler, RothermelCoupler) promotes tan_phi from parameter to variable and connects it to TerrainSlope.tan_phi. couple2(MidflameWindCoupler, RothermelCoupler) promotes U from parameter to variable and connects it to MidflameWind.U. These couplings apply when composing multi-component ESM files; standalone use requires setting sigma, w0, delta, Mx, h, tan_phi, U, Mf as direct parameters.
Tolerance rationale (model-level rel=1e-6): observed-only algebraic system; all equations are closed-form arithmetic and transcendental functions on float64. 1e-6 matches the upstream Julia test suite tolerances (rtol=1e-6)._
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
sigma | 1/m | Surface-area-to-volume ratio of the fuel particle | |
w0 | kg/m^2 | Oven-dry fuel load per unit area | |
delta | m | Fuel bed depth | |
Mx | 1 | Dead fuel moisture of extinction (dimensionless, dry weight basis) | |
h | J/kg | 18608000.0 | Low heat content of dry fuel (default 8000 Btu/lb = 18608000 J/kg) |
S_T | 1 | 0.0555 | Total mineral content (dimensionless fraction) |
S_e | 1 | 0.01 | Effective (silica-free) mineral content (dimensionless fraction) |
rho_p | kg/m^3 | 512.6 | Oven-dry particle density (default 32 lb/ft^3 = 512.6 kg/m^3) |
Mf | 1 | Fuel moisture content (dimensionless, dry weight basis) | |
U | m/s | 0.0 | Wind velocity at midflame height. Default 0.0 so the model stays valid when U is left unbound: it feeds only Rothermel’s own phi_w -> rate R, which the wildland-fire coupling does NOT consume (only R0 + the C/B/E/beta/phi_s coefficients are coupled to the level-set leaf, which recomputes wind directionally). Binders that use Rothermel’s full R still override it. |
tan_phi | 1 | 0.0 | Slope steepness (dimensionless rise/run). Default 0.0 so the model stays valid when tan_phi is left unbound: it feeds only Rothermel’s own phi_s -> rate R, which the wildland-fire coupling does NOT consume (the level-set leaf recomputes slope directionally). Binders that use Rothermel’s full R still override it. |
sigma_ref | 1/m | 1.0 | Reference SAV ratio for non-dimensionalization before non-integer power laws (MTK @constant preserved as parameter) |
U_ref | m/s | 0.005080000000000001 | Reference wind speed = 1 ft/min = 0.3048/60 m/s; non-dimensionalizes U for the wind-factor power law (empirical calibration in ft/min) |
IB_ref | W/m | 1.0 | Reference fireline intensity for non-dimensionalization before the 0.46 power in F_L (MTK @constant preserved as parameter) |
one | 1 | 1.0 | Dimensionless one — MTK unit-balancing literal preserved from upstream @constants |
c_beta_op | 1 | 8.858 | Optimum packing ratio coefficient (SI); upstream US value 3.348 converted via 3.348 * ft_to_m^(-0.8189) |
c_Gamma_denom1 | 1 | 176502.0 | Gamma_max denominator constant 1 (SI, empirical; Table 3 Andrews 2018) |
c_Gamma_denom2 | 1 | 3.564 | Gamma_max denominator constant 2 (SI, empirical; Table 3 Andrews 2018) |
c_Gamma_mult | 1/s | 1.0 | Gamma_max unit conversion factor; gives Gamma_max units of 1/s (reaction velocity) |
c_A | 1 | 340.5 | Coefficient A constant (SI); upstream US value 133 converted via 133 * ft_to_m^(-0.7913) |
c_etaM_1 | 1 | 2.59 | Moisture damping polynomial coefficient 1 (dimensionless; Table 3 Andrews 2018) |
c_etaM_2 | 1 | 5.11 | Moisture damping polynomial coefficient 2 (dimensionless; Table 3 Andrews 2018) |
c_etaM_3 | 1 | 3.52 | Moisture damping polynomial coefficient 3 (dimensionless; Table 3 Andrews 2018) |
c_etas | 1 | 0.174 | Mineral damping coefficient (empirical; Table 3 Andrews 2018): eta_s = 0.174 * S_e^(-0.19) |
c_xi_1 | 1 | 192.0 | Propagating flux ratio denominator coefficient 1 (empirical; Table 3 Andrews 2018) |
c_xi_2 | m | 0.07908 | Propagating flux ratio denominator coefficient 2 (SI, has units m to cancel sigma’s 1/m; Table 3 Andrews 2018) |
c_xi_3 | 1 | 0.792 | Propagating flux ratio exponent coefficient 3 (empirical; Table 3 Andrews 2018) |
c_xi_4 | 1 | 0.376 | Propagating flux ratio exponent coefficient 4 (SI; Table 3 Andrews 2018) |
c_C_1 | 1 | 7.47 | Wind coefficient C pre-exponential constant (empirical; Table 3 Andrews 2018) |
c_C_2 | 1 | 0.0692 | Wind coefficient C exponential constant (SI); upstream US value 0.133 converted via 0.133 * ft_to_m^0.55 |
c_B | 1 | 0.01317 | Wind coefficient B constant (SI); upstream US value 0.02526 converted via 0.02526 * ft_to_m^0.54 |
c_E_1 | 1 | 0.715 | Wind coefficient E pre-exponential constant (empirical; Table 3 Andrews 2018) |
c_E_2 | m | 0.0001094 | Wind coefficient E exponential constant (SI, units m to cancel sigma’s 1/m); upstream US value 3.59e-4 converted via 3.59e-4 * ft_to_m |
c_phis | 1 | 5.275 | Slope factor coefficient (empirical; Table 3 Andrews 2018) |
c_eps | 1/m | 452.7 | Effective heating number coefficient (SI); upstream US value 138 converted via 138 / ft_to_m |
c_Qig_1 | J/kg | 581500.0 | Heat of preignition base constant (SI); upstream US value 250 Btu/lb converted to J/kg |
c_Qig_2 | J/kg | 2595816.0 | Heat of preignition moisture coefficient (SI); upstream US value 1116 Btu/lb converted to J/kg |
c_tr | s/m | 75590.6 | Residence time coefficient (SI); upstream US value 384 min·ft^(-1) converted via 384*60/ft_to_m |
c_FL | m | 0.00323 | Flame length coefficient (SI); upstream US value 0.45 ft converted for IB in W/m |
sigma_floor | 1/m | 1e-06 | Minimum SAV ratio floor to avoid division by zero and negative-power singularity in sigma-dependent expressions |
delta_floor | m | 1e-10 | Minimum fuel bed depth floor to avoid division by zero in rhob = w0/delta |
beta_floor | 1 | 1e-10 | Minimum packing ratio floor to avoid negative-power singularity in phi_s_coeff = c_phis * beta^(-0.3) |
beta_ratio_floor | 1 | 1e-10 | Minimum relative packing ratio floor to avoid negative-power singularity in phi_w and log(beta_ratio) in Gamma_prime |
rhob_floor | kg/m^3 | 1e-10 | Minimum bulk density floor to avoid division by zero in R0 = IRxi / (rhobepsilon*Qig) |
epsilon_floor | 1 | 1e-10 | Minimum effective heating number floor to avoid division by zero in R0 denominator |
Mx_floor | 1 | 1e-10 | Minimum moisture of extinction floor to avoid division by zero in rM = Mf/Mx |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
wn | kg/m^2 | Net (mineral-free) fuel load: wn = w0 * (1 - S_T) | |
rhob | kg/m^3 | Oven-dry bulk density: rhob = w0 / delta | |
beta | 1 | Packing ratio (dimensionless): beta = rhob / rho_p | |
beta_op | 1 | Optimum packing ratio: beta_op = c_beta_op * sigma^(-0.8189) | |
beta_ratio | 1 | Relative packing ratio: beta_ratio = beta / beta_op | |
Gamma_max | 1/s | Maximum reaction velocity: Gamma_max = sigma^1.5 / (c_Gamma_denom1 + c_Gamma_denom2 * sigma^1.5) | |
A_coeff | 1 | Coefficient A for reaction velocity (dimensionless): A = c_A * sigma^(-0.7913) | |
Gamma_prime | 1/s | Optimum reaction velocity: Gamma_prime = Gamma_max * exp(A * (log(beta_ratio) + 1 - beta_ratio)) | |
rM | 1 | Moisture ratio capped at 1.0: rM = min(Mf / Mx, 1) | |
eta_M | 1 | Moisture damping coefficient: eta_M = 1 - 2.59rM + 5.11rM^2 - 3.52*rM^3 | |
eta_s | 1 | Mineral damping coefficient capped at 1.0: eta_s = min(0.174 * S_e^(-0.19), 1) | |
IR | W/m^2 | Reaction intensity: IR = Gamma_prime * wn * h * eta_M * eta_s | |
xi | 1 | Propagating flux ratio (dimensionless): fraction of IR that propagates ahead of fire front | |
C_coeff | 1 | Wind factor coefficient C: C = c_C_1 * exp(-c_C_2 * sigma^0.55) | |
B_coeff | 1 | Wind factor coefficient B (wind-speed exponent): B = c_B * sigma^0.54 | |
E_coeff | 1 | Wind factor coefficient E (packing-ratio exponent): E = c_E_1 * exp(-c_E_2 * sigma) | |
phi_w | 1 | Wind factor (dimensionless): phi_w = C * (U/U_ref)^B * beta_ratio^(-E) | |
phi_s_coeff | 1 | Slope factor coefficient: phi_s_coeff = c_phis * beta^(-0.3) | |
phi_s | 1 | Slope factor (dimensionless): phi_s = phi_s_coeff * tan_phi^2 | |
epsilon | 1 | Effective heating number (dimensionless): epsilon = exp(-c_eps / sigma) | |
Qig | J/kg | Heat of preignition: Qig = c_Qig_1 + c_Qig_2 * Mf | |
R0 | m/s | No-wind no-slope rate of spread: R0 = IR * xi / (rhob * epsilon * Qig) | |
R | m/s | Rate of spread with wind and slope: R = R0 * (1 + phi_w + phi_s) | |
t_r | s | Flame residence time: t_r = c_tr / sigma | |
HA | J/m^2 | Heat per unit area: HA = IR * t_r | |
IB | W/m | Fireline intensity (Byram): IB = HA * R | |
F_L | m | Flame length (Byram): F_L = c_FL * IB^0.46 |
Observed expressions
$$ wn = w0 \cdot \left(one - S_{T}\right) $$Net (mineral-free) fuel load: wn = w0 * (1 - S_T)
$$ rhob = \frac{w0}{\mathrm{max}\left(delta, delta_{floor}\right)} $$Oven-dry bulk density: rhob = w0 / delta
$$ beta = \frac{rhob}{rho_{p}} $$Packing ratio (dimensionless): beta = rhob / rho_p
$$ beta_{op} = c_{beta\,op} \cdot \mathrm{max}\left(\frac{sigma}{sigma_{ref}}, \frac{sigma_{floor}}{sigma_{ref}}\right)^{-0.8189} $$Optimum packing ratio: beta_op = c_beta_op * sigma^(-0.8189)
$$ beta_{ratio} = \frac{beta}{beta_{op}} $$Relative packing ratio: beta_ratio = beta / beta_op
$$ Gamma_{max} = \frac{c_{Gamma\,mult} \cdot \frac{sigma}{sigma_{ref}}^{1.5}}{c_{Gamma\,denom1} + c_{Gamma\,denom2} \cdot \frac{sigma}{sigma_{ref}}^{1.5}} $$Maximum reaction velocity: Gamma_max = sigma^1.5 / (c_Gamma_denom1 + c_Gamma_denom2 * sigma^1.5)
$$ A_{coeff} = c_{A} \cdot \mathrm{max}\left(\frac{sigma}{sigma_{ref}}, \frac{sigma_{floor}}{sigma_{ref}}\right)^{-0.7913} $$Coefficient A for reaction velocity (dimensionless): A = c_A * sigma^(-0.7913)
$$ Gamma_{prime} = Gamma_{max} \cdot e^{A_{coeff} \cdot \left(\ln\left(\mathrm{max}\left(beta_{ratio}, beta_{ratio\,floor}\right)\right) + one - beta_{ratio}\right)} $$Optimum reaction velocity: Gamma_prime = Gamma_max * exp(A * (log(beta_ratio) + 1 - beta_ratio))
$$ rM = \mathrm{min}\left(\frac{Mf}{\mathrm{max}\left(Mx, Mx_{floor}\right)}, one\right) $$Moisture ratio capped at 1.0: rM = min(Mf / Mx, 1)
$$ eta_{M} = one - c_{etaM\,1} \cdot rM + c_{etaM\,2} \cdot rM^{2.0} - c_{etaM\,3} \cdot rM^{3.0} $$Moisture damping coefficient: eta_M = 1 - 2.59rM + 5.11rM^2 - 3.52*rM^3
$$ eta_{s} = \mathrm{min}\left(c_{etas} \cdot S_{e}^{-0.19}, one\right) $$Mineral damping coefficient capped at 1.0: eta_s = min(0.174 * S_e^(-0.19), 1)
$$ IR = Gamma_{prime} \cdot wn \cdot h \cdot eta_{M} \cdot eta_{s} $$Reaction intensity: IR = Gamma_prime * wn * h * eta_M * eta_s
$$ xi = \left(c_{xi\,1} + c_{xi\,2} \cdot sigma\right)^{-1.0} \cdot e^{\left(c_{xi\,3} + c_{xi\,4} \cdot \sqrt{\frac{sigma}{sigma_{ref}}}\right) \cdot \left(beta + 0.1 \cdot one\right)} $$Propagating flux ratio (dimensionless): fraction of IR that propagates ahead of fire front
$$ C_{coeff} = c_{C\,1} \cdot e^{\left(-1.0\right) \cdot c_{C\,2} \cdot \frac{sigma}{sigma_{ref}}^{0.55}} $$Wind factor coefficient C: C = c_C_1 * exp(-c_C_2 * sigma^0.55)
$$ B_{coeff} = c_{B} \cdot \frac{sigma}{sigma_{ref}}^{0.54} $$Wind factor coefficient B (wind-speed exponent): B = c_B * sigma^0.54
$$ E_{coeff} = c_{E\,1} \cdot e^{\left(-1.0\right) \cdot c_{E\,2} \cdot sigma} $$Wind factor coefficient E (packing-ratio exponent): E = c_E_1 * exp(-c_E_2 * sigma)
$$ phi_{w} = C_{coeff} \cdot \frac{U}{U_{ref}}^{B_{coeff}} \cdot \mathrm{max}\left(beta_{ratio}, beta_{ratio\,floor}\right)^{\left(-1.0\right) \cdot E_{coeff}} $$Wind factor (dimensionless): phi_w = C * (U/U_ref)^B * beta_ratio^(-E)
$$ phi_{s\,coeff} = c_{phis} \cdot \mathrm{max}\left(beta, beta_{floor}\right)^{-0.3} $$Slope factor coefficient: phi_s_coeff = c_phis * beta^(-0.3)
$$ phi_{s} = phi_{s\,coeff} \cdot tan_{phi}^{2.0} $$Slope factor (dimensionless): phi_s = phi_s_coeff * tan_phi^2
$$ epsilon = e^{\left(-1.0\right) \cdot c_{eps} \cdot \mathrm{max}\left(sigma, sigma_{floor}\right)^{-1.0}} $$Effective heating number (dimensionless): epsilon = exp(-c_eps / sigma)
$$ Qig = c_{Qig\,1} + c_{Qig\,2} \cdot Mf $$Heat of preignition: Qig = c_Qig_1 + c_Qig_2 * Mf
$$ R0 = \frac{IR \cdot xi}{\mathrm{max}\left(rhob, rhob_{floor}\right) \cdot \mathrm{max}\left(epsilon, epsilon_{floor}\right) \cdot Qig} $$No-wind no-slope rate of spread: R0 = IR * xi / (rhob * epsilon * Qig)
$$ R = R0 \cdot \left(one + phi_{w} + phi_{s}\right) $$Rate of spread with wind and slope: R = R0 * (1 + phi_w + phi_s)
$$ t_{r} = \frac{c_{tr}}{\mathrm{max}\left(sigma, sigma_{floor}\right)} $$Flame residence time: t_r = c_tr / sigma
$$ HA = IR \cdot t_{r} $$Heat per unit area: HA = IR * t_r
$$ IB = HA \cdot R $$Fireline intensity (Byram): IB = HA * R
$$ F_{L} = c_{FL} \cdot \frac{IB}{IB_{ref}}^{0.46} $$Flame length (Byram): F_L = c_FL * IB^0.46
Analyses
spread_rate_vs_wind
Sweep wind speed U from 0 to 10 m/s at Fuel Model 1 conditions (Mf=5%, flat). Shows the power-law wind amplification of fire spread rate: R grows rapidly with wind as the wind factor phi_w = C*(U/U_ref)^B scales with U^B_coeff where B_coeff ~ 2.05.
Time span: 0.0 → 1.0
Swept over: U
spread_rate_vs_slope
Sweep slope tan_phi from 0 to 1.0 (0% to 100% rise/run) at Fuel Model 1 conditions (Mf=5%, no wind). Shows slope factor phi_s = phi_s_coeff * tan_phi^2 growing quadratically with slope.
Time span: 0.0 → 1.0
Swept over: tan_phi
spread_rate_vs_moisture
Sweep fuel moisture Mf from 0.01 (1%) to 0.12 (extinction, Mx) at Fuel Model 1 conditions. Shows moisture damping: eta_M polynomial approaches 0 at Mf=Mx, bringing R→0.
Time span: 0.0 → 1.0
Swept over: Mf
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"notes": "source_ref: WildlandFire.jl@126976f2508ceacca6c486b21ae6da5b168c6f46:src/rothermel.jl:70\n\nUpstream `RothermelFireSpread` is an MTK `@component` with 11 `@parameters` (fuel-bed and environmental inputs), 35 `@constants` (empirical coefficients, reference values, and floor guards), and 27 time-indexed `@variables` defined by 27 purely algebraic equations (no D(x) terms — observed-only system). Structural verification: `length(equations(sys)) == 27`, `length(unknowns(sys)) == 27` (see test_rothermel.jl `Structural Verification`).\n\nUnicode → ASCII identifier transliteration follows the rig convention (components/wildland_fire/terrain_slope.esm, components/wildland_fire/rothermel/effective_midflame_wind.esm):\n σ → sigma ρ_p → rho_p tanϕ → tan_phi\n δ → delta ρb → rhob Γ_max → Gamma_max\n β → beta β_op → beta_op Γ' → Gamma_prime\n β_ratio → beta_ratio η_M → eta_M η_s → eta_s\n ξ → xi φw → phi_w φs → phi_s\n φs_coeff → phi_s_coeff ε → epsilon\n σ_ref → sigma_ref, σ_floor → sigma_floor, δ_floor → delta_floor\n β_floor → beta_floor, β_ratio_floor → beta_ratio_floor\n ρb_floor → rhob_floor, ε_floor → epsilon_floor\n\nMTK `@constants` are unified into ESM `parameter` declarations (same pattern as wind_limit.esm, live_fuel_moisture_extinction.esm). Both the empirical-coefficient constants and the floor-guard constants are preserved as parameters with their upstream default values.\n\nFloor constants rationale: several equations involve bases raised to non-integer powers and denominators. Floor guards prevent 0^negative or 0/0 when fuel is absent (depletion) or non-burnable (σ=0). Only denominators and negative-power bases are guarded; numerators are unguarded so IR→0 and R→0 naturally when fuel is absent.\n\nSI conversion notes (from US customary, Table 3, Andrews 2018):\n c_beta_op = 8.858 (from 3.348 * ft_to_m^(-0.8189))\n c_A = 340.5 (from 133 * ft_to_m^(-0.7913))\n c_C_2 = 0.0692 (from 0.133 * ft_to_m^0.55)\n c_B = 0.01317 (from 0.02526 * ft_to_m^0.54)\n c_E_2 = 1.094e-4 (from 3.59e-4 * ft_to_m)\n c_eps = 452.7 (from 138 / ft_to_m)\n c_Qig_1 = 581500 J/kg, c_Qig_2 = 2595816 J/kg (from 250 and 1116 Btu/lb)\n c_tr = 75590.6 s/m (from 384 min / ft_to_m * 60)\n c_FL = 0.00323 m (from 0.45 ft / (Btu/ft/s → W/m)^0.46)\n U_ref = 0.3048/60 m/s = 1 ft/min (non-dimensionalizes U for the wind-factor power law)\n\nCoupling interface (RothermelCoupler, coupling.jl):\n couple2(FuelModelLookupCoupler, RothermelCoupler) promotes sigma, w0, delta, Mx, h\n from parameters to variables and connects them to FuelModelLookup outputs.\n couple2(TerrainSlopeCoupler, RothermelCoupler) promotes tan_phi from parameter to\n variable and connects it to TerrainSlope.tan_phi.\n couple2(MidflameWindCoupler, RothermelCoupler) promotes U from parameter to variable\n and connects it to MidflameWind.U.\n These couplings apply when composing multi-component ESM files; standalone use\n requires setting sigma, w0, delta, Mx, h, tan_phi, U, Mf as direct parameters.\n\nTolerance rationale (model-level rel=1e-6): observed-only algebraic system; all\nequations are closed-form arithmetic and transcendental functions on float64.\n1e-6 matches the upstream Julia test suite tolerances (rtol=1e-6)."
},
"tolerance": {
"rel": 1e-06
},
"variables": {
"sigma": {
"type": "parameter",
"units": "1/m",
"description": "Surface-area-to-volume ratio of the fuel particle"
},
"w0": {
"type": "parameter",
"units": "kg/m^2",
"description": "Oven-dry fuel load per unit area"
},
"delta": {
"type": "parameter",
"units": "m",
"description": "Fuel bed depth"
},
"Mx": {
"type": "parameter",
"units": "1",
"description": "Dead fuel moisture of extinction (dimensionless, dry weight basis)"
},
"h": {
"type": "parameter",
"units": "J/kg",
"default": 18608000.0,
"description": "Low heat content of dry fuel (default 8000 Btu/lb = 18608000 J/kg)"
},
"S_T": {
"type": "parameter",
"units": "1",
"default": 0.0555,
"description": "Total mineral content (dimensionless fraction)"
},
"S_e": {
"type": "parameter",
"units": "1",
"default": 0.01,
"description": "Effective (silica-free) mineral content (dimensionless fraction)"
},
"rho_p": {
"type": "parameter",
"units": "kg/m^3",
"default": 512.6,
"description": "Oven-dry particle density (default 32 lb/ft^3 = 512.6 kg/m^3)"
},
"Mf": {
"type": "parameter",
"units": "1",
"description": "Fuel moisture content (dimensionless, dry weight basis)"
},
"U": {
"type": "parameter",
"units": "m/s",
"default": 0.0,
"description": "Wind velocity at midflame height. Default 0.0 so the model stays valid when U is left unbound: it feeds only Rothermel's own phi_w -> rate R, which the wildland-fire coupling does NOT consume (only R0 + the C/B/E/beta/phi_s coefficients are coupled to the level-set leaf, which recomputes wind directionally). Binders that use Rothermel's full R still override it."
},
"tan_phi": {
"type": "parameter",
"units": "1",
"default": 0.0,
"description": "Slope steepness (dimensionless rise/run). Default 0.0 so the model stays valid when tan_phi is left unbound: it feeds only Rothermel's own phi_s -> rate R, which the wildland-fire coupling does NOT consume (the level-set leaf recomputes slope directionally). Binders that use Rothermel's full R still override it."
},
"sigma_ref": {
"type": "parameter",
"units": "1/m",
"default": 1.0,
"description": "Reference SAV ratio for non-dimensionalization before non-integer power laws (MTK @constant preserved as parameter)"
},
"U_ref": {
"type": "parameter",
"units": "m/s",
"default": 0.005080000000000001,
"description": "Reference wind speed = 1 ft/min = 0.3048/60 m/s; non-dimensionalizes U for the wind-factor power law (empirical calibration in ft/min)"
},
"IB_ref": {
"type": "parameter",
"units": "W/m",
"default": 1.0,
"description": "Reference fireline intensity for non-dimensionalization before the 0.46 power in F_L (MTK @constant preserved as parameter)"
},
"one": {
"type": "parameter",
"units": "1",
"default": 1.0,
"description": "Dimensionless one — MTK unit-balancing literal preserved from upstream @constants"
},
"c_beta_op": {
"type": "parameter",
"units": "1",
"default": 8.858,
"description": "Optimum packing ratio coefficient (SI); upstream US value 3.348 converted via 3.348 * ft_to_m^(-0.8189)"
},
"c_Gamma_denom1": {
"type": "parameter",
"units": "1",
"default": 176502.0,
"description": "Gamma_max denominator constant 1 (SI, empirical; Table 3 Andrews 2018)"
},
"c_Gamma_denom2": {
"type": "parameter",
"units": "1",
"default": 3.564,
"description": "Gamma_max denominator constant 2 (SI, empirical; Table 3 Andrews 2018)"
},
"c_Gamma_mult": {
"type": "parameter",
"units": "1/s",
"default": 1.0,
"description": "Gamma_max unit conversion factor; gives Gamma_max units of 1/s (reaction velocity)"
},
"c_A": {
"type": "parameter",
"units": "1",
"default": 340.5,
"description": "Coefficient A constant (SI); upstream US value 133 converted via 133 * ft_to_m^(-0.7913)"
},
"c_etaM_1": {
"type": "parameter",
"units": "1",
"default": 2.59,
"description": "Moisture damping polynomial coefficient 1 (dimensionless; Table 3 Andrews 2018)"
},
"c_etaM_2": {
"type": "parameter",
"units": "1",
"default": 5.11,
"description": "Moisture damping polynomial coefficient 2 (dimensionless; Table 3 Andrews 2018)"
},
"c_etaM_3": {
"type": "parameter",
"units": "1",
"default": 3.52,
"description": "Moisture damping polynomial coefficient 3 (dimensionless; Table 3 Andrews 2018)"
},
"c_etas": {
"type": "parameter",
"units": "1",
"default": 0.174,
"description": "Mineral damping coefficient (empirical; Table 3 Andrews 2018): eta_s = 0.174 * S_e^(-0.19)"
},
"c_xi_1": {
"type": "parameter",
"units": "1",
"default": 192.0,
"description": "Propagating flux ratio denominator coefficient 1 (empirical; Table 3 Andrews 2018)"
},
"c_xi_2": {
"type": "parameter",
"units": "m",
"default": 0.07908,
"description": "Propagating flux ratio denominator coefficient 2 (SI, has units m to cancel sigma's 1/m; Table 3 Andrews 2018)"
},
"c_xi_3": {
"type": "parameter",
"units": "1",
"default": 0.792,
"description": "Propagating flux ratio exponent coefficient 3 (empirical; Table 3 Andrews 2018)"
},
"c_xi_4": {
"type": "parameter",
"units": "1",
"default": 0.376,
"description": "Propagating flux ratio exponent coefficient 4 (SI; Table 3 Andrews 2018)"
},
"c_C_1": {
"type": "parameter",
"units": "1",
"default": 7.47,
"description": "Wind coefficient C pre-exponential constant (empirical; Table 3 Andrews 2018)"
},
"c_C_2": {
"type": "parameter",
"units": "1",
"default": 0.0692,
"description": "Wind coefficient C exponential constant (SI); upstream US value 0.133 converted via 0.133 * ft_to_m^0.55"
},
"c_B": {
"type": "parameter",
"units": "1",
"default": 0.01317,
"description": "Wind coefficient B constant (SI); upstream US value 0.02526 converted via 0.02526 * ft_to_m^0.54"
},
"c_E_1": {
"type": "parameter",
"units": "1",
"default": 0.715,
"description": "Wind coefficient E pre-exponential constant (empirical; Table 3 Andrews 2018)"
},
"c_E_2": {
"type": "parameter",
"units": "m",
"default": 0.0001094,
"description": "Wind coefficient E exponential constant (SI, units m to cancel sigma's 1/m); upstream US value 3.59e-4 converted via 3.59e-4 * ft_to_m"
},
"c_phis": {
"type": "parameter",
"units": "1",
"default": 5.275,
"description": "Slope factor coefficient (empirical; Table 3 Andrews 2018)"
},
"c_eps": {
"type": "parameter",
"units": "1/m",
"default": 452.7,
"description": "Effective heating number coefficient (SI); upstream US value 138 converted via 138 / ft_to_m"
},
"c_Qig_1": {
"type": "parameter",
"units": "J/kg",
"default": 581500.0,
"description": "Heat of preignition base constant (SI); upstream US value 250 Btu/lb converted to J/kg"
},
"c_Qig_2": {
"type": "parameter",
"units": "J/kg",
"default": 2595816.0,
"description": "Heat of preignition moisture coefficient (SI); upstream US value 1116 Btu/lb converted to J/kg"
},
"c_tr": {
"type": "parameter",
"units": "s/m",
"default": 75590.6,
"description": "Residence time coefficient (SI); upstream US value 384 min·ft^(-1) converted via 384*60/ft_to_m"
},
"c_FL": {
"type": "parameter",
"units": "m",
"default": 0.00323,
"description": "Flame length coefficient (SI); upstream US value 0.45 ft converted for IB in W/m"
},
"sigma_floor": {
"type": "parameter",
"units": "1/m",
"default": 1e-06,
"description": "Minimum SAV ratio floor to avoid division by zero and negative-power singularity in sigma-dependent expressions"
},
"delta_floor": {
"type": "parameter",
"units": "m",
"default": 1e-10,
"description": "Minimum fuel bed depth floor to avoid division by zero in rhob = w0/delta"
},
"beta_floor": {
"type": "parameter",
"units": "1",
"default": 1e-10,
"description": "Minimum packing ratio floor to avoid negative-power singularity in phi_s_coeff = c_phis * beta^(-0.3)"
},
"beta_ratio_floor": {
"type": "parameter",
"units": "1",
"default": 1e-10,
"description": "Minimum relative packing ratio floor to avoid negative-power singularity in phi_w and log(beta_ratio) in Gamma_prime"
},
"rhob_floor": {
"type": "parameter",
"units": "kg/m^3",
"default": 1e-10,
"description": "Minimum bulk density floor to avoid division by zero in R0 = IR*xi / (rhob*epsilon*Qig)"
},
"epsilon_floor": {
"type": "parameter",
"units": "1",
"default": 1e-10,
"description": "Minimum effective heating number floor to avoid division by zero in R0 denominator"
},
"Mx_floor": {
"type": "parameter",
"units": "1",
"default": 1e-10,
"description": "Minimum moisture of extinction floor to avoid division by zero in rM = Mf/Mx"
},
"wn": {
"type": "unknown",
"units": "kg/m^2",
"description": "Net (mineral-free) fuel load: wn = w0 * (1 - S_T)"
},
"rhob": {
"type": "unknown",
"units": "kg/m^3",
"description": "Oven-dry bulk density: rhob = w0 / delta"
},
"beta": {
"type": "unknown",
"units": "1",
"description": "Packing ratio (dimensionless): beta = rhob / rho_p"
},
"beta_op": {
"type": "unknown",
"units": "1",
"description": "Optimum packing ratio: beta_op = c_beta_op * sigma^(-0.8189)"
},
"beta_ratio": {
"type": "unknown",
"units": "1",
"description": "Relative packing ratio: beta_ratio = beta / beta_op"
},
"Gamma_max": {
"type": "unknown",
"units": "1/s",
"description": "Maximum reaction velocity: Gamma_max = sigma^1.5 / (c_Gamma_denom1 + c_Gamma_denom2 * sigma^1.5)"
},
"A_coeff": {
"type": "unknown",
"units": "1",
"description": "Coefficient A for reaction velocity (dimensionless): A = c_A * sigma^(-0.7913)"
},
"Gamma_prime": {
"type": "unknown",
"units": "1/s",
"description": "Optimum reaction velocity: Gamma_prime = Gamma_max * exp(A * (log(beta_ratio) + 1 - beta_ratio))"
},
"rM": {
"type": "unknown",
"units": "1",
"description": "Moisture ratio capped at 1.0: rM = min(Mf / Mx, 1)"
},
"eta_M": {
"type": "unknown",
"units": "1",
"description": "Moisture damping coefficient: eta_M = 1 - 2.59*rM + 5.11*rM^2 - 3.52*rM^3"
},
"eta_s": {
"type": "unknown",
"units": "1",
"description": "Mineral damping coefficient capped at 1.0: eta_s = min(0.174 * S_e^(-0.19), 1)"
},
"IR": {
"type": "unknown",
"units": "W/m^2",
"description": "Reaction intensity: IR = Gamma_prime * wn * h * eta_M * eta_s"
},
"xi": {
"type": "unknown",
"units": "1",
"description": "Propagating flux ratio (dimensionless): fraction of IR that propagates ahead of fire front"
},
"C_coeff": {
"type": "unknown",
"units": "1",
"description": "Wind factor coefficient C: C = c_C_1 * exp(-c_C_2 * sigma^0.55)"
},
"B_coeff": {
"type": "unknown",
"units": "1",
"description": "Wind factor coefficient B (wind-speed exponent): B = c_B * sigma^0.54"
},
"E_coeff": {
"type": "unknown",
"units": "1",
"description": "Wind factor coefficient E (packing-ratio exponent): E = c_E_1 * exp(-c_E_2 * sigma)"
},
"phi_w": {
"type": "unknown",
"units": "1",
"description": "Wind factor (dimensionless): phi_w = C * (U/U_ref)^B * beta_ratio^(-E)"
},
"phi_s_coeff": {
"type": "unknown",
"units": "1",
"description": "Slope factor coefficient: phi_s_coeff = c_phis * beta^(-0.3)"
},
"phi_s": {
"type": "unknown",
"units": "1",
"description": "Slope factor (dimensionless): phi_s = phi_s_coeff * tan_phi^2"
},
"epsilon": {
"type": "unknown",
"units": "1",
"description": "Effective heating number (dimensionless): epsilon = exp(-c_eps / sigma)"
},
"Qig": {
"type": "unknown",
"units": "J/kg",
"description": "Heat of preignition: Qig = c_Qig_1 + c_Qig_2 * Mf"
},
"R0": {
"type": "unknown",
"units": "m/s",
"description": "No-wind no-slope rate of spread: R0 = IR * xi / (rhob * epsilon * Qig)"
},
"R": {
"type": "unknown",
"units": "m/s",
"description": "Rate of spread with wind and slope: R = R0 * (1 + phi_w + phi_s)"
},
"t_r": {
"type": "unknown",
"units": "s",
"description": "Flame residence time: t_r = c_tr / sigma"
},
"HA": {
"type": "unknown",
"units": "J/m^2",
"description": "Heat per unit area: HA = IR * t_r"
},
"IB": {
"type": "unknown",
"units": "W/m",
"description": "Fireline intensity (Byram): IB = HA * R"
},
"F_L": {
"type": "unknown",
"units": "m",
"description": "Flame length (Byram): F_L = c_FL * IB^0.46"
}
},
"equations": [
{
"lhs": "wn",
"rhs": {
"op": "*",
"args": [
"w0",
{
"op": "-",
"args": [
"one",
"S_T"
]
}
]
}
},
{
"lhs": "rhob",
"rhs": {
"op": "/",
"args": [
"w0",
{
"op": "max",
"args": [
"delta",
"delta_floor"
]
}
]
}
},
{
"lhs": "beta",
"rhs": {
"op": "/",
"args": [
"rhob",
"rho_p"
]
}
},
{
"lhs": "beta_op",
"rhs": {
"op": "*",
"args": [
"c_beta_op",
{
"op": "^",
"args": [
{
"op": "max",
"args": [
{
"op": "/",
"args": [
"sigma",
"sigma_ref"
]
},
{
"op": "/",
"args": [
"sigma_floor",
"sigma_ref"
]
}
]
},
-0.8189
]
}
]
}
},
{
"lhs": "beta_ratio",
"rhs": {
"op": "/",
"args": [
"beta",
"beta_op"
]
}
},
{
"lhs": "Gamma_max",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"c_Gamma_mult",
{
"op": "^",
"args": [
{
"op": "/",
"args": [
"sigma",
"sigma_ref"
]
},
1.5
]
}
]
},
{
"op": "+",
"args": [
"c_Gamma_denom1",
{
"op": "*",
"args": [
"c_Gamma_denom2",
{
"op": "^",
"args": [
{
"op": "/",
"args": [
"sigma",
"sigma_ref"
]
},
1.5
]
}
]
}
]
}
]
}
},
{
"lhs": "A_coeff",
"rhs": {
"op": "*",
"args": [
"c_A",
{
"op": "^",
"args": [
{
"op": "max",
"args": [
{
"op": "/",
"args": [
"sigma",
"sigma_ref"
]
},
{
"op": "/",
"args": [
"sigma_floor",
"sigma_ref"
]
}
]
},
-0.7913
]
}
]
}
},
{
"lhs": "Gamma_prime",
"rhs": {
"op": "*",
"args": [
"Gamma_max",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
"A_coeff",
{
"op": "-",
"args": [
{
"op": "+",
"args": [
{
"op": "log",
"args": [
{
"op": "max",
"args": [
"beta_ratio",
"beta_ratio_floor"
]
}
]
},
"one"
]
},
"beta_ratio"
]
}
]
}
]
}
]
}
},
{
"lhs": "rM",
"rhs": {
"op": "min",
"args": [
{
"op": "/",
"args": [
"Mf",
{
"op": "max",
"args": [
"Mx",
"Mx_floor"
]
}
]
},
"one"
]
}
},
{
"lhs": "eta_M",
"rhs": {
"op": "-",
"args": [
{
"op": "+",
"args": [
{
"op": "-",
"args": [
"one",
{
"op": "*",
"args": [
"c_etaM_1",
"rM"
]
}
]
},
{
"op": "*",
"args": [
"c_etaM_2",
{
"op": "^",
"args": [
"rM",
2.0
]
}
]
}
]
},
{
"op": "*",
"args": [
"c_etaM_3",
{
"op": "^",
"args": [
"rM",
3.0
]
}
]
}
]
}
},
{
"lhs": "eta_s",
"rhs": {
"op": "min",
"args": [
{
"op": "*",
"args": [
"c_etas",
{
"op": "^",
"args": [
"S_e",
-0.19
]
}
]
},
"one"
]
}
},
{
"lhs": "IR",
"rhs": {
"op": "*",
"args": [
"Gamma_prime",
"wn",
"h",
"eta_M",
"eta_s"
]
}
},
{
"lhs": "xi",
"rhs": {
"op": "*",
"args": [
{
"op": "^",
"args": [
{
"op": "+",
"args": [
"c_xi_1",
{
"op": "*",
"args": [
"c_xi_2",
"sigma"
]
}
]
},
-1.0
]
},
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
{
"op": "+",
"args": [
"c_xi_3",
{
"op": "*",
"args": [
"c_xi_4",
{
"op": "sqrt",
"args": [
{
"op": "/",
"args": [
"sigma",
"sigma_ref"
]
}
]
}
]
}
]
},
{
"op": "+",
"args": [
"beta",
{
"op": "*",
"args": [
0.1,
"one"
]
}
]
}
]
}
]
}
]
}
},
{
"lhs": "C_coeff",
"rhs": {
"op": "*",
"args": [
"c_C_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1.0,
"c_C_2",
{
"op": "^",
"args": [
{
"op": "/",
"args": [
"sigma",
"sigma_ref"
]
},
0.55
]
}
]
}
]
}
]
}
},
{
"lhs": "B_coeff",
"rhs": {
"op": "*",
"args": [
"c_B",
{
"op": "^",
"args": [
{
"op": "/",
"args": [
"sigma",
"sigma_ref"
]
},
0.54
]
}
]
}
},
{
"lhs": "E_coeff",
"rhs": {
"op": "*",
"args": [
"c_E_1",
{
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1.0,
"c_E_2",
"sigma"
]
}
]
}
]
}
},
{
"lhs": "phi_w",
"rhs": {
"op": "*",
"args": [
"C_coeff",
{
"op": "^",
"args": [
{
"op": "/",
"args": [
"U",
"U_ref"
]
},
"B_coeff"
]
},
{
"op": "^",
"args": [
{
"op": "max",
"args": [
"beta_ratio",
"beta_ratio_floor"
]
},
{
"op": "*",
"args": [
-1.0,
"E_coeff"
]
}
]
}
]
}
},
{
"lhs": "phi_s_coeff",
"rhs": {
"op": "*",
"args": [
"c_phis",
{
"op": "^",
"args": [
{
"op": "max",
"args": [
"beta",
"beta_floor"
]
},
-0.3
]
}
]
}
},
{
"lhs": "phi_s",
"rhs": {
"op": "*",
"args": [
"phi_s_coeff",
{
"op": "^",
"args": [
"tan_phi",
2.0
]
}
]
}
},
{
"lhs": "epsilon",
"rhs": {
"op": "exp",
"args": [
{
"op": "*",
"args": [
-1.0,
"c_eps",
{
"op": "^",
"args": [
{
"op": "max",
"args": [
"sigma",
"sigma_floor"
]
},
-1.0
]
}
]
}
]
}
},
{
"lhs": "Qig",
"rhs": {
"op": "+",
"args": [
"c_Qig_1",
{
"op": "*",
"args": [
"c_Qig_2",
"Mf"
]
}
]
}
},
{
"lhs": "R0",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
"IR",
"xi"
]
},
{
"op": "*",
"args": [
{
"op": "max",
"args": [
"rhob",
"rhob_floor"
]
},
{
"op": "max",
"args": [
"epsilon",
"epsilon_floor"
]
},
"Qig"
]
}
]
}
},
{
"lhs": "R",
"rhs": {
"op": "*",
"args": [
"R0",
{
"op": "+",
"args": [
"one",
"phi_w",
"phi_s"
]
}
]
}
},
{
"lhs": "t_r",
"rhs": {
"op": "/",
"args": [
"c_tr",
{
"op": "max",
"args": [
"sigma",
"sigma_floor"
]
}
]
}
},
{
"lhs": "HA",
"rhs": {
"op": "*",
"args": [
"IR",
"t_r"
]
}
},
{
"lhs": "IB",
"rhs": {
"op": "*",
"args": [
"HA",
"R"
]
}
},
{
"lhs": "F_L",
"rhs": {
"op": "*",
"args": [
"c_FL",
{
"op": "^",
"args": [
{
"op": "/",
"args": [
"IB",
"IB_ref"
]
},
0.46
]
}
]
}
}
],
"tests": [
{
"id": "fm1_no_wind_flat",
"description": "Fuel Model 1 (short grass, SI): sigma=11482.9 1/m, w0=0.166 kg/m^2, delta=0.3048 m, Mx=0.12, Mf=0.05, no wind, flat. Reference case verifying bulk density, packing ratio, intermediate coefficients, R0=R (no wind/slope), and output variables. Upstream test: 'Fuel Model 1 - Short Grass'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 0.0,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "rhob",
"time": 0.0,
"expected": 0.5446273098918715
},
{
"variable": "beta",
"time": 0.0,
"expected": 0.0010624801365249834
},
{
"variable": "beta_op",
"time": 0.0,
"expected": 0.004193321893073434
},
{
"variable": "epsilon",
"time": 0.0,
"expected": 0.9613433034596717
},
{
"variable": "xi",
"time": 0.0,
"expected": 0.05777953848264748
},
{
"variable": "eta_M",
"time": 0.0,
"expected": 0.5533564814814815
},
{
"variable": "eta_s",
"time": 0.0,
"expected": 0.41739693291481456
},
{
"variable": "IR",
"time": 0.0,
"expected": 159496.04
},
{
"variable": "R0",
"time": 0.0,
"expected": 0.024745647
},
{
"variable": "R",
"time": 0.0,
"expected": 0.024745647,
"tolerance": {
"rel": 1e-05
}
},
{
"variable": "phi_w",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
},
{
"variable": "phi_s",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
},
{
"variable": "t_r",
"time": 0.0,
"expected": 6.582861
},
{
"variable": "IB",
"time": 0.0,
"expected": 25981.456
},
{
"variable": "F_L",
"time": 0.0,
"expected": 0.3466951
}
]
},
{
"id": "fm1_wind_5mph",
"description": "Fuel Model 1 with 5 mi/h wind (440 ft/min = 2.2352 m/s), flat terrain. Verifies wind factor phi_w, wind-enhanced spread rate R > R0, fireline intensity IB, and flame length F_L = c_FL * IB^0.46. Upstream test: 'Wind Effect' and 'Flame Length Relationship'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 2.2352,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "phi_w",
"time": 0.0,
"expected": 18.947278
},
{
"variable": "R0",
"time": 0.0,
"expected": 0.024745647
},
{
"variable": "R",
"time": 0.0,
"expected": 0.49360837
},
{
"variable": "IB",
"time": 0.0,
"expected": 518259.33
},
{
"variable": "F_L",
"time": 0.0,
"expected": 1.3737073
}
]
},
{
"id": "fm1_slope_03",
"description": "Fuel Model 1 with 30% slope (tan_phi=0.3, ~16.7 deg), no wind. Verifies slope factor phi_s > 0 and slope-enhanced R > R0. Upstream test: 'Slope Effect'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 0.0,
"tan_phi": 0.3
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "phi_s",
"time": 0.0,
"expected": 3.703128
},
{
"variable": "R0",
"time": 0.0,
"expected": 0.024745647
},
{
"variable": "R",
"time": 0.0,
"expected": 0.11638196
}
]
},
{
"id": "fm1_high_moisture",
"description": "Fuel Model 1 at 10% moisture (wet). eta_M(10%) < eta_M(5%) ⇒ R_wet < R_dry. Upstream test: 'Moisture Effect'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.1,
"U": 0.0,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "R",
"time": 0.0,
"expected": 0.013358993
}
]
},
{
"id": "extinction_moisture",
"description": "At Mf = Mx = 0.12 (extinction moisture), rM = 1.0 exactly ⇒ eta_M = 1 - 2.59 + 5.11 - 3.52 = 0 ⇒ IR = 0 ⇒ R = 0. Upstream test: 'Extinction Moisture'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.12,
"U": 0.0,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "eta_M",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-10
}
},
{
"variable": "R",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-10
}
}
]
},
{
"id": "nonburnable_h_zero",
"description": "Non-burnable fuel: h=0 ⇒ IR = Gamma_prime * wn * h * eta_M * eta_s = 0 ⇒ R0 = 0 ⇒ R = 0 even with nonzero wind and slope. Upstream test: 'Non-burnable fuel yields R=0'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 2.235,
"tan_phi": 0.3,
"h": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "IR",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
},
{
"variable": "R0",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
},
{
"variable": "R",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
}
]
},
{
"id": "zero_fuel_load",
"description": "w0=0 (no fuel): wn=0 ⇒ IR=0 ⇒ R0=0 ⇒ R=0. Floor guards keep denominators finite. Upstream test: 'Zero fuel load (w0=0) yields finite R=0'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.0,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 2.235,
"tan_phi": 0.3
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "IR",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
},
{
"variable": "R0",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
},
{
"variable": "R",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
},
{
"variable": "F_L",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
}
]
},
{
"id": "residence_time_si",
"description": "Residence time: t_r = c_tr / sigma = 75590.6 / 11482.94 = 6.5829 s. Cross-check: t_r / 60 ≈ t_r_US_min = 384/3500 min. Upstream test: 'Residence Time Relationship'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 0.0,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "t_r",
"time": 0.0,
"expected": 6.5828614
}
]
},
{
"id": "ha_ir_tr_identity",
"description": "Heat per unit area identity: HA = IR * t_r. Cross-check with values from fm1_no_wind_flat: HA = 159496 * 6.583 = 1049940 J/m^2. Upstream test: 'Heat Per Unit Area'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 0.0,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "HA",
"time": 0.0,
"expected": 1049940.3
}
]
},
{
"id": "r_sanity_ft_per_min",
"description": "Sanity check: Fuel Model 1 (short grass), no wind, 5% moisture — spread rate in ft/min should be 1–20. R_SI = 0.02475 m/s → R_US = 0.02475/0.00508 = 4.87 ft/min. Within range. Upstream test: 'Cross-validation with US Customary Units'.",
"parameter_overrides": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 0.0,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "R",
"time": 0.0,
"expected": 0.024745647
}
]
}
],
"analyses": [
{
"id": "spread_rate_vs_wind",
"description": "Sweep wind speed U from 0 to 10 m/s at Fuel Model 1 conditions (Mf=5%, flat). Shows the power-law wind amplification of fire spread rate: R grows rapidly with wind as the wind factor phi_w = C*(U/U_ref)^B scales with U^B_coeff where B_coeff ~ 2.05.",
"initial_state": {},
"parameters": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "U",
"range": {
"start": 0.0,
"stop": 10.0,
"count": 21,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "R_vs_U",
"type": "line",
"description": "Rate of spread R (m/s) vs midflame wind speed U (m/s). Power-law growth characteristic of the Rothermel wind factor.",
"x": {
"variable": "U",
"label": "U (m/s)"
},
"y": {
"variable": "R",
"label": "R (m/s)"
}
}
]
},
{
"id": "spread_rate_vs_slope",
"description": "Sweep slope tan_phi from 0 to 1.0 (0% to 100% rise/run) at Fuel Model 1 conditions (Mf=5%, no wind). Shows slope factor phi_s = phi_s_coeff * tan_phi^2 growing quadratically with slope.",
"initial_state": {},
"parameters": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"Mf": 0.05,
"U": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "tan_phi",
"range": {
"start": 0.0,
"stop": 1.0,
"count": 21,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "R_vs_slope",
"type": "line",
"description": "Rate of spread R (m/s) vs slope steepness tan_phi (rise/run). Quadratic growth from the slope factor phi_s = phi_s_coeff * tan_phi^2.",
"x": {
"variable": "tan_phi",
"label": "tan_phi (rise/run)"
},
"y": {
"variable": "R",
"label": "R (m/s)"
}
}
]
},
{
"id": "spread_rate_vs_moisture",
"description": "Sweep fuel moisture Mf from 0.01 (1%) to 0.12 (extinction, Mx) at Fuel Model 1 conditions. Shows moisture damping: eta_M polynomial approaches 0 at Mf=Mx, bringing R→0.",
"initial_state": {},
"parameters": {
"sigma": 11482.939632545931,
"w0": 0.16600240422703066,
"delta": 0.3048,
"Mx": 0.12,
"U": 0.0,
"tan_phi": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "Mf",
"range": {
"start": 0.01,
"stop": 0.12,
"count": 23,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "R_vs_Mf",
"type": "line",
"description": "Rate of spread R (m/s) vs fuel moisture Mf (fraction). Monotonic decrease to zero at Mf=Mx (extinction).",
"x": {
"variable": "Mf",
"label": "Mf (fraction)"
},
"y": {
"variable": "R",
"label": "R (m/s)"
}
}
]
}
]
}