Summary

In their manuscript the authors study synthetic wide-field-of-view (WFOV) radiometer measurements onboard individual satellites or a constellation thereof to assess how accurately such measurements would quantify Earth’s energy imbalance (EEI). To generate synthetic measurements, the authors use multiple years of the CERES SYN1deg product and mimic radiances by using either Lambertian or anisotropic scene reflection. The authors show that global EEI is largely independent of scene reflection, but strongly varies with type of orbit and multi-satellite constellation, owing angular sampling deficiencies of some orbits. Sorted by latitude, however, the authors present substantial EI differences.  The manuscript is well-written and I recommend publication after minor revisions. As one aspect emerging from individual minor comments, I think the authors should add a discussion section.

Minor points

l. 5 Please add “…sunlight and the observer.” (or similar).

ll. 5-7 The concept of assuming isotropic or anisotropic conditions has not been introduced, yet (and non-synthetic radiance measurements are not affected by such assumptions – only their subsequent L2 and L3 flux products). Consequently, this sentence sticks out and I recommend removing it.

ll. 10ff I recommend adding more specifics (e.g., which CERES product and ADMs used).

Eq. 2: R is also a function of the scene (e.g., cloud cover, surface type). If possible, I would add the scene dependency after the angular dependency.

l. 152 I would use the actual reference “(Su et al., 2015, Loeb et al., 2003) here and add “cloud microphysics (Tornow et al., 2021)”.

ll. 142-152 Similar to potential tendencies in cloud phase and optical depth, there is a chance that simpler ADMs miss anisotropic changes from cloud microphysics (e.g., as a result of fewer cloud condensation nuclei concentrations). I recommend adding this caveat in a designed discussion section (that is currently missing), as it may further impact flux deviations (shown in Fig. 12).

Fig. 4 It is unclear whether WFOV was applied here or not. Please clarify.

Fig. 9 The thin lines are barely visible. Please make those lines thicker.

Tab. 2 I fail to understand how “Ensemble size” is computed. Please improve the description in Section 2.3 and perhaps add another example.

ll. 307-314 It is unclear to me why 98deg performs so poorly. Please discuss in a designated discussion section.

ll. 381-392 I am surprised about the substantial regional differences and think it should be highlighted in the abstract. What are the implications for attribution (e.g., future radiative kernels or similar) that rely on accurate regional fluxes in combination with scene properties? Please discuss (ideally in a designated discussion section).

Fig. 12 The lines are hard to distinguish where there is overlap. I recommend adjusting line properties.

Reference(s)

Tornow, F., C. Domenech, J. N. S. Cole, N. Madenach, and J. Fischer, 2021: Changes in TOA SW Fluxes over Marine Clouds When Estimated via Semiphysical Angular Distribution Models. J. Atmos. Oceanic Technol., 38, 669–684, https://doi.org/10.1175/JTECH-D-20-0107.1.

The authors investigate the error in top-of-atmosphere irradiances derived from a constellation of wide-field-of-view broadband instrument. The authors use ERBE angular distribution models and simulate wide-field-of-view instrument measurements. They consider isotropic radiation fields and radiation fields with anisotropy. They consider four different inclination angles. They express errors by RMS difference from reference truth data. They conclude that although anisotropy changes angular distribution of radiances, ignoring anisotropy does not introduce a significant error in derived irradiances. 

I see a serious flaw in the method treating anisotropy to simulate wide-field-of-view measurements. Specifically, Equation (3) is not correct. In order to simulate wide-field-of-view measurements, the authors need integrate radiances over the field-of-view of the instrument weighted by cosign of the viewing angle. Integrating over the surface area does not include angular dependent of radiation fields properly. This is probably the main reason that the authors find that derived irradiances are insensitive to angular distribution of radiance. Please see a paper by Green et al. (1990) (Section 2) for correctly include angular distribution of radiances within a field-of-view of a wide-field-of-view instrument. Using the approach described in Green et al. the method to simulate wide-field-of-view observation using the SYN1deg-hour product is 1) estimate 1deg by 1deg grid boxes fall withing a field-of-view for a given sub-satellite point (i.e. one footprint), 2) obtain a scene type for each grid box within the field-of-view, 3) obtain viewing angle from the wide-field-of-view instrument to each grid box, 4) obtain solar zenith angle and azimuth angle for each glid box, 5) using the information, use a proper ERBE ADM and TOA flux from SYN1deg to infer the radiance toward the wide-field-of-view instrument, and 6) integrate all radiances weighted by cosign of the viewing angle over the field-of-view of the instrument. 

Using ERBE AMDs to infer radiance in 6) above, you need to scale the SYN TOA irradiance by the ratio of (ADM radiance / ADM irradiance). 

These steps give one measurement of the wide-field-of-view and repeat these steps for all wide-field-of-view instrument footprints. Convert these wide-field-of-view measurements to irradiances at a reference height, you need to integrate changing viewing angles. This is done by shape factors described in Green and Smith (1991), but since you have angular distribution of radiances, you can directly integrate radiances changing viewing angles. The conversion factor to a reference height depends on angular distribution of radiances, hence the conversion factors for isotropic versus anisotropic are different. Loeb et al. (2002) describes how to determine a reference height. You might be able to skip this reference height conversion step by defining the viewing angle at the surface (i.e. the angle measured from the zenith viewing the instrument by an observer at the surface) for the integration in 6). The result is not the exactly the same, but the differences are probably small. These steps are needed to understand the error caused by ignoring anisotropy of radiances. 

Minor comments

I found the description of the method especially the section describing emulating shortwave reflection hard to understand. For instance, the authors use, radiance, irradiance, and radiation in the section. I do not understand what radiation means, it could be either radiance or irradiance. In addition, adding a figure helps explaining angular geometry. 

Lambertian is used to refer an isotropic field. I reserve the use of Lambertian for a perfect surface of which reflectance follows a cosign law. 

References

Green R. N. and coauthors, 1990: Intercomparison of scanner and nonscanner measurements for the Earth Radiation Budget Experiment, J.Geophys. Res.95, 11785-11798. 

Green, R. N., and G. L. Smith, 1991: Shortwave shape factor inversion of Earth Radiation Budget observations, J. Atmos. Sci, 48, 390-402

Loeb, N. G., S. Kato, B. A. Wielicki, 2002: Defining top-of-atmosphere flux reference level for Earth radiation budget studies, J. Climate, 15, 3301-3309.