正模投影應用於有限深度範圍潮流分析之探討

Abstract

潮流為海洋中普遍存在的運動，其流場垂直結構可視為無限多組垂直流場結構(或稱垂直模態)之疊加，理論上可將其拆解為正壓(Barotropic)運動與斜壓(Baroclinic)運動，其所對應之垂直模態分別為正壓模與斜壓模，前者假設流場強度不隨深度改變，後者的海流強度隨深度改變。一般海流觀測皆侷限於有限的深度範圍，無法量測到整層水體的潮流運動，為獲取完整水層的資料，可用水文資料推斷垂直流場結構，再將有限深度量測的資料投影至未量測之深度，進而補足所需水層資料，係為廣泛使用於潮流觀測的正模分析方法。然此方法之適用性鮮少被有系統的探討，基於實際運用，本論文以模擬資料之方式探討在不同深度量測範圍、不同垂直流場結構總和及其伴隨之量測誤差下，對正模投影方法之影響。分析結果顯示，擴大量測範圍可顯著減少以正模投影所解析之誤差。而資料若僅涵蓋上層海域，由於小量測範圍不足以解析高模態結構，垂直流場結構之選取以正壓模與第一斜壓模之加總可達到較好的效果。而增加單點量測點可增加自由度，進一步使誤差降低，且可考量更高的模態，其位置設計於最高模的最底層節點處有較佳的解析結果。若忽略儀器所產生之系統誤差，觀測所伴隨之隨機誤差會使解析結果的誤差增加，對高模態的影響尤其明顯，此結果可能與高模態運動與隨機誤差之量級相當所致。 而實測資料僅涵蓋上層水層，正模投影所選取的模態以正壓模與第一斜壓模時有較佳的解析結果，若考量更高的模態，分析結果與實際情況不符，此與模擬分析之結果一致。

Tidal currents are ubiquitous motions in the ocean. The vertical structure of tidal currents can be regarded as the manifestation of infinite vertical modes. Theoretically, the vertical structure of tidal currents can be identified as the combination of barotropic modes and baroclinic modes. The barotropic mode is assumed that the current magnitude is homogeneous in full depth. The baroclinic mode is assumed that the current magnitude is function of depth. The current measurement usually covers partly water column. Consequently, the full-depth measurement of tidal current is usually unavailable. To complete the measurement lack, the full-depth tidal currents could be obtained using the vertical tidal current structures inferred from the full-depth density profile. The tidal current measured in partly water column can be projected to full-depth measurement according to the vertical tidal current structure. The method is well known as normal mode projection and is extensively applied. However, the performance of the method was rarely identified. In this thesis, using the simulation data, the impact to the method due to (1) different measurement of depth range, (2) different vertical modal structure and (3) the measurement error was analyzed. The analysis revealed that the larger the measurement depth range was, the less the error was produced. If the simulated data is limited in the upper column, the normal mode projection revealed better performance when the barotropic mode and 1st baroclinic mode were only considered in the modal structure. That is because the limited measurement could not resolve the higher mode structure. If one extra measurement below the upper column measurement was added, the higher mode structure can be well-resolved and consequently the error was lowered. The best result presented when the extra measurement was located at the lowest nodal point of the highest mode. The random error of measurement led to the error of normal mode method as well. This kind of error is more conspicuous when the higher mode was used. It is because the order of measurement error was generally close to the magnitude of higher mode structure. The field measurement taken only upper column were used to validate our results from simulation data. The normal mode method shown better performance when the barotropic mode and 1st baroclinic mode were considered. The result coincided with the prediction from the simulation test.