Ice shelves control the dynamic mass loss of ice sheets through buttressing and their integrity depends on the spatial variability of their basal mass balance (BMB) i.e., the difference between refreezing and melting. Here, we present an improved technique - based on satellite observations - to capture the small-scale variability in the BMB of ice shelves. As a case study, we apply the methodology to the Roi Baudouin Ice Shelf, Dronning Maud Land, East Antarctica, and derive its yearly averaged BMB at 10 m horizontal gridding. We use mass conservation in a Lagrangian framework based on high-resolution surface velocities, atmospheric-model surface mass balance and hydrostatic ice-thickness fields (derived from TanDEM-X surface elevation). Spatial derivatives are implemented using the total-variation differentiation, which preserves abrupt changes in flowvelocities and their spatial gradients. Such changes may reflect a dynamic response to localized basal melting and should be included in the mass budget. Our BMB field exhibits much spatial detail and ranges from -14.7 to 8.6 m/a ice equivalent. Highest melt rates are found close to the grounding line where the pressure melting point is high, and the ice-shelf slope is steep. The BMB field agrees well with on-site measurements from phase-sensitive radar, although independent radar profiling indicates unresolved spatial variations in firn density. We show that an elliptical surface depression (10 m deep and with an extent of 0.7 km ×1.3 km) lowers by 0.5 to 1.4 m/a , which we tentatively attribute to a transient adaptation to hydrostatic equilibrium. We find evidence for elevated melting beneath ice shelf channels (with melting being concentrated on the channel'sflanks). However, farther downstream from the grounding line, the majority of ice shelf channels advect passively (i.e. no melting nor refreezing) toward the ice shelf front. Although the absolute, satellite-based BMB values remain uncertain, we have high confidence in the spatial variability on sub-kilometre scales. This study highlights expected challenges for a full coupling between ice and ocean models.

3 rasters data are provided :- the Lagrangian basal mass balance (BMB) is given in (ice-equivalent) m/a and is computed with the methodology described in Berger et al (2017, doi:10.5194/tc-11-2675-2017).- the surface elevation is given in meters relative to the Ellipsoid WGS84 and comes from SAR interferometry on TanDEM-X satellite data of 2013. The elevation data have been filtered using a Gaussian filter with a standard deviation of 7 pixels (see Berger et al, 2017, doi:10.5194/tc-11-2675-2017).- the thickness is given in ice-equivalent meters and is computed by assuming hydrostatic equilibrium with densities of 1027 kg/m³, 910 kg/m³ and 2 kg/m³ for seawater, ice and firn air, respectively. The firn air correction used here comes from Lenaerts et al (2017, doi:10.1038/nclimate3180).

Supplement to: Berger, Sophie; Drews, Reinhard; Helm, Veit; Sun, Sainan; Pattyn, Frank (2017): Detecting high spatial variability of ice-shelf basal mass balance (Roi Baudouin ice shelf, Antarctica). The Cryosphere, 11(6), 2675-2690