the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Aug 2023
Next-generation radiance unfiltering process for the Clouds and Earth’s Radiant Energy System instrument
Abstract. The filtered radiances measured by the Clouds and the Earth’s Radiant Energy System (CERES) instruments are converted to shortwave (SW), longwave (LW), and window unfiltered radiances based on regressions developed from theoretical radiative transfer simulations to relate filtered and unfiltered radiances. This paper describes an update to the existing Edition 4 CERES unfiltering algorithm (Loeb et al., 2001), incorporating the most recent developments in radiative transfer modeling, ancillary input datasets, and increased computational and storage capabilities during the past 20 years. Simulations are performed with MODTRAN 5.4. Over land and snow, the surface Bidirectional Reflectance Distribution Function (BRDF) is characterized by a kernel-based representation in the simulations, instead of the Lambertian surface used in the Edition 4 unfiltering process. Radiance unfiltering is explicitly separated into 4 seasonally dependent land surface groups based on the spectral radiation similarities of different surface types (defined by International Geosphere-Biosphere Programme); over snow, it is separated into fresh snow, permanent snow, and sea ice. It contrasts to the Edition 4 unfiltering process that one set of regressions for land and snow, respectively.
The instantaneous unfiltering errors are estimated with independent test cases generated from radiative transfer simulations in which the ‘true’ unfiltered radiances from radiative transfer simulations are compared with the unfiltered radiances calculated from the regressions. Overall, the relative errors are mostly within ±0.5 % for SW, within ±0.2 % for daytime LW, and within ±0.1 % for nighttime LW for both CERES Terra Flight Model 1 (FM1) and Aqua FM3 instruments. The unfiltered radiances are converted to fluxes and compared to CERES Edition 4 fluxes. The global mean instantaneous fluxes for Aqua FM3 are reduced by less than 0.42 Wm-2 for SW and increased by less than 0.47 Wm-2 for daytime LW; for Terra FM1, they are reduced by less than 0.31 Wm-2 for SW and increased by less than 0.29 Wm-2 for daytime LW, though regional differences can be as large as 2.0 Wm-2. Nighttime LW flux differences are nearly negligible for both instruments.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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RC1: 'Comment on egusphere-2023-1670', Nicolas Clerbaux, 12 Sep 2023
This is overall an interesting paper that suggests many improvements to the NASA CERES unfiltering process. The error analysis is very relevant (section 3). Although this work could be a step toward implementation in future CERES releases (eg Ed5), it does not fully explain the differences wrt to Ed4 that are shown in section 4. Additional validation/verification/documentation would be welcome before implementation in the CERES processing system.
I am not a native speaker but get the feeling that the English for some sentences could be improved. A careful review, eg by the journal editor, is suggested. Similarly, the authors should check the units and symbols (eg micrometer is sometime written as µm, or um, or mm).
I suggest the following points for an improved manuscript:
- Don't use "less than" in the abstract and text body (eg line 23: "... are reduced by less than 0.31 W/m² ..." should be "... are reduced by 0.31 W/m² ...").
- Typos line 16 ("process that used one set ..."), line 46 ("covering"), line 55 ("surface the surface"), line 91 ("relationships"), 132 ("µm").
- line 132, the wavelength range is given in µm and the spectral resolution in wavenumbers. It would be good to indicate how many wavelength steps have been used or to specify the wavelength increments, in µm, at lower end (0.25µm) and upper end (1000µm) of the wavelength range.
- For the MODTRAN radiative transfer calculation in the LW part of the spectrum it would be interesting to specify how the surface emissivity has been considered (especially over desert surface).
- The handling of the far infra-red region should be discussed in more details. The spectral responses seem to be defined until 140µm (or 200 µm?), please confirm. What is the assumed sensitivity beyond this limit? zero? In this case, why are the MODTRAN simulations performed until 1000 µm.
- The FM1 and FM3 have marked difference in terms of spectral response (Figure 1). A brief discussion of the difference would be welcome. Also, the far-IR leakage of the SW filter seems to have an identical effect on the SW spectral response for FM1 and FM3. Please confirm as it seems strange to have difference in TW responses and not in SW in the far IR.
- Figures 20-22 show 4 panels that are said to be for April (a), July (b), October (c) and December (d). This is visibly not the case (eg (a) should be Winter (December?)). Further, the text discusses the results for January (eg line 343). Please check and correct.
- The end-to-end sensitivity study of the unfiltering algorithm (section 4) is really interesting. Given the (significant) observed differences with the Ed4 fluxes, this sections would deserve a longer discussion as well on the methodology as on the interpretation of the observed differences.
- Comparing Figures 21 and 22, it seems that most of the daytime difference in LW flux is coming from the subtraction of the SW component in the TW channel. Please confirm this and consider performing additional studies to confirm this work is an improvement with respect to Ed4.
Citation: https://doi.org/10.5194/egusphere-2023-1670-RC1 - AC1: 'Reply on RC1', Lusheng Liang, 18 Dec 2023
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RC2: 'Comment on egusphere-2023-1670', Anonymous Referee #2, 09 Oct 2023
Review of Next-generation radiance unfiltering process for the Clouds and Earth’s Radiant Energy System instrument.
The paper contains the details and error analysis of an updated unfiltering algorithm for the CERES SW and LW radiances. Uncertainties of the algorithm due to scene mis-identification, ocean wind speed differences and the number of angles used to determine the regressions are addressed by modelling. The effect of the update on the instantaneous fluxes compared to the existing algorithms is also demonstrated.
If these updates are expected to be incorporated into the next edition of the CERES data the information contained in the paper is of good significance, being of relevance to the community and within the scope of the AMT journal. The method makes use of a range of improvements over the existing algorithm and thus presents a clear advancement. The work is of good scientific quality and with some exceptions where more clarification is needed (see specific comments) the description of the method, error analysis and the conclusions reached are clear and valid.
The work is generally well presented and logically ordered, although needs to be edited for minor issues with English grammar throughout (some at noted in Editorial points at the end of this review but I this is not exhaustive).
Specific comments by section:
Section 2: Methodology:
The window channel of FM1 and FM3 and LW channel of FM6 is mentioned but unfiltering of these is not directly addressed. Are these calculations relevant to the window channel, if yes some mention of differences would be useful. If not, then maybe the window channel should not be equally emphasized in the methodology section, or it should be clearly stated that this update does not apply to this channel.
It should also be clarified and made consistent in the remaining text that the unfiltering corrects for overlap between the emitted and reflected radiation streams. This is implied in the methodology but the other sections so of the paper speak specifically of SW and LW both filtered and unfiltered which were defined in terms of the wavelength ranges of the channels in the introduction. A sentence at the end of the methodology to make clear than in the remainder of the paper when the SW and LW unfiltered are referred to they indicate the mu terms corresponding to the reflected and emitted radiation streams defined in this section should be sufficient.
Section 2.2: Spectral radiance simulations.
The number of DISORT streams used for the calculation is not stated. Were tests/error analysis done to show this number was sufficient for all scenes at the angular resolution used particularly for highly anisotropic scenes such near glint angles and for larger particle ice cloud for example. This is a problem I have run into in similar simulations which can even with a relatively high number of streams can result in some unphysical results. It may be of interest to include a ‘sufficient streams’ section in the error analysis section.
Although comparisons with CERES observations are shown for snow, ocean and land surfaces to indicate the improvements of the new simulations, no example is shown for ice cloud. Rather in this case it is just stated (line 247) that ‘As expected the new simulations are able to capture the cloud anistropic characteristics better’, could the justification / evidence behind this statement be provided, is this form the references paper or other information?
For deep convective cloud discussed in lines 250-251 is there some reference that can be given to support the values used as displayed in table 6?
Section 3: Error analysis
The details and distributions of the test cases is a bit unclear in some cases. I think some more detail of this is needed to interpret the bias and rms of the error distribution associated with these cases. For example, for wind speed tests are angular resolution the same as the regression calculations, as wind speed effects are very angle specific is this sufficient to characterize the errors in use and does it include the specific combination of angles that are particularly sensitive to wind speed effects. Would errors be different if the angles were changed from those simulated along with the wind speed? Similar questions arise for the aerosol error analysis.
For interpretation of the surface type grouping results it would be helpful to have some idea of the percentage of land surface in each group in each season. In any case although the analysis here concludes that the correct surface type should be used particularly in the case of bare soil and rocks, the effect of seasonality error is not considered and the changing in grouping that occurs here which presumably is not as clear cut a transition as modelled.
Overall there seem to be a lot of plots associated with this section. A total 30 relative error distributions shown in Figures 8 to 19. Perhaps these results could be presented more succinctly and some of the individual plots moved to the supplementary material. For example in respect of figures 8 and 9, I think it is sufficient to state the results that when regressions are based on only 5 SZA unfiltering errors for intermediate SZA angles are seen to be significant larger than for the SZA on which the regression is based. This difference becomes insignificant when 13 SZAs are used for the regressions. If retained ,either in the main paper or supplementary material the relative error / true radiance scatterplots in figure 8 and 9 should specify what the colour scale is. Also given the lack of structure and minimal variation seen in the 12 plots shown for the LW results (figure 18 and 19) it would again maybe be sufficient to state that differences between the original and test scenes were insignificant.
Finally, it would be useful to put the errors in the context of the magnitude of the differences due to improvements and the stated errors of the existing CERES unfiltering both generally and for the cases known to be most problematic for the existing algorithms (thin cirrus and cloud-free high concentration of submicron absorbing aerosol for the SW and very cold convective clouds for the LW). And summarize any remaining problematic scenes.
Section 4: Impact of the unfiltering on the instantaneous fluxes
This section will be of particular interest to general users of the CERES products. I think that further expansion here would be welcome, putting the differences in the context of the existing uncertainties both from the unfiltering and from other terms. It would also be interesting to know if regional annual biases are likely reinforced or cancel in the annual mean and if there was significant interannual variability. The monthly variations would seem to indicate that this will vary with region/scene. Further discussion of the origin of the differences and seasonality would also be of interest, both in the context of the previously discussed errors in this unfiltering and in the context of the known limitations of the existing CERES unfiltering.
Line 344 states the differences can be greater than 2Wm-2 in magnitude, as the range of the plots only extends to 2Wm-2 it would be useful to know what this number is and where it occurred (I assume it is not significant enough to extend the range shown in the plots).
It is not essential, but it might be interesting to supplement the maps with a distribution plot in terms of percentage differences for more direct comparison to previous distributions.
Section 5: Summary
The paper has primarily discussed results relevant to the unfiltering of the LW and SW channels of FM1 and FM3. It would be helpful to include some discussion of the relevance of the results and error analysis to the newer FM5 and FM6.
Lines 376-380 as well as stating the ‘mostly within’ the specific cases where these norm errors are exceeded it elaborated on in terms of scenes and uncertainties as was done in Loeb 2001.
Some Minor Editorial points
Line 16 “It contrasts to the Edition 4 unfiltering processing that one set of regressions for land and snow, respectively” ->
“In contrast to the Edition 4 unfiltering process where one set of regions are used for land and snow respectively”
Line 24 “…increase to less than 0.47” -> “increased to nearly 0.47”
Line 25 “though regions differences can be as large as 2.0” it is stated in the paper line 344 that they are more than 2.0 and in the summary line 385 ‘as large as 2.0” . Please decide if they are larger or as large and make this statement consistent thoughout.
Line 43 “the reflected and emitted energy is spectrally different among different earth targets” à “the spectral distribution of reflected and emitted energy varies with earth target”
Line 170 “spectral radiation” -> “spectral radiation”
Line 193 “In this paper” -> specify if you mean in the update to be used in the new edition
Line 267 “..shows the error analysis based on ..” -> “presents error analysis based on” ,
Line 271 “they are 0” -> “these are 0”
Line 271 “ to evaluate if the 5 SZAs is sufficient, we used the simulations for clear sky with” -> “to evaluate if 5 SZAs are sufficient, we use clear sky simulation with”
Line 275 “For the number of VZA and RAZ, we verify that 6 VZA (increase one VZA at 70)…” -> “In respect of the number of the VZA and RAZ, it is verified that the increasing to 6 VZA by extending the VZA range to 70…”
Line 283 “ It suggests that contructing ..” -> “These results indicate …”
Line 289 “…the PDFs of errors for other aerosols become broader, and the PDF modes for dust and urban aersols are shifted to opposite directions from one another…” -> “..the error PDFS for other aerosols are broader, and the mode of the PDF for dust and urban aerosols are shifted to negative and positive values respectively”
Line 291 ..”depending on the surface type..” -> add a clarification of this dependence.
Line 301 “…scenes by using the regressions..” -> “scenes unfiltered using the regionssions..”
Line 302 “The large PDF difference…” -> “The broader difference PDF..”
Line 317 “…”but larger otherwise.>” -à provide a more quantitative statement
Line 318 “..can easily be greter than 1%” -> quantify
Line 326 “Errors for LW” -> “Lw unfiltering errors” however as there hasn’t been a SW unfiltering section it would be consistent if all the previous sections didn’t pertin to the LW to make that clear earlier.
Line 348 “differences are positive…” -> include some quantification
Line 352 “nearly negligible” -> provide some maximum limit / quantification of negligible
Line 361 “with many updates compared to “ -> summarize updates or refer to section summarizing them
Line 364 “matches CERES observed SW radiances better’ -> “matches the CERES observed angular variation of the SW radiances better”
Citation: https://doi.org/10.5194/egusphere-2023-1670-RC2 - AC2: 'Reply on RC2', Lusheng Liang, 18 Dec 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-1670', Nicolas Clerbaux, 12 Sep 2023
This is overall an interesting paper that suggests many improvements to the NASA CERES unfiltering process. The error analysis is very relevant (section 3). Although this work could be a step toward implementation in future CERES releases (eg Ed5), it does not fully explain the differences wrt to Ed4 that are shown in section 4. Additional validation/verification/documentation would be welcome before implementation in the CERES processing system.
I am not a native speaker but get the feeling that the English for some sentences could be improved. A careful review, eg by the journal editor, is suggested. Similarly, the authors should check the units and symbols (eg micrometer is sometime written as µm, or um, or mm).
I suggest the following points for an improved manuscript:
- Don't use "less than" in the abstract and text body (eg line 23: "... are reduced by less than 0.31 W/m² ..." should be "... are reduced by 0.31 W/m² ...").
- Typos line 16 ("process that used one set ..."), line 46 ("covering"), line 55 ("surface the surface"), line 91 ("relationships"), 132 ("µm").
- line 132, the wavelength range is given in µm and the spectral resolution in wavenumbers. It would be good to indicate how many wavelength steps have been used or to specify the wavelength increments, in µm, at lower end (0.25µm) and upper end (1000µm) of the wavelength range.
- For the MODTRAN radiative transfer calculation in the LW part of the spectrum it would be interesting to specify how the surface emissivity has been considered (especially over desert surface).
- The handling of the far infra-red region should be discussed in more details. The spectral responses seem to be defined until 140µm (or 200 µm?), please confirm. What is the assumed sensitivity beyond this limit? zero? In this case, why are the MODTRAN simulations performed until 1000 µm.
- The FM1 and FM3 have marked difference in terms of spectral response (Figure 1). A brief discussion of the difference would be welcome. Also, the far-IR leakage of the SW filter seems to have an identical effect on the SW spectral response for FM1 and FM3. Please confirm as it seems strange to have difference in TW responses and not in SW in the far IR.
- Figures 20-22 show 4 panels that are said to be for April (a), July (b), October (c) and December (d). This is visibly not the case (eg (a) should be Winter (December?)). Further, the text discusses the results for January (eg line 343). Please check and correct.
- The end-to-end sensitivity study of the unfiltering algorithm (section 4) is really interesting. Given the (significant) observed differences with the Ed4 fluxes, this sections would deserve a longer discussion as well on the methodology as on the interpretation of the observed differences.
- Comparing Figures 21 and 22, it seems that most of the daytime difference in LW flux is coming from the subtraction of the SW component in the TW channel. Please confirm this and consider performing additional studies to confirm this work is an improvement with respect to Ed4.
Citation: https://doi.org/10.5194/egusphere-2023-1670-RC1 - AC1: 'Reply on RC1', Lusheng Liang, 18 Dec 2023
-
RC2: 'Comment on egusphere-2023-1670', Anonymous Referee #2, 09 Oct 2023
Review of Next-generation radiance unfiltering process for the Clouds and Earth’s Radiant Energy System instrument.
The paper contains the details and error analysis of an updated unfiltering algorithm for the CERES SW and LW radiances. Uncertainties of the algorithm due to scene mis-identification, ocean wind speed differences and the number of angles used to determine the regressions are addressed by modelling. The effect of the update on the instantaneous fluxes compared to the existing algorithms is also demonstrated.
If these updates are expected to be incorporated into the next edition of the CERES data the information contained in the paper is of good significance, being of relevance to the community and within the scope of the AMT journal. The method makes use of a range of improvements over the existing algorithm and thus presents a clear advancement. The work is of good scientific quality and with some exceptions where more clarification is needed (see specific comments) the description of the method, error analysis and the conclusions reached are clear and valid.
The work is generally well presented and logically ordered, although needs to be edited for minor issues with English grammar throughout (some at noted in Editorial points at the end of this review but I this is not exhaustive).
Specific comments by section:
Section 2: Methodology:
The window channel of FM1 and FM3 and LW channel of FM6 is mentioned but unfiltering of these is not directly addressed. Are these calculations relevant to the window channel, if yes some mention of differences would be useful. If not, then maybe the window channel should not be equally emphasized in the methodology section, or it should be clearly stated that this update does not apply to this channel.
It should also be clarified and made consistent in the remaining text that the unfiltering corrects for overlap between the emitted and reflected radiation streams. This is implied in the methodology but the other sections so of the paper speak specifically of SW and LW both filtered and unfiltered which were defined in terms of the wavelength ranges of the channels in the introduction. A sentence at the end of the methodology to make clear than in the remainder of the paper when the SW and LW unfiltered are referred to they indicate the mu terms corresponding to the reflected and emitted radiation streams defined in this section should be sufficient.
Section 2.2: Spectral radiance simulations.
The number of DISORT streams used for the calculation is not stated. Were tests/error analysis done to show this number was sufficient for all scenes at the angular resolution used particularly for highly anisotropic scenes such near glint angles and for larger particle ice cloud for example. This is a problem I have run into in similar simulations which can even with a relatively high number of streams can result in some unphysical results. It may be of interest to include a ‘sufficient streams’ section in the error analysis section.
Although comparisons with CERES observations are shown for snow, ocean and land surfaces to indicate the improvements of the new simulations, no example is shown for ice cloud. Rather in this case it is just stated (line 247) that ‘As expected the new simulations are able to capture the cloud anistropic characteristics better’, could the justification / evidence behind this statement be provided, is this form the references paper or other information?
For deep convective cloud discussed in lines 250-251 is there some reference that can be given to support the values used as displayed in table 6?
Section 3: Error analysis
The details and distributions of the test cases is a bit unclear in some cases. I think some more detail of this is needed to interpret the bias and rms of the error distribution associated with these cases. For example, for wind speed tests are angular resolution the same as the regression calculations, as wind speed effects are very angle specific is this sufficient to characterize the errors in use and does it include the specific combination of angles that are particularly sensitive to wind speed effects. Would errors be different if the angles were changed from those simulated along with the wind speed? Similar questions arise for the aerosol error analysis.
For interpretation of the surface type grouping results it would be helpful to have some idea of the percentage of land surface in each group in each season. In any case although the analysis here concludes that the correct surface type should be used particularly in the case of bare soil and rocks, the effect of seasonality error is not considered and the changing in grouping that occurs here which presumably is not as clear cut a transition as modelled.
Overall there seem to be a lot of plots associated with this section. A total 30 relative error distributions shown in Figures 8 to 19. Perhaps these results could be presented more succinctly and some of the individual plots moved to the supplementary material. For example in respect of figures 8 and 9, I think it is sufficient to state the results that when regressions are based on only 5 SZA unfiltering errors for intermediate SZA angles are seen to be significant larger than for the SZA on which the regression is based. This difference becomes insignificant when 13 SZAs are used for the regressions. If retained ,either in the main paper or supplementary material the relative error / true radiance scatterplots in figure 8 and 9 should specify what the colour scale is. Also given the lack of structure and minimal variation seen in the 12 plots shown for the LW results (figure 18 and 19) it would again maybe be sufficient to state that differences between the original and test scenes were insignificant.
Finally, it would be useful to put the errors in the context of the magnitude of the differences due to improvements and the stated errors of the existing CERES unfiltering both generally and for the cases known to be most problematic for the existing algorithms (thin cirrus and cloud-free high concentration of submicron absorbing aerosol for the SW and very cold convective clouds for the LW). And summarize any remaining problematic scenes.
Section 4: Impact of the unfiltering on the instantaneous fluxes
This section will be of particular interest to general users of the CERES products. I think that further expansion here would be welcome, putting the differences in the context of the existing uncertainties both from the unfiltering and from other terms. It would also be interesting to know if regional annual biases are likely reinforced or cancel in the annual mean and if there was significant interannual variability. The monthly variations would seem to indicate that this will vary with region/scene. Further discussion of the origin of the differences and seasonality would also be of interest, both in the context of the previously discussed errors in this unfiltering and in the context of the known limitations of the existing CERES unfiltering.
Line 344 states the differences can be greater than 2Wm-2 in magnitude, as the range of the plots only extends to 2Wm-2 it would be useful to know what this number is and where it occurred (I assume it is not significant enough to extend the range shown in the plots).
It is not essential, but it might be interesting to supplement the maps with a distribution plot in terms of percentage differences for more direct comparison to previous distributions.
Section 5: Summary
The paper has primarily discussed results relevant to the unfiltering of the LW and SW channels of FM1 and FM3. It would be helpful to include some discussion of the relevance of the results and error analysis to the newer FM5 and FM6.
Lines 376-380 as well as stating the ‘mostly within’ the specific cases where these norm errors are exceeded it elaborated on in terms of scenes and uncertainties as was done in Loeb 2001.
Some Minor Editorial points
Line 16 “It contrasts to the Edition 4 unfiltering processing that one set of regressions for land and snow, respectively” ->
“In contrast to the Edition 4 unfiltering process where one set of regions are used for land and snow respectively”
Line 24 “…increase to less than 0.47” -> “increased to nearly 0.47”
Line 25 “though regions differences can be as large as 2.0” it is stated in the paper line 344 that they are more than 2.0 and in the summary line 385 ‘as large as 2.0” . Please decide if they are larger or as large and make this statement consistent thoughout.
Line 43 “the reflected and emitted energy is spectrally different among different earth targets” à “the spectral distribution of reflected and emitted energy varies with earth target”
Line 170 “spectral radiation” -> “spectral radiation”
Line 193 “In this paper” -> specify if you mean in the update to be used in the new edition
Line 267 “..shows the error analysis based on ..” -> “presents error analysis based on” ,
Line 271 “they are 0” -> “these are 0”
Line 271 “ to evaluate if the 5 SZAs is sufficient, we used the simulations for clear sky with” -> “to evaluate if 5 SZAs are sufficient, we use clear sky simulation with”
Line 275 “For the number of VZA and RAZ, we verify that 6 VZA (increase one VZA at 70)…” -> “In respect of the number of the VZA and RAZ, it is verified that the increasing to 6 VZA by extending the VZA range to 70…”
Line 283 “ It suggests that contructing ..” -> “These results indicate …”
Line 289 “…the PDFs of errors for other aerosols become broader, and the PDF modes for dust and urban aersols are shifted to opposite directions from one another…” -> “..the error PDFS for other aerosols are broader, and the mode of the PDF for dust and urban aerosols are shifted to negative and positive values respectively”
Line 291 ..”depending on the surface type..” -> add a clarification of this dependence.
Line 301 “…scenes by using the regressions..” -> “scenes unfiltered using the regionssions..”
Line 302 “The large PDF difference…” -> “The broader difference PDF..”
Line 317 “…”but larger otherwise.>” -à provide a more quantitative statement
Line 318 “..can easily be greter than 1%” -> quantify
Line 326 “Errors for LW” -> “Lw unfiltering errors” however as there hasn’t been a SW unfiltering section it would be consistent if all the previous sections didn’t pertin to the LW to make that clear earlier.
Line 348 “differences are positive…” -> include some quantification
Line 352 “nearly negligible” -> provide some maximum limit / quantification of negligible
Line 361 “with many updates compared to “ -> summarize updates or refer to section summarizing them
Line 364 “matches CERES observed SW radiances better’ -> “matches the CERES observed angular variation of the SW radiances better”
Citation: https://doi.org/10.5194/egusphere-2023-1670-RC2 - AC2: 'Reply on RC2', Lusheng Liang, 18 Dec 2023
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Lusheng Liang
Wenying Su
Sergio Sejas
Zachary A. Eitzen
Norman G. Loeb
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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