One of the topics that I am studying in my PhD required an implementation of a sky model and we chose to implement the Preetham Sky Model.
Although there has been some criticism about the accuracy of the model (mainly for turbidities farther from the "clear sky" value), in my opinion, it provides a good approximation of what we should expect. We did however found that sky chrominance values were a little bit "too red" when we got close to sunset and sunrise.
Sun radiance is also tricky to compute: you need to attenuate the radiance according to your position on Earth, appropriately accounting for the traversal of the atmosphere (a big thanks to Kevin Beason and Pierre-Yves for helping with this :)).