A Statistical Methodology for Estimating Transport Parameters: Theory and Applications to One‐Dimensional Advectivec‐Dispersive Systems
A Statistical Methodology for Estimating Transport Parameters: Theory and Applications to One‐Dimensional Advectivec‐Dispersive Systems
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估计输运参数的统计方法：一维平流色散系统的理论与应用
DOI：
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
S. Gorelick
中科院分区：
文献类型：
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作者：
B. Wagner;S. Gorelick
开发并演示了一种模拟非线性多重回归方法，用于估计表征污染物传输的参数。有限差分污染物迁移模拟与非线性加权最小二乘多重回归程序相结合。该技术提供了最佳参数估计，并给出了统计数据，用于在有关随机测量误差分布的某些一般假设下评估这些估计的可靠性。蒙特卡罗分析用于估计假设的均质土柱的参数可靠性，该土柱的浓度数据包含较大的随机测量误差。研究了空间收集的数据与时间收集的数据的价值，以估计速度、分散系数、有效孔隙度、一阶衰减率和零阶产量。对于除速度之外的所有参数，使用空间数据得出的估计值比基于时间数据的估计值可靠 2-3 倍。基于蒙特卡罗分析的估计线性和非线性置信区间的比较表明，当随时间收集数据时，线性近似对于离散系数和零阶产生系数来说很差。此外，示例演示了两个真实一维系统的传输参数估计。首先，使用实验室柱数据估算非饱和土的纵向分散性和有效孔隙率。我们比较了基于单个实验室实验数据的估计与基于多个实验汇总数据的估计的可靠性。其次，模拟非线性回归程序被扩展为包括一个额外的控制方程，该方程描述了污染物传输过程中的延迟存储。该模型用于分析加利福尼亚州北部山溪中参数的趋势、变化和相互关系。
A simulation nonlinear multiple-regression methodology for estimating parameters that characterize the transport of contaminants is developed and demonstrated. Finite difference contaminant transport simulation is combined with a nonlinear weighted least squares multiple-regression procedure. The technique provides optimal parameter estimates and gives statistics for assessing the reliability of these estimates under certain general assumptions about the distributions of the random measurement errors. Monte Carlo analysis is used to estimate parameter reliability for a hypothetical homogeneous soil column for which concentration data contain large random measurement errors. The value of data collected spatially versus data collected temporally was investigated for estimation of velocity, dispersion coefficient, effective porosity, first-order decay rate, and zero-order production. The use of spatial data gave estimates that were 2–3 times more reliable than estimates based on temporal data for all parameters except velocity. Comparison of estimated linear and nonlinear confidence intervals based upon Monte Carlo analysis showed that the linear approximation is poor for dispersion coefficient and zero-order production coefficient when data are collected over time. In addition, examples demonstrate transport parameter estimation for two real one-dimensional systems. First, the longitudinal dispersivity and effective porosity of an unsaturated soil are estimated using laboratory column data. We compare the reliability of estimates based upon data from individual laboratory experiments versus estimates based upon pooled data from several experiments. Second, the simulation nonlinear regression procedure is extended to include an additional governing equation that describes delayed storage during contaminant transport. The model is applied to analyze the trends, variability, and interrelationship of parameters in a mourtain stream in northern California.