海洋水深探測不論在船隻航行、水域經營或是海洋生態研究上都扮演了一個重要的角色。隨著衛星科技的進步，被動式的衛星水深探測法(SDB, Satellite Derived Bathymetry)漸漸取代船載回波測深儀或空載光達等主動式水深遙測方法，運用衛星影像大範圍大尺度的調查可有效的改善主動式遙測法因成本高昂、耗時費力且易受到氣候所影響的缺點，而傳統船載回波測深更因地形船載回波測深航行安全性而導致近岸淺海水深資料難以取得。過去利用光學衛星所進行的水深反演演算法大多是建立於比爾─朗伯定律上的物理法則及經驗法則，例如比率演算法(ratio algorithm)、查表法(LUT, Look-Up Table)和透過類神經網路的經驗學習法，不過這些方法皆未考慮海床底質的組成複雜，而是將各個像素都視為只含有單一物質的純像素(pure pixel)。
由於衛星影像的空間解析度，影像中像素大多包含多種不同底質，而成為混合像素(mixed pixel)。本研究結合光譜解混(spectral unmixing)的技術與比爾─朗伯定律，由幾何的角度探討水深對混合像素光譜的影響。光譜解混主要利用線性模型(linear model)，其假設一個像素的光譜是所包含純物質光譜的線性混合，故在多維度空間中該像素皆會位於以純物質為頂點的凸多面體之中。若考慮光譜衰減與水深呈指數相關，又因各光譜波段的衰減係數皆不同且獨立，此多面體將隨水深增加而旋轉並縮小。本研究期望能透過結合光譜解混及比爾─朗伯定律提出新的近岸淺海水深測量演算法，以提高水深估計的準確度，並同時估計棲地底質物質光譜及其含量分布，此外，光譜解混技術使此演算法在較低空間解析度的衛星影像中也可進行水深估算。本研究經由4個模擬實驗觀察此理論在不同條件下的可行性，經由實驗可知道此方法須要有足夠多的像素且各物質皆有含量0.9的高純度像素且分布在水深近乎於0的區域才能得到良好的水深估算。

Bathymetry estimation plays an essential role in navigation, area management, and marine ecological research. With the advancement of satellite technology, passive satellite derived bathymetry (SDB) gradually replaced active bathymetry methods such as shipborne echo sounders or airborne LiDAR. Large-scale surveys by satellite image can effectively improve the disadvantages of active telemetry including high cost, time-consuming, and susceptible to climate. Especially for traditional shipborne echo sounders, because of navigational safety, shallow water areas are often not accessible. Most of the bathymetry estimation performed by optical satellites were based on two kinds of methods, physical method and empirical method, based on Beer-Lambert Law, such as ratio algorithm, look-up table (LUT) and experience learning method. However, these methods do not consider the mixture of the bottom material on the sea bottom, but treat each pixel as a pure pixel containing only a single endmember.
Since the spatial resolutions of satellite images are usually several meters, most pixels contain more than one materials and can be considered as mixed pixels. This study combines the technology of spectral unmixing and Beer-Lambert Law to explore the relationship of radiance spectra and water depth from geometry point of view. The linear mixture model has been widely used for remote sensing and it assumes that the spectrum of each pixel is a linear combination of pure endmembers, so it is located inside a convex polyhedron with vertices of endmembers in multi-dimension. Based on Beer-Lambert Law, spectral extinction is exponentially related to the water depth, and the extinction coefficient of the spectral bands are different and independent, the polyhedron will rotate and shrink with the increasing of water depth. This research proposes a new bathymetry estimation algorithm by combining spectral unmixing and Beer-Lambert law to not only improve the accuracy of coastal bathymetric mapping, but also estimate the spectral signatures of endmembers and their abundances on the seabed. In addition, the spectral unmixing technology enables this algorithm to estimate the depth of water in satellite images with lower spatial resolution. This study observes the feasibility of this theory under different conditions through four simulations. The experimental results showed that this algorithm requires enough pixels with purity level greater than 0.9 and evenly distributed close to water surface to reach good estimation in water depth.

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