Calculating exchange times in a Scottish fjord using a two-dimensional, laterally-integrated numerical model

In order to assess the potential impact of pollutants, particularly soluble wastes discharged by the mariculture industry, on the fjordic sea loch environment in Scotland, simple management models have been developed which estimate steady-state concentrations based on the quantities of effluent released and the residence time of such material within a loch. These models make various simplifications about the hydrodynamic characteristics of Scottish sea lochs, the most important of which is the concept of an exchange time which parametrizes the rate at which pollutants are removed from the system. Exchange times for individual lochs are calculated using the tidal prism method, which has some well-known shortcomings. In this paper, a two-dimensional laterally-integrated circulation model is used to investigate the exchange characteristics of Loch Fyne and its sub-basins. By simulating the transport of a passive, conservative tracer, the turnover times for the loch, two sub-basins and various depth layers are calculated. By varying the starting time of the tracer simulations, the variability in the exchange times is examined. The results from the circulation model are compared with the estimates given by the tidal prism method. The results show that the tidal prism method consistently underestimates the exchange times, although the predicted times tend to lie within the range of the simulated times. Including a simple return flow factor into the tidal prism estimate leads to significant improvements in the comparison.