本研究的目的是以前人所發展出來的有限解析法(Finite-Analytic Method)一維非飽和層水流數值模式為基礎架構，進一步發展未飽和層水流及熱流模式，來計算裸地土壤與大氣介面的水分與熱通量，及土壤含水量與溫度在垂向的分佈。通量的推估愈正確，愈可以改進有關微氣象的預測及地下水補注量的推估。
本研究包括五項主要內容：(a)依據陳主惠(1995)的研究，提出水分與熱流的方程式，改進在蒸發時熱通量在地表的邊界條件。(b)利用有限解析法數值模式以有效的計算高度非線性問題，尤其在土壤及大氣條件劇烈變化的情形。(c)考慮溫度對壓力水頭及水力傳導係數的影響，並利用Hopmans and Dane(1985)的實驗結果來計算壓力水頭與比水容積（specific capacity）對溫度的係數。(d)利用de Vries(1975)提出以含水量、石英及黏土的體積百分比函數的方法，計算熱傳導係數及平均巨觀溫度梯度的改正係數。(e)比較有限解析法模擬結果與Jackson(1973)與Jackson et al.(1973)的地表能量平衡各分量，土壤含水量及土壤溫度垂向分佈等現場實驗資料的差異。
本研究結果顯示，土壤含水量與土壤溫度在白天太陽的照射下，於靠近地表處會有較大的梯度變化，在夜間則變化較為平緩，且地表的土壤含水量會有回升的現象。另外，水力傳導係數、地表粗糙長度及天空雲層的覆蓋度，都會對土壤水分及溫度的變化構成影響。其中，水力傳導係數決定土壤水分向上補充或向下移動的速率；地表粗糙長度決定風對地表蒸發所構成的影響；天空雲層覆蓋度則影響太陽輻射量照射到地表面的多寡。三者之中，以太陽照射到地表的輻射量多寡對模式影響最大。在數值模式方面，本研究所發展之有限解析法解一維非飽和層水力傳導與熱傳導數值模式已能反應裸土在溫度效應下含水量的變化趨勢，唯因仍欠缺更完整的現場實驗資料，故仍有待未來更完整的資料來進行更詳盡的驗證。

The purpose of this study is to develop a Finite-Analytic numerical model to calculate moisture and heat fluxes across the soil-atmosphere interface and the vertical distribution of soil moisture and temperature for the bare soil in the unsaturated zone. With more accurate flux estimates, micrometeorology related predictions are likely to be improved.
The study contains the following features: (a) It provides the equations for moisture and heat transfer following the works of Chen (1995), and reforms the heat flux at the surface boundary condition for evaporation . (b) It provides a Finite-Analytic Numerical Model for efficient solution of strongly non-linear problems for abrupt changes in atmosphere and soil conditions. (c) It accounts for the temperature effect in the metric head and hydraulic conductivity and uses the experimental results of Hopmans and Dane (1985) to calculate the temperature coefficient of the metric head and the water capacity. (d) It uses the method of de Vries (1975) to calculate the thermal conductivity and a correction factor for the average macroscopic temperature gradient, which are strongly affected by water content and the volumetric fraction of quartz and clay. (e) The result are test against field measurement, including surface energy-balance components, water content and soil temperature, which were presented in Jackson (1973) and Jackson et al. (1973).
According to the result, soil water content and soil temperature gradients are typically steeper at day than at night, especially for shallow depths. The moisture in the dry soil surface will tend to rewet during nighttime. Otherwise, hydraulic conductivity, soil surface roughness length, and sky cover will influence the varies of soil moisture and soil temperature. The hydraulic conductivity controls and regulates the water movement upward to the surface or downward to the groundwater table where the evaporation or infiltration occurs. The surface roughness length controls the value of mass transfer and sensible heat transfer coefficients, which affects the evaporation rate, latent heat fluxes, and sensible heat flux. The sky cover determines the quantity of solar energy, which can produce significant differences in water content, soil temperature and evaporation rate. The numerical model in this study shows a well result when compared to the field observations. Because the complete experimental data is deficient, so assuring whether the results obtained by this model are sufficiently realistic for any specific set of conditions, detailed measurements are necessary.

目錄
謝誌一
摘要二
ABSTRACT四
目錄六
表目錄八
圖目錄八
第一章 前 言1
1-1研究動機與目的1
1-2研究方法概述2
1-3前人研究3
第二章 未飽和層水力傳導與熱傳導數學模式的建立10
2-1物理特性描述10
2-2控制方程式的說明12
2-3模式架構23
第三章 溫度效應下的土壤水力特性及熱傳性質26
3-1溫度效應下水力特性曲線的決定26
3-2土壤體積熱容量30
3-3熱傳導係數30
3-4修正因子的探討36
3-5水蒸氣的壓力水頭擴散與溫度擴散37
第四章 地表上邊界的質量平衡與能量平衡38
4-1地表次動力層內的風速分佈38
4-2地表蒸發量39
4-3蒸發潛熱流率的探討42
4-4地表的可感熱流率43
4-5地表與大氣間的能量平衡44
4-6綜合討論48
第五章 模式驗證與參數敏感度分析50
5-1 資料來源50
5-2土壤參數估計與保水曲線分析51
5-3初始條件與邊界條件52
1.初始條件設定53
2.邊界條件的處理53
5-4模式驗證54
5-4-1驗證結果54
5-4-2結果討論55
5-5相關參數的敏感度分析57
5-5-1不同水力傳導係數的敏感度分析57
5-5-2不同地表粗糙長度的敏感度分析58
5-5-3不同天空雲層覆蓋比率的敏感度分析59
第六章 結論與建議60
6-1 研究結論60
6-2建議事項61
參考文獻62
表目錄
表3.1 土壤成分 、冰 、水及空氣的密度、體積熱容量
及熱傳導係數68
表3.2 不同土壤的臨界含水量、田間含水量及飽和含水量68
表5.1 保水曲線的相關係數項69
表5.2 模式使用的初始條件69
表5.3 輸入模式的大氣條件70
圖目錄
圖2.1 雲林縣烏塗仔民生國小站不同深度之土溫變化71
圖2.2 雲林縣烏塗仔民生國小站30公分深土壤張力與10 公分深
之土溫71
圖2.3 未飽和層土壤水力傳導與熱傳導裸土蒸發散模式計算流程圖
72
圖3.1 不同溫度所對應的保水曲線73
圖3.2 不同溫度的導水曲線73
圖3.3 空氣、水及水蒸氣的熱傳導度與溫度的關係曲線74
圖3.4 不同溫度下，土壤熱傳導係數與含水量的關係74
圖3.5 不同溫度下，水蒸氣的壓力水頭擴散度與含水量的關係75
圖3.6 不同溫度下，水蒸氣的溫度擴散度與含水量的關係75
圖4.1 水蒸氣在空氣中的擴散係數、水的粘滯度及空氣的熱擴散度
與溫度的關係圖76
圖4.2 SC數及PR數受溫度的影響76
圖4.3 ，不同風速的質量傳輸係數隨溫度的變化77
圖4.4 ，不同風速的質量傳輸係數隨溫度的變化77
圖4.5 ，不同風速的能量傳輸係數隨溫度的變化78
圖4.6 ，不同風速的能量傳輸係數隨溫度的變化78
圖4.7 ，不同風速的雷諾數隨溫度的變化79
圖4.8 ，不同風速的雷諾數隨溫度的變化79
圖5.1 JACKSON(1973)土壤含水量在不同深度下隨時間變化的原始
實驗資料80
圖5.2 1971年3月5日距地表50CM處氣溫隨時間的分佈80
圖5.3 1971年3月5日距地表50CM處蒸氣壓隨時間的分佈81
圖5.4 1971年3月5日距地表50CM處風速隨時間的分佈81
圖5.5 1971年3月5日地表的蒸發率與潛熱率隨時間的分佈情形
82
圖5.6 由相關資料及計算公式所推估的1971年3月5日的太陽輻
射量隨時間的變化82
圖5.7 由公式套配所得之保水曲線與導水曲線83
圖5.8 深度0.25公分處土壤含水量模擬值與觀測值比較 （驗證段）
84
圖5.9 深度1.5公分處土壤含水量模擬值與觀測值比較（驗證段）
84
圖5.10 深度8公分處土壤含水量模擬值與觀測值比較（驗證段）
85
圖5.11 模擬之不同深度土壤溫度的時間序列圖85
圖5.12 模擬之不同時間的土壤含水量土壤剖面圖86
圖5.13 模擬之不同時間的土壤溫度土壤剖面圖86
圖5.14 蒸發量模擬值與觀測值比較圖87
圖5.15 潛熱流通量模擬值與觀測值比較圖87
圖5.16 可感熱流通量模擬值的時間序列88
圖5.17 地表輻射量模擬值的時間序列圖88
圖5.18 地表熱流通量模擬值的時間序列圖89
圖5.19 模擬之地表各能量變化之時間序列圖89
圖5.20 模擬之質量與能量傳輸係數的時間序列圖90
圖5.21 地表反射率模擬值的時間序列圖90
圖5.24 不同水力傳導度對深度0.25CM之含水量的影響92
圖5.25 不同水力傳導度對深度1.5CM之含水量的影響92
圖5.26 不同水力傳導度對深度8CM之含水量的影響93
圖5.27 不同水力傳導度對土壤溫度的影響93
圖5.28 不同水力傳導度對蒸發率的影響94
圖5.29 不同地表粗糙長度對地表(0CM)含水量的影響94
圖5.30 不同地表粗糙長度對地表溫度的影響95
圖5.31 不同地表粗糙長度的能量變化95
圖5.32 不同地表粗糙長度的質量與能量傳輸係數變化96
圖5.33 不同地表粗糙長度對蒸發率的影響96
圖5.34 不同雲層覆蓋度的地表含水量97
圖5.35 不同雲層覆蓋度在深度0.25CM的含水量97
圖5.36 不同雲層覆蓋度的地表溫度98
圖5.37 不同雲層覆蓋度的蒸發率98

1. 陶方策，「有限解析法在未飽和層水流應用之研究」，國立臺灣大學土木工程學研究所碩士論文，1995。
2. 張高達，「裸土蒸發參數檢定之相關研究」，國立臺灣大學土木工程學研究所碩士論文，1995。
3. 蕭偉松，「未飽和層入滲模擬問題之研究」，國立臺灣大學土木工程學研究所碩士論文，1996。
4. 許瑞峰，「地表與未飽和土層長期水文研究」，國立臺灣大學土木工程學研究所碩士論文，1997。
5. 涂根源，「長期水文模式推估地下水補注量之研究-以濁水溪沖積扇扇頂為例」，國立臺灣大學土木工程學研究 所碩士論文，1998。
6. Alfano, J. J., "A two-layer ground hydrology model interactive with an atmospheric general circulation model", ph. d. dissertation, University of Connecticut, 1981.
7. Brutsaert, W., "A theory for local evaporation (or heat transfer) from rough and smooth surfaces at ground level." Water Resource. Res., 11(4), pp.543-550, 1975.
8. Brutsaert, W., "Evaporation into the atmosphere." D. Reidel Co., 1982.
9. Camillo, P. J., R. J. Gurney, and T. J. Schmugge, A soil and atmospheric boundary layer model for evaportranspiration and soil moisture studies, Water Resource. Res., 19, pp.371-380, 1983.
10. Carslaw, J. S., and Jaeger, J. C., "Conduction of Heat in Solids.", Oxford Univ. Press(Clarendon), London and New York.
11. Chen, C. J. and H. C. Chen, "The finite analytic method." Vol. 1~6, Iowa Institute of Hydraulic Research, 1977.
12. Chen C. J. and H. C. Chen, Finite analytic numerical method for unsteady two-dimensional Navier-Stokes equation. J. Comput. Phys., 53(2), 209-226., 1984.
13. Chow, V. T., D. R. Maidment, and L. W. Mays, "Applied hydrology", McGraw-Hill, 1988.
14. Chen, C. H., "A model for the diurnal variation of simultaneous heat and water transport in a soil profile with an evaporating bare surface and hysteresis", Ph.D. dissertation, University of Cornell, 1995.
15. de Vries, D. A., "Simultaneous transfer of heat and moisture in porous medium." Eos, Trans. AGU, 39(5), pp.909-916, 1958.
16. de Vries, D. A., and Peck, A. J., On the cylindrical probe method of measuring thermal conductivity with special reference to soils. Aust. J. Phys. 11, 255-271; 409-423.
17. de Vries, D. A., Thermal properties of soils, In physics of plant environment, W. R. van Wijk (ed.).North Holland, Amsterdam,pp.210-235, 1963.
18. de Vries, D. A., Heat transfer in soils, In heat and mass transfer in the biosphere, edited by D. A.de Vries and N. H. Afgan, John Wiley and Sons, 5-28, 1975.
19. de Vries, D. A., and Philip, j. R., Soil heat flux, thermal conductivity, and the null alignment method, Soil Sci. Soc. Am. J.,50:12-18, 1986.
20. Eagleson, P. S., "Dynamic hydrology", McGraw-Hill, 1970.
21. Edlefson, N. E. and A. B. C. Anderson, Thermodynamics of soil moisture, Hilgardia, 15(2): 31-298, 1943.
22. Gardner, W.R., and F. J. Miklich, Unsaturated conductivity and diffusivity measurements by a constant flux method, Soil Sci., 93, 271-294, 1962
23. Hopmans, J. W., and J. H. Dane, Effect of temperature dependent hydraulic properties on soil water movement, Soil Sci. Soc. Am. J., 49: 51-58, 1985.
24. Hopmans, J.W., and J. H. Dane, Temperature dependence of soil hydraulics properties, Soil Sci. Soc. Am. J., 50:4-9, 1986a.
25. Hopmans, J.W., and J. H. Dane, Thermal conductivity of two porous media as a function of water content, temperature, and density, Soil Sci. 142(4): 187-195, 1986b.
26. Hillel, D., Fundamentals of Soil Physics, Academic press, 1980.
27. Idso, S. B., R. J. Reginato, R. D. Jackson, B. A. Kimball, and F. S. Nakayama, The three stages of drying of a field soil, Soil Sci. Soc. Am. J., 38: 831-837, 1974.
28. Idso, S. B., R. D. Jackson, R. J. Reginato, B. A. Kimball, and F. S. Nakayama, The dependence of bare soil albedo on soil water content, J. Am. Met.,14(1):109-113, 1975.
29. Jackson, R. D., Diurnal changes in soil water content during drying, p. 37-55. In R. R. Bruce et al. (ed.) Field soil water regime. Special Pub.5.Soil Sci. Soc. Amer. Proc., 1973.
30. Jackson, R. D., B. A. Kimball, R. J. Reginato, and F. S. Nakayama, Diurnal soil-water evaporation: Time-depth-flux patterns, Soil Sci. Soc. Am. J., 37: 505-509, 1973.
31. Jackson, R. D., R. J. Reginato, B. A. Kimball, and F. S. Nakayama, Diurnal soil-water evaporation: Comparison of measured and calculated soil-water fluxes, Soil Sci. Soc. Am. j., 38: 861-866, 1974.
32. Jackson, R. D., B. A. Kimball, R. J. Reginato, S. B. Idso, and F. S. Nakayama, Heat and water transfer in a natural soil environment. p.67-76. In D. A. de Vries and N. H. Afgan (ed.) Transfer processes in plant environment. Scripta Book Co., Washington, D. C., 1975.
33. Jackson, R. D., S. B. Idso, and R. J. Reginato, Calculation of evaporation rates during the transition from energy-limiting to soil-limiting phases using albedo data, Water Resource. Res., 12(1): 23-26, 1976.
34. Jury, W. A., and J. Letey, Jr., Water vapor movement in soil: Reconciliation of theory and experiment, Soil Sci Soc. Am. J., 43: 823-827, 1979.
35. Jury, W. A., W. R. Gardner, and W. H. Gardner, "Soil Physics", 15th, John Wiley and Sons, 1991.
36. Kimball, B. A., R. D. Jackson, R. J. Reginato, F. S. Nakayama, and S. B. Idso, Comparison of field-measured and calculated soil-heat fluxes, Soil Sci. Soc. Am. J., 40: 18-25, 1976a.
37. Kimball, B. A., R. D. Jackson, R. J. Reginato, F. S. Nakayama, and S. B. Idso, Soil heat flux determination: Temperature gradient method with computed thermal conductivities, Soil Sci. Soc. Am. J., 40:25-28, 1976b.
38. Klute, A., "Methods of Soil Analysis-Part 1 Physical and Mineralogical Methods ", 2th, 1986.
39. Kondo, J., N. Saigusa, and T. Sato, A parameterization of evaporation from bare soil surfaces, J., Appl. Meteor, 29, 385-389, 1990.
40. Kondo, J., and N. Saigusa, Modeling the evaporation from bare soil with a formula for vaporization in the soil pores, J., Meteor. Soc. Japan. Proc., 72(3), 413-421, 1990.
41. Kondo, J., N. Saigusa, and T. Sato, A model and experimental study of evaporation from bare soil surfaces, J., Appl. Meteor, 31, 304-312, 1992.
42. Lai, S. H. Tiedje and A. E. Erickson, In situ measurement of gas diffusion coefficient in soils, Soil Sci. Soc. Am. J., 40: 3-6, 1976
43. Mcqueen, I. S. and R. F. Miller, Approximating soil moisture characteristics from limited data: Empirical evidence and tentative model, Water Resource. Res., 10(3): 521-527, 1974.
44. Milly, P. C. D., and P. S. Eagleson, The couple transport of water and heat in a vertical soil column under atmospheric excitation, across the land Tech. Rep.258, R. M. Parsons Lab., Dept. of Civ. Eng., Mass. Inst. of Tech., Cambridge, 1980.
45. Milly, P. C. D., and P. S. Eagleson, Parameterization of moisture and heat fluxes across the land surface for use in atmospheric general circulation models, Tech. Rep. 279, R. M. Parsons Lab., Dept. of Civ. Eng., Mass. Inst. of Tech., Cambridge, 1982.
46. Milly, P. C. D., Moisture and heat transfer in hysteretic, inhomogeneous porous media: a matric head-based formulation and a numerical model, Water Resource. Res., 18(3): 488-498, 1982.
47. Milly, P. C. D., A simulation analysis of thermal effects on evaporation from soil, Water Resource. Res., 20(8), 1087-1098, 1984.
48. Nakano, M., and T. Miyazaki, The diffusion and non-equilibrium thermodynamic equations of water vapor in soils under temperature gradient, Soil Sci., 128(3): 184-188., 1979
49. Oke, T. R., "Boundary Layer Climates", Methuen., 1978.
50. Philip, J. R., and D. A. de Vries, "Moisture in porous materials under temperature gradients." Eos, Trans. AGU, 38(2), pp.222-232, 1957.
51. Richards, S. J., R. M. Hagan, and T. M. McCalla., Soil temperature and plant growth., In B. T. Shaw(ed.)Soil physical conditions and plant growth. Agronomy 2: 304-336.
52. Rose, C. W. Water transport in soil with a daily temperature wave. 1. Theory and experiment, Aust. J. Soil Res.6: 31-44,1968a.
53. Rose, C. W. Water transport in soil with a daily temperature wave. 2. Analysis, Aust. J. Soil Res. 6: 45-57, 1968b
54. Rose, C. W. Evaporation from bare soil under high radiation conditions, Int. Conger. Soil Sci., Trans.9th p.57-66, 1968c.
55. Rosema, A., Simulation of the thermal behavior of bare soils for remote sensing purposes, in Heat and Mass Transfer in the biosphere, edited by D. A. de Vries and N. H. Afgan, John Wiley and Sons, 109-123, 1975.
56. Sasamori, T., A numerical study of atmospheric and soil boundary layers, J. Atmos. Sci. 27: 1122-1137, 1970.
57. Sophocleous, M., Analysis of water and heat flow in unsaturated -saturated porous media, Water Resource Res., 15(5), 1195-1206,1979.