| 03 Sep 2025
Assessing Earth’s sphericity effects in the specific case of geostationary satellites observations: focus on operational land/aerosol applications from Meteosat Third Generation-Imager
Abstract. Geostationary satellites allow a continuous sub-hourly monitoring of the Earth including land surfaces and aerosols, which can now benefit from the advanced measuring performances of the new Meteosat Third Generation-Imager and its Flexible Combined Imager on board (FCI). In this study, we aim to improve our understanding of the impact of the Earth's sphericity on geostationary observations. Although sphericity effects in satellite data have been studied for many years, the curvature of our planet is still not accounted for in many operational radiative transfer-based retrieval algorithms due to the required increase in processing time, and therefore a plane-parallel atmosphere-surface system is assumed instead. While the limitations of this approximation have been widely assessed in the case of low Earth orbit satellites, they must be reevaluated with regard to geostationary satellites, which have a broader range of observing and illumination geometries. Furthermore, we currently lack precise benchmarking of the errors caused by neglecting the Earth's sphericity in the case of land surface and aerosol applications, which show significant differences with respect to the commonly considered ocean color applications. For example, surface/aerosol algorithms use instrument channels in the red and near-infrared spectral ranges where there is a growing impact of molecular absorption compared to the ocean color-sensitive blue channels where Rayleigh scattering predominates. In this context, we perform quantitative analyses of the impact of ignoring the Earth's curvature on FCI-like top-of-atmosphere reflectance calculations using the accurate Monte Carlo radiative transfer code SMART-G. Results enable quantification of important biases introduced by the plane-parallel assumption, with a strong dependency on the satellite acquisition geometry and, to a lesser extent, the measuring wavelength, but without significant dependency on surface and aerosol properties. We also find that 36 % of FCI observations are significantly affected by sphericity effects, in particular in the channels centered at short visible wavelengths (i.e., 444 and 510 nm for FCI). Based on these results, this study makes recommendations on the development of methods to correct geostationary data for sphericity effects so that one can keep using plane-parallel radiative transfer codes for near-real-time operational applications.
The authors present simulation results of the radiance reflected at TOA using the spherical Monte Carlo code SMART-G, and explore the bias of using the plane-parallel assumption instead of the spherical shell assumption. They also explore the dependence of this bias on various parameters such as viewing and illumination geometry, surface albedo, wavelength, and aerosol (layer) type.
Below I state my three major concerns which should be addressed before publication:
In the abstract, Table 9, and the conclusion, the authors conclude a weak dependence of the above-mentioned bias on wavelength and insignificant dependencies on the surface albedo and aerosol properties. However, those effects are explored at a VZA of 45 degrees only, while most significant sphericity effects may be expected at the largest VZAs (which the authors also show for the default settings in their Fig. 1).
This is problematic for the manuscript, because the authors claim novelty of their work based on the large viewing zenith angle range (relevant for geostationary satellites as compared to polar orbiting satellites). The conclusion of the bias dependencies thus may be subjective to the choice of VZA. The editor already suggested the VZA of 45 degrees, but I would like to ask the authors to include simulations at a VZA of 60 degrees (representative for Mid Europe, see e.g. Fig. 1 of Masiello et al. 2015, https://amt.copernicus.org/articles/8/2981/2015/amt-8-2981-2015.pdf), which may possibly change the conclusions of the paper.
Another claimed novelty by the authors of their sphericity analysis is the inclusion of near-infrared (NIR) wavelengths where gaseous absorption plays a role. In Sect. 4.2, they attribute the relatively large errors at the longer wavelengths for SZA > 80 degrees to gaseous absorption, however, no evidence is provided. Could those errors possibly also be related to the wavelength dependence of the Rayleigh scattering efficiency in combination with sphericity effects at large SZA? I would like to ask the authors to include simulation results at a long wavelength, but without gaseous absorption, to prove that gaseous absorption is indeed responsible. This would improve the physical understanding of the simulation results.
In Sect. 2.3., an explanation is provided for the cause of the bias of the PPA results compared to those of the SSA, for large SZA, and for large VZA. The authors state that (1) “high SZA causes an overestimation of the optical path in PPA, leading to an overestimation of the attenuation of the solar beam in the atmosphere, causing the PPA to induce a negative bias in TOA radiance estimation” and (2) “high VZA leads to an overestimation of the illuminated volume and Rayleigh scattering, creating a positive bias induced by the PPA in the simulated TOA radiances”. However, from Adams and Kattawar (1978), I understand that in a spherical atmosphere (1) with increasing SZA, less photons reach the (black) surface, increasing the reflected radiance w.r.t. the PPA (indeed, in the twilight zone, at a SZA of 90 degrees and slightly larger, there is still signal due to horizontal scattering) and (2) with increasing VZA, the optical paths through the atmosphere along the line of sight from the detector are shorter (for VZA defined at TOA, with an optical path approaching 0 for VZA= 90 deg), yielding smaller radiances for SSA w.r.t. PPA. Although the signs of the biases are correct here, I would like the authors to reconsider the explanation of the cause of those biases, because it is key for the physical understanding of the simulations results in this paper. Including a sketch could be helpful. In addition, please cite the relevant literature here where those insights were introduced, for the readers seeking further explanation.
Other comments:
The authors state that pseudo-spherical approximations are not feasible in operational algorithms, however, I think many satellite algorithms use the pseudo-spherical approximation. Do the authors have an example of an algorithm that cannot use the pseudo-spherical approximation due to computational constraints. Could the authors include the remaining error of the pseudo-spherical approximation? This would greatly improve the relevance of the paper.
Figure 1: Why are two satellites and two suns shown? This may be confusing, because also two systems are shown: PPA and SSA. I suggest removing one sun and one satellite in the sketch. I also suggest adding multiple layers to the sketch, as they are mentioned in the first sentence of Sect. 2.2.
Line 150: “Rayleigh scattering is the main radiance-inducing atmospheric process in the short visible spectrum, corresponding to the first measuring channels of most geostationary satellite images. Therefore, the difference between the PPA and SSA geometries will primarily affect Rayleigh scattering.” This is poor logical reasoning: if phenomenon A is dominant, it is not guaranteed that phenomenon B primarily affects A. Please rephrase.
Line 207: Please explain more clearly in one sentence what REPTRAN does.
Line 212: “Since absorption cannot be neglected in the considered long visible and near-infrared channels.” Please state the relevant gases here (probably H2O). Can absorption be neglected at the shorter VIS channels? What about O3?
Sect 3.3: Please include the wavelength ranges of the channels, and the indicate per channel which absorbing gases play a role, because this information is relevant to interpret the simulation results. A table could be helpful.
Line 257: “One should note the negative sign before SZA values in Fig .2 has no physical nor mathematical meaning in this manuscript…” Please remove the minus signs in all figures and add ‘RAA = 0 deg’ and ‘RAA = 180 deg’ labels to the figures.
Line 262: “Indeed, when VZA increases the illuminated volume grows” Do you mean “the observed volume”?
Line 265: “… PPA leads to an overestimation of the solar beam attenuation in Rayleigh dominated wavelengths.” Please reconsider this explanation.
Line 269: “the relative error (in absolute values)” may be confusing. Please explain or remove ‘(in absolute values)’.
Sect. 4.2: Please mention what absorbing gases are relevant at the considered wavelengths. Please note that gaseous absorption (by O3) also occurs at shorter (VIS) wavelengths, at high altitudes, while H2O mainly absorbs at lower altitudes. Does the altitude dependence of the gas abundances affect the sphericity impact (since at large SZA and VZA, the reflected radiances is more sensitive to higher atmospheric layers)?
Figure 3c could be considered redundant and can be removed, because is the combination of Figs. 3a and 3b. The combination is also covered in the main text.
Sect. 4.4: The authors explore the effect of different atmospheric profiles but also mention that ‘fluctuations in Rayleigh optical depth between atmospheric profiles are below 1%’. How do the input profiles differ? Please explain and if relevant, include a figure of the profiles.
Editing suggestions:
Title: ‘… geostationary satellites observations… ‘ --> ‘… geostationary satellite observations …’, remove the s.
line 1: ‘… allow a continuous …’ --> ‘… allow continuous’
line 2: ‘performances’ --> ‘performance’
line 15: ‘measuring wavelength’ --> ‘measurement wavelength’
line 59: ‘well known’ --> ‘well-known’
line 60: Please use a more logical start of a new paragraph, e.g.: ‘An example of an algorithm that uses the PPA is… ‘
line 67: ‘… in the specific of geostationary sensors, which for example provide …’ -->
‘… in the application to geostationary sensors, which provide …’
Line 84: ‘The Earth consists in a near-spherical 3-D system,’ Change ‘consists in’ to ‘consists of’ or rephrase.
Line 91; ‘a scattered radiation being scattered’ --> ‘radiation being scattered’
Line 94: ‘identifying the invariances’, I suggest rephrasing and use another work than ‘invariances’.
Line 99: ‘all the atmospheric layers as infinite parallel planets’ --> ‘all the atmospheric layer boundaries at infinite parallel horizontal planes’
Line 101: Do you mean viewing or solar zenith and azimuth angles here? Please specify.
Line 234: ‘consists in’ --> ‘consists of’ or rephrase
Line 249: ‘simulations results’ --> ‘simulation results’
Line 340: ‘which makes sense considering’ --> ‘because’
Line 390: ‘does corresponds to’ --> ‘corresponds to’