高頻雷達觀測流場補缺值問題之探討─以台灣東北部海域為例

A Study on Data Filling from Incomplete Dataset of HF Radar Measured Ocean Currents─A Case Study of the Flow Field Northeast of Taiwan

陳俞彣(Yu-Wen Chen)

指導教授 ： 王冑

共同指導教授 ： 詹森

國立臺灣大學/理學院/海洋研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.01709

摘要

高頻雷達是近代廣用的一種即時監測海流的遙測工具，但高頻雷達訊號常因環境雜訊以及電離層等干擾影響，會造成在觀測區內出現海流觀測值缺漏的情況，因此如何有效填補缺漏值即成為海流監測即時作業一個重要的課題。本文使用臺灣大學海洋所、海軍軍官學校以及海軍大氣海洋局共同合作在臺灣東北部海域建置的CODAR雷達系統觀測資料做為研究的根據。
　　我們選用實向量經驗正交函數(real-vector EOF)及Karhunen-Loeve展開法(KLE)兩種統計方法探討流場填補缺漏值問題。這兩種方法均是根據長期觀測資料之變量統計求出對應之特徵向量(eigenvector)作為模組(mode)基底，而觀測資料在各基底之投影即為該模組之振幅(amplitude)。經比較分析後，我們選用前20組模組(可解釋96%以上的總變異量)，分別使用最小平方法(least square)與迭代法(iteration)以求解不完整資料情形下各模組之振幅，並以此進行不同個數缺漏值之填補實驗，以檢驗填補效果及填補誤差，藉以推測使用不同方法之缺漏個數上限。
　　填補實驗的統計結果顯示，以最小平方法進行填補實驗時，在缺漏個數小於資料點總數之57%的情況下，其誤差隨缺漏點個數的變化並不大，若以迭代法搭配實向量EOF法或是KLE法分別進行填補，則誤差會隨缺漏點個數變多而呈線性增長，不過各方法在空間上之分佈皆甚為類似，在離雷達站較近處誤差較小；四種方法中以最小平方法配合實向量EOF法填補後之誤差相對較小，效果較佳。當缺漏個數為資料點總數之57%時，最小平方法填補後所得之誤差開始變得明顯，當缺漏個數達資料點總數之71%以上時，其變化趨勢會呈指數成長；而迭代法的實驗結果則是幾乎在所有缺漏情況下，其誤差皆大於最小平方法的誤差。在缺漏個數為資料點總數之71%以上的情形時，這些方法均不適合用來填補缺漏值。

關鍵字

高頻雷達 ； CODAR ； 經驗正交函數 ； Karhunen-Loeve展開法 ； 填補缺值

並列摘要

The Coastal Ocean Dynamics Applications Radar (CODAR) is a High-Frequency (HF) radar system with compact antennas. Recently, CODAR becomes widely used, for monitoring ocean surface currents remotely in nearly real time; its ability of large coverage on ocean surface and high resolution both in time and in space, makes CODAR an ideal tool for the operational oceanography, such as now-cast of currents and data-assimilation tasks. However, environmental effects such as interferences from obstacles, and/or from ionospheric disturbances, often hampers or weakens the strength of CODAR system, might deteriorate the data quality of CODAR, inducing incomplete datasets with missing data or holes in the designated observation region. The development of appropriate methodology for filling missing data is therefore a necessity deserving for further studies, in prior to the development of operational framework.
In the context, we have analyzed a nearly two-year long dataset of CODAR, which was observed by two HF radars located at Suao and Han-Ben, respectively, and provided by the Surface Current Observations at North-East Taiwan (SCONET) project; basic statistics of the measurements show that the SCONET dataset satisfies the normality and weakly stationary condition. Further processing, by using both modal decomposition methods of Real-vector Empirical Orthogonal Function (REOF) and the Karhuren-Loeve Expansion (KLE), respectively, reveals that almost more than 96% of total variances of currents in the whole observation region can be interpreted by the first 20 modes of both methods. Therefore the first 20 modes of both methods are used for data reconstruction and data filling later.
An independent month-long time series of CODAR measurements is adopted for the data filling experiment, by which the incomplete dataset is generated by depleting artificially assigned grid points in the original complete dataset, the measurements are therefore treated as the ground truth for later comparison. Monte Carlo simulation is used for the tests of data filling experiment when the missing points of data exceed 3 points. We have used both the EOF and the KLE methods, in accompany with the least square and the iteration procedures for the estimation of the amplitude of each modes, for the study of data filling experiment. Results show that the EOF method in accompany with the least square procedure is the best among the four methodologies, when the percentage of occurrence of the missing data is less than 57% of the whole dataset. However, all these four methods are not adequate for filling incomplete dataset, if the percentage of occurrence of the missing data exceeds 71%.

並列關鍵字

HF radar ； CODAR ； EOF ； Karhunen-Loeve expansion ； data filling

參考文獻

Alvera-Azcarate, A., A. Barth, M. Rixen, and J. M. Beckers, 2005：”Reconstruction of incomplete oceanographic data sets using empirical orthogonal functions: application to the Adriatic Sea surface temperature”, Ocean Modelling, 9, 325-346.

Barrick, D. E., M. W. Evans, B. L. Weber, 1977：”Ocean Surface Currents Mapped by Radar”, Science, 198, 138–144.

Beckers, J. M., and M. Rixen, 2003：”EOF Calculations and Data Filling from Incomplete Oceanographic Datasets*”, Journal of Atmospheric and Oceanic Technology, 20, 1839-1856.

Bendat, Julius S., and Allan G. Piersol, 1971：“Random data: analysis and measurement procedures”, John Wiley & Sons, New York.

Boyd, Janice D., Eileen P. Kennelly, and Pavel Pistek, 1994：”Estimation of EOF expansion coefficients from incomplete data”, Deep-Sea Research Part I: Oceanographic Research Papers, 41.10, 1479-1488.