應用二維經驗模態分解及快速傅立葉轉換 於衛星影像推算海域地形之研究

Abstract

以船舶上的單束或多束聲納來測量海域地形水深的傳統方法，需要高成本、精密儀器設備及大量人力等缺點；衛星影像具有全面性及多資訊等優點，已被廣泛運用於各領域之研究，亦被本文引用來推估波長及海下的水深。本研究主要應用二維經驗模態分解方法分解衛星影像，擷取雜訊較少的波浪分解影像，再運行二維快速傅立葉轉換方法獲得空間頻譜，以決定衛星影像圖中波向及波長。由切割小影像所決定的波向，連續地推進切割小影像直至近岸，即可獲得波向線；若以衛星影像求得的波長及週期代入線性波浪理論的頻散關係式則可推估水深。 本研究選定宜蘭頭城海岸及屏東縣枋寮漁港海域兩處當為驗證本研究方法可行的基地。由本方法推算衛星影像的頭城海岸的波浪週期與實測值及模式計算之誤差僅為0.14秒與0.54秒，顯示本方法推算波長的正確性。另外本研究選擇頭城海岸8個剖面，檢驗本法所得在水深-6m至-12m的修正水深與實測值的均方根誤差的平均值為0.84m，而在枋寮海域的均方根誤差的平均值為1.23m。本文以理論評估出衛星影像的空間解析度會產生本法推估水深有約1m的誤差。在未來衛星影像的空間解析度提高下，本文方法可提供更精準的海域地形水深，就具有工程可行性。

Bathymetric estimation was traditionally obtained using single/multi-beam echo sounder on boats. However, taking time-consuming, requiring high cost and precise surveying instruments are disadvantages of bathymetric surveying. In recent years, satellite images that provide multi-information of large area have been commonly used in a wide range of researches, including the investigation on wave-length and wave directions. Those sub-images from one original satellite image are decomposed by bi-dimensional empirical mode decomposition (BEMD) and fast Fourier transform (FFT), to get spatial spectra where peak indicates the wave number and direction of primary waves. The track of wave directions from a sequence of sub-images forms a wave ray. The local water depth can be derived using dispersion relation of the linear wave theory from estimated wave-length and period of a sub-image. The Fangliao coast of Pingtung county and the Toucheng coast of northern Ilan county are chosen for examining the accuracy of the proposed method by the root mean squared error between the measured and calculated water depths. Eight selected beach profiles are chosen to have a mean RMSE of 0.84m for the Fangliao coast using corrected wavelengths and a mean RMSE of 1.23m for the Toucheng coast using originally obtained wavelengths. It is proven that 2-m spatial resolution of chosen satellite images can produce an error of about 1 m in depth estimation using the proposed method. When the spatial resolution of satellite images is promoted someday, the proposed method can offer concise bathymetry and is applicable for coastal planning.