SurfaceLayerProfile
Monin-Obukhov surface-layer similarity theory for the atmospheric surface layer, from Seinfeld & Pandis (2006) "Atmospheric Chemistry and Physics", 2nd ed., Chapter 16 "Meteorology of the Local Scale". Observed-only algebraic component: from the friction velocity u_star, surface sensible heat flux q_z, and surface-layer geometry it computes the Monin-Obukhov length L (Eq. 16.70), the dimensionless stability parameter ζ = z/L, the Businger-Dyer stability functions φ_m and φ_h (Eq. 16.75), their integrated forms ψ_m and ψ_h (Eq. 16.78-16.79), and the stability-corrected mean wind speed ū (Eq. 16.66 with the Eq. 16.77 correction). Migrated from AtmosphericDynamics.jl@816cc391 src/local_scale_meteorology.jl:107 (`SurfaceLayerProfile` @component); the 4 upstream @constants (g, κ, ĉ_p, ε_q) are declared as fixed-default parameters.
Description
Monin-Obukhov surface-layer similarity theory for the atmospheric surface layer, from Seinfeld & Pandis (2006) “Atmospheric Chemistry and Physics”, 2nd ed., Chapter 16 “Meteorology of the Local Scale”. Observed-only algebraic component: from the friction velocity u_star, surface sensible heat flux q_z, and surface-layer geometry it computes the Monin-Obukhov length L (Eq. 16.70), the dimensionless stability parameter ζ = z/L, the Businger-Dyer stability functions φ_m and φ_h (Eq. 16.75), their integrated forms ψ_m and ψ_h (Eq. 16.78-16.79), and the stability-corrected mean wind speed ū (Eq. 16.66 with the Eq. 16.77 correction). Migrated from AtmosphericDynamics.jl@816cc391 src/local_scale_meteorology.jl:107 (SurfaceLayerProfile @component); the 4 upstream @constants (g, κ, ĉ_p, ε_q) are declared as fixed-default parameters.
Reference
source_ref: AtmosphericDynamics.jl@816cc391:src/local_scale_meteorology.jl:107
Upstream SurfaceLayerProfile is a ModelingToolkit @component implementing Monin-Obukhov similarity theory for the atmospheric surface layer. g, κ, ĉ_p, ε_q are upstream @constants; z, z₀, T₀, ρ, u_star, q_z are @parameters; L, ζ, φ_m, φ_h, ψ_m, ψ_h, ū are @variables bound by 7 algebraic equations (no time derivative). For standalone serialization the 4 @constants are declared as fixed-default parameters here, matching the sibling scale_height.esm. The 7 equations are unchanged from upstream; mtk2esm reorders commutative */+ operands, rewrites x^(-n) as 1/x^n, and folds ((1-15ζ)^0.25)^2 to (1-15ζ)^0.5 (algebraically identical). The π/2 term of the ψ_m unstable branch is folded to the float literal 1.5707963267948966.
Tolerance rationale (model-level rel=1e-6): observed-only algebraic system (no ODE integration); rel=1e-6 covers float64 roundoff and cross-runner libm differences in the ^/log/atan chain. Near-zero outputs in the neutral regime (ζ, ψ_m, ψ_h ~ 1e-8..1e-13, where π/2 − 2·atan(x≈1) cancels) carry a per-assertion abs=1e-6 — already far tighter than the upstream test suite’s atol=1e-4 for ζ.
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
z | m | 10.0 | Height above ground |
z₀ | m | 0.1 | Roughness length (Table 16.1) |
T₀ | K | 288.15 | Reference temperature (surface) |
ρ | kg/m^3 | 1.225 | Air density |
u_star | m/s | 0.3 | Friction velocity |
q_z | W/m^2 | 0.0 | Surface sensible heat flux (positive upward) |
g | m/s^2 | 9.807 | Gravitational acceleration |
κ | 1 | 0.4 | von Karman constant (dimensionless) |
ĉ_p | J/(kg*K) | 1005.0 | Specific heat of air at constant pressure |
ε_q | W/m^2 | 1e-10 | Small regularization for heat flux |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
L | m | Monin-Obukhov length (Eq. 16.70) | |
ζ | 1 | Stability parameter z/L (dimensionless) | |
φ_m | 1 | Momentum stability function (Eq. 16.75) (dimensionless) | |
φ_h | 1 | Heat stability function (Eq. 16.75) (dimensionless) | |
ψ_m | 1 | Integrated momentum stability function (dimensionless) | |
ψ_h | 1 | Integrated heat stability function (dimensionless) | |
ū | m/s | Mean wind speed at height z (Eq. 16.66 with stability) |
Observed expressions
$$ L = \frac{\left(-1\right) \cdot ĉ_{p} \cdot ρ \cdot u_{star}^{3} \cdot T₀}{κ \cdot g \cdot \left(q_{z} + ε_{q}\right)} $$Monin-Obukhov length (Eq. 16.70)
$$ ζ = \frac{z}{L} $$Stability parameter z/L (dimensionless)
$$ φ_{m} = \mathrm{ifelse}\left(\mathrm{<}\left(ζ, 0\right), \frac{1}{\left(1 + \left(-15\right) \cdot ζ\right)^{0.25}}, 1 + 4.7 \cdot ζ\right) $$Momentum stability function (Eq. 16.75) (dimensionless)
$$ φ_{h} = \mathrm{ifelse}\left(\mathrm{<}\left(ζ, 0\right), \frac{1}{\left(1 + \left(-15\right) \cdot ζ\right)^{0.5}}, 1 + 4.7 \cdot ζ\right) $$Heat stability function (Eq. 16.75) (dimensionless)
$$ ψ_{m} = \mathrm{ifelse}\left(\mathrm{<}\left(ζ, 0\right), 1.5707963267948966 + \left(-2\right) \cdot \mathrm{atan}\left(\left(1 + \left(-15\right) \cdot ζ\right)^{0.25}\right) + 2 \cdot \ln\left(\frac{1 + \left(1 + \left(-15\right) \cdot ζ\right)^{0.25}}{2}\right) + \ln\left(\frac{1 + \left(1 + \left(-15\right) \cdot ζ\right)^{0.5}}{2}\right), \left(-4.7\right) \cdot ζ\right) $$Integrated momentum stability function (dimensionless)
$$ ψ_{h} = \mathrm{ifelse}\left(\mathrm{<}\left(ζ, 0\right), 2 \cdot \ln\left(\frac{1 + \left(1 + \left(-15\right) \cdot ζ\right)^{0.5}}{2}\right), \left(-4.7\right) \cdot ζ\right) $$Integrated heat stability function (dimensionless)
$$ ū = \frac{\left(\left(-1\right) \cdot ψ_{m} + \ln\left(\frac{z}{z₀}\right)\right) \cdot u_{star}}{κ} $$Mean wind speed at height z (Eq. 16.66 with stability)
Analyses
monin_obukhov_length_vs_heat_flux
Monin-Obukhov length L as a function of the surface sensible heat flux q_z over the unstable regime (q_z > 0, surface heating), at the default u_star = 0.3 m/s. Reproduces the unstable branch of the AtmosphericDynamics.jl docs figure “Monin-Obukhov Length vs Heat Flux”: L is negative and grows toward 0 as the heat flux increases.
Time span: 0.0 → 1.0
Swept over: q_z
logarithmic_wind_profile
Mean wind speed ū as a function of height z under neutral conditions (default q_z = 0), with u_star = 0.4 m/s and z₀ = 0.1 m. Reproduces the neutral wind profile of the AtmosphericDynamics.jl docs figure “Wind Profiles for Different Stability Conditions”: ū follows the logarithmic law (u_star/κ)·ln(z/z₀).
Time span: 0.0 → 1.0
Swept over: z
businger_dyer_stability_functions
Businger-Dyer stability functions φ_m and φ_h as functions of the stability parameter ζ = z/L, traced by sweeping the surface heat flux q_z over the unstable regime (q_z > 0 -> ζ < 0). Reproduces the unstable branch of the AtmosphericDynamics.jl docs figure “Businger-Dyer Stability Functions”: both functions fall below 1 as the surface layer becomes more unstable.
Time span: 0.0 → 1.0
Swept over: q_z
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"notes": "source_ref: AtmosphericDynamics.jl@816cc391:src/local_scale_meteorology.jl:107\nUpstream `SurfaceLayerProfile` is a ModelingToolkit `@component` implementing Monin-Obukhov similarity theory for the atmospheric surface layer. g, κ, ĉ_p, ε_q are upstream `@constants`; z, z₀, T₀, ρ, u_star, q_z are `@parameters`; L, ζ, φ_m, φ_h, ψ_m, ψ_h, ū are `@variables` bound by 7 algebraic equations (no time derivative). For standalone serialization the 4 `@constants` are declared as fixed-default parameters here, matching the sibling scale_height.esm. The 7 equations are unchanged from upstream; `mtk2esm` reorders commutative `*`/`+` operands, rewrites `x^(-n)` as `1/x^n`, and folds `((1-15ζ)^0.25)^2` to `(1-15ζ)^0.5` (algebraically identical). The `π/2` term of the ψ_m unstable branch is folded to the float literal 1.5707963267948966.\nTolerance rationale (model-level rel=1e-6): observed-only algebraic system (no ODE integration); rel=1e-6 covers float64 roundoff and cross-runner libm differences in the `^`/`log`/`atan` chain. Near-zero outputs in the neutral regime (ζ, ψ_m, ψ_h ~ 1e-8..1e-13, where π/2 − 2·atan(x≈1) cancels) carry a per-assertion abs=1e-6 — already far tighter than the upstream test suite's atol=1e-4 for ζ."
},
"tolerance": {
"rel": 1e-06
},
"variables": {
"z": {
"type": "parameter",
"units": "m",
"default": 10.0,
"description": "Height above ground"
},
"z₀": {
"type": "parameter",
"units": "m",
"default": 0.1,
"description": "Roughness length (Table 16.1)"
},
"T₀": {
"type": "parameter",
"units": "K",
"default": 288.15,
"description": "Reference temperature (surface)"
},
"ρ": {
"type": "parameter",
"units": "kg/m^3",
"default": 1.225,
"description": "Air density"
},
"u_star": {
"type": "parameter",
"units": "m/s",
"default": 0.3,
"description": "Friction velocity"
},
"q_z": {
"type": "parameter",
"units": "W/m^2",
"default": 0.0,
"description": "Surface sensible heat flux (positive upward)"
},
"g": {
"type": "parameter",
"units": "m/s^2",
"default": 9.807,
"description": "Gravitational acceleration"
},
"κ": {
"type": "parameter",
"units": "1",
"default": 0.4,
"description": "von Karman constant (dimensionless)"
},
"ĉ_p": {
"type": "parameter",
"units": "J/(kg*K)",
"default": 1005.0,
"description": "Specific heat of air at constant pressure"
},
"ε_q": {
"type": "parameter",
"units": "W/m^2",
"default": 1e-10,
"description": "Small regularization for heat flux"
},
"L": {
"type": "unknown",
"units": "m",
"description": "Monin-Obukhov length (Eq. 16.70)"
},
"ζ": {
"type": "unknown",
"units": "1",
"description": "Stability parameter z/L (dimensionless)"
},
"φ_m": {
"type": "unknown",
"units": "1",
"description": "Momentum stability function (Eq. 16.75) (dimensionless)"
},
"φ_h": {
"type": "unknown",
"units": "1",
"description": "Heat stability function (Eq. 16.75) (dimensionless)"
},
"ψ_m": {
"type": "unknown",
"units": "1",
"description": "Integrated momentum stability function (dimensionless)"
},
"ψ_h": {
"type": "unknown",
"units": "1",
"description": "Integrated heat stability function (dimensionless)"
},
"ū": {
"type": "unknown",
"units": "m/s",
"description": "Mean wind speed at height z (Eq. 16.66 with stability)"
}
},
"equations": [
{
"lhs": "L",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
-1,
"ĉ_p",
"ρ",
{
"op": "^",
"args": [
"u_star",
3
]
},
"T₀"
]
},
{
"op": "*",
"args": [
"κ",
"g",
{
"op": "+",
"args": [
"q_z",
"ε_q"
]
}
]
}
]
}
},
{
"lhs": "ζ",
"rhs": {
"op": "/",
"args": [
"z",
"L"
]
}
},
{
"lhs": "φ_m",
"rhs": {
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"ζ",
0
]
},
{
"op": "/",
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{
"op": "^",
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0.25
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1,
{
"op": "*",
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},
{
"lhs": "φ_h",
"rhs": {
"op": "ifelse",
"args": [
{
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"args": [
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0
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},
{
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{
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{
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}
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0.5
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{
"op": "+",
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1,
{
"op": "*",
"args": [
4.7,
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]
}
]
}
]
}
},
{
"lhs": "ψ_m",
"rhs": {
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
"ζ",
0
]
},
{
"op": "+",
"args": [
1.5707963267948966,
{
"op": "*",
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-2,
{
"op": "atan",
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{
"op": "^",
"args": [
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2
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}
]
},
{
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}
]
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},
{
"lhs": "ψ_h",
"rhs": {
"op": "ifelse",
"args": [
{
"op": "<",
"args": [
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0
]
},
{
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{
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}
]
}
]
},
{
"op": "*",
"args": [
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"ζ"
]
}
]
}
},
{
"lhs": "ū",
"rhs": {
"op": "/",
"args": [
{
"op": "*",
"args": [
{
"op": "+",
"args": [
{
"op": "*",
"args": [
-1,
"ψ_m"
]
},
{
"op": "log",
"args": [
{
"op": "/",
"args": [
"z",
"z₀"
]
}
]
}
]
},
"u_star"
]
},
"κ"
]
}
}
],
"tests": [
{
"id": "default_parameters",
"description": "All parameters at their declared defaults (q_z = 0 -> the ε_q heat-flux regularization makes |L| enormous, so the surface layer is effectively neutral). ζ collapses to ~0, φ_m = φ_h -> 1, ψ_m = ψ_h -> 0, and ū reduces to the pure logarithmic profile (u_star/κ)·ln(z/z₀). Guards the serialized parameter defaults.",
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -24416778974839.395
},
{
"variable": "ζ",
"time": 0.0,
"expected": -4.095544301852688e-13,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.9999999999984641
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.9999999999969285
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 1.535438443056002e-12,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 3.0713209753206747e-12,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ū",
"time": 0.0,
"expected": 3.4538776394899164
},
{
"variable": "ū",
"time": 1.0,
"expected": 3.4538776394899164
}
]
},
{
"id": "monin_obukhov_neutral",
"description": "Monin-Obukhov length under near-neutral conditions (q_z = 1e-6 W/m^2, essentially zero heat flux). Upstream \"Monin-Obukhov length\" test 1: |L| must exceed 1e6 m. Here L = -2.44e9 m.",
"parameter_overrides": {
"q_z": 1e-06
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -2441433754.108529
},
{
"variable": "ζ",
"time": 0.0,
"expected": -4.095953856282873e-09,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.9999999846401737
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.9999999692803475
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 1.5359826240762353e-08,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 3.071965325174098e-08,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ū",
"time": 0.0,
"expected": 3.453877627971199
}
]
},
{
"id": "monin_obukhov_unstable",
"description": "Unstable surface layer: positive (upward) heat flux q_z = 100 W/m^2 with u_star = 0.4 m/s. Upstream \"Monin-Obukhov length\" test 2: L must be negative. ζ < 0 selects the Businger-Dyer unstable branch.",
"parameter_overrides": {
"u_star": 0.4,
"q_z": 100.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -57.876809421783676
},
{
"variable": "ζ",
"time": 0.0,
"expected": -0.172780775234583
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.7263979917166654
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.5276540423700046
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 0.40064640265675194
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 0.7398010106000124
},
{
"variable": "ū",
"time": 0.0,
"expected": 4.20452378333134
}
]
},
{
"id": "monin_obukhov_stable",
"description": "Stable surface layer: negative (downward) heat flux q_z = -50 W/m^2 (surface cooling). Upstream \"Monin-Obukhov length\" test 3: L must be positive. ζ > 0 selects the stable branch φ_m = φ_h = 1 + 4.7ζ.",
"parameter_overrides": {
"q_z": -50.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": 48.833557949776456
},
{
"variable": "ζ",
"time": 0.0,
"expected": 0.20477721509222482
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 1.9624529109334565
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 1.9624529109334565
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": -0.9624529109334566
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": -0.9624529109334566
},
{
"variable": "ū",
"time": 0.0,
"expected": 4.175717322691161
}
]
},
{
"id": "businger_dyer_neutral",
"description": "Businger-Dyer stability functions under near-neutral conditions (q_z = 1e-8 W/m^2). Upstream \"Businger-Dyer stability functions\" test 1: ζ ~ 0 and φ_m = φ_h ~ 1.",
"parameter_overrides": {
"q_z": 1e-08
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -241750286879.598
},
{
"variable": "ζ",
"time": 0.0,
"expected": -4.136499744871215e-11,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.9999999998448812
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.9999999996897626
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 1.551183625931671e-10,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 3.102371692635132e-10,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ū",
"time": 0.0,
"expected": 3.45387763937473
}
]
},
{
"id": "businger_dyer_stable",
"description": "Businger-Dyer stability functions under stable conditions (u_star = 0.2 m/s, q_z = -50 W/m^2). Upstream \"Businger-Dyer stability functions\" test 2: ζ > 0 and φ_m = φ_h = 1 + 4.7ζ. Here 1 + 4.7·0.691123 = 4.248279.",
"parameter_overrides": {
"u_star": 0.2,
"q_z": -50.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": 14.469202355489326
},
{
"variable": "ζ",
"time": 0.0,
"expected": 0.6911231009362585
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 4.248278574400414
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 4.248278574400414
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": -3.248278574400415
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": -3.248278574400415
},
{
"variable": "ū",
"time": 0.0,
"expected": 3.926724380194253
}
]
},
{
"id": "businger_dyer_unstable",
"description": "Businger-Dyer stability functions under unstable conditions (q_z = 100 W/m^2). Upstream \"Businger-Dyer stability functions\" test 3: ζ < 0, φ_m = (1 - 15ζ)^(-1/4), φ_h = (1 - 15ζ)^(-1/2). Same parameters as the upstream \"Physical constraints\" test 3, which checks φ_m, φ_h > 0.",
"parameter_overrides": {
"q_z": 100.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -24.416778974814978
},
{
"variable": "ζ",
"time": 0.0,
"expected": -0.40955443018567833
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.6116810518520646
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.37415370919484814
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 0.6862614089616637
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 1.2155589113923662
},
{
"variable": "ū",
"time": 0.0,
"expected": 2.939181582769821
}
]
},
{
"id": "log_wind_profile_neutral",
"description": "Logarithmic wind profile under neutral conditions (u_star = 0.4 m/s, z₀ = 0.1 m, z = 10 m, q_z = 1e-8 W/m^2). Upstream \"Logarithmic wind profile\" test 1: ū ~ (u_star/κ)·ln(z/z₀) = 1·ln(100) = 4.60517 m/s (ψ_m ~ 0).",
"parameter_overrides": {
"u_star": 0.4,
"q_z": 1e-08
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -573037717047.9362
},
{
"variable": "ζ",
"time": 0.0,
"expected": -1.745085829867543e-11,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.9999999999345592
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.9999999998691187
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 6.544076391782967e-11,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 1.3088108374430828e-10,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ū",
"time": 0.0,
"expected": 4.605170185922651
}
]
},
{
"id": "log_wind_profile_wangara",
"description": "Logarithmic wind profile with Wangara-experiment roughness (Seinfeld & Pandis p.745: z₀ = 0.0015 m, u_star = 0.4 m/s). Upstream \"Logarithmic wind profile\" test 2: ū ~ (u_star/κ)·ln(z/z₀) = ln(6666.67) = 8.80488 m/s. L/ζ/φ/ψ are independent of z₀, so they match log_wind_profile_neutral exactly.",
"parameter_overrides": {
"u_star": 0.4,
"z₀": 0.0015,
"q_z": 1e-08
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -573037717047.9362
},
{
"variable": "ζ",
"time": 0.0,
"expected": -1.745085829867543e-11,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.9999999999345592
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.9999999998691187
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 6.544076391782967e-11,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 1.3088108374430828e-10,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ū",
"time": 0.0,
"expected": 8.804875263802577
}
]
},
{
"id": "limiting_neutral_psi_to_zero",
"description": "Limiting behaviour: as |L| -> infinity (q_z = 1e-10 W/m^2, essentially zero heat flux) the surface layer becomes neutral and the integrated stability function ψ_m -> 0, leaving a purely logarithmic wind profile. Upstream \"Limiting behaviors\" test 1.",
"parameter_overrides": {
"q_z": 1e-10
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -12208389487419.697
},
{
"variable": "ζ",
"time": 0.0,
"expected": -8.191088603705376e-13,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.9999999999969285
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.9999999999938567
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 3.0715430199255997e-12,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 6.14353012905633e-12,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ū",
"time": 0.0,
"expected": 3.4538776394887654
}
]
},
{
"id": "wind_profile_z5m",
"description": "Wind speed at z = 5 m under near-neutral conditions (q_z = 1e-8 W/m^2). Lower half of the upstream \"Limiting behaviors\" test 2 (wind speed increases with height): ū(5 m) = 2.93402 m/s.",
"parameter_overrides": {
"z": 5.0,
"q_z": 1e-08
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -241750286879.598
},
{
"variable": "ζ",
"time": 0.0,
"expected": -2.0682498724356076e-11,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.9999999999224407
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.9999999998448814
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 7.755929232038987e-11,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 1.5511858463777203e-10,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ū",
"time": 0.0,
"expected": 2.93401725401294
}
]
},
{
"id": "wind_profile_z20m",
"description": "Wind speed at z = 20 m under near-neutral conditions (q_z = 1e-8 W/m^2). Upper half of the upstream \"Limiting behaviors\" test 2: ū(20 m) = 3.97374 m/s > ū(5 m), confirming wind speed increases with height.",
"parameter_overrides": {
"z": 20.0,
"q_z": 1e-08
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -241750286879.598
},
{
"variable": "ζ",
"time": 0.0,
"expected": -8.27299948974243e-11,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.9999999996897626
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.999999999379525
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 3.102373913081181e-10,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 6.204752266573222e-10,
"tolerance": {
"abs": 1e-06
}
},
{
"variable": "ū",
"time": 0.0,
"expected": 3.973738024678349
}
]
},
{
"id": "summer_afternoon_boundary_layer",
"description": "Summer-afternoon boundary layer from the AtmosphericDynamics.jl docs \"Complete Boundary Layer Analysis\" example (u_star = 0.35 m/s, q_z = 150 W/m^2 strong upward heat flux, T₀ = 300.15 K, ρ = 1.18 kg/m^3): a strongly unstable surface layer with L = -25.94 m and ζ = -0.386.",
"parameter_overrides": {
"u_star": 0.35,
"q_z": 150.0,
"T₀": 300.15,
"ρ": 1.18
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "L",
"time": 0.0,
"expected": -25.936007561545868
},
{
"variable": "ζ",
"time": 0.0,
"expected": -0.3855643539689024
},
{
"variable": "φ_m",
"time": 0.0,
"expected": 0.6196366508538875
},
{
"variable": "φ_h",
"time": 0.0,
"expected": 0.38394957908142247
},
{
"variable": "ψ_m",
"time": 0.0,
"expected": 0.6630617546704188
},
{
"variable": "ψ_h",
"time": 0.0,
"expected": 1.1780765683268124
},
{
"variable": "ū",
"time": 0.0,
"expected": 3.449344877402963
}
]
}
],
"analyses": [
{
"id": "monin_obukhov_length_vs_heat_flux",
"description": "Monin-Obukhov length L as a function of the surface sensible heat flux q_z over the unstable regime (q_z > 0, surface heating), at the default u_star = 0.3 m/s. Reproduces the unstable branch of the AtmosphericDynamics.jl docs figure \"Monin-Obukhov Length vs Heat Flux\": L is negative and grows toward 0 as the heat flux increases.",
"initial_state": {},
"parameters": {},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "q_z",
"range": {
"start": 10.0,
"stop": 300.0,
"count": 30,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "L_vs_q_z",
"type": "line",
"description": "Monin-Obukhov length L vs surface heat flux q_z (Eq. 16.70).",
"x": {
"variable": "q_z",
"label": "Surface sensible heat flux q_z (W/m^2)"
},
"y": {
"variable": "L",
"label": "Monin-Obukhov length L (m)"
}
}
]
},
{
"id": "logarithmic_wind_profile",
"description": "Mean wind speed ū as a function of height z under neutral conditions (default q_z = 0), with u_star = 0.4 m/s and z₀ = 0.1 m. Reproduces the neutral wind profile of the AtmosphericDynamics.jl docs figure \"Wind Profiles for Different Stability Conditions\": ū follows the logarithmic law (u_star/κ)·ln(z/z₀).",
"initial_state": {},
"parameters": {
"u_star": 0.4
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "z",
"range": {
"start": 1.0,
"stop": 50.0,
"count": 30,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "u_vs_z",
"type": "line",
"description": "Logarithmic wind profile ū(z) (Eq. 16.66).",
"x": {
"variable": "z",
"label": "Height z (m)"
},
"y": {
"variable": "ū",
"label": "Mean wind speed ū (m/s)"
}
}
]
},
{
"id": "businger_dyer_stability_functions",
"description": "Businger-Dyer stability functions φ_m and φ_h as functions of the stability parameter ζ = z/L, traced by sweeping the surface heat flux q_z over the unstable regime (q_z > 0 -> ζ < 0). Reproduces the unstable branch of the AtmosphericDynamics.jl docs figure \"Businger-Dyer Stability Functions\": both functions fall below 1 as the surface layer becomes more unstable.",
"initial_state": {},
"parameters": {},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "q_z",
"range": {
"start": 5.0,
"stop": 250.0,
"count": 30,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "phi_m_vs_zeta",
"type": "line",
"description": "Momentum stability function φ_m vs ζ (Eq. 16.75, unstable branch).",
"x": {
"variable": "ζ",
"label": "Stability parameter ζ = z/L"
},
"y": {
"variable": "φ_m",
"label": "Momentum stability function φ_m"
}
},
{
"id": "phi_h_vs_zeta",
"type": "line",
"description": "Heat stability function φ_h vs ζ (Eq. 16.75, unstable branch).",
"x": {
"variable": "ζ",
"label": "Stability parameter ζ = z/L"
},
"y": {
"variable": "φ_h",
"label": "Heat stability function φ_h"
}
}
]
}
]
}