Free · Atmospheric models

Ideal Moist-Air Virtual Temperature: Two Methods

Estimate density-equivalent temperature using a scoped liquid-water dew-point correlation and pressure, or a specified water-vapor mass mixing ratio.

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Formula and method

At 20°C ambient temperature, 0°C liquid-water dew point and 1000 hPa total pressure, the reference vapor pressure is 6.112 hPa and ideal virtual temperature is 20.6789°C.

Tv=T/[1−(1−ε)e/p]=T(1+r/ε)/(1+r); ε=0.62198, r in kg/kg

Worked example

Enter these known values and leave the other values blank.

Method: Liquid-water reference dew point and pressure
Air temperature: 20 °C
Liquid-water reference dew point (−45 to 60°C): 0 °C
Station pressure: 1000 hPa

Reference vapor pressure (enhancement omitted): 6.112 hPa
Ideal virtual temperature: 20.68 °C

Assumptions and limitations

Dry air and water vapor are ideal gases. ε=0.62198 is a fixed rounded molecular-mass-ratio model constant, not an exact universal metrology value. No liquid/ice cloud loading or real-gas compressibility correction is included.
Pressure mode uses WMO’s pure-liquid-water Magnus reference e=6.112exp[17.62Td/(243.12+Td)] in hPa, for Td −45..60°C. The moisture enhancement factor is deliberately omitted; the result is a declared reference approximation rather than a calibrated moist-air pressure measurement.
Dew point is on a liquid-water basis, including supercooled water below 0°C. It must not exceed ambient temperature in this unsupersaturated model. Ice/frost-point correlations are not supplied.
Mass mixing ratio is grams of water vapor per kilogram of dry air, not specific humidity per total air mass. The full ideal-mixture relation permits the zero-humidity limit and avoids the linear approximation’s unbounded virtual warming.
Air-temperature inputs retain the original −90..60°C range. Pressure mode also needs a valid reference dew point, which narrows its usable cold range; mass mode assumes the supplied composition is vapor and does not predict condensation or phase equilibrium.
Pressure and mass inputs have finite, identifiable inverse ranges. At dry equality pressure inversion with finite dew point is impossible; at the pure-vapor temperature limit no finite dry-air mixing ratio can be inferred.

Common questions

Is virtual temperature the measured air temperature?

It is the temperature dry air would require to have the same ideal-gas density and pressure as the specified vapor mixture. It is a density comparison, not extra heating measured by a thermometer.

Why do the two methods use the same ε?

They express the same ideal-mixture density relation through either partial pressure or vapor mass per dry-air mass. Using one declared ratio makes physically equivalent inputs agree.

References

Use the WMO pure-liquid-water Magnus reference correlation over its stated −45 to 60°C dew-point interval, without a moist-air enhancement factor. Both virtual-temperature modes use the same rounded model molecular-mass ratio ε=0.62198. The mixing-ratio mode uses the full ideal dry-air/water-vapor relation instead of the small-humidity linear approximation; update all 11 corresponding direct/inverse expressions. Require positive dry-air partial pressure, unsupersaturated liquid-water dew point within −45 to 60°C, nonnegative mass mixing ratio including dry air, and the ideal-mixture temperature bounds. Explain singular pressure or mass-ratio inverses instead of manufacturing a value. The reference correlation omits pressure enhancement, ice and cloud loading and does not certify real-gas accuracy. A source-specific 1e-55°C/hPa guard band only at closed temperature/correlation endpoints absorbs demonstrated 64-digit exp/log/inverse round-trip noise; physical pressure and composition inequalities remain strict.

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