Stochastic switches of eutrophication and oligotrophication: Modeling extreme weather via non-Gaussian Lévy noise

Disturbances related to extreme weather events, such as hurricanes, heavy precipitation events, and droughts, are important drivers of evolution processes of a shallow lake ecosystem. A non-Gaussian α-stable Lévy process is esteemed to be the most suitable model to describe such extreme events. This paper incorporates extreme weather via α-stable Lévy noise into a parameterized lake model for phosphorus dynamics. We obtain the stationary probability density function of phosphorus concentration and examine the pivotal roles of α-stable Lévy noise on phosphorus dynamics. The switches between the oligotrophic state and the eutrophic state can be induced by the noise intensity σ, skewness parameter β, or stability index α. We calculate the mean first passage time, also referred to as the mean switching time, from the oligotrophic state to the eutrophic state. We observe that the increased noise intensity, skewness parameter, or stability index makes the mean switching time shorter and thus accelerates the switching process and facilitates lake eutrophication. When the frequency of extreme weather events exceeds a critical value, the intensity of extreme events becomes the most key factor for promoting lake eutrophication. As an application, we analyze the available data of Lake Taihu (2014-2018) for monthly precipitation, phosphorus, and chlorophyll-a concentrations and quantify the linkage among them using the Lévy-stable distribution. This study provides a fundamental framework to uncover the impact of any extreme climate event on aquatic nutrient status.