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

葉正霖(Jen-Lin Yeh) ； 鄭皆達(Jie-Dar Cheng) ； 黃良鑫(Liang-Shin Hwang) ； 曹舜評(Shun-Ping Tsao) ； 董小萍(Shaw-Ping Dung) ； 鄧英慧(Ying-Hui Deng)

《台灣林業科學》 18卷4期 (2003/12) Pp. 307-316

https://doi.org/10.7075/TJFS.200312.0307

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 (The equation is abbreviated). 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 (The equation is abbreviated). The differential and integral items were calculated and substituted into the diffusion equation to obtain the relationship of diffusivity and soil volume wetness (The equation is abbreviated), where (The equation is abbreviated). 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.

關鍵字

擴散度 ； 波茲曼轉換常數 ； 圓錐曲線

並列摘要

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 (The equation is abbreviated). 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 (The equation is abbreviated). The differential and integral items were calculated and substituted into the diffusion equation to obtain the relationship of diffusivity and soil volume wetness (The equation is abbreviated), where (The equation is abbreviated). 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.

並列關鍵字

diffusivity ； Boltzmann transform constant ； conic section