Source code for rustmatrix.tmatrix_aux
"""Auxiliary constants and drop-shape relationships.
Direct port of ``pytmatrix.tmatrix_aux``. Wavelength presets (radar
bands), typical ``K_w^2`` factors, canned geometries for backscatter /
forward-scatter, and the Thurai/Pruppacher-Beard/Beard-Chuang drop
axis-ratio formulas.
"""
from __future__ import annotations
VERSION = "0.1.0"
# Typical radar wavelengths [mm] at different bands.
wl_S = 111.0
wl_C = 53.5
wl_X = 33.3
wl_Ku = 22.0
wl_Ka = 8.43
wl_W = 3.19
# Typical water dielectric factors |K_w|^2 at the above bands.
K_w_sqr = {
wl_S: 0.93,
wl_C: 0.93,
wl_X: 0.93,
wl_Ku: 0.93,
wl_Ka: 0.92,
wl_W: 0.75,
}
# Preset (thet0, thet, phi0, phi, alpha, beta) geometries.
geom_horiz_back = (90.0, 90.0, 0.0, 180.0, 0.0, 0.0)
geom_horiz_forw = (90.0, 90.0, 0.0, 0.0, 0.0, 0.0)
geom_vert_back = (0.0, 180.0, 0.0, 0.0, 0.0, 0.0)
geom_vert_forw = (180.0, 180.0, 0.0, 0.0, 0.0, 0.0)
# ---------- Drop shape relationships ----------
# All return vertical/horizontal axis ratio; pass 1/dsr(...) to Scatterer
# since Scatterer expects horizontal/vertical.
[docs]
def dsr_thurai_2007(D_eq: float) -> float:
"""Thurai et al. (2007) equilibrium raindrop axis ratio (v/h).
Parameters
----------
D_eq : float
Equivalent (volume) diameter in mm.
Returns
-------
float
Vertical / horizontal axis ratio (≤ 1 for flattened drops).
Scatterer expects horizontal / vertical, so pass
``1.0 / dsr_thurai_2007(D)`` as ``axis_ratio``.
References
----------
Thurai, M. et al. (2007). Drop shapes, model comparisons, and
calculations of polarimetric radar parameters in rain. *J. Atmos.
Oceanic Technol.*, 24, 1019–1032.
"""
if D_eq < 0.7:
return 1.0
if D_eq < 1.5:
return (
1.173 - 0.5165 * D_eq + 0.4698 * D_eq ** 2
- 0.1317 * D_eq ** 3 - 8.5e-3 * D_eq ** 4
)
return (
1.065 - 6.25e-2 * D_eq - 3.99e-3 * D_eq ** 2
+ 7.66e-4 * D_eq ** 3 - 4.095e-5 * D_eq ** 4
)
[docs]
def dsr_pb(D_eq: float) -> float:
"""Pruppacher & Beard linear drop-shape relation (v/h).
Parameters
----------
D_eq : float
Equivalent diameter in mm.
Returns
-------
float
``1.03 - 0.062 D``. Use ``1 / dsr_pb(D)`` as ``Scatterer.axis_ratio``.
"""
return 1.03 - 0.062 * D_eq
[docs]
def dsr_bc(D_eq: float) -> float:
"""Beard & Chuang drop-shape relation (v/h).
Parameters
----------
D_eq : float
Equivalent diameter in mm.
Returns
-------
float
Fourth-order polynomial fit to the Beard & Chuang (1987)
equilibrium shapes. Use ``1 / dsr_bc(D)`` as
``Scatterer.axis_ratio``.
"""
return (
1.0048 + 5.7e-04 * D_eq - 2.628e-02 * D_eq ** 2
+ 3.682e-03 * D_eq ** 3 - 1.677e-04 * D_eq ** 4
)
