What controls the composition of seawater?
I.
The accumulation hypothesis:
o
The oceanic concentration represents simply the accumulation inflow from rivers since
the ocean came to existence
o
The contrast between the high oceanic and low river concentrations of the elements
clearly suggests that accumulation is occurring in the ocean but can it explain the
observed concentrations?
o
We will develop a mathematical description of how the oceanic mean concentration of
an element A will change with time:
o
The total number of moles of this element in the ocean is the product of its mean
oceanic concentration COc in mmol m-3 multiplied by the oceanic volume VOc
o
The time rate of change of the total number of moles of this element, dMAOc/∂t is
equal to the sum of all the inputs and losses of this element:
dMAOc/∂t = d Voc . COc / ∂t = inputs – losses
(1)
o
In the case of accumulation hypothesis, we assume that there are no losses
o
We also assume that that the inputs are controlled only by the addition of A by rivers
o
We further assume that the oceanic volume has remained constant through time:
VOc .d COc / ∂t = Vriver . Criver
(2)
o
The differential equation (2) has the solution:
Coc(t) - Coc(t=0) = (Vriver . Criver / Voc) . ∆t
(3)
For the change of concentration in the time interval ∆t between t and t=0
o
If we assume that the ocean at t=0 was essentially fresh water then:
Coc(t=0) = 0
o
(4)
We obtain:
Coc(t) = (Vriver . Criver / Voc) . ∆t

(5)
This equation predicts that today’s ocean concentration of any element A is function of its river
concentration Criver

therefore, the ratio of various elements in the ocean should be equal to the ratio of these
elements in rivers (this is not true)
Accumulation age τa = ∆t of an element
 It is the time in the past when, given today’s river input and oceanic mean concentration, the
oceanic mean concentration of this element must have been zero.
 If this hypothesis is correct we expect this age to:

reflect the age of the ocean

Be equal for all elements
 The accumulation age τa is obtained by rearranging equation 5
τa = Voc . Coc / Vriver . Criver = (1.29x1018 m3 / 3.7x1013 m3 yr-1) . (Coc / Criver)
(6)
= 34,500 yr . Coc / Criver
Looking at the accumulation age shown in Table 1, we observe that:
 All of the accumulation times are at least a factor of 30 than what we think the age of the ocean (3.85 billion
years)
 The accumulation times of different elements vary by almost eight orders of magnitude
 This is in strong violation of our prediction on the basis of the accumulation hypothesis
This hypothesis is unlikely to be correct