Elemental carbon (EC) has been widely used as a tracer to track the portion
of co-emitted primary organic carbon (OC) and, by extension, to estimate
secondary OC (SOC) from ambient observations of EC and OC. Key to this EC
tracer method is to determine an appropriate OC

Organic carbon (OC) and elemental carbon (EC) are among the major components
of fine particular matter (PM

Abbreviations.

The key step in the EC tracer method is to determine an appropriate
OC

With ambient OC and EC samples, the accuracy of estimated SOC by different
(OC

Illustration of the minimum

Summary of statistics of OC and EC in ambient samples.

We first examine ambient OC and EC for the purpose of identifying
distribution features that can serve as the reference basis for
parameterizing the numerical experiments. The 1-year hourly EC and OC
measurement data from three sites in the PRD (one suburban site in Guangzhou,
a general urban site and a roadside site in Hong Kong, with more than 7000
data at each site), are plotted in Fig. S1 in the Supplement document for the
whole year data sets and Figs. S2–S4 for the seasonal subsets using the
Nancun site as the example. A brief account of the field ECOC analyzers and
their field operation is provided in the Supplement. A detailed description
of the measurement results and data interpretation for the sites will be
given in a separate paper. The distributions of measured OC, EC and
OC

The probability density function (PDF) for the log-normal distribution of
variable

The Mersenne twister (MT) (Matsumoto and Nishimura, 1998), a pseudorandom
number generator, is used in data generation. MT is provided as a function in
Igor Pro. The system clock is utilized as the initial condition for
generation of pseudorandom numbers. The data generated by MT have a very long
period of 2

The procedure of data generation for the single emission source scenario is
illustrated in Fig. 2 and implemented by scripts written in Igor Pro. EC is
first generated with the following parameters specified: sample size (

Schematic diagram of pseudorandom number generation for the single
emission source scenario that assumes (OC

Three scenarios are considered. Scenario 1 (S1) considers one single primary
emission source. Scenario 2 (S2) considers two correlated primary emission
sources, i.e., two sets of EC, POC, and each source has a single but
different (OC

In the following numerical experiments, three (OC

Both OC

Conceptual diagram illustrating three scenarios of the relationship
between (OC

The above analysis reveals that

SOC estimation bias in S1 as a function of RSD

Bias of SOC determination as a function of

For the representation of (OC

In the real atmosphere, multiple combustion sources impacting a site is
normal. We next evaluate the performance of the MRS method in scenarios of
two primary sources and arbitrarily dictate that the
(OC

SOC bias in Scenario 2 (two correlated primary emission sources of
different (OC

In Scenario 2 (i.e., two correlated primary sources), three factors are
examined, including

In summary, in scenarios of two well-correlated primary combustion sources,
MRS always produces unbiased SOC estimates while OC

As for Scenario 3 in which two independent primary sources co-exist, SOC
estimates by MRS could be biased and the degree and direction of bias depends
on

SOC bias in Scenario 3 (two independent primary emission sources of
different (OC

The bias variation range becomes narrower with increasing

A variant of MRS implementation (denoted as MRS

In scenario 3, the simulation results imply that three factors are associated
with the SOC bias by MRS, including:

Bias of SOC determination as a function of relative measurement
uncertainty (

In the preceding numerical analysis, the simulated EC and OC are not assigned
any measurement uncertainty; however, in reality, every EC and OC measurement
is associated with a certain degree of measurement uncertainty. We next
examine the influence of OC and EC measurement uncertainty on SOC estimation
accuracy by different EC tracer methods. Two uncertainty types are tested,
i.e., constant relative uncertainty (Case A); constant absolute uncertainty
(Case B). This section mainly focuses on sensitivity tests assuming different
degrees of Case A uncertainties. Results assuming Case B uncertainties are
discussed in the next section. The uncertainties are assumed to follow a
uniform distribution and generated separately by MT. It is also assumed that
the uncertainty (

Sensitivity studies of SOC estimation as a function of

MRS relies on correlations of input variables and it is expected that MRS
performance is sensitive to the sample size of input data set. This section
examines the sensitivity on sample size by the three
(OC

The mean SOC bias by MRS is very small (

SOC estimation bias as a function of sample size by different
approaches of estimating (OC

Summary of numerical study results under different scenarios

Besides hourly measurements of OC and EC by online aerosol carbon analyzers,
the MRS method could also be applied to offline measurements of OC and EC
based on filters collected over longer durations (i.e., 24 h), which are
more readily available around the world. To explore the impact of sampling
duration (e.g., hourly vs. daily), we here use 1-year hourly data at the
suburban site of Guangzhou to average them into longer intervals of 2–24 h.
The 24 h averaged samples yield a (OC

OC

Table 3 summarizes the performance in terms of SOC estimation bias by the different implementations of the EC tracer method, assuming typical variation characteristics for ambient ECOC data. When employing the EC tracer method on ambient samples, it is clear that MRS is preferred since it can provide more accurate SOC estimation.

If the sampling site is dominated by a single primary source (similar to
Scenario 1), MRS can perform much better than the traditional OC

If the sampling site is influenced by two correlated primary sources with
distinct (OC

In this study, the accuracy of SOC estimation by EC tracer method is
evaluated by comparing three (OC

Sensitivity tests show that MRS produces mean SOC values with a very small
bias for all sample sizes while the precision worsens as the sample size
decreases. For a data set with a sample size of 60, SOC bias by MRS is
2

This work is supported by the National Science Foundation of China (21177031), and the Fok Ying Tung Graduate School (NRC06/07.SC01). The authors thank Hong Kong Environmental Protection Department for making available the ECOC data at Tsuen Wan and Dui Wu of Institute of Tropical and Marine Meteorology, China Meteorological Administration for providing logistic support of OC EC measurements in Nancun. The authors are also grateful to Stephen M. Griffith for the helpful comments. Edited by: A. Sorooshian