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研究生： 陳亭如
Chen, Ting-Ju
論文名稱： 應用分量迴歸建立懸浮載輸砂量機率分佈
Probabilistic estimation of suspended sediment load using quantile regression
指導教授： 蕭政宗
Shiau, Jenq-Tzong
學位類別： 碩士
Master
系所名稱： 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年： 2014
畢業學年度： 102
語文別： 中文
論文頁數： 69
中文關鍵詞： 輸砂量推估 、分量迴歸 、率定曲線 、機率分佈
外文關鍵詞： Estimation of suspended sediment, Rating curve, Quantile regression, Probability distribution
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    • 台灣位於歐亞板塊交界處，平均地勢陡峭且地質活動頻繁，每逢夏季颱風時節，強大豪雨易造成土石崩塌災害，使得河川輸砂量增加。河川輸砂量是水資源規劃與管理重要數據之一，因其會影響公共給水的淨化處理、水庫的泥沙淤積、河床的沖刷或淤積等。現行對於河川懸浮載 (suspended sediment load) 的推估多半利用有限的流量與懸浮載濃度觀測值建立率定曲線 (rating curve) ，以推估無施測之懸浮載值。由於產生懸浮載的成因眾多，只利用流量來推估無法避免流量與懸浮載間的關係呈現散佈的情況，而率定曲線推估值亦無法了解推估值的不確定性，因此以機率方式推估河川懸浮載為本文主要的研究目的。
    本文首先以分量迴歸 (quantile regression) 建立日平均流量與懸浮載輸砂量間不同分量之迴歸線，其次建立不同流量之懸浮載輸砂量累積機率函數 (cumulative distribution function, CDF)，進而轉換為懸浮載輸砂量機率質量函數 (probability mass function, PMF)，即可利用摺積定理推估年懸浮載輸砂量機率分佈，及推估其平均值、眾數及中位數等統計量的中央趨向值。
    本研究選用台灣地區北、中、南、東四個區域之蘭陽大橋站、桶頭站、荖濃站、仁壽橋站至少50年之日平均流量和懸浮載輸砂量觀測資料，除建立率定曲線外，並以分量迴歸推估日懸浮載輸砂量之機率分佈。結果顯示分量迴歸推估之懸浮載輸砂量中位數推估值平均絕對誤差最小，且利用同樣方法推估年懸浮載輸砂量及年懸浮載機率分佈及其三種不同統計量，若欲以一值代表懸浮載輸砂量，本研究建議以分量迴歸推估之懸浮載輸砂量中位數之推估值代表最佳，因此以本研究所建議之分量迴歸模式較率定曲線模式能提供更詳細的資訊於水資源規劃。

    Inevitable scatter existed between suspended sediment discharge is caused by variation in sediment supply. However, The sediment rating curve only describes the average relation between streamflow and suspended sediment. This study aims to construct a probabilistic framework for estimation of annual suspended sediment loads. Firstly, quantile regression is employed to establish the nonlinear relationship between measured data for various quantiles. The results of various quantiles are integrated into a sediment conditional probability distribution function for a given streamflow. The obtain conditional distribution functions of different streamflow are used in this study to estimate annual suspended sediment loads in terms of probabilistic description by convolution theorem. The stations of Lan-Yang bridge, Tung-Tou, Lao-Nung and Jen-Shou bridge are selected in this study. The results show that the proposed approach offers more information than the traditional sediment rating curve for annual sediment estimation.

    摘要 I Extended Abstract III 致謝 XI 目錄 XII 表目錄 XIV 圖目錄 XV 第一章 緒論 1 1-1 研究動機 1 1-2 研究目的 2 1-3 文獻回顧 3 1-4 論文架構 8 第二章 研究方法 10 2-1 輸砂量率定曲線 10 2-1-1 輸砂量率定曲線模式 10 2-1-2 懸浮載輸砂量之推估 11 2-2 分量迴歸 12 2-3 懸浮載輸砂量機率分佈之建立 14 2-4 推求不同統計量之懸浮載輸砂量 19 第三章 研究區域與資料 21 3-1 測站概述 21 3-2 流量與懸浮載輸砂量特性 23 第四章 結果與討論 28 4-1 輸砂量率定曲線演算結果 28 4-1-1輸砂量率定曲線模式 28 4-1-2 率定曲線推估日懸浮載輸砂量之誤差 30 4-2 懸浮載輸砂量分量迴歸模式 35 4-3 懸浮載輸砂量機率分佈 37 4-3-1 日懸浮載輸砂量機率分佈 37 4-3-2 年懸浮載輸砂量機率分佈 42 4-4 輸砂量率定曲線和分量迴歸之年推估值比較 47 4-5 討論 53 4-5-1 流量與率定曲線年懸浮載輸砂量推估值之關係 53 4-5-2 離群值之影響 54 第五章 結論與建議 56 5-1 結論 56 5-2 建議 57 參考文獻 59 附錄A-率定曲線與分量迴歸之年推估值 66

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