A mathematical model of the manganese cycle in a seasonally anoxic lake

The processes controlling the Mn cycle in a seasonally anoxic lake (Grcifensee, Switzerland) were simulated with a dynamic one-dimensional vertical lake model (CHEMSEE). The chemical parameters comprised Mn(II), particulate Mn, and oxygen concentrations and the processes included in the calculations were the Mn(I1) flux from the sediment, Mn(I1) oxidation, and particulate Mn removal from the water column. Field data from Greifensee obtained in 1988 and 1989 were used to determine the validity ofthe model and to estimate the rate constant values for the processes. Optimal values of the rate constants were determined by comparison of simulated results with field data and were in general agreement with literature values. The Mn(II) flux from the sediment exhibited similar seasonal variations in 1988 and 1989. The results show that it is possible to model the Mn cycle in a dynamic system and highlight the necessity of accurately determining the rate laws of the important processes and their relationships to the oxygen content of the waters. The transport of Mn in lakes and marine systems is greatest at the water-sediment interface where redox gradients are steep. Where oxygen levels in the water column are low, Mn(I1) can be transported by turbulent diffusion from the sediment surface some distance into the water column, creating the typical profiles reported by Davison (198 5). The Mn concentration profiles are governed by a number of physical, chemical, and microbiological processes that interact to create a highly dynamic and sensitive system. The characteristic Mn profiles found in pore waters are not susceptible to rapid changes and have been modeled with steady state calculations (e.g. Burdige and Gieskes 1983). The determination of reaction rates in the water is made difficult by turbulent diffusion. In oceanographic investigations, steady state may be assumed for some reactions for which changes in mixing rates or diffusion have minor significance within the time scale under consideration. Calculations to date have been limited to diffusion rates and Mn(I1) oxidation rates (e.g. Emerson et al. 1979). The modeling of Mn cycling on a macroscopic scale in lakes is more difficult because the smaller dimensions increase boundary influences. Temperature gradients are subject to rapid changes, as are mixing rates and biological activities. Thus, in lakes it is not possible to make calculations with steady state assumptions unless sufficiently short time scales are involved. Instead time-dependent models must be used. For such modeling, lake dimensions and eddy diffusion coefficients must be known. Furthermore, sampling must be sufficiently frequent to resolve rapid changes. In principle, it is possible to model the Mn cycle in a dynamic lake system. Turbulent mixing rates can be estimated from temperature profiles, and estimates of the processes governing the chemical and microbial processes are available in the literature. The difficulties lie in obtaining representative depth profiles of the relevant components and in the assumption that processes can be described by a single rate constant as a function of both depth and time. In this study Mn profiles measured in Greifensee, a seasonally anoxic lake, have been used to show that a simple model can be used to describe Mn cycling in a timevarying system. This approach highlights information that should be determined in order to model Mn cycles in lacustrine systems more accurately.