Modeling and interpreting element ratios in water and sediments: A sensitivity analysis of post-Chernobyl Ru : Cs ratios

When elements are simultaneously added to lakes, experimentally or by accident, their ratios in the water phase and in bottom sediments can change with time due to differential partitioning between solution and suspended particles or sediments. A number of equations are developed to show the change of ratio with time in water and sediments assuming simultaneous pulse inputs followed by a range of combinations of loss processes from solution (i.e. hydraulic losses, sorption to particles followed by settling, and diffusion into the sediments). The pattern of events is discussed both for pulse events with specific limiting assumptions and for combined continuous and pulse inputs. The models show that elemental ratios in sediments are generally less sensitive indicators of differential partitioning than are elemental ratios in water. For lakes with long residence times, the long-term elemental ratio in the sediments does not differ from that in the initial spike to the water column, but for short residence times, it is directly dependent on the ratio of either partition or diffusion coefficients. The models are used to interpret Ru : Cs ratios measured in the water and sediments of Esthwaite Water subsequent to the pulse input of Chernobyl fallout. The ratios can be explained by assuming nuclides were lost either by flushing and sorption or by flushing, sorption, and diffusion. The process combination of flushing and diffusion is incompatible with the observed constant ratios. Several recent studies have modeled the environmental behavior of radionuclides and heavy metals in lakes using either two (Davison et al. 1993; Robbins et al. 1992) or three process components (Hesslein 1987). In particular, the models assume that the lake is a completely mixed reactor and that material can only be lost by hydraulic flushing, sorption of dissolved forms onto particles followed by transport to the sediments, and-if the concentration in the sediment pore water is lower than in the open waterby direct diffusion to the sediment after molecular diffusion across a benthic boundary layer. Although the models have been successfully applied to single element distributions, they are unreliable if data are scarce. Many of the parameters in the equations are defined by physical processes which should be independent of the chemical element. Consequently, in models of elemental ratios it should be possible to eliminate some common variables. Elimination of these common variables would improve predictions of the processes of removal from the water when scarce data are available for one of the elements. The same approach can also be used Acknowledgments This work was partially supported by a contract from the Commission of the European Community, Radiation Protection Department. to analyze sediment data where temporal variability is high. Hesslein (1987) showed that ratios of element concentrations in sediments were much more stable. Ratios of elements in particular environmental compartments, such as sediments, water, or suspended particles, can be expected to change if the rate and extent of the transfer between compartments is not the same for each element (e.g. if the elements have different distribution coefficients or diffusion coefficients). In this paper, we derive the equations describing the change, with respect to time of addition to the lake water, in the ratio of two elements in both the water column and the sediment. We then use sensitivity analysis to develop some insights into the processes of transport of radioactive ruthenium in a freshwater lake in the U.K.