There are a number of these plants growing in the water and also very close to the edge, in the mud--never farther than a foot from the edge of the pool.

Each plant has 2 leaf stalks coming from the base, and the 2 leaf-stalks are different from each other. (I have learned from the plant ID glossary at my elbow that the term for this is heterophyllous!) One is a compound leaf about 10-15" tall with 8 sets of biserrate leaflets; the second compound leaf is somewhat shorter and dissected--most closely resembles a long leaf of Queen Ann's lace. Also on some plants, the leaflets of the compound leaf are much more incised than biserrate. (See third photo, linked below.)

Some plants have more than one of the fine, carrot-like leaves (also many of these leaves persist on the ground from last year, but are wilted and dead) and some plants are sending up a third stalk.

Over the last few days, the third shoot has developed further in this plant shown in my hand (and which plant now is planted in a pot of mud at home); it is another leaf like the one seen on the left here: http://www.flickr.com/photos/hortophile/4576637955/

Here is another view of a plant in situ:
http://www.flickr.com/photos/hortophile/4576637661/

This 3rd photo shows another plant with a slightly different type of leaf in combination with the leaf that looks like carrot: http://www.flickr.com/photos/hortophile/4576637233/

Closest suggestion I received so far is that the plant is water parsnip, but in locating on line more photos of that plant I am not seeing two distinct types of leaves. I may have to wait for the plant to flower before determining what it is.

This plant has me intrigued; hope someone can nail it down for me! Thanks! CK

IDK, just a guess from searching.

Global warming is one thing, but I seriously doubt this plant already has adapted to a vernal pool in central Ohio!
And I can reject with complete confidence that the plants (all in all, several dozen specimens scattered over about 1/3 acre) are escapees from an aquarium--especially since the evidence is that it has overwintered successfully here.

I definitely like the idea of sterile & fertile fronds--that did occur to me as I viewed the pinnate-leaved plant, and pondered horsetail and ferns. Oh, and yes: the two-three fronds definitely are growing from the same rootstock. All the plants are like this.

Thanks for the feedback, missa7. Each possibility I can eliminate brings me a minute step closer to the correct one! CK