Geochemical systems - Geochemistry: An Introduction - page 132

Table 6.1 A carbon cycle. Masses of C in Gt, fluxes in Gt a −1 (Houghton, 2003 )

From
reservoir

To
atmosphere

To surface
ocean

To deep
ocean

To
soil

To
plants

Masses

Atmosphere 780 - 92 0 0 120

Surface ocean 728 90 - 44 0 0

Deep ocean 37 275 0 42 - 0 0

Soil 1500 58 0 0 - 0

Vegetation 550 59 0 0 60 -

10. The two-box ocean model of Broecker and Peng (1982) ; see Fig. 7.16 : the ocean is
divided into two boxes, the surface ocean and the deep ocean, separated by the ther-
mocline. Modify equations (6.15) and (6.16) to take into account (1) the input from
river flux, and (2) the sedimentation of particles formed in the surface ocean: a fraction
of these particles are redissolved below the thermocline, the rest is rapidly exported
into the sediments with no re-equilibration with deep water.
11. Another two-box ocean model: again, the ocean is separated into two boxes, but this
time horizontally, an Atlantic basin and a Pacific basin. Modify equations (6.15) and
(6.16) to take into account (1) the input from river flux into the Atlantic only (a good
approximation!), and (2) sedimentation in each basin.
12. Discuss the oceanic cycle of Sr and its isotopic variations. Include a river flux with
radiogenic Sr, carbonate precipitation, and exchange of seawater with unradiogenic
basalt in ridge-crest hydrothermal systems.
13. A simplified carbon cycle: draw the C cycle with boxes and arrows using the data from
Table 6.1 . Calculate the carbon residence times in each reservoir. Discuss the pathway
of anthropogenic addition of 6.3 Gt a − 1 of carbon from fossil fuel.
14. Write the equations that were used to draw Fig. 6.5 .
15. Let us define a series of one-dimensional “cells” or bins between 0 and 1 (e.g. 0-0.05,
0.05-0.0.10, 0.10-0.15, etc). Use a generator of random deviates from a uniform dis-
tribution (e.g. the function RAND in Excel) to produce n pairs (e.g. start with n

100)
of values. Each sample in a pair can be labelled “Rb” and “Sr.” Sort the pairs, then bin
them. The number of values in each bin is the “concentration” of Rb and Sr in each
particular cell, and the ratio of these numbers is Rb/Sr. Build the histograms of Rb,
Sr, and Rb/Sr. Do the exercise again with a different value of n (e.g. n = 500). How
do you think the histograms will look when n

=

→∞ ? Discuss different applications to

the mantle and the ocean.
16. For readers more motivated by calculations: let us consider a section of the ocean or
the mantle as a two-dimensional enclosure x

= [0-1], y = [0-1] and the position-

v x , v y ) at steady state:

dependent velocity field (

d x
d t =

v x ( x , y ) = cos (π y [ t ] ) sin (π x [ t ] )

d y
d t =

v y ( x , y ) = sin (π y [ t ] ) cos (π x [ t ] )