Prevención/ Integración

The evaluation of the response of hydrometeors to the electromagnetic ra- diation is one of the aims of this thesis. For this purpose two of the most utilized scattering methods were compared. As explained in section 3.2.3, some size relations were retrieved from the NASA database in order to be used as inputs into the T-Matrix code. Utilizing the DDA aggregate database (because the CANTMAT code processes hydrometeors as aggregate-like par- ticles) the density-diameter relation was obtained and is shown in Figure 4.6. The diameter of a sphere equivolume to the ellipsoid circumscribing the ice particles was used as the size representation (see also section 3.2.3). The achieved relationship, where a and b stand, respectively, for the coecient and the exponent of the power law form of the equation, is consistent with the literature relations (e.g. Heymseld et al. 2004). In this analysis the dif-

Fig. 4.6: Density-dimension power law relation of the DDA NASA database. Blue dots represent database of aggregate particles. Red line stands for tting line. The other lines are relationships from the literature for reference.

Fig. 4.7: Aspect ratio-dimension linear relation of the DDA NASA database. Blue dots represent the database of aggregate particles. Red line is a tting line.

ferent habits were not considered and the particles were processed as general aggregate hydrometeors. This is the reason why they are depicted with a unique color in the graphs. That is to comply with the CANTMAT code, in which no habit distinction is made. A linear form, instead, links together the aspect ratio of the particles and their dimensions. Using a linear t, the two coecients were calculated (Figure 4.7) resulting in reasonable agreement with the literature relationships (e.g. Nowell et al. 2013).

By these two relations the CANTMAT code was initialized. The outcomes of T-Matrix computations were compared with the DDA backscattering cross sections. The results are shown in Figure 4.8. Here, the dots depict the cross section values of particle as calculated from the NASA database. The dif- ferent hydrometeor shapes were made explicit through the colors with the aim of highlighting if some habits showed similar patterns to the T-Matrix

Fig. 4.8: Backscattering cross sections at 24 GHz. Dots represent the NASA DDA database values. Lines with stars stand for the CANTMAT T-Matrix calculations in which the density and aspect ratio depend on the particle diameter.

simulations. The latter are drawn as lines and stars and the dierent colors represent the dierent values of the canting angle standard deviation. The two methods seem to be in good agreement at the smaller sizes, where the particles fall within the Rayleigh approximation. Then there is a large dis- crepancy between the methods and the DDA exhibits higher values than the T-Matrix calculations. Moreover, the latter show the classical Mie resonance behavior, not found in the DDA results. That is probably because CANT- MAT considers particles as having a symmetrical structures, whereas, in the NASA database, the aggregates are represented with more details, losing the geometrical symmetry.

To assess the T-Matrix variability due to the dierent size relation set- tings, several simulations were performed. In particular, some calculations were carried out with the canting angle standard deviation set at 10 degrees

Fig. 4.9: Backscattering cross sections at 24 GHz. Dots represent the NASA DDA database values. Lines with stars stand for the CANTMAT T-Matrix calculations: black line represents the computation where the size relations were used and it is depicted as reference, the other lines stand for the simula- tions in which the particle density depends on the particle diameter, whereas the aspect ratio assumes xed values.

and with xed values of the axis ratio, while the density was linked to the hydrometeor size by the aforementioned relation. The results are shown in Figure 4.9. It can be seen how the T-Matrix resonance is strictly related to the axis ratio values. In fact, with the lowest value (ar=0.2) the CANTMAT simulation (red line with stars) exhibits a pattern similar to the DDA, with- out the resonance eects, that instead becomes clear with a quasi-spherical shape (ar=0.98, blue line). However, such a low value of the axis ratio is rather unrealistic for the hydrometeors.

As mentioned on several occasions in this thesis, the scattering properties depend deeply on density. In order to explore the T-Matrix electromagnetic responses with respect to this quantity, several density values were used in the

Fig. 4.10: Backscattering cross sections at 24 GHz. Dots represent the NASA DDA database values. Lines with stars stands for the CANTMAT T-Matrix calculations: black line represents the computation where size relations were used and it is provided as reference, the other lines stand for the simulations in which the aspect ratio depends on the particle diameter, whereas the particle density assumes xed values.

simulations, while the axis ratio was governed by size relation. The results (Figure 4.10) show that, in case of high density, the T-Matrix values are greater than the DDA ones, and the opposite occurs for low density amount. It should be noted that the density value of 0.05 (yellow line) reproduces quite well the NASA database pattern. Such value seems not to be so unrealistic, even though it fails to represent the smaller particles (see Figure 4.6).

Finally, some other simulations were carried out using a canting angle standard deviation depending on hydrometeor diameter, following the litera- ture hints (e.g.Kennedy and Rutledge 2011). The results (not shown) exhibit almost the same patterns of Figures 4.9 and 4.10, meaning that, at least in these CANTMAT computations, the canting angle plays a less fundamental

role on backscattering response variability compared to the particle density and the axis ratio.