Reconstruction performance analysis for Basis Function of the sound speed profile
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摘要: 海水声速剖面通常使用经验正交函数（Empirical Orthogonal Function，EOF）进行稀疏表示，然而基函数会受到数据完备性和数据测量时间的制约，其代表性误差会导致声速剖面重构精度受限。为了提高声速剖面的重构精度，本文利用模糊C均值聚类对BOA_Argo历史数据集进行聚类分析，探讨不同聚类空间的训练集数据对实测声速剖面重构精度的影响。研究表明，声速剖面具有明显的时空聚集特性，聚类后的历史声速剖面集生成的基函数和平均声速剖面具有最优的重构性能。本文研究结果有助于为历史声速剖面训练集的选取提供实际指导意义，进而提高声速剖面重构精度乃至反演精度。Abstract: Empirical Orthogonal Functions (EOFs) are usually used for sparse representation of the sound speed profile (SSP). However, due to the restriction of data completeness and measurement time, the representative error of the EOF will lead to limited accuracy of SSP reconstruction. In order to improve the reconstruction accuracy of SSP, the fuzzy C-means clustering algorithm is used to analyze the BOA_Argo historical data set and the reconstruction accuracy of the measured SSP based on different clustering spaces of data samples is discussed. The results shows that the SSPs are significant temporal-spatial clustering. The EOF and mean SSP generated by the clustered historical SSPs have the best reconstruction performance. The results of this paper are helpful to provide practical guidance for the selection of historical SSP training data and can improve the accuracy of SSP reconstruction.
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图 4 第II型声速剖面进一步聚类结果
Fig. 4 Further clustering results of the sound speed profiles of Type II
图 5 第II-1型与CTD测量得到的声速剖面
Fig. 5 The sound speed profiles of Type II-1 andmeasured by CTDs
图 6 CTD和不同区域的平均声速剖面
a. 第I型；b. 第II型；c. 第III型；d. 第II-1型
Fig. 6 CTD and mean sound speed profiles in different regions
a. Type I; b. Type II; c. Type III; d. Type II-1
图 9 CTD测量声速剖面的重构误差
a. 全区域；b. 第I型；c. 第II型
Fig. 9 The reconstruction error of sound speed profiles measured by CTD
a. Whole area; b. Type I; c. Type II
图 10 重构声速剖面的均方根误差比较
Fig. 10 Comparison of the RMSE of the reconstructed sound speed profiles
图 12 CTD测量声速剖面的重构误差
a. 第II型；b. 第II-1型
Fig. 12 The reconstruction error of sound speed profiles measured by CTD
a. Type II; b. Type II-1
图 13 重构声速剖面的均方根误差比较
Fig. 13 Comparison of the RMSE of the reconstructed sound speed profiles
图 14 各训练集与CTD提取的第1阶EOF基函数幅度随深度的变化
Fig. 14 The variation of first EOF amplitude extracted from training sets and CTD with depth
图 16 ΔC1随深度的变化（a）、以第II型声速剖面作为训练集时 ΔC1和 ΔC2随深度的变化（b）、以第II-1型声速剖面作为训练集时ΔC1和ΔC2随深度的变化（c）、ΔC 随深度的变化（d）
Fig. 16 ΔC1 changed with depth (a), ΔC1 and ΔC2 changed with depth (the Type II sound speed profiles as the training set) (b), ΔC1 and ΔC2 changed with depth (the Type II-1 sound speed profiles as the training set) (c), ΔC changed with depth (d)
图 17 CTD测量声速剖面的重构误差
a. 第II型；b. 12° × 12°
Fig. 17 The reconstruction error of sound speed profiles measured by CTD
a. Type II; b. Type 12° × 12°
图 18 重构声速剖面的均方根误差比较
Fig. 18 Comparison of the RMSE of the reconstructing sound speed profiles
表 1 不同训练集与CTD基函数的相关系数
Tab. 1 The correlation coefficient between different training sets and CTD EOFs
基函数阶数 第1阶 第2阶 第3阶 第4阶 第5阶 第6阶 第II型 0.84 0.05 0.39 0.38 0.37 0.04 第II-1型 0.90 0.51 0.89 0.49 0.51 0.13 
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表 2 不同训练样本下CTD声速剖面的重构误差
Tab. 2 The reconstruction error of CTD profiles under different training samples
误差 训练集 全区域 第I型 第II型 第II-1型 12° × 12°区域 最大声速误差/（m·s−1） 6.22 7.21 4.81 5.28 4.92 最大均方根误差/（m·s−1） 1.36 1.69 1.04 1.18 0.99 平均均方根误差/（m·s−1） 0.88 1.05 0.67 0.71 0.69
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