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研究生:陳進發
研究生(外文):Jin-Fa Chen
論文名稱:未飽和層土壤水平衡模式解析及其應用之研究
論文名稱(外文):Analysis and Application of a Water Budget Model in the Unsaturated Zone
指導教授:李振誥李振誥引用關係
指導教授(外文):Cheng-Haw Lee
學位類別:博士
校院名稱:國立成功大學
系所名稱:資源工程學系碩博士班
學門:工程學門
學類:材料工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:91
語文別:中文
論文頁數:189
中文關鍵詞:未飽和層入滲地下水補注量水平衡模式
外文關鍵詞:unsaturated zonerechargeinfiltrationwater budget model
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  本文主要目的在考慮不同降雨延時、臨前水文條件、氣候條件、土壤水力條件狀態下,結合地表入滲逕流及未飽和層土壤排水模式,建立一未飽和層土壤水平衡解析之模式,進行未飽和層剖面因降雨導致之地表入滲、地表逕流、蒸發散及地下水補注之模擬與推估,並探討模式參數之敏感性分析與土壤有效飽和度之變異分析。首先,選定一試驗地點,進行小區域現地土壤剖面水分動態觀測。經由模式結合現地觀測資料進行模式驗證,並進行試驗地點因降雨對地表入滲、地表逕流、土壤蒸發散、地下水補注之比例長期推估。最後經由小區域水平衡解析及模式之驗證,擴展至大區域淺層土壤水平衡各分量之推估。

  小區域水平衡模式模擬選定本校資源系系館後方作為試驗地點,進行小區域之試驗地點進行土壤試驗及調查,推估試驗地點之飽和水力傳導係數、飽和體積含水量、殘餘體積含水量及土壤特性參數,配合試驗地點之日降雨量資料及相關氣象參數,進行試驗地點地表入滲量、地表逕流量、土壤蒸發散量及地下水補注量之推估。此地點之土壤剖面則依照不同深度進行土壤張力計之埋設,以進行土壤毛細壓力之動態觀測,並結合理論模式與土壤毛細壓力動態觀測結果,進行模式之率定,以校正試驗地點之土壤相關參數。經模式率定過程後,結合校正後之土壤參數,進行試驗地點土壤水平衡各分量模式校正後之推估。而大區域淺層水平衡各分量之模擬與推估,則本文選定雲林地區作為研究區域案例分析,進行大區域未飽和層土壤水平衡分析,進而推求此之地下水補注量。

  參數敏感性分析結果顯示,土壤飽和水力傳導係數變動時,對模式推估之地表入滲及未飽和層垂向滲透能力之敏感性最高,其餘參數變異對土壤入滲能力及排水特性將產生影響,但敏感性較小。另外,土壤潛勢能蒸發散率之變異,對未飽和層土壤蒸發散量推估敏感性頗高,間接影響水流向下滲透之比例,乃是與土壤飽和水力傳導係數影響土壤向下滲透能力不同之處。

  關於土壤初始有效飽和度Se0變異分析部分,當土壤初始值Se0變異時,將對模式於模擬初期之推估結果產生差異性。土壤滲透性越差時,影響模式推估差異之初期時間越長。因此建議於模式推估時,將所有初始值變異推估產生之結果取其平均值,以推求試驗地點水平衡模式各分量。另外,以長期未飽和層淨流入量與淨流出量平衡觀念為出發點,顯示進行模式推估時,若將模式土壤初始飽和度定為與模式推估終止時間點上土壤之有效飽和度相等,則亦為一較合適之未飽和層土壤水平衡推估方法。

  本文小區域試驗地點模擬結果顯示,利用模式配合試驗地點土壤剖面毛細壓力觀測資料進行率定時,若將土壤特性參數l由實驗值0.44向上調整至0.73;土壤飽和進氣潛能ys由-290mm調整至-330mm;時,模式模擬之毛細壓力變化曲線與現地土壤毛細壓力觀測結果,將可達到最佳擬合之結果。同時,顯示未率定與率定後之結果,各水資源分量之配比均有所改變,其中以地下水補注率與土壤蒸發散比率之改變最為明顯。

  另外關於應用本模式於雲林大區域水平衡推估,地下水補注量推估結果顯示,各年平均地下水補注量介於2.68×108 m3/year至5.56×108 m3/year之間。換言之,雲林地區地下水年補注量介於2.68億噸至5.56億噸,七年平均之地下水補注量,經計算結果為4.15×108 m3/year,亦即4.15億噸。
  This dissertation established a water budget model to estimate the infiltration, runoff, evapotranspiration and recharge in unsaturated soil profiles. The proposed model considered the temporal and spatial variability including precipitation, duration of rainfall, meteorological conditions, antecedent moisture, and soil hydraulic properties. Sensitivity analysis of parameters and the variability of effective saturation in unsaturated soil were also discussed. Besides, at NCKU-RE study site, in-situ observations of soil pressure heads were obtained to validate the proposed model in conjunction with related soils and meteorological parameters in homogeneous unsaturated soil profiles. After the model validation and examination processed in homogeneous soil profiles in a small area, the suitable proposed model was employed to estimate the components of water budget in Yun-Lin plain in Taiwan as a case study, finally.

  At first, hydraulic parameters of soil grain size, porosity, related volumetric water content, soil water retention curve, hydraulic conductivity and related meteorological factors were investigated for the NCKU-RE study site. Meanwhile, field observations system of soil water pressure head was set up to collect the series data in different depths from ground surface in this area. Unvalidated and validated model analysis were both tested to estimate the infiltration, runoff, evapotranspiration and recharge in the small area. At last, the proposed model was used to analysis the large-scale water budget, furthering estimated the groundwater recharge in large-scale site, Yun-Lin plane in Taiwan, and compared with other researches.

  Second, the results of sensitivity analysis showed that the effect of saturated hydraulic conductivity on each components of water budget is the most significant. The other factors were less significant. However, the amount of evapotranspiration is significantly influenced by the potential evapotranspiration rate (qEP), and qEP indirectly affected the ratio of recharge during soil profile drainage. Moreover, although the sensitivity of pore size distribution is small, it affected some proportion of all the components of water budget model that is comparatively significant to other insignificant factors.

  Third, variability of initial effective saturation (Se0) analysis showed that the difference of estimation is more obvious, and the affection of duration is longer in initial stage while the permeability of soil is worse. To solve the uncertainty, the idea was suggested that when the model estimation proceeded, the average results of all different Se0 must to be calculated as the final results. Beside, for the viewpoint of long-term simulation when the input fluxes were equal to output fluxes in unsaturated zone, other idea was suggested that the unsaturated soil storage change was set to be equal to zero to solve the uncertainty.

  The simulation results for the NCKU-RE study site showed that the proposed model curve will be better matched with in-situ observation curve, when the pore size distribution l increased from 0.44 to 0.73, and the absolute value of air entry ys decreased from -290 mm to -330 mm. By comparison unvalidated results with validated results, the proportion of each component is changed, especially in the ratio of recharge and evapotranspiration over the precipitation.

  In addition, the proposed model was extended to estimate annual recharge average over the twenty sites in Yun-Lin plain area from 1991 through 1997. The ratio of the groundwater recharge to the precipitation varies from 0.30 to 0.39 for the study period with an average of 0.35. By multiplying the average precipitation area, the total amount of groundwater recharge Yun-Lin plain area varied between 2.68×108 m3/yr and 5.56×108 m3/yr in annually. The average of the groundwater recharge over the seven years in the Yun-Lin plain area is 4.15×108 m3/yr.
摘要 I
誌謝 V
目錄 VI
表目錄 IX
圖目錄 X
符號表 XIII

第一章 緒論 1
  1.1 研究動機 1
  1.2 研究方法 4
  1.3 研究架構 6

第二章 相關理論與文獻回顧 8
  2.1 基本概念 8
    2.1.1 孔隙率(porosity) 8
    2.1.2 土壤含水量(soil water content) 9
    2.1.3 毛細力(capillarity) 9
  2.2 土壤水分函數及相關文獻 10
  2.3 土壤飽和透水係數及相關文獻 16
    2.3.1 飽和水力傳導係數(saturated hydraulic conductivity, ks) 16
    2.3.2 雙環入滲試驗 17
    2.3.3 定水頭試驗 19
    2.3.4 變水頭試驗 20
    2.3.5 溶質傳輸法 21
    2.3.6 經驗公式 22
  2.4 未飽和土壤水流 23
    2.4.1 Darcy-Buckingham方程式 23
    2.4.2 理查方程式 (Richards' equation) 25
    2.4.3 未飽和土壤水力傳導係數k 28
  2.5 入滲理論及相關文獻 35
    2.5.1 恆定入滲(steady infiltration) 35
    2.5.2 非恆定入滲(unsteady infiltration) 37
      2.5.2.1 狄瑞曲邊界(Dirichlet's boundary condition, DBC) 37
      2.5.2.2 紐曼邊界(Neuman's boundary condition, NBC) 49
  2.6 降雨入滲及補注相關文獻 52
    2.6.1 入滲補注量推估相關文獻 52
    2.6.2 入滲補注過程相關文獻 55
  2.7 蒸發散相關文獻 56
    2.7.1 彭門-蒙地斯法(Penman-Montaith method) 57
    2.7.2 溫度估計法(temperature-based method) 59
    2.7.3 太陽輻射能法(radiation-based method) 60
    2.7.4 質量傳遞法(mass-transfer method) 62
    2.7.5水平衡法(water budget method) 62

第三章 未飽和層土壤水平衡模式之建立 64
  3.1 水文循環 64
    3.1.1 自然界水循環 64
    3.1.2 未飽和層土壤水平衡 67
  3.2 土壤水流及基本假設 68
  3.3 入滲及逕流模式 71
  3.4 蒸發散及補注模式 79
    3.4.1 極限解之推求 80
    3.4.2 蒸發散及地下水補注模式一般解 81
  3.5 水平衡模式建立及分析步驟 84
  3.6 參數敏感性分析 86
    3.6.1 土壤飽和水力透水係數ks 87
    3.6.2 土壤特性參數 88
    3.6.3 土壤飽和進氣潛能 89
    3.6.4 土壤有效孔隙率 90
    3.6.5潛勢能蒸發散率 90
    3.6.6 未飽和層土壤厚度 91
  3.7 土壤有效飽和度初始值Se0 分析 100
  3.8 本文模式與其他模式比較 104

第四章 研究案例之應用與討論 108
  4.1 前言 108
  4.2 案例一-小區域一維均質土壤剖面未飽和層水平衡分析 108
    4.2.1 氣象因子 110
    4.2.2土壤水力參數推求與張力計之校正 114
      4.2.2.1 土壤特性分析 115
      4.2.2.2 土壤水分函數調查與分析 115
      4.2.2.3 土壤飽和水力透水係數ks 推求 120
      4.2.2.4 土壤水分張力計之率定 122
      4.2.2.5 現地土壤剖面毛細壓力觀測結果 126
  4.3 未飽和層土壤水平衡分析結果初估 127
  4.4 模式驗證 136
    4.4.1 模式率定 136
    4.4.2 率定後未飽和層土壤水平衡之推估 138
  4.5 案例二-大區域一維土壤剖面未飽和層水平衡分析 143
    4.5.1 研究區概述 143
    4.5.2 研究區參數之推求 144
      4.5.2.1 氣象參數 144
      4.5.2.2 土壤水力參數 146
    4.5.3 雲林地區未飽和層土壤水平衡分析結果 146

第五章 結論與建議 153
  5.1 結論 153
    5.1.1 模式分析之結論 153
    5.1.2 小區域研究之結論 155
    5.1.3 雲林地區研究之結論 156
  5.2 建議 157

附錄A 159
附錄B 167
參考文獻 174
自述 187


表目錄
表2.1 土壤持水曲線模式 15
表2.2 彰雲地區及濁水溪沖積扇地下水補注量推估相關文獻 54
表3.1 未飽和層土壤水平衡模式各分量函數式 84
表3.2 敏感性分析之各項輸入參數 87
表3.3 ks 變異時敏感性分析結果 92
表3.4 l 變異時敏感性分析結果 92
表3.5 ys 變異時敏感性分析結果 92
表3.6 qs-qr 變異時敏感性分析結果 93
表3.7 qEP 變異時敏感性分析結果 93
表3.8 dr 變異時敏感性分析結果 93
表3.9 三種不同土壤之標準水力特性參數表(Bras, 1990) 101
表3.10 Kim模式與本文模式迴歸所獲得之土壤水力參數 105
表3.11 Kim模式與本文模式推估之未飽和層各分量比較結果 106
表4.1 1992-2001年試驗地點主要氣象參數值 111
表4.1 1992-2001年試驗地點主要氣象參數值(續) 112
表4.2 試驗地點土壤特性參數平均值 119
表4.3 土壤飽和水力透水係數定水頭試驗結果 121
表4.4 不同土壤初始有效飽和度情況下模式推估結果 130
表4.4 不同土壤初始有效飽和度情況下模式推估結果(續1) 131
表4.4 不同土壤初始有效飽和度情況下模式推估結果(續2) 132
表4.5 模式率定前所有Se0變異下推估結果之各年度平均值 133
表4.6 模式率定前於DSe=0情況下模式推估之各年度結果 133
表4.7 率定後所有Se0變異下推估結果之各年度平均值 140
表4.8 率定後當DSe=0情況下模式推估之各年度結果 140
表4.9 試驗地點各鄉鎮採樣點年雨量統計資料 145
表4.10 試驗地點各採樣點之土壤試驗調查結果 147
表4.11 雲林地區各採樣點之分量推估年平均比例 150
表4.12 雲林地區各年平均地下水補注量、滲透深度及補注比 150



圖目錄
圖1.1 本文之研究流程架構圖 7
圖2.1 自土壤孔隙中移去水分示意圖 10
圖2.2 典型S型土壤持水曲線圖 12
圖2.3 土壤雙環試驗示意圖 18
圖2.4 定水頭試驗示意圖 19
圖2.5 變水頭試驗示意圖 20
圖2.6 示蹤劑試驗求飽和水力傳導係數示意圖(Yeh et al., 2000) 21
圖2.7 未飽和土壤水流試驗裝置示意圖 25
圖2.8 連續方程式單元體示意圖 27
圖2.9 土壤孔隙組頻率與相應流量分布圖 33
圖2.10 恆定入滲曲線圖 37
圖2.11 地表入滲率與累積入滲量隨時間變化關係圖 39
圖2.12 狄瑞曲邊界情況下砂土及砂質黏土入滲濕潤鋒面剖面圖 40
圖2.13 Green and Ampt's 入滲示意圖 44
圖2.14 紐曼邊界條件下入滲及積水時間式意圖 51
圖3.1 水文循環示意圖(摘自李光敦,2002) 65
圖3.2 未飽和層土壤水平衡示意圖 68
圖3.3 (a)實際降雨及(b)模式降雨示意圖 72
圖3.4 不同初始有效飽和度下入滲曲線比較圖 75
圖3.5 不同土壤型態入滲曲線比較圖 75
圖3.6 雨水供給量與土壤滲透容量關係圖(Palange et al., 1999) 78
圖3.7 實際情況下單一降雨事件土壤入滲示意圖(Palange et al., 1999) 78
圖3.8 兩極限解之個別有效飽和度對時間變化關係圖 82
圖3.9 未飽和層土壤水平衡脈衝模型 86
圖3.10 ks 變異時未飽和層各分量變異關係圖 94
圖3.11 l 變異時未飽和層各分量變異關係圖 95
圖3.12 ys 變異時未飽和層各分量變異關係圖 96
圖3.13 qs-qr 變異時未飽和層各分量變異關係圖 97
圖3.14 qEP 變異時未飽和層各分量變異關係圖 98
圖3.15 dr 變異時未飽和層各分量變異關係圖 99
圖3.16 砂質土壤於Se0 值變異情況下土壤有效飽和度變化曲線圖 102
圖3.17 壤土質土壤於Se0 值變異情況下土壤有效飽和度變化曲線圖 103
圖3.18 黏土質土壤於Se0 值變異情況下土壤有效飽和度變化曲線圖 103
圖3.19 Kim模式與本文模式於砂質與坋質壤土有效飽和度曲線比較圖 107
圖4.1 (a)成功大學資源系場址照片;(b)場址水分張力計埋設示意圖 109
圖4.2 試驗地點年平均降雨量分布圖 113
圖4.3 試驗地點潛勢能蒸發散率qEP 值分布圖 113
圖4.4 試驗地點降雨延時統計分布圖 114
圖4.5 試驗地點未飽和層土壤剖面圖 116
圖4.6 (a) 距地表深度0~30公分粒徑分析圖 116
圖4.6 (b) 距地表深度30~60公分粒徑分析圖 117
圖4.6 (c) 距地表深度60~90公分粒徑分析圖 117
圖4.6 (d) 距地表深度90~120公分粒徑分析圖 118
圖4.6 (e) 距地表深度120~150公分粒徑分析圖 118
圖4.7 壓力鍋實驗裝置圖 119
圖4.8 試驗地點第一組試體土壤持水曲線與迴歸結果關係圖 120
圖4.9 雙環入滲曲線圖 122
圖4.10 電子式張力計率定裝置圖 124
圖4.11 自記式電子張力計紀錄器 124
圖4.12 電子式張力計校正曲線 125
圖4.13 試驗地點不同深度之土壤水分張力計變化曲線圖 126
圖4.14 試驗地點之土壤於Se0 值變異時土壤有效飽和度變化曲線圖 127
圖4.15 率定前所有Se0變異下平均推估結果之各年度分量分布圖 134
圖4.16 率定前DSe=0情況下推估結果之各年度分量分布圖 135
圖4.17 未率定前理論模式模擬與現地土壤毛細壓力觀測資料比較圖 137
圖4.18 率定後理論模式模擬與現地土壤毛細壓力觀測資料比較圖 138
圖4.19 率定後所有Se0變異下平均推估結果之各年度分量分布圖 141
圖4.20 率定後在DSe=0情況下推估結果之各年度分量分布圖 142
圖4.21 研究區域概況及採樣點分布圖 144
圖4.22 雲林地區潛勢能蒸發散率統計月平均分布圖 146
圖4.23 雲林地區各採樣點之未飽和層分量推估比例年平均分布結果 151
圖4.24 雲林地區水平衡各分量年平均分布圖 152
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