Source code for radarx.fundamentals.geometry
"""
Radar Geometry Calculations
============================
Functions related to beam propagation, height, and sampling volume estimation.
.. autosummary::
:nosignatures:
:toctree: generated/
effective_radius
beam_center_height
sample_volume_gaussian
half_power_radius
References
----------
- Rinehart, R. E. (1997). Radar for Meteorologists.
- Bech et al. (2003). JAOT, Beam Blockage Corrections.
"""
import numpy as np
from .constants import EARTH_RADIUS, EFFECTIVE_RADIUS_4_3
[docs]
def effective_radius(dndh=-39e-6):
"""
Compute effective Earth radius considering atmospheric refraction.
Parameters
----------
dndh : float
Vertical gradient of refractivity [N-units/km], default: -39e-6
Returns
-------
float
Effective radius of Earth [m]
"""
return (1.0 / ((1 / (EARTH_RADIUS / 1000.0)) + dndh)) * 1000.0
[docs]
def beam_center_height(
range_m, elevation_deg, radar_height=0.0, reff=EFFECTIVE_RADIUS_4_3
):
"""
Calculate height of beam center above sea level.
Parameters
----------
range_m : float or array-like
Slant range from radar [m]
elevation_deg : float
Elevation angle [degrees]
radar_height : float
Radar site altitude [m]
reff : float
Effective Earth radius [m]
Returns
-------
float or array-like
Beam center height [m]
"""
elev_rad = np.deg2rad(elevation_deg)
term = np.sqrt(range_m**2 + reff**2 + 2 * range_m * reff * np.sin(elev_rad))
return term - reff + radar_height
[docs]
def sample_volume_gaussian(range_m, beamwidth_h_deg, beamwidth_v_deg, pulse_length_m):
"""
Compute radar sample volume assuming Gaussian beam shape.
Parameters
----------
range_m : float or array-like
Distance to sample volume [m]
beamwidth_h_deg : float
Horizontal beamwidth [degrees]
beamwidth_v_deg : float
Vertical beamwidth [degrees]
pulse_length_m : float
Pulse length [m]
Returns
-------
float or array-like
Sample volume [m³]
"""
bwh_rad = np.deg2rad(beamwidth_h_deg)
bwv_rad = np.deg2rad(beamwidth_v_deg)
numerator = np.pi * range_m**2 * bwh_rad * bwv_rad * pulse_length_m
return numerator / (16.0 * np.log(2.0))
[docs]
def half_power_radius(range_m, beamwidth_half_deg):
"""
Compute half-power beam radius.
Parameters
----------
range_m : float or array-like
Range from radar [m]
beamwidth_half_deg : float
Half-power beamwidth [degrees]
Returns
-------
float or array-like
Half-power radius [m]
"""
return (range_m * np.deg2rad(beamwidth_half_deg)) / 2.0
__all__ = [
"beam_center_height",
"effective_radius",
"half_power_radius",
"sample_volume_gaussian",
]
