Source Apportionment of Atmospheric Trace Gases and Particulate Matter: Comparison of Log-ratio and Traditional Approaches

Abstract

In this paper we compare multivariate methods using both traditional approaches, which ignore issues of closure and provide relatively simple methods to deal with censored or missing data, and log-ratio methods to determine the sources of trace constituents in the atmosphere. The data set examined was collected from April to July 2008 at a sampling site near Woods Hole, Massachusetts, along the northeastern United States Atlantic coastline. The data set consists of trace gas mixing ratios (O3, SO2, NOx, elemental mercury [Hgo ], and reactive gaseous mercury [RGM]), and concentrations of trace elements in fine (<2.5 µm) particulate matter (Al, As, Ba, Ca, Cd, Ce, Co, Cs, Fe, Ga, Hg, K, La, Mg, Mn, Na, P, Pb, Rb, Sb, Sr, Th, Ti, V, Y, and Zn) with varying percentages of censored values for each species. The data were separated into two subcompositions: s1, which is comprised by RGM and particulate Hg (HgP), which are both highly censored; and s2 which includes all of the trace elements associated with particulate matter except Hg, and the trace gases O3, SO2, NOx, and Hgo . Principal factor analysis (PFA) was successful in determining the primary sources for constituents in s2 using both traditional and log-ratio approaches. Using the traditional approach, regression between factor scores and RGM and particulate Hg concentrations suggested that none of the sources identified during PFA led to positive contributions of either reactive mercury compound. This finding is counter to most conventional thinking and is likely specious, resulting from removal of censored data (up to >80% of the entire dataset) during the analysis. Log-ratio approaches to find relationships between constituents comprising s2 with RGM and HgP (i.e., s1) focused on log-ratio correlation and regression analyses of alr-transformed data, using Al as the divisor. Regression models accounted for large fractions of the variance in concentrations of the two reactive mercury species and generally agreed with conceptualizations about the formation and behavior of these species. An analysis of independence between the subcompositions demonstrated that the behavior of the two constituents comprising s1 (i.e., RGM and HgP) is dependent on changes in s2. Our findings suggest that although problems related to closure are largely unknown or ignored in the atmospheric sciences, much insight can be gleaned from the application of log-ratio methods to atmospheric chemistry data