Clark1996HeatFluxProfile
Vertical profile of fire-induced sensible (F_s) and latent (F_l) heat fluxes via the simple e-folding extinction-depth formulation of Clark et al. (1996), Eq. 10. F_s(z) = F_s_sfc * exp(-z/alpha_ext); F_l(z) = F_l_sfc * exp(-z/alpha_ext) with alpha_ext = 50 m. Migrated from WildlandFire.jl@126976f2 src/clark1996.jl:206 (`Clark1996HeatFluxProfile` @component). Observed-only: z, F_s_sfc, F_l_sfc are inputs (parameters); F_s, F_l are algebraic outputs.
Description
Vertical profile of fire-induced sensible (F_s) and latent (F_l) heat fluxes via the simple e-folding extinction-depth formulation of Clark et al. (1996), Eq. 10. F_s(z) = F_s_sfc * exp(-z/alpha_ext); F_l(z) = F_l_sfc * exp(-z/alpha_ext) with alpha_ext = 50 m. Migrated from WildlandFire.jl@126976f2 src/clark1996.jl:206 (Clark1996HeatFluxProfile @component). Observed-only: z, F_s_sfc, F_l_sfc are inputs (parameters); F_s, F_l are algebraic outputs.
Reference
_source_ref: WildlandFire.jl@126976f2508ceacca6c486b21ae6da5b168c6f46:src/clark1996.jl:206
Upstream Clark1996HeatFluxProfile is an MTK @component whose three inputs (z, F_s_sfc, F_l_sfc) are @parameters and whose two outputs (F_s, F_l) are time-indexed @variables with one algebraic equation each. Two upstream @constants are declared: alpha_ext (the e-folding extinction depth, 50 m) and one_m (a unit-balancing literal, 1 m). Following the wind_profile.esm pattern (components/wildland_fire/clark1996/wind_profile.esm), upstream @constants are preserved as parameters with their upstream default values to maintain 1:1 fidelity with the upstream component — even when, as with one_m here, they are declared but unused in the equation (upstream keeps it for symmetry with sibling Clark1996 components).
F_s_sfc and F_l_sfc have no defaults upstream (they are driven by a parent surface-flux component); ESM requires concrete defaults for standalone simulation, so we declare them as 0.0 W/m^2 (the trivial null-fire case, matching the convention used for similarly-driven inputs in other observed-only migrations).
Tolerance rationale (model-level rel=1e-12): observed-only single-equation algebraic system per output (no ODE integration); each equation is exp + a single multiply on hardware-supported intrinsics — float64 roundoff is at the ULP level (~1e-15). 1e-12 is comfortably above ULP and far below any plausible physical-discrimination scale on W/m^2 heat-flux magnitudes._
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
z | m | 0.0 | Height above ground level |
F_s_sfc | W/m^2 | 0.0 | Sensible heat flux at the surface (z = 0). Upstream has no default; 0 W/m^2 is the trivial null-fire case for standalone simulation. |
F_l_sfc | W/m^2 | 0.0 | Latent heat flux at the surface (z = 0). Upstream has no default; 0 W/m^2 is the trivial null-fire case for standalone simulation. |
alpha_ext | m | 50.0 | Heat flux e-folding extinction depth (upstream @constant; Clark et al. 1996 Eq. 10 default = 50 m) |
one_m | m | 1.0 | Reference length (upstream @constant; declared but unused — preserved for 1:1 structural fidelity with the upstream component) |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
F_s | W/m^2 | Sensible heat flux at height z | |
F_l | W/m^2 | Latent heat flux at height z |
Observed expressions
$$ F_{s} = F_{s\,sfc} \cdot e^{\frac{-z}{alpha_{ext}}} $$Sensible heat flux at height z
$$ F_{l} = F_{l\,sfc} \cdot e^{\frac{-z}{alpha_{ext}}} $$Latent heat flux at height z
Analyses
heat_flux_profile_curve
Sensible and latent heat flux profiles vs. height — reproduces the canonical Clark et al. (1996) Eq. 10 e-folding decay from the surface (F_s = 100 kW/m^2, F_l = 50 kW/m^2) through 250 m (~5 extinction depths) where the profile is effectively extinguished. Surface fluxes representative of a moderately intense forest fire (Walker, 1981; p. 180 of Clark et al., 1996).
Time span: 0.0 → 1.0
Swept over: z
extinction_depth_sensitivity
Sensitivity of the heat flux profile to alpha_ext — shorter e-folding depths concentrate the heat flux near the surface, while longer depths transport heat further aloft. Reveals how the extinction depth controls vertical coupling between fire and atmosphere.
Time span: 0.0 → 1.0
Swept over: z, alpha_ext
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"notes": "source_ref: WildlandFire.jl@126976f2508ceacca6c486b21ae6da5b168c6f46:src/clark1996.jl:206\nUpstream `Clark1996HeatFluxProfile` is an MTK `@component` whose three inputs (z, F_s_sfc, F_l_sfc) are `@parameters` and whose two outputs (F_s, F_l) are time-indexed `@variables` with one algebraic equation each. Two upstream `@constants` are declared: `alpha_ext` (the e-folding extinction depth, 50 m) and `one_m` (a unit-balancing literal, 1 m). Following the wind_profile.esm pattern (components/wildland_fire/clark1996/wind_profile.esm), upstream `@constants` are preserved as parameters with their upstream default values to maintain 1:1 fidelity with the upstream component — even when, as with `one_m` here, they are declared but unused in the equation (upstream keeps it for symmetry with sibling Clark1996 components).\n\nF_s_sfc and F_l_sfc have no defaults upstream (they are driven by a parent surface-flux component); ESM requires concrete defaults for standalone simulation, so we declare them as 0.0 W/m^2 (the trivial null-fire case, matching the convention used for similarly-driven inputs in other observed-only migrations).\n\nTolerance rationale (model-level rel=1e-12): observed-only single-equation algebraic system per output (no ODE integration); each equation is exp + a single multiply on hardware-supported intrinsics — float64 roundoff is at the ULP level (~1e-15). 1e-12 is comfortably above ULP and far below any plausible physical-discrimination scale on W/m^2 heat-flux magnitudes."
},
"tolerance": {
"rel": 1e-12
},
"variables": {
"z": {
"type": "parameter",
"units": "m",
"default": 0.0,
"description": "Height above ground level"
},
"F_s_sfc": {
"type": "parameter",
"units": "W/m^2",
"default": 0.0,
"description": "Sensible heat flux at the surface (z = 0). Upstream has no default; 0 W/m^2 is the trivial null-fire case for standalone simulation."
},
"F_l_sfc": {
"type": "parameter",
"units": "W/m^2",
"default": 0.0,
"description": "Latent heat flux at the surface (z = 0). Upstream has no default; 0 W/m^2 is the trivial null-fire case for standalone simulation."
},
"alpha_ext": {
"type": "parameter",
"units": "m",
"default": 50.0,
"description": "Heat flux e-folding extinction depth (upstream @constant; Clark et al. 1996 Eq. 10 default = 50 m)"
},
"one_m": {
"type": "parameter",
"units": "m",
"default": 1.0,
"description": "Reference length (upstream @constant; declared but unused — preserved for 1:1 structural fidelity with the upstream component)"
},
"F_s": {
"type": "unknown",
"units": "W/m^2",
"description": "Sensible heat flux at height z"
},
"F_l": {
"type": "unknown",
"units": "W/m^2",
"description": "Latent heat flux at height z"
}
},
"equations": [
{
"lhs": "F_s",
"rhs": {
"op": "*",
"args": [
"F_s_sfc",
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
"z"
]
},
"alpha_ext"
]
}
]
}
]
}
},
{
"lhs": "F_l",
"rhs": {
"op": "*",
"args": [
"F_l_sfc",
{
"op": "exp",
"args": [
{
"op": "/",
"args": [
{
"op": "-",
"args": [
"z"
]
},
"alpha_ext"
]
}
]
}
]
}
}
],
"tests": [
{
"id": "surface",
"description": "At ground level (z = 0), F_s = F_s_sfc and F_l = F_l_sfc — the boundary condition where the profile equals the supplied surface flux. exp(-0/50) = 1.",
"parameter_overrides": {
"z": 0.0,
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 100000.0
},
{
"variable": "F_l",
"time": 0.0,
"expected": 50000.0
}
]
},
{
"id": "shallow_z25",
"description": "Below one extinction depth (z = 25 m, half of alpha_ext). exp(-0.5) ≈ 0.6065 → fluxes retain ~60% of their surface value.",
"parameter_overrides": {
"z": 25.0,
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 60653.06597126334
},
{
"variable": "F_l",
"time": 0.0,
"expected": 30326.53298563167
}
]
},
{
"id": "one_efold",
"description": "At one extinction depth (z = alpha_ext = 50 m), exp(-1) ≈ 0.3679 — the defining e-folding height.",
"parameter_overrides": {
"z": 50.0,
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 36787.94411714423
},
{
"variable": "F_l",
"time": 0.0,
"expected": 18393.972058572115
}
]
},
{
"id": "two_efold",
"description": "At two extinction depths (z = 100 m), exp(-2) ≈ 0.1353 — verifies exponential decay of the profile.",
"parameter_overrides": {
"z": 100.0,
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 13533.52832366127
},
{
"variable": "F_l",
"time": 0.0,
"expected": 6766.764161830635
}
]
},
{
"id": "three_efold",
"description": "At three extinction depths (z = 150 m), exp(-3) ≈ 0.0498 — fluxes have decayed to ~5% of surface values.",
"parameter_overrides": {
"z": 150.0,
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 4978.706836786395
},
{
"variable": "F_l",
"time": 0.0,
"expected": 2489.3534183931974
}
]
},
{
"id": "five_efold_aloft",
"description": "Far aloft (z = 250 m = 5 * alpha_ext), exp(-5) ≈ 0.0067 — confirms the profile is effectively extinguished at this altitude.",
"parameter_overrides": {
"z": 250.0,
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 673.7946999085467
},
{
"variable": "F_l",
"time": 0.0,
"expected": 336.89734995427335
}
]
},
{
"id": "alpha_override",
"description": "Override the @constant alpha_ext to verify it is wired correctly. With alpha_ext = 100 m and z = 30 m, exp(-0.3) ≈ 0.7408 — a deeper extinction depth than the upstream default.",
"parameter_overrides": {
"z": 30.0,
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0,
"alpha_ext": 100.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 74081.8220681718
},
{
"variable": "F_l",
"time": 0.0,
"expected": 37040.9110340859
}
]
},
{
"id": "asymmetric_surface_fluxes",
"description": "Independent F_s_sfc (200 kW/m^2) and F_l_sfc (80 kW/m^2) at z = 75 m (1.5 e-folds): verifies F_s and F_l are independently scaled by their respective surface inputs.",
"parameter_overrides": {
"z": 75.0,
"F_s_sfc": 200000.0,
"F_l_sfc": 80000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 44626.032029685965
},
{
"variable": "F_l",
"time": 0.0,
"expected": 17850.412811874387
}
]
},
{
"id": "zero_surface_flux",
"description": "Zero surface flux (no fire). F_s and F_l vanish identically at any z, regardless of altitude — sanity check the multiplicative coupling.",
"parameter_overrides": {
"z": 50.0,
"F_s_sfc": 0.0,
"F_l_sfc": 0.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "F_s",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
},
{
"variable": "F_l",
"time": 0.0,
"expected": 0.0,
"tolerance": {
"abs": 1e-15
}
}
]
}
],
"analyses": [
{
"id": "heat_flux_profile_curve",
"description": "Sensible and latent heat flux profiles vs. height — reproduces the canonical Clark et al. (1996) Eq. 10 e-folding decay from the surface (F_s = 100 kW/m^2, F_l = 50 kW/m^2) through 250 m (~5 extinction depths) where the profile is effectively extinguished. Surface fluxes representative of a moderately intense forest fire (Walker, 1981; p. 180 of Clark et al., 1996).",
"initial_state": {},
"parameters": {
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "z",
"range": {
"start": 0.0,
"stop": 250.0,
"count": 26,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "F_s_vs_z",
"type": "line",
"description": "Sensible heat flux F_s (W/m^2) vs. height z (m) — Clark et al. (1996) Eq. 10.",
"x": {
"variable": "z",
"label": "Height z (m)"
},
"y": {
"variable": "F_s",
"label": "Sensible heat flux F_s (W/m^2)"
}
},
{
"id": "F_l_vs_z",
"type": "line",
"description": "Latent heat flux F_l (W/m^2) vs. height z (m) — Clark et al. (1996) Eq. 10.",
"x": {
"variable": "z",
"label": "Height z (m)"
},
"y": {
"variable": "F_l",
"label": "Latent heat flux F_l (W/m^2)"
}
}
]
},
{
"id": "extinction_depth_sensitivity",
"description": "Sensitivity of the heat flux profile to alpha_ext — shorter e-folding depths concentrate the heat flux near the surface, while longer depths transport heat further aloft. Reveals how the extinction depth controls vertical coupling between fire and atmosphere.",
"initial_state": {},
"parameters": {
"F_s_sfc": 100000.0,
"F_l_sfc": 50000.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "z",
"range": {
"start": 0.0,
"stop": 250.0,
"count": 21,
"scale": "linear"
}
},
{
"parameter": "alpha_ext",
"range": {
"start": 25.0,
"stop": 100.0,
"count": 4,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "F_s_heatmap",
"type": "heatmap",
"description": "Sensible heat flux F_s over the (z, alpha_ext) plane — surfaces how the extinction depth controls the vertical reach of fire-induced heating.",
"x": {
"variable": "z",
"label": "Height z (m)"
},
"y": {
"variable": "alpha_ext",
"label": "Extinction depth alpha_ext (m)"
},
"value": {
"variable": "F_s",
"reduce": "final"
}
}
]
}
]
}