Mass changes of the Greenland ice sheet may be estimated by the Input Output Method (IOM), satellite gravimetry, or via surface elevation change rates (dh/dt). While the first two methods have been shown to agree well in reconstructing ice-sheet wide mass changes over the approximately the last decade (since 2003 for gravimetry), there are few long records from satellite altimetry and none that provide a time evolving trend that can be readily compared with the other methods. Here, we interpolate radar and laser altimetry data between 1995 and 2014 in both space and time to reconstruct the evolving volume changes. We use a novel interpolation approach that incorporates prior information related to ice dynamics. A firn densification model forced by the output of a regional climate model is used to convert volume to mass. We find that mass changes are dominated by SMB until about 2001, when mass loss rapidly accelerates. The onset of this acceleration is somewhat later, and less gradual, compared to the IOM. Our time averaged mass changes agree well with recently published estimates based on gravimetry, IOM, laser altimetry, and with radar altimetry when merged with airborne data over outlet glaciers. We demonstrate, that with appropriate treatment, satellite radar altimetry can provide reliable estimates of mass trends for the Greenland ice sheet. We also examine the impact of the extreme melt event in 2012 on the volume and, consequent, mass change for that year and compare with GRACE to assess how well our methodology accounts for this anomaly. Our time series could, potentially, be extended back to 1992 with the aid of ERS-1 data but the early part of this mission had varying orbit repeat cycles, which adds complexity to the analysis. The Cryosat-2 data used, since 2010 provides robust results, which can be extended for the length of the mission and supplemented with Sentinel 3 data after its launch.