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 (4)

o 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