MI, simply put, air layering is a method of propagation where a ring of bark is removed on a trunk or branch with the hope of roots forming above the debarked region. The air layered portion is removed once enough roots have grown to sustain it. What you have are cuttings, though large ones, where a portion of the tree is removed without roots and placed in soil or water with the hope that roots will grow. Most woody plants won't develop roots when left in water, though willows apparently will, and I have heard someone say that they did have success doing this with a bald cypress. Certain trees strike easily from cuttings, though they are usually treated with a rooting hormone, placed in a fast draining soil, and kept out of the sun and misted frequently. They're also usually only 4-6" tall

. Any way, I hope this helps.
Dave