This paper presents an interesting approach for extracting aerosol properties from low-cost air quality sensor data. While the method is novel and the results are promising, I would suggest a few additional analyses and clarifications in the work.

First, and most significantly, it seems that the same data are used for both calibrating the OEM method (i.e., extracting the aerosol properties) and for evaluating the performance of this method. The same holds true for the MLR method against which the OEM is being compared. I don’t think that this is a fair way to do these comparisons. If possible, I would suggest separating the data from each season into distinct sets for calibration and evaluation. This separation could be done randomly or (my preference) using e.g. one month of data to run the OEM (and to calibrate the MLR) and the other months to evaluate the calibration performance. I prefer this latter approach since it is more realistic to how these sensors might be used in practice, i.e., calibrated near a reference for some period of time and then deployed to another site. Overall, I think this will be a more realistic evaluation of the method and its strengths/limitations compared to the “traditional” MLR.

Second, there are some comments that the method is quite sensitive to the relative humidity, and that the PurpleAir relative humidity data are of insufficient quality. Can more be said about this? I would suggest, for example, testing the method with the relative humidity as measured by PurpleAir, but using a higher relative uncertainty for these measurements in the covariance matrices within OEM. Is the OEM method still able to resolve the aerosol properties in such cases? While accurate humidity data from a nearby whether station may be available, it would be useful to also see how well the calibration can perform using only the information from the PurpleAir itself (while understanding the relatively lower quality of these data).

Third, the OEM method requires appropriate prior terms, and especially appropriate uncertainties (parameterized in covariance matrices) for these terms. While there is some discussion of the sensitivity of the method to various parameters, there is little quantitative information here which would help other researchers understand the applicability of these findings to their work. I would suggest describing how the measurement error covariance matrix and the state vector covariance matrix were defined in more detail. Furthermore, I would suggest presenting the results of any sensitivity analyses conducted for these terms, possibly in a supplement or appendix.

I also have several specific comments and suggested corrections, listed here:

Line 20: Note that these data are still publicly available, but not freely available.

Line 25: Please provide a source or reference for the description of the operating principles.

Line 30: “was” should be “were”.

Line 43: The calibration is not only applicable to “their” sensor, but also any other sensor, within the range of conditions under which the calibration was created and validated.

Lines 71-72: The meaning of this sentence is unclear. I think you might intend to say that the physics-based correction model which was just described was also compared with a purely statistical correction model incorporating multiple linear regression terms. Please consider rephrasing if this is indeed what you meant.

Line 87: What is meant by “clearly erroneous readings”? Is this the result of the same quality control procedure just described, or are these data erroneous for different reasons?

Section 2.2.3: Not a necessary change, but I would suggest moving most of this information to the introduction, as it is background detail and motivation for the study. The specific model of reference instrument used can be mentioned in Section 2.2.2 instead.

Section 2.3: Values for the a-priori state vector and the error covariance matrices should be provided; this can be done in a supplement or appendix. Some argument should be provided about how these values were selected as well, so that others can make appropriate decisions when replicating this.

Section 3.1: Are there any quantitative results which can be presented based on this analysis to support the conclusions that particle diameter and temperature are of lesser importance? For example, relative magnitudes of terms in the error covariance matrix?

Line 176: remove “from”.

Section 3.2.1: Are the same results observed for the empirical calibration, or is this over-correction unique to the physical calibration? There is a comment addressing this in lines 229-230; maybe this could be moved up and expanded on. The comment seems to suggest that, based on the data, the calibration dependence on humidity should in fact be linear, as opposed to nonlinear as in the physical calibration. This could potentially mean that humidity is impacting the sensor performance in more complex ways than just the hygroscopicity of the particles.

Line 196: I would suggest using the measured humidity from the PurpleAir as your input and calibrating the uncertainty for this term using your comparison to a nearby weather station. This could give a sense of how robust the measurements are to the data quality of the internal humidity sensor, which you have noted is not high.

Lines 218-219: This argument seems to contradict the previous statements that the method is not sensitive to particle diameter.  

Line 221: “2.5” should be subscripted.

Table 2: Why is the R-squared of the raw data not reported? Reporting the biases across the different methods could also be useful.

Line 254: The bias of the linear correction being zero indicates that it is being assessed on the same data on which it is calibrated. I’d suggest defining separate calibration and evaluation datasets for each month; see my general comment on this from above.

The authors compared one year of daily average PurpleAir PM2.5 observations in London Ontario with a provincial Thermo Scientific SHARP 5030 monitor ~6 km away and temperature/humidity observations with a federal automated weather station ~12 km away. They developed an optical estimation method for estimating bulk hygroscopicity of the PurpleAir measurements and bias corrected the PM2.5 concentrations. Their method reduced the mean error/bias for their PurpleAir observations on average and produced reportedly reasonable hygroscopicity estimates for each season. The authors suggest expanding on this work using a larger network of colocated stations.

Overall Thoughts

• The OEM modelled hygroscopicity is a useful enhancement to the PurpleAir observations and could be a key piece in determining the best bias correction for PurpleAir observations. This is especially important given the growing reliance of communities and health agencies on PurpleAir and other low-cost monitors for situational awareness during PM2.5 events.
• I suggest being more consistent with the use of the words “monitor” and “sensor” as they are used interchangeably throughout. I tend to use “monitor” to describe the PurpleAir (including its motherboard, WiFi chip, and sensors), and “sensor” to refer to the PM2.5, temperature, and RH sensors within the PurpleAir. The US EPA uses monitor to refer to regulatory methods (the London ministry monitor in this study) and sensor to refer to low cost methods (PurpleAir etc).
• The paper needs some reorganization of content within sections and some expansion to the introduction/methodology. Additional references would make the introduction more robust, most of the current citations pertain to the data quality from the PurpleAir monitors. Some of the text from the methodology section belongs in the introduction instead, and the methods of this study should be expanded on for replicability. The results section requires more focus on the results shown in the figures instead of describing the figure display. The text from the discussion that presents results should be moved to the results, and any functional description of the figures belongs in figure captions (and only if it is unclear). 
• I have concerns about the lack of training/testing data split and the limited data used for this study (see my comment near the end of the specific points). Without splitting the data, observations used to build the model were also used to evaluate it which will likely overfit the results. This should be corrected or at least emphasized in the limitations/conclusions as further work is required to assess the transferability of these results to other sites and time periods and the model is likely overoptimistic.

See the attached pdf for line by line comments