臺灣博碩士論文加值系統

設計良好的雨量站網可提供精確且可靠的雨量資料，以作為水資源工程之規劃及設計。本研究引入訊息熵理論並評估多種站網設計方法中與本研究較相關的五種站網設計方法之優劣及其適合性，以決定淡水河流域內包括37個雨量站之站網設計方法。
研究中選取淡水河流域連續時雨量之颱風資料加以分析。在建立雨量站網時，應優先考慮研究區域內降雨在空間分佈之趨勢。因此研究中首先求得掌握研究區域平均降雨變異之二維趨勢，再將此變化趨勢予以移除使得研究區域可視為一定常性之隨機變域。此時整個區域中每個測站之熵值皆會相同，即可以利用聯合熵之概念在研究區域內加以選站。聯合熵值越大相對地共同資訊量越小，即選取的測站所含之不確定性越大且越具代表性。因此本研究站網的評估標準為每一階段之選站皆以該階段中所求得之聯合熵最大為原則進行區域中的加站。計算結果可發現以六個基本站為基礎逐次加站時，會先加入不確定性較大即位於四周降雨特性較難掌握，變異較大的測站。再利用所選取測站之聯合熵值和整個研究區域內所有測站之聯合熵值的比值以評估站數的多寡。
最後，比較以最大聯合熵、傳統克利金和全域克利金三種方法對站網設計之影響。結果可發現以最大聯合熵值法和傳統克利金法之選站順序皆是由研究區域四周降雨變異較大的測站優先
選入，其次再考慮區域內之測站。但傳統克利金法所選出的測站無法代表整個區域之降雨變化。因其只考慮單站的克利金變異數，所以選擇的測站無法代表整個研究區域之降雨變化。而利用全域克利金變異數加以選站時，可考慮區域內每個網格之降雨變異，如此所選出的測站可代表整個區域之降雨變化情形。因此，本研究評估站網設計的方法以全域克利金變異數為最佳。

An effective raingauge network capable of providing reliable and accurate rainfall records is essential for flood control and water resources planning and design. In order to evaluate the effectiveness of an existing raingauge network, we conducted a thorough investigation of network design algorithms, including the maximum kriging variance approach, the minimum global kriging variance approach, and the maximum joint entropy approach.
Hourly rainfall data collected by a flood-control-oriented network of 37 raingauges in Tanshui River watershed was used for this study. We first removed the spatial trend of average rainfall using a second order polynomial model. The residuals were then modeled as a stationary random field with a constant entropy at all spatial locations. The existing raingauges were prioritized based on the effectiveness of the raingauge network.
The maximum kriging approach and the maximum joint entropy approach of raingauge network evaluation yield similar results. A drawback of these two approaches is that they focus on increasing the joint entropy or reducing the average kriging variance of a raingauge subset, and fail to consider the joint entropy or average kriging variance of the whole study area. We conclude that the minimum global kriging variance approach is superior to other approaches with regard to minimization of global kriging variance.

第一章 緒論 1
第二章 文獻回顧 3
第一節 熵之歷史發展 3
第二節 雨量站網之研究4
第三章 訊息熵之理論 6
第一節 訊息理論 6
第二節 熵之理論 7
（一)離機隨機變數之熵 7
1.邊際熵 7
2.聯合熵 8
3.條件熵 9
4.可轉移資訊 10
（二)連續隨機變數之熵 11
1.定義 11
2.三種連續特殊分佈的熵 12
（三)多變量隨機變數之熵 14
1.離散隨機變數14
2.連續隨機變數 17
第四章 站網設計評估方法之檢討 19
第一節 區域平均降雨變異數分析 19
第二節 水文不確定性之量測 29
第三節 利用熵計算雨量站網 34
第四節 以熵為基礎評估水質監測站網 37
第五節 區域化變數理論與隨機變域模擬在雨量站網
設計之研究 40
第五章 監測站網設計概念 44
第六章 淡水河流域雨量站網評估 49
第一節 淡水河流域概況49
第二節 資料分析 50
第三節 雨量站網設計流程 50
第四節 雨量站網的評估與分析 55
（一）最大聯合熵值法 55
（二）傳統式克利金變異數 62
（三）比較最大聯合熵值法與傳統克利金法 62
第七章 結論與建議 65

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