. ▁ ▁Thus ▁Q ▁is ▁− 1 ▁and ▁U ▁remains ▁ 0 . ▁ ▁Al ong ▁the ▁horizon ▁U ▁is ▁always ▁ 0 . ▁Q ▁is ▁always ▁− 1 ▁except ▁in ▁the ▁East ▁and ▁West . ▁ ▁The ▁scatter ing ▁angle ▁( the ▁angle ▁at ▁the ▁z en ith ▁between ▁the ▁solar ▁direction ▁and ▁the ▁observer ▁direction ) ▁along ▁the ▁horizon ▁is ▁a ▁circle . ▁ ▁From ▁the ▁East ▁through ▁the ▁West ▁it ▁is ▁ 1 8 0 ° ▁and ▁from ▁the ▁West ▁through ▁the ▁East ▁it ▁is ▁ 9 0 ° ▁at ▁tw il ight . ▁ ▁When ▁the ▁sun ▁is ▁setting ▁in ▁the ▁West , ▁the ▁angle ▁is ▁then ▁ 1 8 0 ° ▁East ▁through ▁West , ▁and ▁only ▁ 9 0 ° ▁West ▁through ▁East . ▁ ▁The ▁scatter ing ▁angle ▁at ▁an ▁alt itude ▁of ▁ 4 5 ° ▁is ▁consistent . ▁ ▁The ▁input ▁st okes ▁parameters ▁q ▁and ▁u ▁are ▁then ▁with ▁respect ▁to ▁North ▁but ▁in ▁the ▁alt itude - az im uth ▁frame . ▁We ▁can ▁easily ▁un wrap ▁q ▁assuming ▁it ▁is ▁in ▁the ▁+ alt itude ▁direction . ▁ ▁From ▁the ▁basic ▁definition ▁we ▁know ▁that ▁+ Q ▁is ▁an ▁angle ▁of ▁ 0 ° ▁and ▁- Q ▁is ▁an ▁angle ▁of ▁ 9 0 ° . ▁Therefore , ▁Q ▁is ▁calculated ▁from ▁a ▁s ine ▁function . ▁Similarly ▁U ▁is ▁calculated ▁from ▁a ▁cos ine ▁function . ▁The ▁angle ▁of ▁polar ization ▁is ▁always ▁per pend icular ▁to ▁the ▁scatter ing