The use of unsupervised methods, such as Positive Matrix Factorization (PMF), in the source apportionment of Total Gaseous Mercury (TGM) has proven to be highly insightful. PMF provides a data-driven, top-down approach to estimate mercury fluxes by breaking down the observed concentrations into potential sources and their relative contributions. The strength of PMF lies in its ability to reveal hidden patterns in large datasets without predefined assumptions about the sources. This makes it a powerful tool for identifying unknown or unexpected sources of mercury emissions and for quantifying their impacts on the environment.

However, despite its advantages, the PMF model—especially as implemented in the U.S. EPA’s PMF software—has some significant limitations. One of the main drawbacks is that it operates as a black box, where users have limited control over the relationships between the variables loaded into the model. While this makes the tool remarkably user-friendly and accessible to non-experts, it can also introduce risks when interpreting the results. Since users have little insight into the inner workings of the model, there is a danger of not fully understanding the factors driving the apportionment. This becomes particularly critical in environmental science, where subtle changes in the data can lead to vastly “different source contributions”.

Moreover, a key issue with PMF is that it will always produce an output, regardless of the quality or representativeness of the input data. This brings about the risk of "garbage in, garbage out." If the input data is not carefully curated, or if the underlying assumptions about the sources and their relationships are flawed, the model can generate misleading or incorrect apportionments. This is particularly concerning in mercury studies, where TGM concentrations are influenced by various factors, including natural emissions, re-emissions, and anthropogenic activities. The complexity of mercury’s behavior in the atmosphere makes it imperative for researchers to critically assess the outputs of PMF, and not blindly trust the results.

Therefore, while PMF serves as a valuable tool for source apportionment, particularly in a top-down framework for estimating mercury fluxes, it must be used with caution. Researchers should be aware of the potential pitfalls and ensure that the input data is thoroughly vetted. Additionally, incorporating other methods to validate PMF results could mitigate the risks of misinterpretation. This reflective and cautious approach will ensure that PMF’s insights into TGM source apportionment remain robust and scientifically sound.

In the source apportionment presented by the authors, several systematic issues have been identified, ranging from variable selection to the model run setup. One notable concern is the inclusion of temperature as a variable alongside atmospheric tracers. While temperature is a fundamental environmental parameter, its use in this context introduces a significant risk of spurious correlations due to its high amplitude variations throughout the year. These fluctuations can heavily influence the eigenvector decomposition in the rotational factorization, constraining the results based on seasonal temperature trends rather than genuine emission sources.

The problem arises when temperature, with its pronounced seasonal patterns, overwhelms the underlying relationships between the atmospheric tracers and the sources of mercury emissions. This can lead to misleading factor identifications, where the eigenvectors are more reflective of the temperature’s seasonal cycle than of the true emission dynamics of the tracers. When eigenvectors are primarily driven by trends or seasonality, there is a high risk that the source apportionment is dictated by external variables not directly linked to the emission processes themselves. As a result, the interpretation of the PMF output can become compromised, leading to inaccurate conclusions about source contributions.

Furthermore, it is crucial to emphasize the importance of sensitivity tests and residual analysis to ensure the robustness of the PMF solution. Sensitivity tests help to evaluate how the model responds to changes in variable selection and model parameters, offering insights into the stability and reliability of the source apportionment. Residual analysis, on the other hand, provides a valuable check on the quality of the model fit, indicating whether the factors identified by the PMF model adequately explain the observed data or if there are unexplained variances that need further investigation.

I find it puzzling why the authors chose to perform a separate PMF run for each individual year, as this approach undermines the potential insights that could be gained from analyzing the full, continuous time series together. Running the entire time series as a single dataset would provide a more robust and comprehensive analysis, allowing the model to capture long-term trends, interannual variability, and potential seasonality in a more holistic way. A year-by-year analysis may artificially constrain the factors identified, leading to fragmented or incomplete source apportionment, and it limits the ability to understand how certain sources or processes evolve over time.

Furthermore, I also do not understand why the authors did not merge all the sites into a single analysis. In a data-driven model like PMF, the number of receptors (sampling sites) is crucial for increasing the model’s ability to discern distinct sources. By running the sites separately, the authors miss out on the advantage of having a broader spatial coverage and a larger dataset, both of which can significantly improve the resolution of source identification. Combining data from multiple receptors across different sites increases the model’s power to detect and distinguish between sources, especially when there are overlapping emission signatures that might vary in strength and frequency across locations.

Increasing the number of receptors also enhances the model's capacity to address complex atmospheric dynamics, as it allows for a richer dataset that captures variations due to both local sources and regional transport processes. When multiple sites are analyzed together, the model has more information to work with, potentially identifying regional patterns that might be missed when each site is treated independently. The inclusion of multiple receptors also reduces the risk of overfitting the model to local conditions or short-term fluctuations at any single site, leading to a more generalizable and reliable source apportionment.

The number of species used in the factorization performed by the authors appears insufficient to properly apportion the sources they claim to resolve. The profiles of the factors presented do not convincingly align with the expected "fingerprints" of the emission sources they attribute them to. For example, in Figure 12, the "local combustion" factor is primarily characterized by SO2 only, yet it lacks loading of CO, which is a well-known combustion tracer. Instead, CO is predominantly loaded in the "background" factor, which should typically be dominated by long-lived species. This misallocation raises concerns about the accuracy of the factor assignments and suggests that the model may not be adequately capturing the true source profiles.

Moreover, it seems that the authors constrained the number of factors to a level that exceeds what the available data can reliably cluster (with physical apportionment mean). The factorization results in some clusters that are difficult to justify from a source attribution perspective. For instance, there is a factor which unlikely represen a source, this suggests that the model may be overfitting, potentially driven by non-source-related variables.

There are also several indications in the presented profiles that attempting to resolve six sources from the limited number of species (or variables) used in the analysis constitutes an over-extrapolation of what is feasible through this factorization method. Some factors, for example, the cluster is basically loaded with Ca and Mg, other that is loaded with Cl and Na only. These elemental groupings suggest that the model is forming clusters based on chemical similarity only, rather than true source-specific emissions. This is further evidence that the factorization may be over-constrained, leading to artificial factors that do not accurately represent distinct sources.

Based on the issues discussed, I recommend a major revision of the manuscript. It is clear that the authors have put significant effort into this work, but there are substantial improvements that need to be made, particularly in the source apportionment performing and analysis. I strongly encourage the authors to further explore the capabilities of source apportionment resource. While there is certainly a learning curve, catching up in this area will greatly enhance the robustness and accuracy of the study. I am confident that it will be worth the effort and will lead to more defensible results and insightful discussions.

Given the concerns raised about the current factorization and its interpretation, revisiting the apportionment process will likely result in significant changes to the manuscript’s overall findings and discussion. I recommend that the authors reanalyze the data, addressing the over-extrapolation issues and ensuring that the profiles correspond more clearly to recognizable emission sources. Once the source apportionment is properly refined, I encourage the authors to resubmit the manuscript, as I believe it has the potential to make a valuable contribution to the field.

In addition, I suggest that the authors expand on the differences between the two analyzers used (2537B and 2537X) as part of their revised manuscript. A thorough comparison of these instruments would be highly interesting, especially regarding any differences in performance or measurement outcomes. I would be very keen to see these comparisons and an error vector decomposition.

Ðanilo Custódio

Max-Planck-Institut für Biogeochemie 

Hans-Knoell-Str. 10, D-07745 JENA (Germany)

Cheng et al. performed a thorough analysis of TGM from three Canadian sites using PMF. I have a couple of concerns. First, I am not entirely convinced how some of the factors were identified, i.e., the background factor and the reemission/biomass burning factor. The background factor was identified because of the high abundance of CO and TGM, and the authors cited Weiss-Penzias et al. (2007) to back the decision. What was their definition of “background”? I took it as the baseline level at the site. Did they look into the correlation between CO and TGM? Chances are the two are correlated due to their similar seasonal patterns. CO has always been used as an anthropogenic tracer in the literature. The very reference, Weiss-Penzias et al. (2007), they cited used the CO-TGM correlation to demonstrate the impact of Asian pollution. Therefore, the authors’ decision to use CO as a background tracer did not make sense to me. Numerous studies in the literature used TGM-CO correlation at sites to identify anthropogenic influence; yet the two compounds do not really share common sources. There is in fact a deeper meaning to this correlation, which is, in this reviewer’s opinion, that the relationship really reflects the anthropogenic or wildfire burning emission ratios of TGM and CO over a studied region. Regarding the reemission/biomass burning factor, there were quite jarring inconsistencies in the concentrations of supposedly fire tracers. As is commonly known, biomass burning emissions can enhance CO, TGM, and K⁺. However, Fig. 2 showed K⁺ at ~10%, similar to the values for the local combustion and fresh SSA factors and lower than the K⁺ values (~15%) in the background, secondary sulfate and aged SSA factors, and also showed the lowest CO in this factor.

Second, what does the “secondary sulfate factor” really mean? If I am not mistaken, it could indicate the role of secondary production of TGM. If it was correct, then the assumption of chemistry being negligible would be invalid. I’m curious how such a paradox can be reconciled.

The manuscript is quite tedious to read. The approach is mechanical. The interpretation of the analysis results is somewhat arbitrary. There is potential to this study, but the authors might want to put more effort into thinking through the interpretation of their results.