Nonlinear data assimilation for shallow water equations in branched channels
Nonlinear data assimilation for shallow water equations in branched channels
复制标题
分支河道浅水方程的非线性数据同化
DOI：
10.1029/jc091ic09p10633
复制
发表时间：
1986
期刊：
影响因子：
--
通讯作者：
W. Budgell
中科院分区：
文献类型：
--
作者：
W. Budgell
建立了时间序列观测网络与分支通道中非线性浅水传播数值模型的最佳组合框架。根据模式结果和观测值的可靠性对其进行加权，以估算地表高程和运输。采用两种滤波技术进行动态随机建模。对于弱非线性条件，采用改进的增量协方差chandrasekhar算法，而对于更强的非线性动力学，采用扩展卡尔曼滤波器的Bierman平方根形式。利用新罕布什尔州大湾河口的参数进行的数值实验表明，在随机强迫（模式误差）和测量噪声的条件下，这两种滤波器都能成功地估计随时间和空间变化的海拔和输运分布。尽管钱德拉塞卡算法低估了滤波器估计的协方差，但它的性能几乎与完全非线性算法一样好，即使对于明显非线性的测试用例也是如此。结果表明，当该算法应用于过程噪声和测量噪声结构为纯正弦的系统时，钱德拉塞卡滤波器的性能不会下降，从而违反了推导该滤波算法时的白噪声假设。
A framework has been developed for the optimal combination of a network of time series observations with a numerical model of nonlinear shallow water wave propagation in branched channels. The model results and observations are weighted according to their reliability to produce estimates of surface elevation and transport. Two filtering techniques are adopted to perform the dynamic-stochastic modeling. For weakly nonlinear conditions a modified incremental covariance Chandrasekhar-type algorithm is employed, whereas for more strongly nonlinear dynamics a Bierman square root form of the extended Kalman filter is used. Numerical experiments performed using parameters from the Great Bay estuary in New Hampshire demonstrate that both filters successfully estimate the time- and space-dependent elevation and transport distributions under conditions of stochastic forcing (model error) and measurement noise. Although the Chandrasekhar algorithm underestimates the covariances of the filter estimates, it performs nearly as well as the fully nonlinear algorithm, even for the significantly nonlinear test case. It is shown that the Chandrasekhar filter performance does not degrade when the algorithm is applied to systems in which the process noise and measurement noise structures are purely sinusoidal, thus violating the assumption of white noise under which the filter algorithm is derived.