Assessment of lake eutrophication recovery: the filtering trajectory method (FTM) and its application to Dianchi Lake, China.

Lake ecosystems follow convoluted trajectories impacted by climate change and human stress. In this study, we developed the filtering trajectory method (FTM), a mathematical model, to establish the empirical relationships between chlorophyll a (CHLa) and nutrient concentrations in eutrophic Dianchi Lake, China. FTM can identify cause-effect relationships over time in apparently stochastic data, and a filtering trajectory diagram is used to describe the driving forces of the complex trajectories of individual lake ecosystems. Our analysis showed that the nutrient concentrations of overlying water in Dianchi Lake have decreased to the levels recorded in the late 1980s and early 1990s, but CHLa has not declined synchronously. The ecosystem trajectories revealed the ups and downs of complex processes, which can be divided into four stages: (1) pollution stage (1988-1999): a macrophyte-to-phytoplankton transition occurred with an increase in nutrient inputs and a rise in temperature; (2) initial restoration stage (2000-2006): the response of CHLa to the nutrient load reduction presented an apparent time lag, or hysteresis effect; (3) recurrence stage (2007-2011): excessive water consumption and continuous drought in the watershed resulted in an increasing trend in CHLa, TP and TN; and (4) re-restoration stage (2012-2016): the implementation of a water-replenishment project resulted in a declining trend. Our approach can greatly improve our understanding of how lakes respond to broad changes in environmental conditions (e.g. climate warming) and improve water quality via targeted nutrient management, from "static" to "dynamic management" and from "One Standard for One Lake" to "Multiple Standards for One Lake".