def rain_attenuation_probability(self,
lat,
lon,
el,
hs=None,
Ls=None,
P0=None):
Re = 8500
if hs is None:
hs = topographic_altitude(lat, lon).to(u.km).value
# Step 1: Estimate the probability of rain, at the earth station either
# from Recommendation ITU-R P.837 or from local measured rainfall
# rate data
if P0 is None:
P0 = rainfall_probability(lat, lon).\
to(u.dimensionless_unscaled).value
# Step 2: Calculate the parameter alpha using the inverse of the
# Q-function alpha = Q^{-1}(P0) -> Q(alpha) = P0
alpha = stats.norm.ppf(1 - P0)
# Step 3: Calculate the spatial correlation function, rho:
hr = rain_height(lat, lon).value
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
d = Ls * np.cos(np.deg2rad(el))
rho = 0.59 * np.exp(-abs(d) / 31) + 0.41 * np.exp(-abs(d) / 800)
# Step 4: Calculate the complementary bivariate normal distribution
biva_fcn = np.vectorize(__CDF_bivariate_normal__)
c_B = biva_fcn(alpha, alpha, rho)
# Step 5: Calculate the probability of rain attenuation on the slant
# path:
P = 1 - (1 - P0) * ((c_B - P0**2) / (P0 * (1 - P0)))**P0
return P
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