SME
Climatology · Problem type
Warming with feedbacks
Use this for “Without feedbacks a CO₂ doubling warms Earth by 1.2 K. With a feedback factor of 0.6, what are the gain and the warming?”
Chart
1.2 K
This is an example. Type your own values to start a new problem.
ΔT (K)
=
G
×
ΔT₀ (K)
G is the gain, 1 ÷ (1 − f): how many times the feedbacks multiply the no-feedback warming ΔT₀.
f
Feedback factor
example
Formulas
G
=
1
1 −
f
2.5
=
1
1 − 0.6
ΔT
=
G
×
ΔT₀
3 = 2.5 × 1.2
Assumptions
•
ΔT₀ is the warming if nothing but temperature changed: about 1.2 K for a doubling of CO₂.
•
Feedbacks (water vapour, melting ice, clouds) send back a share f of each warming as more warming.
•
Each round adds f times the last, so the rounds add up to 1 ÷ (1 − f); f must stay below 1.
Step-by-step
WE KNOW
ΔT₀ = 1.2 K, f = 0.6
FIND
gain (G), warming (ΔT)
Step 1 · Find gain (G)
Use G = 1 ÷ (1 − f)
Each
round
of
feedback
adds
f
times
the
last,
and
the
rounds
sum
to
1
1 −
f
.
G
=
1
1 − 0.6
1 − 0.6 = 0.4
G
=
2.5
Step 2 · Find warming (ΔT)
Use ΔT = G × ΔT₀
The feedbacks multiply the no-feedback warming by the gain.
ΔT = 2.5 × 1.2
ΔT = 3 K
Check
Put the numbers back in. Both sides should match.
2.5
=
1
1 − 0.6
✓
3 = 2.5 × 1.2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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