This paper presents a new method to extend the typically used surface LER with a direction dependency. The DLER concept is applied to GOME-2 measurements, and the relation with the surface BRDF is analyzed both theoretically and practically. This paper is well-organized and well-written, and the content is of interest to the community involved in satellite retrieval of atmospheric properties. I recommend publication in AMT after the authors address minor comments below.

P1 L21 Please give the full names of the different species.

P2 Could you also comment on the pros and cons of the Loyola et al., 2020 method with respect to DLER?

P9 L11 The spatial resolution has changed to 40 km *40 km for GOME-2A. How large is the influence of combining measurements from two instruments with different spatial resolution? Is the instrumental degradation an issue in the DLER retrieval?

P12 L31 What is the reason of applying Eq 9 at 758 nm? P12 L29 concludes that 758 nm can be treated monochromatically.

P14 L26 Maybe it is good to show surface albedo maps here?

The paper by Tilstra et al, Directionally dependent Lambertian-equivalent reflectivity (DLER) of the Earth’s surface measured by the GOME-2 satellite instruments, presents the next evolution of the Lambertian-equivalent reflectivity (LER) surface databases, as derived from high spectral resolution grating spectrometers covering the UV, visible and towards the near and short-wave infrared spectral region. LER surface databases derived from such instruments have the advantage to provide their data at significantly more atmospheric window or well controlled absorption wavelengths, i.e. at higher spectral resolution, than the familiar surface databases derived from band imagers like AVHRR, MODIS, Meteosat, or Sentinel-3. However, up to now, the original LER approach assumed homogenous, non-directional reflection of the surface, which is known to lead to significant biases in particular in the backscatter direction.

The directional evolution of the LER surface retrieval approach (DLER), applied to the meanwhile considerable GOME-2 data record of more than 10 years from two Metop platforms at 9:30 LT and over an observation angle range of -55 to 55 degrees, is therefore a very significant improvement to the currently existing (and frequently used) LER databases (Tilstra et al., 2017).  The results show that the anisotropy is considerable depending on surface types (in particular for vegetation), as is expected, and that at least for such surface types and at large observation angles the previously used LER databases introduces significant biases.

The paper presents a comparison to the principally more accurate bi-directional reflectance distribution function (BRDF) approach, e.g. as applied to MODIS observations, which however is limited in its available spectral resolution. The comparison of synthetic data from radiative transfer calculations shows a good correspondence between the two approaches above 500 nm improving towards longer wavelength. A validation comparing BRDF reflectivity values with DLER values for the MODIS 640 nm band confirms the significant improvements of DLER with respect to LER in the backscatter regime (West-viewing for GOME-2 daylight descending orbits).

The scientific results presented here are significant and will be of high interest to users of grating spectrometer data in the UV to near infrared. The paper is well written and I can therefore recommend it for publication in AMT, noting a couple of aspects for the authors to consider.

One of the main advantages using DLER (and LER) with respect to imager derived BRDF databases is its higher spectral resolution. While the comparison of BRDF and DLER values derived from synthetic Top-Of-Atmosphere (TOA) data identifies the spectral regime in which both perform similar and where not, the validation results of section 7 provides results only at 640 nm.  A tabulated statistics of slope, intercepts and correlation wavelength at other MODIS wavelength (in particular towards the blue) would be very helpful for users to decide where to use or not to use DLER for their applications. In particular, since close to 50% of the provided DLER wavelength are in the <500 nm regime.  In this respect, a comparison of DLER performance with respect to the frequently used combination of MODIS BRDF and spectral principle components provided by the ESA ADAM surface reflectance database would be of value for follow on studies.

Also the paper is only discussing in passing DLER results over persistently snow covered (high mountains and polar regions) regions, and is not discussing ocean surfaces (or/and water bodies in general) at all. Both surface types are either missing or filtered out in BRDF land databases like the ones derived from MODIS, because of considerable uncertainties in the BRDF coefficients for snow surfaces so far, or are generally neglected (like ocean colour variation and potentially associated directional effects apart from glint). Appendix B seems to indicate that DLER (like the previous LER database) also provides values over oceans, although this is never explicitly mentioned or even discussed in the body text of the paper, as it seems. It would surely be very interesting to understand how well DLER performs for these two surface types, which are (or seem) both included in the discussed database.  

Finally, it is not very clear to me why in the “Case studies” part of the validation section (Section 7.1) the authors emphasize the need for focussing on largely homogenous surfaces. A proper averaging of MODIS BRDF sub-pixels to the DLER grid pixel should in principle provide an accurate comparison independent of sub-pixel surface variations. And it would be also interesting to provide the corresponding averaged MODIS BRDF results in Figure 8 for comparison with the DLER grid pixel results along with the individual ones (and ideally show similar comparisons for non-homogeneous cases too).

This work is a great addition to the currently available angular dependent LER products that have considered surface BRDF effects based on the LER concept. It provides important improvements to the author's previous LER climatology product based on GOME-2 observations, which include directional LER (DLER) at as many as 26 wavelengths from 328 to 772 nm. It fits well to the scope of AMT and should be considered publishing after addressing the following issues.

1. Although bidirectional reflectance distribution function (BRDF) mathematically describes the scattering of a parallel beam of incident light from one direction in the hemisphere into another direction in the hemisphere, the BRDF itself, as a ratio of infinitesimals, is a derivative with “instantaneous” [in angle] values that can never be measured directly, as stated in Nicodemus et al. (1977). 

Therefore, it seems more proper to use BRF or simply reflectance in many places throughout the manuscript when referring to directional reflectance datasets. BRF (Bidirectional Reflectance Factor) is defined as the ratio of the radiant flux reflected by a surface to that reflected into the same reflected-beam geometry by an ideal (lossless) and diffuse (Lambertian) standard surface, irradiated under the same conditions. 

So in remote sensing community, BRF is commonly used to describe the reflectance factor calculated from either ground measurements or satellite observations that have finite field-of-view (FOV). The authors can refer to Schaepman-Strub et al., (2006) for more details regarding use of BRDF and BRF. 

The suggestion here is to only keep BRDF before 'model', 'parameter', 'product', 'database' etc (i.e., only use it as an adjective) and replace BRDF with BRF in other places when referring to directional data set itself, such as at line 9,  l1, 14 in page 1, as well as many instances in the rest of the manuscript. 

2. It seems not proper by calling LER (defined in Eq.2) as albedo (see line 21, page 3) because albedo is defined as the ratio of the radiant flux reflected into the whole upper hemisphere (i.e., the integal from all viewing angles) to the incident radiant flux. In other words, albedo is independent of viewing directions, but LER does for a non-Lambertian surface. That is the physical basis for DLER in this study, GE_LER (Loyola et al., 2020) and GLER (Vasilkov et al., 2017). Also as shown in Eq.3, LER has the same unit as R.  

3. The authors should mention in the figure caption that Fig.1b only applies to land surfaces because reflection from a non-Lambertian surface, in general, could have another peak in the forward scattering direction, i.e., specular (mirror) reflection over snow/ice or water surfaces (so-called sunglint) in addtion to the hot spot peak (retroreflection) over rough surfaces like vegetation due to shadow hiding. 

4. The authors should provide reference(s) to justify the use of a parabolic function to simulate directionality of surface reflection for vegetated surfaces as shown in Eq.5. There have been many publications from BRDF modeling community in land remote sesing that demonstrated such parabolic function only applies to non-vegetated surfaces such as desert or bare soil. That's why in MODIS BRDF products, a linear combination of different kernels is used to describle surface drectional reflection in general as described by Eq.6.  

5. The title of section 3.1 should be changed to 'MODIS BRDF model'.

6. Though I believe DLER is derived from the real GOME-2 measurements as mentioned in the 2nd paragraph (lines 9-14, page 4) of section 2.2, it also says DLER product is based on simulated TOA reflectances with DAK (line 23, page 6), That would create some confusion for readers and should be clarified. 

7. Since real GOME-2 observations are used to derive DLER, it is not clear how the aerosol and cloud contaminated data is removed and the data screening criteria used. How data gaps (due to aerosol and/or cloud contaminations) are handled? All these need to be addressed in the manuscript. 

8. It looks like DLER product only has five viewing direction bins since the data is sorted out through five sub-containers (see line 12, page 4). What are the exact angular widths for these five bins, any justification that these five anglular bins can adquently describe the angular distribution of GOME-2 measurements? What is the angular resolution in the GOME-2 x-track scan positions and is that the basis for selecting the five view angle bins?  All these need to be deliberated a little more.

Since this is not a full consideration of BRDF effects but a rough approximation, it should be said so in item 5 of page 10 (lines 22-23). 

Although this approximation may work for not too large SZAs where the angular width of the hot spot is pretty broad. However, when SZA is high (e.g., larger than 45 deg), the hot spot width becomes very narrow. In such situation if GOME-2 viewing angle falls into the hot spot region, the peak will be smoothed out by the large angular bin as shown in figure 1b, resulting in much smaller DLER value. Same is true for the sunglint effect over ocean should this five viewing angle scheme be applied to water surfaces, 

9. Fig.7 shows results at 772 nm. Readers may also be interesed to see results for short wavelengths (e.g., 363, 380, 340 or shorter) since some of the short wavelengths in Table 1 are widely used in trace gas retrieval based on UV/VIS data such as ozone, NO2, aerosol via aersol index and clouds via O2-O2 or rotational Raman scattering algorithm.

10. For Figs. 8-9, DLER from 645 nm is compared with MODIS band 1. Can the authors show comparisons with the shortest wavelength in MCD43C2 product like band 3 (centered at 470 nm)? Though the difference would be larger as expected, readers may be interested to see how DLER and MODIS BRF follow with each other in angular distributions.

References    

  

Nicodemus, F. E., et al. (1977). Geometrical considerations and nomenclature for reflectance. Washington, DC: National Bureau of Standards, US Department of Commerce. URL: http://physics.nist.gov/Divisions/Div844/facilities/specphoto/pdf/geoConsid.pdf

Schaepman-Strub, G., Schaepman, M. E., Painter, T. H., Dangel, S., Martonchik, J. V., Reflectance quantities in optical remote sensing–definitions and case studies, Remote Sens. Environ., 103, 27–42, 2006