應用不規則三角網計算水庫容量

Abstract

目前國內各大小水庫的蓄水容量調查與計算，大都採用橫斷面法，該法有以下的缺點：不能精確地計算支流端處或匯交處的庫容；橫斷面之間往往缺少獨立高程點，難以充分掌握庫底地形，即或能增測之，處理模式也難建立。

一般水庫的年平均淤積率約 1 %，國內大型水庫，蓄水容量調查的施測週期多為一年。除了測量的誤差外，橫斷面法計算庫容的模式誤差常超過 1 %，相對的淤積資訊或有參考價值，而絕對的確實庫容卻是不夠精準的。

隨著時空演變，水域內大量且均勻分布的獨立高程點測取，已不再是件困難的事。如何因應未來 DGPS 與測深儀結合後的大量資料所衍生的庫容計算問題，是本研究的探討重點。

水庫地形的數值地型模擬，由不規則測點所構成的不規則三角網佈滿水域，逐一計算各三角形小區域內的體積，累計之而可獲得水庫蓄水容量的計算模式，理論上是沒有爭議性的，但實際上卻有一些問題值得研究。

首先是如何應用電腦將這些眾多點位組網的效率問題。研發完成的 ICDC 演算法可以在幾乎線性時間內，有效率地解決處理這項耗時的工作。其次是應用個人電腦時的工作能量問題，透過"無限制點數的組網技術"，此一瓶頸也已突破。最後是應用不規則三角網計算庫容的計算模式的精度問題，理論上的誤差傳播計算式已然導出。藉由實體模型與數學模型模擬的試驗，當三角網的圖形因子達到 0.7 以上時，滿水位容量計算成果的精度已可達 1%以內。此外，並瞭解一些內插模式的應用，於提昇庫容計算成果精度上的效果。

三座水庫的實際測算例子顯示，組網效率與庫容計算這兩項問題已然順利解決。萬大水庫的成果誤差傳播分析顯示，未來 DGPS 的定位誤差在 30 公分以下時，中、高水位時的計算成果模式誤差將不超過 0.2 %。儘管如此，應用不規則三角網計算庫容的方式不是沒有缺點的。本研究彙整十項注意要點與因應對策，提供是項作業時的參考。

最後，指出六個與測量、計算、誤差評估模式相關的研究題材，是未來繼續努力的重點。

With the facilities and the efficiencies either in field work or in office work, cross-section method is a great favorite with surveyors in finding the capacity of a reservoir. Some of drawbacks existed in it, such as : lack of spot heights to depict the real topographic surface; hard to tackle them if they were observed; can not deal with the region which converged of two or more tributary streams, and even with the head of a tributary stream, that would lead the computed results to be of great error.

The average annual sedimentation rate of a reservoir is around 1 %. Beside the errors caused in field work, the accuracy of the computed capacity generally exceeds 1 % if cross-section method is adopted. Sedimentation information may relatively be available for reference. The real capacity of the reservoir is still of no accuracy.

Integration DGPS with bathymetry makes a great amount of spot heights acquisition easier. The surface modelling with these data may be viewed as a TIN model in terms of DTM. The spatial tessellation constructed from a TIN model could then be analyzed numerically. The accompanied problems are worth mentioning.

Because TIN construction is a time-consuming task, the first problem is how to deal with these data effeciently. The newly devised algorithm ICDC works well in nearly linear time complexity. Unlimited points are also allowed.

Next to it is how to compute the capacity in a proper way. By means of several model tests, the accuracy may reach to less than 1 % if the shape factor of TIN is larger than 0.7. Besides, some available interpolation models are also observed whether they can improve the capacity accuracy or not.

The study concluded with some accompanied disadvantages in TIN-based volume computation. Ten strategies are submitted for suggestions in such a work. Six future research topics about surveying, computation and error model evaluation are proposed.