The widely used 15-year Gravity Recovery and Climate Experiment (GRACE) data sets do not conserve global total mass. They have a spurious decreasing trend of ~ 280 Gt/year. Various regions contribute differently to the global total mass loss error, with the Greenland Ice Sheet (GrIS) generating ~ 10% of the error alone. Atmospheric parameters from reanalysis datasets drive a well-tested ice model to generate mass variation time series over the GrIS for 2002–2015. Because shorter timescale spikes of ~ 10–30 Gt in GRACE measurements are physically based, only the overall trend of ~ 30 Gt/year requires correcting. A more accurate mass loss rate estimate for 2002–2015 is ~ 120 Gt/year, considerably below previous estimates. With the water redistribution to lower latitudes and other effects from a warming climate, the nontidal Earth moment of inertia (MOI) also increases. After rectification, the GRACE measured mass redistribution shows a steady, statistically robust (passed a two-tailed t-test at p = 0.04 for dof = 15) rate of MOI increase reaching ~ 10.1 × 1027 kg m2/year, equivalent to a 10.91 μs/year increase in the length of a day, during 2002–2017.