General points

The manuscript describes the algorithm to obtain spectrally unfiltered shortwave (SW) and longwave (LW) radiances at top-of-atmosphere from the observations by the BBR instrument on board of EarthCARE. The spectral unfiltering is needed to correct for the spectral sensitivities of the instrument and for the contamination of SW radiation in the LW channel and vice versa. This paper is part of the special issue describing the algorithms for EarthCARE.

The structure and overall story of the manuscript is quite clear. However, when it comes to the details of the algorithm, the equations, and the steps that are taken, the paper is not clear and sometimes ambiguous, especially in Section 2. Since the BM-RAD algorithm should be perfectly clear to avoid errors later on, corrections in the manuscript are needed. These changes are not very difficult but necessary, and therefore these are major revisions.  Furthermore, several technical corrections should be applied throughout the paper. 

Specific points

-    In the Introduction (Section 1) more high-level information on the aim of the BBR instrument in combination with other EarthCARE instruments is needed.

-    The paragraph starting on L. 29 seems too detailed for the Introduction.

-    L. 25: what is the function phi? Please mention that it is the spectral response function, and is needed to separate between reflected solar and emitted thermal fluxes.  

-    L. 29: all three references should be between brackets.

-    Section 2: This section contains bugs, is unclear and should be improved and clarified. The symbols are unclear, the different unfiltering steps are not clearly separated. 

-    Equation 1: please give the integration limits; this holds for all integrations. 

-    L. 58: SW channel: do you mean SW radiation ?

-    L. 58: efficient > an efficient

-    L. 62, Eq. 5: subscript SW - in other places you use sw. Please be consistent in the subscripts throughout the paper. SW and LW are clearer subscripts than sw and lw.

-    L. 64: observed. > observed:

-    Eqs. 7 and 8: I find it confusing that the spectrally integrated radiance has the same symbol L as is used for the spectrally dependent L(\lambda). Please use a clear distinction in symbols.

-    L. 76-79: “This conversion …. solar radiation”: Please clearly separate these 3 factors.

-    Eqs. 8-9: The terminology in these equations, e.g. the subscripts “sw,sol” and “lw,th”, is not  clear.

-    L. 85: L_sol,L_th: where is now the subscript unfil, which was used in Equations 7-10 ?

-    L. 93-94: please clearly separate these different steps.

-    Eqs. 13-14: what happened to the fil and unfil subscripts introduced in earlier equations? 

-    L. 97: alpha_sw, alpha_lw: these are new variables! Where are alpha_sol and alpha_th  introduced in Eqs. 9-10?

-    L. 97: the name “unfiltering process” is quite confusing: there is an unfiltering step and a decontamination step. Please clarify the entire Section 2.

-    L. 102: double bracket ) 

-    L. 103: physical > geophysical 

-    L. 104: remove , in such as, 

-    L. 106: aerosols: how about clouds? what are the ranges in optical thickness and height of aerosols and clouds?

-    L. 114: droplets

-    L. 119: are the three spectral response functions of the instrument independent of the (3) viewing directions?

-    L. 136: MSI-based algorithm

-    Figure 2: please use the same font style for the symbols and equations in this figure.

-    L. 140: The Fig. > Figure; same comment on L. 156.

-    L. 148: It is quite remarkable that alpha does not depend on cloudiness. What is the explanation that the solar contamination in the longwave channel does not depend on cloudiness, since thick clouds in the daytime reflect a lot of radiation.

-    L. 150: m/s; note that all units should be written in upright font.

-    Fig. 3: the red colored dots in the two lower plots are unrelated, I assume, to the legend of the upper plots. Then please make these dots black, and define the residual in the main text.

-    Eq. 16: symbol a is already used in Eq. 15, and has a different meaning there. Please use unique symbols for each quantity. The same remark holds for the next equations. Please be consistent in symbols and terminology.

-    Fig. 4: On the basis which points did you determine the precise relationship shown in the 4 plots? The a and b coefficients are exactly the same, but the data points are different. That seems strange.

-    Caption Fig. 4: please explain the two typs of points in each subplot.

-    Sect. 4.4, first sentence: Please explain where we are in the procedure of the flow diagram. Do you mean spectral unfiltering to obtain the correct SW radiances? Is this the step after the decontamination?

-    Eq. 17: apart from the reuse of earlier symbols, this is an unclear formula. Please make a multiplication with the inverse or add brackets.

-    Fig. 5: the plots and their legends are poorly readable. Please use a larger font.

-    L. 190: stand-alone algorithm

-    L. 196: “much smaller than for the CERES and GERB instruments”: what is the reason?

-    Fig. 6:  what are the fit coefficients? This fit function does not hold for larger radiances.

-    Caption Fig. 6: use correct ordering: (a) ..., (b) ..... 

-    Caption Fig. 6: please explain: are these the alpha factors of Eq. 10 or of Eq. 14?

-    Table 1 header: what is the reason that you switch between LW and th, and between SW and sol?

-    Section 5: Section 5 is very short. How did you do the analysis? Please explain how you arrive at Table 1. 

-    Title Section 5: do you mean algorithm verification instead of performance verification? The next section is about performance verification.

-    L. 217: Table 2

-    L. 225: Please summarize the results of Fig. 7: which conclusions do you draw from it?

-    Fig. 7: The plots in the right column are somewhat smaller than in the other columns. Please make all subplots the same size. How will you orient this figure to make it readable? Preferably landscape.

-    Caption Fig. 7: "RT sim (truth)"

-    References: Please correct all references, because the initials should be put after the surname.

Technical corrections throughout the manuscript

-    level 1 > level-1, level 2 > level-2 

-    Subscripts which are words, abbreviations or acronyms should be in upright font. For example, fil in L_fil on l. 50 should be upright. This occurs many times in the manuscript. 

-    Symbols should be in italic font.

-    L. 67: Fig. 5 > Figure 5. If it is the starting word of a sentence, Fig. should be written in full. 

-    Always use a space between number and unit: e.g. L. 91: 5 µm

-    Units should be written in upright font (e.g. l. 152, and many other places)

-    Fig., Eq., Sect. should be written with capital. 

-    Tables: please put the table caption above the table.