土壤持水曲线van Genuchten模型求参的Matlab实现

PARAMETERS ESTIMATION OF VAN GENUCHTEN MODEL FOR SOIL WATER RETENTION CURVES USING MATLAB

土壤持水曲线是研究土壤水力学性质必不可少的 ,在已经建立的众多数学模型中 ,vanGenuchten模型是目前运用最广泛的模型 ,而运用该模型的关键是其 4个参数的求解。为此 ,本文对同一组东北褐土的土壤水吸力和对应的土壤含水量数据较详细地介绍了Matlab软件的非线性拟合和非线性回归函数的运用 ,得出了该土壤vanGenuchten模型的 4个参数值 ,分别建立了该土壤的vanGenuchten模型 ,并利用Mat lab强大的绘图功能对它们进行了直观比较。最后运用方差分析和残差分析对该模型的计算值与实测数据进行了分析 ,结果表明 :非线性拟合和非线性回归函数求参结果的显著水平均达到p<0 0 0 0 1,残差平方和均小于 0 0 0 0 5 ,其中非线性回归函数的求参结果较非线性拟合好。因此 ,运用Matlab软件的非线性拟合和非线性回归函数对土壤持水曲线的vanGenuchten模型进行求参是切实可行的 ,从而为土壤学工作者寻求出了一条运用数值计算方法的新途径。

Soil water retention curves play an essential role in determination of soil hydraulic characteristics. Among the developed mathematical models, van-Genuchten model historically has been the most widely adopted. Its four parameters are the key to application of this model. With the same set of experimental data (namely soil water suctions and corresponding soil water contents in cinnamon soil in northeast China), this paper introduced in detail the application of nonlinear curve fitting and nonlinear regression function, two useful functions of Matlab software, in obtaining values of the four parameters,based on which van Genuchten models were established respectively. By taking advantage of the powerful plotting function of matlab, visual comparison of them was easily made, showing differences between them were very small. Finally, using the methods of variance analysis and residual analysis, the calculated values by the models and measured values were analyzed. Results showed that in both nonlinear curve fitting and nonlinear regression good significant levels were achieved both to p<0.000 1 and the sums of residual squares were both lower than 0.000 5. Especially the results from the nonlinear regression function were better than those from the nonlinear curve fitting. Therefore, it is practical and feasible to obtain values of the parameters of van Genuchten model for soil water retention curves using Matlab software, which may serve as a new promising approach to application of numerical methods for the soil scientists.