SME
Ecology · Problem type
Residence time
Use this for “A reservoir holds 750 Gt of carbon and exchanges 120 Gt a year. How long does carbon stay?”
Diagram
Each slice of the bar is one year’s flux in and out, 120 Gt.
750
120
=
6.25:
the
stock
is
replaced
once
every
6.25
years,
its
residence
time.
This is an example. Type your own values to start a new problem.
τ (yr)
=
S (Gt)
F (Gt/yr)
Formulas
τ
=
S
F
6.25
=
750
120
Assumptions
•
The reservoir is at steady state: as much carbon flows out each year as flows in, so the stock stays the same.
•
The residence time τ is the average time one atom of carbon stays before it leaves: τ = stock ÷ flux.
•
The flux F is the carbon flowing out each year (or in: at steady state they are equal).
Step-by-step
WE KNOW
S = 750 Gt, F = 120 Gt/yr
FIND
residence time (τ)
Step 1 · Find residence time (τ)
Use τ = S ÷ F
How many years of flow it takes to turn over the whole stock.
τ
=
750
120
τ
=
6.25
yr
Check
Put the numbers back in. Both sides should match.
6.25
=
750
120
✓
Topic check
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