• Title/Summary/Keyword: Lagrange interpolation

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Time-series Analysis of Seawater Temperature in the Garolim Bay, the West Coast of Korea (서해 가로림만 수온의 시계열 분석)

  • Yang, Joon-Yong;Cho, Sunghee;Lee, Joon-Soo;Han, Changhoon;Heo, Seung
    • Journal of Environmental Science International
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    • v.30 no.7
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    • pp.585-595
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    • 2021
  • We used seawater temperature data, measured in the Garolim Bay, to analyze temperature variation on an hourly and daily basis. Lagrange's interpolation using before and after data was applied to restore nonconsecutive missing temperature data. The estimated error of the data restoration was 0.11℃. Spectral analyses of seawater temperature showed significant periodicities of approximately 12.4 h (semidiurnal tide) and 15.0 d (long-period tide), which is close to those of M2 and Mf partial tides. Variation in seawater temperature was correlated more with tidal height than with air temperature around the Garolim Bay. In June and December, when the seawater temperature difference between the inside and outside of the Garolim Bay was very large, the periodicities of 12.4 h and 15.0 d were highly prominent. These results indicate that the exchange of seawater between the inside and outside of the Garolim Bay induced variations in seawater temperature owing to tide. Understanding temperature variation because of tide helps to prevent abnormal mortality of cultured fish and to predict seawater temperature in the Garolim Bay.

Comparative Studies of Methods for Continuation and Derivatives of Potential Fields (포텐셜장(場)의 상하향연속(上下向連續) 및 미분법(微分法)에 대(對)한 비교연구(比較硏究))

  • Kwon, Byung Doo
    • Economic and Environmental Geology
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    • v.14 no.2
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    • pp.93-102
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    • 1981
  • Studies of model potential fields continued upward and downward show differences depending on the method of continuation. Beginning with a magnetic field computed over a buried vertical cylinder, the field was continued to various levels by a method introduced by Henderson (Lagrangian interpolation) and by a spectral method (frequency domain analysis). Resultant fields show (1) no significant differences in upward continued values, (2) in downward continuation, accurate values are obtained with the spectral method over the central part of the anomaly, and (3) accurate values are obtained with Henderson's method on the flanks of the anomaly, while oscillations usually characterize the spectral method in this region. Essentially the same observations are made for derivative calculations. Field oscillations are empirically predicted at levels continued to approximately two-thirds of the depth of the source. Our spectral computer program output yields marked oscillations at one-half of the depth of the source. Henderson's method shows no oscillations at this depth and only minor oscillations at the top of the body (some negative values appear on the flanks of the anomaly). The Henderson output is a smooth field even if continued below the top of the body. These results suggest that the presence of oscillations cannot be used to identify the top of a buried source without careful consideration of the method used to continue the field. Use of the derivative to outline and isolate anomalies must similarly include consideration of the method of calculation.

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