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In monitoring ocean current by HF radar under different circumstances, we need various kinds of data analysis for obtaining a better estimation of the current field. This article is intended to summar...ize and describe several fundamental ideas and algorithms for interpolating and estimating the current field based on data of limited accuracy. In particular, harmonic interpolation is stressed as a simple and useful method for stable estimation. It is shown that harmonic interpolation of two-dimensional flow field has an intriguing meaning from a viewpoint of fluid dynamics. That is, harmonic interpolation minimizes the sum of the squared divergence and vorticity of the current field. Similarly biharmonic interpolation minimizes the sum of the squared gradients of divergence and vorticity. Discussion is given also for the over-determined situation provided by more than a couple of HF radar, In that case, reliability of the resulting current vector can be estimated as well. In addition a general procedure called the least square method with harmonic relaxtion is presented which not only makes a full use of the information available, but also adapts the estimation to surrounding values. Finally a scheme is proposed to estimate the current field even for quite limited a number of data under some assumptions of smooth current field.続きを見る
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