湖泊科学   2021, Vol. 33 Issue (1): 49-63.  DOI: 10.18307/2021.0103. 0

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[复制中文]
Liu Yong, Jiang Qingsong, Liang Zhongyao, Wu Zhen, Liu Xiaoyu, Feng Qiuyuan, Zou Rui, Guo Huaicheng. Lake eutrophication responses modeling and watershed management optimization algorithm: A review. Journal of Lake Sciences, 2021, 33(1): 49-63. DOI: 10.18307/2021.0103.
[复制英文]

2020-04-22 收稿
2020-06-10 收修改稿

### 码上扫一扫

(1: 北京大学环境科学与工程学院, 国家环境保护河流全物质通量重点实验室, 北京 100871)
(2: 北京英特利为环境科技有限公司, 北京 100191)

Lake eutrophication responses modeling and watershed management optimization algorithm: A review
Liu Yong1 , Jiang Qingsong1 , Liang Zhongyao1 , Wu Zhen1 , Liu Xiaoyu1 , Feng Qiuyuan1 , Zou Rui1,2 , Guo Huaicheng1
(1: College of Environmental Sciences and Engineering, State Environmental Protection Key Laboratory of All Materials Flux in Rivers, Peking University, Beijing 100871, P. R. China)
(2: Beijing Inteliway Co., Ltd, Beijing 100191, P. R. China)
Abstract: Lake eutrophication is a global challenge. The models of eutrophication response and watershed optimization control decision-making are the key to formulating economic and efficient action plans. However, the existing reviews of eutrophication model mainly focus on the single aspects of model development, case study, sensitivity analysis, uncertainty analysis, simplification and surrogate model. There is a lack of the summary of studies on the coupling of macro and micro aspects, such as the non-linear response, treatment decision and water quality improvement and long-term evolution of ecosystems. Therefore the models and methods of lake eutrophication response simulation and pollution-reduction optimization were summarized and analyzed in this study. The eutrophication models are divided into (a) data-driven statistical models, (b) causal-driven mechanism models, and (c) decision-oriented optimization models. Generalized statistical models including classic statistics, Bayesian statistics, and machine learning are often used on response relationships establishment, time series analysis, and spatio-temporal forecasting and early warning. The mechanism model consists of the hydrological, hydrodynamic, water quality, aquatic ecology, and other processes. It is usually used to simulate the change on different spatial and temporal scales, in conjunction with the watershed models. Among them, sensitivity analysis, parameter verification, and model uncertainty will cause high computing costs. The decision-oriented optimization model combines the mechanism model to form a "simulation-optimization" system, which derives a variety of methods such as stochastic optimization and interval optimization under uncertainty. It can deal with the cost of computing time through parallel calculation, simplification, and surrogate models. The challenges for future lake management were identified, including: (a) integration of the external input and the heterogeneity of the lake's nitrogen, phosphorus and algae; (b) improving the correlation and accuracy of optimal control decisions and water quality targets; and (c) exploring the long-term changes of lake ecosystems trajectory and driven factors. Several research focus were proposed to deal with the challenges, including (a) prediction of lake water quality response based on multivariate data fusion and machine learning algorithms; (b) upscaling or downscaling coupling of mechanism models based on biomass and action-driven agent-based model to express the interaction process of population at multiple scales; (c) machine learning algorithms and mechanism models are directly coupled or data assimilation to reduce simulation errors; and (d) multiple simulation models with different spatial-temporal scales are fused to achieve precise and dynamic optimization.
Keywords: Lake eutrophication    nonlinear    statistical model    mechanism model    optimization model    model fusion

1 湖泊富营养化响应的模型研究进展 1.1 数据驱动的统计模型

1.2 因果驱动的机理模型

2 流域优化调控决策的模型研究进展

 $\min f(x)$ (1)
 $\text { s.t. } g_{j}(x, y) \leqslant 0, j=1, 2, \cdots, m$ (2)
 $h_{i}(x, y)=0, i=1, 2, \cdots, n$ (3)
 $\begin{array}{c} y=U(x, w) \end{array}$ (4)

3 湖泊治理面临的挑战与模型研究展望 3.1 湖泊治理面临的挑战

3.2 湖泊响应与流域调控的模型研究展望

1) 多源数据的融合

2) 生态系统动力学模型与个体行为驱动模型的耦合

 图 1 水动力-水质-生态模型与个体模型耦合的方法[108] Fig.1 Framework of agent-based model coupling with hydrodynamic and water quality model[108]

3) 因果驱动模型与数据驱动模型的结合

4) 多尺度融合的流域精准优化调控决策模型

 图 2 流域精准治污模型体系 Fig.2 Framework of simulation on refined pollution control decisions on watershed
4 结论

1) 湖泊富营养化响应与流域优化调控决策模型分为数据驱动的统计模型、因果驱动的机理模型和决策导向的优化模型.其中，统计模型包含经典统计、贝叶斯统计和机器学习，常用于建立多指标间响应关系、时间序列特征分析以及敏感指标的预报预警，但对于机理规律解释不足.机理模型可实现不同时空尺度的流域和湖泊变化过程模拟，但由于存在时间精细化、空间多维化、机理过程多样、状态变量繁多、参数数量庞大和参数交互性强等特征，导致模型的敏感性分析、参数校验、不确定性分析等需要较高的计算成本.决策导向的优化模型结合机理模型形成“模拟-优化”体系，在不确定性条件下衍生出随机、区间优化等多种方法，可通过并行计算、简化与替代模型等方法应对计算成本过高的问题.

2) 湖泊富营养化治理依然面临较大的挑战，一是在外源输入非线性的叠加下如何定量解析各个污染源的贡献，如何衡量外源输入与内部循环的关联及贡献；二是工程总量减排与水质改善间的关联并不明晰，实现精准的污染治理需要解决非线性响应的时空尺度转化与海量组合方案评估、模型运算成本与等效替代、工程运行与动态调度、不确定性分析与决策稳健性等挑战；三是湖泊的氮、磷浓度等表观监测指标难以反映生态系统的长期演化趋势、恢复潜力与系统稳定性.

3) 为应对挑战，未来在模型方面仍需开展深入研究，主要包括：将原生数据、次生数据以及机器学习等算法进行融合，更加全面和准确地表征变量的动态变化，揭示常规监测不能反映的规律；将以生物量为基础单元的生态系统动力学模型与以个体行为驱动的个体模型进行升尺度或降尺度耦合，以表达物种间与物种内不同尺度的差异性；将机器学习算法与机理模型进行耦合，提高机理模型的参数准确度；将多介质的模型在时空尺度上进行融合，以综合评估从治理工程到湖体的多级响应关系，为湖泊治理提供系统、精确、动态和科学的决策支撑.

5 参考文献