Hong Life CalculatorsUnderstanding the cloud base (LCL) calculator — concept and principle
The lifting condensation level (LCL) is the height at which a parcel of air rising from the surface cools enough to become saturated, so water vapour starts condensing into cloud droplets. Glider pilots, paragliders and storm spotters use it to estimate the base of cumulus clouds from two surface readings: temperature and dew point.
How it is calculated
LCL ≈ 125 m × (T − Td)
- T is the surface air temperature in °C.
- Td is the surface dew point in °C.
- The difference T − Td is called the dew-point depression or spread.
The calculator multiplies the spread by 125 m per °C and also converts the height to feet (1 m = 3.28084 ft). The height is above the ground where the readings were taken, not above sea level.
The principle
Rising air expands as pressure falls and cools at the dry adiabatic lapse rate, about 9.8 °C per kilometre. Its dew point also falls as it rises, but much more slowly, roughly 1.8 °C per kilometre, because only the expansion of the vapour lowers it. The temperature therefore closes in on the dew point at about 9.8 − 1.8 = 8 °C per kilometre. Dividing 1000 m by 8 °C gives 125 m for every degree of spread. This rule is usually credited to the 19th-century meteorologist James Espy. It assumes a well-mixed surface layer, typical of sunny afternoons.
Worked example
- Inputs: T = 25 °C, Td = 15 °C.
- Spread: 25 − 15 = 10 °C.
- LCL = 125 × 10 = 1,250 m above ground.
- In feet: 1,250 × 3.28084 = 4,101.05 ft.
| Surface temperature (°C) | Cloud base (m) |
|---|---|
| 6.25 | -1,093.75 |
| 12.5 | -312.5 |
| 18.8 | 468.75 |
| 25 | 1,250 |
| 31.2 | 2,031.25 |
| 37.5 | 2,812.5 |
| 50 | 4,375 |
How to read the result
A small spread means humid air and low cloud: a spread of 2 °C gives about 250 m, typical of murky, low-based cloud or fog risk. A spread of 10–15 °C gives bases around 1,250–1,900 m, common for fair-weather cumulus on summer days. Very large spreads in dry climates can put the base above 3,000 m. For severe-weather forecasting a low LCL, often quoted as below about 1,000 m, is associated with a greater chance of tornadoes in supercell storms.
Common mistakes
- Mixing °F and °C; a spread in °F must be multiplied by about 69 m instead of 125 m.
- Reading the result as altitude above sea level instead of height above the station.
- Using the morning dew point when convection only starts in the afternoon.
Frequently asked questions
What is the difference between LCL and the level of free convection?
The LCL is where clouds form; the level of free convection is higher, where the cloudy parcel becomes warmer than its surroundings and keeps rising on its own.
Why is the dew point needed instead of relative humidity?
The dew point directly states how far the air must cool to saturate. Relative humidity depends on temperature, so it is less convenient, although it can be converted to a dew point.
Does the formula work for fog?
When the spread is near zero the LCL is near the ground, which is consistent with fog or very low stratus.
Sources: J. M. Wallace and P. V. Hobbs, Atmospheric Science: An Introductory Survey, 2nd ed., Academic Press, 2006