Northern peatlands sequester carbon and emit methane, and thus have both cooling and warming impacts on the climate system through their influence on atmospheric burdens of CO2 and CH4. These competing impacts are usually compared by the global warming potential (GWP) methodology, which determines the equivalent CO2 annual emission that would have the same integrated radiative forcing impact over a chosen time horizon as the annual CH4 emission. We use a simple model of CH4 and CO2 pools in the atmosphere to extend this analysis to quantify the dynamics, over years to millennia, of the net radiative forcing impact of a peatland that continuously emits CH4 and sequesters C. We find that for observed ratios of CH4 emission to C sequestration (roughly 0.1--2 mol mol-1), the radiative forcing impact of a northern peatland begins, at peatland formation, as a net warming that peaks after about 50 years, remains a diminishing net warming for the next several hundred to several thousand years, depending on the rate of C sequestration, and thereafter is or will be an ever increasing net cooling impact. We then use the model to evaluate the radiative forcing impact of various changes in CH4 and/or CO2 emissions. In all cases, the impact of a change in CH4 emissions dominates the radiative forcing impact in the first few decades, and then the impact of the change in CO2 emissions slowly exerts its influence.