The Jakobshavn glacier was responsible for approximately 1 mm eustatic sea level rise in the period of 2000 to 2010 [Howat et al. 2011]. As such, the Jakobshavn glacier became one of the largest outlet glaciers in Greenland [Joughin et al. 2004]. Ice flow velocities within the same period reached over 10 km/yr with strong seasonal variation [Howat et al. 2011, Joughin et al. 2012]. More recently from 2011 until 2013, even higher ice flow velocities of at least 15 km/yr were observed [Lemos et al. 2018]. Due to the relatively high ice flow velocities, the ice discharge plays the largest role in the mass balance (MB) of the Jakobshavn glacier. Quantification of the ice discharge from ice flow velocities is however, not a common procedure. Yet the evolution of the ice discharge of single glaciers not only improves understanding of the climate-cryosphere system, but also aids quantification of sea level contribution on a drainage basin scale. To that end, this study embodies an indirect ice discharge estimation of the Jakobshavn glacier over the period of November 2010 until March 2016 using altimetry (CryoSat-2 Level 1b (L1b)) and gravimetry (GRACE Level 2 (L2)) data in combination with a regional climate model (RACMO 2.3p2). By subtraction of the altimetric and gravimetric mass balance estimates from the atmospheric component (i.e. the surface mass balance (SMB)), two ice discharge estimates are obtained. This approach does not suffer from the drawbacks involved when estimating ice discharge from velocity fields directly, which are based on offset tracking. Data gaps for long polar nights and clouds in the visible spectrum and decorrelation in general, when the duration between subsequent images over the same location is long, are thus avoided. This is because offset tracking algorithms require recognisable characteristics in subsequent satellite recordings to determine the velocity, i.e. satellite recordings need to be sufficiently correlated. To derive the mass balance from altimetry data, adequate spatial sampling is desired. To that end, this study applies swath processing to CryoSat-2 L1b data with an adapted waveform sample selection criterion to obtain an unprecedented spatial sampling with about 2 order of magnitude more height observations compared to conventional retracking techniques. As a consequence, elevation changes can be derived at a relatively high spatial resolution (250 m).
The elevations are converted to elevation changes, volume change and mass change using weighted least squares estimations (WLSE), hypsometric averaging and density models, respectively. The GRACE-based mass change estimate is acquired using a point-mass assumption at the location of the Jakobshavn glacier. The known, simulated point mass is then scaled to the observed mass by GRACE. In addition, data weighting of GRACE Stokes' coefficients is attempted using the full noise covariance matrix. Subsequently, a LSE is used to infer the mass balance from the two time series (with and without weighting of the Stokes' coefficients).