A lot will leach out spread in the field too, either as methane or nitrate. Only way to save all the nitrogen is to bury it. Compost doesn't have any nitrogen, but does have high levels of P K, and carbon, and is readily available when spread. Nitrogen is cheap to buy compared to phosphorus.That smell that burns the nose is nitrogen leaving. I am a big believer in allowing it to compost in a thin layer spread over the field. I would much rather have that nitrogen in the field than have it leave the pile out to the atmosphere.