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# Copyright Cartopy Contributors
#
# This file is part of Cartopy and is released under the LGPL license.
# See COPYING and COPYING.LESSER in the root of the repository for full
# licensing details.
import datetime
import numpy as np
import shapely.geometry as sgeom
from . import ShapelyFeature
from .. import crs as ccrs
class Nightshade(ShapelyFeature):
def __init__(self, date=None, delta=0.1, refraction=-0.83,
color="k", alpha=0.5, **kwargs):
"""
Shade the darkside of the Earth, accounting for refraction.
Parameters
----------
date : datetime
A UTC datetime object used to calculate the position of the sun.
Default: datetime.datetime.utcnow()
delta : float
Stepsize in degrees to determine the resolution of the
night polygon feature (``npts = 180 / delta``).
refraction : float
The adjustment in degrees due to refraction,
thickness of the solar disc, elevation etc...
Note
----
Matplotlib keyword arguments can be used when drawing the feature.
This allows standard Matplotlib control over aspects such as
'color', 'alpha', etc.
"""
if date is None:
date = datetime.datetime.utcnow()
# make sure date is UTC, or naive with respect to time zones
if date.utcoffset():
raise ValueError(
f'datetime instance must be UTC, not {date.tzname()}')
# Returns the Greenwich hour angle,
# need longitude (opposite direction)
lat, lon = _solar_position(date)
pole_lon = lon
if lat > 0:
pole_lat = -90 + lat
central_lon = 180
else:
pole_lat = 90 + lat
central_lon = 0
rotated_pole = ccrs.RotatedPole(pole_latitude=pole_lat,
pole_longitude=pole_lon,
central_rotated_longitude=central_lon)
npts = int(180 / delta)
x = np.empty(npts * 2)
y = np.empty(npts * 2)
# Solve the equation for sunrise/sunset:
# https://en.wikipedia.org/wiki/Sunrise_equation#Generalized_equation
# NOTE: In the generalized equation on Wikipedia,
# delta == 0. in the rotated pole coordinate system.
# Therefore, the max/min latitude is +/- (90+refraction)
# Fill latitudes up and then down
y[:npts] = np.linspace(-(90 + refraction), 90 + refraction, npts)
y[npts:] = y[:npts][::-1]
# Solve the generalized equation for omega0, which is the
# angle of sunrise/sunset from solar noon
# We need to clip the input to arccos to [-1, 1] due to floating
# point precision and arccos creating nans for values outside
# of the domain
arccos_tmp = np.clip(np.sin(np.deg2rad(refraction)) /
np.cos(np.deg2rad(y)), -1, 1)
omega0 = np.rad2deg(np.arccos(arccos_tmp))
# Fill the longitude values from the offset for midnight.
# This needs to be a closed loop to fill the polygon.
# Negative longitudes
x[:npts] = -(180 - omega0[:npts])
# Positive longitudes
x[npts:] = 180 - omega0[npts:]
kwargs.setdefault('facecolor', color)
kwargs.setdefault('alpha', alpha)
geom = sgeom.Polygon(np.column_stack((x, y)))
return super().__init__(
[geom], rotated_pole, **kwargs)
def _julian_day(date):
"""
Calculate the Julian day from an input datetime.
Parameters
----------
date
A UTC datetime object.
Note
----
Algorithm implemented following equations from Chapter 3 (Algorithm 14):
Vallado, David 'Fundamentals of Astrodynamics and Applications', (2007)
Julian day epoch is: noon on January 1, 4713 BC (proleptic Julian)
noon on November 24, 4714 BC (proleptic Gregorian)
"""
year = date.year
month = date.month
day = date.day
hour = date.hour
minute = date.minute
second = date.second
# January/February correspond to months 13/14 respectively
# for the constants to work out properly
if month < 3:
month += 12
year -= 1
B = 2 - year // 100 + (year // 100) // 4
C = ((second / 60 + minute) / 60 + hour) / 24
JD = (int(365.25 * (year + 4716)) + int(30.6001 * (month + 1)) +
day + B - 1524.5 + C)
return JD
def _solar_position(date):
"""
Calculate the latitude and longitude point where the sun is
directly overhead for the given date.
Parameters
----------
date
A UTC datetime object.
Returns
-------
(latitude, longitude) in degrees
Note
----
Algorithm implemented following equations from Chapter 5 (Algorithm 29):
Vallado, David 'Fundamentals of Astrodynamics and Applications', (2007)
"""
# NOTE: Constants are in degrees in the textbook,
# so we need to convert the values from deg2rad when taking sin/cos
# Centuries from J2000
T_UT1 = (_julian_day(date) - 2451545.0) / 36525
# solar longitude (deg)
lambda_M_sun = (280.460 + 36000.771 * T_UT1) % 360
# solar anomaly (deg)
M_sun = (357.5277233 + 35999.05034 * T_UT1) % 360
# ecliptic longitude
lambda_ecliptic = (lambda_M_sun + 1.914666471 * np.sin(np.deg2rad(M_sun)) +
0.019994643 * np.sin(np.deg2rad(2 * M_sun)))
# obliquity of the ecliptic (epsilon in Vallado's notation)
epsilon = 23.439291 - 0.0130042 * T_UT1
# declination of the sun
delta_sun = np.rad2deg(np.arcsin(np.sin(np.deg2rad(epsilon)) *
np.sin(np.deg2rad(lambda_ecliptic))))
# Greenwich mean sidereal time (seconds)
theta_GMST = (67310.54841 +
(876600 * 3600 + 8640184.812866) * T_UT1 +
0.093104 * T_UT1**2 -
6.2e-6 * T_UT1**3)
# Convert to degrees
theta_GMST = (theta_GMST % 86400) / 240
# Right ascension calculations
numerator = (np.cos(np.deg2rad(epsilon)) *
np.sin(np.deg2rad(lambda_ecliptic)) /
np.cos(np.deg2rad(delta_sun)))
denominator = (np.cos(np.deg2rad(lambda_ecliptic)) /
np.cos(np.deg2rad(delta_sun)))
alpha_sun = np.rad2deg(np.arctan2(numerator, denominator))
# longitude is opposite of Greenwich Hour Angle (GHA)
# GHA == theta_GMST - alpha_sun
lon = -(theta_GMST - alpha_sun)
if lon < -180:
lon += 360
return (delta_sun, lon)
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