Does organic farming have an "enormous carbon footproot"

Gary Jones thinks it does, as do others that he points to:

Organic farming is not the best option from a climate change point of view.
. . .
Farms only represent ~2% of US CO2 emissions but around a third of the anthropogenic methane (a gas which is 21-24 times as potent as a greenhouse gas) and nearly 80% of the anthropogenic nitrous oxide (295-310 times as potent as CO2).
. . .
a major climate change advantage almost universally claimed for Organic (no fossil energy to produce the N), actually represents a carbon footprint that is enormous.