轉換方法對土壤水分擴散度推估之影響

本文使用λ_1＝xt^n、λ_2＝x^mt^(-1)及λ_3＝x^at^b三種轉換方法，來將Richards方程式由偏微分方程式轉換爲常微分方程式，以求得土壤水分擴散度，由分析結果得知土壤水分擴散度值隨土壤含水量、時間及轉換關係式不同而異，而於固定時間時，本文所提之三種轉換關係與傳統Boltzmann轉換方式所得結果為倍數關係，即D（θ）表示傳統Boltzmann轉換所得之土壤水分擴散度，則三種不同轉換方式所得之土壤水分擴散度分別為D_1（θ）＝（-2n）D（θ），D_2（θ）＝（2/m^2）D（θ）與D_3（θ）＝（-2b/a^2）D（θ）。

關鍵字

Richards方程式；非飽和土壤； Boltzmann轉換；土壤水分擴散度

並列摘要

The study applied three transformation methods, namely λ_1=xt^n, λ_2=x^mt^(-1), and λ_3=x^at^b to transform Richard equation from partial differential equation to ordinary differential equation in order to find diffusivity of soil moisture. In constant time, the relationship between traditional Boltzmann transformation method and the three transformation methods in this study is a proportional one. Suppose D(θ) indicate the diffusivity of soil moisture by traditional Boltzmann transformation, then the diffusivity by the three transformation methods is D_1(θ)=(-2n)D(θ),D_2(θ)=(2/m^2)D(θ), and D_3(θ)=(-2b/a^2)D(θ), respectively.

並列關鍵字

Richards equation ； Unsaturated soil ； Boltzmann transformation ； Soil water diffusivity

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