The Research on the Lake Eutrophication with CNOP Method

Using a dynamical model for nutrient cycling in shallow lakes, the approach of conditional nonlinear optimal perturbation (CNOP) was adopted to investigate the instability and the sensitivity of the lake ecosystem to finite-amplitude perturbations both related to the initial condition and the parameter. The results show that the ecosystem can be transformed from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state with a CNOP as the perturbation, no matter how large the nutrient loading rate is. Above all, with the same restraints related to the initial perturbation and the parameter perturbation, CNOP has the largest effect on the lake ecosystem, which may be helpful to govern the lake ecosystem.

The Sensitivity Analysis of a Lake Ecosystem with the Conditional Nonlinear Optimal Perturbation Method

The instability and sensitivity of a lake ecosystem to the finite-amplitude perturbations related to the initial condition and the parameter correspondingly are studied. The CNOP-I and CNOP-P methods are adopted to investigate this nonlinear system. The numerical results with CNOP-I method show that the lake ecosystem can be nonlinearly unstable with finite-amplitude initial perturbations when the nutrient loading rate is between the two bifurcation points. A large enough finite amplitude initial perturbation, that is, CNOP-I, can induce a transition from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state. With CNOP-P method, it is shown that the lake ecosystem can be transformed from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state with a large enough finite amplitude parameter perturbation, that is, CNOP-P, no matter how large the nutrient loading rate is.

Effects of Daphnia on the response of mesotrophic lakes to experimental enrichment

We are currently involved in a whole-lake experiment designed to assess how Daphnia affect the response of mesotrophic lakes to increased nutrient loading. In the first year of the experiment, we wished to demonstrate that there are P loading rates which eutrophy lakes without Daphnia but not lakes with Daphnia. In order to do this, we needed to choose an appropriate level and schedule for the experimental enrichment. This paper describes how we made that choice, then evaluates whether our choice was successful. Based on the literature, a simulation model, and a mesocosm experiment, we decided that enriching at a rate of 1 μg P L−1 d−1 would create the desired contrast between lakes with and without Daphnia. Model simulations indicated that mean algal response to enrichment would be comparable under monthly, weekly, or continuous additions. We chose to add nutrients continuously at ambient N:P ratios. Experimental results from 1993 suggest that we achieved a nutrient loading rate consistent with our goal: chlorophyll responded less to enrichment in the lake with Daphnia than in the lake without Daphnia. The modeling, mesocosm, and whole-lake studies summarized here support the idea that Daphnia reduce chlorophyll at P loads ≤1 μg P L−1 d−1. However, cyanobacteria may escape control by all grazers at relatively low P loading rates.