Geoscience Reference
In-Depth Information
elements, i.e. elements whose partition coefficients
D
i
are very small, have long residence
times. Their concentrations therefore remain very stable. These elements are highly con-
centrated (i.e. they are major elements), their residence time is long, and they display no
fast temporal variations. This is the case of strontium in the ocean, for which we have
calculated a residence time of 4.4 Ma. By contrast, reactive elements with high partition
coefficients
D
i
and therefore short residence times are very quickly depleted in the reser-
voir (i.e. they are minor elements). Their short residence time means they readjust quickly
after a disturbance, but their concentration level fluctuates wildly about steady state. To
use an analogy, a reservoir such as a lake, the ocean, or the mantle, behaves like a low pass
filter, eliminating fluctuations in concentration with shorter time characteristics than the
residence time of the element. If a time characteristic
τ
m
of mixing in the reservoir can be
i
of an element
i
is such that
i
defined and the residence time
>τ
m
, this element will
reside long enough in the reservoir to be well homogenized. If its residence time is shorter
than the reservoir mixing time, the element will be drained away in the outflow before it is
effectively mixed and will be distributed heterogeneously around the system. For instance,
concentrations of Sr (8 ppm) and
87
Sr
τ
τ
86
Sr (0.7093) are homogeneous across the entire
/
ocean.
In the ocean, the export process of most elements is sedimentation and the partition coef-
ficient measures sediment particle/seawater fractionation. In the mantle, the export process
is magmatism and the coefficient
D
i
that measures the magma/residual solid fractionation
is the inverse of the partition coefficient usually considered by petrologists. Inert elements
or ions are residual, very homogeneous, abundant, and of invariable concentration: this is
the case for Mg, Ni, and Cr in the mantle, of Cl, Na, and SO
4
in the ocean, and of N
2
,O
2
,
and Ar in the atmosphere. In contrast, reactive elements are normally at the trace level and
exhibit wide variability in space and time: this is the case for the incompatible lithophile
elements (Th, Ba, La, Rb, etc.) in the mantle, of Pb, Cd, Zn, and La in the ocean, and of
methane and ozone in the atmosphere.
In the absence of any input from upstream,
(6.2)
can be reformulated as:
d
C
i
C
i
d
t
=
PD
i
M
=
1
τ
H
+
1
τ
H
+
1
τ
−
(6.6)
i
S
This equation expresses that the total probability of an atom
i
leaving the system per unit
time is the sum of two probabilities: the probability of
i
exiting downstream, which is equal
to the inverse of the renewal time of the water
τ
H
, plus the probability of
i
being lost to
the sediment, which is the inverse of removal time by the solid
PD
i
.Asasimple
but powerful rule, the probabilities of removal through various routes are independent and
therefore additive and so are the inverse residence times. We will see below that a third
removal mechanism is radioactivity and that the probability of removal by this process is
simply the decay constant
i
τ
S
=
M
/
.
A third aspect of residence time is that of the distribution of the “ages” of atoms within
the reservoir. To understand the concept of birth and death processes, let us take another
analogy, namely the reservoir of a human population. Suppose, for simplicity, that the num-
ber of births every year is constant. A healthy population is a poorly “mixed” population
since the exit, i.e. death, draws off the elderly preferentially. A trip around a graveyard
might show that the average age of death is about 70-80 years, the mean span of our
λ
