Th 234 applied to particle removal rates from the surface ocean ' a mathematical treatment revisited

It has been recognized since the 1950's that radioisotopic disequilibrium between naturally occurring parentdaughter isotope pairs in seawater can provide information on the rate of processes segregating them. In the surface ocean, the U-238:Th-234 parent-daughter pair tends to display measurable disequilibrium that is attributable to the effects of scavenging on particle reactive thorium. A range of approaches has been applied to deriving quantitative information on particle scavenging and sinking rates from U238:Th-234 measurements. Here, we review the mathematical underpinnings of a very basic conceptual model of the removal process in order to correct a misunderstanding that has arisen in recent literature. uniform in ocean waters. Particle reactive Th-234 can then be adsorbed onto particles and removed from the surface either by sinking of particles, by radiodecay or by mixing. If it is assumed that: (1) mixing rates are negligible with respect to radiodecay and the rate at which particles sink from surface waters; (2) adsorption obeys a first order rate law with respect to the dissolved Th-234 concentration; and (3) the loss of particulate Th-234 via sinking also obeys a first order rate law with respect to the concentration of particulate Th-234, then the following cquations hold: 0t = ,•Au .kA•h kdA•h (1)