Revised January 2008 • NREL/TP-560-34302
Solar Position Algorithm for
Solar Radiation Applications
Ibrahim Reda and Afshin Andreas
National Renewable Energy Laboratory
1617 Cole Boulevard
Golden, Colorado 80401-3393
NREL is a U.S. Department of Energy Laboratory
Operated by Midwest Research Institute • Battelle • Bechtel
Contract No. DE-AC36-99-GO10337
Revised January 2008 • NREL/TP-560-34302
Solar Position Algorithm for
Solar Radiation Applications
Ibrahim Reda and Afshin Andreas
Prepared under Task No. WU1D5600
National Renewable Energy Laboratory
1617 Cole Boulevard
Golden, Colorado 80401-3393
NREL is a U.S. Department of Energy Laboratory
Operated by Midwest Research Institute • Battelle • Bechtel
Contract No. DE-AC36-99-GO10337
Acknowledgment
We thank Bev Kay for all her support by manually typing all the data tables in the report into
text files, which made it easy and timely to transport to the report text and all of our software
code. We also thank Daryl Myers for all his technical expertise in solar radiation applications.
NOTICE
This report was prepared as an account of work sponsored by an agency of the United States
government. Neither the United States government nor any agency thereof, nor any of their employees,
makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy,
completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents
that its use would not infringe privately owned rights. Reference herein to any specific commercial
product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily
constitute or imply its endorsement, recommendation, or favoring by the United States government or any
agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect
those of the United States government or any agency thereof.
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Table of Contents
Abstract .....................................................................v
Introduction ..................................................................1
Time Scale ...................................................................2
Procedure ....................................................................3
SPA Evaluation and Conclusion .................................................12
List of Figures
Figure 1. Uncertainty of cosine the solar zenith angle resulting from 0.01
/
and 0.0003
/
uncertainty in the angle calculation..........................................13
Figure 2. Difference between the Almanac and SPA for the ecliptic longitude & latitude, and the
apparent right ascension & declination on the second day of each month at 0-TT for
the years 1994, 1995, 1996, and 2004 ......................................14
Figure 3. Difference between the Almanac and SPA for the solar zenith and azimuth angles on
the second day of each month at 0-TT for the years 1994, 1995, 1996, and 2004. ....15
References ..................................................................16
Appendix
Equation of Time ........................................................... A-1
Sunrise, Sun Transit, and Sunset ............................................... A-1
Calculation of Calendar Date from Julian Day .................................... A-6
Example ................................................................. A-15
C Code: SPA header file (SPA.h) ............................................. A-17
C Code: SPA source file (SPA.c) ............................................. A-19
iii
List of Appendix Figures
Figure A2.1. Difference between the Almanac and SPA for the Ephemeris Transit on the second
day of each month at 0-TT for the years 1994, 1995, 1996, and 2004. ........ A-5
List of Appendix Tables
Table A4.1. Examples for Testing any Program to Calculate the Julian Day ............. A-7
Table A4.2. Earth Periodic Terms .............................................. A-7
Table A4.3. Periodic Terms for the Nutation in Longitude and Obliquity .............. A-13
Table A5.1. Results for Example.............................................. A-15
iv
