Our responses to the reviewers‘ comments:

R1: I only had a couple of issues of any significance. Somewhere around H=18, certainly by H=19, the sample contains very few asteroids. Any bias found is likely to be dominated by whatever random difference in aspect there was between the catalog and the observations, especially considering that small asteroids will be elongated. Although care is taken to define small asteroids as being below 25km, I think it might be worth considering a cut-off at H=19, below which  analysis is left for a later work. At the least, there should be a paragraph in the text about the accuracy of considering bias for H >19.

A: We have added three sentences to the 3rd paragraph of section 3, commenting on that the trends towards the faint end of the studied H range (where NEAs predominate) will need to be studied on a larger sample in the future.  We didn’t shift the cut-off of our analysis in the paper to a smaller H though, as we see no obvious change in the trend for the (H_catalog - H) values in the range H = 19-20 wrt the points at H = 14-19, so we have kept the current analysis unchanged.

R1: It was well-publicised that the WISE survey found fewer smaller 100-1000 m diameter asteroids than expected. A casual reader might incorrectly surmise that this paper could shed some light on possible biases in that regime. Although it is correctly stated that the de-biasing of the albedos of the WISE survey has negligible impact on diameters directly determined from thermal observations, you can use H-magnitudes to determine size frequency distributions from average albedos of different taxonomic type, in which case it would have an effect on your derived size frequency distribution (this is mentioned in passing later). In fact this is what Mainzer et al (2011b) did using catalogued H-magnitudes for NEAs H<22 mag. The biases in that catalog could affect significantly affect the determined size-frequency distribution at those sizes, but alas we still do not know what the biases are at that size range. I think some prominence needs to given to this problem.

A: We agree with the reviewer that this problem needs to be studied in the future.  It is beyond the scope of our present paper.

R1: It is stated that Mainzer et al 2011b and Masiero et al 2011b allowed H to be free-floating best-fitting it from an initial value. It appears this information comes from a private communication. It will not work to best-fit H using NEATM because you cannot get a unique residual if you allow eta to be free-floating also. Therefore their H values will be no improvement from the catalog magnitudes, and neutral with respect to your correction. Suggest you refer to their H values as "slightly adjusted" or some such as opposed to "best-fit" and indicate the extent to the difference from the catalog and why it does not affect your correction significantly.

NEATM eta-values will be affected as well as albedos from inaccurate H magnitudes.

A: We have modified the sentence in section 4 accordingly and we added a footnote to the paragraph commenting on the issue.

R1: Minor comments and suggestions for grammar/clarity:
Abstract:
"with the median" -> "with a median"
 "but a major reason" -> "but the reason"
 "a main problem" -> delete "main"
 "There is apparent only a small, marginally significant difference... asteroids" Going in what direction? i.e. is the albedo higher or lower for smaller asteroids?
 "The apparent small difference" -> delete "apparent small"

A: All changes made.

R1: Introduction:
 para. 1
 "Diameters and albedos of asteroids are their basic physical paramters." Matter of opinion - perhaps mass or composition are, albeit harder to measure.

A: Ok.

R1: "An efficient use of the direct techniques is, however, limited" -> However, an efficient use of the direct techniques is limited..."

A: Changed.

R1: "Among indirect...thermal models". Actually, are there ANY other indirect techniques that fulfil these criteria?

A: We have changed the first paragraph of the Introduction section, mentioning the other indirect technique of polarimetry.

R1: para. 2
 "and modeling its phase function" -> "and a model of its phase function"
 "from the distance" -> "from a distance"

A: Changed.

R1: "at zero phase angle" -> define phase angle here.

A: We have improved the sentence there.

R1: para. 3
 "of a dependence" -> "of the dependence"
 "A systematic model" -> "The systematic model"
 para. 4
 "estimating diameters" -> "estimates of diameters"
 para. 5
 "that an accuracy" -> "that the accuracy"

A: All changes made.

R1: Section 2
 para. 1
 "asteroids that we made" -> delete "that we"
 "of spins" -> "of the spins"
 "About a half" delete "a"
 "(see their list below..." -> "(listed below..."
 "A part of the H estimates is new data..." -> "The rest is new data..."
 "in following paragraphs" -> "in the following paragraphs"

A: All changes made.

R1: Section 2.1
 para. 1
 "Many of the asteroids were, however, observed" -> " However, many of the asteroids were observed"
 "observations as" -> "observations, as"
 "with the CCD" delete "the"
 "cameras we got a higher" -> "cameras we acheived a higher"
 "extinction with observations in R than in the V band" -> "extinction compared to the V band"
"A spectral transmission" -> "The spectral transmission"
 "note that the most common C and S asteroid types have the mean... 1998)." -> delete "note that", "the mean" -> "a mean", move rest as a sentence and put before "With such..."
 "With such filter" -> "With such a filter"

A: All changes made.

R1: Section 2.2
 para. 1
 "asteroid corresponding -> "asteroid, corresponding"
 "magnitude: that is the" delete "that is"
 "resuced to the unit" delete "the"

A: All changes made.

R1: "to a normal phase angle" Do you mean at right-angles to sometihng, or typical? Don't quite understand what is meant here.

A: The sentence was changed to be more understandable.

R1: "In most cases...<0.2 mag.." Contains long sentence, suggest: "The series would commonly be 1-period, but would be 2-period for tumplers, or two additive 1-period Fourier series in the case of a binary asteroid where lightcurves of both the primary and the secondary components were observed. Fourier series were fitted to photometric observations made over one or more nearby nights, that covered the rotation lightcurve sufficiently (see the references below Table 2 for details of the technique). In these cases, we estimated the mean reduced magnitude to be <0.01 mag. In a fraction of asteroids in our sample, mostly long-period where we did not obtain sufficient data to get an accurate Fourier series fit or where the rotation period has not been measured with sufficient accuracy, we estimated the asteroid's mean brightness. This was estimated as the mean value of a range in which the Fourier series zeroth order lies for possible and plausible fits to the observations or as an average of observations made during one or more nearby nights. In cases where even a range of possible Fourier series fits could not be obtained , it was estimated; in those cases, we ensured that the resulting mean magnitude estimate had an uncertainty < 0.2 mag."

A: We have rewritten the section 2.2, also according to comments by Reviewer 2.

R1: "required an evidence" delete "an"
 "moderate so" -> "moderate, so"
 "phases so that" delete "so"

A: All changes made.

R1: Section 2.3
 para. 1
 "and conclusive or on" -> "and conclusive, or on"
 "resulted H" -> "resulting H"

A: All changes made.

R1: para. 2
 "in the G values were" ->"in G were"

A: Changed.

R1: "As we aimed... justified cases." Does this bias your sample at smaller sizes, for example fewer NEAs than general population. Probably not significant numbers to have any effect though.

A: Yes, by limiting our sample to include only asteroids that were observed at solar phases <~30 deg, we excluded a number of NEAs that we observed at higher phase angles.  But apart from decreasing the number of NEAs in our sample, it didn’t have any significant effect in our study, as selecting asteroids observed at low-moderate solar phases is only a geometric effect, not related to asteroid albedo or color.

R1: Section 2.4
 para. 1
 "values to H {IDENTITY} H_V" -> "values to H_V"
 "for known" -> "for the known"

A: All changes made.

R1: "according to its orbital group membership" Can you list what you assume for each orbital group. e.g. do you assumed S-type for NEAs, C-type for outer-main belt etc. What proportion of your asteroids have unknown class or V-R colours?

A: We refer to Table 2 of Warner et al. (2009) further down in the section 2.4, which we think is sufficient.  As a proportion of asteroids with unknown class/V-R changes with size (H), their overall number wouldn’t tell much.

R1: Section 2.5
 para 1.
 "0.38 mag we suspect is due" -> "0.38 mag; we suspect this is due"

A: Changed.

R1: Section 2.6
 para.1
 "A magnitude of the difference" -> "The difference"
 "on a shape" -> "on the shape"

A: All changes made.

R1: Note to Table 2
 "Entries from reference (12)...original paper" Would it be possible to reproduce them in your Table?
 
A: The \delta G values in the Table completed and the note below the table removed.

R1: Section 3
 para 1.
 "with their H" delete "their"

A: Changed.

R1: para 2.
 "without a pole" delete "a"

A: Changed.

R1: para. 3
 "Analyzing the behavior" -> "To analyse the behavior"
 "with the box size" -> "with a box size"
 "dependence with fitting" -> "dependence by fitting"

A: All changes made.

R1: para. 4
 "are following" -> "are the following"
 
A: Changed.

R1: Fig.1, Fig.2, Fig.3
 Do the outliers have large lightcurve amplitude? Consider labelling and discussing briefly the specific extreme outliers ~1.5 mag. what you speculate the reason is the catalog has them so wrong.

A: Overally, the outliers don't have prominently larger amplitudes than the rest of the points.  In Figs. 7-9, we have highlighted points with amplitudes greater than 0.4 mag; accounting for the overall systematic shift of the high-amplitude points to higher negative mean offset, the proportion of gross errors in the catalog H values doesn't appear to increase prominently with increasing lightcurve amplitude.

R1: para. 4
 "with the standard" -> "with a standard"

A: Changed.

R1: para. 5
 "in following" -> "in the following"

A: Changed.

R1: Section 3.1
 para. 1
 "low-albedo ones" -> delete "ones"

A: Changed.

R1: para. 3
 "visually predominate" Not quite sure what you mean. Theres a bias to be observed because brighter. Also there really are more of them because parent population is in inner main belt.

A: We have improved wording of the sentence.

R1: para. 4
 "between the mean offsets of the medium- and the low-albedo ones in the orbit catalogs H values" -> "between the medium and low-albedo mean offsets"
 "0.043 mag in" -> "0.043 mag, in"
 
A: All changes made.

R1: para. 5
 "having the systematically" -> "having a systematically"
 "type) ones having the systematically" -> "type) having a systematically"
 "is due to that the orbit" -> "is because the orbit"
 "of the assumed" -> "of an assumed"
 "0.40 they used" delete "they"
 "estimates..red)" "estimates, that are made most effectively in the R-band, since the maximum sensitivity of standard CCDs lies there."
 "types have actually" -> "actually have types"
 "albedo type" -> "albedo-type"
 
A: All changes made.

R1: Section 3.2
 para. 1
 "The high amplitude asteroids" More important is the dispersion which is much greater due to observing different aspects, aspecially for higher H.

A: We have added one sentence on the issue to the end of the 1st paragraph of section 3.2.

R1: "offset, estimated with the" -> "offset, as shown by the"
"the figures which is shifted" -> "the Figures shifted"
"asteroids at" -> "asteroids, at"

A: All changes made.

R1: para. 2
"There may be a few reasons" -> "There are a few possible reasons"
"offset of the" -> "offset from the"
"could made" -> "could have made"
"ratio so" -> "ratio, so"
"choose measuring images" -> "choose to measure images"

A: All changes made.

R1: "detected more frequently close to the lightcurve maximum". Actually I'm surprised this effect isn't much bigger. I suspect it will be for higher H, but can't be seen in your sample.

A: Ok.

R1: "at time when" -> "at times when"
"aspect if" -> "aspect, if"

A: All changes made.

R1: Section 3.3
para. 1
"One particularly interesting work is Parker et al. (2008). They compared" -> "Parker et al. (2008) compared"
"data that they derived" -> "data derived"
"assuming the mean" -> "assuming a mean"

A: All changes made.

R1: para. 2
"Worth mentioning is also the earlier work using SDSS data by Juric et al (2002). They did an analysis..." -> "Juric et al (2002) undertook an analysis..."
"also analysed a" -> "also considered a"
"measurements from the" -> "measurements in the"
"Release for a sample of 1335 asteroids to" -> "Release, a sample of 1335 asteroids, to"
"reflect their different" -> "reflect the different"
They also...respectively" move to start of para. 4
"with the SDSS" delete "the"
"with the median" delete "the"

A: All changes made.

R1: para. 3
"The offset... is unclear". How uncertain is their (V_MPCORB-V)? Maybe they agree within the uncertainties anyway and there is no need to seek an explanation.

A: There is not much information on the uncertainties of the offset they found in Juric et al. (2002), so we cannot really judge whether the difference isn’t within the uncertainties and we leave it without comment in our paper.

R1: "The offset... of -0.36" -> "The MPCORB offset they found is somewhat lower than the offset we obtained for asteroids with similar absolute magnitudes; for H in the range 12-16, we found an average (H_MPCORB - H) of -0.36."

A: Changed.

R1: para. 4
(after moving end of para. 2 here) delete "of the offset with the SDSS asteroid color that they found"
"cause; both we and Juric et al speculate that" -> "cause; Juric et al speculates similarly that"
"in, or close to, the red band to V, for the asteroids" -> "in the red band to to V for asteroids"

A: All changes made.

R1: para. 5
"Another interesting earlier work is Galad (2010). He analysed" -> "Galad (2010) analysed"
"with rotation periods estimated in previous works, estimated" -> "with measured  rotation periods, estimated"
"MPCORB H values" delete "H values"
"17.7 (the median" -> delete "the"
"estimated with assuming" delete "with"
"The resulted corrected" -> "The resulting corrected"
"Galad also mentioned a" -> "Galad also discussed a"

A: All changes made.

R1: Section 4
para. 1
"in following" -> "here"

A: Changed.

R1: para. 2
"NEOWISE diameter estimates were generally stable" Clarify. They are unchanged by your albedo estimates. Nevertheless, there are big systematic uncertanities in their diameters still remaining. 

A: We think that the text and reference to Harris and Harris (1997) suffices there.

R1: para. 4
"4. As the WISE" -> "4. The WISE"
"0.20 mag and considering" -> "0.20 mag. Considering"
"contribute with a" -> "contribute a"
"than or at worst equal to the" -> "than or at worst equal to the"
"available an information" -> "available information"
"was a contribution" -> "was the contribution"

A: All changes made.

R1: para. 5
"10. In the figure, we highligted" -> "10. We highlighted"

A: Changed.

R1: "we highlighted points of known low-, medium and high-albedo type asteroids". Unclear what you mean. Do you mean you highlighted asteroids of known taxonomic type?

A: The sentence has been improved.

R1: "but we consider that" -> "but we caution that"
"errors may be" -> "errors will be"

A: All changes made.

R1: para. 6
"Our data reveal that it was largely due to the systematic bias of MPCORB H values for smaller asteroids in the range H > 10." Below 4km you have few low albedo asteroids in your sample, where there is still a large affect from the selection bias. If you were to draw a best-fit line at that size, there would be an apparent increase. Therefore you can say that between 4-30km they apparent trend was due to the MPCORM systematic bias. Below 4km, selection biases against low albedo asteroids may play a bigger role in indicating a false trend.

A: We have pointed out it in the abstract that the apparent increase of WISE albedos is from D ~ 30 km down to ~ 5 km (from H ~ 10 to ~ 14).

R1: "the mean errors" -> "the standard errors"

A: Changed.

R1: "e.g. due to...applied thermal models." Perhaps you should caution that you only include a small sample of small NEAS with presumably young surfaces in this study.

A: We have reworded the sentence.

Section 5
para. 1
"cannot really analysr reasons for the" -> "cannot rigorously determine causes of the"

A: Changed.

R1: para. 2
"that a number of" -> "that many of"
"could be done not very high above the magnitude limits" -> "could not be done much above the magnitude limits"
"close to their aphelions" -> "close to aphelion"
"elongations" -> "elongation"
delete "to things like a"
"field, an accuracy" delete "an"
"and a quality" delete "a"

A: All changes made.

R1: para. 3
"way how main" -> "way for main"
could got biased" -> "could have biased"
"procedures or" -> "procedures, or"
"or a way how they" -> "in the method by which"
"inherrited" -> "inherited"
"from the photographic plate time" -> "from the days of photographic plates"
"and they are converted" -> "and converted"
"V with subtracting" -> "V by subtracting"
"two or some other errors occured" -> "two, or some other errors, occurred"
"enough so that" -> "enough that"
"offset. Anyway, a thorough" -> "offset. A thorough"
"be good" -> "be advisable"

A: All changes made.

R1: para. 4
"A reason for" -> "An explanation for"
"The MBA/NEA turning point" -> "A turning point"
"The reason may be in that some or many NEAs got a" -> "It may be that many NEAs receive a"

A: All changes made.

R1: para. 5
"Of an interest is also that" -> "Also of interest is that"
"but they are slightly more" -> "but slightly more"
"good work in" -> "good job in"

A: All changes made.

R1: para. 6
"with stating that" -> "with re-stating that"
"be very necessary" -> "be a necessary"
"urgent to" -> "urgent task to"
"ands ways of" -> "and methods of"
"e.g. a use" -> "e.g. use"
"values, tying magnitude" -> "values, corresponding magnitude"
"could fix the" -> "could improve the"
"situation at least partially as well" -> "situation partially"
"subsequent data" -> "subsequent assumption-dependent data"
"always the preferred way" -> "always prefered"
"catalogs are to be used" -> "are intended to be used"
"should be seriously more accurate than they are now" -> "are required to be much more accurate than at present."

A: All changes made.

R2: This paper addresses a long-standing problem in asteroid science, that of deriving accurate absolute visible magnitudes (H, or more properly, H_{V}).  It provides revised H values for ~500 objects.  However, the paper does not determine the sample biases (which may be significant) that would allow the results to be generalized to the current catalog of ~500,000 objects.  As a person who uses published H values for computing thermal models, this paper does not tell me what do with the results beyond using the revised H values for the ~500 that were actually measured.

A: What we have shown is a systematic offset in the sample of 583 objects measured carefully.  We are mainly presenting this as a caution to others of the offset, and also the dispersion of wrong H values.  For the first time, we analyse a dependence of the bias in the catalog data with H.  How one might apply our results to a survey of 500,000 objects is beyond the scope of our paper; we do not propose a definite recipe.  However, users of the catalog H values should be aware of the bias and they could consider how to account for it for their particular purposes.  One might shift catalog H values by the mean offset we find, or increase the uncertainty estimate in H to include that offset.  What we have done for the small sample of 583 is adjust the H values to our corrected values, and then note that the trend in albedo that appeared in the WISE values for the objects goes away when the corrected H values are used.  

We added or strengthened these points in our paper now, in the (new) Conclusions section as well.  We have also added the subsection „Biases in the data sample“ (it is section 3.3 in the revised paper) where we present that the apparent biases in our data set do not have an effect greater than 0.1 mag in the derived catalog H mean offset.

R2: Futhermore, because the paper does not determine sample biases, it overreaches in its conclusions, stating for example that average albedos for various taxonomic types have been conclusively determined.

A: We have never used the words „conclusively determined“ there.  To make the things more clear, we have improved the wording of the last two sentences in the abstract and we have elaborated on it in more detail in Section 4, three paragraphs added there. 

R2: Another major concern is the lack of proper consideration of uncertainties in the H magnitudes themselves. While formal errors within the dataset are given, the authors do not present the absolute errors on H, putting the conclusions into question and making the work considerably less useful to those seeking to use revised H values, for example in thermal models.

A: We have accounted for one additional uncertainty source in the H estimation that we didn’t account for in our original paper: the H-G model error which we take to be about 0.03 mag.  We have revised the H uncertainties in Table 2 by quadratically adding this model error in the delta H values.  We have improved the section 2.6 that describes the H uncertainty sources involved.

We believe that now we accounted properly for all major uncertainty sources in the H estimation, except aspect-related changes of H, which we estimate to make an uncertainty ~0.07 mag as we describe in Sect. 2.6.  So, our uncertainties actually represent the absolute errors on H, with the exception of that the aspect-related changes in H have to be accounted for, e.g., by quadratically adding 0.07 mag to the quoted errors of the one-apparition H estimates.  We also believe that our estimates *are* useful to those seeking revised H values; in most cases, there can hardly be obtained a significantly better H estimate unless photometric data over a few different aspects and a shape/spin model are obtained.   We have tried to clarify it in Sect. 2.6 now.

R2: Major Issues - Detailed Comments:
It is difficult to know how representative these measurements are of the entire population of asteroids.  The authors should define or determine the sample's biases in lightcurve amplitude, taxonomic type, color, etc.  For example, in Figures 7-9, the authors show that most of the H offset is caused by high amplitude objects ....

A: No.  Only a small part of the H offset is related to an effect of high amplitude.  We have commented on the apparent small correlation of the (H_catalog – H) values with lightcurve amplitude in the first paragraph of Section 3.2, which we believe is adequate for this apparently small effect.

R2: .... However, this is done knowing that they have excluded many objects because they have incomplete rotational phase coverage (see section 2.2).  Excluding objects from the sample changes the prevelance of the offsets in H due to high amplitude objects.  Apparently there are objects in the sample for which the amplitude could not be determined, so they were discarded.  Is the sample representative, and what are the rules by which offsets to H should be applied when the lightcurve has not been directly measured? By not discussing the criteria by which objects were selected and/or discarded (and their numbers), it is impossible to determine whether the sample is representative.

A: We comment on a small systematic bias that a selection effect favoring asteroids with moderate amplitudes in our sample could cause due to the  small correlation of the H offset with lightcurve amplitude in the last paragraph of Section 3.3.

R2: … This sample consists of ~500 asteroids, but we need H values for ~200,000 for NEOWISE.  In order to maximize the usefulness of this paper, the authors should determine the sample biases in rotational period, visible color, and time of discovery (in case some observatory codes are partially responsible for the offset).

A: We have added to section 3.3 a sentence mentioning that a bias against slow rotators, which could be moderate in our sample, has an insignificant effect to the derived H offset as slow rotators have similar lightcurve amplitudes as faster rotators that predominate in our sample.  Re. the reviewer’s comment on a possible bias in asteroid color and time of discovery: We added two sentences to the first paragraph of Section 2, commenting on that our target selection procedure was blind as to asteroid color or discovery circumstances.

R2: … Otherwise, there is no way to know whether or not these offsets should be generalized from the sample here to the whole catalog when computing thermal models.  Figures 7-9 seem to imply that the sample is dominated by high amplitude objects, but how does this compare to other debiased samples of lightcurve amplitudes?  Comparing Figures 4 and 7 suggests that the entire offset effect is due to high amplitude objects.  

A: We point out that the amplitude effect on the H offset is a small effect – the two curves in Fig. 7 tell the story. 
For benefit of readers, we have included the number (140 of the 583) of the high-amplitude asteroids presented in Fig. 7 to 9 to the text of the 1st paragraph of section 3.2.

R2: … But nowhere in the paper is it discussed whether or not this sample is actually representative of the entire asteroid population.  If the authors are unwilling to figure out the sample biases, then the sweeping
conclusions that these results are universal to all objects need to be toned down. 

A: We reiterate on our previous answer above: We are not proposing that thermal modelers take any account of this H-bias for computing diameters, as it has almost no effect there.  Obviously, the catalog H offset has to be considered in computing albedos.  Whether to infer a correction based on an estimated mean bias or leave alone objects without accurate H determinations is beyond the scope of our paper.  We are not proposing to produce, or even offer a recipe for producing, a "bias corrected catalog" of all hundreds of thousands of objects in the WISE catalog.

R2: … For example, recomputing the average albedos for various taxonomic types seems to be overextending what has really been shown here.  

A: Actually, we think that presenting our average albedos for S/A/L types and C/C-like types is useful.  There may be a small bias towards higher albedo asteroids in our sample even within the individual taxonomic groups, as we comment in the last three paragraphs of Section 4, but we show that with our accurate H values, we corrected what appeared to be the most significant systematic error in the albedo data and estimating the small residual bias towards higher albedos within the individual taxonomic groups is beyond the scope of our paper.

R2: -The notion that the trend of increasing albedo with decreasing size *for the objects with visible/NIR taxonomic classifications only* should be ascribed solely to a bias in the MPCORB magnitudes is not supported.  There is a very strong selection bias against small, faint (e.g. low albedo) asteroids in all the visible surveys that have discovered the objects that have been observed spectroscopically.  The authors have not removed the biases of the visible surveys, or their own sample, and so there is no way to definitively say what causes the trend.  

A: What we say is that the trend in increasing WISE albedos with decreasing size found in Mainzer et al. (2011a) goes away in our sample when the H values are corrected.

R2: … Drawing a straight line in Figure 10 using only the objects with known taxonomic types isn't reasonable; you are throwing away the rest of the taxonomically classified sample that you did not observe, which may or may not have offset H values - we don't know because they weren't measured.  

A: We can only include the sample of objects we observed and have verified measures of H. From this limited sample we determine that the trend in albedo goes away. It is reasonable to infer that it does so for the larger sample of objects with WISE diameters but not verified albedos. Indeed, the mean offset in H for all the objects suggests that it does, but we can't quantitatively measure trends in separate taxonomic classes except for the subset of objects for which we have (a) a taxonomic classification, (b) a verified H value, and of course, (c) a reliable diameter.

R2: … The authors may speculate that an offset in H is partially responsible for the trend, but claiming that this is conclusively the cause is
not supported. As noted in the WISE NEO paper (Mainzer et al. 2011 ApJ 743, 156) and in Masiero et al. (2011), there is NO observed trend in albedo vs. diameter for the all of the objects detected by NEOWISE using a thermal infrared selection rather than visible light selection.  This result strongly suggests that the trend in the optically-selected sample is influenced by the visible surveys' biases against small, dark objects.  

A: What Mainzer et al. (2011b) showed -though it is difficult to read it out from their Figure 14- is that there is no strong trend of albedo with diameter among NEAs smaller than about 2-3 km.  (There are not many NEAs in their sample larger than 3 km to check a possible trend of albedo vs size among larger NEAs; though from their Figure 14 it seems that there may be a lack of high-albedo NEAs larger than ~2 km, but this would need to be looked at in detail to see whether the apparent paucity of high-albedo asteroids among larger NEAs in their data is statistically significant.)  The trend of increasing albedo with decreasing size found in Mainzer et al. (2011a) is for MBAs with sizes (for S-type asteroids) from about 30 km down to about 5 km.  We have explained this latter trend as being due to the increasing offset of the MPC catalog H values with H increasing from 10 to 14 (which corresponds to diameters from ~30 downto ~5 km for S-type asteroids).  Our data for NEAs with H >~16 (corresponding to D <~2 km for S types asteroids) may be consistent with the Mainzer et al.'s finding of no albedo trend with size there, but we have a relatively low number of data there for small asteroids so we have not studied whether the H offset vs size flattens out at H >~16 (D <~2 km).  So, the work Mainzer et al. (2011b) doesn't actually address the trend found among 5-30 km MBAs in Mainzer et al. (2011a).

R2: … You can see this in the lack of small C types.  While there most certainly are problems with the catalog H values, the authors have done nothing to disentangle the two effects because their sample biases are not determined. The last sentence in the abstract should be deleted as the authors have not proven their assertion firmly.  

A: The last sentence in abstract was modified, we believe that it correctly describes what we found.

R2: -page 9, first paragraph:  The authors say that most of the asteroids were targeted according to a set of selection criteria for "specific photometric projects", mostly aimed at deriving spin states and shapes.  These selection criteria no doubt impose a set of selection biases that should be discussed.  For example, were certain taxonomic types selected at the expense of others (this is almost certainly the case, as visible surveys preferentially detect bright S-complex objects over dark C-complex objects)?  

A: We mention the selection criteria in the 1st paragraph of section 2 and comment on the biases in the (new) section 3.3 now.

R2: -A major issue here is that the observations were primarily carried out in R band.  If the authors are attempting to make photometrically precise corrections to H, why introduce the significant uncertainty associated with trying to extrapolate to V band using color corrections that depend on taxonomic type (which is largely unknown)?  The authors state that the mean (V-I) color for C and S types is 0.73 and 0.90 mags.  Also, is Shevchenko & Lupishko (1998) really the most recent work on color terms vs. taxonomic type that the authors could find?  This work predates much of the thousands of spectra collected by Binzel's group.  

A: We prefer to use the mean color indices by Shevchenko&Lupishko (1998) for the C, S and M (X) classes, as they were direct measurements of the asteroid color indices in the Johnson-Cousins BVRI system - we have pointed it out in section 2.4 now.  More recent works measured asteroid color indices in other photometric systems, and a transformation to the Johnson-Cousins system could introduce a small but non-zero transformation error, which we believe is unnecessary as we have available the directly measured color indices by Shevchenko&Lupishko; the fact that they measured them for a smaller sample seems to be no obvious problem.

R2: … On page 10 of the manuscript, the authors state that they used this reference for the S, C, and M classes, but derived their own color terms for Q, A, D, Xc, Xe, and V.  There is no reason to treat different classes differently - color terms should be derived in a uniform way for all types using the most recent spectral libraries.  

A: As we mention above and have pointed out in section 2.4, the preferred way is to use color indices that were directly measured in the standard system.  For classes Q, A, D, Xc, Xe, and V where there are not available direct estimates of their mean (V-R), we had to derive them from the mean spectra by DeMeo et al. (2009).

R2: … If an object's
taxnomic type is unknown (which is most often the case), you are likely instroducing a 0.17 mag error into the observations that are converted to H_{V}, which is much larger than many of the errors in H that the authors claim to be fixing.  There is likely a bias in the relative numbers of S type vs. C type asteroids that the authors have observed. How do we know that this uncertain color correction isn't partially responsible for the offsets in H_{V} that the authors derive?  No discussion of the possible errors in the color correction terms and the impacts that they could have on the subsequently derived H_{V} values is given, and it should be.  

A: We have added a paragraph commenting on a magnitude of this bias to Section 3.3.  In following, we give a few more details.

With using the mean (V-R) for the class predominating in a particular orbital group, there will of course occur errors for present interloper asteroids.  Some asteroids for which we assumed a S-type's (V-R) will be C or C-like types, so with assuming (V-R) = 0.49 +/- 0.05 for them, we overcorrect their H by about 0.11 mag.  Similarly, S types in orbital groups where we assumed C-type's (V-R) get undercorrected H by the same amount.  But as long as the given types predominate (for observations in the visual) in the individual orbital groups or families, a resulting systematic error in our derived mean H offset will be on an order of a few 0.01 mag only.  Even in the worst possible case of the equal ratio of C and S types in an orbital group, assuming a C (or S) type’s mean (V-R) for all asteroids in the group would introduce a systematic error in the estimated mean H offset of 0.11/2 = 0.055 mag only; in existing asteroid groups with a predominating type, the resulting systematic error will be lower.

R2: If the desire is to really produce precise H values, why not simply report H in the band that the observations were actually taken (in this case, R), rather than convert them to H_{V}?  For the purposes of producing improved, precise albedo measurements, it would be preferable to have a better value of p_{R} than an inaccurate value of p_{V} computed from spurious color correction terms.  I encourage the authors to be bold here: if the desire is to truly come up with a way to improve absolute H magnitudes, then they should advocate for doing away with a major source of uncertainty, the color correction terms, and report H in the band at which the observations were taken. 

A: We have put the original H_R values, plus their estimated uncertainties, to Table 2.  (We considered to add the two colums with the H_R and dH_R to Table 2 in the original submitted version, but as the H_R values could be found in the original references and they were not relevant to our analyses we present in the paper, we opted for saving space and not giving the two additional columns there originally.)

As regards to estimating p_R rather than p_V: A geometric albedo in R cannot be directly estimated; the parameter in the thermal modeling is the bolometric Bond albedo A that is approximately equal to A_V = q * p_V.  When p_R is needed for some purpose, it can be scaled from p_V by the factor of (V-R), or derived from H_R and an estimated diameter of the asteroid.  But we don't think there are many purposes for which p_R is needed.

R2: Another major issue: The absolute errors in H are not discussed.  While Table 2 seems to give formal errors, which are very small in some cases (<0.01 mag), this cannot be the actual absolute error that must be used for example when computing thermal models.  The knowledge of the calibration stars' absolute photometry is not typically better than 0.03 mag, and the authors cannot be using the same standard star for each of the asteroids' various epochs.  So what is the correct absolute H error?  

A: As we wrote to a previous point above, now we have accounted for one additional uncertainty source in the H estimation that we didn’t account for in our original paper: the H-G model error which we take to be about 0.03 mag.  We believe that now we accounted properly for all major uncertainty sources in the H estimation, except aspect-related changes of H, as discussed in section 2.6 (see also our previous comments above).  Re. knowledge of the standard stars magnitudes: With the use of several Landolt standard stars for the calibrations on photometric nights, we defined the magnitude system's zero point with accuracy of 0.01 mag; we have pointed out it in section 2.1 now.

R2: -page 8 of the article: If the authors were not able to obtain rotational periods for some of the objects, how is it possible to unambiguously claim that you have bracketed the mean magnitude uncertainty to <0.2 mag? If the object has a rotational period longer than the span over which it was observed, how is it possible to unambiguously know that that is really the maximum brightness excursion?  How many objects had unconstrained rotational periods?  These objects should be clearly indicated in the table. 

A: We improved section 2.2 and estimate a bias due to the preferrence for moderate-amplitude asteroids in our sample in the 4th paragraph of section 3.3.  For convenience of the reviewer, we add a few more details in following.

There are a few different kinds of cases where we were not able to get (unique) rotational periods.

The easiest kind are cases where we got just an ambiguity in the period solution but the amplitude could be constrained reasonably.  A negligible uncertainty in the mean magnitude level estimate resulted in these cases.

A little bit more uncertain, but still easy are cases where we got certain constraints on the period and the amplitude and we were able to constrain the mean brightness level to a certain interval, which we propagate to the uncertainty of the estimated H value.

Then there are cases where we got just a lower limit on the lightcurve amplitude; in such cases, we assumed that at the low-moderate solar phases (as we included asteroids measured at solar phase not greater than 30 deg),  the lightcurve amplitude was not greater than 1.2 mag - there are very few larger amplitudes in asteroids observed at low-moderate solar phases.  With the measured lower limit and the assumed upper limit on the lightcurve amplitude, we were able to constrain the mean brightness level to better than ± 0.2 mag in a number of these cases.

And the final kind, possibly the most problematic, are cases where we did not see a brightness change over a few nights greater than 0.1 mag or so.  There, we assumed a low amplitude (though we could not really constrain it as we did not estimate a period), but obviously some fraction of the cases could be actually high-amplitude asteroids with very long periods or periods commensurate with 1 day that we observed close to a lightcurve maximum on each of the few nights.  (Cases where the observations would be actually close to a lightcurve minimum rather than maximum should be less frequent, as high-amplitude asteroid lightcurves have typically broader maxima and narrower minima.)  Anyway, a small fraction of the cases where we were off with the assumption of low lightcurve amplitude couldn‘t substantially bias our derived mean H offset.  In any case, these cases would bias the H values towards brighter values, i.e., they could underestimate, not overestimate the derived mean H offset.

We do not think that the above details would be much beneficial to readers to be elaborated in detail in our paper and that the brief description we give in sections 2.2 and 3.3 is sufficient to give an idea on how the uncertainties in H in the small fraction of cases with uncertain or no Fourier fits were estimated.

R2: -page 9-10: Assuming a value of G based on taxonomic type or orbital parameters is dangerous.  Where do they assumptions of family grouping come from?  

A: See the paper Warner et al. (2009) that we refer to there in our paper.  We have also added a footnote there to section 2.3 with the original reference with the asteroid groups/families definition.

R2: … As shown in Parker et al. (2008) and Masiero et al. (2011), even though an asteroid appears to have orbital parameters consistent with a particular group, it could very easily be an interloper, so assuming a particular G/color correction/spectral type based on orbit alone is not valid.  As with those without well-known rotational periods, objects for which G was assumed rather than measured directly should be clearly noted in the table.  How do you know that these are the right G values to be using?  Half of the sample has color corrections and G values based on what amounts to guesses that can lead to large uncertainties in their derived H values.  Surely these will have much higher H errors.  The effect of half the sample having such high uncertainties in H should be discussed in the paper.  What about the effects of color
selection biases in the determination of G vs. taxonomic type?  As the authors note, the errors in G are usually dominant, so this effect can make a big difference to the derived H values. What would happen to Figures 4-6 if the objects for which G was assumed rather than measured were excluded?  If you reported H as H_{R} rather than H_{V}, you wouldn't have to make these sorts of imprecise assumptions.

A: We have flagged the assumed G values in Table 2.  However, a bias in the estimated mean catalog H offset introduced by that some assumed G values for individual asteroids will be off can be only minor.  We have added a paragraph commenting on this to section 3.3.  We give a few more comments in following.

The assumption is based on the known correlation between G and taxonomic classes.  Yes, there will be interlopers.  For an individual object without determined taxonomic class, the best we could do would be to estimate a probability distribution of the G value taking into account a ratio of different taxonomic types appearing in the given range of heliocentric orbits.  The G-value probability distribution would be, for asteroids in orbits where a particular taxonomic class predominates (for observations in the visual), the distribution of G values for the predominating class with an additional excess forming tail(s) to one or both sides caused by the presence of interloppers.  The excess of G values outside the ±1 sigma interval around the mean G for the predominating class will produce some fraction of outliers.  A presence of such outlying H values can be handled statistically as outliers are normally handled.  However, their effect on the estimated mean H offset is very minor, as we comment in Section 3.3.

Re. „If you reported H as H_{R} rather than H_{V}, you wouldn't have to make these sorts of imprecise assumptions.“:  How reporting H_R rather than H_V could eliminate uncertainties caused by assumed G values?

R2: -Page 48: You are not able to revise the diameter values, as diameters derived from NEOWISE do not depend on H.  Diameters can be derived without any visible magnitudes at all.  You should therefore remove the diameter "revisions" from the paper, since you are not revising the diameters.  This is a major problem.

A: An approximate estimate of D can be indeed derived without any H at all, but by incorporating the information from optical data, a more accurate value of D is obtained.  And it was what Mainzer/Masiero et al. (2011) did.  Holding D constant and revising only albedo, as the reviewer suggests, would be inconsistent.  A consistent way is to use the Harris&Harris (1997) formula.  There are presented examples in H&H showing that their approximation, while resulting in only small changes in D, did match the full thermal modeling better than holding D constant.

R2: -I caution that using the equation from Harris & Harris (1998) disregards the error on H, and it might not be a significant improvement on the derived albedo (pV) compared to the NEOWISE thermal fits, where the errors on all input variables were weighted in the least squares minimization fit that actually determined albedo as a free parameter.  As we have shown in our papers, we assume that the error in H is 0.2-0.3 mag, and this is often a much larger source of error than the errors in the 3.4 and 4.6 micron bands.  The authors have not actually given the absolute H magnitude errors for their sample, and instead as discussed above have only have given formal errors, overestimating the accuracy of their albedo derivations.

A: We have provided the absolute H errors now (see our comments above).  Uncertainties of the revised p_V values can be computed using Eq. 8 of Harris&Harris (1997) from the thermal dD and our dH.  However, upon analysis of the reported WISE dD values, we found that they were largely underestimated and thus we opted to don’t give formal dp_V for our revised albedos calculated from the formal dD in Table 4, as they would be underestimated too.  We have described this in the 4th paragraph of Section 4 now.

R2: Final sentence in the conclusions: "If the H values from orbit catalogs are to be used for purposes like asteroid albedo estimation or size-frequency distribution determination, they should be seriously more accurate than they are now."  This sentence is incorrect.  Size frequency determinations derived from thermal measurements do not (as discussed above) depend on H or visible measurements in any significant way.  Furthermore, contributing improved H values for a few hundred asteroids is a long way from contributing H measurements for the >158,000 asteroids with thermal IR data from WISE.  This paper has not convinced me that offsets should be unilaterally applied to all asteroids; in our thermal modeling, I would only apply corrected H values for the objects which have actually had H and G measured directly.  A more reasonble conclusion is that the authors have shown that it is of great interest to have high accuracy visible light photometry of asteroids on a similarly
large scale to that provided by NEOWISE, and that light curve observations are a good way to get these accurate H values.

A: We comment on that in the last paragraph of the (new) Conclusions section.  We have also changed „size-frequency“, which was incorrect there, to „magnitude-frequency“.

R2: Minor Issues - Detailed Comments:
-page 8, end of the first paragraph: "The procedures that most of the astrometric surveys.used for estimating the apparent magnitudes and derivation of the H values have not been comprehensively published so far." The MPC has published some details of their observer magnitude weighting system on their website; this site should certainly be cited and discussed here.  Have you discussed this with the MPC to see if there are additional details describing the computation of H from the observers' visible magnitudes?  What about Horizons and NEODys?  Surely there are some details available that should be discussed and cited.

A: Before submitting our original paper in February, we were in contact with Gareth Williams from the MPC and Alan Chamberlin and Steve Chesley from the JPL (we got around the JPL’s email filter eventually).  They saw our draft paper and we discussed a few points with them, but we have got no citable information on what magnitude correction/weighting procedures they used for the MPCORB and the Horizons catalogs.  Re. NEODyS, we have received no reply from Andrea Milani at all.

R2: There are a number of sentences that are long and difficult to understand.  It would help to have revisions to clarify sentences that run on and are grammatically incorrect (particularly on p8 in the text).

A: We have tried to fix/improve a number of the language of grammar problems (many of them were corrected following comments by Reviewer 1).

Petr Pravec