History, development and characteristics of lake ecological models

This paper provides some introductory information on the history, development, and characteristics of various lake ecosystem models. The modeling of lake ecological processes began to gain importance in the early 1960s. There are a number of models available today, with varying levels of complexity to cope with the variety of environmental problems found in lake environments, e.g. eutrophication, acidification, oxygen depletion, wetland management, heavy metal and pesticide pollution, as well as hydrodynamic problems. In particular, this paper focuses on lake eutrophication and wetland models, as well as addressing strategies appropriate for the design and development of reliable lake ecological models.

A model to determine the lake nutrient standards for drinking water sources in Yunnan-Guizhou Plateau Ecoregion, China

Lake eutrophication （LE） has become an increasingly severe environmental problem recently. However, there has been no nutrient standard established for LE control in many developing countries such as China. This study proposes a structural equation model to assist in the establishment of a lake nutrient standard for drinking water sources in Yunnan-Guizhou Plateau Ecoregion （Yungui Ecoregion）, China. The modeling results indicate that the most predictive indicator for designated use-attainment is total phosphorus （TP） （total effect =-0.43）, and chlorophyll a （Chl-a） is recommended as the second important indicator （total effect =-0.41）. The model is further used for estimating the probability of use-attainment associated with lake water as a drinking water source and various levels of candidate criteria （based on the reference conditions and the current environmental quality standards for surface water）. It is found that these candidate criteria cannot satisfy the designated 100% use-attainment. To achieve the short-term target （85% attainment of the designated use）, TP and Chl-a values ought to be less than 0.02 mg/L and 1.4 μg/L, respectively. When used as a long-term target （90% or greater attainment of the designated use）, the TP and Chl-a values are suggested to be less than 0.018 mg/L and 1 μg/L, respectively.

Slowing down critical transitions via Gaussian white noise and periodic force

Stochastic perturbations and periodic excitations are generally regarded as sources to induce critical transitions in complex systems. However, we find that they are also able to slow down an imminent critical transition. To illustrate this phenomenon, a periodically driven bistable eutrophication model with Gaussian white noise is introduced as a prototype class of real systems.The residence probability(RP) is presented to measure the possibility that the given system stays in the oligotrophic state versus Gaussian white noise and periodic force. Variations in the mean first passage time(MFPT) and the mean velocity(MV) of the first right-crossing process are also calculated respectively. We show that the frequency of the periodic force can increase the MFPT while reduce the MV under different control parameters. Nevertheless, the noise intensity or the amplitude may result in an increase of the RP only in the case of control parameters approaching the critical values. Furthermore, for an impending critical transition, an increase of the RP appears with the interaction between the amplitude and noise intensity or the combination of the noise intensity and frequency, while the interaction of the frequency and amplitude leads to an extension of the MFPT or a decrease of the MV. As a result, an increase of the RP and MFPT, and a decrease of the MVobtained from our results claim that it is possible to slow down an imminent critical transition via Gaussian white noise and periodic force.