| 08 Sep 2025
Seeking TOA SW Flux Closure over Synthetic 3D Cloud Fields: Exploring the Accuracy of two Angular Distribution Models
Abstract. To accurately estimate outgoing top-of-atmosphere (TOA) shortwave (SW) fluxes from measurements of broadband radiances, angular distribution models (ADMs) are necessary. ADMs rely on radiance-predicting models that are trained on hemispherically-resolved CERES TOA radiance observations. The estimation of SW fluxes is particularly challenging for cloudy skies due to clouds’ anisotropy, which substantially varies with their optical properties for any given sun-object-observer geometry. The aim of this study is to investigate, the influence of micro- and macrophysical properties of liquid clouds on SW fluxes estimated by ADMs that are based on a semi-physical model and compare to operational ADMs. We hypothesize that a microphysically-aware ADM performs better in observation angles influenced by single-scattering features.
The semi-physical model relies on an optimized asymmetry parameter g∆ that depends on the cloud effective radius. To improve the radiance prediction, g∆ is adjusted for the different viewing geometries during the training of the model. In this work these adjustments are linked to single scattering features as the shift of cloud bow and glory with varying cloud droplet size.
For the investigation synthetic 3D cloud scenes based on observations and theoretical assumptions are created. Using a Monte Carlo Model the TOA broad band SW radiances and fluxes of the synthetic cloud scenes are simulated for different scenarios with varying viewing angles (θv) along the principle plane and solar angles (θs). Analyzing the scenarios the sensitivity and accuracy of the two SW radiance-to-irradiance conversion approaches to cloud droplet size, spatial distribution of liquid water path, and mean optical thickness is quantified.
The study emphasizes that the inclusion of liquid droplet effective radius in the generation of ADMs can result in more accurate SW flux estimates. Particularly for viewing geometries that exhibit single scattering phenomena, such as cloud glory and cloud bow, instantaneous flux estimates can benefit from microphysical-aware ADMs. For instantaneous flux estimates, we found that the error in the SW flux estimates could be reduced by up to 25 W /m2. For cases with very large or small droplets, the median error was reduced by 5 W /m2.
Review of a paper by Madenach et al. entitled “Seeking TOA SW flux closure over synthetic 3D cloud fields: exploring the accuracy of two angular distribution models”.
The paper quantifies errors caused by Angular Distribution Models (ADMs) that ignore water cloud microphysical variability. The authors used MODIS observations, computed broadband radiances, applied two sets of ADMs, and compared TOA fluxes. The optical thicknesses of clouds range from 2.8 to 20.1 and shape factors range from 2 to 26. The authors used empirical relationship of optical thickness, effective radius, and number concentration. The effective radius is inversely proportional to the number concentration and the optical thickness is proportional to 1/3 power of the number concentration. The authors analyzed flux differences on the principal plane as a function of number concentration. They found that the mean flux error due to ignoring particle size dependency is 5 Wm-2 but can go up to 25 Wm-2.
The paper address TOA flux errors derived from ADMs. The topic addressed in the paper is somewhat unique to the EarthCARE mission. I only have minor comments on this version.
Equation 7: Need a reference of the two-stream albedo. In addition, asymmetry parameter is not used/discussed in the rest of the paper very much. How is the asymmetry parameter related with variables used in Eq. 12? The asymmetry parameter for water cloud droplets does not vary very much (0.86). How much does the asymmetry parameter vary in this study?
Line 92: Is ACWV = 0 an assumption for the entire study?
Table 1: How are the results sensitive to these values and how are thee values realistic to the scenes analyzed in this study?
Eqs. (8) and (12): Are As used in these equations the same?
Line 137: The relationship of droplet size and tau is nothing to do with scattering. It is the consequence of Eq. 12.
Figure 10: Are these results based on the principal plane? Larger flux differences come from glory. I would think that the difference is negligible outside glory angles and outside the principal plane. If the mean difference of 5 Wm-2 considers only the principal plane, the authors need to state clearly. In addition, EarthCARE BBR views scenes outside the principal plane. It is worthwhile to consider actual viewing geometry of BBR, this is especially true since BBR is taking data now.
Line 220: how the error changes with tau and nu is not shown and discussed in the paper.