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題名 | 應用圓錐曲線擬合方法推導土壤水分擴散方程式=Deriving Soil Water Diffusion Equations with the Conic Section Fitting Method |
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作者 | 葉正霖; 鄭皆達; 黃良鑫; 曹舜評; 董小萍; 鄧英慧; Yeh, Jen-lin; Cheng, Jie-dar; Hwang, Liang-shin; Tsao, Shun-ping; Dung, Shaw-ping; Deng, Ying-hui; |
期刊 | 臺灣林業科學 |
出版日期 | 20031200 |
卷期 | 18:4 2003.12[民92.12] |
頁次 | 頁307-316 |
分類號 | 434.222 |
語文 | chi |
關鍵詞 | 擴散度; 波茲曼轉換常數; 圓錐曲線; Diffusivity; Boltzmann transform constant; Conic section; |
中文摘要 | 土壤水分擴散度之計算通常是應用擴散方程式(略),式中的微分及積分項以實驗數據求取波茲曼轉換常數(λ)對土壤體積濕度(θ)之斜率及面積來替代,再以此計算出土壤水分擴散度,通常需要重複進行實驗以獲得更大量的實驗數據以減低誤差。在本觀察實驗數據後發現λ對θ之圖形有圓錐曲線的趨勢,因此採用圓錐曲線型方程式r =εD/(1-εcosθ)來擬合λ與θ之關係方程式,當離心率ε<1時為橢圓方程式、ε=1為拋物線方程式、ε>1為雙曲線方程式;用最小二乘法對實驗數據進行擬合,並用高斯-西第爾迭代方法解非線性方程組。擬合結果顯示離心率ε皆大於1,表示λ與θ呈現雙曲線方程式型式(略),其中a0 =ε, a1 = D;計算此式之微分及積分項並代入擴散方程式中,求得土壤水分擴散方程式(略),其中(略)、(略)、(略).經由這樣的推導方法所得之擴散方程式,較Gardner提出之經驗式(D(θ)=aebθ)複雜。但研究結果也顯示此方法能求得平順且接近物理意義之函數型擴散方程式。 |
英文摘要 | Measuring diffusivity usually applies the Boltzmann transformation of λ vs. slope and area of soil volume wetness, θ, of experiment data to replace the differential and integral items in the diffusion equation . This study assumed that the relationship between the Boltzmann transform constant, λ, and the soil volume wetness, θ, has a conic section equation type (r =εD/(1-εcosθ) ellipse as ε< 1.0, parabola as ε= 1.0, and hyperbola as ε> 1.0). Experiment data were used to fit the least squares method and solve the non-linear equations using the Gauss-Seidel method. The fitting results are of the hyperbola type(...), a0 =ε a1 = D. The differential and integral items were calculated and substituted into the diffusion equation to obtain the relationship of diffusivity and soil volume wetness (, where , , and τ=θ+b0). Diffusivity equations derived by this method are more complex than those using Gardner’s method. However, it is an alternative for obtaining functional diffusivity equations based on soil physics. |
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