利用希伯特-黃轉換於淹水模擬之地形數據處理

Abstract

由於以往所使用的水利計算程式無法處理複雜的地形與建物，究其原因為其數值計算無法容忍劇烈的地形變化而造成發散。因此以往進行模擬時，選擇忽略複雜地形與建物，僅輸入大尺度、地形變化緩和的地形圖處理之，但這不免有失真之虞。近年之測量技術已有大幅進展，能利用航測影像或是衛星遙測對包含建物的都市地形或有村落群聚的鄉村地形作精確的量測，故水利技術也需因應測量技術的進展而與日俱進。 考慮到希伯特－黃轉換可對高低變化劇烈的曲線，按照其平滑度而層層剝離之，進而得到數個內含物理意義的內建模態函數，故可將原始複雜地形按粗糙度逐步提高，以取得計算容忍度和地形複雜程度的平衡點。然而受到台灣的地理環境與氣候條件的影響，當土地利用不當及排水系統不良時，很容易發生淹水災害，因此本研究選擇淹水模擬作為觀察是否能取得淹水模式與地形複雜程度之平衡點的目 標。 本研究利用希伯特－黃處理之二維鄉村和都市地形輸入水平二維水動力計算模式，以取得模式計算容忍度和地形複雜程度的平衡點，進行淹水境況模擬。計算結果顯示大水瞬間從模擬區的上游，依崎嶇地形向下游各處蔓延，能將位於低窪地區的凸起物或地形慢慢淹沒，而當大水退去時，又逐漸顯露出來。計算區域內的水深及流速分佈結果，與目前淹水模式輸入的簡化地形之模擬結果相較之下，確實較為貼近實際的淹水過程。 本研究是提出解決複雜地形與水利計算模式容忍度所產生的問題之改革性作法，應可提供往後進行水理分析計算改進的參考。

Since shallow water computation can not tolerate rapid terrain variation without divergence, the conventional hydrodynamic simulation can not handle problems with complicate terrain and buildings. Therefore, only large scaled, mild variation terrain is considered in conventional hydrodynamic simulation. However, due to the fact that survey technology has improved a lot recently, both urban and suburban terrains can be measured accurately either by aircraft or satellite, hydrodynamic simulation should improve accordingly. Because Hilbert-Huang Transform(HHT)can follow the smoothness of a rapidly varied curve to obtain intrinsic model functions layer by layer, we therefore can use HHT to handle complicated terrain data according to its roughness and hopefully to achieve the balance point of computation model tolerance and terrain complication degree. Under the constraint of Taiwan’s terrain and climate, inappropriate land usage and drainage system are easy to result in flood. Hence this research aims on the balance point of computation model tolerance and terrain complicated degree by observing the result of flood inundation simulation. The present study just applies the aforementioned HHT to handle urban and suburban terrain data and uses HHM to carry out the flood inundation simulation in order to achieve the balance point of computation model tolerance and terrain complicated degree. Comparing the simulation result of the present study to that of the conventional flood inundation simulation without complicated terrain the present study is indeed realistic. The present study provides a revolutionary measure to solve the problem induced by urban and suburban terrain complication degree and computation model tolerance of hydrodynamic simulation. It can serve as reference for future improvement of hydrodynamic simulation.