The phosphorus budget model to predict phosphorus concentration in lake water was improved in order to be applied to a plug flow system. The model for a plug flow system was examined and applied to Lake Inbanuma, a shallow eutrophic lake in Japan. The retention coefficient (R) and the phosphorus concentration in lake water discharging from the lake (Pout) were expressed for a plug flow system by the following equations : R = v / qs, P0 ut = L(1-R)/qs, where v is the apparent settling velocity

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... total phosphorus, qs is the areal water loading and L is the phosphorus loading per unit lake area. The phosphorus concentrations in Lake Inbanuma were calculated by use of the improved phosphorus budget model. The predicted values and the observed values were in good agreement in the case of the data from 1979 to 1984 of which changes with time were smoothed by means of the moving average method.