sunposition.py

# The MIT License (MIT)
# 
# Copyright (c) 2016 Samuel Bear Powell
# 
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# 
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.

import numpy as np
from datetime import datetime

class _sp:
    @staticmethod
    def calendar_time(dt):
        try:
            x = dt.year, dt.month, dt.day, dt.hour, dt.minute, dt.second, dt.microsecond
            return x
        except AttributeError:
            try:
                return _sp.calendar_time(datetime.utcfromtimestamp(dt)) #will raise OSError if dt is not acceptable
            except:
                raise TypeError('dt must be datetime object or POSIX timestamp')

    @staticmethod
    def julian_day(dt):
        """Calculate the Julian Day from a datetime.datetime object in UTC"""
        # year and month numbers
        yr, mo, dy, hr, mn, sc, us = _sp.calendar_time(dt)
        if mo <= 2:  # From paper: "if M = 1 or 2, then Y = Y - 1 and M = M + 12"
            mo += 12
            yr -= 1
        # day of the month with decimal time
        dy = dy + hr/24.0 + mn/(24.0*60.0) + sc/(24.0*60.0*60.0) + us/(24.0*60.0*60.0*1e6)
        # b is equal to 0 for the julian calendar and is equal to (2- A +
        # INT(A/4)), A = INT(Y/100), for the gregorian calendar
        a = int(yr / 100)
        b = 2 - a + int(a / 4)
        jd = int(365.25 * (yr + 4716)) + int(30.6001 * (mo + 1)) + dy + b - 1524.5
        return jd

    @staticmethod
    def julian_ephemeris_day(jd, deltat):
        """Calculate the Julian Ephemeris Day from the Julian Day and delta-time = (terrestrial time - universal time) in seconds"""
        return jd + deltat / 86400.0

    @staticmethod
    def julian_century(jd):
        """Caluclate the Julian Century from Julian Day or Julian Ephemeris Day"""
        return (jd - 2451545.0) / 36525.0

    @staticmethod
    def julian_millennium(jc):
        """Calculate the Julian Millennium from Julian Ephemeris Century"""
        return jc / 10.0

    # Earth Periodic Terms
    # Earth Heliocentric Longitude coefficients (L0, L1, L2, L3, L4, and L5 in paper)
    _EHL_ = [#L0:
                [(175347046, 0.0, 0.0), (3341656, 4.6692568, 6283.07585), (34894, 4.6261, 12566.1517),
                (3497, 2.7441, 5753.3849), (3418, 2.8289, 3.5231), (3136, 3.6277, 77713.7715),
                (2676, 4.4181, 7860.4194), (2343, 6.1352, 3930.2097), (1324, 0.7425, 11506.7698),
                (1273, 2.0371, 529.691), (1199, 1.1096, 1577.3435), (990, 5.233, 5884.927),
                (902, 2.045, 26.298), (857, 3.508, 398.149), (780, 1.179, 5223.694),
                (753, 2.533, 5507.553), (505, 4.583, 18849.228), (492, 4.205, 775.523),
                (357, 2.92, 0.067), (317, 5.849, 11790.629), (284, 1.899, 796.298),
                (271, 0.315, 10977.079), (243, 0.345, 5486.778), (206, 4.806, 2544.314),
                (205, 1.869, 5573.143), (202, 2.4458, 6069.777), (156, 0.833, 213.299),
                (132, 3.411, 2942.463), (126, 1.083, 20.775), (115, 0.645, 0.98),
                (103, 0.636, 4694.003), (102, 0.976, 15720.839), (102, 4.267, 7.114),
                (99, 6.21, 2146.17), (98, 0.68, 155.42), (86, 5.98, 161000.69),
                (85, 1.3, 6275.96), (85, 3.67, 71430.7), (80, 1.81, 17260.15),
                (79, 3.04, 12036.46), (71, 1.76, 5088.63), (74, 3.5, 3154.69),
                (74, 4.68, 801.82), (70, 0.83, 9437.76), (62, 3.98, 8827.39),
                (61, 1.82, 7084.9), (57, 2.78, 6286.6), (56, 4.39, 14143.5),
                (56, 3.47, 6279.55), (52, 0.19, 12139.55), (52, 1.33, 1748.02),
                (51, 0.28, 5856.48), (49, 0.49, 1194.45), (41, 5.37, 8429.24),
                (41, 2.4, 19651.05), (39, 6.17, 10447.39), (37, 6.04, 10213.29),
                (37, 2.57, 1059.38), (36, 1.71, 2352.87), (36, 1.78, 6812.77),
                (33, 0.59, 17789.85), (30, 0.44, 83996.85), (30, 2.74, 1349.87),
                (25, 3.16, 4690.48)],
            #L1:
                [(628331966747, 0.0, 0.0), (206059, 2.678235, 6283.07585), (4303, 2.6351, 12566.1517),
                (425, 1.59, 3.523), (119, 5.796, 26.298), (109, 2.966, 1577.344),
                (93, 2.59, 18849.23), (72, 1.14, 529.69), (68, 1.87, 398.15),
                (67, 4.41, 5507.55), (59, 2.89, 5223.69), (56, 2.17, 155.42),
                (45, 0.4, 796.3), (36, 0.47, 775.52), (29, 2.65, 7.11),
                (21, 5.34, 0.98), (19, 1.85, 5486.78), (19, 4.97, 213.3),
                (17, 2.99, 6275.96), (16, 0.03, 2544.31), (16, 1.43, 2146.17),
                (15, 1.21, 10977.08), (12, 2.83, 1748.02), (12, 3.26, 5088.63),
                (12, 5.27, 1194.45), (12, 2.08, 4694), (11, 0.77, 553.57),
                (10, 1.3, 3286.6), (10, 4.24, 1349.87), (9, 2.7, 242.73),
                (9, 5.64, 951.72), (8, 5.3, 2352.87), (6, 2.65, 9437.76),
                (6, 4.67, 4690.48)],
            #L2:
                [(52919, 0.0, 0.0), (8720, 1.0721, 6283.0758), (309, 0.867, 12566.152),
                (27, 0.05, 3.52), (16, 5.19, 26.3), (16, 3.68, 155.42),
                (10, 0.76, 18849.23), (9, 2.06, 77713.77), (7, 0.83, 775.52),
                (5, 4.66, 1577.34), (4, 1.03, 7.11), (4, 3.44, 5573.14),
                (3, 5.14, 796.3), (3, 6.05, 5507.55), (3, 1.19, 242.73),
                (3, 6.12, 529.69), (3, 0.31, 398.15), (3, 2.28, 553.57),
                (2, 4.38, 5223.69), (2, 3.75, 0.98)],
            #L3:
                [(289, 5.844, 6283.076), (35, 0.0, 0.0,), (17, 5.49, 12566.15),
                (3, 5.2, 155.42), (1, 4.72, 3.52), (1, 5.3, 18849.23),
                (1, 5.97, 242.73)],
            #L4:
               [(114, 3.142, 0.0), (8, 4.13, 6283.08), (1, 3.84, 12566.15)],
            #L5:
               [(1, 3.14, 0.0)]
            ]

    #Earth Heliocentric Longitude coefficients (B0 and B1 in paper)
    _EHB_ = [ #B0:
                [(280, 3.199, 84334.662), (102, 5.422, 5507.553), (80, 3.88, 5223.69),
                (44, 3.7, 2352.87), (32, 4.0, 1577.34)],
            #B1:
                [(9, 3.9, 5507.55), (6, 1.73, 5223.69)]
            ]

    #Earth Heliocentric Radius coefficients (R0, R1, R2, R3, R4)
    _EHR_ = [#R0:
                [(100013989, 0.0, 0.0), (1670700, 3.0984635, 6283.07585), (13956, 3.05525, 12566.1517),
                (3084, 5.1985, 77713.7715), (1628, 1.1739, 5753.3849), (1576, 2.8469, 7860.4194),
                (925, 5.453, 11506.77), (542, 4.564, 3930.21), (472, 3.661, 5884.927),
                (346, 0.964, 5507.553), (329, 5.9, 5223.694), (307, 0.299, 5573.143),
                (243, 4.273, 11790.629), (212, 5.847, 1577.344), (186, 5.022, 10977.079),
                (175, 3.012, 18849.228), (110, 5.055, 5486.778), (98, 0.89, 6069.78),
                (86, 5.69, 15720.84), (86, 1.27, 161000.69), (85, 0.27, 17260.15),
                (63, 0.92, 529.69), (57, 2.01, 83996.85), (56, 5.24, 71430.7),
                (49, 3.25, 2544.31), (47, 2.58, 775.52), (45, 5.54, 9437.76),
                (43, 6.01, 6275.96), (39, 5.36, 4694), (38, 2.39, 8827.39),
                (37, 0.83, 19651.05), (37, 4.9, 12139.55), (36, 1.67, 12036.46),
                (35, 1.84, 2942.46), (33, 0.24, 7084.9), (32, 0.18, 5088.63),
                (32, 1.78, 398.15), (28, 1.21, 6286.6), (28, 1.9, 6279.55),
                (26, 4.59, 10447.39)],
            #R1:
                [(103019, 1.10749, 6283.07585), (1721, 1.0644, 12566.1517), (702, 3.142, 0.0),
                (32, 1.02, 18849.23), (31, 2.84, 5507.55), (25, 1.32, 5223.69),
                (18, 1.42, 1577.34), (10, 5.91, 10977.08), (9, 1.42, 6275.96),
                (9, 0.27, 5486.78)],
            #R2:
                [(4359, 5.7846, 6283.0758), (124, 5.579, 12566.152), (12, 3.14, 0.0),
                (9, 3.63, 77713.77), (6, 1.87, 5573.14), (3, 5.47, 18849)],
            #R3:
                [(145, 4.273, 6283.076), (7, 3.92, 12566.15)],
            #R4:
                [(4, 2.56, 6283.08)]
            ]

    @staticmethod
    def heliocentric_longitude(jme):
        """Compute the Earth Heliocentric Longitude (L) in degrees given the Julian Ephemeris Millennium"""
        #L5, ..., L0
        Li = [sum(a*np.cos(b + c*jme) for a,b,c in abcs) for abcs in reversed(_sp._EHL_)]
        L = np.polyval(Li, jme) / 1e8
        L = np.rad2deg(L) % 360
        return L
    @staticmethod
    def heliocentric_latitude(jme):
        """Compute the Earth Heliocentric Latitude (B) in degrees given the Julian Ephemeris Millennium"""
        Bi = [sum(a*np.cos(b + c*jme) for a,b,c in abcs) for abcs in reversed(_sp._EHB_)]
        B = np.polyval(Bi, jme) / 1e8
        B = np.rad2deg(B) % 360
        return B
    @staticmethod
    def heliocentric_radius(jme):
        """Compute the Earth Heliocentric Radius (R) in astronimical units given the Julian Ephemeris Millennium"""
        Ri = [sum(a*np.cos(b + c*jme) for a,b,c in abcs) for abcs in reversed(_sp._EHR_)]
        R = np.polyval(Ri, jme) / 1e8
        return R
    @staticmethod
    def heliocentric_position(jme):
        """Compute the Earth Heliocentric Longitude, Latitude, and Radius given the Julian Ephemeris Millennium
            Returns (L, B, R) where L = longitude in degrees, B = latitude in degrees, and R = radius in astronimical units
        """
        return _sp.heliocentric_longitude(jme), _sp.heliocentric_latitude(jme), _sp.heliocentric_radius(jme)
    @staticmethod
    def geocentric_position(helio_pos):
        """Compute the geocentric latitude (Theta) and longitude (beta) (in degrees) of the sun given the earth's heliocentric position (L, B, R)"""
        L,B,R = helio_pos
        th = L + 180
        b = -B
        return (th, b)

    #Nutation Longitude and Obliquity coefficients (Y)
    _NLOY_ = [(0,   0,   0,   0,   1), (-2,  0,   0,   2,   2), (0,   0,   0,   2,   2),
              (0,   0,   0,   0,   2), (0,   1,   0,   0,   0), (0,   0,   1,   0,   0),
              (-2,  1,   0,   2,   2), (0,   0,   0,   2,   1), (0,   0,   1,   2,   2),
              (-2,  -1,  0,   2,   2), (-2,  0,   1,   0,   0), (-2,  0,   0,   2,   1),
              (0,   0,   -1,  2,   2), (2,   0,   0,   0,   0), (0,   0,   1,   0,   1),
              (2,   0,   -1,  2,   2), (0,   0,   -1,  0,   1), (0,   0,   1,   2,   1),
              (-2,  0,   2,   0,   0), (0,   0,   -2,  2,   1), (2,   0,   0,   2,   2),
              (0,   0,   2,   2,   2), (0,   0,   2,   0,   0), (-2,  0,   1,   2,   2),
              (0,   0,   0,   2,   0), (-2,  0,   0,   2,   0), (0,   0,   -1,  2,   1),
              (0,   2,   0,   0,   0), (2,   0,   -1,  0,   1), (-2,  2,   0,   2,   2),
              (0,   1,   0,   0,   1), (-2,  0,   1,   0,   1), (0,   -1,  0,   0,   1),
              (0,   0,   2,   -2,  0), (2,   0,   -1,  2,   1), (2,   0,   1,   2,   2),
              (0,   1,   0,   2,   2), (-2,  1,   1,   0,   0), (0,   -1,  0,   2,   2),
              (2,   0,   0,   2,   1), (2,   0,   1,   0,   0), (-2,  0,   2,   2,   2),
              (-2,  0,   1,   2,   1), (2,   0,   -2,  0,   1), (2,   0,   0,   0,   1),
              (0,   -1,  1,   0,   0), (-2,  -1,  0,   2,   1), (-2,  0,   0,   0,   1),
              (0,   0,   2,   2,   1), (-2,  0,   2,   0,   1), (-2,  1,   0,   2,   1),
              (0,   0,   1,   -2,  0), (-1,  0,   1,   0,   0), (-2,  1,   0,   0,   0),
              (1,   0,   0,   0,   0), (0,   0,   1,   2,   0), (0,   0,   -2,  2,   2),
              (-1,  -1,  1,   0,   0), (0,   1,   1,   0,   0), (0,   -1,  1,   2,   2),
              (2,   -1,  -1,  2,   2), (0,   0,   3,   2,   2), (2,   -1,  0,   2,   2)]
    #Nutation Longitude and Obliquity coefficients (a,b)
    _NLOab_ = [(-171996, -174.2), (-13187, -1.6), (-2274, -0.2), (2062, 0.2), (1426, -3.4), (712, 0.1),
               (-517, 1.2), (-386, -0.4), (-301, 0), (217, -0.5), (-158, 0), (129, 0.1),
               (123, 0), (63,  0), (63,  0.1), (-59, 0), (-58, -0.1), (-51, 0),
               (48,  0), (46,  0), (-38, 0), (-31, 0), (29,  0), (29,  0),
               (26,  0), (-22, 0), (21,  0), (17,  -0.1), (16,  0), (-16, 0.1),
               (-15, 0), (-13, 0), (-12, 0), (11,  0), (-10, 0), (-8,  0),
               (7,   0), (-7,  0), (-7,  0), (-7,  0), (6,   0), (6,   0),
               (6,   0), (-6,  0), (-6,  0), (5,   0), (-5,  0), (-5,  0),
               (-5,  0), (4,   0), (4,   0), (4,   0), (-4,  0), (-4,  0),
               (-4,  0), (3,   0), (-3,  0), (-3,  0), (-3,  0), (-3,  0),
               (-3,  0), (-3,  0), (-3,  0)]
    #Nutation Longitude and Obliquity coefficients (c,d)
    _NLOcd_ = [(92025,   8.9), (5736,    -3.1), (977, -0.5), (-895,    0.5),
               (54,  -0.1), (-7,  0), (224, -0.6), (200, 0),
               (129, -0.1), (-95, 0.3), (0,   0), (-70, 0),
               (-53, 0), (0,   0), (-33, 0), (26,  0),
               (32,  0), (27,  0), (0,   0), (-24, 0),
               (16,  0), (13,  0), (0,   0), (-12, 0),
               (0,   0), (0,   0), (-10, 0), (0,   0),
               (-8,  0), (7,   0), (9,   0), (7,   0),
               (6,   0), (0,   0), (5,   0), (3,   0),
               (-3,  0), (0,   0), (3,   0), (3,   0),
               (0,   0), (-3,  0), (-3,  0), (3,   0),
               (3,   0), (0,   0), (3,   0), (3,   0),
               (3,   0)]

    @staticmethod
    def ecliptic_obliquity(jme, delta_epsilon):
        """Calculate the true obliquity of the ecliptic (epsilon, in degrees) given the Julian Ephemeris Millennium and the obliquity"""
        u = jme/10
        e0 = np.polyval([2.45, 5.79, 27.87, 7.12, -39.05, -249.67, -51.38, 1999.25, -1.55, -4680.93, 84381.448], u)
        e = e0/3600.0 + delta_epsilon
        return e

    @staticmethod
    def nutation_obliquity(jce):
        """compute the nutation in longitude (delta_psi) and the true obliquity (epsilon) given the Julian Ephemeris Century"""
        
        #mean elongation of the moon from the sun, in radians:
        #x0 = 297.85036 + 445267.111480*jce - 0.0019142*(jce**2) + (jce**3)/189474
        x0 = np.deg2rad(np.polyval([1./189474, -0.0019142, 445267.111480, 297.85036],jce))
        #mean anomaly of the sun (Earth), in radians:
        x1 = np.deg2rad(np.polyval([-1/3e5, -0.0001603, 35999.050340, 357.52772], jce))
        #mean anomaly of the moon, in radians:
        x2 = np.deg2rad(np.polyval([1./56250, 0.0086972, 477198.867398, 134.96298], jce))
        #moon's argument of latitude, in radians:
        x3 = np.deg2rad(np.polyval([1./327270, -0.0036825, 483202.017538, 93.27191], jce))
        #Longitude of the ascending node of the moon's mean orbit on the ecliptic
        # measured from the mean equinox of the date, in radians
        x4 = np.deg2rad(np.polyval([1./45e4, 0.0020708, -1934.136261, 125.04452], jce))

        x = (x0, x1, x2, x3, x4)

        dp = 0.0
        for y, ab in zip(_sp._NLOY_, _sp._NLOab_):
            a,b = ab
            dp += (a + b*jce)*np.sin(np.dot(x, y))
        dp = np.rad2deg(dp)/36e6

        de = 0.0
        for y, cd in zip(_sp._NLOY_, _sp._NLOcd_):
            c,d = cd
            de += (c + d*jce)*np.cos(np.dot(x, y))
        de = np.rad2deg(de)/36e6

        e = _sp.ecliptic_obliquity(_sp.julian_millennium(jce), de)

        return dp, e
    
    @staticmethod
    def abberation_correction(R):
        """Calculate the abberation correction (delta_tau, in degrees) given the Earth Heliocentric Radius (in AU)"""
        return -20.4898/(3600*R)
    
    @staticmethod
    def sun_longitude(helio_pos, delta_psi):
        """Calculate the apparent sun longitude (lambda, in degrees) and geocentric longitude (beta, in degrees) given the earth heliocentric position and delta_psi"""
        L,B,R = helio_pos
        theta = L + 180 #geocentric latitude
        beta = -B
        ll = theta + delta_psi + _sp.abberation_correction(R)
        return ll, beta
    
    @staticmethod
    def greenwich_sidereal_time(jd, delta_psi, epsilon):
        """Calculate the apparent Greenwich sidereal time (v, in degrees) given the Julian Day"""
        jc = _sp.julian_century(jd)
        #mean sidereal time at greenwich, in degrees:
        v0 = (280.46061837 + 360.98564736629*(jd - 2451545) + 0.000387933*(jc**2) - (jc**3)/38710000) % 360
        v = v0 + delta_psi*np.cos(np.deg2rad(epsilon))
        return v
    
    @staticmethod
    def sun_ra_decl(llambda, epsilon, beta):
        """Calculate the sun's geocentric right ascension (alpha, in degrees) and declination (delta, in degrees)"""
        l, e, b = map(np.deg2rad, (llambda, epsilon, beta))
        alpha = np.arctan2(np.sin(l)*np.cos(e) - np.tan(b)*np.sin(e), np.cos(l)) #x1 / x2
        alpha = np.rad2deg(alpha) % 360
        delta = np.arcsin(np.sin(b)*np.cos(e) + np.cos(b)*np.sin(e)*np.sin(l))
        delta = np.rad2deg(delta)
        return alpha, delta
    
    @staticmethod
    def sun_topo_ra_decl_hour(latitude, longitude, elevation, jd, delta_t = 0):
        """Calculate the sun's topocentric right ascension (alpha'), declination (delta'), and hour angle (H')"""
        
        jde = _sp.julian_ephemeris_day(jd, delta_t)
        jce = _sp.julian_century(jde)
        jme = _sp.julian_millennium(jce)

        helio_pos = _sp.heliocentric_position(jme)
        R = helio_pos[-1]
        phi, sigma, E = latitude, longitude, elevation
        #equatorial horizontal parallax of the sun, in radians
        xi = np.deg2rad(8.794/(3600*R)) #
        #rho = distance from center of earth in units of the equatorial radius
        #phi-prime = geocentric latitude
        #NB: These equations look like their based on WGS-84, but are rounded slightly
        # The WGS-84 reference ellipsoid has major axis a = 6378137 m, and flattening factor 1/f = 298.257223563
        # minor axis b = a*(1-f) = 6356752.3142 = 0.996647189335*a
        u = np.arctan(0.99664719*np.tan(phi)) #
        x = np.cos(u) + E*np.cos(phi)/6378140 #rho sin(phi-prime)
        y = 0.99664719*np.sin(u) + E*np.sin(phi)/6378140 #rho cos(phi-prime)

        delta_psi, epsilon = _sp.nutation_obliquity(jce) #

        llambda, beta = _sp.sun_longitude(helio_pos, delta_psi) #
        
        alpha, delta = _sp.sun_ra_decl(llambda, epsilon, beta) #

        v = _sp.greenwich_sidereal_time(jd, delta_psi, epsilon) #

        H = v + longitude - alpha #
        Hr, dr = map(np.deg2rad,(H,delta))

        dar = np.arctan2(-x*np.sin(xi)*np.sin(Hr), np.cos(dr)-x*np.sin(xi)*np.cos(Hr))
        delta_alpha = np.rad2deg(dar) #
        
        alpha_prime = alpha + delta_alpha #
        delta_prime = np.rad2deg(np.arctan2((np.sin(dr) - y*np.sin(xi))*np.cos(dar), np.cos(dr) - y*np.sin(xi)*np.cos(Hr))) #
        H_prime = H - delta_alpha #

        return alpha_prime, delta_prime, H_prime
    
    @staticmethod
    def sun_topo_azimuth_zenith(latitude, delta_prime, H_prime, temperature=14.6, pressure=1013):
        """Compute the sun's topocentric azimuth and zenith angles
        azimuth is measured eastward from north, zenith from vertical
        temperature = average temperature in C (default is 14.6 = global average in 2013)
        pressure = average pressure in mBar (default 1013 = global average)
        """
        phi = np.deg2rad(latitude)
        dr, Hr = map(np.deg2rad,(delta_prime, H_prime))
        P, T = pressure, temperature
        e0 = np.rad2deg(np.arcsin(np.sin(phi)*np.sin(dr) + np.cos(phi)*np.cos(dr)*np.cos(Hr)))
        tmp = np.deg2rad(e0 + 10.3/(e0+5.11))
        delta_e = (P/1010.0)*(283.0/(273+T))*(1.02/(60*np.tan(tmp)))
        e = e0 + delta_e
        zenith = 90 - e

        gamma = np.rad2deg(np.arctan2(np.sin(Hr), np.cos(Hr)*np.sin(phi) - np.tan(dr)*np.cos(phi))) % 360
        Phi = (gamma + 180) % 360 #azimuth from north
        return Phi, zenith

    @staticmethod
    def norm_lat_lon(lat,lon):
        if lat < -90 or lat > 90:
            #convert to cartesian and back
            x = np.cos(np.deg2rad(lon))*np.cos(np.deg2rad(lat))
            y = np.sin(np.deg2rad(lon))*np.cos(np.deg2rad(lat))
            z = np.sin(np.deg2rad(lat))
            r = np.sqrt(x**2 + y**2 + z**2)
            lon = np.rad2deg(np.arctan2(y,x)) % 360
            lat = np.rad2deg(np.arcsin(z/r))
        elif lon < 0 or lon > 360:
            lon = lon % 360
        return lat,lon

    @staticmethod
    def topo_pos(t,lat,lon,elev,temp,press,dt):
        """compute RA,dec,H, all in degrees"""
        lat,lon = _sp.norm_lat_lon(lat,lon)
        jd = _sp.julian_day(t)
        RA, dec, H = _sp.sun_topo_ra_decl_hour(lat, lon, elev, jd, dt)
        return RA, dec, H

    @staticmethod
    def pos(t,lat,lon,elev,temp,press,dt):
        """Compute azimute,zenith,RA,dec,H all in degrees"""
        lat,lon = _sp.norm_lat_lon(lat,lon)
        jd = _sp.julian_day(t)
        RA, dec, H = _sp.sun_topo_ra_decl_hour(lat, lon, elev, jd, dt)
        azimuth, zenith = _sp.sun_topo_azimuth_zenith(lat, dec, H, temp, press)
        return azimuth,zenith,RA,dec,H

def julian_day(dt):
    """Convert UTC datetimes or UTC timestamps to Julian days

    Parameters
    ----------
    dt : array_like
        UTC datetime objects or UTC timestamps (as per datetime.utcfromtimestamp)

    Returns
    -------
    jd : ndarray
        datetimes converted to fractional Julian days
    """
    dts = np.array(dt)
    if len(dts.shape) == 0:
        return _sp.julian_day(dt)

    jds = np.empty(dts.shape)
    for i,d in enumerate(dts.flat):
        jds.flat[i] = _sp.julian_day(d)
    return jds

def arcdist(p0,p1,radians=False):
    """Angular distance between azimuth,zenith pairs
    
    Parameters
    ----------
    p0 : array_like, shape (..., 2)
    p1 : array_like, shape (..., 2)
        p[...,0] = azimuth angles, p[...,1] = zenith angles
    radians : boolean (default False)
        If False, angles are in degrees, otherwise in radians

    Returns
    -------
    ad :  array_like, shape is broadcast(p0,p1).shape
        Arcdistances between corresponding pairs in p0,p1
        In degrees by default, in radians if radians=True
    """
    #formula comes from translating points into cartesian coordinates
    #taking the dot product to get the cosine between the two vectors
    #then arccos to return to angle, and simplify everything assuming real inputs
    p0,p1 = np.array(p0), np.array(p1)
    if not radians:
        p0,p1 = np.deg2rad(p0), np.deg2rad(p1)
    a0,z0 = p0[...,0], p0[...,1]
    a1,z1 = p1[...,0], p1[...,1]
    d = np.arccos(np.cos(z0)*np.cos(z1)+np.cos(a0-a1)*np.sin(z0)*np.sin(z1))
    if radians:
        return d
    else:
        return np.rad2deg(d)

def observed_sunpos(dt, latitude, longitude, elevation, temperature=None, pressure=None, delta_t=0, radians=False):
    """Compute the observed coordinates of the sun as viewed at the given time and location.

    Parameters
    ----------
    dt : array_like
        UTC datetime objects or UTC timestamps (as per datetime.utcfromtimestamp) representing the times of observations
    latitude, longitude : float
        decimal degrees, positive for north of the equator and east of Greenwich
    elevation : float
        meters, relative to the WGS-84 ellipsoid
    temperature : array_like or None, optional
        celcius, default is 14.6 (global average in 2013)
    pressure : array_like or None, optional
        millibar, default is 1013 (global average in ??)
    delta_t : array_like, optional
        seconds, default is 0, difference between the earth's rotation time (TT) and universal time (UT)
    radians : {True, False}, optional
        return results in radians if True, degrees if False (default)

    Returns
    -------
    coords : ndarray, (...,2)
        The shape of the array is parameters broadcast together, plus a final dimension for the coordinates.
        coords[...,0] = observed azimuth angle, measured eastward from north
        coords[...,1] = observed zenith angle, measured down from vertical
    """
    if temperature is None:
        temperature = 14.6
    if pressure is None:
        pressure = 1013
    
    #6367444 = radius of earth
    #numpy broadcasting
    b = np.broadcast(dt,latitude,longitude,elevation,temperature,pressure,delta_t)
    res = np.empty(b.shape+(2,))
    res_vec = res.reshape((-1,2))
    for i,x in enumerate(b):
        res_vec[i] = _sp.pos(*x)[:2]
    if radians:
        res = np.deg2rad(res)
    return res

def topocentric_sunpos(dt, latitude, longitude, temperature=None, pressure=None, delta_t=0, radians=False):
    """Compute the topocentric coordinates of the sun as viewed at the given time and location.

    Parameters
    ----------
    dt : array_like
        UTC datetime objects or UTC timestamps (as per datetime.utcfromtimestamp) representing the times of observations
    latitude, longitude : array_like
        decimal degrees, positive for north of the equator and east of Greenwich
    elevation : array_like
        meters, relative to the WGS-84 ellipsoid
    temperature : array_like or None, optional
        celcius, default is 14.6 (global average in 2013)
    pressure : array_like or None, optional
        millibar, default is 1013 (global average in ??)
    delta_t : array_like, optional
        seconds, default is 0, difference between the earth's rotation time (TT) and universal time (UT)
    radians : {True, False}, optional
        return results in radians if True, degrees if False (default)

    Returns
    -------
    coords : ndarray, (...,3)
        The shape of the array is parameters broadcast together, plus a final dimension for the coordinates.
        coords[...,0] = topocentric right ascension
        coords[...,1] = topocentric declination
        coords[...,2] = topocentric hour angle
    """
    if temperature is None:
        temperature = 14.6
    if pressure is None:
        pressure = 1013
    
    #6367444 = radius of earth
    #numpy broadcasting
    b = np.broadcast(dt,latitude,longitude,elevation,temperature,pressure,delta_t)
    res = np.empty(b.shape+(2,))
    res_vec = res.reshape((-1,2))
    for i,x in enumerate(b):
        res_vec[i] = _sp.topo_pos(*x)
    if radians:
        res = np.deg2rad(res)
    return res   

def sunpos(dt, latitude, longitude, elevation, temperature=None, pressure=None, delta_t=0, radians=False):
    """Compute the observed and topocentric coordinates of the sun as viewed at the given time and location.

    Parameters
    ----------
    dt : array_like
        UTC datetime objects or UTC timestamps (as per datetime.utcfromtimestamp) representing the times of observations
    latitude, longitude : array_like
        decimal degrees, positive for north of the equator and east of Greenwich
    elevation : array_like
        meters, relative to the WGS-84 ellipsoid
    temperature : array_like or None, optional
        celcius, default is 14.6 (global average in 2013)
    pressure : array_like or None, optional
        millibar, default is 1013 (global average in ??)
    delta_t : array_like, optional
        seconds, default is 0, difference between the earth's rotation time (TT) and universal time (UT)
    radians : {True, False}, optional
        return results in radians if True, degrees if False (default)

    Returns
    -------
    coords : ndarray, (...,5)
        The shape of the array is parameters broadcast together, plus a final dimension for the coordinates.
        coords[...,0] = observed azimuth angle, measured eastward from north
        coords[...,1] = observed zenith angle, measured down from vertical
        coords[...,2] = topocentric right ascension
        coords[...,3] = topocentric declination
        coords[...,4] = topocentric hour angle
    """

    if temperature is None:
        temperature = 14.6
    if pressure is None:
        pressure = 1013
    
    #6367444 = radius of earth
    #numpy broadcasting
    b = np.broadcast(dt,latitude,longitude,elevation,temperature,pressure,delta_t)
    res = np.empty(b.shape+(5,))
    res_vec = res.reshape((-1,5))
    for i,x in enumerate(b):
        res_vec[i] = _sp.pos(*x)
    if radians:
        res = np.deg2rad(res)
    return res

def main(args):
    az, zen, ra, dec, h = sunpos(args.t, args.lat, args.lon, args.elev, args.temp, args.p, args.dt, args.rad)
    if args.csv:
        #machine readable
        print('{t}, {dt}, {lat}, {lon}, {elev}, {temp}, {p}, {az}, {zen}, {ra}, {dec}, {h}'.format(t=args.t, dt=args.dt, lat=args.lat, lon=args.lon, elev=args.elev,temp=args.temp, p=args.p,az=az, zen=zen, ra=ra, dec=dec, h=h))
    else:
        dr='deg'
        if args.rad:
            dr='rad'
        print("Computing sun position at T = {t} + {dt} s".format(t=args.t, dt=args.dt))
        print("Lat, Lon, Elev = {lat} deg, {lon} deg, {elev} m".format(lat=args.lat, lon=args.lon, elev=args.elev))
        print("T, P = {temp} C, {press} mbar".format(temp=args.temp, press=args.p))
        print("Results:")
        print("Azimuth, zenith = {az} {dr}, {zen} {dr}".format(az=az,zen=zen,dr=dr))
        print("RA, dec, H = {ra} {dr}, {dec} {dr}, {h} {dr}".format(ra=ra, dec=dec, h=h, dr=dr))

if __name__ == '__main__':
    from argparse import ArgumentParser
    import datetime, sys
    parser = ArgumentParser(prog='sunposition',description='Compute sun position parameters given the time and location')
    parser.add_argument('--version',action='version',version='%(prog)s 1.0')
    parser.add_argument('--citation',dest='cite',action='store_true',help='Print citation information')
    parser.add_argument('-t,--time',dest='t',type=str,default='now',help='"now" or date and time (UTC) in "YYYY-MM-DD hh:mm:ss.ssssss" format or a (UTC) POSIX timestamp')
    parser.add_argument('-lat,--latitude',dest='lat',type=float,default=51.48,help='latitude, in decimal degrees, positive for north')
    parser.add_argument('-lon,--longitude',dest='lon',type=float,default=0.0,help='longitude, in decimal degrees, positive for east')
    parser.add_argument('-e,--elevation',dest='elev',type=float,default=0,help='elevation, in meters')
    parser.add_argument('-T,--temperature',dest='temp',type=float,default=14.6,help='temperature, in degrees celcius')
    parser.add_argument('-p,--pressure',dest='p',type=float,default=1013.0,help='atmospheric pressure, in millibar')
    parser.add_argument('-dt',type=float,default=0.0,help='difference between earth\'s rotation time (TT) and universal time (UT1)')
    parser.add_argument('-r,--radians',dest='rad',action='store_true',help='Output in radians instead of degrees')
    parser.add_argument('--csv',dest='csv',action='store_true',help='Comma separated values (time,dt,lat,lon,elev,temp,pressure,az,zen,RA,dec,H)')
    args = parser.parse_args()
    if args.cite:
        print("Implementation: Samuel Bear Powell, 2016")
        print("Algorithm:")
        print("Ibrahim Reda, Afshin Andreas, \"Solar position algorithm for solar radiation applications\", Solar Energy, Volume 76, Issue 5, 2004, Pages 577-589, ISSN 0038-092X, doi:10.1016/j.solener.2003.12.003")
        sys.exit(0)
    if args.t == "now":
        args.t = datetime.datetime.utcnow()
    elif ":" in args.t and "-" in args.t:
        try:
            args.t = datetime.datetime.strptime(args.t,'%Y-%m-%d %H:%M:%S.%f') #with microseconds
        except:
            try:
                args.t = datetime.datetime.strptime(args.t,'%Y-%m-%d %H:%M:%S.') #without microseconds
            except:
                args.t = datetime.datetime.strptime(args.t,'%Y-%m-%d %H:%M:%S')
    else:
        args.t = datetime.datetime.utcfromtimestamp(int(args.t))
    main(args)