SME
Oceanography · Problem type
Residence time
Use this for “The ocean holds 6 × 10¹⁸ kg of a dissolved element, and rivers add 1.5 × 10¹¹ kg a year. What is its residence time?”
Diagram
Each slice of the bar is one year’s flux in and out, 1.5 × 10¹¹ kg.
6 ×
10
18
1.5
×
10
11
=
4 ×
10
7
:
the
stock
is
replaced
once
every
4 ×
10
7
years,
its
residence
time.
This is an example. Type your own values to start a new problem.
τ (yr)
=
M (kg)
÷
F (kg/yr)
Formulas
τ
=
M
F
4 ×
10
7
=
6 ×
10
18
1.5 ×
10
11
Assumptions
•
Steady state: what rivers and vents add each year, sediments remove, so the amount in the ocean stays the same.
•
The yearly input F is in kilograms per year, so M ÷ F comes out in years.
•
τ is an average stay; elements the sea floor grabs quickly (iron, aluminum) have short ones.
Step-by-step
WE KNOW
M = 6 × 10¹⁸ kg, F = 1.5 × 10¹¹ kg/yr
FIND
residence time (τ)
Step 1 · Find residence time (τ)
Use τ = M ÷ F
The store divided by what comes in each year: how many years’ supply the sea holds.
τ
=
6 ×
10
18
1.5 ×
10
11
τ
=
4 ×
10
7
yr
Check
Put the numbers back in. Both sides should match.
4 ×
10
7
=
6 ×
10
18
1.5 ×
10
11
✓
Topic check
See what you know: 5 questions on this topic
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