Visibility
Visibility calculation from extinction coefficient. Computes visual range using the Koschmeider equation (Eq. 15.36) and related visibility metrics. Visual range is the distance at which a black object against a white background reaches the threshold contrast of 0.02.
Description
Visibility calculation from extinction coefficient. Computes visual range using the Koschmeider equation (Eq. 15.36) and related visibility metrics. Visual range is the distance at which a black object against a white background reaches the threshold contrast of 0.02.
Reference
Coupler identity: this model was serialized with the model-level field coupletype: "Visibility", the EarthSciMLBase CoupleType metadata tag naming the Julia coupler struct that EarthSciMLBase.couple2 dispatches on to find this component’s pairwise coupling rules. The esm schema defined coupletype only before 0.8.0 (“informational label identifying this system’s role in coupling”); 0.8.0 removed it in favour of explicit coupling — coupling entries naming components directly, or coupling_roles + coupling_import in a coupling-library file (esm-spec §10.9–§10.11). esm 1.0.0 has no model-level coupler-identity field, so the tag is recorded here to keep it recoverable.
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
Koschmeider_const | 1 | 3.912 | Koschmeider constant = -ln(0.02) (dimensionless) |
one_km | m | 1000.0 | One kilometer in meters |
b_ext | m^-1 | 0.0001 | Total extinction coefficient |
b_sg | m^-1 | 1.32e-05 | Rayleigh scattering coefficient (gas) |
b_ag | m^-1 | 0.0 | Absorption coefficient due to gases (mainly NO2) |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
x_v | m | Visual range | |
τ_per_km | 1 | Optical depth per kilometer (dimensionless) | |
b_sp | m^-1 | Scattering coefficient due to particles |
Observed expressions
$$ x_{v} = \frac{Koschmeider_{const}}{b_{ext}} $$Visual range
$$ τ_{per\,km} = b_{ext} \cdot one_{km} $$Optical depth per kilometer (dimensionless)
$$ b_{sp} = b_{ext} - b_{sg} - b_{ag} $$Scattering coefficient due to particles
Analyses
koschmeider_curve
Koschmeider equation (Eq. 15.36): visual range x_v vs extinction coefficient b_ext. At sea level in a clean Rayleigh atmosphere (b_ext ~13.2e-6 m^-1), maximum visual range is ~296 km. Urban conditions (b_ext ~1e-4 to 1e-3 m^-1) reduce visibility to 4-40 km. Reproduces the characteristic curve from S&P Chapter 15.
Time span: 0.0 → 0.0
Swept over: b_ext
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"notes": "Coupler identity: this model was serialized with the model-level field `coupletype: \"Visibility\"`, the EarthSciMLBase `CoupleType` metadata tag naming the Julia coupler struct that `EarthSciMLBase.couple2` dispatches on to find this component's pairwise coupling rules. The esm schema defined `coupletype` only before 0.8.0 (\"informational label identifying this system's role in coupling\"); 0.8.0 removed it in favour of explicit coupling — `coupling` entries naming components directly, or `coupling_roles` + `coupling_import` in a coupling-library file (esm-spec §10.9–§10.11). esm 1.0.0 has no model-level coupler-identity field, so the tag is recorded here to keep it recoverable."
},
"variables": {
"Koschmeider_const": {
"type": "parameter",
"units": "1",
"default": 3.912,
"description": "Koschmeider constant = -ln(0.02) (dimensionless)"
},
"one_km": {
"type": "parameter",
"units": "m",
"default": 1000.0,
"description": "One kilometer in meters"
},
"b_ext": {
"type": "parameter",
"units": "m^-1",
"default": 0.0001,
"description": "Total extinction coefficient"
},
"b_sg": {
"type": "parameter",
"units": "m^-1",
"default": 1.32e-05,
"description": "Rayleigh scattering coefficient (gas)"
},
"b_ag": {
"type": "parameter",
"units": "m^-1",
"default": 0.0,
"description": "Absorption coefficient due to gases (mainly NO2)"
},
"x_v": {
"type": "unknown",
"units": "m",
"description": "Visual range"
},
"τ_per_km": {
"type": "unknown",
"units": "1",
"description": "Optical depth per kilometer (dimensionless)"
},
"b_sp": {
"type": "unknown",
"units": "m^-1",
"description": "Scattering coefficient due to particles"
}
},
"equations": [
{
"lhs": "x_v",
"rhs": {
"op": "/",
"args": [
"Koschmeider_const",
"b_ext"
]
}
},
{
"lhs": "τ_per_km",
"rhs": {
"op": "*",
"args": [
"b_ext",
"one_km"
]
}
},
{
"lhs": "b_sp",
"rhs": {
"op": "-",
"args": [
{
"op": "-",
"args": [
"b_ext",
"b_sg"
]
},
"b_ag"
]
}
}
],
"tests": [
{
"id": "koschmeider_default",
"description": "Visual range at default parameters (b_ext=1e-4 m^-1): x_v = 3.912 / 1e-4 = 39120 m",
"time_span": {
"start": 0.0,
"end": 0.0
},
"assertions": [
{
"variable": "x_v",
"time": 0,
"expected": 39120.0,
"tolerance": {
"abs": 0.01
}
}
]
},
{
"id": "optical_depth_default",
"description": "Optical depth per km at default parameters (b_ext=1e-4): tau_per_km = 1e-4 x 1000 = 0.1",
"time_span": {
"start": 0.0,
"end": 0.0
},
"assertions": [
{
"variable": "τ_per_km",
"time": 0,
"expected": 0.1,
"tolerance": {
"abs": 1e-10
}
}
]
},
{
"id": "particle_scattering_default",
"description": "Particle scattering at defaults: b_sp = 1e-4 - 13.2e-6 - 0 = 8.68e-5 m^-1",
"time_span": {
"start": 0.0,
"end": 0.0
},
"assertions": [
{
"variable": "b_sp",
"time": 0,
"expected": 8.68e-05,
"tolerance": {
"abs": 1e-10
}
}
]
},
{
"id": "rayleigh_clean_atmosphere",
"description": "Clean Rayleigh atmosphere (S&P p.705): b_ext = b_sg = 13.2e-6 m^-1, x_v = 3.912 / 13.2e-6 = 296363.6 m (~296 km), no particle contribution",
"time_span": {
"start": 0.0,
"end": 0.0
},
"parameter_overrides": {
"b_ext": 1.32e-05,
"b_sg": 1.32e-05,
"b_ag": 0.0
},
"assertions": [
{
"variable": "x_v",
"time": 0,
"expected": 296363.636,
"tolerance": {
"rel": 0.001
}
},
{
"variable": "b_sp",
"time": 0,
"expected": 0.0,
"tolerance": {
"abs": 1e-12
}
}
]
},
{
"id": "urban_polluted",
"description": "Urban polluted conditions (b_ext=2e-4 m^-1): x_v = 3.912 / 2e-4 = 19560 m (~20 km), tau_per_km = 0.2",
"time_span": {
"start": 0.0,
"end": 0.0
},
"parameter_overrides": {
"b_ext": 0.0002
},
"assertions": [
{
"variable": "x_v",
"time": 0,
"expected": 19560.0,
"tolerance": {
"abs": 0.01
}
},
{
"variable": "τ_per_km",
"time": 0,
"expected": 0.2,
"tolerance": {
"abs": 1e-10
}
}
]
},
{
"id": "gas_absorption_contribution",
"description": "With NO2 absorption (b_ag=5e-6 m^-1): b_sp = 1e-4 - 13.2e-6 - 5e-6 = 8.18e-5 m^-1",
"time_span": {
"start": 0.0,
"end": 0.0
},
"parameter_overrides": {
"b_ag": 5e-06
},
"assertions": [
{
"variable": "b_sp",
"time": 0,
"expected": 8.18e-05,
"tolerance": {
"abs": 1e-10
}
}
]
}
],
"analyses": [
{
"id": "koschmeider_curve",
"description": "Koschmeider equation (Eq. 15.36): visual range x_v vs extinction coefficient b_ext. At sea level in a clean Rayleigh atmosphere (b_ext ~13.2e-6 m^-1), maximum visual range is ~296 km. Urban conditions (b_ext ~1e-4 to 1e-3 m^-1) reduce visibility to 4-40 km. Reproduces the characteristic curve from S&P Chapter 15.",
"initial_state": {},
"time_span": {
"start": 0.0,
"end": 0.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "b_ext",
"range": {
"start": 1e-05,
"stop": 0.001,
"count": 50,
"scale": "log"
}
}
]
},
"plots": [
{
"id": "visual_range_vs_extinction",
"type": "line",
"description": "Visual range x_v (m) vs extinction coefficient b_ext (m^-1), reproducing the Koschmeider relationship (Eq. 15.36).",
"x": {
"variable": "b_ext",
"label": "Extinction coefficient b_ext (m^-1)"
},
"y": {
"variable": "x_v",
"label": "Visual range x_v (m)"
}
}
]
}
]
}