Towards a generalized model for the primary and secondary contamination of lakes by Chernobyl-derived radiocesium

As part of the UK Ministry of Agriculture Fisheries and Food Directorate of Fisheries Research (MAFF/DFR) post-Chernobyl monitoring program, a detailed study was carried out of the change over time in dissolved-phase ¹³⁷Cs concentrations in a number of lakes in Cumbria, UK. These measurements have been combined with published data on ¹³⁷Cs in Cumbrian and other European lakes in order to develop and test a “double exponential” model for changes in lakewater concentrations: A exp(−k,t) + B exp(−kzt) where the exponential terms correspond, respectively, to the initial fast flush of activity through the system followed by longer-term transfers (timescale, years) from the catchment. Parameter values have been determined for this model by curve-fitting to the set of measurements of post-Chernobyl ¹³⁷Cs activities in lakes. Values of fitted parameters are shown to be related, in a simple manner, to the physical characteristics of the system, in particular water residence time and mean lake depth. These parameters are generalized to give a simple empirical model for the full set of study lakes. The model is shown to give estimates of ¹³⁷Cs activity to within a factor of 5 of field data for a period of several years after the fallout. Initial fractional losses of activity from catchment to lake were determined to be within the range 0.44–8.7% per year, declining exponentially with a mean rate constant 0.98 × 10⁻³ d⁻¹.