The link you posted just goes to the ArtefactoryLab home page but I'm assuming it's this in which case there are multiple layers to it.
You've got the curved fabric like bubble on the outer, then a straighter less bubbled piece on the inner.
A quick search for "Bruther Pavillion" gives lots of diagrams about it's construction.
As far as recreating the material - I don't think there is any fade in the opacity of the material. It looks like it could be an optical illusion due to the bubble like shape.
The green shimmer - isn't that just a reflection of the grass/trees?
There's definitely some kind of dirt map in play in those renders, perhaps to simulate the natural weathering you'd expect to see on something exposed to the elements as that pavillion is. The material looks relatively delicate so subtle scratches, dirt and smudges in the reflection/gloss and the renders look kind of overcast and damp/humid, so maybe they've tried to simulate that fogged/condensation type effect you'd get expect to see on clear panels in those environmental conditions.
I stayed in a geodesic dome type tent once, and the clear panels demonstrated that fogging effect in the right conditions too. Reference attached.
Either way the renders are very good.