The northern annular mode (NAM) is the leading mode of variability in the Northern Hemisphere. The NAM consists of a meridional dipole of the zonal mean zonal wind that extends into the stratosphere during the winter season. During the high-index state of the NAM, high-latitude westerly winds are stronger than normal, leading to a stronger and colder polar vortex. Over the past few decades, observations show a trend toward higher NAM index values. To investigate whether this trend is a result of natural variability or is related to greenhouse warming, a mechanistic model is developed that provides a simple analogue of the NAM. The model represents the interaction between the zonally symmetric flow and planetary waves for two meridional modes of variation. Greenhouse warming is specified in the model by varying the radiative equilibrium meridional temperature gradient. Variations in the second meridional mode qualitatively resemble those of the observed NAM. Model runs that correspond to larger greenhouse gas concentrations yield on average higher NAM index values.