The aperiodic variations in GNSS station position time series are generally best described by a combination of white and flicker noise. The importance of accounting for the presence of flicker noise when extracting geophysical signals from GNSS time series is commonly recognized. However, the origins of the observed flicker noise are still unclear. Here, we analyze the aperiodic content of 15-year long GRACE-derived equivalent water height time series. We find that they exhibit power-law noise in hydrologically active areas, which is well correlated among different GRACE solutions, and must therefore represent real surface mass transport. Then, we quantify how much of the flicker noise in GNSS time series can be explained by loading deformation under such aperiodic surface mass transport.