Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2023, Vol. 59 ›› Issue (4): 695-703.DOI: 10.13209/j.0479-8023.2023.036

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Nonlinearity Strength Indicators for Numerical Simulation Based Load Reduction-Water Quality Responses

SU Han1,2, ZOU Rui2, LIANG Zhongyao2, YE Rui3, WANG Zhiyun4, LIU Yong5,†   

  1. 1. Multidisciplinary Water Management group, Faculty of Engineering Technology, University of Twente, Enschede 7500AE 2. Rays Computational Intelligence Lab, Beijing Inteliway Environmental Co. Ltd., Beijing 100085 3. Nanjing Smart Water Co. Ltd., Nanjing 210012 4. Yunnan Research Academy of Eco-environmental Sciences, Kunming 650034 5. State Environmental Protection Key Laboratory of All Materials Flux in Rivers, College of Environmental Science and Engineering, Peking University, Beijing 100871
  • Received:2022-07-11 Revised:2022-09-05 Online:2023-07-20 Published:2023-07-20
  • Contact: LIU Yong, E-mail: yongliu(at)


苏晗1,2, 邹锐2, 梁中耀2, 叶瑞3, 王志芸4, 刘永5,†   

  1. 1. Multidisciplinary Water Management Group, Faculty of Engineering Technology, University of Twente, Enschede 7500AE 2. 锐思计算智能实验室, 北京英特利为环境科技有限公司, 北京 100085 3. 南京智水环境科技有限公司, 南京 210012 4. 云南省生态环境科学研究院, 昆明 650034 5. 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
  • 通讯作者: 刘永, E-mail: yongliu(at)
  • 基金资助:
    国家自然科学基金(51721006, 42142047)和云南省高原湖泊流域污染过程与管理重点实验室开放基金(2016PL03)资助


This study developed four nonlinearity strength indicators for water quality responses based on cross sample entropy, Fourier transformation, non-sequence counting, and adjusted R2 according to typical nonlinear load reduction-water quality responses suggested by previous studies. All the indicators were applied on typical numerical water quality simulation samples. Based on the calculation, the four indicators were compared with each other to provide suggestions on how to use them to detect the nonlinearity and measure the nonlinearity strength. Results show some overlaps among the four indicators, however, they are not interchangeable. The four indicators suggest seasonal differences, peak changes, short-term water quality deterioration, and averaged water quality changes respectively. After providing suggestions on how to use the four indicators to detect nonlinearity of water quality responses, this study further discusses the limitations on the nonlinearity definition and potential applications of the four indicators. This study will contribute to understanding, distinguishing, and analyzing the type of nonlinear water quality responses.

Key words: nonlinearity, water quality response, load reduction, numerical simulation


基于现有研究中典型的水质响应非线性行为, 定义基于交叉样本熵、傅里叶变化、乱序计数和调整R2的4种负荷削减–水质响应非线性强度指标。在典型水质响应样本的基础上进行指标的计算和比选, 为基于数值模拟的水质管理提供可参考的非线性强度衡量指标和非线性判断依据。研究结果表明, 4种水质响应非线性强度指标虽然有一定的重叠, 但不可以互相替代, 它们分别指示季节差异、峰值变化、短期水质恶化以及水质均值变化等不同类型的非线性行为。结合计算结果, 给出使用4种非线性指标判断非线性行为的方法, 并讨论非线性定义的局限性以及所提指标的应用前景。研究结果有助于进一步区分和认识水体水质响应不同类型的非线性行为, 以便针对非线性水质响应行为的特定类型进行分析。

关键词: 非线性, 水质响应, 负荷削减, 数值模拟