基于水流物理耦合与PSO-NLS混合的水位流量关系模型研究
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1.湖北省荆州市水文水资源勘测局

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P332

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湖北省水文水资源中心重点科技科研项目(HBSWKJ-2026-02)


Research on a Stage–Discharge Relationship Model Integrating Hydrodynamic Coupling and a Hybrid PSO–NLS Approach
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Jingzhou Hydrology and Water Resources Survey Bureau of Hubei Province

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    摘要:

    针对天然河道水位流量关系受变动回水、洪水涨落及两者共同作用影响而呈现非单值关系问题,构建基于水流物理耦合与PSO-NLS混合率定水位流量关系模型。模型以断面面积和上下游有效落差为基本输水骨架,引入回水水位阈值、回水强度和水位涨落率,分别表征下游顶托、回水强度调制及洪水涨落滞回效应;参数采用粒子群算法(PSO)全局搜索,并以多起点非线性最小二乘法(NLS)进行局部精修。以沙溪坪站为实例,以2020-2021年实测水位流量资料为例,提出水位-落差、有效落差、回水强度修正和完整耦合4类模型开展对比。结果表明,完整耦合模型在2020年、2021年水位流量关系的决定系数分别为0.9983、0.9993,RMSE分别为22.44m3·s-1、7.39m3·s-1,MAE分别为3.95m3·s-1、0.88m3·s-1。模型比较表明,面积指数、有效落差门槛和综合输水系数对计算结果影响较大,是参数率定的重点。研究成果能够较好降低复杂水力条件下水位流量关系离散程度,可为受下游顶托和洪水涨落影响的河道推流提供参考。

    Abstract:

    To address the issue that the stage–discharge relationship in natural watercourses exhibits a non-monotonic relationship due to the combined effects of variable backwater, rising and falling limbs of floods, and their interaction, a hybrid PSO-NLS calibration model for the stage–discharge relationship was developed based on the physical coupling of water flow. The model uses cross-sectional area and effective head upstream and downstream as the basic framework for water conveyance, incorporating backwater water level thresholds, backwater intensity, and water level fluctuation rates to characterize downstream backwater, backwater intensity modulation, and flood fluctuation hysteresis effects, respectively. Parameters are globally searched using the Particle Swarm Optimization (PSO) algorithm and locally refined using multi-start Nonlinear Least Squares (NLS). Using the Shaxiping Station as a case study and based on observed water level and discharge data from 2020–2021, four model types were proposed and compared: water level–head, effective head, backwater intensity correction, and fully coupled models. The results show that for the stage–discharge relationships in 2020 and 2021, the complete coupling model achieved determination coefficients of 0.9983 and 0.9993, respectively, with RMSEs of 22.44 m3·s?1 and 7.39 m3·s?1, and MAEs of 3.95 m3·s?1 and 0.88 m3·s?1, respectively. The model comparison indicates that the area index, effective head threshold, and comprehensive conveyance coefficient have a significant impact on the calculation results and are key parameters for calibration. The research findings effectively reduce the variability of the stage–discharge relationship under complex hydraulic conditions and can serve as a reference for discharge estimation in watercourses affected by downstream backwater and flood fluctuations.

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  • 收稿日期:2026-02-11
  • 最后修改日期:2026-08-21
  • 录用日期:2026-08-28
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