def inverse_rain_attenuation(self,
lat,
lon,
d,
f,
el,
Ap,
tau=45,
R001=None):
""" Implementation of 'inverse_rain_attenuation' method for
recommendation ITU-P R.530-16. See documentation for function
'ITUR530.inverse_rain_attenuation'
"""
# Step 1: Obtain the rain rate R0.01 exceeded for 0.01% of the time
# (with an integration time of 1 min).
if R001 is None:
R001 = rainfall_rate(lat, lon, 0.01).value
# Step 2: Compute the specific attenuation, gammar (dB/km) for the
# frequency, polarization and rain rate of interest using
# Recommendation ITU-R P.838
gammar = rain_specific_attenuation(R001, f, el, tau).value
_, alpha = rain_specific_attenuation_coefficients(f, el, tau).value
# Step 3: Compute the effective path length, deff, of the link by
# multiplying the actual path length d by a distance factor r
r = 1 / (0.477 * d**0.633 * R001**(0.073 * alpha) * f**(0.123) -
10.579 * (1 - np.exp(-0.024 * d)))
deff = np.minimum(r, 2.5) * d
# Step 4: An estimate of the path attenuation exceeded for 0.01% of
# the time is given by:
A001 = gammar * deff
# Step 5: The attenuation exceeded for other percentages of time p in
# the range 0.001% to 1% may be deduced from the following power law
C0 = np.where(f >= 10, 0.12 * 0.4 * (np.log10(f / 10)**0.8), 0.12)
C1 = (0.07**C0) * (0.12**(1 - C0))
C2 = 0.855 * C0 + 0.546 * (1 - C0)
C3 = 0.139 * C0 + 0.043 * (1 - C0)
def func_bisect(p):
return A001 * C1 * p**(-(C2 + C3 * np.log10(p))) - Ap
return bisect(func_bisect, 0, 100)
def rain_attenuation(self,
lat,
lon,
f,
el,
hs=None,
p=0.01,
R001=None,
tau=45,
Ls=None):
if p < 0.001 or p > 5:
warnings.warn(
RuntimeWarning('The method to compute the rain attenuation in '
'recommendation ITU-P 618-12 is only valid for '
'unavailability values between 0.001 and 5'))
Re = 8500 # Efective radius of the Earth (8500 km)
if hs is None:
hs = topographic_altitude(lat, lon).to(u.km).value
# Step 1: Compute the rain height (hr) based on ITU - R P.839
hr = rain_height(lat, lon).value
# Step 2: Compute the slant path length
if Ls is None:
Ls = np.where(
el >= 5,
(hr - hs) / (np.sin(np.deg2rad(el))), # Eq. 1
2 * (hr - hs) / (((np.sin(np.deg2rad(el)))**2 + 2 *
(hr - hs) / Re)**0.5 +
(np.sin(np.deg2rad(el))))) # Eq. 2
# Step 3: Calculate the horizontal projection, LG, of the
# slant-path length
Lg = np.abs(Ls * np.cos(np.deg2rad(el)))
# Obtain the raingall rate, exceeded for 0.01% of an average year,
# if not provided, as described in ITU-R P.837.
if R001 is None:
R001 = rainfall_rate(lat, lon, 0.01).to(u.mm / u.hr).value
# Step 5: Obtain the specific attenuation gammar using the frequency
# dependent coefficients as given in ITU-R P.838
gammar = rain_specific_attenuation(R001, f, el,
tau).to(u.dB / u.km).value
# Step 6: Calculate the horizontal reduction factor, r0.01,
# for 0.01% of the time:
r001 = 1. / (1 + 0.78 * np.sqrt(Lg * gammar / f) - 0.38 *
(1 - np.exp(-2 * Lg)))
# Step 7: Calculate the vertical adjustment factor, v0.01,
# for 0.01% of the time:
eta = np.rad2deg(np.arctan2(hr - hs, Lg * r001))
Lr = np.where(eta > el, Lg * r001 / np.cos(np.deg2rad(el)),
(hr - hs) / np.sin(np.deg2rad(el)))
xi = np.where(np.abs(lat) < 36, 36 - np.abs(lat), 0)
v001 = 1. / (
1 + np.sqrt(np.sin(np.deg2rad(el))) *
(31 *
(1 - np.exp(-(el /
(1 + xi)))) * np.sqrt(Lr * gammar) / f**2 - 0.45))
# Step 8: calculate the effective path length:
Le = Lr * v001 # (km)
# Step 9: The predicted attenuation exceeded for 0.01% of an average
# year
A001 = gammar * Le # (dB)
# Step 10: The estimated attenuation to be exceeded for other
# percentages of an average year
if p >= 1:
beta = np.zeros_like(A001)
else:
beta = np.where(
np.abs(lat) > 36, np.zeros_like(A001),
np.where((np.abs(lat) < 36) & (el > 25),
-0.005 * (np.abs(lat) - 36),
-0.005 * (np.abs(lat) - 36) + 1.8 -
4.25 * np.sin(np.deg2rad(el))))
A = A001 * (p / 0.01)**(
-(0.655 + 0.033 * np.log(p) - 0.045 * np.log(A001) - beta *
(1 - p) * np.sin(np.deg2rad(el))))
return A