SME
Meteorology · Problem type
The lifting condensation level
Use this for “Air at the ground is 30 °C with a dew point of 14 °C. How high is the cloud base, and how warm is it there?”
Diagram
The
parcel
cools
9.8
°C
per
km
and
its
dew
point
falls
1.8
°C
per
km,
so
they
close
8
°C
per
km:
h
=
30 − 14
8
=
2
km
=
2,000
m.
There the air is 10.4 °C, saturated, and a cloud forms; above it the parcel cools about 6 °C per km.
This is an example. Type your own values to start a new problem.
zLCL (m)
=
125
×
(
T (°C)
−
Td (°C)
)
ΔT
Spread
calculated · °C
Tbase
Temperature at the base
calculated · °C
Formulas
ΔT
=
T
−
Td
16 = 30 − 14
zLCL = 125 × ΔT
2,000 = 125 × 16
Tbase
=
T
−
9.8
×
zLCL
1,000
10.4
=
30
−
9.8
×
2,000
1,000
Assumptions
•
A rising parcel cools 9.8 °C per km (dry adiabatic) and its dew point falls 1.8 °C per km.
•
They close 8 °C per km, so they meet, and a cloud forms, 125 m up for each °C of spread.
•
The dew point is never above the temperature.
Step-by-step
WE KNOW
T = 30 °C, Td = 14 °C
FIND
spread (ΔT), cloud base (zLCL), temperature at the base (Tbase)
Step 1 · Find spread (ΔT)
Use ΔT = T − Td
How far the air is from saturation.
ΔT = 30 − 14
ΔT = 16 °C
Step 2 · Find cloud base (zLCL)
Use zLCL = 125 × ΔT
The
two
lines
close
9.8
−
1.8
=
8
°C
per
km,
so
they
meet
1,000
8
=
125
m
up
per
°C.
zLCL = 125 × 16
zLCL = 2,000 m
Step 3 · Find temperature at the base (Tbase)
Use Tbase = T − 9.8 × zLCL ÷ 1,000
The parcel cools 9.8 °C for each km it rises, dry.
Tbase
=
30
−
9.8
×
2,000
1,000
Tbase
=
30
−
19,600
1,000
Tbase = 30 − 19.6
Tbase = 10.4 °C
Check
Put the numbers back in. Both sides should match.
16 = 30 − 14 ✓
2,000 = 125 × 16 ✓
10.4
=
30
−
9.8
×
2,000
1,000
✓
← Previous lesson
Atmospheric thermodynamics
Next lesson →
Saturation vapor pressure, humidity and mixing ratio
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Atmospheric thermodynamics
Main lesson
Saturation vapor pressure, humidity and mixing ratio
Use this for “Air at 25 °C has a dew point of 15 °C at 1,000 hPa. Find eₛ, e, the relative humidity and the mixing ratio.”
Stable or unstable air
Use this for “The air cools 7.5 °C per km above the ground. Is it stable, conditionally unstable or unstable?”