Virtual Temperature from Humidity

Virtual temperature from humidity

Virtual temperature (Tv) answers a simple question: what temperature would dry air need to match the density of your actual moist air sample at the same pressure? You get it from Tv = T · (1 + 0.61 · q), where T is the absolute temperature in Kelvin and q is the specific humidity (kg of water vapour per kg of moist air; the mixing ratio is sometimes plugged in with the same coefficient). Tv comes out always ≥ T, and the reason is that water vapour (M ≈ 18 g/mol) is lighter than dry air (M ≈ 29 g/mol), which makes moist air less dense. Run the numbers for T = 293.15 K (20 °C) and q = 0.012 kg/kg: Tv ≈ 293.15 · (1 + 0.61 · 0.012) ≈ 295.3 K. A couple of degrees sounds like nothing, but it matters a lot for aircraft lift, where a humid go-around runway leaves you less density-altitude margin, and it feeds into atmospheric stability calculations.

Applications

It turns up in aviation work (ATIS density altitude, takeoff performance, the landing skid risk that comes with moist air) and across numerical weather prediction in WRF, GFS and ECMWF. You will also find it behind atmospheric energy and stability budgets, in CAPE/CIN computation for severe weather, and in flight planning for balloons and drones.

FAQ

Why is moist air less dense than dry air? Water vapour weighs less per molecule (18 g/mol) than the average of the dry-air mixture (29 g/mol). When H₂O takes the place of N₂/O₂ molecules at the same pressure and temperature, the density drops.

What is the difference between Tv and dew point? Dew point tells you the temperature at which the air would saturate, while Tv is the dry-air temperature that gives the same density. Each one captures a different side of what humidity does.

When can Tv ≈ T be used? Once the air is very dry (q < 0.001 kg/kg), the correction falls under 0.1 K and you can drop it. Near tropical surfaces, though, q climbs to 0.020-0.025, which pushes Tv as much as 3-4 K above T.