This is a technique post, not a particularly pretty picture.
For Christmas I converted a camera body to infrared (720nm filter). I came across a hazy mid-day scene recently which was great for demonstrating how well infrared cuts through haze (more accurately how much less infrared light scatters from haze than visible light). For comparison I also shot with a polarizer, in this case the sun was at nearly a 90 degree angle to the shot so this is about as much as a polarizer will ever be able to do.
All three are crops of a larger shot, processed identically at standard settings in LR with the only alteration being spot WB for the IR shot to keep it mostly neutral. Notice the differences in detail and contrast in the distant mountains.
Finally, just for kicks, here is the full frame shot with some quick post-processing applied (contrast, clarity, curves and a gradient adjustment for the sky and background):
Quick update, someone on DPR asked about blending the IR and color versions. The clouds moved a fair bit between the two shots, but here is a luminance blend of the IR version over the polarizer version:
No other post processing besides the blend, perhaps with some color work (probably in LAB) an interesting color/IR hybrid that didn't look too wacky could be made (presuming you shot intending to do this and didn't let the clouds move while you goofed off with other things in between the shots like I did ).
If you are looking at false color in your IR, it is often better to do your RAW conversion from DPP and adjusting the WB eyedropper there, rather than in ACR. Life Pixel is pretty emphatic about using it. For monochrome not necessary. IR does cut through haze very well. Nice conversion.
. Rick