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Vectorized Solar Azimuth and Elevation Estimation

version (3.58 KB) by Darin Koblick
Predict the topocentric solar position defined by geodetic lat, lon, Alt, and a universal time


Updated 18 Apr 2013

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Predict the azimuth and elevation of the Sun within +/- 1 degree at any geodetic latitude, longitude and altitude. Due to popular demand, this routine has been vectorized for speed.

Function Call: [Az El] = SolarAzEl('2008/02/18 13:10:00',60,15,0)

Input List:
UTC Date and Time - Use format YYYY/MM/DD hh:mm:ss or MATLAB date vector dimensions can be [N x 1]
Latitude - Site Latitude in degrees -90:90 -> S(-) N(+) dimensions can be [N x 1]
Longitude - Site Longitude in degrees -180:180 W(-) E(+) dimensions can be [N x 1]
Altitude - Site Altitude in km dimensions can be [N x 1]

Output List:
Az - Solar Azimuth angle in degrees [N x 1]
El - Solar Elevation/Altitude Angle in degrees [N x 1]

Cite As

Darin Koblick (2021). Vectorized Solar Azimuth and Elevation Estimation (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (13)

christie harper

in the following line
zequat = yeclip.*sin(23.4406.*(pi/180))+zeclip*cos(oblecl.*(pi/180));

the 23.4406 should be oblecl (the 23.4406 is for the example case from the website you cited)

AMIRI Abdessatar

Very helpful and very well documented Thank you so much

Khalid CHOUA


No correction for atmospheric refraction, which is around 0.5 deg when sun is on the horizon. So this routine give the Sun's true azel not apparent azel. Otherwise the accuracy appears to be much better then +-1 deg.

Ned Gulley

Thanks for the file! I used it to write this blog entry:


Here is a metricised version that can be 80x faster in some cases.

function [Az,El] = SolarAzElq(UTC,Lat,Lon,Alt)
%Sun possition from time and location (matricised)
% [Az,El] = SolarAzEl(UTC,Lat,Lon,Alt)
%UTC: UTC Time (MatLab's datenum or 'yyyy-mm-dd HH:MM:SS' cellstr or char)
%Lat: Latitude [-90 90] (deg)
%Lon: Longitude [-180 180] (deg)
%Alt: Altitude above sea level, optional (km)
%Az: Azimuth location of the sun (deg)
%El: Elevation location of the sun (deg)
% [Az,El] = SolarAzElq('1991-05-19 13:00:00',50,10,0)
% [UTC,Lat,Lon] = ndgrid(730486:1/24:730487,-90:5:90,-180:5:180);
% tic,[Az,El] = SolarAzElq(UTC,Lat,Lon);toc
% RA,DEC to Az,Alt

% Darin C. Koblick 02/17/2009 Authos
% Darin C. Koblick 04/16/2013 Vectorized
% Serge Kharabash 09/02/2016 Metricised

% [UTC,Lat,Lon] = ndgrid(730486:10:730852,-90:5:90,-180:5:180);
% tic,[Az1,El1] = SolarAzElq(UTC(:),Lat(:),Lon(:));toc,t1=toc;
% tic,[Az2,El2] = SolarAzEl(UTC(:),Lat(:),Lon(:),0);toc,t2=toc;
% max(abs(Az1-Az2)),max(abs(El1-El2)),t2/t1

if nargin<4 || isempty(Alt), Alt = 0; end
d2r = pi/180; %radiance to degrees conversion factor
r2d = 180/pi; %radiance to degrees conversion factor

if ischar(UTC)
UTC = cellstr(UTC);
if iscell(UTC)
UTC = reshape(datenum(UTC(:),'yyyy-mm-dd HH:MM:SS'),size(UTC));

%julian date
[year,month,day,hour,min,sec] = datevec(UTC);
if ndims(UTC)>2 %#ok<ISMAT>
year = reshape(year ,size(UTC));
month = reshape(month,size(UTC));
day = reshape(day ,size(UTC));
hour = reshape(hour ,size(UTC));
min = reshape(min ,size(UTC));
sec = reshape(sec ,size(UTC));
[jd,UTH] = juliandate(year,month,day,hour,min,sec);
day = jd - 2451543.5;

%Keplerian elements for the Sun (geocentric)
w = 282.9404 + 4.70935e-5 * day; %longitude of perihelion degrees
e = 0.016709 - 1.151e-9 * day; %eccentricity
M = mod(356.0470 + 0.9856002585 * day, 360); %mean anomaly degrees
L = w + M; %Sun's mean longitude degrees
oblecl = (23.4393 - 3.563e-7 * day)*d2r; %Sun's obliquity of the ecliptic, rad

%auxiliary angle
E = M + r2d*e.*sin(M*d2r).*(1+e.*cos(M*d2r));

%rectangular coordinates in the plane of the ecliptic (x toward perhilion)
x = cos(E*d2r)-e;
year = sin(E*d2r).*sqrt(1-e.^2);

%distance and true anomaly
r = sqrt(x.^2 + year.^2);
v = atan2(year,x)*r2d;

%longitude of the sun
lon = v + w;

%ecliptic rectangular coordinates
xeclip = r.*cos(lon*d2r);
yeclip = r.*sin(lon*d2r);
zeclip = 0;

%rotate to equitorial rectangular coordinates
xequat = xeclip;
yequat = yeclip.*cos(oblecl) + zeclip*sin(oblecl);
zequat = yeclip.*sin(0.409115648642983) + zeclip*cos(oblecl);

%convert to RA and Dec
r = sqrt(xequat.^2 + yequat.^2 + zequat.^2) - (Alt/149598000); %roll up the altitude correction
RA = atan2(yequat,xequat); %rad
delta = asin(zequat./r); %rad

%local siderial time
GMST0 = mod(L+180,360)/15;
SIDTIME = GMST0 + UTH + Lon/15;

%replace RA with hour angle HA
HA = 15*SIDTIME - RA * r2d;

%convert to rectangular coordinate system
x = cos(HA*d2r).*cos(delta);
year = sin(HA*d2r).*cos(delta);
z = sin(delta);

%rotate along an axis going east-west
xhor = x.*cos((90-Lat)*d2r) - z.*sin((90-Lat)*d2r);
yhor = year;
zhor = x.*sin((90-Lat)*d2r) + z.*cos((90-Lat)*d2r);

%find Az and El
Az = atan2(yhor,xhor) * r2d + 180;
El = asin(zhor) * r2d;

function [jd,UTH] = juliandate(year,month,day,hour,min,sec)
%calculate julian date & J2000 value
UTH = hour + min/60 + sec/3600; %J2000
idx = month <= 2;
year(idx) = year(idx) - 1;
month(idx) = month(idx) + 12;
jd = floor(365.25*(year+4716)) + floor(30.6001*(month+1)) + 2 - ...
floor(year/100) + floor(floor(year/100)/4) + day - 1524.5 + ...

Tunahan Liman

I need a code something like that. How can I get the codes?

Chad Greene

Superb. This function is well written and well documented. Thanks for sharing!

L. He

very nice program. I compare it with

the result is almost same. That one is more accurate,but not Vectorized yet.

Note: please change this line
jd = juliandate(datestr([y,mo,d,h,mi,s],'yyyy/mm/dd HH:MM:SS'),'yyyy/mm/dd HH:MM:SS');
do not use datestr but use date_num directly.
this will boost the speed, a lot


Very useful function. With a few updates it can handle vector time input. I would prefer the use of matlab UTC time input in order to speed up.


Ropey when using vector times: (line 36 generates a vector eccentricity: line 42 then requires an edit to force array multiply not matrix multiply). Still unable to get vector time version to agree with loop version....
As Mr. Picky, I would prefer time argin to be Matlab datenum, not string.
HOWEVER, this is the only code I've found that gives Azimuth round the full 360: most are 0-180 and it's up to you to find if its in the east or west... due to using code like

Anthony Kendall

Excellent function, it's fast, compact, and easily modified for my particular needs. Thank you very much! BTW, I compared it with sun position tables, ( and it does very well.

MATLAB Release Compatibility
Created with R2008b
Compatible with any release
Platform Compatibility
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