Long-term prediction of [Formula: see text]Cs in Lake Onuma on Mt. Akagi after the Fukushima accident using fractional diffusion model.

The Fukushima Daiichi Nuclear Power Plant accident also contaminates lakes in Japan. Especially in closed lakes, there is a problem of prolonged low-level $$^{137}$$ Cs contamination because the activity concentration of $$^{137}$$ Cs declines sharply immediately after the accident, but then begins to decrease slowly. In this paper, we derived a long-term prediction formula based on the fractional diffusion model (FDM) for the temporal variation in $$^{137}$$ Cs activity concentrations of the water in Lake Onuma on Mt. Akagi, one of the closed lakes, and of pond smelt (Hypomesus nipponensis), a typical fish species inhabiting in the lake. The formula reproduced well the measured $$^{137}$$ Cs activity concentration of the lake water and pond smelt for 5.4 years after the accident. Next, we performed long-term prediction for 10,000 days using this formula and compared it with the prediction results of the two-component decay function model (TDM), which is the most common model. The results suggest that the FDM prediction will lead to a longer period of contamination with low-level $$^{137}$$ Cs than the TDM prediction.