Comparison

Here's a current render from my sky simulator compared with one from Hosek and Wilkie's (one of the path tracer renders from their paper, scaled up to the same size as my render). I purposely matched the lens, the solar elevation angle, and the exposure, however I did not try to match the atmospheric properties, ground albedo, or tone-mapping. There are a few images in the Hosek–Wilkie paper with a solar elevation angle of 4°, and I simply chose the one that matched my render from the previous post most closely (which was the one with a turbidity of 6), then I re-exposed my (HDR) render to match the Hosek–Wilkie one as well as possible. Besides the numerous differences in the simulations themselves, there a few notable differences between these two images: Hosek and Wilkie's is tone-mapped while mine is not, mine uses a fisheye lens that extends beyond 180° to show the ground, and mine includes the solar disc. In spite of the differences, the images look remarkably similar to me. Using the lightbox, you can toggle between the two images.

My sky simulator.

Hosek and Wilkie's sky simulator.