水动力学模型与集合卡尔曼滤波耦合的实时校正多变量分析方法

Real-updating multivariate analysis for unsteady flows with ensemble Kalman filter

为减少非恒定水流计算中的不确定性,在水流随机运动系统状态空间模型基础上,应用集合卡尔曼滤波(EnKF)技术建立了非恒定水流分析的实时更新(校正)方法。该方法适用于非线性的随机微分方程,过程和观测噪声可以是非正态分布。同时,为充分利用水位、流量等误差量级相差巨大的观测中所蕴含的有效信息,导出了EnKF多变量分析格式。以明渠单峰洪水过程的合成数据为例,考察了运用建立的实时更新方法分析预报一维洪水演进的性能。重点对比了采用不同精度等级下的水位和流量观测资料进行滤波的效果。在中国现行标准规定的允许观测误差范围内,以水位观测进行一维洪水动力学模型的滤波分析可有效地控制误差、估计流量、识别水流运动系统状态。长江干流清溪场至万县江段实际洪水计算还证实:该方法通过插入即时观测,可实时更新模型状态,给出与实际更为接近的计算。

To reduce uncertainty in the forecast or analysis of unsteady flows, the ensemble Kalman filter technique （EnKF） is introduced based on the stochastic unsteady flow system with a stochastic state space model. The multivariate analysis scheme is proposed for updating flow states when the water stage and the discharge measurements are both assimilated. Taking a single-wave flood event in open channel as an example, the performance of EnKF is investigated with the experiments of 13 groups. The investigation mainly focuses on the comparisons of the effects of water stage or discharge measurements with different order of the available accuracy on the EnKF analysis. Main results show that one can identify flow states well by assimilating the water stage measurements with less than 5cm standard deviation alone. And the results using discharge measurement with 5% relative standard deviation are close to those using water stage with 10cm standard deviation. Further, when both kinds of measurements are assimilated, the appropriate variable transformation is required to remedy the tnmcation errors of the numerical computation.