testing:math2

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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 in the range $-3\,^\circ\mathrm{C}$ to $-8\,^\circ\mathrm{C}$. 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 (KDP) 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 KDP in snow is usually associated with high particle number concentrations, only few studies attributed KDP to certain hydrometeor types and sizes. We found that at W-band, KDP > 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 KDP values. T-matrix simulations indicated that high KDP 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 in the range -3°C to -8°C. POLICE exploited quasi-vertical profile (QVP) data of reflectivity (ZH), differential reflectivity (ZDR), and depolarization ratio (DR). Similar to ZDR, 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 ZDR and cross-correlation coefficient (ρhv) 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.

LaTeX
$K_{DP}$
Unicode
KDP
LaTeX
$Z_H$
Unicode
ZH
LaTeX
$Z_{DR}$
Unicode
ZDR
LaTeX
$\rho_{hv}$
Unicode
ρhv
LaTeX
$N_0$
Unicode
N0
LaTeX
$D_{\mathrm{max}}$
Unicode
Dmax
LaTeX
$T_{\mathrm{env}}$
Unicode
Tenv
LaTeX
$v_{\mathrm{term}}$
Unicode
vterm
LaTeX
$\lambda$
Unicode
λ
LaTeX
$\theta$
Unicode
θ
LaTeX
$\phi$
Unicode
φ
LaTeX
$\sigma$
Unicode
σ
LaTeX
$\mu$
Unicode
μ
LaTeX
$\alpha$
Unicode
α
LaTeX
$\beta$
Unicode
β
LaTeX
$\gamma$
Unicode
γ
LaTeX
$\Delta T$
Unicode
ΔT
LaTeX
$\Sigma$
Unicode
Σ
LaTeX
$\Omega$
Unicode
Ω
LaTeX
$\psi$
Unicode
ψ
LaTeX
$2\,^\circ\,\mathrm{km}^{-1}$
Unicode
2 °km⁻¹
LaTeX
$100\,\mathrm{L}^{-1}$
Unicode
100 L⁻¹
LaTeX
$1.5\,\mathrm{m}\,\mathrm{s}^{-1}$
Unicode
1.5 m/s
LaTeX
$10\,\mathrm{mm}\,\mathrm{h}^{-1}$
Unicode
10 mm/h
LaTeX
$0.8\,\mathrm{mm}$
Unicode
0.8 mm
LaTeX
$2-4\,\mathrm{dB}$
Unicode
2-4 dB
LaTeX
$850\,\mathrm{hPa}$
Unicode
850 hPa
LaTeX
$3.2\,\mathrm{cm}$
Unicode
3.2 cm
LaTeX
$K_{DP} > 2$
Unicode
KDP > 2
LaTeX
$Z_H \geq 40$
Unicode
ZH ≥ 40
LaTeX
$T \leq 0\,^\circ\mathrm{C}$
Unicode
T ≤ 0°C
LaTeX
$\Delta T \approx 5\,^\circ\mathrm{C}$
Unicode
ΔT ≈ 5°C
LaTeX
$\rho \neq 1$
Unicode
ρ ≠ 1
LaTeX
$v \pm 0.5$
Unicode
v ± 0.5
LaTeX
$N \propto D^{-4}$
Unicode
N ∝ D⁻⁴
LaTeX
$a \times b$
Unicode
a × b
LaTeX
$N_0 = 8 \times 10^6$
Unicode
N0 = 8 × 106
LaTeX
$Z = aR^b$
Unicode
Z = aRb
LaTeX
$\frac{dZ}{dH}$
Unicode
dZ/dH
LaTeX
$\sqrt{a^2 + b^2}$
Unicode
√(a² + b²)
LaTeX
$e^{-\lambda t}$
Unicode
e-λt
LaTeX
$\frac{\partial T}{\partial t}$
Unicode
∂T/∂t
LaTeX
$\sum_{i=1}^{n} x_i$
Unicode
Σi=1n xi
LaTeX
$\int_0^H f(h)\,dh$
Unicode
0H f(h) dh

  • testing/math2.1761075179.txt.gz
  • Last modified: 2025/10/21 19:32
  • by ayush