土壤溶质迁移的高次幂函数近似解析模型

Approximate analytical model for high-order power function of solute transport in soil

为了利用解析模型模拟土壤溶质迁移过程、估计土壤溶质迁移参数,在假定土壤溶质质量浓度分布为n次幂函数的基础上,结合边界层方法,将描述土壤溶质质量浓度分布的低次幂函数进一步推广,得到土壤溶质迁移的n次幂函数近似解析模型.在2个时刻(t=360,720 min)、较大距离(120～450 cm)时,利用不同次幂函数模型对溶质迁移过程进行比较分析,模拟结果表明孔隙水流速度较小(v=0.01 cm/min)时,在短历时(t=360 min)、长距离(x>50 cm)处,六次幂边界层解与其他次幂边界层解相比具有较高精确度;对边界层距离公式受各参数的影响进行模拟计算,分析结果表明:较小的孔隙水流速度(v≤0.01 cm/min)对边界层距离影响甚小;基于较小土壤孔隙水流速(v=0.01 cm/min)及测量仪器的不同灵敏度,利用不同次幂边界层距离公式对土壤溶质迁移参数进行数值计算比较及误差分析,结果表明用较高灵敏度的仪器进行测量,结合六次幂的边界层距离公式可准确地推求土壤溶质迁移参数弥散系数D及延迟因子R.

To simulate the soil solute transport and estimate the transport parameters with a simple analytical model,an approximate six-power function model for describing the distribution of solute concentration was developed based on six-power function concentration profile assumed and the extended boundary layer theory describing the soil solute transport.The solute concentration profiles predicted by using the model proposed with different power indexes were compared and analyzed at two time instances（t=360,720 min） and a long distance（120-450 cm）.The simulated results showed that the solution of six-power function method is more close to the exact solution compared with other power models when the pore water velocity is 0.01 cm/min at a short time experienced（t=360 min） in a long traveling distance（x＆gt;50 cm）.More computations indicated that the small pore water velocity（v≤0.01 cm/min） has little effect on the boundary layer distance.In that case,a series of error analysis on the transport parameters estimated with different boundary layer distance formulas were also carried out.The results indicated that the transport parameters such as diffusion coefficient and delay factor in the solute convection-dispersion equation can be decided precisely by using the boundary layer distance predicted with six-power function model based on measured results by means of instrument with higher sensitivity.