## The reaction kinetics for one flushWe are concerned here with the chemistry of the initial wet phase of a single flush. The time epoch for the post-flush reaction is the duration of the wet phase, T.Disregarding diffusion and flow of COC laden salt water across the marsh after a flush, we may focus on the chemistry ongoing within a single cell of rhizosphere. Considering a single COC, we propose a hierarchy of models for its geobiochemical interaction with the bacteria of the rhizosphere, beginning with the most naive. #### First approximation: exponential decayIn this model we assume that the flush of COC does not significantly decriment the rhizobacterial population, and is independent of the carbon cycle of the salt marsh ecosystem. We take the availability of bacteria in the rhizosphere as a constant, B, throughout the diffusion-reaction following each flush. In that case, the kinetics are first-order, and linear, and the conversion of COC is by exponential decay.
COC -> Resultant X' = -K_{XB}BX X = concentration of one COC in one cell K_{XB}= reaction rate, a constant B = rhizobacterial population, a constant throughout the root layer of the salt marsh in this model
#### Second approximation: second order kineticsIn this model we assume that rhizobacterial population is consumed in the COC conversion. Then the kinetics for the two concentrations, X and B, may be taken as follows.
COC + bacteria -> Resultant. X' = -K_{XB}BX B' = -K_{BX}BX X = concentration of one COC in one cell B = rhizobacterial population in cell K_{XB}= reaction rate, a constant K_{BX}= reaction rate, a constant
#### Third approximation: Monod kineticsIn this model we assume that rhizobacterial population is consumed in the COC conversion, as above, and also that it is regenerated by the rhizospheric substrate. The Monod rule is one way of accounting for the regeneration of B in the rhizosphere ecosystem. Then the kinetics for the two concentrations, X and B, may be taken as follows.
COC + bacteria -> Resultant. Cf. (Koch, 1998, p. 65) for explication of this. X' = -K_{XB}BX B' = -K_{BX}BX + MS/(K_{m}- S) X = concentration of one COC in one cell B = rhizobacterial population in cell K_{XB}= reaction rate, a constant K_{BX}= reaction rate, a constant M = Monod constant, maximum growth rate for B K_{m}= Michaelis/Menton constant S = measure of rhizospheric substrate, assumed proportional to the biomass of cordgrass, a control parameter in this model (it varies seasonally)
#### Fourth approximation: geobiochemistryNext we consider more realistic and complex chemistry. For example, if the COC is ammonium, then assimilation as R-NH _{2}might be the primary reaction. We might thus take a nitrogen cycle model to account for the full complexity of the COC reaction. But as aerobic oxygen respiration and sulfate reduction are of primary importance in the salt marsh ecology (cf. Howarth) we would probably combine three cycles in this approximation.
Revised by Ralph Abraham 26 August 1998 |