The trophic state index (TSI) and trophic level index (TLI) are commonly used methods for evaluating the eutrophication state of lakes and reservoirs. However, they are unable to overcome uncertainties such as calculation errors and spatial heterogeneity of evaluation indicators. To comprehensively evaluate the eutrophication state of a region, we introduce a probability density function and propose the stochastic trophic level index model (STLI). The probability density function of each trophic level is derived through the principle of maximum entropy, and membership vector F (F1, F2, F3, F4, F5) for each trophic level is established to quantify the risk of regional eutrophication. We utilized STLI to evaluate the eutrophication status of Songhua Lake, China, and determined that the method can be used for uncertainty and risk assessment. Our results show that the Jiaohe River backwater area has the highest eutrophication level (light eutropher), with a 0.12 probability of further deterioration to middle eutropher. The eutrophication status of the Main Scenic Area of the Songhua Lake Scenic Resort was shown to be mesotropher, with 0.26 and 0.08 probabilities of further deterioration to light eutropher and middle eutropher, respectively. Finally, the eutrophication status of the Songhua River Three Lakes Reserve Experimental Area was shown to be mesotropher, with a 0.24 probability of further deterioration to light eutropher. Overall, the Songhua River Three Lakes Reserve Experimental Area is the most promising for the lowest level of eutrophication. We recommend that the management department take effective targeted measures against the Jiaohe River backwater area first. The probability density and membership vector of STLI can effectively solve the uncertainties presented by traditional methods for evaluating regional eutrophication status.
Keywords: Eutrophication evaluation; Probability density function; Songhua lake; Stochastic trophic level index model.
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