Double Sunrise and Sunset

The northern (southern) high latitudes with steep slope produce two sunrises, (sun­sets) 0sr1, 0sr2, with 0sr1 > 0sr2 (0ss1, 0ss2, with 0SS2 > 0sst) hour angles. For in­

stance, if the critical slope in Fig. 3.29 is exceeded then a shaded slope is produced during an interval that would otherwise be in light. This slope may be insolated prior to and after that interval of darkness hence causing to two sunrises and two sunsets. The first sunrise occurs when the sun first shines on the slope on any clear-sky day. The first sunset ends the first period of insolation, at which time darkness sets in on the slope until the second sunrise (0sr2) restarts insolation. The latter ends with the second sunset (0ss2). In this case the energy input Eq. 3.68 can be expressed as

where all the intervening terms are defined exactly in association with Eq. 3.59.

The angles are expressed in radians. Hence, 0sri = ф8Го, 0ssi = Ф81:, Фей = Ф88, and 0ss2 = 0ss0, where 08r0 and ф880 are defined in Eqs. 3.107 and 3.108, respectively, and correspond to the horizontal-case hour angles. In the case of double sunrise and sunset situations the duration of daily insolation can be expressed as follows:

1

Ddi = ^ssl – Фsr1 + Фss2 – Фsr2) • (3.114)

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