# Copyright Brandon Stafford # # This file is part of Pysolar. # # Pysolar is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # Pysolar is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License along # with Pysolar. If not, see . # Disable linting as this is a work in progress # flake8: noqa from . import numeric as math from .constants import standard_pressure # single-scattering albedo used to calculate aerosol scattering transmittance; # not used for sky or ground albedo for backscattering estimate albedo = {} albedo["high-frequency"] = 0.92 albedo["low-frequency"] = 0.84 standard_pressure_millibars = standard_pressure / 100 un = 0.0003 # atm*cm, from [Gueymard 2008], p. 280 E0n = {"high-frequency": 635.4, # extra-atmospheric irradiance, 290-700 nm (UV and visible) "low-frequency": 709.7} # extra-atmospheric irradiance, 700-4000 nm (short infrared) def get_aerosol_forward_scatterance_factor(altitude_deg): Z = 90 - altitude_deg return 1 - math.e ** (-0.6931 - 1.8326 * math.cos(math.radians(Z))) def get_aerosol_optical_depth(turbidity_beta, effective_wavelength, turbidity_alpha): # returns tau_a return turbidity_beta * effective_wavelength ** -turbidity_alpha def get_aerosol_scattering_correction_factor(band, ma, tau_a): # returns F if band == "high-frequency": g0 = (3.715 + 0.368 * ma + 0.036294 * ma ** 2) / \ (1 + 0.0009391 * ma ** 2) g1 = (-0.164 - 0.72567 * ma + 0.20701 * ma ** 2) / \ (1 + 0.001901 * ma ** 2) g2 = (-0.052288 + 0.31902 * ma + 0.17871 * ma ** 2) / \ (1 + 0.0069592 * ma ** 2) return (g0 + g1 * tau_a) / (1 + g2 * tau_a) else: h0 = (3.4352 + 0.65267 * ma + 0.00034328 * ma ** 2) / \ (1 + 0.034388 * ma ** 1.5) h1 = (1.231 - 1.63853 * ma + 0.20667 * ma ** 2) / \ (1 + 0.1451 * ma ** 1.5) h2 = (0.8889 - 0.55063 * ma + 0.50152 * ma ** 2) / \ (1 + 0.14865 * ma ** 1.5) return (h0 + h1 * tau_a) / (1 + h2 * tau_a) def get_aerosol_transmittance(band, ma, tau_a): # returns Ta return math.exp(-ma * tau_a) def get_aerosol_scattering_transmittance(band, ma, tau_a): # returns Tas return math.exp(-ma * albedo[band] * tau_a) def get_backscattered_diffuse_broadband_irradiance(band, turbidity_alpha=1.3, turbidity_beta=0.6): return get_backscattered_diffuse_broadband_irradiance_by_band("high-frequency", turbidity_alpha, turbidity_beta) + get_backscattered_diffuse_broadband_irradiance_by_band("low-frequency", turbidity_alpha, turbidity_beta) def get_backscattered_diffuse_irradiance_by_band(band, Ebi, Edpi, turbidity_alpha=1.3, turbidity_beta=0.6): rhos = get_sky_albedo(band, turbidity_alpha, turbidity_beta) rhog = get_ground_albedo(band) Eddi = rhog * rhos * (Ebi + Edpi) / (1 - rhog * rhos) return Eddi def get_beam_broadband_irradiance(altitude_deg, pressure_millibars=standard_pressure_millibars, ozone_atm_cm=0.35, nitrogen_atm_cm=0.0002, precipitable_water_cm=5.0, turbidity_alpha=1.3, turbidity_beta=0.6): Z = 90 - altitude_deg Ebn = get_broadband_direct_normal_irradiance(altitude_deg, pressure_millibars, ozone_atm_cm, nitrogen_atm_cm, precipitable_water_cm, turbidity_alpha, turbidity_beta) return Ebn * math.cos(math.radians(Z)) def get_beam_irradiance_by_band(band, altitude_deg, pressure_millibars=standard_pressure_millibars, ozone_atm_cm=0.35, nitrogen_atm_cm=0.0002, precipitable_water_cm=5.0, turbidity_alpha=1.3, turbidity_beta=0.6): Z = 90 - altitude_deg Ebni = get_direct_normal_irradiance_by_band(band, altitude_deg, pressure_millibars, ozone_atm_cm, nitrogen_atm_cm, precipitable_water_cm, turbidity_alpha, turbidity_beta) return Ebni * math.cos(math.radians(Z)) def get_diffuse_broadband_irradiance(air_mass=1.66, turbidity_alpha=1.3, turbidity_beta=0.6): return get_diffuse_irradiance_by_band("high-frequency", air_mass, turbidity_alpha, turbidity_beta) + get_diffuse_irradiance_by_band("low-frequency", air_mass, turbidity_alpha, turbidity_beta) def get_diffuse_irradiance_by_band(band, air_mass=1.66, turbidity_alpha=1.3, turbidity_beta=0.6): Z = 90 - altitude_deg effective_wavelength = get_effective_aerosol_wavelength(band, turbidity_alpha) tau_a = get_aerosol_optical_depth( turbidity_beta, effective_wavelength, turbidity_alpha) ma = get_optical_mass_aerosol(altitude_deg) mo = get_optical_mass_ozone(altitude_deg) mR = get_optical_mass_rayleigh(altitude_deg, pressure_millibars) To = get_ozone_transmittance(band, mo) Tg = get_gas_transmittance(band, mR) Tn = get_nitrogen_transmittance(band, 1.66) Tw = get_water_vapor_transmittance(band, 1.66) TR = get_rayleigh_transmittance(band, mR) Ta = get_aerosol_transmittance(band, ma, tau_a) Tas = get_aerosol_scattering_transmittance(band, ma, tau_a) BR = get_rayleigh_extinction_forward_scattering_fraction(band, air_mass) Ba = get_aerosol_forward_scatterance_factor(altitude_deg) F = get_aerosol_scattering_correction_factor(band, ma, tau_a) Edpi = To * Tg * Tn * Tw * \ (BR * (1 - TR) * Ta ** 0.25 + Ba * F * TR * (1 - Tas ** 0.25)) * \ E0n[band] return Edpi def get_broadband_direct_normal_irradiance(altitude_deg, pressure_millibars=standard_pressure_millibars, ozone_atm_cm=0.35, nitrogen_atm_cm=0.0002, precipitable_water_cm=5.0, turbidity_alpha=1.3, turbidity_beta=0.6): high = get_direct_normal_irradiance_by_band("high-frequency", altitude_deg, pressure_millibars, ozone_atm_cm, nitrogen_atm_cm, precipitable_water_cm, turbidity_alpha, turbidity_beta) low = get_direct_normal_irradiance_by_band("low-frequency", altitude_deg, pressure_millibars, ozone_atm_cm, nitrogen_atm_cm, precipitable_water_cm, turbidity_alpha, turbidity_beta) return high + low def get_direct_normal_irradiance_by_band(band, altitude_deg, pressure_millibars=standard_pressure_millibars, ozone_atm_cm=0.35, nitrogen_atm_cm=0.0002, precipitable_water_cm=5.0, turbidity_alpha=1.3, turbidity_beta=0.6): ma = get_optical_mass_aerosol(altitude_deg) mo = get_optical_mass_ozone(altitude_deg) mR = get_optical_mass_rayleigh(altitude_deg, pressure_millibars) mRprime = mR * pressure_millibars / standard_pressure_millibars mw = get_optical_mass_water(altitude_deg) effective_wavelength = get_effective_aerosol_wavelength( band, ma, turbidity_alpha, turbidity_beta) tau_a = get_aerosol_optical_depth( turbidity_beta, effective_wavelength, turbidity_alpha) TR = get_rayleigh_transmittance(band, mRprime) Tg = get_gas_transmittance(band, mRprime) To = get_ozone_transmittance(band, mo, ozone_atm_cm) # is water_optical_mass really used for nitrogen calc? Tn = get_nitrogen_transmittance(band, mw, nitrogen_atm_cm) Tw = get_water_vapor_transmittance(band, mw, precipitable_water_cm) Ta = get_aerosol_transmittance(band, ma, tau_a) return E0n[band] * TR * Tg * To * Tn * Tw * Ta def get_effective_aerosol_wavelength(band, ma, turbidity_alpha, turbidity_beta): # This function has an error somewhere. It returns negative values sometimes, but wavelength should always be positive. ua = math.log(1 + ma * turbidity_beta) if band == "high-frequency": a1 = turbidity_alpha # just renaming to keep equations short d0 = 0.57664 - 0.024743 * a1 d1 = (0.093942 - 0.2269 * a1 + 0.12848 * a1 ** 2) / (1 + 0.6418 * a1) d2 = (-0.093819 + 0.36668 * a1 - 0.12775 * a1 ** 2) / \ (1 - 0.11651 * a1) d3 = a1 * (0.15232 - 0.087214 * a1 + 0.012664 * a1 ** 2) / \ (1 - 0.90454 * a1 + 0.26167 * a1 ** 2) return (d0 + d1 * ua + d2 * ua ** 2) / (1 + d3 * ua ** 2) else: a2 = turbidity_alpha e0 = (1.183 - 0.022989 * a2 + 0.020829 * a2 ** 2) / (1 + 0.11133 * a2) e1 = (-0.50003 - 0.18329 * a2 + 0.23835 * a2 ** 2) / (1 + 1.6756 * a2) e2 = (-0.50001 + 1.1414 * a2 + 0.0083589 * a2 ** 2) / (1 + 11.168 * a2) e3 = (-0.70003 - 0.73587 * a2 + 0.51509 * a2 ** 2) / (1 + 4.7665 * a2) return (e0 + e1 * ua + e2 * ua ** 2) / (1 + e3 * ua) def get_gas_transmittance(band, mRprime): if band == "high-frequency": return (1 + 0.95885 * mRprime + 0.012871 * mRprime ** 2) / (1 + 0.96321 * mRprime + 0.015455 * mRprime ** 2) else: return (1 + 0.27284 * mRprime - 0.00063699 * mRprime ** 2) / (1 + 0.30306 * mRprime) def get_global_broadband_irradiance(altitude_deg, pressure_millibars=standard_pressure_millibars, ozone_atm_cm=0.35, nitrogen_atm_cm=0.0002, precipitable_water_cm=5.0, turbidity_alpha=1.3, turbidity_beta=0.6): Eb_high = get_beam_irradiance_by_band("high-frequency", altitude_deg, pressure_millibars, ozone_atm_cm, nitrogen_atm_cm, precipitable_water_cm, turbidity_alpha, turbidity_beta) Eb_low = get_beam_irradiance_by_band("low-frequency", altitude_deg, pressure_millibars, ozone_atm_cm, nitrogen_atm_cm, precipitable_water_cm, turbidity_alpha, turbidity_beta) Edp_high = get_diffuse_irradiance_by_band("high-frequency", air_mass, turbidity_alpha, turbidity_beta) Edp_low = get_diffuse_irradiance_by_band("low-frequency", air_mass, turbidity_alpha, turbidity_beta) Edd_high = get_backscattered_diffuse_irradiance_by_band("high-frequency", Eb_high, Edp_high, turbidity_alpha, turbidity_beta) Edd_low = get_backscattered_diffuse_irradiance_by_band("low-frequency", Eb_low, Edp_low, turbidity_alpha, turbidity_beta) return Eb_high + Eb_low + Edp_high + Edp_low + Edd_high + Edd_low def get_ground_albedo(band): # This could probably be improved with [Gueymard, 1993: Mathematically integrable parameterization of clear-sky beam and global irradiances and its use in daily irradiation applications] # http://www.sciencedirect.com/science/article/pii/0038092X9390059W] return 0.150 # mean ground albedo from [Gueymard, 2008], Table 1 def get_nitrogen_transmittance(band, mw, nitrogen_atm_cm): if band == "high-frequency": g1 = (0.17499 + 41.654 * un - 2146.4 * un ** 2) / \ (1 + 22295.0 * un ** 2) g2 = un * (-1.2134 + 59.324 * un) / (1 + 8847.8 * un ** 2) g3 = (0.17499 + 61.658 * un + 9196.4 * un ** 2) / \ (1 + 74109.0 * un ** 2) return min(1, (1 + g1 * mw + g2 * mw ** 2) / (1 + g3 * mw)) else: return 1.0 # from Appendix B of [Gueymard, 2003] def get_optical_mass_rayleigh(altitude_deg, pressure_millibars): Z = 90 - altitude_deg Z_rad = math.radians(Z) return (pressure_millibars / standard_pressure_millibars) / ((math.cos(Z_rad) + 0.48353 * Z_rad ** 0.095846) / (96.741 - Z_rad) ** 1.754) def get_optical_mass_ozone(altitude_deg): # from Appendix B of [Gueymard, 2003] Z = 90 - altitude_deg Z_rad = math.radians(Z) return 1 / ((math.cos(Z_rad) + 1.0651 * Z_rad ** 0.6379) / (101.8 - Z_rad) ** 2.2694) def get_optical_mass_water(altitude_deg): # from Appendix B of [Gueymard, 2003] Z = 90 - altitude_deg Z_rad = math.radians(Z) return 1 / ((math.cos(Z_rad) + 0.10648 * Z_rad ** 0.11423) / (93.781 - Z_rad) ** 1.9203) def get_optical_mass_aerosol(altitude_deg): # from Appendix B of [Gueymard, 2003] Z = 90 - altitude_deg Z_rad = math.radians(Z) return 1 / ((math.cos(Z_rad) + 0.16851 * Z_rad ** 0.18198) / (95.318 - Z_rad) ** 1.9542) def get_ozone_transmittance(band, mo, uo): if band == "high-frequency": f1 = uo * (10.979 - 8.5421 * uo) / (1 + 2.0115 * uo + 40.189 * uo ** 2) f2 = uo * (-0.027589 - 0.005138 * uo) / \ (1 - 2.4857 * uo + 13.942 * uo ** 2) f3 = uo * (10.995 - 5.5001 * uo) / (1 + 1.6784 * uo + 42.406 * uo ** 2) return (1 + f1 * mo + f2 * mo ** 2) / (1 + f3 * mo) else: return 1.0 def get_rayleigh_extinction_forward_scattering_fraction(band, mR): # returns BR if band == "high-frequency": return 0.5 * (0.89013 - 0.049558 * mR + 0.000045721 * mR ** 2) else: return 0.5 def get_rayleigh_transmittance(band, mRprime): if band == "high-frequency": return (1 + 1.8169 * mRprime + 0.033454 * mRprime ** 2) / (1 + 2.063 * mRprime + 0.31978 * mRprime ** 2) else: return (1 - 0.010394 * mRprime) / (1 - 0.00011042 * mRprime ** 2) def get_sky_albedo(band, turbidity_alpha, turbidity_beta): if band == "high-frequency": a1 = turbidity_alpha # just renaming to keep equations short b1 = turbidity_beta rhos = (0.13363 + 0.00077358 * a1 + b1 * (0.37567 + 0.22946 * a1) / (1 - 0.10832 * a1)) / (1 + b1 * (0.84057 + 0.68683 * a1) / (1 - 0.08158 * a1)) else: a2 = turbidity_alpha # just renaming to keep equations short b2 = turbidity_beta rhos = (0.010191 + 0.00085547 * a2 + b2 * (0.14618 + 0.062758 * a2) / (1 - 0.19402 * a2)) / (1 + b2 * (0.58101 + 0.17426 * a2) / (1 - 0.17586 * a2)) return rhos def get_water_vapor_transmittance(band, mw, w): if band == "high-frequency": h = get_water_vapor_transmittance_coefficients(band, w) return (1 + h[1] * mw) / (1 + h[2] * mw) else: c = get_water_vapor_transmittance_coefficients(band, w) return (1 + c[1] * mw + c[2] * mw ** 2) / (1 + c[3] * mw + c[4] * mw ** 2) def get_water_vapor_transmittance_coefficients(band, w): if band == "high-frequency": h1 = w * (0.065445 + 0.00029901 * w) / (1 + 1.2728 * w) h2 = w * (0.065687 + 0.0013218 * w) / (1 + 1.2008 * w) return [float('NaN'), h1, h2] else: c1 = w * (19.566 - 1.6506 * w + 1.0672 * w ** 2) / \ (1 + 5.4248 * w + 1.6005 * w ** 2) c2 = w * (0.50158 - 0.14732 * w + 0.047584 * w ** 2) / \ (1 + 1.1811 * w + 1.0699 * w ** 2) c3 = w * (21.286 - 0.39232 * w + 1.2692 * w ** 2) / \ (1 + 4.8318 * w + 1.412 * w ** 2) c4 = w * (0.70992 - 0.23155 * w + 0.096514 * w ** 2) / \ (1 + 0.44907 * w + 0.75425 * w ** 2) return [float('NaN'), c1, c2, c3, c4]