Wishful thinking at best. Most of the nitrogen fixing green manures will root 1-3 feet deep, some even to 5-6 feet.

Deeper rooting is better overall for soil improvement. It will distribute the nutrients and organic matter leading to better rooting of following crops.

Look at some of the clovers and perhaps mix with a grass for added organic matter.

Here is a link that might be useful: Overview of Cover Crops & Green Manures

bons: I don't think I can help, but I'm curious: why only 1", what causes you to make this (really) unworkable stipulation? Furthermore, you're too late for an over-winter nitrogen-fixing cover (I'm in zone 5 also). They usually need to flower for the best fixation. You're not too late for cereal rye, of course, but this won't fix nitrogen, and at 1" it would be a dead loss because the roots are so massy. Now if you want a year-long cover, hairy vetch or white clover would be great, but (again) not at 1" depth. Regards, Peter.

i am also curious why so shallow.And are you talking about a ground cover that will die off and decompose or are you talking about something you want to turn under. Are you wanting something to grow then decompose over spring flowering bulbs.usually the reason for planting what you yourself called " green manure " is to allow the roots to bring up different minerals etc . , die then add the humus created by the roots and foliage. If you want something to use over spring flowering bulbs maybe something like alfalfa meal Or pellets and dried blood would do the same thing along with a little bone meal. I use the cereal rye but more to add humus and help the soil perc better. I can buy 40 pound bags of composted cow manure for as low as $ 1.19 around here so nitrogen is not a big concern for me.The 1 inch thing befuddles me but then I am easily befuddled. happy gardening Johnny