A rising parcel cools at the dry rate until it reaches its dew point. Then vapor condenses and a cloud begins. That height is the cloud base, and you can predict it from a thermometer and a dew-point reading at the ground.
Key idea
As a parcel rises, its temperature falls about 10 °C per km and its dew point falls about 2 °C per km, so the gap between them closes about 8 °C per km. The cloud base is about $$h \approx 125\ \text{m} \times (T - T_d)$$ with $T - T_d$ in °C (about 228 ft per °F of spread).
Why it works
Why does the dew point fall at all? The parcel keeps its vapor, but as it expands, the vapor is spread through more volume, so the vapor pressure drops along with the total pressure. Lower vapor pressure means a lower dew point: about 1.8 to 2 °C per km. Meanwhile the temperature drops about 9.8 °C per km. So the two close in at about $9.8 - 1.8 = 8$ °C per km, and each degree of spread takes about $1000 \div 8 = 125$ m to close.
Worked example: A summer afternoon
At the ground the temperature is 30 °C and the dew point is 22 °C. About how high is the base of the cumulus clouds?
- Spread: $30 - 22 = 8$ °C.
- Height: $8 \times 125 = 1000$ m.
- Check: rising 1 km, the parcel cools to about $30 - 10 = 20$ °C, and its dew point drops to $22 - 2 = 20$ °C. They meet.
Answer: About 1000 m
Worked example: In feet
A pilot reads 75 °F with a dew point of 53 °F. About how high is the cloud base, in feet?
- Spread: $75 - 53 = 22$ °F.
- Height: $22 \times 228 \approx 5000$ ft.
- Pilots often use the same rule as "spread in °F ÷ 4.4, in thousands of feet": $22 \div 4.4 = 5$ thousand feet.
Answer: About 5000 ft
Worked example: Working backward
Cumulus bases are at 1500 m on an afternoon when the temperature is 27 °C. Estimate the dew point.
- Spread: $1500 \div 125 = 12$ °C.
- $T_d \approx 27 - 12 = 15$ °C.
Answer: About 15 °C
Common mistake
Keeping the rising parcel's dew point fixed. That makes the gap close at 10 °C per km, giving 100 m per degree, and puts the cloud base too low. The dew point also drops about 2 °C per km, so the gap closes at about 8 °C per km: 125 m per degree. Check: at the cloud base, the parcel's temperature and dew point should both have dropped, and be equal.
This is why fair-weather cumulus all have flat bases at the same height: every bubble from the same ground air reaches its dew point at the same level. When the spread is near zero, the "cloud base" is at the ground: fog.