Predicting the migration of dissolved toxic substances from catchments by a collective model

In the present paper a collective model for predicting the migration of dissolved toxic substances through drainage areas is described. The model has been validated using data for 137Cs and 90Sr concentrations in water of some European contaminated rivers following the atmospheric fall-out from the accident at the Chernobyl power plant. It has been demonstrated that the migration rate λ (s−1) of a dissolved toxic substance from a catchment may be evaluated by the following approximate formula: λ=(c ln t+d)/t, where t is the time from a pulse deposition event and the coefficients c and d depend on the characteristics of the substance. It has been shown that the mathematical form of the transfer function (flux of dissolved substance at time t following a single pulse deposition of a pollutant onto the catchment) of a toxic substance from a drainage area is very simple. Moreover, the values of the transfer function parameters are slightly variable despite the large range of characteristics of the catchments here examined. Indeed, the statistical aggregation of competing migration processes can lead to ‘stable’ collective behaviours that are less variable than each single process.