Research Library Resource management technical reports Natural resources research 1-1-1992 Methods for calculating solar position and day length including computer programs and subroutines M L. Roderick Follow this and additional works at: https://researchlibrary.agric.wa.gov.au/rmtr Part of the Numerical Analysis and Scientific Computing Commons, and the The Sun and the Solar System Commons Recommended Citation Roderick, M L. (1992), Methods for calculating solar position and day length including computer programs and subroutines. Department of Primary Industries and Regional Development, Western Australia, Perth. Report 137. This report is brought to you for free and open access by the Natural resources research at Research Library. It has been accepted for inclusion in Resource management technical reports by an authorized administrator of Research Library. For more information, please contact [email protected]. ISSN 0729-3135 1992 Methods for Calculating Solar Position and Day Length including Computer Programs and Subroutines Prepared by: M.L. Roderick Land Management Western Australian Department of Agriculture South Perth Western Australia 6151 Resource Management Technical Report No. 137 Disclaimer The contents of this report were based on the best available information at the time of publication. It is based in part on various assumptions and predictions. Conditions may change over time and conclusions should be interpreted in the light of the latest information available. ¤ Director General, Department of Agriculture Western Australia 2004 METHODS FOR CALCULATING SOLAR POSITION AND DAY LENGTH Contents Page 1.0 Introduction ....................................................................................................... 1 2.0 Theoretical background .................................................................................... 2 2.1 Earth-Sun geometry ................................................................................... 2 2.2 Coordinate systems used in solar prediction .............................................. 3 2.2.1 Longitude/latitude ........................................................................... 3 2.2.2 Right ascension/declination coordinates ........................................ 3 2.2.3 Time ............................................................................................... 5 2.3 The Astronomic Triangle ............................................................................ 6 2.3.1 Solution of the Astronomic Triangle ................................................ 7 2.4 Corrections ................................................................................................ 8 2.4.1 Zenith ............................................................................................. 8 2.4.1.1 Parallax .............................................................................. 8 2.4.1.2 Atmospheric refraction ....................................................... 9 2.4.2 Azimuth .......................................................................................... 11 2.5 Solar ephemeris ......................................................................................... 11 3.0 Computing the length of day ............................................................................ 13 4.0 Uncertainty in solar position ............................................................................ 17 5.0 Computer routines ............................................................................................ 19 6.0 Summary ....................................................................................................... 21 Acknowledgments ................................................................................................. 22 References ............................................................................................................. 22 Bibliography ........................................................................................................... 22 Appendices ............................................................................................................ 23 A. Test data for computing solar position ................................................... 23 B. Documented source code and instruction for using subroutines ................................................................................ 23 iii METHODS FOR CALCULATING SOLAR POSITION AND DAY LENGTH List of Figures Page Figure 1. Orientation of Ecliptic and Equator (per Montenbruck, 1989, p3) ............ 2 Figure 2. Geographic Coordinate System .............................................................. 4 Figure 3. Right Ascension/Declination Coordinate System .................................... 4 Figure 4. Relationship between time based coordinate systems ............................ 6 Figure 5. The Astronomical Triangle ...................................................................... 7 Figure 6. Parallax correction .................................................................................. 9 Figure 7. Refraction correction ............................................................................... 10 Figure 8. Grid/true bearings ................................................................................... 11 Figure 9. Solar zenith at sun rise/set ...................................................................... 13 Figure 10. Day length (hrs) as a function of latitude for 1992. Latitudes shown are 0 to 40 degrees ................................................... 15 iv METHODS FOR CALCULATING SOLAR POSITION AND DAY LENGTH 1.0 Introduction Predicting the position of the sun is critical for any remote sensing studies in the visible and infra-red regions of the electromagnetic spectrum. In this part of the spectrum, the radiance recorded by a sensor is totally composed of reflected solar radiation. The sensor, target, sun geometry has an important effect on the nature of the recorded reflectances, according to the bidirectional reflectance of the target, and the position of shadows. In studies detecting change using multi-temporal imagery, modelling of the variable solar position is an important component in removing variation in radiance, not attributable to changes on the land surface. In addition to these remote sensing applications, agricultural scientists are interested in calculating the amount of solar radiation and day length as inputs to crop models. This paper briefly describes the theory underlying the calculation of solar position and the length of daylight hours. A number of corrections are described, as well as methods of integrating the data into a Geographic Information System (GIS). Traditional methods of calculating solar position use specific sets of tables such as The Star Almanac for Land Surveyors. These tables list solar ephemeris data for each day of the year (often at 6 hourly intervals). The use of such tables is not convenient for large numbers of calculations and a computer based method is preferred. A permanent almanac has been developed from formula given in The Astronomical Almanac. This almanac will generate predictions of solar ephemeris data, for any time in the period 1950 to 2050. Using the predictions of solar ephemeris, the solar azimuth and zenith angles may be computed with an approximate accuracy of 1’ of arc. Techniques for estimating the uncertainty in solar azimuth and zenith predictions, given uncertainty in the input data are derived using propagation of variance techniques. A method to calculate the length of day is developed. This is designed for the specific use of Agricultural scientists, in studies of the influence of day length on plant development. The theory has been implemented in a number of computer subroutines. The source code and documentation for these routines are included in a separate document (Appendix B) They are written in ANSI standard C and have been compiled on a number of platforms without any problems. In addition, a number of compiled programs are available for IBM PCs. 1 METHODS FOR CALCULATING SOLAR POSITION AND DAY LENGTH 2.0 Theoretical Background 2.1 Earth-Sun geometry The plane of the Earth’s orbit around the Sun is described as the ecliptic and is shown in Figure 1. The projection of the Earth’s equatorial plane (to infinity) is described as the celestial equator. The line of intersection of this plane with the ecliptic defines the equinoxes. The earth’s position at the vernal and autumnal equinoxes is shown in figure 1. The celestial equator remains practically fixed in position, although for very precise work such as geodetic Surveying, the variations in the Earth’s orbit and gravitational effects of other celestial objects need to be considered. The angle between the ecliptic and equatorial planes is termed the obliquity of the ecliptic. Figure 1. Orientation of Ecliptic and Equator (per Montenbruck, 1989, p3). In the southern hemisphere, the vernal equinox marks the point where the next season will be summer (i.e. Sun crosses the equator in a southerly direction), and the autumnal equinox indicates winter will soon arrive. These equinoxes occur on approximately 23rd September (vernal) and 21st March (autumnal) each year, although the exact time will vary slightly from year to year. These variations are caused by perturbations in the earth’s orbit and gravitational effects of the moon and other planets. It is common in precise applications, to actually define the datum year for the equinoxes. While the Earth