{ "cells": [ { "cell_type": "markdown", "id": "67576ac4", "metadata": {}, "source": [ "# Tutorial 12 — Spectral polarimetry of a SLW / rain / hail mixture at 500 hPa\n", "\n", "**Reference.** Lakshmi K., K., Sahoo, S., Biswas, S. K., and\n", "Chandrasekar, V., 2024: Study of Microphysical Signatures Based on\n", "Spectral Polarimetry during the RELAMPAGO Field Experiment in\n", "Argentina. *J. Atmos. Oceanic Technol.*, 41, 235–256,\n", "[doi:10.1175/JTECH-D-22-0113.1](https://doi.org/10.1175/JTECH-D-22-0113.1).\n", "\n", "Lakshmi et al. (2024) used C-band Doppler spectral polarimetry from\n", "the CSU-CHIVO radar during RELAMPAGO to dissect mixed-phase and\n", "convective precipitation volumes. Their central point is that\n", "*spectral* $Z_h$, $Z_\\mathrm{dr}$, $K_\\mathrm{dp}$, $\\rho_\\mathrm{hv}$\n", "separate hydrometeor populations that the *bulk* observables mash\n", "into one number — because each species occupies a distinct\n", "Doppler-velocity window set by its terminal fall speed.\n", "\n", "Here we build a synthetic C-band radar resolution volume at altitude\n", "where $P = 500$ hPa ($T \\approx 252$ K, $\\rho \\approx 0.69$ kg/m³,\n", "reached near 6 km MSL in a convective updraft). Three populations\n", "coexist:\n", "\n", "* **Supercooled cloud liquid water** (SLW) — spherical droplets,\n", " $D \\lesssim 0.2$ mm, $v_t \\lesssim 0.1$ m/s.\n", "* **Rain** — oblate drops following the Thurai (2007) shape,\n", " $D \\lesssim 5$ mm.\n", "* **Small wet (melting) hail** — water-coated ice, 30 %% meltwater\n", " by volume via Maxwell-Garnett EMA, axis ratio 0.75, canting σ = 40°,\n", " $D$ up to 12 mm. The water coating drives a strong C-band Mie\n", " resonance near $D \\approx 8$–10 mm with large $|\\delta_\\mathrm{hv}|$\n", " — the rain-hail mixing regime flagged by Lakshmi et al. (2024) at the\n", " melting layer.\n", "\n", "## Slant geometry\n", "Polarimetric observables require a slant beam: oblate raindrops at\n", "nadir project to circles, collapsing $Z_\\mathrm{dr}$ and\n", "$K_\\mathrm{dp}$ to zero. We use an elevation angle $\\phi = 30°$,\n", "so the radial velocity of a particle of diameter $D$ is\n", "$v_r(D) = v_t(D)\\,\\sin\\phi$ and the scattering matrices come from\n", "the slant back-/forward-scatter geometries $(\\theta_0, \\theta) =\n", "(60°, 120°)$ and $(60°, 60°)$. Lakshmi et al. (2024) work with\n", "CSU-CHIVO RHI scans at elevation angles that span $0°$–$45°$; our\n", "$\\phi = 30°$ sits in their mid-elevation band where horizontal-wind\n", "and fall-speed contributions to the radial velocity are both\n", "meaningful.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "c1f97ff6", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:01.038358Z", "iopub.status.busy": "2026-04-21T19:42:01.038227Z", "iopub.status.idle": "2026-04-21T19:42:02.405265Z", "shell.execute_reply": "2026-04-21T19:42:02.404759Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ρ_air = 0.691 kg/m³, ρ₀/ρ = 1.772\n", "rain fall-speed ×1.257, hail ×1.331\n", "φ = 30°, sin φ = 0.500\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from rustmatrix import (HydroMix, MixtureComponent, Scatterer,\n", " SpectralIntegrator, orientation, radar, spectra)\n", "from rustmatrix.psd import ExponentialPSD, GammaPSD, PSDIntegrator\n", "from rustmatrix.refractive import m_w_0C, mg_refractive, mi\n", "from rustmatrix.tmatrix_aux import K_w_sqr, dsr_thurai_2007, wl_C\n", "\n", "# Ambient state at 500 hPa.\n", "P_HPA = 500.0\n", "T_K = 252.0\n", "R_D = 287.05\n", "RHO_AIR = P_HPA * 100.0 / (R_D * T_K)\n", "RHO_0 = 1.225\n", "RHO_RATIO = RHO_0 / RHO_AIR\n", "DENS_CORR_POW4 = RHO_RATIO ** 0.4 # Foote-duToit for rain\n", "DENS_CORR_SQRT = RHO_RATIO ** 0.5 # hail / large particles\n", "\n", "# 30° slant geometry.\n", "PHI_DEG = 30.0\n", "SIN_PHI = np.sin(np.deg2rad(PHI_DEG))\n", "THETA0 = 90.0 - PHI_DEG\n", "GEOM_BACK = (THETA0, 180.0 - THETA0, 0.0, 180.0, 0.0, 0.0)\n", "GEOM_FORW = (THETA0, THETA0, 0.0, 0.0, 0.0, 0.0)\n", "\n", "V_MIN, V_MAX, N_BINS = -2.0, 15.0, 512\n", "\n", "print(f'ρ_air = {RHO_AIR:.3f} kg/m³, ρ₀/ρ = {RHO_RATIO:.3f}')\n", "print(f'rain fall-speed ×{DENS_CORR_POW4:.3f}, hail ×{DENS_CORR_SQRT:.3f}')\n", "print(f'φ = {PHI_DEG:.0f}°, sin φ = {SIN_PHI:.3f}')\n" ] }, { "cell_type": "markdown", "id": "34ceac6a", "metadata": {}, "source": [ "## Build the three hydrometeor scatterers\n", "\n", "Each species uses the slant geometry tables for its scattering matrix.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "365b9297", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:02.408364Z", "iopub.status.busy": "2026-04-21T19:42:02.408207Z", "iopub.status.idle": "2026-04-21T19:42:02.421149Z", "shell.execute_reply": "2026-04-21T19:42:02.420785Z" } }, "outputs": [], "source": [ "def build_rain():\n", " s = Scatterer(wavelength=wl_C, m=m_w_0C[wl_C], Kw_sqr=K_w_sqr[wl_C],\n", " ddelt=1e-4, ndgs=2)\n", " integ = PSDIntegrator()\n", " integ.D_max = 5.0\n", " integ.num_points = 64\n", " integ.axis_ratio_func = lambda D: 1.0 / dsr_thurai_2007(D)\n", " integ.geometries = (GEOM_BACK, GEOM_FORW)\n", " s.psd_integrator = integ\n", " s.psd_integrator.init_scatter_table(s)\n", " # Heavy convective rain: D0 = 2.0 mm, Nw = 8e4 ⇒ Z_h ≈ 52 dBZ.\n", " s.psd = GammaPSD(D0=2.0, Nw=8e4, mu=2, D_max=5.0)\n", " return s\n", "\n", "def build_slw():\n", " s = Scatterer(wavelength=wl_C, m=m_w_0C[wl_C], Kw_sqr=K_w_sqr[wl_C],\n", " axis_ratio=1.0, ddelt=1e-4, ndgs=2)\n", " integ = PSDIntegrator()\n", " integ.D_max = 0.2\n", " integ.num_points = 64\n", " integ.geometries = (GEOM_BACK, GEOM_FORW)\n", " s.psd_integrator = integ\n", " s.psd_integrator.init_scatter_table(s)\n", " # D₀ ≈ 30 µm, LWC ≈ 0.5 g/m³.\n", " s.psd = GammaPSD(D0=0.03, Nw=1e11, mu=4, D_max=0.2)\n", " return s\n", "\n", "# Wet-hail effective refractive index: Maxwell-Garnett with water as\n", "# the matrix (30% meltwater by volume) and ice as the inclusion.\n", "m_wet_hail = mg_refractive((m_w_0C[wl_C], mi(wl_C, 0.917)),\n", " (0.30, 0.70))\n", "\n", "def build_hail():\n", " s = Scatterer(wavelength=wl_C, m=m_wet_hail, Kw_sqr=K_w_sqr[wl_C],\n", " axis_ratio=0.75, ddelt=1e-4, ndgs=2)\n", " s.orient = orientation.orient_averaged_fixed\n", " s.or_pdf = orientation.gaussian_pdf(std=40.0, mean=90.0)\n", " s.n_alpha = 6; s.n_beta = 12\n", " integ = PSDIntegrator()\n", " integ.D_max = 12.0\n", " integ.num_points = 64\n", " integ.geometries = (GEOM_BACK, GEOM_FORW)\n", " s.psd_integrator = integ\n", " s.psd_integrator.init_scatter_table(s)\n", " # Small-wet-hail PSD: N0 = 150 m⁻³ mm⁻¹, Λ = 0.6 mm⁻¹, D_max = 12 mm.\n", " s.psd = ExponentialPSD(N0=150.0, Lambda=0.6, D_max=12.0)\n", " return s\n", "\n", "rain = build_rain()\n", "slw = build_slw()\n", "hail = build_hail()\n" ] }, { "cell_type": "markdown", "id": "c49b868c", "metadata": {}, "source": [ "## Fall-speed callables\n", "\n", "Each callable returns the radial velocity (already projected onto the\n", "slant beam by $\\sin\\varepsilon$) and includes the $(\\rho_0/\\rho)$\n", "correction appropriate for its size regime.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "cf590ea5", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:02.422632Z", "iopub.status.busy": "2026-04-21T19:42:02.422554Z", "iopub.status.idle": "2026-04-21T19:42:02.426067Z", "shell.execute_reply": "2026-04-21T19:42:02.425644Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " D [mm] v_slw v_rain v_hail [m/s]\n", " 0.030 0.002 0.000 0.145\n", " 0.100 0.019 0.252 0.314\n", " 1.000 1.886 2.608 1.372\n", " 3.000 16.972 5.312 2.772\n", " 5.000 47.146 6.020 3.844\n", " 10.000 188.582 6.222 5.991\n", " 20.000 754.329 0.000 9.335\n" ] } ], "source": [ "def v_rain(D):\n", " # Beard 1976 handles (T, P) density correction itself.\n", " v_t = spectra.fall_speed.beard_1976(D, T=T_K, P=P_HPA * 100.0)\n", " return v_t * SIN_PHI\n", "\n", "_hail_power = spectra.fall_speed.power_law(a=9.0, b=0.64, D_ref=10.0)\n", "\n", "def v_hail(D):\n", " # Matson-Huggins v ≈ 9 (D/1cm)^0.64, density-corrected.\n", " return _hail_power(D) * DENS_CORR_SQRT * SIN_PHI\n", "\n", "def v_slw(D):\n", " # Stokes-regime drag scaled by (ρ₀/ρ)^0.4.\n", " return 3.0 * np.asarray(D, dtype=float) ** 2 * DENS_CORR_POW4 * SIN_PHI\n", "\n", "D_probe = np.array([0.03, 0.1, 1.0, 3.0, 5.0, 10.0, 20.0])\n", "print(f'{\"D [mm]\":>8} {\"v_slw\":>8} {\"v_rain\":>8} {\"v_hail\":>8} [m/s]')\n", "for D in D_probe:\n", " vs, vr, vh = np.atleast_1d(v_slw(D))[0], np.atleast_1d(v_rain(D))[0], np.atleast_1d(v_hail(D))[0]\n", " print(f'{D:>8.3f} {vs:>8.3f} {vr:>8.3f} {vh:>8.3f}')\n" ] }, { "cell_type": "markdown", "id": "9ff9cadf", "metadata": {}, "source": [ "## Bulk single-species observables\n", "\n", "Before slicing spectra, print the bulk $Z_h$, $Z_\\mathrm{dr}$,\n", "$\\rho_\\mathrm{hv}$, $K_\\mathrm{dp}$ for each species alone. Note\n", "three things in the printout below:\n", "\n", "* **Rain dominates $K_\\mathrm{dp}$** ($\\sim$17 °/km vs $\\sim$1.5 for\n", " hail). Wet hail has a broad canting distribution (σ = 40°), which\n", " smears its forward-scatter differential phase toward zero, while\n", " Thurai-shaped raindrops aligned with gravity produce strong,\n", " coherent $K_\\mathrm{dp}$.\n", "* **Hail's reflectivity is comparable to rain's** at these\n", " concentrations (62.9 vs 57.8 dBZ) — the C-band resonance on the\n", " wet-hail PSD tail is loud.\n", "* **Hail's $\\rho_\\mathrm{hv}$ sits well below unity** (≈ 0.86)\n", " because the resonant oscillations in $f_h - f_v$ span a wide\n", " diameter range.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "d76a154a", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:02.427186Z", "iopub.status.busy": "2026-04-21T19:42:02.427106Z", "iopub.status.idle": "2026-04-21T19:42:02.430622Z", "shell.execute_reply": "2026-04-21T19:42:02.430277Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " species Z_h Z_dr ρ_hv K_dp\n", " [dBZ] [dB] [°/km]\n", " SLW -9.37 -0.000 1.00000 +0.0000\n", " rain 57.76 +1.175 0.99768 +16.8697\n", " hail 62.91 -0.690 0.85953 +1.4923\n" ] } ], "source": [ "def bulk(sc):\n", " sc.set_geometry(GEOM_BACK)\n", " Z = 10 * np.log10(radar.refl(sc))\n", " Zdr = 10 * np.log10(radar.Zdr(sc))\n", " rho = radar.rho_hv(sc)\n", " sc.set_geometry(GEOM_FORW)\n", " Kdp = radar.Kdp(sc)\n", " return Z, Zdr, rho, Kdp\n", "\n", "print(f\" {'species':<8} {'Z_h':>8} {'Z_dr':>7} {'ρ_hv':>8} {'K_dp':>9}\")\n", "print(f\" {'':<8} {'[dBZ]':>8} {'[dB]':>7} {'':>8} {'[°/km]':>9}\")\n", "for name, sc in (('SLW', slw), ('rain', rain), ('hail', hail)):\n", " Z, Zdr, rho, Kdp = bulk(sc)\n", " print(f' {name:<8} {Z:>8.2f} {Zdr:>+7.3f} {rho:>8.5f} {Kdp:>+9.4f}')\n" ] }, { "cell_type": "markdown", "id": "25d5d75a", "metadata": {}, "source": [ "## Spectral integrators\n", "\n", "Run one `SpectralIntegrator` per species (so we can plot the\n", "contribution of each component) plus one on a `HydroMix` with\n", "per-component kinematics (the combined spectrum).\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "7db13df6", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:02.432301Z", "iopub.status.busy": "2026-04-21T19:42:02.432174Z", "iopub.status.idle": "2026-04-21T19:42:02.468136Z", "shell.execute_reply": "2026-04-21T19:42:02.467565Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v-grid: -2.00 … +15.00 m/s, N=512\n" ] } ], "source": [ "turb = spectra.GaussianTurbulence(0.5)\n", "\n", "def run_single(sc, fall):\n", " return SpectralIntegrator(\n", " sc, fall_speed=fall, turbulence=turb,\n", " v_min=V_MIN, v_max=V_MAX, n_bins=N_BINS,\n", " geometry_backscatter=GEOM_BACK,\n", " geometry_forward=GEOM_FORW,\n", " ).run()\n", "\n", "r_slw = run_single(slw, v_slw)\n", "r_rain = run_single(rain, v_rain)\n", "r_hail = run_single(hail, v_hail)\n", "\n", "mix = HydroMix([\n", " MixtureComponent(slw, slw.psd, 'slw'),\n", " MixtureComponent(rain, rain.psd, 'rain'),\n", " MixtureComponent(hail, hail.psd, 'hail'),\n", "])\n", "r_mix = SpectralIntegrator(\n", " mix, component_kinematics={\n", " 'slw': (v_slw, turb),\n", " 'rain': (v_rain, turb),\n", " 'hail': (v_hail, turb),\n", " },\n", " v_min=V_MIN, v_max=V_MAX, n_bins=N_BINS,\n", " geometry_backscatter=GEOM_BACK,\n", " geometry_forward=GEOM_FORW,\n", ").run()\n", "\n", "# Second scenario: hail concentration halved (N0 = 75) so we can\n", "# compare the spectrum of each observable against the baseline mix.\n", "hail_psd_half = ExponentialPSD(N0=75.0, Lambda=0.6, D_max=12.0)\n", "mix_half = HydroMix([\n", " MixtureComponent(slw, slw.psd, 'slw'),\n", " MixtureComponent(rain, rain.psd, 'rain'),\n", " MixtureComponent(hail, hail_psd_half, 'hail'),\n", "])\n", "r_mix_half = SpectralIntegrator(\n", " mix_half, component_kinematics={\n", " 'slw': (v_slw, turb),\n", " 'rain': (v_rain, turb),\n", " 'hail': (v_hail, turb),\n", " },\n", " v_min=V_MIN, v_max=V_MAX, n_bins=N_BINS,\n", " geometry_backscatter=GEOM_BACK,\n", " geometry_forward=GEOM_FORW,\n", ").run()\n", "\n", "v = r_mix.v\n", "print(f'v-grid: {v[0]:+.2f} … {v[-1]:+.2f} m/s, N={len(v)}')\n" ] }, { "cell_type": "markdown", "id": "6a53181f", "metadata": {}, "source": [ "## Spectral reflectivity $sZ_h(v)$\n", "\n", "Each species occupies its own Doppler-velocity window. SLW sits at\n", "$v \\approx 0$, rain peaks near 3–5 m/s (with its large-drop tail\n", "extending a bit further), and hail's spectral peak is near $v \\approx\n", "5$ m/s — its exponential PSD front-loads the small-diameter (slow)\n", "end, so most hail mass moves at modest velocities, with the\n", "large-hail tail extending out to $v \\approx 7$ m/s. Hail *dominates*\n", "the spectrum past $v \\approx 7$ m/s simply because rain has run out of\n", "drops by then ($D_\\mathrm{max}^\\mathrm{rain} = 5$ mm). The mixture\n", "spectrum is the incoherent sum — the loudest species wins each bin.\n", "\n", "**Compared with Lakshmi et al. (2024).** Their Fig. 8 (the 14 Dec\n", "2018 convective case, altitudes 1.5–2.5 km below the melting layer)\n", "shows broad, sometimes bimodal $sZ_h$ spectra in the 22–30 dB range\n", "whenever rain and partially melted hail share the volume. Their\n", "Fig. 2 reports bulk $Z_h \\ge 35$–40 dBZ in the rain layer below the\n", "melting band. Our synthetic bulk $Z_h$ in the mix is $\\sim$63 dBZ\n", "(very heavy convection, brighter than either of their case studies)\n", "but the *shape* of the spectrum — rain peak near 3–5 m/s, broad\n", "continuation into a hail-dominated fast tail — reproduces the\n", "rain+hail bimodality they report at 5 km altitude in their 240°\n", "RHI scan (paper text, p. 242).\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "89822c3b", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:02.470000Z", "iopub.status.busy": "2026-04-21T19:42:02.469883Z", "iopub.status.idle": "2026-04-21T19:42:02.668061Z", "shell.execute_reply": "2026-04-21T19:42:02.667498Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def dB(x):\n", " return 10 * np.log10(np.maximum(x, 1e-12))\n", "\n", "fig, ax = plt.subplots(figsize=(8, 4))\n", "ax.plot(v, dB(r_slw.sZ_h), color='tab:blue', lw=1.2, label='SLW')\n", "ax.plot(v, dB(r_rain.sZ_h), color='tab:green', lw=1.2, label='rain')\n", "ax.plot(v, dB(r_hail.sZ_h), color='tab:red', lw=1.2, label='hail')\n", "ax.plot(v, dB(r_mix.sZ_h), color='black', lw=1.8,\n", " label='mixture', linestyle='--')\n", "ax.plot(v, dB(r_mix_half.sZ_h), color='dimgray', lw=1.8,\n", " label='mixture (½ hail)', linestyle=':')\n", "ax.set_xlabel('Doppler velocity [m/s]')\n", "ax.set_ylabel(r'$sZ_h$ [dBZ / (m s$^{-1}$)]')\n", "ax.set_title(r'Spectral reflectivity at C-band, $\\phi$ = 30°, 500 hPa')\n", "ax.set_xlim(V_MIN, V_MAX)\n", "ax.set_ylim(-40, 80)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(loc='upper right')\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "91fb042c", "metadata": {}, "source": [ "## Spectral differential reflectivity $sZ_\\mathrm{dr}(v)$\n", "\n", "Rain's $sZ_\\mathrm{dr}$ climbs from 0 dB at the small-drop end to\n", "$\\sim$+2.5 dB at the fast end — a clean size-sorting signal, since\n", "larger drops fall faster and are more oblate.\n", "\n", "Wet hail shows the hallmark **C-band Mie resonance notch**: slightly\n", "positive at small $v$ (small D, Rayleigh), then diving to ≈ −1 dB as\n", "the $D \\sim 8$–10 mm wet-hail population hits the C-band resonance\n", "(the water coating pushes the resonance to smaller $D$ than dry hail;\n", "see Kumjian, Ryzhkov et al. for the phenomenology).\n", "\n", "The **mixture** curve is the interesting one. Around $v \\approx 5$ m/s\n", "rain's positive $sZ_\\mathrm{dr}$ (≈ +1 dB) and hail's negative swing\n", "(≈ −0.4 dB) carry comparable power, and the mixture $sZ_\\mathrm{dr}$\n", "collapses toward zero — a velocity bin where neither species wins.\n", "\n", "**Compared with Lakshmi et al. (2024).** Their Fig. 8 shows\n", "$sZ_\\mathrm{dr}$ climbing monotonically with radial velocity in the\n", "liquid-phase rain layer — slopes of +0.455 and +0.57 dB (m s⁻¹)⁻¹ at\n", "2.5- and 2-km altitudes, interpreted explicitly as shear-induced\n", "size sorting where larger/more-oblate drops sit at higher $v$ (paper\n", "pp. 242–243). Our rain-alone curve rises from $\\sim$0 to +2.5 dB\n", "across a $\\sim$12 m/s window — the same qualitative signature,\n", "offset by our 30° elevation and without the paper's strong shear\n", "advecting small drops. Lakshmi et al. also report $Z_\\mathrm{dr}$\n", "values of 6–8 dB in the convective core at 2 km, attributed\n", "explicitly to *partially melted hail* depolarising horizontally —\n", "that is the regime our wet-hail EMA is modelling, although our\n", "narrower wet-hail PSD produces a spectral *notch* rather than a\n", "broad +6 dB plateau.\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "ba6fcbde", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:02.669416Z", "iopub.status.busy": "2026-04-21T19:42:02.669317Z", "iopub.status.idle": "2026-04-21T19:42:02.737073Z", "shell.execute_reply": "2026-04-21T19:42:02.736610Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 4))\n", "ax.plot(v, dB(r_slw.sZ_dr), color='tab:blue', lw=1.2, label='SLW')\n", "ax.plot(v, dB(r_rain.sZ_dr), color='tab:green', lw=1.2, label='rain')\n", "ax.plot(v, dB(r_hail.sZ_dr), color='tab:red', lw=1.2, label='hail')\n", "ax.plot(v, dB(r_mix.sZ_dr), color='black', lw=1.8,\n", " label='mixture', linestyle='--')\n", "ax.plot(v, dB(r_mix_half.sZ_dr), color='dimgray', lw=1.8,\n", " label='mixture (½ hail)', linestyle=':')\n", "ax.set_xlabel('Doppler velocity [m/s]')\n", "ax.set_ylabel(r'$sZ_\\mathrm{dr}$ [dB]')\n", "ax.set_title(r'Spectral differential reflectivity')\n", "ax.set_xlim(V_MIN, V_MAX)\n", "ax.set_ylim(-10, 4)\n", "ax.axhline(0.0, color='gray', lw=0.6)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(loc='lower left')\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "ecf53375", "metadata": {}, "source": [ "## Spectral specific differential phase $sK_\\mathrm{dp}(v)$\n", "\n", "The spectral proxy for $\\phi_\\mathrm{dp}$ is $sK_\\mathrm{dp}$: the\n", "forward-scatter differential phase contributed by particles in each\n", "velocity bin. In this mixture it is **rain-dominated**. The bulk\n", "$K_\\mathrm{dp}$ was $\\sim$17 °/km for rain versus $\\sim$1.5 °/km for\n", "wet hail — Thurai-shaped, gravity-aligned raindrops are nearly ideal\n", "oblate forward-scatterers, while wet hail's broad canting\n", "distribution (σ = 40°) smears its differential phase toward zero.\n", "\n", "The rain peak in $sK_\\mathrm{dp}(v)$ lands at $v \\approx 5$ m/s —\n", "that is where the large oblate raindrops ($D \\sim 3$–5 mm, the ones\n", "that carry almost all the differential phase shift) sit in Doppler\n", "space. Hail contributes only a small bump at similar velocities and\n", "is essentially invisible against rain in the mixture curve. Halving\n", "hail's concentration (gray dotted) barely moves $sK_\\mathrm{dp}$ at\n", "all.\n", "\n", "**Compared with Lakshmi et al. (2024).** The paper does not show\n", "$sK_\\mathrm{dp}$ spectra directly — their spectral analysis is\n", "restricted to $sZ_h$, $sZ_\\mathrm{dr}$, and $s\\rho_\\mathrm{hv}$\n", "(Eqs. 3–5, p. 240). The physics our curves illustrate — differential\n", "phase is *rain-dominated* whenever rain coexists with tumbling\n", "ice-phase scatterers — is why Lakshmi et al. rely on\n", "$sZ_\\mathrm{dr}$ and $s\\rho_\\mathrm{hv}$ rather than $K_\\mathrm{dp}$\n", "to fingerprint the ice fraction of a mixed-phase volume.\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "9fe957a3", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:02.738378Z", "iopub.status.busy": "2026-04-21T19:42:02.738276Z", "iopub.status.idle": "2026-04-21T19:42:02.812142Z", "shell.execute_reply": "2026-04-21T19:42:02.811491Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 4))\n", "ax.plot(v, r_slw.sKdp, color='tab:blue', lw=1.2, label='SLW')\n", "ax.plot(v, r_rain.sKdp, color='tab:green', lw=1.2, label='rain')\n", "ax.plot(v, r_hail.sKdp, color='tab:red', lw=1.2, label='hail')\n", "ax.plot(v, r_mix.sKdp, color='black', lw=1.8,\n", " label='mixture', linestyle='--')\n", "ax.plot(v, r_mix_half.sKdp, color='dimgray', lw=1.8,\n", " label='mixture (½ hail)', linestyle=':')\n", "ax.set_xlabel('Doppler velocity [m/s]')\n", "ax.set_ylabel(r'$sK_\\mathrm{dp}$ [° / km / (m s$^{-1}$)]')\n", "ax.set_title(r'Spectral specific differential phase')\n", "ax.set_xlim(V_MIN, V_MAX)\n", "ax.axhline(0.0, color='gray', lw=0.6)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(loc='upper right')\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "60d5f093", "metadata": {}, "source": [ "## Spectral copolar correlation coefficient $s\\rho_\\mathrm{hv}(v)$\n", "\n", "Per-species $s\\rho_\\mathrm{hv}$ is close to 1 wherever the species has\n", "a single, narrowly distributed polarimetric response. Wet hail drops\n", "to ≈ 0.81 at its fast-velocity end — the Mie-resonant mix of\n", "water-coated oblate hailstones spans enough backscatter-phase spread\n", "that the H–V correlation falls sharply.\n", "\n", "The **mixture** curve tracks hail wherever hail dominates. Where rain\n", "contributes comparable power (v ≈ 3–5 m/s), the mixture\n", "$s\\rho_\\mathrm{hv}$ sits *between* rain (≈ 1) and hail (≈ 0.89) —\n", "rain is effectively diluting hail's phase spread with its own\n", "well-correlated H–V returns. Dropping the mixture curve *below* both\n", "components would require rain and hail to have opposite-signed\n", "$\\delta_\\mathrm{hv}$ at the same velocity, which does not quite\n", "happen here; the melting-layer classical $\\rho_\\mathrm{hv}$ dip\n", "(0.85–0.9) needs that extra ingredient.\n", "\n", "Halving the hail concentration (gray dotted curve) drags the\n", "mixture $s\\rho_\\mathrm{hv}$ *closer to unity* in the overlap region\n", "— with less hail phase spread contaminating the volume, the\n", "well-correlated rain returns dominate.\n", "\n", "**Compared with Lakshmi et al. (2024).** The paper reports\n", "$s\\rho_\\mathrm{hv}$ dropping to $\\sim$0.84–0.99 near the melting\n", "layer in the 30 Nov 2018 stratiform case (Fig. 13, altitudes 3–5 km\n", "at 33 km range), with the lowest values coinciding with the\n", "rain+hail mixture class in their DROPS2 hydrometeor classification\n", "(Fig. 11). Our wet-hail-alone curve bottoms at $\\sim$0.81 at the\n", "resonance tail and the mixture curve is pulled to $\\sim$0.92 in the\n", "rain-hail overlap region — a quantitative match to the mid- and\n", "low-$s\\rho_\\mathrm{hv}$ signatures Lakshmi et al. use to flag\n", "mixed-phase volumes. More broadly, their Fig. 2 shows bulk\n", "$\\rho_\\mathrm{hv} \\approx 1$ in pure rain below the melting layer\n", "and a sharp drop crossing it — exactly the rain-to-mixture drop our\n", "spectrum traces as $v$ climbs from rain-dominated (≈ 1) into the\n", "hail-resonance tail (≈ 0.82).\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "61c11c30", "metadata": { "execution": { "iopub.execute_input": "2026-04-21T19:42:02.813639Z", "iopub.status.busy": "2026-04-21T19:42:02.813536Z", "iopub.status.idle": "2026-04-21T19:42:02.882283Z", "shell.execute_reply": "2026-04-21T19:42:02.881633Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 4))\n", "ax.plot(v, r_slw.srho_hv, color='tab:blue', lw=1.2, label='SLW')\n", "ax.plot(v, r_rain.srho_hv, color='tab:green', lw=1.2, label='rain')\n", "ax.plot(v, r_hail.srho_hv, color='tab:red', lw=1.2, label='hail')\n", "ax.plot(v, r_mix.srho_hv, color='black', lw=1.8,\n", " label='mixture', linestyle='--')\n", "ax.plot(v, r_mix_half.srho_hv, color='dimgray', lw=1.8,\n", " label='mixture (½ hail)', linestyle=':')\n", "ax.set_xlabel('Doppler velocity [m/s]')\n", "ax.set_ylabel(r'$s\\rho_\\mathrm{hv}$')\n", "ax.set_title(r'Spectral copolar correlation coefficient')\n", "ax.set_xlim(V_MIN, V_MAX)\n", "ax.set_ylim(0.4, 1.01)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(loc='lower left')\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "9fcf4528", "metadata": {}, "source": [ "## Takeaways\n", "\n", "* **Fall-speed separation is the whole game.** At $\\phi = 30°$, SLW,\n", " rain, and hail occupy disjoint velocity windows and spectral\n", " polarimetry reads each species out directly — something bulk $Z_h$\n", " + $Z_\\mathrm{dr}$ cannot do for this mixture. Lakshmi et al. (2024)\n", " use exactly this separation throughout their paper: ice crystals,\n", " aggregates, graupel, and rain+hail mixtures each stake out different\n", " Doppler windows in their RHI-scan spectra (their Figs. 7, 8, 13, 15,\n", " 19, 20).\n", "* **Rain $sZ_\\mathrm{dr}$ rises monotonically with $v$** because fast\n", " drops are big and oblate — the classic size-sorting diagnostic of\n", " Kumjian & Ryzhkov (2012) and Wang et al. (2019).\n", "* **Wet hail's C-band resonance notch** in $sZ_\\mathrm{dr}$ and\n", " $s\\rho_\\mathrm{hv}$ at the fast-velocity end is the fingerprint of\n", " melting $D \\sim$ 8–10 mm hailstones — exactly the rain+hail\n", " signature Lakshmi et al. (2024) flag in their Fig. 5 case-study\n", " region below the melting layer.\n", "* **Mixture $sZ_\\mathrm{dr}$ collapses toward zero** at $v \\approx$\n", " 5 m/s, where rain's positive $Z_\\mathrm{dr}$ and hail's\n", " resonance-driven negative $Z_\\mathrm{dr}$ carry comparable power —\n", " a direct mixed-species signature.\n", "* **Per-species vs mixture plots** are the practical interpretive\n", " tool: anywhere the mixture curve diverges from the dominant\n", " single-species curve, two (or more) populations are contributing\n", " coherently to that velocity bin.\n", "* **Halving the hail concentration (gray dotted curve)** re-weights\n", " the species contributions in a physically intuitive way. $sZ_h$\n", " drops by $\\approx$3 dB at hail-dominated velocities but is barely\n", " touched where rain or SLW dominate. $sK_\\mathrm{dp}$ hardly moves\n", " at all, because rain — not hail — carries almost all of the\n", " forward-scatter differential phase in this mixture.\n", " $sZ_\\mathrm{dr}$ and $s\\rho_\\mathrm{hv}$ shift *toward* rain\n", " wherever rain and hail carry comparable power — with less hail\n", " power around $\\approx$ 5 m/s the mixture $sZ_\\mathrm{dr}$ climbs\n", " back toward rain's positive values and $s\\rho_\\mathrm{hv}$ rises\n", " toward unity. This is exactly the lever Lakshmi et al. (2024)\n", " exploit when they use spectral polarimetry to infer the\n", " *proportion* of ice-phase scatterers within a resolution volume.\n" ] }, { "cell_type": "markdown", "id": "0dd033df", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.15" } }, "nbformat": 4, "nbformat_minor": 5 }