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研究生： 虞凱鈞
Kai-Chun Yu
論文名稱： 以小波及多元線性迴歸分析估算與驗證區域地下水位
Regional Groundwater Level Estimation and Validation using Wavelet and Multiple Linear Regression Techniques
指導教授： 吳瑞賢
Ray-Shyan Wu
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2020
畢業學年度： 108
語文別： 中文
論文頁數： 102
中文關鍵詞： 降雨 、地下水 、小波轉換 、多元線性迴歸
外文關鍵詞： rainfall, groundwater level, wavelet transform, multiple linear regression
相關次數： 點閱：18  下載：0 
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    • 因受到降雨時空分布不均及氣候變遷影響，水文不確定性相對提高，故如何有效利用及永續經營有限的水資源，便是非常重要的課題。本文將降雨及地下水水位進行小波分析後，藉由小波時頻能量、小波分解及小波相關分析彼此的關係，並依此關係透過多元線性迴歸來建立降雨及地下水水位的關係式，可了解因降雨所導致的地下水水位變動為何。透過小波分析，得到降雨與地下水的大致關為拆解出來的d4(第四段細節)、d5、d6、d7、d8、d9、d10及a10(第十段近似)波段。其中此區域的四個雨量站因為波段型態非常相似，因此可以使用平均雨量來代替四個不同雨量站資料。而迴歸分析時，則要跳脫一般對於降雨地下水水位的直覺認識，將不同頻率段資料各自看成一個不同的變數來進行迴歸，能夠更好的將結果貼近每個地下水水位的觀測資料。

    Due to the uneven spatial and temporal distribution of rainfall and the impact of the climate change, hydrological uncertainty has been increasing. Therefore, how to manage limited water resources effectively and sustainably is a crucial issue. This paper analyzes the relationship between rainfall and groundwater level through wavelet transform, wavelet decomposition and wavelet coherence. And then establishes the multiple linear regression between rainfall and groundwater level based on this relationship was established. Through wavelet analysis, the approximate relationship between rainfall and groundwater is identified, which are the disassembled d4 (fourth detail), d5, d6, d7, d8, d9, d10 and a10 (tenth approximate) bands. Among them, the four rainfall stations in this area present similar patterns, therefore the average rainfall was utilized to replace the dataset of four different rainfall stations. When it comes to regression analysis, we need to get rid of the general intuition about the relationship between rainfall and groundwater level. The data in different frequency bands as regarded as different variables for regression, the results show a better fit to the observation data of each groundwater level.

    摘要 I Abstract II 致謝 III 目錄 IV 圖目錄 VI 表目錄 XII 第一章 緒論 1 1.1 前言 1 1.2 研究動機與目的 1 1.3 本文架構 2 1.4 研究流程 3 第二章 文獻回顧 4 2.1 小波理論 4 2.2 迴歸分析 6 2.3 小波與迴歸分析用於水文系統之模型 9 第三章 研究區域與方法 13 3.1 研究區域 13 3.2 小波理論 20 3.2.1 小波轉換 20 3.2.2 小波拆解 22 3.2.3 交叉小波及小波相關 23 3.3 多元線性迴歸理論 24 第四章 結果與討論 25 4.1 小波分析 25 4.1.1 降雨與地下水水位測站基本小波分析 25 4.1.1.1 降雨測站基本小波分析 25 4.1.1.2 地下水水位測站基本小波分析 27 4.1.2 小波相關 32 4.1.2.1 降雨測站間小波相關 32 4.1.2.2 地下水水位測站間小波相關 35 4.1.2.3 平均雨量及地下水水位測站間小波相關 37 4.1.3 小波拆解與重組 40 4.2 多元迴歸 44 4.2.1 整段重組資料迴歸 44 4.2.2 分段資料迴歸 47 4.3 估算與驗證 51 4.3.1 估算結果 51 4.3.2 測站所使用係數 57 4.3.3 驗證結果 60 第五章 結論與建議 67 5.1 結論 67 5.2 建議 68 參考文獻 69 附錄 75

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