To my understanding, this manuscript proposes a neural network method to fill for missing/invalid values in particle size distributions (PSDs) measured in situ, based on correct values measured at other size bins and on knowledge of meteorological parameters. They train a number of neural networks in which one out of 23 bins in the considered size distributions is considered missing, and is predicted based on meteorological parameters and/or on the other 22 size bins.

The study seems to show that, if PSD values are known at 22 size bins, meteorological data do not add much information for the prediction of the missing value. This finding  does not sound particularly surprising to me, as I would expect PSDs to be relatively smooth, and knowing their values at 22 size bins should indeed provide a good deal of information about its value at some neighbouring bins. 

MAIN COMMENTS

•    While the technical work of setting up and training the neural networks looks correct as far as I can see, the main problems I see with this paper are the following:

1)    The first problem is that I had to carefully peruse the manuscript several times before understanding what the main goal exactly was. This means that the Authors should be more upfront in describing the goals of the study and its setup in the introduction. In particular, looking at the Introduction from Line 146 onwards, I had the impression that the scope was much broader than just interpolating a PSD at some missing values. Maybe also the title can be made more informative: instead of reading “Neural network modelling … on other particle sections, etc.” it may be something like “Replacement of missing values in in situ measured particle size distributions by means of neural networks”. This would give the reader a more immediate idea of what they are going to find in this paper.

2)    The second problem is that I am not entirely sure what the scientific significance of this study is. Training a neural network to fill in a single value in a PSD based on knowledge of other 22 values looks like a rather standard technical exercise to me. I am not sure if it makes sense to write a scientific paper about this, but since I am not part of the in situ measurement community I may not be the most appropriate person to comment on this. In general, when you use a NN to fill for missing values in the PSD you are basically developing a functional relationship between the PSD value at the missing bin and its values at other bins, and it is quite obvious that this relationship will work well or less well depending on how the real PSD actually behaves. I am not sure what general conclusions can be drawn from the analysis presented in section 4, except for the one –  widely expected in my opinion – that knowing already the PSD at almost all size bins helps a lot in predicting the missing value, compared to only knowing some meteorological information.

•    To have a clearer idea of the added value of using a NN to replace a missing size bin in a PSD, it would be interesting to see how the NN method performs compared to a simpler approaches such as linear interpolation.

•    While it is fair to say that a NN predicting PSD solely based on meteorological inputs constitutes indeed a predictive model (you can try to predict the PSD anytime and anywhere you have the needed meteorological input), I am not sure the same holds for the NN that also uses measurements of the PSD itself. I mean, if you are not measuring the PSD I guess you cannot operate such NN. Therefore, I would say that the NN using PSD values as input is not a “model to estimate the PSD” but just a “NN to interpolate missing values in the PSD”. Can you please elaborate on the impact that using PSD values as input has on the operational applicability of your NN?

OTHER COMMENTS

•    P1, L18, “which are able to deposit…”. What is the subject of this sentence?

•    P1, L21, “invert” -> “solve”

•    P2, L47. I guess Dp is the particle diameter. You should state this explicitly in the text.

•    P3, L109 and L118. What are these “kernel functions”, and what does it mean that they are “not optimally configured”?

•    P3, L112, and P5, L184. It looks to me like the acronym CPC has not been defined anywhere.

•    P4, L146, “objectives” -> “objective”

•    P5, L182 and L185. I think the acronym DMA is also not defined anywhere in the paper.

•    P6, L211. I guess you mean “linearly interpolated in time” here

•    Section 2.3. Please summarize the inputs you used in your NNs (which and how many), preferably in a table. This information is hard to find in the paper as it is now, and should be readily available to the reader.

•    P6, L226. What do you mean by "generate a signal or remain silent"? Are you using a binary threshold activation function? Later on you say that you are using a sigmoid.

•    P10, several instances. What do you mean by “mutual size distribution”? “mutual” between what?

•    P11, L384, I guess “which leads to a lower predictably” contains some typo. What do you actually mean?

•    P12, L455, by “trivial” do you mean “negligible”?

•    P13, L466, “ill-configured” -> “misconfiguration” ?

General Comments

The aim of the study is to predict ambient particle number size distributions from 0.01 to 10 μm using meteorological data and partial size-fractionated particle data. The authors provide a good overview of the lack of particle size distribution measurements in the MENA region and application of machine learning models for atmospheric aerosol research. The authors utilized an urban aerosol dataset collected in Amman, Jordan via tandem SMPS/OPS measurements. 70% was allocated as the training set and 30% for the testing set for the feedforward neural network (FFNN) modeling analysis. Seasonal and diurnal trends in the SMPS/OPS data are concisely described. The authors provide a thorough breakdown of the performance of the three modeling approaches considered: (1) meteorological data, (2) partial particle data from remaining size bins, and (3) a combination of (1) and (2). The authors found meteorological data to be of limited value to their modeling process and noted issues with predicting particle size distributions from 0.01 to 10 μm based on partial size-fractionated particle data. The study is of value for those conducting ambient aerosol measurements with the TSI NanoScan SMPS 3910 and TSI OPS 3330, which is a common configuration with noted limitations. The authors identified size fractions where their model did not perform well, notably near the lower limit of detection for the SMPS, near the upper limit of detection for the OPS, and in the overlapping region between the two instruments. The study provides a new way for handling particle number size distribution data collected from the TSI NanoScan SMPS 3910 and TSI OPS 3330 that forgos deletion of negative values in the dataset. The proposed FFNN modeling approach can be used to predict particle number size distributions in urban environments similar to the one considered in the study. 

Specific Comments

1)    Pg. 5, Ln. 170: what refractive index (default or otherwise) was used for processing the data from the TSI OPS 3330? 

2)    Pg. 5, Ln. 175: please describe the configuration of the aerosol inlet assembly. Also: was a diffusion dryer used? I am curious if the authors encountered any issues with SMPS/OPS sampling at high RH (RH of 100% reported on pg. 8)?

3)    Pg. 5, Ln. 180: it would be helpful to explain some of the limitations of the unipolar charger and radial DMA used within the TSI NanoScan SMPS 3910 as it pertains to the counting efficiency issues discussed in this section.

4)    Pg. 20, Fig. 6: please specify the cold and warm months in the figure caption.

Technical Corrections

1)    General: consider writing “Dp” with “p” as a sub-script.

2)    Pg. 1, Ln. 1: consider making “particle size distribution” plural in the title. 

3)    Pg. 1, Ln. 16: please clarify if you mean size-integrated particle mass concentrations, e.g. PM_2.5, PM₁₀.