The atmospheric angular momentum is closely related to variations in the Earth rotation. The atmospheric excitation function (AEF), known also as the atmospheric effective angular momentum function, is introduced in studying the atmospheric excitation of the Earth's variable rotation. It may be separated into two portions, i.e., the "wind" terms due to the atmospheric motion relative to the mantle and the "pressure" terms due to the variations of atmospheric mass distribution evident through surface pressure changes. The AEF wind terms during the period of 1948--2004 are reprocessed from the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP/NCAR) reanalysis 6-hourly wind and pressure fields. Some previous calculations were approximate, in that the wind terms were integrated from an isobaric lower boundary of 1000 hPa. To consider the surface topography effect, however, the AEF is computed by integration using the winds from the Earth's surface to 10 hPa, the top atmospheric model level, instead of from 1000 hPa. For these two cases, only a minor difference, equivalent to ~0.004 ms in length-of-day variation, exists with respect to the axial wind term. However, considerable differences, equivalent to 5~6 milliseconds of arc in polar motion, are found regarding equatorial wind terms. We further compare the total equatorial AEF (with and without the topography effect) with the polar motion excitation function (PMEF) during the period of 1980--2003. The equatorial AEF gets generally closer to the PMEF, and improved coherences are found between them when the topography effect is included.