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水力发电学报

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基于伴随方程的浅水湖泊水质参数协同反演方法

  

  • 出版日期:2026-07-07 发布日期:2026-07-07

Collaborative inversion method for water quality parameters of shallow lakes based on adjoint equations

  • Online:2026-07-07 Published:2026-07-07

摘要: 大型浅水湖泊水动力条件较弱,生化过程在水质演化中占据主导作用,使降解系数与内源源强等关键参数对水质模拟结果具有显著影响。然而,由于自然水体生化过程高度复杂,上述参数通常难以直接获取,成为制约水质模型精度提升的关键问题。本文以降解系数与内源源强为研究对象,基于伴随方程法推导深度平均对流–扩散方程的伴随系统,建立模拟误差对参数的梯度解析表达。在此基础上,结合Broyden-Fletcher-Goldfarb-Shanno (BFGS)优化算法,构建水质参数协同反演框架,并在OpenFOAM数值平台上实现。以南水北调东线南四湖CODMn模拟为例,优化得到降解系数 k=0.0185d?1,内源源强 S=0.179 g·m?2·d?1,均处于合理物理范围;模型模拟RMSE的相对误差小于16.6%,较初始参数方案显著降低;优化过程收敛稳定,计算效率较高。结果表明,该方法能够有效提升浅水湖泊水质模型的参数识别精度,为复杂水环境条件下的参数反演提供方法支撑。

Abstract: In large shallow lakes, where hydrodynamic conditions are relatively weak, biochemical processes play a dominant role in water quality evolution. This makes key parameters such as degradation coefficient and internal source strength significantly influential in water quality simulation results. However, due to the high complexity of biochemical processes in natural water bodies, these parameters are often difficult to obtain directly, posing a key challenge in improving the accuracy of water quality models. This paper focuses on the degradation coefficient and internal source strength, derives the adjoint system of the depth-averaged convection-diffusion equation based on the adjoint equation method, and establishes a gradient analytical expression for simulation errors with respect to parameters. On this basis, combined with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization algorithm, a collaborative inversion framework for water quality parameters is constructed and implemented on the OpenFOAM numerical platform. Taking the simulation of CODMn in the South Four Lakes of the East Route of the South-to-North Water Diversion Project as an example, the optimized degradation coefficient k=0.0185d?1 and internal source strength S=0.179 g·m?2·d?1 are both within a reasonable physical range; the relative error of the model simulation RMSE is less than 16.6%, significantly reduced compared to the initial parameter scheme; the optimization process converges stably with high computational efficiency. The results show that this method can effectively improve the parameter identification accuracy of shallow lake water quality models, providing methodological support for parameter inversion under complex water environmental conditions.

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