Review of An Improved BRDF Hotspot Model and its Use in VLIDORT to Study the Impact

of Atmospheric Scattering on Hotspot Directional Signatures in the Atmosphere” by Xiaozhen Xiong et al. Submitted for possible publication in AMT.

The so-called Hot Spot is the increased in surface reflectance as the observation geometry nears backscatter.  It has a significant impact over a few degree around this particular direction.  Note that the Hot Spot is difficult to observe on the ground as the Hot Spot is then hidden by the observer own shadow.  In this paper, the authors modify an existing analytical model of the BRDF, including the Hot Spot, so that it can be efficiently used by the VLIDORT radiative transfer modeling that uses Fourier expansion.  As such, it should be made clear that the “improvement” of the model is not in its ability to reproduce the truth but in its ability to be used by LIDORT.

Having the ability to model the Hot Spot in VLIDORT is certainly a useful feature that could be used in the community and I therefore welcome the efforts of the author in that direction.  However, as describe below, the paper does not demonstrate that the modeling is accurate and reproduces the specific signatures of the Hot Spot.  In particular,

• The modified model does reproduce a “Hot Spot like” signature, but this signature is significantly different than the original modeling by Maignan and Breon that has been validated against observations. Thus, it may not be appropriate for those who need an exact representation of the Hot Spot angular signature
• the figures in the paper not have the angular resolution that is necessary to properly investigate the impact of atmospheric scattering on the Hot Spot width, which is one of the claimed results of the paper.

Therefore, significant improvements of the papers are needed before it can be published

Detailed comments

In the paper, the authors seem to agree that the RossThickHT-M modeling is the reference as it has been validated against POLDER data in its ability to reproduce the amplitude but also the angular shape of the Hot Spot.  The authors have developed a modified version, RossThickHT-X for its ability to be efficiently developed with a Fourier expansion.  However, Figure 1 shows that the two models have an angular shape that is significantly different.  Such differences may not be acceptable for those who have a specific interest in the Hot Spot signature.  The “X” version of the model may certainly be acceptable for some application that just need to show some kind of a Hot Spot, but not for all applications.  Thus the “improved” qualification to this new model is only numerical.  This should be made clear.  Also, the differences shown in Figure 1 should be discussed.

One conclusion from the study is that the Hot Spot Width is not affected by the atmospheric scattering.  This is deduced from the results shown in Figure 3.  However, this angular resolution of this figure is by far insufficient to analyze the width of the Hot Spot.  The statement must be removed or this figure improved.

Also, there is insufficient information about the hypothesis on the aerosol load that are used in the simulations

The paper makes several statements about the amplitude of the Hot Spot as a function of wavelength.  However, the results they obtain (ie an amplitude that is smaller in the visible than in the near IR) is entirely a consequence of their hypothesis on the surface reflectance.  Obviously, if the amplitude of the HS (at the surface) is large, it is also so at the TOA.  I strongly suggest (i) to add the surface reflectance (at the surface) on Figure 5 and (ii) to cleary indicate in the text how much this result is because of the lower amplitude is because of the lower reflectance and because of the increased atmospheric scattering

Atmospheric scattering reduces the Hot Spot amplitude.  This is shown in Figure 8. At the first order, the amplitude is reduced by a factor exp(-to m) where m is the air mass computed from the solar and view zenith angles, and to is the optical depth.  I strongly suggest to (i) compare the result of Figure 8 with this simple estimate, and (ii) discuss in the text .

Also, I see that the computations are made for an optical depth of 0.2.  It may be worthwhile to mention that this is rather high and that most satellite observation are less affected by the aerosols than this simulation may suggest

On line 495 it is said that the HS amplitude in Bréon et al might be underestimated.  By how much is that ?  A factor of 2 or 1% ?  Obviously, the impact would not be the same.

Also, the authors comment on the fact that different studies use different version of the BRDF kernels that differ by a factor 3p/4.  They claim that this explain difference between their results and those from others.  However, a Kernel is always used associated with a weight.  Obviously, when one uses a version of a Kernel that differs by a constant factor, the weight must be adjusted accordingly.  In fact Kernel models are mostly used to fit remote sensing measurements.  Using a Kernels that differ by a constant multiplying factor just leads to a different inverted weight, withno impact on the retrieved BRDFs.  The current text is somewhat misleading on this subject and must be corrected

Regarding the conclusions:

We also showed the new hotspot model agrees very well with the original RossThick model away the hotspot region, thus allowing the use of this single model in the condition with and without hotspot.

It should be clear that the new hotspot model does not agree well with the corrected “Hot Spot” model close to the Hot Spot direction.

In agreement with previous analysis using POLDER measurement data, hotspot signatures in the near-infrared are larger than those in the visible

This is a conclusion that only derives from the hypothesis made on the surface reflectance.

and the hotspot amplitude is reduced when aerosols are added to an otherwise clear atmosphere.

It should be made clear whether this reduction is by the direct transmission factor, or by a different value

These results also showed that atmospheric scattering does not generate hotspot-like signatures

Some authors have claimed that there may be coherent backscatter.  As this potential feature is not accounted for in Vlidort, the modeling is not realy a demonstration of its inexistence in the true world.  In addition, some aerosol models show an increase of the phase function close to the 180 scattering angle.  Such aerosols would generate an Hot Spot like signature, but may not have been tested in the author simulations

does not change the width of the BRDF-induced hotspot

The figures shown in the paper cannot be used to make that conclusion

 It is also clear that VLIDORT makes accurate simulations of the hotspot

There is no validation in that paper to make that statement.  In fact, if one trust the RossThickHT-M modeling, as it has been somewhat compared to POLDER observations, then Figure 1 indicates that the modified model (RossThickHT-X) makes an inaccurate simulation of the HotSpot

the results obtained here can be used as benchmarks

As discussed above, the differences between RossThickHT-M and RossThickHT-X indicate that the Hot Spot signature is uncertain for those who have a specific interest in the Hot Spot signature.  Therefore, the RossThickHT-X cannot be used as benchmarks

Our improved hotspot kernel is now a standard feature in the latest version of the VLIDORT BRDF supplement code

It should be made clear that the improvement is only to increase the numerical efficiency, and not to obtain more accurate simulation of the Hot Spot signature

Other comments

Line 19 : almost coincide

Line 20-23: This sentence is wrong.  The RTLSR model is analytical and does not require, therefore Fourier expansion.  Only its use within models such as Vlidort does.

Line 24 : Not clear what “converge” refers to here

Line 38 : attenuation => attention

Line 65 : What is the “forward scatter direction” ?

At many places, reference Vermont et al [2009] is used.  This ref does not exist and is probably Vermote et al [2009]

Line 204 : The equation seems to be for the phase angle, not the scattering angle

Line 264 : it => It

Line 270 : numerical accuracy of10-4 . Is that an absolute accuracy (in which case, what is the unit) or a relative accuracy ?

This study presents an alternative model of the hotspot correction that was designed to improve numerical computation efficiency. The new formulation then is compared with the conventional hotspot correction approach for the Reciprocal-Ross-Li BRDF model in the VLIDORT package. With the new development, authors also examined the impact of atmospheric scattering on the simulated hotspot behavior as observed from the TOA. 

I appreciate that authors provided a detailed and interesting history of the BRDF developments and RTM modeling developments. The manuscript was well written and results were presented with substantial discussions. Although this is an interesting study, the work needs a substantial improvement in its focus and conclusions. 

The innovative part of the paper is the presentation of a new hotspot correction formulation (Eq 9) of computational advantage. This formulation is similar to that proposed by Bréon et al. [2002] but replacing scattering angle by sin^x(scatter angle). However, authors didn’t provide why the sine function is introduced here. 

Comparing with other hotspot correction functions, the proposed new function requires less number of streams and Fourier terms to achieve a similar accuracy. How about the computational efficiency? Would this contribute a significant improvement in practical satellite remote sensing algorithms? 

With the new development, authors examined the impact of atmospheric scattering on the simulated hotspot behavior as observed from the TOA. From several simulation experiments, authors come up 4 major findings that are listed in the Summary and Conclusion section. Three of those findings, however, were demonstrations of previous studies or known physics. That means, they can be demonstrated even without the development of the new hotspot correction function. So, these analysis should not be the focus of this study. 

505-511: A same set of BRDF weight factors were used for simulations in Figure 7 for various hotspot correction approaches. The results showed the RossThickHT-L (Lorente et al., 2018) approach were higher than other methods due to the lack of the 4/3pi term. Authors concluded that the hotspot peak using RossThickHT-L seemed too high. I don’t think it is a reasonable conclusion. Because it is not appropriate to apply a same set BRDF weight factors to different approaches at the first place. Without constraints (fitting with) observations, such comparisons make no sense.  

Also, MODIS BRDF products an be only applied to the Ross-Li-Reciprocal model to construct the BRDF, because the retrieval (i.e., observation fittings) were based on this model. Direct application of them to a different model (no matter which hotspot correction for the Ross-Li-Reciprocal model) would have a chance to deviate from the observation constraints. 

The major finding #2 is not reasonably explained by the authors. The trends of hotspot amplitudes with respect to solar zenith angle at 469 and 645 nm are different from that in the near-infrared; this difference is mainly due to the stronger Rayleigh scattering in the shorter wavelengths, which is more pronounced for longer path length at larger solar zenith angles. 

Specific comments

Line 81: An expansion is needed for RTLSR at its first appearance.

Figure 8: Should the x-axis be Solar zenith angle? 

Line 514: It might be arbitrary to say “the best model is the ….”. How about “the commonly used model is the …”