def extrarad(J, lat, G_sc= 0.0820):
"""
args:
J: day of year
lat: Latitude in angular degrees
Calculates:
inverse relative distance Earth-sun (dr) and\
solar declination (delta)
Sunset hour angle (Ws)
returns:
Ra: Extraterrestrial radiation in MJ/m2/day
"""
Ra = np.zeros(J.shape)
for i in J:
dr = 1 + (0.033*np.cos((2*np.pi/365)*int(i)))
delta = 0.4093 * np.sin(((2*np.pi/365)*int(i))-1.39)
Ws = np.arccos(-np.tan(uc.deg2rad(lat))*np.tan(delta))
extrarad = ((24 * 60) / np.pi) * G_sc * dr * (Ws * np.sin(uc.deg2rad(lat)) * np.sin(delta) +\
np.cos(uc.deg2rad(lat)) * np.cos(delta) * np.sin(Ws))
extrarad = np.divide(extrarad, 2.45)
Ra = np.append(Ra, extrarad)
Ra = Ra[1:]
return Ra
def extrarad_2d(J, lat, nvals, nrow, ncol, G_sc= 0.0820, LHV = 0.408):
"""
args:
J: day of year
lat: Latitude in angular degrees
G_Sc : SOLAR_CONSTANT_MIN = 0.0820 MJ/m2.min
LATENT_HEAT_VAPORIZATION = 0.408 in MJ/kg
Calculates:
inverse relative distance Earth-sun (dr) and\
solar declination (delta)
Sunset hour angle (Ws)
returns:
Ra: Extraterrestrial radiation in MJ/m2/day
"""
dr = 1 + (0.033*np.cos((2*np.pi/365)*J))
dr_2d = np.reshape(np.repeat(dr, nrow*ncol), (nvals, nrow, ncol))
delta = 0.4093 * np.sin(((2*np.pi/365)*J)-1.39)
delta_2d = np.reshape(np.repeat(delta, nrow*ncol), (nvals, nrow, ncol))
Ws_2d = np.arccos(-np.tan(uc.deg2rad(lat))*np.tan(delta_2d))
extrarad_2d = ((24 * 60) / np.pi) * G_sc * dr_2d * (Ws_2d * np.sin(uc.deg2rad(lat)) * np.sin(delta_2d) + \
np.cos(uc.deg2rad(lat)) * np.cos(delta_2d) * np.sin(Ws_2d))
extrarad_2d = np.divide(extrarad_2d, 2.45)
return extrarad_2d
def solar_azimuthangle(Sphi, lat, delta, units = 'degrees', Td = 12, Sn = 12 ):
"""
Computes solar azimuth angle (horizontal angle between
due south and the sun; radians)
args:
Sphi : solar elevation/ altitude angle (in degrees; converted to radians within the fucn)
J: day of year
delta: solar declination angle (in degrees converted to radians within the fucn)
Td: Time of day in (hrs)
Sn: time of solar noon (hrs)
units: "radians" or "degrees"
"""
if units == 'degrees':
lat = deg2rad(lat)
else:
lat = lat
azs = np.arccos(np.divide((np.subtract(np.multiply(np.sin(Sphi), np.sin(lat)), np.sin(delta))),np.multiply(np.cos(Sphi), np.cos(lat))))
azs = np.where(Td > Sn, np.add(pi, azs), np.subtract(pi, azs))
return azs
def extrarad(J, lat, units = 'degrees'):
"""
args:
J: day of year
lat: Latitude in angular degrees (converted to rad in func)
Calculates:
inverse relative distance Earth-sun (dr) and\
solar declination (delta)
Sunset hour angle (Ws)
returns:
Ra: Extraterrestrial radiation in mm/day
"""
if units == 'degrees':
lat = deg2rad(lat)
else:
lat = lat
dr = 1 + (0.033*np.cos((2*pi/365)*int(J)))
delta = 0.4093 * np.sin(((2*np.pi/365)*int(J))-1.39)
Ws = np.arccos(-np.tan(lat)*np.tan(delta))
extrarad = ((24 * 60) /pi) * G_sc_min * dr * (Ws * np.sin(lat) * np.sin(delta) +\
np.cos(lat) * np.cos(delta) * np.sin(Ws))
extrarad = np.multiply(extrarad, LHV)
return extrarad
def qs(lat, J, slope, aspect, TS =0.0, C_f = 0.0, units = 'degrees'):
"""
Calcualtes Incident solar radiaiton on sloping surface(MJ/m2)
args:
lat: latitude (in angular degrees)
J: day of year
C_f: forest Canopy Factor
a = albedo of snow
qd: direct solar radiation on falt surface (MJ/m2) / Extraterrestrial Rad
Si : solar incidence angle (in radians)
Sphi : solar elevation/ altitude angle (in radians)
"""
if units == 'degrees':
lat = deg2rad(lat)
slope = deg2rad(slope)
aspect = deg2rad(aspect)
else:
lat = lat
slope = slope
aspect = aspect
#solar declination angle
delta = 0.4093 * np.sin(((2*np.pi/365)*int(J))-1.39)
#solar elevation angle
Sphi = solar_elevationangle(lat, delta)
# solar azimuth angle
azs = solar_azimuthangle(Sphi, lat, delta)
#solar radiation incident on a flat surface
qd = extrarad(J ,lat)
# albedo of snow
a = albedo(TS)
# solar incidence angle
i = solar_incidenceangle(slope, aspect, azs, Sphi)
qs = np.multiply(max(0.1,(1-C_f)), (1-a)*qd*max(0,(np.sin(i)/np.sin(Sphi))))
return qs
def solar_incidenceangle(slope, aspect, az, Sphi, units = 'degrees'):
"""
computes angle between insolation and horizontal surface
args:
slope: slope of land surface
aspect: aspect of land surface
az: solar azimuth angle (horizontal angle between
due south and the sun; radians)
Sphi: solar elevatio angle (in radians)
units: "radians" or "degrees"
"""
if units == 'degrees':
slope = deg2rad(slope)
aspect = deg2rad(aspect)
else:
slope = slope
aspect = aspect
i = np.arcsin(np.multiply(np.sin(np.arctan(slope)), np.multiply(np.cos(Sphi), np.cos(np.subtract(az, slope)))))
np.where(i>0.0, i, 0.0)
return i
def solar_elevationangle(lat, delta, Td = 12.0, Sn = 12.0 , units= 'degrees'):
"""
computes solar elevatio angle (in radians)
It is the angle between solar rays and horizontal surface
args:
lat: latitude in angular degrees ( converted to rads in this func)
delta: solar declination angle (in radians)
Td: Time of day in (hrs)
Sn: time of solar noon (hrs)
units: "radians" or "degrees" default is degrees
"""
if units == 'degrees':
lat = deg2rad(lat)
else:
lat = lat
sinphi = np.add(np.multiply(np.sin(lat), np.sin(delta)),\
np.multiply((np.multiplty(np.cos(lat), np.cos(delta)),np.cos(np.divide(np.multiply(pi, np.subtract(Td-Sn)),12.0)))))
return np.arcsin(sinphi)