PartialPressureMixingRatio
Relates the volume mixing ratio of an atmospheric species to its partial pressure: xi = p_i / p (Seinfeld & Pandis, Atmospheric Chemistry and Physics, Ch. 1, Eq. 1.8). The mixing ratio equals the ratio of the species' partial pressure to the total atmospheric pressure. Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:308 (`PartialPressureMixingRatio` @component). Parameterized as observed-only: the partial pressure p_i and total pressure p are inputs (parameters in standalone form), xi is the algebraic output. Upstream the Julia @component declares p_i, p, and xi as @variables for composition into a parent system; for standalone serialization (3 unknowns vs 1 equation otherwise), p_i and p are declared as parameters here, mirroring the IdealGasLaw / ScaleHeight serialization pattern in the same module.
Description
Relates the volume mixing ratio of an atmospheric species to its partial pressure: xi = p_i / p (Seinfeld & Pandis, Atmospheric Chemistry and Physics, Ch. 1, Eq. 1.8). The mixing ratio equals the ratio of the species’ partial pressure to the total atmospheric pressure. Migrated from AtmosphericDynamics.jl@816cc391 src/seinfeld_pandis_ch1.jl:308 (PartialPressureMixingRatio @component). Parameterized as observed-only: the partial pressure p_i and total pressure p are inputs (parameters in standalone form), xi is the algebraic output. Upstream the Julia @component declares p_i, p, and xi as @variables for composition into a parent system; for standalone serialization (3 unknowns vs 1 equation otherwise), p_i and p are declared as parameters here, mirroring the IdealGasLaw / ScaleHeight serialization pattern in the same module.
Reference
_source_ref: AtmosphericDynamics.jl@816cc391:src/seinfeld_pandis_ch1.jl:308
Upstream PartialPressureMixingRatio is an MTK @component where p_i, p, and xi are @variables driven by a parent system. For standalone serialization — and to make the component well-posed in isolation (3 unknowns would be under-determined by the single equation otherwise) — the input partial pressure p_i and total pressure p are declared as parameters here; xi remains the algebraic state. This matches the (S, observed-only) classification in docs/migration-tracker.md and the IdealGasLaw / ScaleHeight pattern in the same module. The single algebraic equation xi = p_i / p (Seinfeld & Pandis Eq. 1.8) is unchanged from upstream.
Tolerance rationale (model-level rel=1e-6): observed-only single-equation algebraic system (no ODE integration); 1e-6 covers float64 roundoff in the single p_i / p division across the atmospheric mixing-ratio range (~4e-4 for CO2 up to 1.0 for a pure single-component gas)._
Parameters
| Name | Units | Default | Description |
|---|---|---|---|
p_i | Pa | 21227.5875 | Partial pressure of species i (default: oxygen partial pressure at standard sea-level pressure, dry-air mole fraction 0.2095) |
p | Pa | 101325.0 | Total atmospheric pressure (default: standard sea-level pressure) |
Observed
| Name | Units | Default | Description |
|---|---|---|---|
xi | 1 | Volume mixing ratio of species i (dimensionless ratio of partial pressure to total pressure) |
Observed expressions
$$ xi = \frac{p_{i}}{p} $$Volume mixing ratio of species i (dimensionless ratio of partial pressure to total pressure)
Analyses
xi_vs_partial_pressure
Volume mixing ratio as a function of partial pressure at fixed total pressure (p = 101325 Pa, standard sea level). xi rises linearly from 0 to 1 as the species’ partial pressure increases from 0 to the total pressure (Seinfeld & Pandis Eq. 1.8).
Time span: 0.0 → 1.0
Swept over: p_i
xi_vs_total_pressure
Volume mixing ratio as a function of total atmospheric pressure at fixed partial pressure (p_i = 21227.5875 Pa, the oxygen partial pressure at sea level). Holding p_i fixed, xi follows the inverse relation xi proportional to 1/p across the tropospheric pressure range (22.6-110 kPa) — an illustrative mathematical sweep rather than a physical altitude profile, since a species’ partial pressure normally falls together with the total pressure.
Time span: 0.0 → 1.0
Swept over: p
mixing_ratio_heatmap
Two-dimensional sweep of the volume mixing ratio over partial pressure p_i and total pressure p. Surfaces the full xi = p_i / p relation across the physical regime p_i <= p (so xi <= 1); xi approaches 1 only where the partial pressure approaches the smallest total pressure in the sweep.
Time span: 0.0 → 1.0
Swept over: p_i, p
Raw .esm
Raw .esm JSON (this component)
{
"reference": {
"notes": "source_ref: AtmosphericDynamics.jl@816cc391:src/seinfeld_pandis_ch1.jl:308\nUpstream `PartialPressureMixingRatio` is an MTK `@component` where p_i, p, and xi are `@variables` driven by a parent system. For standalone serialization — and to make the component well-posed in isolation (3 unknowns would be under-determined by the single equation otherwise) — the input partial pressure p_i and total pressure p are declared as parameters here; xi remains the algebraic state. This matches the (S, observed-only) classification in docs/migration-tracker.md and the IdealGasLaw / ScaleHeight pattern in the same module. The single algebraic equation xi = p_i / p (Seinfeld & Pandis Eq. 1.8) is unchanged from upstream.\n\nTolerance rationale (model-level rel=1e-6): observed-only single-equation algebraic system (no ODE integration); 1e-6 covers float64 roundoff in the single p_i / p division across the atmospheric mixing-ratio range (~4e-4 for CO2 up to 1.0 for a pure single-component gas)."
},
"tolerance": {
"rel": 1e-06
},
"variables": {
"p_i": {
"type": "parameter",
"units": "Pa",
"default": 21227.5875,
"description": "Partial pressure of species i (default: oxygen partial pressure at standard sea-level pressure, dry-air mole fraction 0.2095)"
},
"p": {
"type": "parameter",
"units": "Pa",
"default": 101325.0,
"description": "Total atmospheric pressure (default: standard sea-level pressure)"
},
"xi": {
"type": "unknown",
"units": "1",
"description": "Volume mixing ratio of species i (dimensionless ratio of partial pressure to total pressure)"
}
},
"equations": [
{
"lhs": "xi",
"rhs": {
"op": "/",
"args": [
"p_i",
"p"
]
}
}
],
"tests": [
{
"id": "nitrogen_sea_level",
"description": "Molecular nitrogen, the dominant constituent of dry air (mole fraction 0.7808). At standard sea-level pressure (p = 101325 Pa) its partial pressure is p_i = 79114.56 Pa, recovering the mixing ratio xi ~ 0.7808 (Seinfeld & Pandis Ch 1, dry-air composition).",
"parameter_overrides": {
"p_i": 79114.56,
"p": 101325.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "xi",
"time": 0.0,
"expected": 0.7807999999999999
}
]
},
{
"id": "oxygen_sea_level",
"description": "Molecular oxygen at standard sea-level pressure (mole fraction 0.2095). Partial pressure p_i = 21227.5875 Pa with p = 101325 Pa gives xi ~ 0.2095 — the second-most-abundant component of dry air.",
"parameter_overrides": {
"p_i": 21227.5875,
"p": 101325.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "xi",
"time": 0.0,
"expected": 0.20950000000000002
}
]
},
{
"id": "water_vapor_humid_surface",
"description": "Water vapor at saturation over liquid water near 20 degC: saturation vapor pressure p_i ~ 2339 Pa at total pressure p = 101325 Pa yields a mixing ratio xi ~ 0.0231 — humid surface air is roughly 2.3% water vapor by volume.",
"parameter_overrides": {
"p_i": 2339.0,
"p": 101325.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "xi",
"time": 0.0,
"expected": 0.02308413520848754
}
]
},
{
"id": "argon_sea_level",
"description": "Argon, the most abundant trace gas in dry air (mole fraction 0.0093). Partial pressure p_i = 942.3225 Pa at p = 101325 Pa gives xi = 0.0093 — exercises the sub-1% mixing-ratio regime.",
"parameter_overrides": {
"p_i": 942.3225,
"p": 101325.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "xi",
"time": 0.0,
"expected": 0.0093
}
]
},
{
"id": "co2_present_day",
"description": "Carbon dioxide at a representative recent global mean abundance (~421 ppm). Partial pressure p_i = 42.657825 Pa at p = 101325 Pa yields xi ~ 4.21e-4 — exercises the trace-gas (parts-per-million) mixing-ratio regime.",
"parameter_overrides": {
"p_i": 42.657825,
"p": 101325.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "xi",
"time": 0.0,
"expected": 0.00042100000000000004
}
]
},
{
"id": "unit_ratio_pure_component",
"description": "Boundary case: a single-component gas whose partial pressure equals the total pressure (p_i = p = 101325 Pa). The mixing ratio saturates at xi = 1.0 — the species accounts for the entire gas mixture.",
"parameter_overrides": {
"p_i": 101325.0,
"p": 101325.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "xi",
"time": 0.0,
"expected": 1.0
}
]
},
{
"id": "oxygen_tropopause",
"description": "Oxygen at the U.S. Standard Atmosphere tropopause (~11 km, p = 22632 Pa). With O2 retaining its dry-air mole fraction 0.2095, the partial pressure scales to p_i = 4741.404 Pa and xi ~ 0.2095 — identical to the sea-level case, confirming that the mixing ratio is a pure pressure ratio independent of the absolute pressure level.",
"parameter_overrides": {
"p_i": 4741.404,
"p": 22632.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"assertions": [
{
"variable": "xi",
"time": 0.0,
"expected": 0.20950000000000002
}
]
}
],
"analyses": [
{
"id": "xi_vs_partial_pressure",
"description": "Volume mixing ratio as a function of partial pressure at fixed total pressure (p = 101325 Pa, standard sea level). xi rises linearly from 0 to 1 as the species' partial pressure increases from 0 to the total pressure (Seinfeld & Pandis Eq. 1.8).",
"initial_state": {},
"parameters": {
"p": 101325.0
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "p_i",
"range": {
"start": 0.0,
"stop": 101325.0,
"count": 25,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "xi_vs_pi",
"type": "line",
"description": "Volume mixing ratio xi as a function of partial pressure p_i at p = 101325 Pa.",
"x": {
"variable": "p_i",
"label": "Partial pressure p_i (Pa)"
},
"y": {
"variable": "xi",
"label": "Volume mixing ratio xi (dimensionless)"
}
}
]
},
{
"id": "xi_vs_total_pressure",
"description": "Volume mixing ratio as a function of total atmospheric pressure at fixed partial pressure (p_i = 21227.5875 Pa, the oxygen partial pressure at sea level). Holding p_i fixed, xi follows the inverse relation xi proportional to 1/p across the tropospheric pressure range (22.6-110 kPa) — an illustrative mathematical sweep rather than a physical altitude profile, since a species' partial pressure normally falls together with the total pressure.",
"initial_state": {},
"parameters": {
"p_i": 21227.5875
},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "p",
"range": {
"start": 22632.0,
"stop": 110000.0,
"count": 25,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "xi_vs_p",
"type": "line",
"description": "Volume mixing ratio xi as a function of total pressure p at fixed p_i = 21227.5875 Pa.",
"x": {
"variable": "p",
"label": "Total pressure p (Pa)"
},
"y": {
"variable": "xi",
"label": "Volume mixing ratio xi (dimensionless)"
}
}
]
},
{
"id": "mixing_ratio_heatmap",
"description": "Two-dimensional sweep of the volume mixing ratio over partial pressure p_i and total pressure p. Surfaces the full xi = p_i / p relation across the physical regime p_i <= p (so xi <= 1); xi approaches 1 only where the partial pressure approaches the smallest total pressure in the sweep.",
"initial_state": {},
"parameters": {},
"time_span": {
"start": 0.0,
"end": 1.0
},
"parameter_sweep": {
"type": "cartesian",
"dimensions": [
{
"parameter": "p_i",
"range": {
"start": 0.0,
"stop": 22632.0,
"count": 12,
"scale": "linear"
}
},
{
"parameter": "p",
"range": {
"start": 22632.0,
"stop": 110000.0,
"count": 12,
"scale": "linear"
}
}
]
},
"plots": [
{
"id": "xi_heatmap",
"type": "heatmap",
"description": "Volume mixing ratio xi as a function of partial pressure p_i and total pressure p.",
"x": {
"variable": "p_i",
"label": "Partial pressure p_i (Pa)"
},
"y": {
"variable": "p",
"label": "Total pressure p (Pa)"
},
"value": {
"variable": "xi",
"reduce": "final"
}
}
]
}
]
}