Fertilized paddy rice soils emit methane while flooded, emit nitrous oxide during flooding and draining transitions, and can be a source or sink of carbon dioxide. Changing water management of rice paddies can affect net emissions of all three of these greenhouse gases. We used a process-based biogeochemistry model to evaluate the annual emissions of CH4, N2O, and CO2 for continuously-flooded, single-, double-, and triple-cropped rice (3 baseline scenarios), and in further simulations, the change in emissions with changing water management to mid-season draining of the paddies, and to alternating crops of mid-season drained rice and upland crops (2 alternatives for each baseline scenario). We used a set of first-order atmospheric model to track the atmospheric burden of each gas over 500 years. We evaluated the dynamics of the radiative forcing due to the changes in emissions of CH4, N2O, and CO2 (alternative minus baseline), and compared this to standard calculations of CO2-equivalent emissions using Global Warming Potentials (GWPs). All alternative scenarios had lower CH4 emissions and higher N2O emissions than their corresponding baseline cases, and all but one sequestered carbon in the soil more slowly. Because of differences in emissions, in radiative forcing per molecule, and in atmospheric time constants (lifetimes), the relative radiative impacts of CH4, N2O, and CO2 varied over the 500-year simulations. In three of the six cases, the initial change in radiative forcing was dominated by reduced CH4 emissions (i.e., a cooling for the first few decades); in five of the six cases, the long-term radiative forcing was dominated by increased N2O emissions (i.e., a warming over several centuries). The overall complexity of the radiative forcing response to changing water management could not easily be captured with conventional GWP calculations.