摘要
本文用数学分析的方法研究了等日照时间ＥＩＤ和等日照方位ＥＳＡ的存在条件、存在范围及其分布规律，找到了计算ＥＩＤ和ＥＳＡ的具体数学表达式。
In this paper, the authors study the existing conditions, ranges and distributional laws of the EID and ESA on a slope with an analytical method. EID (Equal Insolation Duration) means that the insloation duration on a slope is not variable according to the data. In the other words, the insolation duration on a slope is equal in every day of a year. ESA (Equal Sunshine Azimuth) is the azimuth of a slope on which EID is existing. The insolation duration of a slope is relative to the sunrise and sunset hour angles ω 1 , ω 2 . ω 1 and ω 2 are composed of the sunrise and sunset hour angies ω s1 , ω s2 on the non horizental surface and the sunrise and sunset hour angles - ω 0 , ω 0 on the horizental surface. There are many different combined relations. For a slope with given latitude, gradient α and slope azimuth β , the combined relation can vary with the sun declination δ . When one combined relation changes into another one, there are two critical sun declinations δ c . They meet the following condition: tan 2δ c= sin 2 cos 2φ/(1- sin 2β cos 2φ) Becaus the sun declination δ vary on the range of (-23.45°,23.45°), the following relation is necessary for δ c existing: sin 2β cos 2φ≤ sin 223 45°On the other hand, when sin 2β cos 2φ> sin 223 45°,we can not get the critical sun declination δ c . In other words, the combined relations of the sunrise and sunset hour angles on a slope is not variable with the sun declination δ . On this condition the sunrise and sunset hour angles is identical in every day of a year. To go a step further, when sin β cos φ >sin23 45°, ω 1=ω s1 , ω 2=ω 0 ; when sin β cos φ <-sin23.45°, ω 1=-ω 0, ω 2=ω s2 . Based on the exhaustive study on this problem, we can get the conclusion: Only when the combined relation is not variable with the sun declination for given a latitude and slope, it is possible for EID and ESA to exist. For sin 2 β cos 2 φ >sin 223.45°, the insolation duration of a slope can be expressed byT s1 =E·(ω 0-ω s1 ) or T s2 =E·(ω 0+ω s2 ) They can be changed into following form with two parameters ω x and ω m :T s1 =E·(ω 0+ω x-ω m) T s2 =E·(ω 0+ω x+ω m)where ω x =arc cos(-tan x tan δ ), sin x =sin φ cos α -cos φ sin α cos β . According to the concepts of EID and ESA , we can get(ω x+ω 0)δ=0 Substituting ω x and ω 0 with arccos(-tan x tanδ) and arccos(-tan φ tan δ ) respectively, thenx=-φ and ω x+ω 0= π so we get the following expression: tan φ(1+ cos α)= sin α cos β To sum up, we obtain the existing conditions of EID and ESA as follows: sin 2β cos φ> sin 223 45° tan φ(1+ cos α)= sin α cos β As to the existing ranges of EID and ESA , it is clear that there is not restiction on gradient α for EID and ESA existance, orα∈0, π 2 According to the condition of tan φ (1+cos α )=sin α cos β , for given β,|φ| increases with α . When α =π/2, |φ| reaches its maximm and tan φ =cos β . To take place of β in inequality sin 2 β cos 2 φ >sin 223.45° with β in equality cos β =tan φ , we can get the range of latitude as follows: tan 2φ<1/(1+2 tan 223 45°) or |φ|<40 444° When φ =0, we can get the range of slope azimuth β as follows: sin 2β> sin 223 45° or 23 45°<|β|<156 55° For the Northern Hemisphere: 23.45°<| φ |≤90 and for the southern Hemisphere 90°≤ β <156 55°. Finally, we obtain the expressions for claculation EID and ESA EID=E·( π - arc cos ( tan 2φ+ cos α/ cos 2φ)) E
出处
《地理学报》
EI
CSSCI
CSCD
北大核心
1997年第5期412-420,共9页
Acta Geographica Sinica
