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Ocatne Daylight Model is very great sky model, fully configurable and looks near as good as Hosek & Wilkie model but it has one serious issue. It doesn't have sky glow around Sun on higher turbidity levels that cause very flat shadowing without contact shadow on opposite to Sun areas. Please add sky glow, halo around Sun for this model just like Hosek & Wilkie.

From the second video, it appears that when "Custom Sky" is enabled, when you change the "Clear <-> Cloudy" parameter it's actually the sun size that gets changed, not the turbidity. In Octane standalone I can produce a very prominent sky glow around the sun with the Octane model by increasing turbidity. So I think this is an issue where the parameter from C4D is hooked up to Octane incorrectly.

I tried to reproduce this issue, but I've been unable to find that UI in C4D. A Google search for "clear sky sun power" gives no results. All I can find is the C4doctane DayLight Tag which has a different set of parameters and appears to work correctly. Which version of C4D are you using, and how do you create that setup? I am far from an expert in C4D so please excuse my lack of knowledge if it's something obvious.

I using my own Sky rig which increase Sun size during increasing Turbidity just like in reality where cloudy sky produce soft shadows. This works great using Hosek&Wilkie model but it looks that this doesn't work using Octane model because it produce too small amount of glow around Sun by default. This is why increasing Sun size during increasing Turbidity doesn't work here - increasing glow around Sun by Turbidity in Octane model is too small.

I see. Would it work to just decrease sun intensity? Note that the maximum turbidity value of 15 only represents a moderately hazy sky - if you are trying to reproduce actual overcast conditions your best option is to use an HDRI. The Hosek-Wilkie model actually only goes up to a turbidity of 10 (referred to by Hosek and Wilkie in their paper as "a slightly hazy day"). You may be able to mimic more overcast conditions with workarounds like increasing sun size, but this is not what any of the daylight models are designed for, and will produce other problems such as the one seen here.

Generally transition from clear sky to overcast can be done in Hosek&Wilkie using custom rig like I did. It can be mimic using Octane model by the same way but absence of big glow around Sun while increasing it size cause that we have not as detailed soft shadowing in shadows area.

I noticed that Turbidity above 10 doesn't make any visible changes to overall lighting look.