Download Homework Problem Set, Chapters 5 and 6, Week 3

Homework Problem Set, Week 6. Due Wednesday, February 15
Name________________________
In this problem set, we are going to calculate the amount of carbon (as CO2) that is input into
seawater by the formation of oceanic crust by seafloor spreading - and by rivers. The goal will be
to compare riverine input of carbon (recycled stuff) - to NEW carbon input via ocean crust
formation.
a. Assume that the total length of all seafloor spreading centers (globally) is 59,200 km and
that the average spreading rate is 55.7 ± 3.4 mm/year. Also assume that oceanic crust is
about 6 km thick, with the Upper Crust is made up of a 1 km thickness of extrusive
(volcanic) basalts and upper feeder dikes, and the Lower Crust is a 5 km thick layer of
lower dikes and gabbros (a frozen magma chamber). Calculate the total global
production of oceanic crustal (including both upper and lower crust) rate in km3/year.
b. Upper Oceanic Crust (the basalts and upper dikes) are about 0.04 % CO2 by weight and
has a density of 3.0 gm/cm3. Assume that all of the CO2 in the Upper Crust is removed
immediately after formation – the gas is ejected by the rocks as they solidify and carried
by hydrothermal circulation into bottom seawater at the ridge axis. Calculate the amount
of CO2 (in kilograms/year) that is injected into seawater each year from the formation of
Upper Crust.
c. The Lower Oceanic Crust (the 5 km thickness of lower dikes and gabbros) has a much
smaller CO2 content (0.006 % by weight). There is considerable debate if this CO2 is
‘extracted‘ from the lower crust immediately after formation, or is vented in older, offaxis vents. We will assume that it is all vented immediately at the axis. Calculate the
total input of CO2 from the formation of lower crust in units of kg/year.
d. Total CO2 emitted from crustal formation (under the above assumptions) is (b) plus (c).
Assume that the total carbon inventory in the ocean is stable over geological time and the
hydrothermal input above is balanced by the transport of carbon-rich sediments into the
mantle at subduction zones. The carbon (not CO2) inventory in seawater is 38 x 10+15
kg. What is the residence time of carbon in the ocean, with respect to seafloor
spreading?
e. The flux of carbon (not CO2) into the sea via the rivers is about 0.8 x 10+15 g C/year.
Assume that this is also balanced by sedimentation and calculate the residence time of
riverine carbon in the oceans. Watch your units!
f.
The balance of carbon input into the ocean from crustal formation AND riverine input
(assuming equilibrium) is largely accomplished by the consumption of sediments at
subduction zones. This occurs consumption of sediments into trenches occurs at a global
rate of about 3 km3/year. These sediments are about 50% pore water and 50% solid
material. If the grain density of the sediments (the density of the solid material, without
the pore water) is 2.4 gm/cm3 as a global average, what is the weight percentage of
carbon of the solid material in these sediments that is due to crustal formation in order to
balance the hydrothermal input in parts (b) and (c) and the riverine input in part (e)?
g. Now, calculate the Total Residence Time of carbon in the oceans due to input from
hydrothermal vents and rivers, which is balanced by the transport of sediments back into
the mantle by subduction.