Put the lifting of air by a mountain together with the moist rate and you get one of the clearest patterns on any climate map: a wet side and a dry side of every big mountain range, and warm, dry winds pouring down the lee slope.
Key idea
Air forced up a mountain cools at the dry rate to its cloud base, then at the slower moist rate while it rains out its moisture. Coming down the far side it is no longer saturated, so it warms at the dry rate the whole way. It arrives warmer and drier than it started: a rain shadow and a warm downslope wind (a foehn, or in the Rocky Mountains a chinook).
Why it works
The trip down is not the trip up in reverse. On the way up, part of the climb happens at the moist rate (about 6 °C per km), so the air loses less temperature than it would have dry. On the way down there are no droplets left to evaporate, so it gains temperature at the full dry rate (about 10 °C per km). The extra warmth is the latent heat released when its vapor condensed and fell as rain on the windward side. The water left; the heat stayed in the air.
Worked example: Over a 3 km range
Air at 20 °C with a dew point of 12 °C crosses a 3 km mountain range. Use 10 °C per km (dry), 2 °C per km (dew point) and 6 °C per km (moist). Find its temperature at the lee foot, back at the starting height.
- Cloud base: spread 8 °C, closing at 8 °C per km: 1 km up, at $20 - 10 = 10$ °C.
- From 1 km to the 3 km peak, moist: $10 - 6 \times 2 = -2$ °C at the top.
- Down 3 km, dry: $-2 + 10 \times 3 = 28$ °C.
- It ends 8 °C warmer than it started.
Answer: 28 °C
Worked example: How dry is it?
In the example above, the air at the top is saturated at −2 °C, so its dew point is −2 °C. Coming down, its dew point rises about 2 °C per km. What are its dew point and relative humidity at the lee foot? ($e_s$ at 4 °C ≈ 8.1 hPa; at 28 °C ≈ 37.8 hPa.)
- Dew point at the foot: $-2 + 2 \times 3 = 4$ °C, down from 12 °C at the start.
- RH = $e_s(T_d)/e_s(T) = 8.1 \div 37.8 \approx 0.21$, about 21%.
- Warm and dry: grass and brush dry out fast in such winds.
Answer: Dew point 4 °C, RH about 21%
Worked example: No cloud, no warming
Air at 15 °C with a dew point of 0 °C crosses a 1 km ridge. Where does it end up?
- Its cloud base would be $15 \times 125 = 1875$ m, above the ridge, so no cloud forms.
- It cools 10 °C going up and warms 10 °C coming down: it ends at 15 °C, just where it started.
- Without condensation there is no rain shadow and no extra warmth.
Answer: 15 °C, unchanged
Common mistake
Thinking a warm downslope wind blows in from somewhere warm. It is the same air that left the windward side; it warms by being squeezed as it sinks, and ends warmer than it started because it kept the latent heat released when its vapor rained out. Check: the extra warmth only appears if a cloud formed and rained on the way up.