"""
radiation solves for radiation due to the enviorment for a particular datetime and altitude.
"""
import math
import fluids
import numpy as np
import EarthSHAB.config_earth as config_earth
# Horizon correction values (arcminutes converted to degrees).
# Source: https://github.com/KosherJava/zmanim/blob/master/src/main/java/com/kosherjava/zmanim/util/AstronomicalCalculator.java#L176
_REFRACTION_DEG = 4.478885263888294 / 60. # atmospheric refraction at the horizon
_SOLAR_RADIUS_DEG = 16 / 60. # apparent angular radius of the solar disk
def solar_zenith_adjusted(t_utc, lat, lon, alt_m):
"""Altitude-adjusted solar zenith angle in radians.
At altitude the geometric horizon is depressed, so the sun sets later than
at ground level. The result also corrects for atmospheric refraction and
the apparent solar disk radius (upper-limb definition of sunset).
Sunset occurs when the returned value >= math.pi / 2.
"""
solpos = fluids.solar_position(t_utc, lat, lon)
zen = math.radians(solpos[0])
earth_radius_km = 6356.9
elev_adj = math.acos(earth_radius_km / (earth_radius_km + max(alt_m, 0.0) / 1000.))
return zen - elev_adj + math.radians(_SOLAR_RADIUS_DEG + _REFRACTION_DEG)
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class Radiation:
# Constants
I0 = 1358 # Direct Solar Radiation Level
e = 0.016708 # Eccentricity of Earth's Orbit
P0 = 101325 # Standard Atmospheric Pressure at Sea Level
cloudElev = 3000 # (m)
cloudFrac = 0.0 # Percent cloud coverage [0,1]
cloudAlbedo = .65 # [0,1]
albedoGround = .2 # Ground albedo [0,1]
tGround = 293 # (K) Temperature of Ground
emissGround = .95 # [0,1]
SB = 5.670373E-8 # Stefan Boltzman Constant
RE = 6371000 # (m) Radius of Earth
radRef= .1 # [0,1] Balloon Reflectivity
radTrans = .1 # [0,1] Balloon Transmitivity
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def __init__(self):
d = config_earth.balloon_properties['d']
self.emissEnv = config_earth.balloon_properties['emissEnv']
self.absEnv = config_earth.balloon_properties['absEnv']
self.projArea = 0.25 * math.pi * d * d
self.surfArea = math.pi * d * d
self.Ls = config_earth.simulation['start_time'].timetuple().tm_yday
def getTemp(self, el):
atm = fluids.atmosphere.ATMOSPHERE_1976(el)
return atm.T
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def getTempForecast(self, coord):
r""" Looks up the forecast temperature at the current coordinate and altitude
.. important:: TODO. This function is not operational yet.
:param coord: current coordinate
:type coord: dict
:returns: atmospheric temperature (k)
:rtype: float
"""
return temp
def getPressure(self, el):
atm = fluids.atmosphere.ATMOSPHERE_1976(el)
return atm.P
def getDensity(self, el):
atm = fluids.atmosphere.ATMOSPHERE_1976(el)
return atm.rho
def getGravity(self, el):
atm = fluids.atmosphere.ATMOSPHERE_1976(el)
return atm.g
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def get_SI0(self):
r""" Incident solar radiation above Earth's atmosphere (W/m^2)
.. math:: I_{sun,0}= I_0 \cdot [1+0.5(\frac{1+e}{1-e})^2-1) \cdot cos(f)]
:returns: The incident solar radiation above Earths atm (W/m^2)
:rtype: float
"""
f = 2*math.pi*self.Ls/365 #true anomaly
e2 = pow(((1.+Radiation.e)/(1.-Radiation.e)),2) -1.
return Radiation.I0*(1.+0.5*e2*math.cos(f))
def get_declination(self):
#This function is unused
return -.4091*math.cos(2*math.pi*(self.Ls+10)/365)
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def get_zenith(self, t, coord):
""" Calculates adjusted solar zenith angle at elevation
:param t: Lattitude (rad)
:type t: Datetime
:param coord: Solar Hour Angle (rad)
:type coord: dict
:returns: The approximate solar zenith angle (rad)
:rtype: float
"""
return solar_zenith_adjusted(t, coord["lat"], coord["lon"], coord["alt"])
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def get_air_mass(self,zen, el):
r"""Air Mass at elevation
.. math:: AM = 1229+(614cos(\zeta)^2)^{\frac{1}{2}}-614cos(\zeta)
:param zen: Solar Angle (rad)
:type zen: float
:param el: Elevation (m)
:type el: float
:returns: The approximate air mass (unitless)
:rtype: float
"""
p = self.getPressure(el) #pressure at current elevation
am = (p/Radiation.P0)*(math.sqrt(1229 + pow((614*math.cos(zen)),2))-614*math.cos(zen))
return am
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def get_trans_atm(self,zen,el):
r"""The amount of solar radiation that permeates through the atmosphere at a
certain altitude, I_{sun} is driven by the atmospheric transmittance.
.. math:: \tau_{atm}= \frac{1}{2}(e^{-0.65AM}+e^{-0.095AM})
:param zen: Solar Angle (rad)
:type zen: float
:param el: Elevation (m)
:type el: float
:returns: The atmospheric trasmittance (unitless)
:rtype: float
"""
am = self.get_air_mass(zen, el)
trans = 0.5*(math.exp(-0.65*am) + math.exp(-0.095*am))
return trans
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def get_direct_SI(self,zen,el):
"""Calculates Direct Solar Radiation
:param zen: Solar Angle (rad)
:type zen: float
:param el: Elevation (m)
:type el: float
:returns: Tntensity of the direct solar radiation (W/m^2)
:rtype: float
"""
SI0 = self.get_SI0()
trans = self.get_trans_atm(zen, el)
if zen > math.pi/2 :
direct_SI = 0
else:
direct_SI = trans*SI0
return direct_SI
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def get_diffuse_SI(self,zen,el):
"""Calculates Diffuse Solar Radiation from sky
:param zen: Solar Angle (rad)
:type zen: float
:param el: Elevation (m)
:type el: float
:returns: The intensity of the diffuse solar radiation from the sky (W/m^2)
:rtype: float
"""
if(zen > math.pi/2.):
return 0.0
SI0 = self.get_SI0()
trans = self.get_trans_atm(zen, el)
if el < Radiation.cloudElev:
return (1-Radiation.cloudFrac)*0.5*SI0*math.sin(math.pi/2.-zen)*(1.-trans)/(1-1.4*math.log(trans))
else:
return 0.5*SI0*math.sin(math.pi/2.-zen)*(1.-trans)/(1-1.4*math.log(trans))
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def get_reflected_SI(self,zen,el):
"""Calculates Reflected Solar Radiation from from the Earth's Surface
:param zen: Solar Angle (rad)
:type zen: float
:param el: Elevation (m)
:type el: float
:returns: The intensity solar radiation reflected by the Earth (W/m^2)
:rtype: float
"""
incident_SI = self.get_SI0()
tau_atm = self.get_trans_atm(zen,el)
if el < Radiation.cloudElev:
albedo = (1.-Radiation.cloudFrac)*Radiation.albedoGround;
else:
albedo = (1.-Radiation.cloudFrac)*(1-Radiation.cloudFrac)*Radiation.albedoGround + Radiation.cloudAlbedo*Radiation.cloudFrac
return albedo*tau_atm*incident_SI*math.sin(math.pi/2.-zen)
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def get_earth_IR(self,el):
"""Calculates Infared Radiation emitted from Earth's surface
:param el: Elevation (m)
:type el: float
:returns: Intensity of IR radiation emitted from earth (W/m^2)
:rtype: float
"""
p = self.getPressure(el)#pressure at current elevation
IR_trans = 1.716-0.5*(math.exp(-0.65*p/Radiation.P0) + math.exp(-0.095*p/Radiation.P0))
if el < Radiation.cloudElev:
tEarth = Radiation.tGround
else:
clouds = fluids.atmosphere.ATMOSPHERE_1976(Radiation.cloudElev)
tEarth = Radiation.tGround*(1.-Radiation.cloudFrac) + clouds.T*Radiation.cloudFrac
return IR_trans*Radiation.emissGround*Radiation.SB*pow(tEarth,4)
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def get_sky_IR(self,el):
"""Calculates Infared Radiation emitted the from Sky
:param el: Elevation (m)
:type el: float
:returns: Intensity of IR radiation emitted from sky (W/m^2)
:rtype: float
"""
return np.fmax(-0.03*el+300.,50.0)
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def get_rad_total(self,datetime,coord):
"""Calculates total radiation sources as a function of altitude, time, and balloon surface area.
The figure below shows how different altitudes effects the radiation sources on
a particular date and coordinate for Tucson Arizona (at sruface level and 25 km altitudes)
.. image:: ../../img/Tucson_Radiation_Comparison.png
"""
zen = self.get_zenith(datetime, coord)
el = coord["alt"]
#radRef = Radiation.radRef + Radiation.radRef*Radiation.radRef + Radiation.radRef*Radiation.radRef*Radiation.radRef
totAbs = self.absEnv
hca = math.asin(Radiation.RE/(Radiation.RE+el)) #half cone angle
vf = 0.5*(1. - math.cos(hca)) #viewfactor
direct_I = self.get_direct_SI(zen, el)
power_direct = direct_I*totAbs*self.projArea
diffuse_I = self.get_diffuse_SI(zen, el)
power_diffuse = diffuse_I*totAbs*(1.-vf)*self.surfArea
reflected_I = self.get_reflected_SI(zen, el)
power_reflected = reflected_I*totAbs*vf*self.surfArea
earth_IR = self.get_earth_IR(el)
power_earth_IR = earth_IR*self.emissEnv*vf*self.surfArea
sky_IR = self.get_sky_IR(el)
power_sky_IR = sky_IR*self.emissEnv*(1.-vf)*self.surfArea
rad_tot_bal = power_direct + power_diffuse + power_reflected + power_earth_IR + power_sky_IR
return rad_tot_bal