The suitability of pde‐solvers in rhizosphere modeling,exemplified by three mechanistic rhizosphere models

Mechanistic rhizosphere models are mathematical models that calculate the uptake of solutes (e.g. nutrients such as P or K) in a plant root and/or the concentration profiles of ions or microorganisms across the rhizosphere. They consist of partial differential equations (pde's) and their associated initial and boundary conditions, and often require numerical solutions due to non‐linearity. The suitability of the pde‐solver FlexPDE for rhizosphere modeling was evaluated by reproducing the outputs of three original rhizosphere models and comparing the results with the original model outputs. The models considered were NST 3.0 (Syring and Claassen, 1996), Kirk (1999), and Newman and Watson (1977). From visual comparison, the curves as produced by the original model and FlexPDE match very well. All calculated R²s (coefficients of determination) were equal to 1 with a rounding precision of three decimal places. Rescaling the time, using an upwind scheme in the presence of convection terms and controlling the relative error with the FlexPDE function errlimit were helpful in finding the most accurate numerical solution. These results showed that FlexPDE is a valuable tool in rhizosphere modeling.     

基于FlexPDE的膜孔灌土壤水分运动数值模拟

基于实测扩散率资料和土壤水分特征曲线,利用FlexPDE软件对膜孔灌溉的土壤水分运动进行模拟,探索恒定水头条件下膜孔灌溉土壤水分入渗特性和剖面水分分布特征。结果表明：FlexPDE软件模拟粉粘壤土（处理2、3）和砂壤土（处理1、4）的含水率与实测之间的平均相对误差分别为5.930%、8.340%、9.600%和14.040%,其中粉粘壤土模拟与实测土壤含水率相对误差小于5%、10%和20%的比例分别为40%、68%和84%,砂壤土相对误差小于5%、10%和20%的比例分别为12%、40%和72%,粉粘壤土的模拟效果较砂壤土理想;基于模拟获取的土壤储水量与土壤实测累积入渗量呈线性关系,相关系数均大于0.9,且二者与入渗时间呈幂函数关系,随入渗时间增加而增大,但增速逐渐变缓;利用FlexPDE预测分析膜孔间距、膜孔直径和入渗水深对粉粘壤土膜孔灌溉单向交汇时刻、水分分布和储水量的影响,发现膜孔间距对于交汇初期土壤的水分分布影响较大,膜孔直径对于土壤交汇时间以及储水量影响显著。