引用本文:  闫一凡,李晓鹏,张佳宝,刘建立.基于GLUE的土壤溶质运移参数反演及不确定性[J].土壤学报,2018,55(5):11081119. 
 YAN Yifan,LI Xiaopeng,ZHANG Jiabao,LIU Jianli.Parameter Estimation and Uncertainty Evaluation of a Soil Solute Transport Model Using GLUE[J].Acta Pedologica Sinica,2018,55(5):11081119 



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基于GLUE的土壤溶质运移参数反演及不确定性 
闫一凡, 李晓鹏, 张佳宝, 刘建立

中国科学院南京土壤研究所


摘要: 
溶质运移模型参数的识别结果常存在较高的不确定性，制约了模型的实际应用。以土壤中Cu^{2+}运移过程为例，采用广义似然不确定性估计（Generalized likelihood uncertainty estimation, GLUE）并引入最大似然值（Maximum NashSutcliffe，MNS）等三种定量指标，探讨了数值反演估计弥散系数等参数的不确定性。结果表明，非线性最小二乘法（Nonlinear least squares，NLLS）得到的唯一“最优”参数组合对Cu^{2+}出流曲线拟合效果很好（R^{2} >0.937），但因“异参同效”，无法刻画预测结果的不确定性。GLUE则可明确溶质运移参数及其响应界面的不确定性，MNS对应的参数组合对Cu^{2+}出流曲线拟合R^{2} >0.937，效果与NLLS的拟合结果高度一致。GLUE计算的95%置信区间覆盖了80%以上的观测点（NLLS为46.3%），其反演参数的取值范围也远大于NLLS的结果。在模型参数及响应界面不确定性分析两方面GLUE方法均优于NLLS方法。 
关键词: 溶质运移模型 参数反演 广义似然不确定性估计（GLUE）方法 不确定性分析 
DOI：10.11766/trxb201801260022 
分类号: 
基金项目:国家自然科学基金项目（41771265）、国家重点研发计划课题（2016YFD0300601,2016YFD0200603）和南京土壤研究所“一三五”（领域前沿）项目（ISSASIP1661）资助 

Parameter Estimation and Uncertainty Evaluation of a Soil Solute Transport Model Using GLUE 
YAN Yifan, LI Xiaopeng, ZHANG Jiabao, LIU Jianli

Institute of Soil Science, Chinese Academy of Sciences

Abstract: 
【Objective】Computer programs, such as CXTFIT, are commonly used to calibrate soil hydraulic and transport parameters, such as dispersion coefficient and retardation factor. CXTFIT can be used to fit observations quite well, which leave researchers in this aspect such an impression that the “optimum” parameter sets simulated with this program can be used directly for modeling prediction. However, in the process of parameter simulation, inherent uncertainties do exist and are often underestimated. The objectives of this study were to assess and even quantify the uncertainties that may occur in parameter estimation using the convectiondispersion equation (CDE) and in adoption of the parameters in modeling prediction with the nonlinear least squares (NLLS) and generalized likelihood uncertainty estimation (GLUE) methods. 【Method】 In this study, with the aid of CXTFIT, NLLS and GLUE coupled with the Latin hypercube sampling strategy was used to fit concentrations of bromide and copper nitrate in transport through three oil columns different in texture (i.e. Sandy loam, loamy sand and sandy clay loam), separately. And the parameters were optimized and analyzed to quantify the uncertainties that may occur in these processes by means of three quantitative metrics, that is, MNS (maximum coefficient determination coefficient ), P_{95CI} (the percentage of observations included within the 95% confidence intervals) and ARIL (average relative interval length).【Result】Results show that the only “optimum” parameter set obtained with the NLLS technique fits the curve of solute outflow quite well with determination coefficients (R^{2} ) all > 0.98 for fitting Br transport and > 0.937 for fitting Cu^{2+} transport, and with root mean square error lingering at the magnitude of 10^{2}, but it fails to cope with a large number of equivalent parameters. R^{2} being high in value only indicates the “optimum” parameter set is a proper fit of observation, but it does not mean the “optimum” parameter set is the true characterization of solute transport. The parameter set corresponding to the MNS of solute outflow fitted with can be used to simulate the observation as well as NLLS (R^{2} >0.937). But the value range of acceptable parameters determined by GLUE are much wider than that of NLLS (the length of 95% confidence intervals of GLUE is about more than 5 times as high as that of NLLS), which means that a large number of parameter sets that are high in likelihood value fall outside of the 95% confidence intervals determined by NLLS. The 95% confidence intervals of outflow concentration determined by NLLS covered 28.13%, 64.00%, and 46.01% of the data observed separately in the soil columns different in texture, leaving almost half uncovered on average, whereas those determined by GLUE did 87.62%, 80.93%, and 84.3%, separately, which indicates that it is not a good choice to use NLLS to optimize parameters and uncertainties of the model output. 【Conclusion】 To put all into a nutshell, GLUE performs better than NLLS in both parameter and response surface uncertainty analysis, for NLLS underestimates significantly the uncertainties in estimation of major transport parameters. GLUE has a much wider acceptable parameter valuation range and 95% confidence intervals for outflow concentration, which indicates that the “optimum” solution acquired by NLLS does not show any robustness as the solution acquired by CXTFIT does. So the usage of only “optimum” parameter sets to predict solute transport has to face high risk and high uncertainty. 
Key words: Solute transport model Parameter estimation Generalized likelihood uncertainty estimation (GLUE) Uncertainty analysis 





