Source code for wradlib.georef.misc
#!/usr/bin/env python
# -*- coding: UTF-8 -*-
# Copyright (c) 2011-2020, wradlib developers.
# Distributed under the MIT License. See LICENSE.txt for more info.
"""
Miscellaneous
^^^^^^^^^^^^^
.. autosummary::
:nosignatures:
:toctree: generated/
{}
"""
__all__ = ["bin_altitude", "bin_distance", "site_distance"]
__doc__ = __doc__.format("\n ".join(__all__))
import numpy as np
[docs]def bin_altitude(r, theta, sitealt, re, ke=4.0 / 3.0):
"""Calculates the height of a radar bin taking the refractivity of the \
atmosphere into account.
Based on :cite:`Doviak1993` the bin altitude is calculated as
.. math::
h = \\sqrt{r^2 + (k_e r_e)^2 + 2 r k_e r_e \\sin\\theta} - k_e r_e
Parameters
----------
r : :class:`numpy:numpy.ndarray`
Array of ranges [m]
theta : scalar or :class:`numpy:numpy.ndarray`
Array broadcastable to the shape of r elevation angles in degrees with 0°
at horizontal and +90° pointing vertically upwards from the radar
sitealt : float
Altitude in [m] a.s.l. of the referencing radar site
re : float
earth's radius [m]
ke : float
adjustment factor to account for the refractivity gradient that
affects radar beam propagation. In principle this is wavelength-
dependend. The default of 4/3 is a good approximation for most
weather radar wavelengths
Returns
-------
altitude : :class:`numpy:numpy.ndarray`
Array of heights of the radar bins in [m]
"""
reff = ke * re
sr = reff + sitealt
return np.sqrt(r**2 + sr**2 + 2 * r * sr * np.sin(np.radians(theta))) - reff
[docs]def bin_distance(r, theta, sitealt, re, ke=4.0 / 3.0):
"""Calculates great circle distance from radar site to radar bin over \
spherical earth, taking the refractivity of the atmosphere into account.
.. math::
s = k_e r_e \\arctan\\left(
\\frac{r \\cos\\theta}{r \\cos\\theta + k_e r_e + h}\\right)
where :math:`h` would be the radar site altitude amsl.
Parameters
----------
r : :class:`numpy:numpy.ndarray`
Array of ranges [m]
theta : scalar or :class:`numpy:numpy.ndarray`
Array broadcastable to the shape of r elevation angles in degrees with 0°
at horizontal and +90° pointing vertically upwards from the radar
sitealt : float
site altitude [m] amsl.
re : float
earth's radius [m]
ke : float
adjustment factor to account for the refractivity gradient that
affects radar beam propagation. In principle this is wavelength-
dependent. The default of 4/3 is a good approximation for most
weather radar wavelengths
Returns
-------
distance : :class:`numpy:numpy.ndarray`
Array of great circle arc distances [m]
"""
reff = ke * re
sr = reff + sitealt
theta = np.radians(theta)
return reff * np.arctan(r * np.cos(theta) / (r * np.sin(theta) + sr))
[docs]def site_distance(r, theta, binalt, re=None, ke=4.0 / 3.0):
"""Calculates great circle distance from bin at certain altitude to the \
radar site over spherical earth, taking the refractivity of the \
atmosphere into account.
Based on :cite:`Doviak1993` the site distance may be calculated as
.. math::
s = k_e r_e \\arcsin\\left(
\\frac{r \\cos\\theta}{k_e r_e + h_n(r, \\theta, r_e, k_e)}\\right)
where :math:`h_n` would be provided by
:func:`~wradlib.georef.misc.bin_altitude`.
Parameters
----------
r : :class:`numpy:numpy.ndarray`
Array of ranges [m]
theta : scalar or :class:`numpy:numpy.ndarray`
Array broadcastable to the shape of r elevation angles in degrees with 0°
at horizontal and +90° pointing vertically upwards from the radar
binalt : :class:`numpy:numpy.ndarray`
site altitude [m] amsl. same shape as r.
re : float
earth's radius [m]
ke : float
adjustment factor to account for the refractivity gradient that
affects radar beam propagation. In principle this is wavelength-
dependent. The default of 4/3 is a good approximation for most
weather radar wavelengths
Returns
-------
distance : :class:`numpy:numpy.ndarray`
Array of great circle arc distances [m]
"""
reff = ke * re
return reff * np.arcsin(r * np.cos(np.radians(theta)) / (reff + binalt))
