Hong Life CalculatorsUnderstanding the foehn wind temperature calculator — concept and principle
A foehn is a warm, dry wind that descends the lee side of a mountain range. This calculator follows a parcel up and over a mountain to estimate the cloud base, the summit temperature and the temperature after it descends.
How it is calculated
- Cloud base (lifting condensation level): h_c ≈ 125 m × (T − T_d), capped at the mountain height H.
- Up to cloud base: the parcel cools at the dry adiabatic rate of 9.8 °C per km.
- From cloud base to summit: it cools at a moist rate of about 6 °C per km, because condensation releases latent heat. Summit temperature: T_s = T − 0.0098 × h_c − 0.006 × (H − h_c).
- Down the lee side: assuming the cloud water has rained out, the parcel warms at the dry rate all the way down: T_lee = T_s + 0.0098 × H.
Temperatures are in °C and heights in metres above the windward base.
The principle
Rising air expands and cools; sinking air is compressed and warms. Without condensation this happens at the dry adiabatic lapse rate, g/c_p ≈ 9.8 °C/km. The dew point falls much more slowly with height, so the gap between temperature and dew point closes by about 8 °C per km, which is where the 125 m per degree rule comes from. Once saturated, condensing water vapour releases heat, so the cooling slows. If the condensed water falls as rain or snow on the windward slope, the descending air has nothing left to evaporate and warms at the full dry rate. It ends warmer than it started, by the latent heat released by the water that fell out.
Worked example
- Inputs: T = 15 °C, T_d = 10 °C, H = 2000 m.
- Cloud base: 125 × (15 − 10) = 625 m.
- Dry cooling to 625 m: 0.0098 × 625 = 6.125 °C. Moist cooling over 1,375 m: 0.006 × 1375 = 8.25 °C.
- Summit: 15 − 6.125 − 8.25 = 0.625 °C.
- Lee base: 0.625 + 0.0098 × 2000 = 0.625 + 19.6 = 20.225 °C, a gain of about 5.2 °C.
| Windward temperature at base (°C) | Cloud base on windward side (m) |
|---|---|
| 3.75 | -781.25 |
| 7.5 | -312.5 |
| 11.2 | 156.25 |
| 15 | 625 |
| 18.8 | 1,093.75 |
| 22.5 | 1,562.5 |
| 30 | 2,000 |
How to read the result
The larger the part of the climb that is saturated, the bigger the warming on the lee side. If the cloud base is at or above the summit, no condensation occurs and the leeward temperature equals the windward one. Warming of a few degrees with a sharp drop in humidity is typical and raises wildfire risk downwind. Korea's nopsae, a late-spring northeasterly crossing the Taebaek Mountains into the Yeongseo region, is a classic example.
Common mistakes
- Using the dry rate all the way up even when the air saturates.
- Treating the moist rate as a constant; it is smaller in warm air and larger in cold air.
- Entering altitude above sea level instead of height above the windward base.
Frequently asked questions
Why is foehn air so dry?
Its water vapour condensed and fell out on the windward side, and the air warmed on descent, so relative humidity drops sharply.
Where does the 125 m per °C rule come from?
The temperature falls by 9.8 °C/km and the dew point by roughly 1.8 to 2 °C/km, so their gap shrinks by about 8 °C/km.
Sources: J. M. Wallace and P. V. Hobbs, Atmospheric Science: An Introductory Survey, Academic Press · C. D. Ahrens and R. Henson, Meteorology Today, Cengage Learning