solar.c

/* solar.c -- Solar position source
   This file is part of Redshift.

   Redshift is free software: you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation, either version 3 of the License, or
   (at your option) any later version.

   Redshift is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with Redshift.  If not, see <http://www.gnu.org/licenses/>.

   Copyright (c) 2010  Jon Lund Steffensen <jonlst@gmail.com>
*/

/* Ported from javascript code by U.S. Department of Commerce,
   National Oceanic & Atmospheric Administration:
   http://www.srrb.noaa.gov/highlights/sunrise/calcdetails.html
   It is based on equations from "Astronomical Algorithms" by
   Jean Meeus. */

#include <math.h>

#include "solar.h"
#include "time.h"

#define RAD(x)  ((x)*(M_PI/180))
#define DEG(x)  ((x)*(180/M_PI))


/* Angels of various times of day. */
static const double time_angle[] = {
	[SOLAR_TIME_ASTRO_DAWN] = RAD(-90.0 + SOLAR_ASTRO_TWILIGHT_ELEV),
	[SOLAR_TIME_NAUT_DAWN] = RAD(-90.0 + SOLAR_NAUT_TWILIGHT_ELEV),
	[SOLAR_TIME_CIVIL_DAWN] = RAD(-90.0 + SOLAR_CIVIL_TWILIGHT_ELEV),
	[SOLAR_TIME_SUNRISE] = RAD(-90.0 + SOLAR_DAYTIME_ELEV),
	[SOLAR_TIME_NOON] = RAD(0.0),
	[SOLAR_TIME_SUNSET] = RAD(90.0 - SOLAR_DAYTIME_ELEV),
	[SOLAR_TIME_CIVIL_DUSK] = RAD(90.0 - SOLAR_CIVIL_TWILIGHT_ELEV),
	[SOLAR_TIME_NAUT_DUSK] = RAD(90.0 - SOLAR_NAUT_TWILIGHT_ELEV),
	[SOLAR_TIME_ASTRO_DUSK] = RAD(90.0 - SOLAR_ASTRO_TWILIGHT_ELEV)
};


/* Unix epoch from Julian day */
static double
epoch_from_jd(double jd)
{
	return 86400.0*(jd - 2440587.5);
}



/* Julian day from unix epoch */
static double
jd_from_epoch(double t)
{
	return (t / 86400.0) + 2440587.5;
}

/* Julian centuries since J2000.0 from Julian day */
static double
jcent_from_jd(double jd)
{
	return (jd - 2451545.0) / 36525.0;
}

/* Julian day from Julian centuries since J2000.0 */
static double
jd_from_jcent(double t)
{
	return 36525.0*t + 2451545.0;
}

/* Geometric mean longitude of the sun.
   t: Julian centuries since J2000.0
   Return: Geometric mean logitude in radians. */
static double
sun_geom_mean_lon(double t)
{
	/* FIXME returned value should always be positive */
	return RAD(fmod(280.46646 + t*(36000.76983 + t*0.0003032), 360));
}

/* Geometric mean anomaly of the sun.
   t: Julian centuries since J2000.0
   Return: Geometric mean anomaly in radians. */
static double
sun_geom_mean_anomaly(double t)
{
	return RAD(357.52911 + t*(35999.05029 - t*0.0001537));
}

/* Eccentricity of earth orbit.
   t: Julian centuries since J2000.0
   Return: Eccentricity (unitless). */
static double
earth_orbit_eccentricity(double t)
{
	return 0.016708634 - t*(0.000042037 + t*0.0000001267);
}

/* Equation of center of the sun.
   t: Julian centuries since J2000.0
   Return: Center(?) in radians */
static double
sun_equation_of_center(double t)
{
	/* Use the first three terms of the equation. */
	double m = sun_geom_mean_anomaly(t);
	double c = sin(m)*(1.914602 - t*(0.004817 + 0.000014*t)) +
		sin(2*m)*(0.019993 - 0.000101*t) +
		sin(3*m)*0.000289;
	return RAD(c);
}

/* True longitude of the sun.
   t: Julian centuries since J2000.0
   Return: True longitude in radians */
static double
sun_true_lon(double t)
{
	double l_0 = sun_geom_mean_lon(t);
	double c = sun_equation_of_center(t);
	return l_0 + c;
}

/* Apparent longitude of the sun. (Right ascension).
   t: Julian centuries since J2000.0
   Return: Apparent longitude in radians */
static double
sun_apparent_lon(double t)
{
	double o = sun_true_lon(t);
	return RAD(DEG(o) - 0.00569 - 0.00478*sin(RAD(125.04 - 1934.136*t)));
}

/* Mean obliquity of the ecliptic
   t: Julian centuries since J2000.0
   Return: Mean obliquity in radians */
static double
mean_ecliptic_obliquity(double t)
{
	double sec = 21.448 - t*(46.815 + t*(0.00059 - t*0.001813));
	return RAD(23.0 + (26.0 + (sec/60.0))/60.0);
}

/* Corrected obliquity of the ecliptic.
   t: Julian centuries since J2000.0
   Return: Currected obliquity in radians */
static double
obliquity_corr(double t)
{
	double e_0 = mean_ecliptic_obliquity(t);
	double omega = 125.04 - t*1934.136;
	return RAD(DEG(e_0) + 0.00256*cos(RAD(omega)));
}

/* Declination of the sun.
   t: Julian centuries since J2000.0
   Return: Declination in radians */
static double
solar_declination(double t)
{
	double e = obliquity_corr(t);
	double lambda = sun_apparent_lon(t);
	return asin(sin(e)*sin(lambda));
}

/* Difference between true solar time and mean solar time.
   t: Julian centuries since J2000.0
   Return: Difference in minutes */
static double
equation_of_time(double t)
{
	double epsilon = obliquity_corr(t);
	double l_0 = sun_geom_mean_lon(t);
	double e = earth_orbit_eccentricity(t);
	double m = sun_geom_mean_anomaly(t);
	double y = pow(tan(epsilon/2.0), 2.0);

	double eq_time = y*sin(2*l_0) - 2*e*sin(m) +
		4*e*y*sin(m)*cos(2*l_0) -
		0.5*y*y*sin(4*l_0) -
		1.25*e*e*sin(2*m);
	return 4*DEG(eq_time);
}

/* Hour angle at the location for the given angular elevation.
   lat: Latitude of location in degrees
   decl: Declination in radians
   elev: Angular elevation angle in radians
   Return: Hour angle in radians */
static double
hour_angle_from_elevation(double lat, double decl, double elev)
{
	double omega = acos((cos(fabs(elev)) - sin(RAD(lat))*sin(decl))/
			    (cos(RAD(lat))*cos(decl)));
	return copysign(omega, -elev);
}

/* Angular elevation at the location for the given hour angle.
   lat: Latitude of location in degrees
   decl: Declination in radians
   ha: Hour angle in radians
   Return: Angular elevation in radians */
static double
elevation_from_hour_angle(double lat, double decl, double ha)
{
	return asin(cos(ha)*cos(RAD(lat))*cos(decl) +
		    sin(RAD(lat))*sin(decl));
}

/* Time of apparent solar noon of location on earth.
   t: Julian centuries since J2000.0
   lon: Longitude of location in degrees
   Return: Time difference from mean solar midnigth in minutes */
static double
time_of_solar_noon(double t, double lon)
{
	/* First pass uses approximate solar noon to
	   calculate equation of time. */
	double t_noon = jcent_from_jd(jd_from_jcent(t) - lon/360.0);
	double eq_time = equation_of_time(t_noon);
	double sol_noon = 720 - 4*lon - eq_time;

	/* Recalculate using new solar noon. */
	t_noon = jcent_from_jd(jd_from_jcent(t) - 0.5 + sol_noon/1440.0);
	eq_time = equation_of_time(t_noon);
	sol_noon = 720 - 4*lon - eq_time;

	/* No need to do more iterations */
	return sol_noon;
}

/* Time of given apparent solar angular elevation of location on earth.
   t: Julian centuries since J2000.0
   t_noon: Apparent solar noon in Julian centuries since J2000.0
   lat: Latitude of location in degrees
   lon: Longtitude of location in degrees
   elev: Solar angular elevation in radians
   Return: Time difference from mean solar midnight in minutes */
static double
time_of_solar_elevation(double t, double t_noon,
			double lat, double lon, double elev)
{
	/* First pass uses approximate sunrise to
	   calculate equation of time. */
	double eq_time = equation_of_time(t_noon);
	double sol_decl = solar_declination(t_noon);
	double ha = hour_angle_from_elevation(lat, sol_decl, elev);
	double sol_offset = 720 - 4*(lon + DEG(ha)) - eq_time;

	/* Recalculate using new sunrise. */
	double t_rise = jcent_from_jd(jd_from_jcent(t) + sol_offset/1440.0);
	eq_time = equation_of_time(t_rise);
	sol_decl = solar_declination(t_rise);
	ha = hour_angle_from_elevation(lat, sol_decl, elev);
	sol_offset = 720 - 4*(lon + DEG(ha)) - eq_time;

	/* No need to do more iterations */
	return sol_offset;
}

/* Solar angular elevation at the given location and time.
   t: Julian centuries since J2000.0
   lat: Latitude of location
   lon: Longitude of location
   Return: Solar angular elevation in radians */
static double
solar_elevation_from_time(double t, double lat, double lon)
{
	/* Minutes from midnight */
	double jd = jd_from_jcent(t);
	double offset = (jd - round(jd) - 0.5)*1440.0;

	double eq_time = equation_of_time(t);
	double ha = RAD((720 - offset - eq_time)/4 - lon);
	double decl = solar_declination(t);
	return elevation_from_hour_angle(lat, decl, ha);
}

/* Solar angular elevation at the given location and time.
   date: Seconds since unix epoch
   lat: Latitude of location
   lon: Longitude of location
   Return: Solar angular elevation in degrees */
double
solar_elevation(double date, double lat, double lon)
{
	double jd = jd_from_epoch(date);
	return DEG(solar_elevation_from_time(jcent_from_jd(jd), lat, lon));
}

void
solar_table_fill(double date, double lat, double lon, double *table)
{
	/* Calculate Julian day */
	double jd = jd_from_epoch(date);

	/* Calculate Julian day number */
	double jdn = round(jd);
	double t = jcent_from_jd(jdn);

	/* Calculate apparent solar noon */
	double sol_noon = time_of_solar_noon(t, lon);
	double j_noon = jdn - 0.5 + sol_noon/1440.0;
	double t_noon = jcent_from_jd(j_noon);
	table[SOLAR_TIME_NOON] = epoch_from_jd(j_noon);

	/* Calculate solar midnight */
	table[SOLAR_TIME_MIDNIGHT] = epoch_from_jd(j_noon + 0.5);

	/* Calulate absoute time of other phenomena */
	for (int i = 2; i < SOLAR_TIME_MAX; i++) {
		double angle = time_angle[i];
		double offset =
			time_of_solar_elevation(t, t_noon, lat, lon, angle);
		table[i] = epoch_from_jd(jdn - 0.5 + offset/1440.0);
	}
}