#!/usr/bin/env python # -*- coding: iso-8859-1 -*- """ SUNRISET.C - computes Sun rise/set times, start/end of twilight, and the length of the day at any date and latitude Written as DAYLEN.C, 1989-08-16 Modified to SUNRISET.C, 1992-12-01 (c) Paul Schlyter, 1989, 1992 Released to the public domain by Paul Schlyter, December 1992 Direct conversion to Java Sean Russell Conversion to Python Class, 2002-03-21 Henrik Härkönen Solar Altitude added by Miguel Tremblay 2005-01-16 Solar flux, equation of time and import of python library added by Miguel Tremblay 2007-11-22 2007-12-12 - v1.5 by Miguel Tremblay: bug fix to solar flux calculation """ SUN_PY_VERSION = 1.5 import math from math import pi import calendar class Sun: def __init__(self): """""" # Some conversion factors between radians and degrees self.RADEG = 180.0 / pi self.DEGRAD = pi / 180.0 self.INV360 = 1.0 / 360.0 def daysSince2000Jan0(self, y, m, d): """A macro to compute the number of days elapsed since 2000 Jan 0.0 (which is equal to 1999 Dec 31, 0h UT)""" return (367*(y)-((7*((y)+(((m)+9)/12)))/4)+((275*(m))/9)+(d)-730530) # The trigonometric functions in degrees def sind(self, x): """Returns the sin in degrees""" return math.sin(x * self.DEGRAD) def cosd(self, x): """Returns the cos in degrees""" return math.cos(x * self.DEGRAD) def tand(self, x): """Returns the tan in degrees""" return math.tan(x * self.DEGRAD) def atand(self, x): """Returns the arc tan in degrees""" return math.atan(x) * self.RADEG def asind(self, x): """Returns the arc sin in degrees""" return math.asin(x) * self.RADEG def acosd(self, x): """Returns the arc cos in degrees""" return math.acos(x) * self.RADEG def atan2d(self, y, x): """Returns the atan2 in degrees""" return math.atan2(y, x) * self.RADEG # Following are some macros around the "workhorse" function __daylen__ # They mainly fill in the desired values for the reference altitude # below the horizon, and also selects whether this altitude should # refer to the Sun's center or its upper limb. def dayLength(self, year, month, day, lon, lat): """ This macro computes the length of the day, from sunrise to sunset. Sunrise/set is considered to occur when the Sun's upper limb is 35 arc minutes below the horizon (this accounts for the refraction of the Earth's atmosphere). """ return self.__daylen__(year, month, day, lon, lat, -35.0/60.0, 1) def dayCivilTwilightLength(self, year, month, day, lon, lat): """ This macro computes the length of the day, including civil twilight. Civil twilight starts/ends when the Sun's center is 6 degrees below the horizon. """ return self.__daylen__(year, month, day, lon, lat, -6.0, 0) def dayNauticalTwilightLength(self, year, month, day, lon, lat): """ This macro computes the length of the day, incl. nautical twilight. Nautical twilight starts/ends when the Sun's center is 12 degrees below the horizon. """ return self.__daylen__(year, month, day, lon, lat, -12.0, 0) def dayAstronomicalTwilightLength(self, year, month, day, lon, lat): """ This macro computes the length of the day, incl. astronomical twilight. Astronomical twilight starts/ends when the Sun's center is 18 degrees below the horizon. """ return self.__daylen__(year, month, day, lon, lat, -18.0, 0) def sunRiseSet(self, year, month, day, lon, lat): """ This macro computes times for sunrise/sunset. Sunrise/set is considered to occur when the Sun's upper limb is 35 arc minutes below the horizon (this accounts for the refraction of the Earth's atmosphere). """ return self.__sunriset__(year, month, day, lon, lat, -35.0/60.0, 1) def civilTwilight(self, year, month, day, lon, lat): """ This macro computes the start and end times of civil twilight. Civil twilight starts/ends when the Sun's center is 6 degrees below the horizon. """ return self.__sunriset__(year, month, day, lon, lat, -6.0, 0) def nauticalTwilight(self, year, month, day, lon, lat): """ This macro computes the start and end times of nautical twilight. Nautical twilight starts/ends when the Sun's center is 12 degrees below the horizon. """ return self.__sunriset__(year, month, day, lon, lat, -12.0, 0) def astronomicalTwilight(self, year, month, day, lon, lat): """ This macro computes the start and end times of astronomical twilight. Astronomical twilight starts/ends when the Sun's center is 18 degrees below the horizon. """ return self.__sunriset__(year, month, day, lon, lat, -18.0, 0) # The "workhorse" function for sun rise/set times def __sunriset__(self, year, month, day, lon, lat, altit, upper_limb): """ Note: year,month,date = calendar date, 1801-2099 only. Eastern longitude positive, Western longitude negative Northern latitude positive, Southern latitude negative The longitude value IS critical in this function! altit = the altitude which the Sun should cross Set to -35/60 degrees for rise/set, -6 degrees for civil, -12 degrees for nautical and -18 degrees for astronomical twilight. upper_limb: non-zero -> upper limb, zero -> center Set to non-zero (e.g. 1) when computing rise/set times, and to zero when computing start/end of twilight. *rise = where to store the rise time *set = where to store the set time Both times are relative to the specified altitude, and thus this function can be used to compute various twilight times, as well as rise/set times Return value: 0 = sun rises/sets this day, times stored at *trise and *tset. +1 = sun above the specified 'horizon' 24 hours. *trise set to time when the sun is at south, minus 12 hours while *tset is set to the south time plus 12 hours. 'Day' length = 24 hours -1 = sun is below the specified 'horizon' 24 hours 'Day' length = 0 hours, *trise and *tset are both set to the time when the sun is at south. """ # Compute d of 12h local mean solar time d = self.daysSince2000Jan0(year,month,day) + 0.5 - (lon/360.0) # Compute local sidereal time of this moment sidtime = self.revolution(self.GMST0(d) + 180.0 + lon) # Compute Sun's RA + Decl at this moment res = self.sunRADec(d) sRA = res[0] sdec = res[1] sr = res[2] # Compute time when Sun is at south - in hours UT tsouth = 12.0 - self.rev180(sidtime - sRA)/15.0; # Compute the Sun's apparent radius, degrees sradius = 0.2666 / sr; # Do correction to upper limb, if necessary if upper_limb: altit = altit - sradius # Compute the diurnal arc that the Sun traverses to reach # the specified altitude altit: cost = (self.sind(altit) - self.sind(lat) * self.sind(sdec))/\ (self.cosd(lat) * self.cosd(sdec)) if cost >= 1.0: rc = -1 t = 0.0 # Sun always below altit elif cost <= -1.0: rc = +1 t = 12.0; # Sun always above altit else: t = self.acosd(cost)/15.0 # The diurnal arc, hours # Store rise and set times - in hours UT return (tsouth-t, tsouth+t) def __daylen__(self, year, month, day, lon, lat, altit, upper_limb): """ Note: year,month,date = calendar date, 1801-2099 only. Eastern longitude positive, Western longitude negative Northern latitude positive, Southern latitude negative The longitude value is not critical. Set it to the correct longitude if you're picky, otherwise set to, say, 0.0 The latitude however IS critical - be sure to get it correct altit = the altitude which the Sun should cross Set to -35/60 degrees for rise/set, -6 degrees for civil, -12 degrees for nautical and -18 degrees for astronomical twilight. upper_limb: non-zero -> upper limb, zero -> center Set to non-zero (e.g. 1) when computing day length and to zero when computing day+twilight length. """ # Compute d of 12h local mean solar time d = self.daysSince2000Jan0(year,month,day) + 0.5 - (lon/360.0) # Compute obliquity of ecliptic (inclination of Earth's axis) obl_ecl = 23.4393 - 3.563E-7 * d # Compute Sun's position res = self.sunpos(d) slon = res[0] sr = res[1] # Compute sine and cosine of Sun's declination sin_sdecl = self.sind(obl_ecl) * self.sind(slon) cos_sdecl = math.sqrt(1.0 - sin_sdecl * sin_sdecl) # Compute the Sun's apparent radius, degrees sradius = 0.2666 / sr # Do correction to upper limb, if necessary if upper_limb: altit = altit - sradius cost = (self.sind(altit) - self.sind(lat) * sin_sdecl) / \ (self.cosd(lat) * cos_sdecl) if cost >= 1.0: t = 0.0 # Sun always below altit elif cost <= -1.0: t = 24.0 # Sun always above altit else: t = (2.0/15.0) * self.acosd(cost); # The diurnal arc, hours return t def sunpos(self, d): """ Computes the Sun's ecliptic longitude and distance at an instant given in d, number of days since 2000 Jan 0.0. The Sun's ecliptic latitude is not computed, since it's always very near 0. """ # Compute mean elements M = self.revolution(356.0470 + 0.9856002585 * d) w = 282.9404 + 4.70935E-5 * d e = 0.016709 - 1.151E-9 * d # Compute true longitude and radius vector E = M + e * self.RADEG * self.sind(M) * (1.0 + e * self.cosd(M)) x = self.cosd(E) - e y = math.sqrt(1.0 - e*e) * self.sind(E) r = math.sqrt(x*x + y*y) #Solar distance v = self.atan2d(y, x) # True anomaly lon = v + w # True solar longitude if lon >= 360.0: lon = lon - 360.0 # Make it 0..360 degrees return (lon,r) def sunRADec(self, d): """ Returns the angle of the Sun (RA) the declination (dec) and the distance of the Sun (r) for a given day d. """ # Compute Sun's ecliptical coordinates res = self.sunpos(d) lon = res[0] # True solar longitude r = res[1] # Solar distance # Compute ecliptic rectangular coordinates (z=0) x = r * self.cosd(lon) y = r * self.sind(lon) # Compute obliquity of ecliptic (inclination of Earth's axis) obl_ecl = 23.4393 - 3.563E-7 * d # Convert to equatorial rectangular coordinates - x is unchanged z = y * self.sind(obl_ecl) y = y * self.cosd(obl_ecl) # Convert to spherical coordinates RA = self.atan2d(y, x) dec = self.atan2d(z, math.sqrt(x*x + y*y)) return (RA, dec, r) def revolution(self, x): """ This function reduces any angle to within the first revolution by subtracting or adding even multiples of 360.0 until the result is >= 0.0 and < 360.0 Reduce angle to within 0..360 degrees """ return (x - 360.0 * math.floor(x * self.INV360)) def rev180(self, x): """ Reduce angle to within +180..+180 degrees """ return (x - 360.0 * math.floor(x * self.INV360 + 0.5)) def GMST0(self, d): """ This function computes GMST0, the Greenwich Mean Sidereal Time at 0h UT (i.e. the sidereal time at the Greenwhich meridian at 0h UT). GMST is then the sidereal time at Greenwich at any time of the day. I've generalized GMST0 as well, and define it as: GMST0 = GMST - UT -- this allows GMST0 to be computed at other times than 0h UT as well. While this sounds somewhat contradictory, it is very practical: instead of computing GMST like: GMST = (GMST0) + UT * (366.2422/365.2422) where (GMST0) is the GMST last time UT was 0 hours, one simply computes: GMST = GMST0 + UT where GMST0 is the GMST "at 0h UT" but at the current moment! Defined in this way, GMST0 will increase with about 4 min a day. It also happens that GMST0 (in degrees, 1 hr = 15 degr) is equal to the Sun's mean longitude plus/minus 180 degrees! (if we neglect aberration, which amounts to 20 seconds of arc or 1.33 seconds of time) """ # Sidtime at 0h UT = L (Sun's mean longitude) + 180.0 degr # L = M + w, as defined in sunpos(). Since I'm too lazy to # add these numbers, I'll let the C compiler do it for me. # Any decent C compiler will add the constants at compile # time, imposing no runtime or code overhead. sidtim0 = self.revolution((180.0 + 356.0470 + 282.9404) + (0.9856002585 + 4.70935E-5) * d) return sidtim0; def solar_altitude(self, latitude, year, month, day): """ Compute the altitude of the sun. No atmospherical refraction taken in account. Altitude of the southern hemisphere are given relative to true north. Altitude of the northern hemisphere are given relative to true south. Declination is between 23.5° North and 23.5° South depending on the period of the year. Source of formula for altitude is PhysicalGeography.net http://www.physicalgeography.net/fundamentals/6h.html """ # Compute declination N = self.daysSince2000Jan0(year, month, day) res = self.sunRADec(N) declination = res[1] sr = res[2] # Compute the altitude altitude = 90.0 - latitude + declination # In the tropical and in extreme latitude, values over 90 may occurs. if altitude > 90: altitude = 90 - (altitude-90) if altitude < 0: altitude = 0 return altitude def get_max_solar_flux(self, latitude, year, month, day): """ Compute the maximal solar flux to reach the ground for this date and latitude. Originaly comes from Environment Canada weather forecast model. Information was of the public domain before release by Environment Canada Output is in W/M^2. """ (fEot, fR0r, tDeclsc) = self.equation_of_time(year, month, day, latitude) fSF = (tDeclsc[0]+tDeclsc[1])*fR0r # In the case of a negative declinaison, solar flux is null if fSF < 0: fCoeff = 0 else: fCoeff = -1.56e-12*fSF**4 + 5.972e-9*fSF**3 -\ 8.364e-6*fSF**2 + 5.183e-3*fSF - 0.435 fSFT = fSF * fCoeff if fSFT < 0: fSFT=0 return fSFT def equation_of_time(self, year, month, day, latitude): """ Description: Subroutine computing the part of the equation of time needed in the computing of the theoritical solar flux Correction originating of the CMC GEM model. Parameters: int nTime : cTime for the correction of the time. Returns: tuple (double fEot, double fR0r, tuple tDeclsc) dEot: Correction for the equation of time dR0r: Corrected solar constant for the equation of time tDeclsc: Declinaison """ # Julian date nJulianDate = self.Julian(year, month, day) # Check if it is a leap year if(calendar.isleap(year)): fDivide = 366.0 else: fDivide = 365.0 # Correction for "equation of time" fA = nJulianDate/fDivide*2*pi fR0r = self.__Solcons(fA)*0.1367e4 fRdecl = 0.412*math.cos((nJulianDate+10.0)*2.0*pi/fDivide-pi) fDeclsc1 = self.sind(latitude)*math.sin(fRdecl) fDeclsc2 = self.cosd(latitude)*math.cos(fRdecl) tDeclsc = (fDeclsc1, fDeclsc2) # in minutes fEot = 0.002733 -7.343*math.sin(fA)+ .5519*math.cos(fA) \ - 9.47*math.sin(2.0*fA) - 3.02*math.cos(2.0*fA) \ - 0.3289*math.sin(3.*fA) -0.07581*math.cos(3.0*fA) \ -0.1935*math.sin(4.0*fA) -0.1245*math.cos(4.0*fA) # Express in fraction of hour fEot = fEot/60.0 # Express in radians fEot = fEot*15*pi/180.0 return (fEot, fR0r, tDeclsc) def __Solcons(self, dAlf): """ Name: __Solcons Parameters: [I] double dAlf : Solar constant to correct the excentricity Returns: double dVar : Variation of the solar constant Functions Called: cos, sin Description: Statement function that calculates the variation of the solar constant as a function of the julian day. (dAlf, in radians) Notes: Comes from the Revision History: Author Date Reason Miguel Tremblay June 30th 2004 """ dVar = 1.0/(1.0-9.464e-4*math.sin(dAlf)-0.01671*math.cos(dAlf)- \ + 1.489e-4*math.cos(2.0*dAlf)-2.917e-5*math.sin(3.0*dAlf)- \ + 3.438e-4*math.cos(4.0*dAlf))**2 return dVar def Julian(self, year, month, day): """ Return julian day. """ if calendar.isleap(year): # Bissextil year, 366 days lMonth = [0, 31, 60, 91, 121, 152, 182, 213, 244, 274, 305, 335, 366] else: # Normal year, 365 days lMonth = [0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334, 365] nJulian = lMonth[month-1] + day return nJulian if __name__ == "__main__": k = Sun() print k.get_max_solar_flux(46.2, 2004, 01, 30) # print k.sunRiseSet(2002, 3, 22, 25.42, 62.15)