坡面日出日没时角的配置关系与太阳赤纬

若坡面的坡向β和纬度φ满足条件| sinβcosφ|≥sin 23°26',则坡面日出日没时角的配置关系不随太阳赤纬的变化而变化;反之,则存在两个绝对值相等、符号相反的一般临界赤纬δc,以-δc、δc为界,坡面日出日没时角的配置关系具有三种不同的形式。坡面日出日没时角的配置关系及其随太阳赤纬的变化,可根据δ=δc时,非水平面日出日没时角和水平面日出日没时角的相等关系、坡向、坡度确定。在水平面或非水平面极昼、极夜前后,坡面日出日没时角的配置关系也会发生变化。

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

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=-ω₀,ω₂ =ω_s2 for slope azimuth β between 0°and 180°,or ω₁ =ω_s1,ω₂ =ω₀ 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=-ω₀,ω₂ =ω_s2 for slope azimuth β is between 0°and 180°,or ω₁ =ω_s1,ω₂ =ω₀ 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=-ω₀,ω₂=ω_s2 when δ>δ_c, then the match relation is ω₁ =ω_s1,ω₂ =ω₀ when δ<δ_c. If the match relation is no sunshine when δ>δ_c, then the match relation is two sunshines when δ<δ_c,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.