基于总体最小二乘法的系统响应修正方法

A new version of system response method for error correction based on total least squares

为了提高实时洪水预报的预报精度,提出了基于总体最小二乘平差理论的系统响应方法。传统的系统响应方法基于最小二乘法,只能考虑观测值的误差,因而传统的系统响应方法不能考虑动态系统响应矩阵存在的误差。对传统方法进行了分析并引入了总体最小二乘平差理论,改进方法同时考虑了动态系统响应矩阵和观测值的误差。针对动态系统响应矩阵的病态情形,通过总体最小二乘的岭估计解法给出稳定解。通过改进方法对新安江模型中的土壤含水量进行修正,应用于七里街流域,并与传统的系统响应方法进行比较。结果表明,两种方法都能提高模拟精度,改进方法相比于传统方法精度明显提升;改进方法的修正效果要优于传统方法,更加稳定。

To improve the accuracy of real-time flood forecasting, a new version of system response meth- od which is based on total least squares is proposed. Original system response method involves a least squares problem suited for problems in which the observed value is known approximately but fails to deter- mine the error in system response matrix. We analyze the system response method and apply total least squares to consider the perturbation in both system response matrix and the observation. It is necessary to use ridge estimation to stabilize the solution for ill-posed system response matrix. The improved correction method has been adopted in Qilijie basin to update the estimates of soil moisture content and the improved method is compared with the original method. Both of the methods can lead to better accuracy. The new version of system response method leads to better and more stable performance than the original method.