拉格朗日基函数重建稳态海面地形方法的参数化分析

稳态海面地形的参数化方法对于融合平均海平面和大地水准面求解高精度稳态海面地形信号具有重要作用。研究了基于高阶拉格朗日基函数重建稳态海面地形的方法，构建了含有4参数、16参数及36参数的拉格朗日基函数进行海面地形建模，重点分析了基函数的选取对稳态海面地形重建的影响。研究结果表明，基于16参数的拉格朗日基函数重建的海面地形和外部数据的一致性更高，其求解的海面地形与对比数据的差异标准差为3.1 cm，较基于4参数和36参数基函数求解的结果分别减小0.9 cm和1.1 cm。在海流运动活跃的区域，基于16参数基函数重建的海面地形与对比数据的差异较基于4参数和36参数的结果有5 cm的改善。此外，基于16参数基函数求解结果的地转流信号与对比数据符合较好，其中纬向地转流分量与对比数据的差异标准差较基于4参数和36参数的结果分别减小0.4 cm/s和2.8 cm/s。

Parameterization Analysis of the Lagrange Basis Function Method for the Reconstruction of the Mean Dynamic Topography

  Objectives  The reconstruction of the mean dynamic topography (MDT) plays an important role in the fusion of the mean sea surface and geoid for high-precision MDT modelling.  Methods  The parameterization algorithm based on the Lagrange basis functions (LBFs) is investigated, and the performance of the MDT solutions based on different choice of the LBFs is studied in detail, where the LBFs consist of 4/16/36 parameters (P) are introduced and analyzed.  Results  The results show that the MDT solution based on 16 parameters is more consistent with the comparative data. The standard deviation (SD) of misfits between the solved MDT using 16P and the comparative data is 3.1 cm, which is 0.9 cm/1.1 cm smaller than that of the 4P/36P; and the misfits using 16P are improved by 5 cm than that using 4P/36P in regions with a strong variation of ocean current.  Conclustions  The geostrophic velocities based on the 16P-solution are in good agreement with the comparative data, where the SD of misfits between the zonal geostrophic component by the 16P and the comparison data is reduced by 0.4 cm/s and 2.8 cm/s compared to the results of 4P/36P.