Revive the REST2 radiation model.

tuxiano · Apr 19, 2015 · 551a5e7 · 551a5e7
1 parent b864472
commit 551a5e7
Showing 1 changed file with 228 additions and 0 deletions.
diff --git a/pysolar/rest.py b/pysolar/rest.py
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+#    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 <http://www.gnu.org/licenses/>.
+
+import math
+from .constants import standard_pressure
+
+albedo = {} # single-scattering albedo used to calculate aerosol scattering transmittance
+
+albedo["high-frequency"] = 0.92
+albedo["low-frequency"] = 0.84
+standard_pressure_millibars = standard_pressure / 100
+
+rhogi = 0.150 # mean ground albedo from [Gueymard, 2008], Table 1
+
+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 GetAerosolForwardScatteranceFactor(altitude_deg):
+    Z = 90 - altitude_deg
+    return 1 - math.e ** (-0.6931 - 1.8326 * math.cos(math.radians(Z)))
+
+def GetAerosolOpticalDepth(turbidity_beta, effective_wavelength, turbidity_alpha):
+    # returns tau_a
+    return turbidity_beta * effective_wavelength ** -turbidity_alpha
+
+def GetAerosolScatteringCorrectionFactor(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 GetAerosolTransmittance(band, ma, tau_a):
+    # returns Ta
+    return math.exp(-ma * tau_a)
+
+def GetAerosolScatteringTransmittance(band, ma, tau_a):
+    # returns Tas
+    return math.exp(-ma * albedo[band] * tau_a)
+
+def GetBeamBroadbandIrradiance(Ebn, altitude_deg):
+    Z = 90 - altitude_deg
+    return Ebn * math.cos(math.radians(Z))
+
+def GetDiffuseIrradiance():
+    return GetDiffuseIrradianceByBand("high-frequency") + GetDiffuseIrradianceByBand("low-frequency")
+
+def GetDiffuseIrradianceByBand(band, air_mass=1.66, turbidity_alpha=1.3, turbidity_beta=0.6):
+    Z = 90 - altitude_deg
+    effective_wavelength = GetEffectiveAerosolWavelength(band, turbidity_alpha)
+    tau_a = GetAerosolOpticalDepth(turbidity_beta, effective_wavelength, turbidity_alpha)
+    rhosi = GetSkyAlbedo(band, turbidity_alpha, turbidity_beta)
+
+    ma = GetOpticalMassAerosol(altitude_deg)
+    mo = GetOpticalMassOzone(altitude_deg)
+    mR = GetOpticalMassRayleigh(altitude_deg, pressure_millibars)
+
+    To = GetOzoneTransmittance(band, mo)
+    Tg = GetGasTransmittance(band, mR)
+    Tn = GetNitrogenTransmittance(band, 1.66)
+    Tw = GetWaterVaporTransmittance(band, 1.66)
+    TR = GetRayleighTransmittance(band, mR)
+    Ta = GetAerosolTransmittance(band, ma, tau_a)
+    Tas = GetAerosolScatteringTransmittance(band, ma, tau_a)
+
+    BR = GetRayleighExtinctionForwardScatteringFraction(band, air_mass)
+    Ba = GetAerosolForwardScatteranceFactor(altitude_deg)
+    F = GetAerosolScatteringCorrectionFactor(band, ma, tau_a)
+
+    Edp = To * Tg * Tn * Tw * (BR * (1 - TR) * Ta ** 0.25 + Ba * F * TR * (1 - Tas ** 0.25)) * E0n[band]
+    Edd = rhogi * rhosi * (Eb + Edp)/(1 - rhogi * rhosi)
+    return Edp + Edd
+
+def GetDirectNormalIrradiance(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 = GetDirectNormalIrradianceByBand("high-frequency", altitude_deg, pressure_millibars, ozone_atm_cm, nitrogen_atm_cm, precipitable_water_cm, turbidity_alpha, turbidity_beta)
+    low = GetDirectNormalIrradianceByBand("low-frequency", altitude_deg, pressure_millibars, ozone_atm_cm, nitrogen_atm_cm, precipitable_water_cm, turbidity_alpha, turbidity_beta)
+    return high + low
+
+def GetDirectNormalIrradianceByBand(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 = GetOpticalMassAerosol(altitude_deg)
+    mo = GetOpticalMassOzone(altitude_deg)
+    mR = GetOpticalMassRayleigh(altitude_deg, pressure_millibars)
+    mRprime = mR * pressure_millibars / standard_pressure_millibars
+    mw = GetOpticalMassWater(altitude_deg)
+
+    effective_wavelength = GetEffectiveAerosolWavelength(band, ma, turbidity_alpha, turbidity_beta)
+    tau_a = GetAerosolOpticalDepth(turbidity_beta, effective_wavelength, turbidity_alpha)
+
+    TR = GetRayleighTransmittance(band, mRprime)
+    Tg = GetGasTransmittance(band, mRprime)
+    To = GetOzoneTransmittance(band, mo, ozone_atm_cm)
+    Tn = GetNitrogenTransmittance(band, mw, nitrogen_atm_cm) # is water_optical_mass really used for nitrogen calc?
+    Tw = GetWaterVaporTransmittance(band, mw, precipitable_water_cm)
+    Ta = GetAerosolTransmittance(band, ma, tau_a)
+    return E0n[band] * TR * Tg * To * Tn * Tw * Ta
+
+def GetEffectiveAerosolWavelength(band, ma, turbidity_alpha, turbidity_beta):
+    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 ** 2)
+
+def GetGasTransmittance(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 GetBroadbandGlobalIrradiance(Ebn, altitude_deg, Ed):
+    return GetBeamBroadbandIrradiance(Ebn, altitude_deg) + Ed
+
+def GetNitrogenTransmittance(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
+
+def GetOpticalMassRayleigh(altitude_deg, pressure_millibars): # from Appendix B of [Gueymard, 2003]
+    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 GetOpticalMassOzone(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 GetOpticalMassWater(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 GetOpticalMassAerosol(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 GetOzoneTransmittance(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 GetRayleighExtinctionForwardScatteringFraction(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 GetRayleighTransmittance(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 GetSkyAlbedo(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 GetWaterVaporTransmittance(band, mw, w):
+    if band == "high-frequency":
+        h = GetWaterVaporTransmittanceCoefficients(band, w)
+        return (1 + h[1] * mw)/(1 + h[2] * mw)
+    else:
+        c = GetWaterVaporTransmittanceCoefficients(band, w)
+        return (1 + c[1] * mw + c[2] * mw ** 2)/(1 + c[3] * mw + c[4] * mw ** 2)
+
+def GetWaterVaporTransmittanceCoefficients(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]
+