# -*- coding: utf-8 -*-
"""
pyradarmet.variables
====================
Functions to calculate radar-derived variables.
References
----------
Rinehart (1997), Radar for Meteorologists.
Aydin et al. (1986; JCAM), Remote Sensing of Hail with Dual Linear
Polarization Radar
"""
import numpy as np
def reflectivity(power_t, gain, pulse_width, wavelength, bw_h, bw_v,
aloss, rloss, power_return, r, dielectric=0.93):
"""
Radar reflectivity [mm^6/m^3].
From Rinehart (1993), Eqn 5.17 (See Eqn 5.14-5.16 also)
Parameters
----------
power_t : float
Transmitted power [W]
gain : float
Antenna Gain [dB]
pulse_width : float
Pulse Width [s]
wavelength : float
Radar wavelength [m]
bwidth : float
Antenna beamwidth [degrees]
aloss : float
Antenna/waveguide/coupler loss [dB]
rloss : float
Receiver loss [dB]
dielectric : float
Dielectric factor [unitless]
power_return : float
Returned power [W]
r : float or array
Range to target [m]
Notes
-----
This routine calls the radar_constant function.
The default is for a dielectric factor value for water. This can be
changed by the user, e.g. K=0.208 for particle sizes of equivalent melted
diameters or K=0.176 for particle sizes of equivalent ice spheres.
"""
# Call the radar constant function
C1 = radar_constant(power_t, gain, pulse_width, wavelength, bw_h, bw_v, aloss, rloss)
return power_return * np.asarray(r)**2 / (C1 * dielectric**2)
def radial_velocity(frequency, wavelength):
"""
Radial velocity [m/s].
From Rinehart (1997), Eqn 6.6
Parameters
----------
frequency : float or array
Frequency shift [Hz]
wavelength : float or array
Radar wavelength [m]
Notes
-----
If arrays are used, either for one okay, or both must be the same length.
"""
return np.asarray(frequency) * np.asarray(wavelength) / 2.
def cdr(refl_parallel, refl_orthogonal):
"""
Circular depolarization ratio [dB].
From Rinehart (1997), Eqn 10.2
Parameters
----------
refl_parallel : float or array
Reflectivity in the parallel channel [mm^6/m^3]
refl_orthogonal : float or array
Reflectivity in the orthogonal channel [mm^6/m^3]
Notes
-----
Ensure that both powers have the same units!
Radars that transmit right-hand circular polarization and receive and
receive both left- and right-hand circular polarization (using two
antennas) and acquiring the same pulse.
The parallel (orthogonal) component refers to the same
(opposite) polarization as transmitted. Non-spericity of hydrometeors
may be detected (inf long, thin scatterers have CDR = 0 dB, while perfect
spheres have CDR = -infinity
Can also use power measurements instead of reflectivity.
If arrays are used, either for one okay, or both must be the same length.
"""
return 10. * np.log10(np.asarray(refl_parallel)/np.asarray(refl_orthogonal))
def ldr(z_h, z_v):
"""
Linear depolarization ratio [dB].
From Rinehart (1997), Eqn 10.3
Parameters
----------
z_h : float or array
Horizontal reflectivity [mm^6/m^3]
z_v : float or array
Vertical reflectivity [mm^6/m^3]
Notes
-----
Ensure that both powers have the same units!
Uses both polarizations in a dual-pol radar from a single pulse.
Perfect spheres yield LDR => -infinity (though antenna limitations limit
LDR values to -40 dB for small spheres.
Long, thin targets, LDR => 0
Typical values in the range -15 > LDR > -35 dB
If arrays are used, either for one okay, or both must be the same length.
"""
return 10. * np.log10(np.asarray(z_h) / np.asarray(z_v))
def zdr(z_h, z_v):
"""
Differential reflectivity [dB].
From Rinehart (1997), Eqn 10.3 and Seliga and Bringi (1976)
Parameters
----------
z_h : float or array
Horizontal reflectivity [mm^6/m^3]
z_v : float or array
Vertical reflectivity [mm^6/m^3]
Notes
-----
Ensure that both powers have the same units!
Alternating horizontally and linearly polarized pulses are averaged.
Notes
-----
If arrays are used, either for one okay, or both must be the same length.
"""
return 10. * np.log10(np.asarray(z_h) / np.asarray(z_v))
def zdp(z_h, z_v):
"""
Reflectivity difference [dB].
From Rinehart (1997), Eqn 10.3
Parameters
----------
z_h : float
Horizontal reflectivity [mm^6/m^3]
z_v : float
Horizontal reflectivity [mm^6/m^3]
Notes
-----
Ensure that both powers have the same units!
Alternating horizontally and linearly polarized pulses are averaged.
"""
zh = np.atleast_1d(z_h)
zv = np.atleast_1d(z_v)
if len(zh) != len(zv):
raise ValueError('Input variables must be same length')
return
zdp = np.full_like(zh, np.nan)
good = np.where(zh > zv)
zdp[good] = 10.* np.log10(zh[good] - zv[good])
return zdp
def hdr(dbz_h, zdr):
"""
Differential reflectivity [dB] hail signature.
From Aydin et al. (1986), Eqns 4-5
Parameters
----------
dbz_h : float or array
Horizontal reflectivity [dBZ]
zdr : float or array
Differential reflectivity [dBZ]
Notes
-----
Ensure that both powers have the same units!
Positive HDR and strong gradients at edges signify ice. The larger HDR,
the greater likelihood that ice is present.
Considerations for this equation (see paper for more details):
1) Standar error of disdrometer data allowed for
2) Drop oscillation accounted for based on 50% model of Seliga et al (1984)
3) Lower (27) bound chose to provide constant Zh ref level
4) Upper cutoff of 60 (may be too low)
Picca and Ryzhkof (2012) mention that this does not take into account
the hail melting process. So use at your own risk!
"""
zdr = np.atleast_1d(zdr)
# Set the f(zdr) based upon observations
f = np.full_like(zdr, np.nan)
negind = np.where(zdr <= 0)
lowind = np.where((zdr > 0) & (zdr <= 1.74))
highind = np.where(zdr > 1.74)
f[negind] = 27.
f[lowind] = 19. * zdr[lowind] + 27.
f[highind] = 60.
# Calculate HDR
return np.asarray(dbz_h) - f
