Mathematical Notation Rendering Comparison: Visual Quality Assessment

Polarimetric radars provide variables like the specific differential phase ($K_{DP}$) to detect fingerprints of dendritic growth in the dendritic growth layer (DGL) and secondary ice production, both critical for precipitation formation. A key challenge in interpreting radar observations is the lack of in situ validation of particle properties within the radar measurement volume. While high $K_{DP}$ in snow is usually associated with high particle number concentrations, only few studies attributed $K_{DP}$ to certain hydrometeor types and sizes. We found that at W-band, $K_{DP} > 2\,^\circ\,\mathrm{km}^{-1}$ can result from a broad range of particle number concentrations, between $1$ and $100\,\mathrm{L}^{-1}$. Blowing snow and increased ice collisional fragmentation in a turbulent layer enhanced observed $K_{DP}$ values. T-matrix simulations indicated that high $K_{DP}$ values were primarily produced by particles smaller than $0.8\,\mathrm{mm}$ in the DGL and $1.5\,\mathrm{mm}$ near the surface.

The distinction between aggregation and riming below the DGL is important, because the latter signals the presence of super-cooled liquid water (SLW). Riming favors secondary ice production through the Hallet-Mossop process (rime splintering), which is active between $-3\,^\circ\mathrm{C}$ and $-8\,^\circ\mathrm{C}$. POLICE exploited quasi-vertical profile (QVP) data of reflectivity ($Z_H$), differential reflectivity ($Z_{DR}$), and depolarization ratio ($DR$). Similar to $Z_{DR}$, the variable $DR$ tends to decrease in rimed snow relative to aggregated snow, but the corresponding difference in $DR$ is $2$–$4\,\mathrm{dB}$ larger (e.g., Ryzhkov et al., 2017). Naturally, $DR$ combines the information content of $Z_{DR}$ and cross-correlation coefficient ($\rho_{hv}$) in a single quantity. The MISPs of mean Doppler velocity ($MDV$) are used to identify regions with particles falling faster than $1.5\,\mathrm{m}\,\mathrm{s}^{-1}$ and accordingly associated with riming.

Polarimetric radars provide variables like the specific differential phase (K_DP) to detect fingerprints of dendritic growth in the dendritic growth layer (DGL) and secondary ice production, both critical for precipitation formation. A key challenge in interpreting radar observations is the lack of in situ validation of particle properties within the radar measurement volume. While high K_DP in snow is usually associated with high particle number concentrations, only few studies attributed K_DP to certain hydrometeor types and sizes. We found that at W-band, K_DP > 2 °km⁻¹ can result from a broad range of particle number concentrations, between 1 and 100 L⁻¹. Blowing snow and increased ice collisional fragmentation in a turbulent layer enhanced observed K_DP values. T-matrix simulations indicated that high K_DP values were primarily produced by particles smaller than 0.8 mm in the DGL and 1.5 mm near the surface.

The distinction between aggregation and riming below the DGL is important, because the latter signals the presence of super-cooled liquid water (SLW). Riming favors secondary ice production through the Hallet-Mossop process (rime splintering), which is active between -3°C and -8°C. POLICE exploited quasi-vertical profile (QVP) data of reflectivity (Z_H), differential reflectivity (Z_DR), and depolarization ratio (DR). Similar to Z_DR, the variable DR tends to decrease in rimed snow relative to aggregated snow, but the corresponding difference in DR is 2-4 dB larger (e.g., Ryzhkov et al., 2017). Naturally, DR combines the information content of Z_DR and cross-correlation coefficient (ρ_hv) in a single quantity. The MISPs of mean Doppler velocity (MDV) are used to identify regions with particles falling faster than 1.5 m/s and accordingly associated with riming.