/
spa.py
1428 lines (1227 loc) · 47.3 KB
/
spa.py
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"""
Calculate the solar position using the NREL SPA algorithm either using
numpy arrays or compiling the code to machine language with numba.
"""
# Contributors:
# Created by Tony Lorenzo (@alorenzo175), Univ. of Arizona, 2015
from __future__ import division
import os
import threading
import warnings
import numpy as np
# this block is a way to use an environment variable to switch between
# compiling the functions with numba or just use numpy
def nocompile(*args, **kwargs):
return lambda func: func
if os.getenv('PVLIB_USE_NUMBA', '0') != '0':
try:
from numba import jit, __version__
except ImportError:
warnings.warn('Could not import numba, falling back to numpy ' +
'calculation')
jcompile = nocompile
USE_NUMBA = False
else:
major, minor = __version__.split('.')[:2]
if int(major + minor) >= 17:
# need at least numba >= 0.17.0
jcompile = jit
USE_NUMBA = True
else:
warnings.warn('Numba version must be >= 0.17.0, falling back to ' +
'numpy')
jcompile = nocompile
USE_NUMBA = False
else:
jcompile = nocompile
USE_NUMBA = False
TABLE_1_DICT = {
'L0': np.array(
[[175347046.0, 0.0, 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],
[990.0, 5.233, 5884.927],
[902.0, 2.045, 26.298],
[857.0, 3.508, 398.149],
[780.0, 1.179, 5223.694],
[753.0, 2.533, 5507.553],
[505.0, 4.583, 18849.228],
[492.0, 4.205, 775.523],
[357.0, 2.92, 0.067],
[317.0, 5.849, 11790.629],
[284.0, 1.899, 796.298],
[271.0, 0.315, 10977.079],
[243.0, 0.345, 5486.778],
[206.0, 4.806, 2544.314],
[205.0, 1.869, 5573.143],
[202.0, 2.458, 6069.777],
[156.0, 0.833, 213.299],
[132.0, 3.411, 2942.463],
[126.0, 1.083, 20.775],
[115.0, 0.645, 0.98],
[103.0, 0.636, 4694.003],
[102.0, 0.976, 15720.839],
[102.0, 4.267, 7.114],
[99.0, 6.21, 2146.17],
[98.0, 0.68, 155.42],
[86.0, 5.98, 161000.69],
[85.0, 1.3, 6275.96],
[85.0, 3.67, 71430.7],
[80.0, 1.81, 17260.15],
[79.0, 3.04, 12036.46],
[75.0, 1.76, 5088.63],
[74.0, 3.5, 3154.69],
[74.0, 4.68, 801.82],
[70.0, 0.83, 9437.76],
[62.0, 3.98, 8827.39],
[61.0, 1.82, 7084.9],
[57.0, 2.78, 6286.6],
[56.0, 4.39, 14143.5],
[56.0, 3.47, 6279.55],
[52.0, 0.19, 12139.55],
[52.0, 1.33, 1748.02],
[51.0, 0.28, 5856.48],
[49.0, 0.49, 1194.45],
[41.0, 5.37, 8429.24],
[41.0, 2.4, 19651.05],
[39.0, 6.17, 10447.39],
[37.0, 6.04, 10213.29],
[37.0, 2.57, 1059.38],
[36.0, 1.71, 2352.87],
[36.0, 1.78, 6812.77],
[33.0, 0.59, 17789.85],
[30.0, 0.44, 83996.85],
[30.0, 2.74, 1349.87],
[25.0, 3.16, 4690.48]]),
'L1': np.array(
[[628331966747.0, 0.0, 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],
[93.0, 2.59, 18849.23],
[72.0, 1.14, 529.69],
[68.0, 1.87, 398.15],
[67.0, 4.41, 5507.55],
[59.0, 2.89, 5223.69],
[56.0, 2.17, 155.42],
[45.0, 0.4, 796.3],
[36.0, 0.47, 775.52],
[29.0, 2.65, 7.11],
[21.0, 5.34, 0.98],
[19.0, 1.85, 5486.78],
[19.0, 4.97, 213.3],
[17.0, 2.99, 6275.96],
[16.0, 0.03, 2544.31],
[16.0, 1.43, 2146.17],
[15.0, 1.21, 10977.08],
[12.0, 2.83, 1748.02],
[12.0, 3.26, 5088.63],
[12.0, 5.27, 1194.45],
[12.0, 2.08, 4694.0],
[11.0, 0.77, 553.57],
[10.0, 1.3, 6286.6],
[10.0, 4.24, 1349.87],
[9.0, 2.7, 242.73],
[9.0, 5.64, 951.72],
[8.0, 5.3, 2352.87],
[6.0, 2.65, 9437.76],
[6.0, 4.67, 4690.48]]),
'L2': np.array(
[[52919.0, 0.0, 0.0],
[8720.0, 1.0721, 6283.0758],
[309.0, 0.867, 12566.152],
[27.0, 0.05, 3.52],
[16.0, 5.19, 26.3],
[16.0, 3.68, 155.42],
[10.0, 0.76, 18849.23],
[9.0, 2.06, 77713.77],
[7.0, 0.83, 775.52],
[5.0, 4.66, 1577.34],
[4.0, 1.03, 7.11],
[4.0, 3.44, 5573.14],
[3.0, 5.14, 796.3],
[3.0, 6.05, 5507.55],
[3.0, 1.19, 242.73],
[3.0, 6.12, 529.69],
[3.0, 0.31, 398.15],
[3.0, 2.28, 553.57],
[2.0, 4.38, 5223.69],
[2.0, 3.75, 0.98]]),
'L3': np.array(
[[289.0, 5.844, 6283.076],
[35.0, 0.0, 0.0],
[17.0, 5.49, 12566.15],
[3.0, 5.2, 155.42],
[1.0, 4.72, 3.52],
[1.0, 5.3, 18849.23],
[1.0, 5.97, 242.73]]),
'L4': np.array(
[[114.0, 3.142, 0.0],
[8.0, 4.13, 6283.08],
[1.0, 3.84, 12566.15]]),
'L5': np.array(
[[1.0, 3.14, 0.0]]),
'B0': np.array(
[[280.0, 3.199, 84334.662],
[102.0, 5.422, 5507.553],
[80.0, 3.88, 5223.69],
[44.0, 3.7, 2352.87],
[32.0, 4.0, 1577.34]]),
'B1': np.array(
[[9.0, 3.9, 5507.55],
[6.0, 1.73, 5223.69]]),
'R0': np.array(
[[100013989.0, 0.0, 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, 0.89, 6069.78],
[86.0, 5.69, 15720.84],
[86.0, 1.27, 161000.69],
[65.0, 0.27, 17260.15],
[63.0, 0.92, 529.69],
[57.0, 2.01, 83996.85],
[56.0, 5.24, 71430.7],
[49.0, 3.25, 2544.31],
[47.0, 2.58, 775.52],
[45.0, 5.54, 9437.76],
[43.0, 6.01, 6275.96],
[39.0, 5.36, 4694.0],
[38.0, 2.39, 8827.39],
[37.0, 0.83, 19651.05],
[37.0, 4.9, 12139.55],
[36.0, 1.67, 12036.46],
[35.0, 1.84, 2942.46],
[33.0, 0.24, 7084.9],
[32.0, 0.18, 5088.63],
[32.0, 1.78, 398.15],
[28.0, 1.21, 6286.6],
[28.0, 1.9, 6279.55],
[26.0, 4.59, 10447.39]]),
'R1': np.array(
[[103019.0, 1.10749, 6283.07585],
[1721.0, 1.0644, 12566.1517],
[702.0, 3.142, 0.0],
[32.0, 1.02, 18849.23],
[31.0, 2.84, 5507.55],
[25.0, 1.32, 5223.69],
[18.0, 1.42, 1577.34],
[10.0, 5.91, 10977.08],
[9.0, 1.42, 6275.96],
[9.0, 0.27, 5486.78]]),
'R2': np.array(
[[4359.0, 5.7846, 6283.0758],
[124.0, 5.579, 12566.152],
[12.0, 3.14, 0.0],
[9.0, 3.63, 77713.77],
[6.0, 1.87, 5573.14],
[3.0, 5.47, 18849.23]]),
'R3': np.array(
[[145.0, 4.273, 6283.076],
[7.0, 3.92, 12566.15]]),
'R4': np.array(
[[4.0, 2.56, 6283.08]])
}
TABLE_1_DICT['L1'].resize((64, 3))
TABLE_1_DICT['L2'].resize((64, 3))
TABLE_1_DICT['L3'].resize((64, 3))
TABLE_1_DICT['L4'].resize((64, 3))
TABLE_1_DICT['L5'].resize((64, 3))
TABLE_1_DICT['B1'].resize((5, 3))
TABLE_1_DICT['R1'].resize((40, 3))
TABLE_1_DICT['R2'].resize((40, 3))
TABLE_1_DICT['R3'].resize((40, 3))
TABLE_1_DICT['R4'].resize((40, 3))
HELIO_LONG_TABLE = np.array([TABLE_1_DICT['L0'],
TABLE_1_DICT['L1'],
TABLE_1_DICT['L2'],
TABLE_1_DICT['L3'],
TABLE_1_DICT['L4'],
TABLE_1_DICT['L5']])
HELIO_LAT_TABLE = np.array([TABLE_1_DICT['B0'],
TABLE_1_DICT['B1']])
HELIO_RADIUS_TABLE = np.array([TABLE_1_DICT['R0'],
TABLE_1_DICT['R1'],
TABLE_1_DICT['R2'],
TABLE_1_DICT['R3'],
TABLE_1_DICT['R4']])
NUTATION_ABCD_ARRAY = 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],
])
NUTATION_YTERM_ARRAY = 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],
])
@jcompile('float64(int64, int64, int64, int64, int64, int64, int64)',
nopython=True)
def julian_day_dt(year, month, day, hour, minute, second, microsecond):
"""This is the original way to calculate the julian day from the NREL paper.
However, it is much faster to convert to unix/epoch time and then convert
to julian day. Note that the date must be UTC."""
if month <= 2:
year = year-1
month = month+12
a = int(year/100)
b = 2 - a + int(a * 0.25)
frac_of_day = (microsecond + (second + minute * 60 + hour * 3600)
) * 1.0 / (3600*24)
d = day + frac_of_day
jd = (int(365.25 * (year + 4716)) + int(30.6001 * (month + 1)) + d +
b - 1524.5)
return jd
@jcompile('float64(float64)', nopython=True)
def julian_day(unixtime):
jd = unixtime * 1.0 / 86400 + 2440587.5
return jd
@jcompile('float64(float64, float64)', nopython=True)
def julian_ephemeris_day(julian_day, delta_t):
jde = julian_day + delta_t * 1.0 / 86400
return jde
@jcompile('float64(float64)', nopython=True)
def julian_century(julian_day):
jc = (julian_day - 2451545) * 1.0 / 36525
return jc
@jcompile('float64(float64)', nopython=True)
def julian_ephemeris_century(julian_ephemeris_day):
jce = (julian_ephemeris_day - 2451545) * 1.0 / 36525
return jce
@jcompile('float64(float64)', nopython=True)
def julian_ephemeris_millennium(julian_ephemeris_century):
jme = julian_ephemeris_century * 1.0 / 10
return jme
@jcompile('float64(float64)', nopython=True)
def heliocentric_longitude(jme):
l0 = 0.0
l1 = 0.0
l2 = 0.0
l3 = 0.0
l4 = 0.0
l5 = 0.0
for row in range(HELIO_LONG_TABLE.shape[1]):
l0 += (HELIO_LONG_TABLE[0, row, 0]
* np.cos(HELIO_LONG_TABLE[0, row, 1]
+ HELIO_LONG_TABLE[0, row, 2] * jme)
)
l1 += (HELIO_LONG_TABLE[1, row, 0]
* np.cos(HELIO_LONG_TABLE[1, row, 1]
+ HELIO_LONG_TABLE[1, row, 2] * jme)
)
l2 += (HELIO_LONG_TABLE[2, row, 0]
* np.cos(HELIO_LONG_TABLE[2, row, 1]
+ HELIO_LONG_TABLE[2, row, 2] * jme)
)
l3 += (HELIO_LONG_TABLE[3, row, 0]
* np.cos(HELIO_LONG_TABLE[3, row, 1]
+ HELIO_LONG_TABLE[3, row, 2] * jme)
)
l4 += (HELIO_LONG_TABLE[4, row, 0]
* np.cos(HELIO_LONG_TABLE[4, row, 1]
+ HELIO_LONG_TABLE[4, row, 2] * jme)
)
l5 += (HELIO_LONG_TABLE[5, row, 0]
* np.cos(HELIO_LONG_TABLE[5, row, 1]
+ HELIO_LONG_TABLE[5, row, 2] * jme)
)
l_rad = (l0 + l1 * jme + l2 * jme**2 + l3 * jme**3 + l4 * jme**4 +
l5 * jme**5)/10**8
l = np.rad2deg(l_rad)
return l % 360
@jcompile('float64(float64)', nopython=True)
def heliocentric_latitude(jme):
b0 = 0.0
b1 = 0.0
for row in range(HELIO_LAT_TABLE.shape[1]):
b0 += (HELIO_LAT_TABLE[0, row, 0]
* np.cos(HELIO_LAT_TABLE[0, row, 1]
+ HELIO_LAT_TABLE[0, row, 2] * jme)
)
b1 += (HELIO_LAT_TABLE[1, row, 0]
* np.cos(HELIO_LAT_TABLE[1, row, 1]
+ HELIO_LAT_TABLE[1, row, 2] * jme)
)
b_rad = (b0 + b1 * jme)/10**8
b = np.rad2deg(b_rad)
return b
@jcompile('float64(float64)', nopython=True)
def heliocentric_radius_vector(jme):
r0 = 0.0
r1 = 0.0
r2 = 0.0
r3 = 0.0
r4 = 0.0
for row in range(HELIO_RADIUS_TABLE.shape[1]):
r0 += (HELIO_RADIUS_TABLE[0, row, 0]
* np.cos(HELIO_RADIUS_TABLE[0, row, 1]
+ HELIO_RADIUS_TABLE[0, row, 2] * jme)
)
r1 += (HELIO_RADIUS_TABLE[1, row, 0]
* np.cos(HELIO_RADIUS_TABLE[1, row, 1]
+ HELIO_RADIUS_TABLE[1, row, 2] * jme)
)
r2 += (HELIO_RADIUS_TABLE[2, row, 0]
* np.cos(HELIO_RADIUS_TABLE[2, row, 1]
+ HELIO_RADIUS_TABLE[2, row, 2] * jme)
)
r3 += (HELIO_RADIUS_TABLE[3, row, 0]
* np.cos(HELIO_RADIUS_TABLE[3, row, 1]
+ HELIO_RADIUS_TABLE[3, row, 2] * jme)
)
r4 += (HELIO_RADIUS_TABLE[4, row, 0]
* np.cos(HELIO_RADIUS_TABLE[4, row, 1]
+ HELIO_RADIUS_TABLE[4, row, 2] * jme)
)
r = (r0 + r1 * jme + r2 * jme**2 + r3 * jme**3 + r4 * jme**4)/10**8
return r
@jcompile('float64(float64)', nopython=True)
def geocentric_longitude(heliocentric_longitude):
theta = heliocentric_longitude + 180.0
return theta % 360
@jcompile('float64(float64)', nopython=True)
def geocentric_latitude(heliocentric_latitude):
beta = -1.0*heliocentric_latitude
return beta
@jcompile('float64(float64)', nopython=True)
def mean_elongation(julian_ephemeris_century):
x0 = (297.85036
+ 445267.111480 * julian_ephemeris_century
- 0.0019142 * julian_ephemeris_century**2
+ julian_ephemeris_century**3 / 189474)
return x0
@jcompile('float64(float64)', nopython=True)
def mean_anomaly_sun(julian_ephemeris_century):
x1 = (357.52772
+ 35999.050340 * julian_ephemeris_century
- 0.0001603 * julian_ephemeris_century**2
- julian_ephemeris_century**3 / 300000)
return x1
@jcompile('float64(float64)', nopython=True)
def mean_anomaly_moon(julian_ephemeris_century):
x2 = (134.96298
+ 477198.867398 * julian_ephemeris_century
+ 0.0086972 * julian_ephemeris_century**2
+ julian_ephemeris_century**3 / 56250)
return x2
@jcompile('float64(float64)', nopython=True)
def moon_argument_latitude(julian_ephemeris_century):
x3 = (93.27191
+ 483202.017538 * julian_ephemeris_century
- 0.0036825 * julian_ephemeris_century**2
+ julian_ephemeris_century**3 / 327270)
return x3
@jcompile('float64(float64)', nopython=True)
def moon_ascending_longitude(julian_ephemeris_century):
x4 = (125.04452
- 1934.136261 * julian_ephemeris_century
+ 0.0020708 * julian_ephemeris_century**2
+ julian_ephemeris_century**3 / 450000)
return x4
@jcompile('float64(float64, float64, float64, float64, float64, float64)',
nopython=True)
def longitude_nutation(julian_ephemeris_century, x0, x1, x2, x3, x4):
delta_psi_sum = 0
for row in range(NUTATION_YTERM_ARRAY.shape[0]):
a = NUTATION_ABCD_ARRAY[row, 0]
b = NUTATION_ABCD_ARRAY[row, 1]
argsin = (NUTATION_YTERM_ARRAY[row, 0]*x0 +
NUTATION_YTERM_ARRAY[row, 1]*x1 +
NUTATION_YTERM_ARRAY[row, 2]*x2 +
NUTATION_YTERM_ARRAY[row, 3]*x3 +
NUTATION_YTERM_ARRAY[row, 4]*x4)
term = (a + b * julian_ephemeris_century) * np.sin(np.radians(argsin))
delta_psi_sum += term
delta_psi = delta_psi_sum*1.0/36000000
return delta_psi
@jcompile('float64(float64, float64, float64, float64, float64, float64)',
nopython=True)
def obliquity_nutation(julian_ephemeris_century, x0, x1, x2, x3, x4):
delta_eps_sum = 0.0
for row in range(NUTATION_YTERM_ARRAY.shape[0]):
c = NUTATION_ABCD_ARRAY[row, 2]
d = NUTATION_ABCD_ARRAY[row, 3]
argcos = (NUTATION_YTERM_ARRAY[row, 0]*x0 +
NUTATION_YTERM_ARRAY[row, 1]*x1 +
NUTATION_YTERM_ARRAY[row, 2]*x2 +
NUTATION_YTERM_ARRAY[row, 3]*x3 +
NUTATION_YTERM_ARRAY[row, 4]*x4)
term = (c + d * julian_ephemeris_century) * np.cos(np.radians(argcos))
delta_eps_sum += term
delta_eps = delta_eps_sum*1.0/36000000
return delta_eps
@jcompile('float64(float64)', nopython=True)
def mean_ecliptic_obliquity(julian_ephemeris_millennium):
U = 1.0*julian_ephemeris_millennium/10
e0 = (84381.448 - 4680.93 * U - 1.55 * U**2
+ 1999.25 * U**3 - 51.38 * U**4 - 249.67 * U**5
- 39.05 * U**6 + 7.12 * U**7 + 27.87 * U**8
+ 5.79 * U**9 + 2.45 * U**10)
return e0
@jcompile('float64(float64, float64)', nopython=True)
def true_ecliptic_obliquity(mean_ecliptic_obliquity, obliquity_nutation):
e0 = mean_ecliptic_obliquity
deleps = obliquity_nutation
e = e0*1.0/3600 + deleps
return e
@jcompile('float64(float64)', nopython=True)
def aberration_correction(earth_radius_vector):
deltau = -20.4898 / (3600 * earth_radius_vector)
return deltau
@jcompile('float64(float64, float64, float64)', nopython=True)
def apparent_sun_longitude(geocentric_longitude, longitude_nutation,
aberration_correction):
lamd = geocentric_longitude + longitude_nutation + aberration_correction
return lamd
@jcompile('float64(float64, float64)', nopython=True)
def mean_sidereal_time(julian_day, julian_century):
v0 = (280.46061837 + 360.98564736629 * (julian_day - 2451545)
+ 0.000387933 * julian_century**2 - julian_century**3 / 38710000)
return v0 % 360.0
@jcompile('float64(float64, float64, float64)', nopython=True)
def apparent_sidereal_time(mean_sidereal_time, longitude_nutation,
true_ecliptic_obliquity):
v = mean_sidereal_time + longitude_nutation * np.cos(
np.radians(true_ecliptic_obliquity))
return v
@jcompile('float64(float64, float64, float64)', nopython=True)
def geocentric_sun_right_ascension(apparent_sun_longitude,
true_ecliptic_obliquity,
geocentric_latitude):
num = (np.sin(np.radians(apparent_sun_longitude))
* np.cos(np.radians(true_ecliptic_obliquity))
- np.tan(np.radians(geocentric_latitude))
* np.sin(np.radians(true_ecliptic_obliquity)))
alpha = np.degrees(np.arctan2(num, np.cos(
np.radians(apparent_sun_longitude))))
return alpha % 360
@jcompile('float64(float64, float64, float64)', nopython=True)
def geocentric_sun_declination(apparent_sun_longitude, true_ecliptic_obliquity,
geocentric_latitude):
delta = np.degrees(np.arcsin(np.sin(np.radians(geocentric_latitude)) *
np.cos(np.radians(true_ecliptic_obliquity)) +
np.cos(np.radians(geocentric_latitude)) *
np.sin(np.radians(true_ecliptic_obliquity)) *
np.sin(np.radians(apparent_sun_longitude))))
return delta
@jcompile('float64(float64, float64, float64)', nopython=True)
def local_hour_angle(apparent_sidereal_time, observer_longitude,
sun_right_ascension):
"""Measured westward from south"""
H = apparent_sidereal_time + observer_longitude - sun_right_ascension
return H % 360
@jcompile('float64(float64)', nopython=True)
def equatorial_horizontal_parallax(earth_radius_vector):
xi = 8.794 / (3600 * earth_radius_vector)
return xi
@jcompile('float64(float64)', nopython=True)
def uterm(observer_latitude):
u = np.arctan(0.99664719 * np.tan(np.radians(observer_latitude)))
return u
@jcompile('float64(float64, float64, float64)', nopython=True)
def xterm(u, observer_latitude, observer_elevation):
x = (np.cos(u) + observer_elevation / 6378140
* np.cos(np.radians(observer_latitude)))
return x
@jcompile('float64(float64, float64, float64)', nopython=True)
def yterm(u, observer_latitude, observer_elevation):
y = (0.99664719 * np.sin(u) + observer_elevation / 6378140
* np.sin(np.radians(observer_latitude)))
return y
@jcompile('float64(float64, float64,float64, float64)', nopython=True)
def parallax_sun_right_ascension(xterm, equatorial_horizontal_parallax,
local_hour_angle, geocentric_sun_declination):
num = (-xterm * np.sin(np.radians(equatorial_horizontal_parallax))
* np.sin(np.radians(local_hour_angle)))
denom = (np.cos(np.radians(geocentric_sun_declination))
- xterm * np.sin(np.radians(equatorial_horizontal_parallax))
* np.cos(np.radians(local_hour_angle)))
delta_alpha = np.degrees(np.arctan2(num, denom))
return delta_alpha
@jcompile('float64(float64, float64)', nopython=True)
def topocentric_sun_right_ascension(geocentric_sun_right_ascension,
parallax_sun_right_ascension):
alpha_prime = geocentric_sun_right_ascension + parallax_sun_right_ascension
return alpha_prime
@jcompile('float64(float64, float64, float64, float64, float64, float64)',
nopython=True)
def topocentric_sun_declination(geocentric_sun_declination, xterm, yterm,
equatorial_horizontal_parallax,
parallax_sun_right_ascension,
local_hour_angle):
num = ((np.sin(np.radians(geocentric_sun_declination)) - yterm
* np.sin(np.radians(equatorial_horizontal_parallax)))
* np.cos(np.radians(parallax_sun_right_ascension)))
denom = (np.cos(np.radians(geocentric_sun_declination)) - xterm
* np.sin(np.radians(equatorial_horizontal_parallax))
* np.cos(np.radians(local_hour_angle)))
delta = np.degrees(np.arctan2(num, denom))
return delta
@jcompile('float64(float64, float64)', nopython=True)
def topocentric_local_hour_angle(local_hour_angle,
parallax_sun_right_ascension):
H_prime = local_hour_angle - parallax_sun_right_ascension
return H_prime
@jcompile('float64(float64, float64, float64)', nopython=True)
def topocentric_elevation_angle_without_atmosphere(observer_latitude,
topocentric_sun_declination,
topocentric_local_hour_angle
):
e0 = np.degrees(np.arcsin(
np.sin(np.radians(observer_latitude))
* np.sin(np.radians(topocentric_sun_declination))
+ np.cos(np.radians(observer_latitude))
* np.cos(np.radians(topocentric_sun_declination))
* np.cos(np.radians(topocentric_local_hour_angle))))
return e0
@jcompile('float64(float64, float64, float64, float64)', nopython=True)
def atmospheric_refraction_correction(local_pressure, local_temp,
topocentric_elevation_angle_wo_atmosphere,
atmos_refract):
# switch sets delta_e when the sun is below the horizon
switch = topocentric_elevation_angle_wo_atmosphere >= -1.0 * (
0.26667 + atmos_refract)
delta_e = ((local_pressure / 1010.0) * (283.0 / (273 + local_temp))
* 1.02 / (60 * np.tan(np.radians(
topocentric_elevation_angle_wo_atmosphere
+ 10.3 / (topocentric_elevation_angle_wo_atmosphere
+ 5.11))))) * switch
return delta_e
@jcompile('float64(float64, float64)', nopython=True)
def topocentric_elevation_angle(topocentric_elevation_angle_without_atmosphere,
atmospheric_refraction_correction):
e = (topocentric_elevation_angle_without_atmosphere
+ atmospheric_refraction_correction)
return e
@jcompile('float64(float64)', nopython=True)
def topocentric_zenith_angle(topocentric_elevation_angle):
theta = 90 - topocentric_elevation_angle
return theta
@jcompile('float64(float64, float64, float64)', nopython=True)
def topocentric_astronomers_azimuth(topocentric_local_hour_angle,
topocentric_sun_declination,
observer_latitude):
num = np.sin(np.radians(topocentric_local_hour_angle))
denom = (np.cos(np.radians(topocentric_local_hour_angle))
* np.sin(np.radians(observer_latitude))
- np.tan(np.radians(topocentric_sun_declination))
* np.cos(np.radians(observer_latitude)))
gamma = np.degrees(np.arctan2(num, denom))
return gamma % 360
@jcompile('float64(float64)', nopython=True)
def topocentric_azimuth_angle(topocentric_astronomers_azimuth):
phi = topocentric_astronomers_azimuth + 180
return phi % 360
@jcompile('float64(float64)', nopython=True)
def sun_mean_longitude(julian_ephemeris_millennium):
M = (280.4664567 + 360007.6982779 * julian_ephemeris_millennium
+ 0.03032028 * julian_ephemeris_millennium**2
+ julian_ephemeris_millennium**3 / 49931
- julian_ephemeris_millennium**4 / 15300
- julian_ephemeris_millennium**5 / 2000000)
return M
@jcompile('float64(float64, float64, float64, float64)', nopython=True)
def equation_of_time(sun_mean_longitude, geocentric_sun_right_ascension,
longitude_nutation, true_ecliptic_obliquity):
E = (sun_mean_longitude - 0.0057183 - geocentric_sun_right_ascension +
longitude_nutation * np.cos(np.radians(true_ecliptic_obliquity)))
# limit between 0 and 360
E = E % 360
# convert to minutes
E *= 4
greater = E > 20
less = E < -20
other = (E <= 20) & (E >= -20)
E = greater * (E - 1440) + less * (E + 1440) + other * E
return E
@jcompile('void(float64[:], float64[:], float64[:,:])', nopython=True,
nogil=True)
def solar_position_loop(unixtime, loc_args, out):
"""Loop through the time array and calculate the solar position"""
lat = loc_args[0]
lon = loc_args[1]
elev = loc_args[2]
pressure = loc_args[3]
temp = loc_args[4]
delta_t = loc_args[5]
atmos_refract = loc_args[6]
sst = loc_args[7]
esd = loc_args[8]
for i in range(unixtime.shape[0]):
utime = unixtime[i]
jd = julian_day(utime)
jde = julian_ephemeris_day(jd, delta_t)
jc = julian_century(jd)
jce = julian_ephemeris_century(jde)
jme = julian_ephemeris_millennium(jce)
R = heliocentric_radius_vector(jme)
if esd:
out[0, i] = R
continue
L = heliocentric_longitude(jme)
B = heliocentric_latitude(jme)
Theta = geocentric_longitude(L)
beta = geocentric_latitude(B)
x0 = mean_elongation(jce)
x1 = mean_anomaly_sun(jce)
x2 = mean_anomaly_moon(jce)
x3 = moon_argument_latitude(jce)
x4 = moon_ascending_longitude(jce)
delta_psi = longitude_nutation(jce, x0, x1, x2, x3, x4)
delta_epsilon = obliquity_nutation(jce, x0, x1, x2, x3, x4)
epsilon0 = mean_ecliptic_obliquity(jme)
epsilon = true_ecliptic_obliquity(epsilon0, delta_epsilon)
delta_tau = aberration_correction(R)
lamd = apparent_sun_longitude(Theta, delta_psi, delta_tau)
v0 = mean_sidereal_time(jd, jc)
v = apparent_sidereal_time(v0, delta_psi, epsilon)
alpha = geocentric_sun_right_ascension(lamd, epsilon, beta)
delta = geocentric_sun_declination(lamd, epsilon, beta)
if sst:
out[0, i] = v
out[1, i] = alpha
out[2, i] = delta
continue
m = sun_mean_longitude(jme)
eot = equation_of_time(m, alpha, delta_psi, epsilon)
H = local_hour_angle(v, lon, alpha)
xi = equatorial_horizontal_parallax(R)
u = uterm(lat)
x = xterm(u, lat, elev)
y = yterm(u, lat, elev)
delta_alpha = parallax_sun_right_ascension(x, xi, H, delta)
delta_prime = topocentric_sun_declination(delta, x, y, xi, delta_alpha,
H)
H_prime = topocentric_local_hour_angle(H, delta_alpha)
e0 = topocentric_elevation_angle_without_atmosphere(lat, delta_prime,
H_prime)
delta_e = atmospheric_refraction_correction(pressure, temp, e0,
atmos_refract)
e = topocentric_elevation_angle(e0, delta_e)
theta = topocentric_zenith_angle(e)
theta0 = topocentric_zenith_angle(e0)
gamma = topocentric_astronomers_azimuth(H_prime, delta_prime, lat)
phi = topocentric_azimuth_angle(gamma)
out[0, i] = theta
out[1, i] = theta0
out[2, i] = e
out[3, i] = e0
out[4, i] = phi
out[5, i] = eot
def solar_position_numba(unixtime, lat, lon, elev, pressure, temp, delta_t,
atmos_refract, numthreads, sst=False, esd=False):
"""Calculate the solar position using the numba compiled functions
and multiple threads. Very slow if functions are not numba compiled.
"""
# these args are the same for each thread
loc_args = np.array([lat, lon, elev, pressure, temp, delta_t,
atmos_refract, sst, esd])
# construct dims x ulength array to put the results in
ulength = unixtime.shape[0]
if sst:
dims = 3
elif esd:
dims = 1
else:
dims = 6
result = np.empty((dims, ulength), dtype=np.float64)
if unixtime.dtype != np.float64:
unixtime = unixtime.astype(np.float64)
if ulength < numthreads:
warnings.warn('The number of threads is more than the length of '
'the time array. Only using %s threads.'.format(ulength))
numthreads = ulength
if numthreads <= 1:
solar_position_loop(unixtime, loc_args, result)