PMF模型解析土壤重金属来源的不确定性

正定因子矩阵分解（PMF）是目前污染源解析领域应用最为广泛的受体模型之一，其不确定性研究一直是源解析研究的前沿和热点.利用拔靴法（BS）、替换法（DISP）和拔靴-替换法（BS-DISP）3种不确定性分析方法探讨了PMF模型应用于土壤重金属源解析的不确定性，并以德兴铜矿周边土壤重金属为对象开展案例研究.结果表明，6因子情景是PMF模型最佳运行结果；在6因子情景的源成分谱中，除Cr和Ti外，DISP和BS不确定性区间均处于标识元素基本值的0.6~1.5倍之间，BS-DISP不确定性区间处于基本值的0.6~1.6倍之间；模型结果的不确定性更多源于因子旋转误差.通过这3种不确定性分析方法可以获得PMF模型运算中的随机误差和因子旋转误差.其中，BS-DISP法和BS法得到的结果能够辅助判断因子数是否过拟合，并有助于理解源谱的不确定性，而DISP法能够用于理解旋转的不确定性，可作为评价旋转过程可行性的方法.

Uncertainty analysis of soil heavy metal source apportionment by PMF model

Positive matrix factorization (PMF) model is one of widely used technologies in pollutant source apportionment, and its uncertain analysis have always been the frontier issue as well as hotspot. Three error estimation methods, including bootstrap (BS), displacement (DISP) and bootstrap enhanced by displacement (BS-DISP), were used to evaluate the uncertainties of source apportionment by PMF model, and heavy metals in soils in Dexing, China were carried out as a case study. Six-factor scenario was the best solution for PMF model run, except for Cr and Ti, the uncertainty intervals of DISP and BS were between 0.6 and 1.5 times the basic value of the identified element and the BS-DISP uncertainty interval was between 0.6 and 1.6 times the basic value in the source profiles under six-factor scenario, the uncertainty of the model results was more due to the uncertainty generated in the factor decomposition process. The three uncertainty analysis methods could obtain the random error and factor rotation error in the operation of PMF model. Among them, the results obtained by BS-DISP and BS can assist in determining whether the factor number was over-fitting and help understand the uncertainty of the source profile. While, DISP could be used to understand the uncertainty of rotation and be used as a method to evaluate the feasibility of rotation process. This study provides a good sample for evaluating the reliability of soil heavy metal source apportionment that calculated by PMF model.