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.

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。