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sun_position.py
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# -*- coding: utf-8 -*-
from __future__ import division
import datetime
import numpy as np
def sun_position(time, location):
"""
% sun = sun_position(time, location)
%
% This function compute the sun position (zenith and azimuth angle at the observer
% location) as a function of the observer local time and position.
%
% It is an implementation of the algorithm presented by Reda et Andreas in:
% Reda, I., Andreas, A. (2003) Solar position algorithm for solar
% radiation application. National Renewable Energy Laboratory (NREL)
% Technical report NREL/TP-560-34302.
% This document is avalaible at www.osti.gov/bridge
%
% This algorithm is based on numerical approximation of the exact equations.
% The authors of the original paper state that this algorithm should be
% precise at +/- 0.0003 degrees. I have compared it to NOAA solar table
% (http://www.srrb.noaa.gov/highlights/sunrise/azel.html) and to USNO solar
% table (http://aa.usno.navy.mil/data/docs/AltAz.html) and found very good
% correspondance (up to the precision of those tables), except for large
% zenith angle, where the refraction by the atmosphere is significant
% (difference of about 1 degree). Note that in this code the correction
% for refraction in the atmosphere as been implemented for a temperature
% of 10C (283 kelvins) and a pressure of 1010 mbar. See the subfunction
% �sun_topocentric_zenith_angle_calculation� for a possible modification
% to explicitely model the effect of temperature and pressure as describe
% in Reda & Andreas (2003).
%
% Input parameters:
% time: a structure that specify the time when the sun position is
% calculated.
% time.year: year. Valid for [-2000, 6000]
% time.month: month [1-12]
% time.day: calendar day [1-31]
% time.hour: local hour [0-23]
% time.min: minute [0-59]
% time.sec: second [0-59]
% time.UTC: offset hour from UTC. Local time = Greenwich time + time.UTC
% This input can also be passed using the Matlab time format ('dd-mmm-yyyy HH:MM:SS').
% In that case, the time has to be specified as UTC time (time.UTC = 0)
%
% location: a structure that specify the location of the observer
% location.latitude: latitude (in degrees, north of equator is
% positive)
% location.longitude: longitude (in degrees, positive for east of
% Greenwich)
% location.altitude: altitude above mean sea level (in meters)
%
% Output parameters
% sun: a structure with the calculated sun position
% sun.zenith = zenith angle in degrees (angle from the vertical)
% sun.azimuth = azimuth angle in degrees, eastward from the north.
% Only the sun zenith and azimuth angles are returned as output, but a lot
% of other parameters are calculated that could also extracted as output of
% this function.
%
% Exemple of use
%
% location.longitude = -105.1786;
% location.latitude = 39.742476;
% location.altitude = 1830.14;
% time.year = 2005;
% time.month = 10;
% time.day = 17;
% time.hour = 6;
% time.min = 30;
% time.sec = 30;
% time.UTC = -7;
% %
% location.longitude = 11.94;
% location.latitude = 57.70;
% location.altitude = 3.0;
% time.UTC = 1;
% sun = sun_position(time, location);
%
% sun =
%
% zenith: 50.1080438859849
% azimuth: 194.341174010338
%
% History
% 09/03/2004 Original creation by Vincent Roy (vincent.roy@drdc-rddc.gc.ca)
% 10/03/2004 Fixed a bug in julian_calculation subfunction (was
% incorrect for year 1582 only), Vincent Roy
% 18/03/2004 Correction to the header (help display) only. No changes to
% the code. (changed the �elevation� field in �location� structure
% information to �altitude�), Vincent Roy
% 13/04/2004 Following a suggestion from Jody Klymak (jklymak@ucsd.edu),
% allowed the 'time' input to be passed as a Matlab time string.
% 22/08/2005 Following a bug report from Bruce Bowler
% (bbowler@bigelow.org), modified the julian_calculation function. Bug
% was 'MATLAB has allowed structure assignment to a non-empty non-structure
% to overwrite the previous value. This behavior will continue in this release,
% but will be an error in a future version of MATLAB. For advice on how to
% write code that will both avoid this warning and work in future versions of
% MATLAB, see R14SP2 Release Notes'. Script should now be
% compliant with futher release of Matlab...
"""
# 1. Calculate the Julian Day, and Century. Julian Ephemeris day, century
# and millenium are calculated using a mean delta_t of 33.184 seconds.
julian = julian_calculation(time)
#print(julian)
# 2. Calculate the Earth heliocentric longitude, latitude, and radius
# vector (L, B, and R)
earth_heliocentric_position = earth_heliocentric_position_calculation(julian)
# 3. Calculate the geocentric longitude and latitude
sun_geocentric_position = sun_geocentric_position_calculation(earth_heliocentric_position)
# 4. Calculate the nutation in longitude and obliquity (in degrees).
nutation = nutation_calculation(julian)
# 5. Calculate the true obliquity of the ecliptic (in degrees).
true_obliquity = true_obliquity_calculation(julian, nutation)
# 6. Calculate the aberration correction (in degrees)
aberration_correction = abberation_correction_calculation(earth_heliocentric_position)
# 7. Calculate the apparent sun longitude in degrees)
apparent_sun_longitude = apparent_sun_longitude_calculation(sun_geocentric_position, nutation, aberration_correction)
# 8. Calculate the apparent sideral time at Greenwich (in degrees)
apparent_stime_at_greenwich = apparent_stime_at_greenwich_calculation(julian, nutation, true_obliquity)
# 9. Calculate the sun rigth ascension (in degrees)
sun_rigth_ascension = sun_rigth_ascension_calculation(apparent_sun_longitude, true_obliquity, sun_geocentric_position)
# 10. Calculate the geocentric sun declination (in degrees). Positive or
# negative if the sun is north or south of the celestial equator.
sun_geocentric_declination = sun_geocentric_declination_calculation(apparent_sun_longitude, true_obliquity,
sun_geocentric_position)
# 11. Calculate the observer local hour angle (in degrees, westward from south).
observer_local_hour = observer_local_hour_calculation(apparent_stime_at_greenwich, location, sun_rigth_ascension)
# 12. Calculate the topocentric sun position (rigth ascension, declination and
# rigth ascension parallax in degrees)
topocentric_sun_position = topocentric_sun_position_calculate(earth_heliocentric_position, location,
observer_local_hour, sun_rigth_ascension,
sun_geocentric_declination)
# 13. Calculate the topocentric local hour angle (in degrees)
topocentric_local_hour = topocentric_local_hour_calculate(observer_local_hour, topocentric_sun_position)
# 14. Calculate the topocentric zenith and azimuth angle (in degrees)
sun = sun_topocentric_zenith_angle_calculate(location, topocentric_sun_position, topocentric_local_hour)
return sun
def julian_calculation(t_input):
"""
% This function compute the julian day and julian century from the local
% time and timezone information. Ephemeris are calculated with a delta_t=0
% seconds.
% If time input is a Matlab time string, extract the information from
% this string and create the structure as defined in the main header of
% this script.
"""
if not isinstance(t_input, dict):
# tt = datetime.datetime.strptime(t_input, "%Y-%m-%d %H:%M:%S.%f") # if t_input is a string of this format
# t_input should be a datetime object
time = dict()
time['UTC'] = 0
time['year'] = t_input.year
time['month'] = t_input.month
time['day'] = t_input.day
time['hour'] = t_input.hour
time['min'] = t_input.minute
time['sec'] = t_input.second
else:
time = t_input
if time['month'] == 1 or time['month'] == 2:
Y = time['year'] - 1
M = time['month'] + 12
else:
Y = time['year']
M = time['month']
ut_time = ((time['hour'] - time['UTC'])/24) + (time['min']/(60*24)) + (time['sec']/(60*60*24)) # time of day in UT time.
D = time['day'] + ut_time # Day of month in decimal time, ex. 2sd day of month at 12:30:30UT, D=2.521180556
# In 1582, the gregorian calendar was adopted
if time['year'] == 1582:
if time['month'] == 10:
if time['day'] <= 4: # The Julian calendar ended on October 4, 1582
B = (0)
elif time['day'] >= 15: # The Gregorian calendar started on October 15, 1582
A = np.floor(Y/100)
B = 2 - A + np.floor(A/4)
else:
print('This date never existed!. Date automatically set to October 4, 1582')
time['month'] = 10
time['day'] = 4
B = 0
elif time['month'] < 10: # Julian calendar
B = 0
else: # Gregorian calendar
A = np.floor(Y/100)
B = 2 - A + np.floor(A/4)
elif time['year'] < 1582: # Julian calendar
B = 0
else:
A = np.floor(Y/100) # Gregorian calendar
B = 2 - A + np.floor(A/4)
julian = dict()
julian['day'] = D + B + np.floor(365.25*(Y+4716)) + np.floor(30.6001*(M+1)) - 1524.5
delta_t = 0 # 33.184;
julian['ephemeris_day'] = (julian['day']) + (delta_t/86400)
julian['century'] = (julian['day'] - 2451545) / 36525
julian['ephemeris_century'] = (julian['ephemeris_day'] - 2451545) / 36525
julian['ephemeris_millenium'] = (julian['ephemeris_century']) / 10
return julian
def earth_heliocentric_position_calculation(julian):
"""
% This function compute the earth position relative to the sun, using
% tabulated values.
% Tabulated values for the longitude calculation
% L terms from the original code.
"""
# Tabulated values for the longitude calculation
# L terms from the original code.
L0_terms = np.array([[175347046.0, 0, 0],
[3341656.0, 4.6692568, 6283.07585],
[34894.0, 4.6261, 12566.1517],
[3497.0, 2.7441, 5753.3849],
[3418.0, 2.8289, 3.5231],
[3136.0, 3.6277, 77713.7715],
[2676.0, 4.4181, 7860.4194],
[2343.0, 6.1352, 3930.2097],
[1324.0, 0.7425, 11506.7698],
[1273.0, 2.0371, 529.691],
[1199.0, 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_terms = np.array([[628331966747.0, 0, 0],
[206059.0, 2.678235, 6283.07585],
[4303.0, 2.6351, 12566.1517],
[425.0, 1.59, 3.523],
[119.0, 5.796, 26.298],
[109.0, 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_terms = np.array([[52919.0, 0, 0],
[8720.0, 1.0721, 6283.0758],
[309.0, 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_terms = np.array([[289.0, 5.844, 6283.076],
[35, 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_terms = np.array([[114.0, 3.142, 0],
[8, 4.13, 6283.08],
[1, 3.84, 12566.15]])
L5_terms = np.array([1, 3.14, 0])
L5_terms = np.atleast_2d(L5_terms) # since L5_terms is 1D, we have to convert it to 2D to avoid indexErrors
A0 = L0_terms[:, 0]
B0 = L0_terms[:, 1]
C0 = L0_terms[:, 2]
A1 = L1_terms[:, 0]
B1 = L1_terms[:, 1]
C1 = L1_terms[:, 2]
A2 = L2_terms[:, 0]
B2 = L2_terms[:, 1]
C2 = L2_terms[:, 2]
A3 = L3_terms[:, 0]
B3 = L3_terms[:, 1]
C3 = L3_terms[:, 2]
A4 = L4_terms[:, 0]
B4 = L4_terms[:, 1]
C4 = L4_terms[:, 2]
A5 = L5_terms[:, 0]
B5 = L5_terms[:, 1]
C5 = L5_terms[:, 2]
JME = julian['ephemeris_millenium']
# Compute the Earth Heliochentric longitude from the tabulated values.
L0 = np.sum(A0 * np.cos(B0 + (C0 * JME)))
L1 = np.sum(A1 * np.cos(B1 + (C1 * JME)))
L2 = np.sum(A2 * np.cos(B2 + (C2 * JME)))
L3 = np.sum(A3 * np.cos(B3 + (C3 * JME)))
L4 = np.sum(A4 * np.cos(B4 + (C4 * JME)))
L5 = A5 * np.cos(B5 + (C5 * JME))
earth_heliocentric_position = dict()
earth_heliocentric_position['longitude'] = (L0 + (L1 * JME) + (L2 * np.power(JME, 2)) +
(L3 * np.power(JME, 3)) +
(L4 * np.power(JME, 4)) +
(L5 * np.power(JME, 5))) / 1e8
# Convert the longitude to degrees.
earth_heliocentric_position['longitude'] = earth_heliocentric_position['longitude'] * 180/np.pi
# Limit the range to [0,360]
earth_heliocentric_position['longitude'] = set_to_range(earth_heliocentric_position['longitude'], 0, 360)
# Tabulated values for the earth heliocentric latitude.
# B terms from the original code.
B0_terms = np.array([[280.0, 3.199, 84334.662],
[102.0, 5.422, 5507.553],
[80, 3.88, 5223.69],
[44, 3.7, 2352.87],
[32, 4, 1577.34]])
B1_terms = np.array([[9, 3.9, 5507.55],
[6, 1.73, 5223.69]])
A0 = B0_terms[:, 0]
B0 = B0_terms[:, 1]
C0 = B0_terms[:, 2]
A1 = B1_terms[:, 0]
B1 = B1_terms[:, 1]
C1 = B1_terms[:, 2]
L0 = np.sum(A0 * np.cos(B0 + (C0 * JME)))
L1 = np.sum(A1 * np.cos(B1 + (C1 * JME)))
earth_heliocentric_position['latitude'] = (L0 + (L1 * JME)) / 1e8
# Convert the latitude to degrees.
earth_heliocentric_position['latitude'] = earth_heliocentric_position['latitude'] * 180/np.pi
# Limit the range to [0,360];
earth_heliocentric_position['latitude'] = set_to_range(earth_heliocentric_position['latitude'], 0, 360)
# Tabulated values for radius vector.
# R terms from the original code
R0_terms = np.array([[100013989.0, 0, 0],
[1670700.0, 3.0984635, 6283.07585],
[13956.0, 3.05525, 12566.1517],
[3084.0, 5.1985, 77713.7715],
[1628.0, 1.1739, 5753.3849],
[1576.0, 2.8469, 7860.4194],
[925.0, 5.453, 11506.77],
[542.0, 4.564, 3930.21],
[472.0, 3.661, 5884.927],
[346.0, 0.964, 5507.553],
[329.0, 5.9, 5223.694],
[307.0, 0.299, 5573.143],
[243.0, 4.273, 11790.629],
[212.0, 5.847, 1577.344],
[186.0, 5.022, 10977.079],
[175.0, 3.012, 18849.228],
[110.0, 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_terms = np.array([[103019.0, 1.10749, 6283.07585],
[1721.0, 1.0644, 12566.1517],
[702.0, 3.142, 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_terms = np.array([[4359.0, 5.7846, 6283.0758],
[124.0, 5.579, 12566.152],
[12, 3.14, 0],
[9, 3.63, 77713.77],
[6, 1.87, 5573.14],
[3, 5.47, 18849]])
R3_terms = np.array([[145.0, 4.273, 6283.076],
[7, 3.92, 12566.15]])
R4_terms = [4, 2.56, 6283.08]
R4_terms = np.atleast_2d(R4_terms) # since L5_terms is 1D, we have to convert it to 2D to avoid indexErrors
A0 = R0_terms[:, 0]
B0 = R0_terms[:, 1]
C0 = R0_terms[:, 2]
A1 = R1_terms[:, 0]
B1 = R1_terms[:, 1]
C1 = R1_terms[:, 2]
A2 = R2_terms[:, 0]
B2 = R2_terms[:, 1]
C2 = R2_terms[:, 2]
A3 = R3_terms[:, 0]
B3 = R3_terms[:, 1]
C3 = R3_terms[:, 2]
A4 = R4_terms[:, 0]
B4 = R4_terms[:, 1]
C4 = R4_terms[:, 2]
# Compute the Earth heliocentric radius vector
L0 = np.sum(A0 * np.cos(B0 + (C0 * JME)))
L1 = np.sum(A1 * np.cos(B1 + (C1 * JME)))
L2 = np.sum(A2 * np.cos(B2 + (C2 * JME)))
L3 = np.sum(A3 * np.cos(B3 + (C3 * JME)))
L4 = A4 * np.cos(B4 + (C4 * JME))
# Units are in AU
earth_heliocentric_position['radius'] = (L0 + (L1 * JME) + (L2 * np.power(JME, 2)) +
(L3 * np.power(JME, 3)) +
(L4 * np.power(JME, 4))) / 1e8
return earth_heliocentric_position
def sun_geocentric_position_calculation(earth_heliocentric_position):
"""
% This function compute the sun position relative to the earth.
"""
sun_geocentric_position = dict()
sun_geocentric_position['longitude'] = earth_heliocentric_position['longitude'] + 180
# Limit the range to [0,360];
sun_geocentric_position['longitude'] = set_to_range(sun_geocentric_position['longitude'], 0, 360)
sun_geocentric_position['latitude'] = -earth_heliocentric_position['latitude']
# Limit the range to [0,360]
sun_geocentric_position['latitude'] = set_to_range(sun_geocentric_position['latitude'], 0, 360)
return sun_geocentric_position
def nutation_calculation(julian):
"""
% This function compute the nutation in longtitude and in obliquity, in
% degrees.
:param julian:
:return: nutation
"""
# All Xi are in degrees.
JCE = julian['ephemeris_century']
# 1. Mean elongation of the moon from the sun
p = np.atleast_2d([(1/189474), -0.0019142, 445267.11148, 297.85036])
# X0 = polyval(p, JCE);
X0 = p[0, 0] * np.power(JCE, 3) + p[0, 1] * np.power(JCE, 2) + p[0, 2] * JCE + p[0, 3] # This is faster than polyval...
# 2. Mean anomaly of the sun (earth)
p = np.atleast_2d([-(1/300000), -0.0001603, 35999.05034, 357.52772])
# X1 = polyval(p, JCE)
X1 = p[0, 0] * np.power(JCE, 3) + p[0, 1] * np.power(JCE, 2) + p[0, 2] * JCE + p[0, 3]
# 3. Mean anomaly of the moon
p = np.atleast_2d([(1/56250), 0.0086972, 477198.867398, 134.96298])
# X2 = polyval(p, JCE);
X2 = p[0, 0] * np.power(JCE, 3) + p[0, 1] * np.power(JCE, 2) + p[0, 2] * JCE + p[0, 3]
# 4. Moon argument of latitude
p = np.atleast_2d([(1/327270), -0.0036825, 483202.017538, 93.27191])
# X3 = polyval(p, JCE)
X3 = p[0, 0] * np.power(JCE, 3) + p[0, 1] * np.power(JCE, 2) + p[0, 2] * JCE + p[0, 3]
# 5. Longitude of the ascending node of the moon's mean orbit on the
# ecliptic, measured from the mean equinox of the date
p = np.atleast_2d([(1/450000), 0.0020708, -1934.136261, 125.04452])
# X4 = polyval(p, JCE);
X4 = p[0, 0] * np.power(JCE, 3) + p[0, 1] * np.power(JCE, 2) + p[0, 2] * JCE + p[0, 3]
# Y tabulated terms from the original code
Y_terms = np.array([[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_terms = np.array([[-171996, -174.2, 92025, 8.9],
[-13187, -1.6, 5736, -3.1],
[-2274, -0.2, 977, -0.5],
[2062, 0.2, -895, 0.5],
[1426, -3.4, 54, -0.1],
[712, 0.1, -7, 0],
[-517, 1.2, 224, -0.6],
[-386, -0.4, 200, 0],
[-301, 0, 129, -0.1],
[217, -0.5, -95, 0.3],
[-158, 0, 0, 0],
[129, 0.1, -70, 0],
[123, 0, -53, 0],
[63, 0, 0, 0],
[63, 0.1, -33, 0],
[-59, 0, 26, 0],
[-58, -0.1, 32, 0],
[-51, 0, 27, 0],
[48, 0, 0, 0],
[46, 0, -24, 0],
[-38, 0, 16, 0],
[-31, 0, 13, 0],
[29, 0, 0, 0],
[29, 0, -12, 0],
[26, 0, 0, 0],
[-22, 0, 0, 0],
[21, 0, -10, 0],
[17, -0.1, 0, 0],
[16, 0, -8, 0],
[-16, 0.1, 7, 0],
[-15, 0, 9, 0],
[-13, 0, 7, 0],
[-12, 0, 6, 0],
[11, 0, 0, 0],
[-10, 0, 5, 0],
[-8, 0, 3, 0],
[7, 0, -3, 0],
[-7, 0, 0, 0],
[-7, 0, 3, 0],
[-7, 0, 3, 0],
[6, 0, 0, 0],
[6, 0, -3, 0],
[6, 0, -3, 0],
[-6, 0, 3, 0],
[-6, 0, 3, 0],
[5, 0, 0, 0],
[-5, 0, 3, 0],
[-5, 0, 3, 0],
[-5, 0, 3, 0],
[4, 0, 0, 0],
[4, 0, 0, 0],
[4, 0, 0, 0],
[-4, 0, 0, 0],
[-4, 0, 0, 0],
[-4, 0, 0, 0],
[3, 0, 0, 0],
[-3, 0, 0, 0],
[-3, 0, 0, 0],
[-3, 0, 0, 0],
[-3, 0, 0, 0],
[-3, 0, 0, 0],
[-3, 0, 0, 0],
[-3, 0, 0, 0]])
# Using the tabulated values, compute the delta_longitude and
# delta_obliquity.
Xi = np.array([X0, X1, X2, X3, X4]) # a col mat in octave
tabulated_argument = Y_terms.dot(np.transpose(Xi)) * (np.pi/180)
delta_longitude = (nutation_terms[:, 0] + (nutation_terms[:, 1] * JCE)) * np.sin(tabulated_argument)
delta_obliquity = (nutation_terms[:, 2] + (nutation_terms[:, 3] * JCE)) * np.cos(tabulated_argument)
nutation = dict() # init nutation dictionary
# Nutation in longitude
nutation['longitude'] = np.sum(delta_longitude) / 36000000
# Nutation in obliquity
nutation['obliquity'] = np.sum(delta_obliquity) / 36000000
return nutation
def true_obliquity_calculation(julian, nutation):
"""
This function compute the true obliquity of the ecliptic.
:param julian:
:param nutation:
:return:
"""
p = np.atleast_2d([2.45, 5.79, 27.87, 7.12, -39.05, -249.67, -51.38, 1999.25, -1.55, -4680.93, 84381.448])
# mean_obliquity = polyval(p, julian.ephemeris_millenium/10);
U = julian['ephemeris_millenium'] / 10
mean_obliquity = p[0, 0] * np.power(U, 10) + p[0, 1] * np.power(U, 9) + \
p[0, 2] * np.power(U, 8) + p[0, 3] * np.power(U, 7) + \
p[0, 4] * np.power(U, 6) + p[0, 5] * np.power(U, 5) + \
p[0, 6] * np.power(U, 4) + p[0, 7] * np.power(U, 3) + \
p[0, 8] * np.power(U, 2) + p[0, 9] * U + p[0, 10]
true_obliquity = (mean_obliquity/3600) + nutation['obliquity']
return true_obliquity
def abberation_correction_calculation(earth_heliocentric_position):
"""
This function compute the aberration_correction, as a function of the
earth-sun distance.
:param earth_heliocentric_position:
:return:
"""
aberration_correction = -20.4898/(3600*earth_heliocentric_position['radius'])
return aberration_correction
def apparent_sun_longitude_calculation(sun_geocentric_position, nutation, aberration_correction):
"""
This function compute the sun apparent longitude
:param sun_geocentric_position:
:param nutation:
:param aberration_correction:
:return:
"""
apparent_sun_longitude = sun_geocentric_position['longitude'] + nutation['longitude'] + aberration_correction
return apparent_sun_longitude
def apparent_stime_at_greenwich_calculation(julian, nutation, true_obliquity):
"""
This function compute the apparent sideral time at Greenwich.
:param julian:
:param nutation:
:param true_obliquity:
:return:
"""
JD = julian['day']
JC = julian['century']
# Mean sideral time, in degrees
mean_stime = 280.46061837 + (360.98564736629*(JD-2451545)) + \
(0.000387933*np.power(JC, 2)) - \
(np.power(JC, 3)/38710000)
# Limit the range to [0-360];
mean_stime = set_to_range(mean_stime, 0, 360)
apparent_stime_at_greenwich = mean_stime + (nutation['longitude'] * np.cos(true_obliquity * np.pi/180))
return apparent_stime_at_greenwich
def sun_rigth_ascension_calculation(apparent_sun_longitude, true_obliquity, sun_geocentric_position):
"""
This function compute the sun rigth ascension.
:param apparent_sun_longitude:
:param true_obliquity:
:param sun_geocentric_position:
:return:
"""
argument_numerator = (np.sin(apparent_sun_longitude * np.pi/180) * np.cos(true_obliquity * np.pi/180)) - \
(np.tan(sun_geocentric_position['latitude'] * np.pi/180) * np.sin(true_obliquity * np.pi/180))
argument_denominator = np.cos(apparent_sun_longitude * np.pi/180);
sun_rigth_ascension = np.arctan2(argument_numerator, argument_denominator) * 180/np.pi
# Limit the range to [0,360];
sun_rigth_ascension = set_to_range(sun_rigth_ascension, 0, 360)
return sun_rigth_ascension
def sun_geocentric_declination_calculation(apparent_sun_longitude, true_obliquity, sun_geocentric_position):
"""
:param apparent_sun_longitude:
:param true_obliquity:
:param sun_geocentric_position:
:return:
"""
argument = (np.sin(sun_geocentric_position['latitude'] * np.pi/180) * np.cos(true_obliquity * np.pi/180)) + \
(np.cos(sun_geocentric_position['latitude'] * np.pi/180) * np.sin(true_obliquity * np.pi/180) *
np.sin(apparent_sun_longitude * np.pi/180))
sun_geocentric_declination = np.arcsin(argument) * 180/np.pi
return sun_geocentric_declination
def observer_local_hour_calculation(apparent_stime_at_greenwich, location, sun_rigth_ascension):
"""
This function computes observer local hour.
:param apparent_stime_at_greenwich:
:param location:
:param sun_rigth_ascension:
:return:
"""
observer_local_hour = apparent_stime_at_greenwich + location['longitude'] - sun_rigth_ascension
# Set the range to [0-360]
observer_local_hour = set_to_range(observer_local_hour, 0, 360)
return observer_local_hour
def topocentric_sun_position_calculate(earth_heliocentric_position, location,
observer_local_hour, sun_rigth_ascension, sun_geocentric_declination):
"""
This function compute the sun position (rigth ascension and declination)
with respect to the observer local position at the Earth surface.
:param earth_heliocentric_position:
:param location:
:param observer_local_hour:
:param sun_rigth_ascension:
:param sun_geocentric_declination:
:return:
"""
# Equatorial horizontal parallax of the sun in degrees
eq_horizontal_parallax = 8.794 / (3600 * earth_heliocentric_position['radius'])
# Term u, used in the following calculations (in radians)
u = np.arctan(0.99664719 * np.tan(location['latitude'] * np.pi/180))
# Term x, used in the following calculations
x = np.cos(u) + ((location['altitude']/6378140) * np.cos(location['latitude'] * np.pi/180))
# Term y, used in the following calculations
y = (0.99664719 * np.sin(u)) + ((location['altitude']/6378140) * np.sin(location['latitude'] * np.pi/180))
# Parallax in the sun rigth ascension (in radians)
nominator = -x * np.sin(eq_horizontal_parallax * np.pi/180) * np.sin(observer_local_hour * np.pi/180)
denominator = np.cos(sun_geocentric_declination * np.pi/180) - (x * np.sin(eq_horizontal_parallax * np.pi/180) *
np.cos(observer_local_hour * np.pi/180))
sun_rigth_ascension_parallax = np.arctan2(nominator, denominator)
# Conversion to degrees.
topocentric_sun_position = dict()
topocentric_sun_position['rigth_ascension_parallax'] = sun_rigth_ascension_parallax * 180/np.pi
# Topocentric sun rigth ascension (in degrees)
topocentric_sun_position['rigth_ascension'] = sun_rigth_ascension + (sun_rigth_ascension_parallax * 180/np.pi)
# Topocentric sun declination (in degrees)
nominator = (np.sin(sun_geocentric_declination * np.pi/180) - (y*np.sin(eq_horizontal_parallax * np.pi/180))) * \
np.cos(sun_rigth_ascension_parallax)
denominator = np.cos(sun_geocentric_declination * np.pi/180) - (y*np.sin(eq_horizontal_parallax * np.pi/180)) * \
np.cos(observer_local_hour * np.pi/180)
topocentric_sun_position['declination'] = np.arctan2(nominator, denominator) * 180/np.pi
return topocentric_sun_position
def topocentric_local_hour_calculate(observer_local_hour, topocentric_sun_position):
"""
This function compute the topocentric local jour angle in degrees
:param observer_local_hour:
:param topocentric_sun_position:
:return:
"""
topocentric_local_hour = observer_local_hour - topocentric_sun_position['rigth_ascension_parallax']
return topocentric_local_hour
def sun_topocentric_zenith_angle_calculate(location, topocentric_sun_position, topocentric_local_hour):
"""
This function compute the sun zenith angle, taking into account the
atmospheric refraction. A default temperature of 283K and a
default pressure of 1010 mbar are used.
:param location:
:param topocentric_sun_position:
:param topocentric_local_hour:
:return:
"""
# Topocentric elevation, without atmospheric refraction
argument = (np.sin(location['latitude'] * np.pi/180) * np.sin(topocentric_sun_position['declination'] * np.pi/180)) + \
(np.cos(location['latitude'] * np.pi/180) * np.cos(topocentric_sun_position['declination'] * np.pi/180) *
np.cos(topocentric_local_hour * np.pi/180))
true_elevation = np.arcsin(argument) * 180/np.pi
# Atmospheric refraction correction (in degrees)
argument = true_elevation + (10.3/(true_elevation + 5.11))
refraction_corr = 1.02 / (60 * np.tan(argument * np.pi/180))
# For exact pressure and temperature correction, use this,
# with P the pressure in mbar amd T the temperature in Kelvins:
# refraction_corr = (P/1010) * (283/T) * 1.02 / (60 * tan(argument * pi/180));
# Apparent elevation
apparent_elevation = true_elevation + refraction_corr
sun = dict()
sun['zenith'] = 90 - apparent_elevation
# Topocentric azimuth angle. The +180 conversion is to pass from astronomer
# notation (westward from south) to navigation notation (eastward from
# north);
nominator = np.sin(topocentric_local_hour * np.pi/180)
denominator = (np.cos(topocentric_local_hour * np.pi/180) * np.sin(location['latitude'] * np.pi/180)) - \
(np.tan(topocentric_sun_position['declination'] * np.pi/180) * np.cos(location['latitude'] * np.pi/180))
sun['azimuth'] = (np.arctan2(nominator, denominator) * 180/np.pi) + 180
# Set the range to [0-360]
sun['azimuth'] = set_to_range(sun['azimuth'], 0, 360)
return sun
def set_to_range(var, min_interval, max_interval):
"""
Sets a variable in range min_interval and max_interval
:param var:
:param min_interval:
:param max_interval:
:return:
"""
var = var - max_interval * np.floor(var/max_interval)
if var < min_interval:
var = var + max_interval
return var