Like in other render engines which use Hosek&Wilkie sky model turbidity parameter is not connected to Sun strenght, shadow softness, overall sky power and ambient strenght/color. I made another script ( after automated Exposure viewtopic.php?f=9&t=80367&p=415184&hilit=exposure#p415184 ) that automate lighting using only turbidity strenght. So you can simulate clear sky <-> cloudy sky using only one parameter in realtime which is very useful in animation.
All parameters were very carefully implemented and they are physically accurate.
Main idea was to make automated transition from clear sky to cloudy ambient lighting without changing other parameters than Turbidity. Fully working script with user interface will be ready within days. Small preview how it works :