# Estimate Solar Azimuth and Elevation given GPS position and time.

C++ code to estimate Solar Azimuth and Elevation given GPS position and time.

For reasons that I won’t go into here I found it necessary to estimate Solar Azimuth and Elevation given GPS position and time.

Now there is quite a bit of information on how to this on the old inter-web, none of it could be described as being ‘easy’, and most methods use the ‘equation of time’ and require you to know your current time zone in order to to calculate Local Solar Time (LST) so that you can then calculate the current hour angle.

However dynamically determining which time zone you’re in is very difficult, most approaches involve using a web API – but what can you do if you have no internet connection?

Lucky I found some Mathlab code written by Darin C. Koblick which calculates Solar Azimuth and Elevation using just latitude, longitude, UTC time and altitude. It models the Sun orbiting the Earth and does not require to know your time zone! It seems to work very well and I am very happy with the results so far (thanks Darin!)

I ported the code over to C++, trying to change as little from the original Mathlab code as possible, I have included the code here, please note the license text at the end.

For example, to estimate Azimuth and Elevation for Lat/Lon 52.975/-6.0494 at sea level for the current time:
[cpp]
//
double lat = 52.975;
double lon = -6.0494;
double altitude = 0;

double Az = 0.0;
double El = 0.0;
SolarAzEl(time(NULL), lat, lon, 0, &amp;Az, &amp;El);

printf("Azimuth: %f\n", Az);
printf("Elevation: %f\n", El);
//
</pre>
And, here is the C++ code for SolarAzEl():
<pre>#include
#include
#include

#ifndef M_PI
#define M_PI (3.14159265358979323846264338327950288)
#endif /* M_PI */

// Programed by Darin C.Koblick 2 / 17 / 2009
//
// Darin C.Koblick 4 / 16 / 2013 Vectorized for Speed
// Allow for MATLAB Datevec input in
// addition to a UTC string.
// Cleaned up comments and code to
// avoid warnings in MATLAB editor.
//
// Kevin Godden 9/1/2020 Ported from Matlab to C++, tried to change as little as possible.
// this is a non-vectorised port.
//
//————————————————————————–
//
// External Function Call Sequence :
//
// double lat = 52.975;
// double lon = -6.0494;
// double altitude = 0;
//
// double Az = 0.0;
// double El = 0.0;
// SolarAzEl(time(NULL), lat, lon, 0, &amp;Az, &amp;El);
//
// printf("Azimuth: %f\n", Az);
// printf("Elevation: %f\n", El);
//
// Or to calculate Az &amp; El for an arbitary UTC time:
//
//
// tm utc;
// tm_year is time since 1900
// utc.tm_year = y – 1900;
// Month is zero based, i.e. Jan is month 0
// utc.tm_mon = m – 1;
// utc.tm_mday = d;
// utc.tm_hour = 10;
// utc.tm_min = 16;
// utc.tm_sec = 00;
// utc.tm_isdst = 0;
//
// Get UTC time_t val
// tim = timegm(&amp;utc); // or _mkgmtime() on windows
//
// double altitude = 0;
// double Az = 0.0;
// double El = 0.0;
//
// double lat = 52.975;
// double lon = -6.0494;
//
// SolarAzEl(tim, lat, lon, 0, &amp;Az, &amp;El);
//
// printf("Az: %f\n", Az);
// printf("El: %f\n", El);
//
//
// Function Description :
//
// SolarAzEl will ingest a Universal Time, and specific site location on earth
// it will then output the solar Azimuth and Elevation angles relative to that
// site.
//
// Input Description :
//
// utc_time_point : time_t containing target time for sun position calculations.
//
// Lat : Site Latitude in degrees -90:90-&gt;S(-) N(+)
//
// Lon : Site Longitude in degrees -180:180 W(-) E(+)
//
// Alt : Altitude of the site above sea level(Km)
//
// Output Description :
// Az Azimuth location of the sun(deg)
// El Elevation location of the sun(deg)
//
//
// Source References :
// Solar Position obtained from :
// http ://stjarnhimlen.se/comp/tutorial.html#5
//

double julian_day(time_t utc_time_point);

void SolarAzEl(time_t utc_time_point, double Lat, double Lon, double Alt, double* Az, double* El) {
double jd = julian_day(utc_time_point);

double d = jd – 2451543.5;

// Keplerian Elements for the Sun(geocentric)
double w = 282.9404 + 4.70935e-5*d; // (longitude of perihelion degrees)
// a = 1.000000; % (mean distance, a.u.)
double e = 0.016709 – 1.151e-9*d; // (eccentricity)
double M = fmod(356.0470 + 0.9856002585*d, 360.0); // (mean anomaly degrees)

double L = w + M; // (Sun’s mean longitude degrees)

double oblecl = 23.4393 – 3.563e-7*d; // (Sun’s obliquity of the ecliptic)

// auxiliary angle
double E = M + (180 / M_PI)*e*sin(M*(M_PI / 180))*(1 + e*cos(M*(M_PI / 180)));

// rectangular coordinates in the plane of the ecliptic(x axis toward perhilion)
double x = cos(E*(M_PI / 180)) – e;
double y = sin(E*(M_PI / 180))*sqrt(1 – pow(e, 2));

// find the distance and true anomaly
double r = sqrt(pow(x,2) + pow(y,2));
double v = atan2(y, x)*(180 / M_PI);

// find the longitude of the sun
double lon = v + w;

// compute the ecliptic rectangular coordinates
double xeclip = r*cos(lon*(M_PI / 180));
double yeclip = r*sin(lon*(M_PI / 180));
double zeclip = 0.0;
//rotate these coordinates to equitorial rectangular coordinates
double xequat = xeclip;

double yequat = yeclip*cos(oblecl*(M_PI / 180)) + zeclip * sin(oblecl*(M_PI / 180));

double zequat = yeclip*sin(23.4406*(M_PI / 180)) + zeclip * cos(oblecl*(M_PI / 180));
// convert equatorial rectangular coordinates to RA and Decl:
r = sqrt(pow(xequat, 2) + pow(yequat, 2) + pow(zequat, 2)) – (Alt / 149598000); //roll up the altitude correction
double RA = atan2(yequat, xequat)*(180 / M_PI);

double delta = asin(zequat / r)*(180 / M_PI);

// Following the RA DEC to Az Alt conversion sequence explained here :
// http ://www.stargazing.net/kepler/altaz.html
// Find the J2000 value
// J2000 = jd – 2451545.0;
//hourvec = datevec(UTC);
//UTH = hourvec(:, 4) + hourvec(:, 5) / 60 + hourvec(:, 6) / 3600;

// Get UTC representation of time / C++ Specific
tm *ptm;
ptm = gmtime(&amp;utc_time_point);
double UTH = (double)ptm-&gt;tm_hour + (double)ptm-&gt;tm_min / 60 + (double)ptm-&gt;tm_sec / 3600;

// Calculate local siderial time
double GMST0 = fmod(L + 180, 360.0) / 15;

double SIDTIME = GMST0 + UTH + Lon / 15;

// Replace RA with hour angle HA
double HA = (SIDTIME*15 – RA);

// convert to rectangular coordinate system
x = cos(HA*(M_PI / 180))*cos(delta*(M_PI / 180));

y = sin(HA*(M_PI / 180))*cos(delta*(M_PI / 180));
double z = sin(delta*(M_PI / 180));

// rotate this along an axis going east – west.
double xhor = x*cos((90 – Lat)*(M_PI / 180)) – z*sin((90 – Lat)*(M_PI / 180));

double yhor = y;
double zhor = x*sin((90 – Lat)*(M_PI / 180)) + z*cos((90 – Lat)*(M_PI / 180));

// Find the h and AZ
*Az = atan2(yhor, xhor)*(180 / M_PI) + 180;
*El = asin(zhor)*(180 / M_PI);
}

double julian_day(time_t utc_time_point) {

// Extract UTC Time
struct tm* tm = gmtime(&amp;utc_time_point);

double year = tm-&gt;tm_year + 1900;
double month = tm-&gt;tm_mon + 1;
double day = tm-&gt;tm_mday;
double hour = tm-&gt;tm_hour;
double min = tm-&gt;tm_min;
double sec = tm-&gt;tm_sec;

if (month &lt;= 2) {
year -= 1;
month += 12;
}

double jd = floor(365.25*(year + 4716.0)) + floor(30.6001*(month + 1.0)) + 2.0 –
floor(year / 100.0) + floor(floor(year / 100.0) / 4.0) + day – 1524.5 +
(hour + min / 60 + sec / 3600) / 24;

return jd;
}

/*

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modification, are permitted provided that the following conditions are met :

*Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice,
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and/or other materials provided with the distribution

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED.IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

*/
[/cpp]