Numerical Simulation of the Effects of Surface Roughness on Light Scattering by Hexagonal Ice Plates
Abstract
:1. Introduction
2. Materials and Methods
2.1. Scattering Theory
2.2. A Simple Implementation of Surface Roughness
2.2.1. Particle Orientations
- .
- ,, , , , , , , , , , , , , , , .
- ,, , , , , .
2.3. Numerical Methods
3. Results
3.1. Discrete Dipole Approximation
- Close to Direct Forward Scattering: The scattered intensity close to is shown in the upper left inset of the figure. A linear scale is used in the upper left insets here since small fractional differences have a significant effect on the asymmetry parameter. It is found that, at this size parameter, the smooth plate has the strongest forward scattered intensity, while increasing values of result in smaller amplitudes. Interestingly, the data show that scattering by particles with is almost indistinguishable to those with . In summary, the data suggest that surface roughness has almost no effect on the forward scattering if .
- Halo Region: The broad halo peak centred at ∼ can be attributed to the angle of minimum deviation associated with light passing between 2 non-adjacent rectangular facets of the plate [20]. The relative height of this peak, known as the halo ratio, can be defined as . The value of the halo ratio has been proposed as a quantitative measure for identifying the presence of cirrus [30]. Compared to computations with geometric optics (e.g., [9,31]), the halo observed here is broader and relatively weak. The height of this peak can be explained by the large aspect ratio of the plate. More columnar-type ice particles have larger rectangular facets, which in turn leads to a larger fraction of the incident energy being scattered into the halo region. The broadness of the peak is due to the fact that the prism facets have dimensions comparable to the wavelength. This leads to a significant broadening of scattering due to diffractive effects, which cannot be accounted for with classical geometric optics. Similar to the findings of the direct forward scattering, the halo region is almost unaffected by the presence of surface roughness with an amplitude much smaller than the wavelength. The halo peak diminishes as the roughness increases up until , wherein the peak is no longer distinguishable, which agrees with the findings of other studies [32,33,34]. This finding has implications for practical applications which use the halo region as a means of identifying the presence of ice particles. The results show that the absence of a distinguishable halo peak does not necessarily mean that there is an absence of hexagonal ice plates in the sample. Rather, it merely indicates the absence of pristine hexagonal prisms. This agrees with other studies, which have found that classical geometric optics overestimates the intensity of the halo peak [19,35]. Further incorporation of the halo ratio in measuring techniques could provide a useful method of estimating surface roughness and irregularity, especially when combined with the analysis of other experimental evidence, such as scattering pattern symmetry and particle imaging.
- Backscattering: The backscattering in the region – is shown in the upper right insets of Figure 5. Unlike for the forward scattering and halo regions, even small-scale roughness appears to have an effect on the backscattering. As may be expected, the smooth hexagonal plate () shows the strongest backscattering peak. Due to the normalisation of each phase function and the difference in scattering cross sections between datasets, comparing the values at does not provide a very useful insight. Instead, the backscattering ratio is introduced, which is defined here as . The backscattering ratios for increasing values of at are found to be 3.74, 2.86, 1.76, 1.56, 1.41, and 1.42. Increasing the amplitude of surface roughness decreases the backscattering ratio until a value of ∼, where the asymptote appears. Recent studies indicate that two main factors contribute to the backscattering ratio: corner retro-reflection events [36] and coherent backscattering [37]. A retro-reflection can occur when a particle with multiple right-angled facets is illuminated at certain ranges of orientations. Under these conditions, there exist bundles of parallel ray paths which can be shown using geometric optics to scatter into the direct backscattering direction. One possible explanation for the decreasing backscattering ratio is that, as the roughness amplitude increases, the effect of retro-reflection events is reduced, and therefore the backscattering ratio becomes primarily due to coherent backscattering. The effect of coherent backscattering is a well-known wave phenomenon that leads to constructive interference in and close to . The effect can be explained by studying a pair of reciprocal ray paths as shown in Figure 6a. If an incident ray undergoes multiple scattering events and is scattered back along the direction of incidence, then there exists a reciprocal ray which travels along the exact same path but in the opposite direction. This follows as a result of the time-reversal symmetry of Maxwell’s equations. Consequently, the 2 rays travel the same distance and therefore always interfere constructively in the direct backscattering, which leads to a peak in the backscattered intensity. Even without consideration of the phase of the electric field, classical geometric optics often overestimates the backscattering ratio for pristine hexagonal prisms due to the omission of diffraction of outgoing bundles of rays.
3.2. PBT Results vs. DDA
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
DDA | Discrete Dipole Approximation |
PBT | Parent Beam Tracer |
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Ballington, H.; Hesse, E. Numerical Simulation of the Effects of Surface Roughness on Light Scattering by Hexagonal Ice Plates. Atmosphere 2024, 15, 1051. https://doi.org/10.3390/atmos15091051
Ballington H, Hesse E. Numerical Simulation of the Effects of Surface Roughness on Light Scattering by Hexagonal Ice Plates. Atmosphere. 2024; 15(9):1051. https://doi.org/10.3390/atmos15091051
Chicago/Turabian StyleBallington, Harry, and Evelyn Hesse. 2024. "Numerical Simulation of the Effects of Surface Roughness on Light Scattering by Hexagonal Ice Plates" Atmosphere 15, no. 9: 1051. https://doi.org/10.3390/atmos15091051