SCIENTIA GEOGRAPHICA SINICA ›› 2005, Vol. 25 ›› Issue (3): 361-366.

### Match Relations Between Sunrise and Sunset Hour Angles of Slope Surfaces and Solar Declination

SUN Han-Qun

1. Geography Department, Jiangsu Institute of Education, Nanjing, Jiangsu, 210013
• Received:2004-04-22 Revised:2004-08-24 Online:2005-05-20 Published:2005-05-20

Abstract: For any given slope surface, if slope azimuth β and latitude φ meet with the condition: |sinβcosφ|≥sin 23°26ˊ= 0.3977,then,the match relations between sunrise and sunset hour angles will not alter with the solar declination. And, in this condition, the match relation is always ω1=-ω02s2 for slope azimuth β between 0°and 180°,or ω1s120 for slope azimuth β between 0°and -180°within all the year. On the other hand, if |sinβcosφ|c, which are called general critical solar declinations, where their absolute values are equal but their signs are oppositional. Between the two general critical solar declinations, the match relation is always ω1=-ω02s2 for slope azimuth β is between 0°and 180°,or ω1s120 for slope azimuth β is between 0°and -180°. Beyond the two general critical solar declinations, match relations are alternate with eath other. If the match relation is ω1=-ω02s2 when δ>δc, then the match relation is ω1s120 when δ<δc. If the match relation is no sunshine when δ>δc, then the match relation is two sunshines when δ<δc,vice versa. Beyond the two general critical solar declinations, the match relation are symmetrical about slope azimuth β and solar declination between the northern hemisphere and southern hemisphere. The solar declinations,when the horizontal surfaces or no-horizontal surfaces are just polar day or just polar night,are called special critical solar declination. The absolute value of special critical solar declination is larger than the the absolute value of general critical solar declination.So the match relations between sunrise and sunset hour angles may be dealt with separately after the polar day or polar night appear on the horizontal surfaces or no-horizontal surfaces. Beyond the two general critical solar declinations,dividing with a special critical solar declination,there are maybe two different match relations between sunrise and sunset hour angles. The match relations of two sunshines before polar day on the no-horizental surfaces can be transformed into one sunshine after polar day. The match relations of one sunshine before polar night on the no-horizental surfaces can be transformed into no sunshine after polar night.After polar day appears on the horizental surfaces,There may be three different match relations:one sunshine,two sunshine and slope polar day. After polar night appears on the horizental surfaces,the slope will be no sunshine.

CLC Number:

• Q463.21