Haze 2 filter is like a super duper UV filter that actually works in filtering unwanted light.
UV light reflecting off of water vapour in the air causes a bluish haze in pictures. Since water vapour is the culprit, the haze is most appearant in long distance shots over water or mountains (vegetation gives off water vapour). This problem is not so appearant in desert landscape shots.
Picture below is shot without any UV filtration. Distant mountain is appx 10 miles away.
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This bluish haze is very difficult to remove thru Photoshop. So the haze 2 filter is great help for landscape shots in mountains.
I'm not a big proponent of adding filters in front of lenses because the more layers of glass you add, the more likely you'll get flare. In general, I like to use Photoshop to duplicate filter effects instead of using real filters. But the effect of polarizer & haze 2 filters are very difficult to dupliate in Photoshop so these are 2 filters I like to carry around.
BTW, polarizers reduces out of phase light that is most appearant in reflections. If the landscapes you shoot has a lot of blue sky or reflected light, polarizers will help deepen the colors by reducing the reflected light. If it doesn't contain much reflected light, then it has no use other than acting as a ND filter.