Dear Alan Dunker,

Thank you for the detailed revision of your manuscript.
I am happy to accept your paper for publication subject to minor changes.
The changes refer to the citation of my own work and hence are delicate since it may be seen as an interferrence with my position as editor.
Therefore, I decided, after also consulting an executive editor, to mention these points and leave it to you how you want to include it in your revision.

At various places you mention that

"The PIM does provide insights not available from other methods. It provides contributions for anthropogenic sources that sum up to the difference (?ci) between a simulation with and a simulation without the anthropogenic sources."

On the other hand you cite Grewe et al. (2010), who also show that their tagging approach, or you may call it source apportionment, provides the same sort of information. An example is given in Grewe et al., Atmospehric Environment (2012). This tagging mechanism is set up in a way that - sort of similar to PIM - follows chemical pathways.
A side effect is that the sum of the differences are adding up to the difference between the base and perturbation simulation as shown mathematically in Grewe et al. (2010) and in a 3D example in Grewe et al. (2012).

So in my view the statement on page 2 l 28 ff is not true at least for the mentioned tagging mechanism, since it does not require chemical asumptions nor assumptions on being positive definite, and it is complete, which means that the sum of all contributions automatically gives the regarded concentration of both primary and secondary species.
"However, various chemical assumptions (beyond those in the chemical mechanism) are needed to track production of the secondary pollutant in nonlinear reactions. In addition, the source contributions are often restricted to be positive ... "

Also on page 2 and 3:
"Lastly, the PIM provides source contributions for all species in the chemical mechanism simultaneously, e.g., O3, NO2,
and air toxics, without additional assumptions exterior to the model, e.g., when the chemistry is VOC-limited vs. NOx-limited."

“Because the sensitivities are integrated .."
Both also hold for the Grewe et al., tagging approach.
In Grewe (2013; equation 10 therein) it has been mathematically shown that the Grewe et al. (2010) tagging
approach is equivalent to the integration of sensitivities.


Page 7:
"The above statement highlights the difference between sensitivity and source apportionment methods.
Negative “contribution” indicates that this is a sensitivity method, not a mass attribution method.
NOx emissions can contribute to ozone production even when ozone has a negative sensitivity to
changes in NOx emissions, and source attribution methods such as OSAT in CAMx are designed to quantify
the mass contribution of NOx to O3. Thus, the PIM method is not quantifying the mass contribution
to ozone production (in the sense that it evaluated in a source apportionment approach), rather,
it is characterizing the negative sensitivity of ozone to NOx.
Response: The anthropogenic increment can be negative. (See O3 in Figure 2, hours 0 to 12). This means that removing the anthropogenic emissions actually increases the O3 concentration, which is due to the titration of O3 by NO emissions. If the anthropogenic source contributions are all positive, then the implication is that eliminating the anthropogenic sources will reduce O3, which is incorrect. The PIM integrates the sensitivities over the anthropogenic emissions and accumulates the effects of both positive and negative sensitivities to the emissions. The integral of the sensitivity is no longer a sensitivity, but a source contribution. If the anthropogenic increment is negative, then the sum of the anthropogenic source contributions will be negative, which is a consistent and correct result."

Please consider whether Grewe (2013; equation 10 therein) would support your argument.

Best regards,
Volker Grewe