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論文中文名稱:以連續機率分佈熵及克利金建構雨量站網 [以論文名稱查詢館藏系統]
論文英文名稱:Rainfall Network Design by Using Entropy with Probability Distribution Function and Kriging [以論文名稱查詢館藏系統]
院校名稱:臺北科技大學
學院名稱:工程學院
系所名稱:土木與防災研究所
中文姓名:陳茹蕙
英文姓名:Ru-Huei Chen
研究生學號:94428015
學位類別:碩士
語文別:中文
口試日期:2007-06-25
論文頁數:92
指導教授中文名:陳彥璋
指導教授英文名:Yen-Chang Chen
口試委員中文名:葉惠中;衛強
口試委員英文名:Hui-Chung Yeh;Chiang Wei
中文關鍵詞:連續機率分佈克利金法資訊熵雨量站網
英文關鍵詞:Probability Distribution FunctionOriginal KringingEntropyRainfall network
論文中文摘要:水文資訊為構成水資源規劃、水工結構物以及水利運轉之最基本要素。規劃良好的雨量站網可以提供代表該流域特性之精確且可靠的降雨資訊,影響雨量站網之設立通常包含地形、降雨型態、集水區特性、交通、人力及預算等因子,諸等因子將會影響到雨量站之位置與密度。過去雖投入大量人力、物力於集水區雨量站網設計之研究,但對於雨量站設站之位置以及所需設站的最小站數仍無法得到確切的答案。故有必要進一步研究集水區雨量設站之位置,以及可能反映該集水區之最少站數之問題。
本研究乃結合地理統計之克利金法以推估可能設站位置及其所能提供之降雨資訊,之後再藉由資訊熵以評估各測站之資訊量及不確定性,藉由此二方法之結合即可推估集水區飽和雨量站之數目及其位置。此法將可提供流域管理單位設置雨量站之依據,用以評估現有雨量站是否可提供所需之降雨資訊,若不足則需增站,若重複性太高則需減站,期望可用以評估或調整現有集水區之雨量站網。
論文英文摘要:Hydrological data are the basic ingredients for the planning, design and operation of water objects. A well designed hydrometeorological network can accurately represent and provide the information of rainfall in the catchment.
The proposed model is composed of kriging and entropy. The original kriging can be used to generate the rainfall data of the location that can be used to install rainfall station. Entropy based on probability can be used to measure uncertainty. In this study, the probability distribution functions will be introduced for fitting the statistical characteristics of the data of the raingage stations. By calculating the joint entropy and the transmitted information, the existing rain gage stations are prioritized. Therefore the maximum number of rainfall stations and the locations of the rainfall stations in the catchment can be obtained. In addition, the saturation of rainfall information can be used to establish or remove the rain gage stations.
論文目次:摘 要 i
ABSTRACT ii
誌 謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
1.1 研究背景 1
1.2 研究目的 2
1.3 研究方法 3
第二章 文獻回顧 5
2.1 熵之歷史發展 5
2.2 雨量站網之研究 6
第三章 克利金法(Kriging technique) 9
3.1 水文的定常性 9
3.1.1 嚴謹的定常性(Strict-Sense Stationarity, SSS) 9
3.1.2 廣義的定常性(Wide-Sense Stationarity) 11
3.2 資料空間統計結構分析 11
3.2.1 定常性假設與內在假設 11
3.2.2 變異圖和半變異模式 12
3.2.3 等向性和非等向性 14
3.3 最佳線性不偏估估計 14
3.3.1 一般克利金法(Ordinary Kriging) 15
3.3.2 簡單克利金法(Simple Kriging) 16
3.4 平均值具有空間變化趨勢的內差估計 17
3.4.1 平均值具空間變化趨勢的隨機變數 17
3.4.2 平均值具空間變化趨勢的最佳線性無偏估估計 17
第四章 訊息和熵 20
4.1 訊息理論 20
4.2 熵(Entropy)之理論 21
4.2.1 離散隨機變數之熵(Entropy of Discrete Random Variable) 21
4.2.2 連續隨機變數之熵(Entropy of Continuous Random Variables) 23
4.2.3 多變量隨機變數之熵(Entropy of Multivariate Random Variables) 26
4.3 常態轉換與檢定 29
4.3.1 常態分佈的轉換 29
4.3.2 統計假設檢定 29
第五章 雨量站網設計 33
5.1 設計架構 33
5.2 資料說明 38
5.3 程式結果說明 44
5.4 連續機率分佈熵以及離散機率分佈熵結果之比較 71
第六章 結論與建議 83
6.1 結論 83
6.2 建議 83
參考文獻 85
附錄:克利金法推估之影響範圍 90
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