Given the data availability for such properties is limited due to the limited number of daily almucantar sky radiance scans and cloudiness, but AOD measurements are significantly more frequent, as they can be even every minute and are affected only by clouds being too close or covering the solar disk, so the authors selected four common stations of GAW-PFR and AERONET and used GRASP to retrieve the bimodal size distribution parameters from AOD measured by GAW-PFR instruments (PFRs). The authors assessed the homogeneity with the AERONET output parameters and investigated the effect of the spectral range on such retrievals, as well as assessed the performance for certain dust and biomass burning cases. The results showed good agreement between PFR AOD-based and AERONET sky radiance inversions for AOD modal separation and volume concentrations.

In summary, the paper proposes a method for inverting aerosol particle size distribution parameters based on high temporal resolution AOD data (GAW-PFR) and the GRASP algorithm, verifies its applicability under various aerosol conditions, and explores the impact of spectral range on inversion. The research design is rigorous and the data is detailed (long-term observations at 4 stations), which is of great value to the field of aerosol remote sensing. So, I recommend this paper to be published in AMT after minor revision, but I still have some questions that the authors should take into consideration as below:

1. Please add the specific latitude and longitude information of the four stations in Section 2.1.
2. In ground-based instrument observations, calibration is an important factor affecting inversion accuracy. In Section 2.1, many instruments (CIMEL, PFR, BTS) in the manuscript have conducted continuous observations for many years. Please provide additional information on how often these instruments are calibrated.
3. In Section 2.1.3, it is mentioned that BTS has two detector arrays, and there is a part of the repeated spectra (300–1050 nm and 950–2150 nm). How are the repeated spectral ranges, such as 1020 nm, selected and processed?
4. In Figure 1, there are slight differences in the criteria used for the observed and extrapolated AODs for 7 and 16 bands. For example, in the 7 bands, AOD-obs uses 0.015, but AOD-ext uses 0.011, and so on. Why not use the same filter criteria for the same number of channels?
5. What does "P95-P5" mean in Table 1? Please explain.
6. In Figures 6 (c) and (d), what does "a" mean in the last item of the title filtering conditions? Is it AE? Please check.
7. For better comparison, it is recommended to unify the horizontal axis range of the upper and lower groups of Figure 8.
8. In the table, some table parameter columns (Table 2) use bold fonts, and some table parameter columns (Tables 3-6) use normal fonts. Please check and unify them according to the requirements of the journal.
9. In Section 4 (Line 635), the manuscript mentions that there is an underestimation of radius and concentration in the GRASP inversion results, but according to Figure 12 and the previous description, it seems to be an overestimation. Please check.

The manuscript describes the results of applying the GRASP-AOD inversion procedure to the PFR instrument, with the final aim to provide size distribution information to the GAW-PFR network. The writing is somewhat unwieldy, cluttered with parentheses, abbreviations and acronyms. More importantly, the methodology lacks rigor in certain aspects. A major revision would be needed for the paper to be suitable for publication in AMT. The following comments are intended to help in such revision.

Major comments

1. There is an overall strategy to "improve" the comparisons by removing "bad" data and fine-tuning the retrievals. Data in which the AOD differences are "too high" are removed. (line 271). Interpolated AOD from BTS is removed if R2<0.8.  (line 268). The authors retain the best cases only, ignoring all the difficulties that yield to discrepancies and that such circumstance will always come together with real data. Line 301: how could differences be large if all discrepant data points were previously removed?

The same applies to the retrievals: thresholds to residuals are changed ad-hoc to "improve" results (Figure 1). And the initial guess (line 466, 541, 550, 594), the settings (line 495), the wavelength range (line 499) or the refractive index are changed to adapt to certain cases. Or the dataset is restricted to the most favorable conditions (line 366, 546).

And my quotes in "improve" are put to emphasize that this is not a real improvement, just artificial clean-up of presumed outliers.

2. The focus of the study gets lost throughout the text: the title speaks about "Direct Solar Irradiance Measurements with High Temporal Resolution and Spectral Range". The abstract speaks about GAW-PFR, which provides AOD at 4 spectral channels. High temporal resolution is true, but not high spectral range. And the rest of the manuscript includes a mix-up of PFR, BTS, AERONET-SDA, CIMEL in various aspects (only direct, radiances). Is the main focus the application of GRASP-AOD to the GAW-PFR network (line 138); or something else? For instance, the use of BTS could me focused to assess what is lost when using the PFR spectral range instead of a larger one. In this way, it would contribute to the main goal of the study. Instead, it seems to be an attempt to explore the performance of the GRASP-AOD itself, which in my view is a different analysis.

Why/in which aspect is relevant for the study the high temporal resolution indicated in the title?

By the way, the input for the GRASP-AOD retrieval is the AOD, not direct solar irradiance.

Other comments

Abstract

Line18: "they can be every minute" The verb is missing. Please rewrite.

L23: Size >> Particle size

L36: "GRASP-BTS AOD-based dataset": this is hard to understand. There are plenty of such acronyms in the manuscript. The GRASP papers (https://www.grasp-open.com/publications-2/) frequently adopt a nick for frequent applications: GRASP-AOD is one of them (Torres and Fuertes, 2021). And that's the application (settings included) that is used in this case. Therefore the name cannot be changed depending on the instrument (GRASP-BTS, GRASP-PFR, and so on). This creates much of confusion.  Many other instances in the manuscript (e.g. line 297) are in the same direction.

Introduction

It is overall too long in providing aerosol generalities that are well known and could be much reduced by citing a few key references. Better come to the point, focus in introducing the elements that are needed in this particular study.

L65: correlates with aerosol COLUMN concentration

L66: size >> size predominance. This must be changed throughout the text (e.g. Line 113). Otherwise it would speak about a single size instead of a size distribution in which a specific size range dominates (in terms of mass or volume, by the way; not number).

L90-94: the AERONET inversion uses AOD and sky radiances (not only radiances, not only almucantar geometry). The version 3 inversions (Sinyuk et al) could be cited here. 

L105: it may be worth mentioning here that index of refraction needs to be known or assumed.

L111: this is very well known since decades. A classic reference to some old book is more desirable here; otherwise it looks like a recent finding. Same for line 123.

Section 2

Line 184: the 1640nm channel is missing.

L188: 30 seconds >> 1 minute.

L190: the alignment is done by the 4 quadrant detector, not the collimator. The latter is used for straylight rejection in the sky scans.

L201: Sun angular size in 0.5deg and FOV is 3deg. It's unavoidable that some sky light leaks into the DSI.

L204: please provide a reference on the BTS calibration. Same about the AOD retrieval with BTS (line 209).

L213: not all those inputs are needed for GRASP to run. Please rewrite.

L214: the GRASP-AOD requires AOD plus the assumption of index of refraction.

L216: check repetition.

L221: exclusively >> separately?

L226: PFR AOD >> AOD obtained with the PFR (to improve readability).

Line 230: AOD500nm>0.03. Why? What do GRASP-AOD papers say about this minimum AOD?

Same about the criteria on Angstrom exponent and fine/coarse mode AOD. It brings me again to the main comment #1.

L250: Why 1.45-0.003 ? Some justification is needed. Otherwise it looks totally arbitrary. Same for line 288.

L258: the 1640nm channel (available in the Cimel) is not used in this list. Why?

Figure 1: I would recommend changing to Table format.

Section 3

L297: AER-SKY: not only radiances are used (as already mentioned). And the abbreviations are awful.

L300: "In this section": check repetitions.

L303: better quantify than give the valuation ("Excellent"). The goodness will depend on the intended application or the uncertainty estimates.

Table 1: table captions are preferably self-explicative, but this is not possible with all the abbreviations.

L345: the differences between using climatology or fix value are small. What about using the closest AERONET retrieval of the refractive index? This magnitude is very much related to aerosol composition and can depart significantly from the site average value.

L362: depend >> affect

L381: extrapolated >> interpolated?

L383: reference needed.

L399: please clarify why is this expected. 

L466-467: you try to retrieve the SD, therefore you don't know it. What does it mean “using prior knowledge”? Moreover, the use of AERONET inversion information as initial guess to improve the result is a trick (main comment #1). The approach in line 564 is far more reasonable. 

Figure 11: excellent example of data not fitting to the Angstrom law. Why is the fit to the Angstrom law used in the manuscript? Is it justified? Why not using just AOD observations? This is actually realized by the authors (line 618).

L500: not that unusual. See Eck et al (1999; 2023)

L572: is 1640nm channel considered in the Cimel? It's almost 2 times longer than the 862nm of the PFR.

L590: please re-think. It's obvious that the lesser number of data, the better fit. With 2 points a  linear fit is just perfect. But there must be more information (lower uncertainty) if more data are used in the input. Moreover, using the Angstrom approximation makes you lose real AOD features (see my previous comment on that).

Table A1:

GRASP-BTS: ...and GRASP-AOD as retrieval.

AER-SKY: the input is AOD and radiance (almucantar or hybrid geometries).