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and
PROD = IN + DIS
(11)
Furthermore, we can define the dissolution (or recycling) efficiency
DIS
PROD
α =
(12)
where 0
is on the order of 0.97, reflecting very efficient
silica recycling. Combining Equations (11) and (12), we obtain
IN
PROD = (1
α
1. In the modern ocean,
α
(13)
α
)
The denominator in Equation (13), (1
−α
), can also be viewed as the ocean-wide biogenic
silica preservation efficiency.
According to Equation (13), for marine production of biogenic silica to increase
either the external supply of H 4 SiO 4 must increase or the preservation efficiency must
decrease, or both. The numerator and denominator of the right-hand side of Equation (13)
are related to processes such as silicate weathering, volcanic-seawater interaction,
dissolution plus ageing of biosiliceous shells, and sediment burial. In other words,
Equation (13) links the global rate of silica biomineralization in the oceans to geological
and geochemical processes that regulate the oceanic sources and sinks of silica.
Weathering
The main source of new silica for the oceans is delivery by rivers of H 4 SiO 4
produced by weathering of silicate rocks on the continents. Broadly speaking, silicate
minerals consist of SiO 4 4− tetrahedra that are linked together by strong (covalent)
ŁSi
SiŁ (siloxane) bonds. The exception is olivine where the SiO 4 4− units are not
linked, but instead separated from one another by cations, mainly Fe 2+ and Mg 2+ . Because
its mineral structure is held together by much weaker electrostatic forces, olivine
dissolves much faster than other silicates. Olivine is a major constituent of the basaltic
oceanic crust, it is relatively rare in continental rocks. Therefore, the rate-controlling
steps in the dissolution of silicate minerals commonly exposed on land are rather similar
and involve the breaking, or hydrolysis, of ŁSi
O
O
SiŁ and, in alumino-silicates, also
ŁSi
AlŁ bonds.
With the exception of olivine, dissolution rates of silicate minerals measured in the
laboratory fall in a fairly narrow range. At room temperature and under near-neutral
conditions the rates are typically on the order of 10 −12 to 10 −11 mol Si m 2 s −1 (e.g., Brady
and Walther 1989). A long-standing problem in geochemistry is to relate these
experimental dissolution rates to regional or global scale weathering rates (e.g., Velbel
1993). To illustrate the magnitude of the problem, a theoretical weathering flux of
dissolved silicic acid is calculated by extrapolating the experimental dissolution rates.
The calculation also illustrates the type of rough approximations that are often involved
in making global flux estimates.
The main difficulty is to estimate the amount of silicate mineral surface area exposed
on the continents. Let us start by assuming that limestones, which cover about 15% of the
continental surface area (Garrels and Mackenzie 1971), do not contribute significantly to
silicate weathering. Let us further assume that a 10 cm deep weathering layer covers 50%
of the remaining continental area. The volume of the active weathering layer is then
approximately 6.5
O
10 12 m 3 . This is likely a minimum estimate, as nearly 60% of the
continental surface are assumed not to be subjected to chemical weathering. Using (low)
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