nsrdb.solar_position.spa.SPA

class SPA(time_index, lat_lon, elev=0)

Bases: object

Solar position algorithm

Parameters:

• time_index (ndarray | pandas.DatetimeIndex | str) – Datetime stamps of interest

• lat_lon (ndarray) – (latitude, longitude) for site(s) of interest

• elev (ndarray) – Elevation above sea-level for site(s) of interest in meters

Methods

aberration_correction(r)	Compute aberration correction
apparent_elevation(time_index, lat_lon[, ...])	Compute the solar elevation after atmospheric refraction correction
apparent_elevation_angle(e0[, pres, temp, ...])	The apparent topocentric elevation angle after refraction
apparent_position(time_index, lat_lon[, ...])	Compute the solar position after atmospheric refraction correction - elevation - zenith
apparent_sidereal_time(v0, delta_psi, e)	Compute apparent sidereal time
apparent_solar_position([pressure, ...])	Compute the apparent (atmospheric refraction corrected) solar position for all locations and times: - elevation (e) - zenith (theta)
apparent_sun_longitude(beta, delta_psi, delta_u)	Compute apparent sun longitude
apparent_zenith(time_index, lat_lon[, elev, ...])	Compute the solar zenith angle after atmospheric refraction correction
atmospheric_refraction_correction(e0[, ...])	Compute the atmospheric refraction correction value for all sites
azimuth(time_index, lat_lon[, elev, delta_t])	Compute the solar elevation
elevation(time_index, lat_lon[, elev, delta_t])	Compute the solar elevation
equation_of_time(jme, alpha, delta_psi, e)	Equation of time
equatorial_horizontal_parallax(r)	Computes equatorial horizonatl parallax
geocentric_latitude(heliocentric_latitude)	Compute geocentric latitude from heliocentric Latitude
geocentric_longitude(heliocentric_longitude)	Compute geocentric longitude from heliocentric longitude
geocentric_sun_position(lamd, e, beta)	Compute geocentric sun position
heliocentric_latitude(jme)	Compute heliocentric latitude
heliocentric_longitude(jme)	Compute heliocentric Longitude
heliocentric_radius_vector(jme)	Compute heliocentric radius
local_hour_angle(v, obs_lon, alpha)	Compute local hour angle measured westward from south
mean_anomaly_moon(jce)	Compute mean moon anomaly
mean_anomaly_sun(jce)	Compute mean sun anomaly
mean_ecliptic_obliquity(jme)	Compute mean ecliptic obliquity
mean_elongation(jce)	Compute mean elongation
mean_sidereal_time(jd, jc)	Compute mean sidereal time
moon_argument_latitude(jce)	Compute moon latitude
moon_ascending_longitude(jce)	Compute moon ascending longitude
nutation_coefficients(jce)	Compute the nutation coefficients: x0 = mean elongation x1 = mean sun anomaly x2 = mean moon anomaly x3 = moon latitude x4 = moon ascending longitude
nutation_position(jce)	Compute nutation longitude for all timesteps
observer_xy(obs_lat, obs_elev)	Compute the observer x and y terms
parallax_sun_right_ascension(obs_x, xi, H, delta)	Computer sun right ascension parallax
position(time_index, lat_lon[, elev, delta_t])	Compute the solar position: - elevation - azimuth - zenith
solar_position([delta_t])	Compute the solar position for all locations and times: - elevation (e0) - azimuth (phi) - zenith (theta0)
sun_mean_longitude(jme)	Compute mean sun longitude for all timesteps
topocentric_local_hour_angle(H, delta_alpha)	Compute topocentric local hour angle
topocentric_solar_position(obs_lat, ...)	Compute the topocentric sun position: elevation and azimuth - without atmospheric correction
topocentric_sun_declination(obs_x, obs_y, ...)	Compute topocentric sun position: right ascention and declination
topocentric_zenith_angle(e)	Topocentric zenith angle
true_ecliptic_obliquity(e0, delta_eps)	Compute true ecliptic obliquity
zenith(time_index, lat_lon[, elev, delta_t])	Compute the solar elevation

Attributes

altitude	elevation above sea-level of site(s)
latitude	Latitudes of site(s)
longitude	longitude of site(s)
time_index	Datetime stamp(s) of interest

property time_index

Datetime stamp(s) of interest

Returns:

time_index (pandas.DatetimeIndex)

property latitude

Latitudes of site(s)

Returns:

lat (ndarray)

property longitude

longitude of site(s)

Returns:

lon (ndarray)

property altitude

elevation above sea-level of site(s)

static heliocentric_longitude(jme)

Compute heliocentric Longitude

Parameters:

jme (ndarray) – Julian ephemeris millennium

Returns:

lon (ndarray) – Heliocentric longitude in degrees

static heliocentric_latitude(jme)

Compute heliocentric latitude

Parameters:

jme (ndarray) – Julian ephemeris millennium

Returns:

b (ndarray) – Heliocentric longitude in degrees

static heliocentric_radius_vector(jme)

Compute heliocentric radius

Parameters:

jme (ndarray) – Julian ephemeris millennium

Returns:

r (ndarray) – Heliocentric radius in radians

static geocentric_longitude(heliocentric_longitude)

Compute geocentric longitude from heliocentric longitude

Parameters:

heliocentric_longitude (ndarray) – heliocentric longitude for each available timestep

Returns:

theta (ndarray) – geocentric longitude for each available timestep

static geocentric_latitude(heliocentric_latitude)

Compute geocentric latitude from heliocentric Latitude

Parameters:

heliocentric_latitude (ndarray) – heliocentric latitude for each available timestep

Returns:

beta (ndarray) – geocentric latitude for each available timestep

static mean_elongation(jce)

Compute mean elongation

Parameters:

jce (ndarray) – Julian ephemeris century for all timesteps

Returns:

x0 (ndarray) – Mean elogation for all timesteps

static mean_anomaly_sun(jce)

Compute mean sun anomaly

Parameters:

jce (ndarray) – Julian ephemeris century for all timesteps

Returns:

x1 (ndarray) – Mean sun anomaly for all timesteps

static mean_anomaly_moon(jce)

Compute mean moon anomaly

Parameters:

jce (ndarray) – Julian ephemeris century for all timesteps

Returns:

x2 (ndarray) – Mean moon anomaly for all timesteps

static moon_argument_latitude(jce)

Compute moon latitude

Parameters:

jce (ndarray) – Julian ephemeris century for all timesteps

Returns:

x3 (ndarray) – Moon latitude for all timesteps

static moon_ascending_longitude(jce)

Compute moon ascending longitude

Parameters:

jce (ndarray) – Julian ephemeris century for all timesteps

Returns:

x4 (ndarray) – Moon ascending longitude for all timesteps

static nutation_coefficients(jce)

Compute the nutation coefficients: x0 = mean elongation x1 = mean sun anomaly x2 = mean moon anomaly x3 = moon latitude x4 = moon ascending longitude

Parameters:

jce (ndarray) – Julian ephemeris century for all timesteps

Returns:

x_arr (ndarray) – Array of nutation coeffiecients [x0, x1, x2, x3, x4]

static nutation_position(jce)

Compute nutation longitude for all timesteps

Parameters:

jce (ndarray) – Julian ephemeris century for all timesteps

Returns:

delta_psi (ndarray) – nutation longitude

static mean_ecliptic_obliquity(jme)

Compute mean ecliptic obliquity

Parameters:

jme (ndarray) – Julian ephemeris millennium for all timesteps

Returns:

e0 (ndarray) – Mean ecliptic obliquity for all timesteps

static true_ecliptic_obliquity(e0, delta_eps)

Compute true ecliptic obliquity

Parameters:

• e0 (ndarray) – Mean elciptic obliquity

• delta_eps (ndarray) – Nutation obliquity

Returns:

e (ndarray) – True ecliptic obliquity

static aberration_correction(r)

Compute aberration correction

Parameters:

r (ndarray) – Heliocentric or earth radius vector

Returns:

delta_u (ndarray) – Aberation correction

static apparent_sun_longitude(beta, delta_psi, delta_u)

Compute apparent sun longitude

Parameters:

• beta (ndarray) – Geocentric latitude

• delta_psi (ndarray) – Nutation longitude

• delta_u (ndarray) – Aberration correction

Returns:

lamd (ndarray) – Apparent sun longitude

static mean_sidereal_time(jd, jc)

Compute mean sidereal time

Parameters:

• jd (ndarray) – Julian day for all timesteps

• jc (ndarray) – Julian century for all timesteps

• v0 (ndarray) – Mean sidereal time in degrees

static apparent_sidereal_time(v0, delta_psi, e)

Compute apparent sidereal time

Parameters:

• v0 (ndarray) – Mean sidreal time

• delta_psi (ndarray) – Nutation longitude

• e (ndarray) – True ecliptic obliquity

Returns:

v (ndarray) – Apparent sidereal time degrees

static geocentric_sun_position(lamd, e, beta)

Compute geocentric sun position

Parameters:

• lamd (ndarray) – Apparent sun longitude

• e (ndarray) – True ecliptic obliquity

• beta (ndarray) – Geocentric latitude

Returns:

• alpha (ndarray) – Geocentric sun right ascension in degrees

• delta (ndarray) – Geocentric sun delication in degrees

static local_hour_angle(v, obs_lon, alpha)

Compute local hour angle measured westward from south

Parameters:

• v (ndarray) – Apparent sidreal time

• obs_lon (ndarray) – Observers longitudes

• alpha (ndarray) – Sun right ascension

Returns:

H (ndarray) – Local hour angle in degrees from westward from south

static equatorial_horizontal_parallax(r)

Computes equatorial horizonatl parallax

Parameters:

r (ndarray) – heliocentric or earth radius vector

Returns:

xi (ndarray) – Equatorial horizontal parallax

static observer_xy(obs_lat, obs_elev)

Compute the observer x and y terms

Parameters:

• obs_lat (ndarray) – Observers latitudes

• obs_elev (ndarray) – Observers elevations (above sealevel in m)

Returns:

• obs_x (ndarray) – Observers x terms

• obs_y (ndarray) – Observers y terms

static parallax_sun_right_ascension(obs_x, xi, H, delta)

Computer sun right ascension parallax

Parameters:

• obs_x (ndarray) – Observers x terms

• xi (ndarray) – Equatorial horizontal parallax

• H (ndarray) – Local hour angle

• delta (ndarray) – Geocentric sun declination

Returns:

delta_alpha (ndarray) – Sun right ascension parallax

static topocentric_sun_declination(obs_x, obs_y, xi, H, delta, delta_alpha)

Compute topocentric sun position: right ascention and declination

Parameters:

• obs_x (ndarray) – Observers x terms

• obs_y (ndarray) – Observers y terms

• xi (ndarray) – Equatorial horizontal parallax

• H (ndarray) – Local hour angle

• delta (ndarray) – Geocentric sun declination

• delta_alpha (ndarray) – Sun right ascensoin parallax

Returns:

delta_prime (ndarray) – Topocentric sun declination angle in degrees

static topocentric_local_hour_angle(H, delta_alpha)

Compute topocentric local hour angle

Parameters:

• H (ndarray) – Local hour angle

• delta_alpha (ndarray) – Sun right ascension parallax

Returns:

H_prime (ndarray) – Topocentric local hour angle

static topocentric_solar_position(obs_lat, obs_elev, xi, H, delta)

Compute the topocentric sun position: elevation and azimuth - without atmospheric correction

Parameters:

• obs_lat (ndarray) – Observers latitudes

• obs_elev (ndarray) – Observers elevations

• xi (ndarray) – Equatorial horizontal parallax

• H (ndarray) – Local hour angle

• delta (ndarray) – Geocentric sun declination

Returns:

• e0 (ndarray) – Topocentric elevation angle in degrees

• phi (ndarray) – Topocentric azimuth angle

static atmospheric_refraction_correction(e0, pres=1013.25, temp=12, atmos_refract=0.5667)

Compute the atmospheric refraction correction value for all sites

Parameters:

• e0 (ndarray) – Topocentric elevation angle

• pres (ndarray) – Pressure at all sites in millibars

• temp (ndarray) – Temperature at all sites in C

• atmos_refract (float) – Atmospheric refraction constant

Returns:

delta_e (ndarray) – Atmospheric refraction correction

static apparent_elevation_angle(e0, pres=1013.25, temp=12, atmos_refract=0.5667)

The apparent topocentric elevation angle after refraction

Parameters:

• e0 (ndarray) – Topocentric elevation angle

• pres (ndarray) – Pressure at all sites in millibar

• temp (ndarray) – Temperature at all sites in C

• atmos_refract (float) – Atmospheric refraction constant

Returns:

e (ndarray) – Apparent topocentric elevation angle after refraction

static topocentric_zenith_angle(e)

Topocentric zenith angle

Parameters:

e (ndarray) – Topocentric elevation angle

Returns:

theta (ndarray) – Topocentric zenith angle

static sun_mean_longitude(jme)

Compute mean sun longitude for all timesteps

Parameters:

jme (ndarray) – Julian ephemeris millennium

Returns:

M (ndarray) – Mean sun longitude

static equation_of_time(jme, alpha, delta_psi, e)

Equation of time

Parameters:

• jme (ndarray) – Julian ephemeris millennium

• alpha (ndarray) – geocentric sun right ascension

• delta_psi (ndarray) – nutation longitude

• e (ndarray) – True ecliptic obliquity

Returns:

E (ndarray) – Equation of time values for all timesteps

solar_position(delta_t=None)

Compute the solar position for all locations and times: - elevation (e0) - azimuth (phi) - zenith (theta0)

Parameters:

delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

• e0 (ndarray) – Solar elevation in degrees

• phi (ndarray) – Solar azimuth in degrees

• theta0 (ndarray) – Solar zenith in degrees

apparent_solar_position(pressure=1013.25, temperature=12, atmospheric_refraction=0.5667, delta_t=None)

Compute the apparent (atmospheric refraction corrected) solar position for all locations and times: - elevation (e) - zenith (theta)

Parameters:

• pressure (ndarray) – Pressure at all sites in millibar

• temperature (ndarray) – Temperature at all sites in C

• atmospheric_refract (float) – Atmospheric refraction constant

• delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

• e (ndarray) – Solar elevation after atmospheric refraction correction in degrees

• theta (ndarray) – Solar zenith after atmospheric refraction correction in degrees

classmethod position(time_index, lat_lon, elev=0, delta_t=None)

Compute the solar position: - elevation - azimuth - zenith

Parameters:

• time_index (ndarray | pandas.DatetimeIndex | str) – Datetime stamps of interest

• lat_lon (ndarray) – (latitude, longitude) for site(s) of interest

• elev (ndarray) – Elevation above sea-level for site(s) of interest

• delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

• e0 (ndarray) – Solar elevation in degrees

• phi (ndarray) – Solar azimuth in degrees

• theta0 (ndarray) – Solar zenith in degrees

classmethod elevation(time_index, lat_lon, elev=0, delta_t=None)

Compute the solar elevation

Parameters:

• time_index (ndarray | pandas.DatetimeIndex | str) – Datetime stamps of interest

• lat_lon (ndarray) – (latitude, longitude) for site(s) of interest

• elev (ndarray) – Elevation above sea-level for site(s) of interest

• delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

e0 (ndarray) – Solar elevation in degrees

classmethod azimuth(time_index, lat_lon, elev=0, delta_t=None)

Compute the solar elevation

Parameters:

• time_index (ndarray | pandas.DatetimeIndex | str) – Datetime stamps of interest

• lat_lon (ndarray) – (latitude, longitude) for site(s) of interest

• elev (ndarray) – Elevation above sea-level for site(s) of interest

• delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

phi (ndarray) – Solar azimuth in degrees

classmethod zenith(time_index, lat_lon, elev=0, delta_t=None)

Compute the solar elevation

Parameters:

• time_index (ndarray | pandas.DatetimeIndex | str) – Datetime stamps of interest

• lat_lon (ndarray) – (latitude, longitude) for site(s) of interest

• elev (ndarray) – Elevation above sea-level for site(s) of interest

• delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

theta0 (ndarray) – Solar zenith in degrees

classmethod apparent_position(time_index, lat_lon, elev=0, pressure=1013.25, temperature=12, atmospheric_refraction=0.5667, delta_t=None)

Compute the solar position after atmospheric refraction correction - elevation - zenith

Parameters:

• time_index (ndarray | pandas.DatetimeIndex | str) – Datetime stamps of interest

• lat_lon (ndarray) – (latitude, longitude) for site(s) of interest

• elev (ndarray) – Elevation above sea-level for site(s) of interest

• pressure (ndarray) – Pressure at all sites in millibar

• temperature (ndarray) – Temperature at all sites in C

• atmospheric_refract (float) – Atmospheric refraction constant

• delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

• e (ndarray) – Solar elevation after atmospheric refraction correction in degrees

• theta (ndarray) – Solar zenith after atmospheric refraction correction in degrees

classmethod apparent_elevation(time_index, lat_lon, elev=0, pressure=1013.25, temperature=12, atmospheric_refraction=0.5667, delta_t=None)

Compute the solar elevation after atmospheric refraction correction

Parameters:

• time_index (ndarray | pandas.DatetimeIndex | str) – Datetime stamps of interest

• lat_lon (ndarray) – (latitude, longitude) for site(s) of interest

• elev (ndarray) – Elevation above sea-level for site(s) of interest

• pressure (ndarray) – Pressure at all sites in millibar

• temperature (ndarray) – Temperature at all sites in C

• atmospheric_refract (float) – Atmospheric refraction constant

• delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

e (ndarray) – Solar elevation after atmospheric refraction correction in degrees

classmethod apparent_zenith(time_index, lat_lon, elev=0, pressure=1013.25, temperature=12, atmospheric_refraction=0.5667, delta_t=None)

Compute the solar zenith angle after atmospheric refraction correction

Parameters:

• time_index (ndarray | pandas.DatetimeIndex | str) – Datetime stamps of interest

• lat_lon (ndarray) – (latitude, longitude) for site(s) of interest

• elev (ndarray) – Elevation above sea-level for site(s) of interest

• pressure (ndarray) – Pressure at all sites in millibar

• temperature (ndarray) – Temperature at all sites in C

• atmospheric_refract (float) – Atmospheric refraction constant

• delta_t (float | None) – Difference between terrestrial time and UT1. Dependent on year. None will infer delta_t value from time index (recommended).

Returns:

theta (ndarray) – Solar zenith after atmospheric refraction correction in degrees