Reflections on post-OECD eutrophication models

Abstract

In recent years a contrast has become apparent between oversimplified models (regression lines) relating primary production in lakes to phosphate loadings, and complicated conceptual models, depending on the rate constants of the most important processes. In the latter, rate constants from the literature are used. Most modellers assume that such constants are valid everywhere and always, but very little research concerning their validity has been carried out.

It is generally believed that Smith's equation for photosynthesis and Monod's for bacterial growth under nutrient limited conditions are ‘proven’ conceptual models — and that Monod's equation may be used for algal growth as well.

The imprecision of experimental tests is too great, at present, to permit us to make a sensible choice: both Monod's and Smith's equations can be used equally well to describe light dependence of photosynthesis quantitatively. Monod's equation has the great advantage that the summation (integration) over depth is still valid at low radiant energy fluxes and this makes it preferable to Smith's equation.

We may consider the fact that this equation does not become invalid forI _o < 1/2I _k to be an indication that Monod's equation expresses the light/photosynthesis relation better than Smith's.

A similar problem arises for the description of adsorption of e.g. phosphate on sediments. The choice between the Langmuir equation or a hyperbolic one, e.g. Freundlich, depends on whether it is assumed that a plateau exists for the maximum quantity of a certain compound that can be adsorbed. This maximum (and the other constant) of the Langmuir equation not only cannot be measured precisely (for adsorption on sediments), and indeed, cannot even be approached by realistic concentrations.