The chemistry of natural waters - Geochemistry: An Introduction - page 156

respectively; P part stands for the flux of i carried downward by sinking particles. We first
write that, at steady state, inputs and outputs of i must be equal so that:

F river C river + F mix C deep = F mix C surface + P part (7.49)

The fraction g of the downgoing flux of i carried by particles is therefore:

P i part
F mix C surface +

g = (7.50)

P part

or:

C surface
C river

F mix
F river

g = 1 − (7.51)

C deep
C river

F mix
F river

1 +

Because, at steady state, dissolved elements that enter the ocean in rivers must leave it as
sediments, the fraction f of settling particles that eventually exit the deep-water reservoir
as sediments is such that:

fP i part = F river C river (7.52)

and therefore:

1

C deep

f = (7.53)

C surface
C river

F mix
F river

1 +

C river −

The quantity 1 fg indicates the proportion of the riverine input of i to the ocean that

is recycled through the thermocline instead of being sedimented. Using the carbon res-
idence time in the deep ocean calculated from (6.14) as an estimate of F mix , we obtain
F mix /

−

C river =
0.15, which emphasizes the depletion of surface waters in nutrients. We therefore obtain
g

30. For phosphates, we use the values C deep / C river = 3 and C surface / F river ≈

= 0.95 (95% of the riverine input of phosphate is exported to the deep ocean as particles),

1% of the riverine phosphate is actually
exported to sediments while 99% is recycled through the thermocline by upwelling. For
silica we would obtain 95%. An alternative statement is that a phosphorus atom is recycled
100 times and a silicon atom 20 times through the thermocline before they find their way
into the sediments.

f = 0.01, and fg = 0.01, which indicates that ≈