Ring-diagram analyses have become a powerful local helioseismic tool for studying large-scale flows in the upper solar convection zone. Using this technique on a dense-pack mosaic of many small regions extracted from the full-disk Doppler velocity data taken with the Michelson Doppler Imager (MDI) on SOHO, we study how the mean meridional and zonal flows vary with depth and latitude over the course of the advancing solar cycle from 1996 to 2000.