SME
Physical Geography · Problem type
Treeline elevation
Use this for “The warmest month averages 24 °C at sea level. About how high is the treeline?”
Diagram
In the troposphere the air cools about 6.5 °C for each km up: 10 °C at 2.154 km.
This is an example. Type your own values to start a new problem.
Tₜ (°C)
=
T₀ (°C)
−
6.5
°C/km
×
z (km)
T₀ is the warmest month’s average at sea level, where the picture’s line starts, and Tₜ the warmth trees need.
Formulas
Tₜ
=
T₀
−
6.5
×
z
10 = 24 − 6.5 × 2.1538
Assumptions
•
Trees need a warmest month of about 10 °C; above the height where it is colder, only tundra grows.
•
The air cools 6.5 °C for each km of height (the standard troposphere).
•
Slope, wind and snow move a real treeline up or down by a few hundred meters.
Step-by-step
WE KNOW
T₀ = 24 °C, Tₜ = 10 °C
FIND
treeline altitude (z)
Step 1 · Find treeline altitude (z)
Use Tₜ = T₀ − 6.5 × z
The
air
must
cool
from
T₀
down
to
Tₜ
;
each
km
of
height
takes
off
6.5
°C.
z
=
T₀
−
Tₜ
6.5
z
=
24 − 10
6.5
z
=
14
6.5
z
=
2.1538
km
Check
Put the numbers back in. Both sides should match.
10 = 24 − 6.5 × 2.1538 ✓
Topic check
See what you know: 5 questions on this topic
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