for the rhizomes, so that was interesting. I also noted she's in zone 3 which is brrrrrrrrr cold. I'm in 6B/7A and it's much warmer. I moved from zone 10, so I have always left much more on top of the soil. As a matter of fact, last year, I was separating irises and I didn't have time to plant them, so I took large clumps and simply put the whole affair on top of the ground with the full intention of coming back and planting properly. They completely took root and may actually put out flowers. That encouraged me to keep on thinning that bed. These are naturalizing irises. I started out with about a dozen rhizomes from a neighbor when we moved in about 10 years ago and I have separated and moved and given away and separated them. They are quite lovely and faithfully bloom each year, but I digress!
I find that irises do much better when most of the rhizome is above ground, I usually leave out about 1/2 on top and separate when they get too crowded. They are also groundhogs and don't like other plants around them, so create nice beds for them and you'll be rewarded for years and years to come.