Main points

1. The comparison of the ‘improved’ product and the operational product still needs clarifications. The discussion of the results and the reporting of the statistics of the comparisons still needs to be made more transparent.
• Table 5: The current caption, column headers and row headers are confusing. The use of the subscripts S1, S2 and M, and “vs” is confusing. Clarify what exactly the reported numbers mean.
• Which numbers support the statement that the present results compare better with the ground-based reference? How are the correlations coefficients, slopes and intercept of comparisons shown in Figure 10 to be understood in this regard?
• Please clarify whether the improved HCHO product yields better slant column densities as compared to the operational product, as stated in the abstract (line 19). Which numbers support this statement? How are the correlations coefficients, slopes and intercept of comparisons shown in Figure 10 to be understood in this regard?
• It is stated that the use of prior information in the aerosol profile from MAX-DOAS improves the data; Figure 10: it appears that the use of this information does not improve the data.
• Line 356-358: Clarify what is meant with the “control variable method” that is used to evaluate the improvement in terms of SCD. It is not clear what is meant with “we use SCD in our retrieval and AMFs in operational retrieval …”

2. The caption of Table 3 is unclear. It seems that the row “this study” refers to a reference case, and that the rows further below report performance values for cases where specific settings are modified with respect to the reference case (while all other settings are kept unchanged). Please explain in the caption what RMS and the sigma value mean. Clarify to which parameter they belong (SCD or DSCD). What is meant with “4th baseline and scaling polynomials”: a polynomial of 4th order? What is meant with “TROPOMI ISRF Calibration Key Data (CKD) v1.0.0”? is here an alternative ISRF employed?

3. Line 302: the introduction of the Standard Error (SE) is not understood. Is eq 18 defining this Standard Error (SE)? The quantity on the left hand side of Eq 18 should be labelled by something more specific than “Error”.

4. The reporting of values with associated uncertainties is unclear and made using various different notations. E.g. the expressions “0.57(± 0.68, ± SD)×10^16molec cm-2 ” (Line 334), “0.21± 0.41×10^16 molec cm-2, average± SD” (Line 335/335), and “7.00 % (± 1.71 %, ± Error)” (Line 360) are not clear. What should the reader do with the SD and Error? Please clarify and make consistent (the notation used in “0.36(± 0.60)×10^16 molec cm-2” (Line 334/335) is looks ok and will be understood by the reader.

5. Line 268: The “first order Taylor series approach for O3 SCDs” needs to be explained. If the approach by Puķīte et al. (2010) is meant, this needs to be referenced (Puķīte, J., Kühl, S., Deutschmann, T., Platt, U., and Wagner, T.: Extending differential optical absorption spectroscopy for limb measurements in the UV, Atmos. Meas. Tech., 3, 631-653, 2010.)




Minor Editorials

Legend S5: The caption indicates that the RMS data from the operational (DOAS) product are depicted in the left and the data from the present study (BOAS) in the right panel. The legend suggests the opposite.

Figure 10 legend of panel f. Typo: “Operatioanl”  “Operational”; Typo: legend of magenta and pink have the same text “(a-priori from MAX-DOAS)”

Table 5 caption: Expand the acronym “NMB”, and “SE”

The symbol Ns is used for both SCD and DSCD; please use different symbols.
Line 234: what is introduced as an “SCD correction” is, according to equations 9 and 10, a “DSCD correction”. Proposed to rename.

Line 256: Introduce the covariance matrix. Clarify the elements of the state vector.

Equation 14: Introduce the index j. Clarify how the expression is to be evaluated, which value for j is to be taken. If the term Cj,j is supposed to be squared please use the square symbol.