A divergence‐free spatial interpolator for large sparse velocity data sets
A divergence‐free spatial interpolator for large sparse velocity data sets
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DOI：
10.1029/2008jc004973
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发表时间：
2009-10
影响因子：
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通讯作者：
R. Vennell;R. Beatson
中科院分区：
文献类型：
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作者：
R. Vennell;R. Beatson
提出了一种二维无散度插值方法，与独立插值速度分量相比，该方法能在稀疏速度数据之间给出更真实的值。内插器通过确保质量守恒来加强速度分量之间的物理依赖性。使用合成涡流数据进行的测试表明，分量的独立插值可能会在大间距数据之间给出不切实际的速度。然而，无散度插值对稀疏数据和密集数据的再现效果几乎一样好。在综合测试中，无发散径向基函数（RBF）插值器的性能与最优插值一样好，甚至更好。这里实现的“贪婪拟合”RBF插值器的一个显著优点是描述插值曲面所需的系数很少。对于大型数据集，这使得插值器比最优插值（Optimal Interpolation）等需要每个数据点一个系数的技术具有显著的计算优势。RBF的参数经济性和无散度约束的物理性使得稀疏数据的RBF插值更能抵抗噪声的跟随。二维无散度插值器可用于插值地转速度或潮汐流等高频流的水平输运。对局部动力学实验系泊数据和移动船舶声学多普勒流廓仪潮汐流测量数据的测试表明，无散度插值器比单独插值速度分量能更好地再现插值中遗漏的数据。
[1] A 2-D divergence-free interpolator is presented which is demonstrated to give more realistic values between sparse velocity data than interpolating velocity components independently. The interpolator enforces physical dependence between the velocity components by ensuring mass is conserved. Tests using data for a synthetic eddy show that independent interpolation of components can give unrealistic velocities between widely spaced data. However, divergence-free interpolation can reproduce the eddy almost as well with sparse data as with dense data. In the synthetic tests the divergence-free radial basis function (RBF) interpolator performed as well as, or better than, optimal interpolation. A significant advantage of the “greedy fit” RBF interpolator implemented here is the small number of coefficients required to describe the interpolating surface. For large data sets this gives the interpolator a significant computational advantage over techniques, like Optimal Interpolation, which require one coefficient per data point. The RBF's economy of parameters and imposing physics with the divergence-free constraint makes RBF interpolation of sparse data much more resistant to following the noise. The 2-D divergence-free interpolator can be used to interpolate geostrophic velocities or the horizontal transport of high-frequency flows such as tidal currents. Tests with data from the local dynamics experiment moorings and from moving vessel acoustic Doppler current profiler measurements of tidal flow show the divergence-free interpolator is better able to reproduce data left out of the interpolation than interpolating velocity components independently.