We followed the spirit of RTopo-1 and compiled global fields for

bedrock topography (ocean bathymetry, surface topography of continents, bedrock topography under grounded or floating ice);

RTopo-2 has been compiled by combining various gridded data sets (Table ) with different grid spacings, projections, and coverages (Fig. ) into global maps. For data handling, interpolation, and blending we developed a command script written in Interactive Data Language (IDL). Using a global bathymetry data set (see below for details) as a backbone, regional grids have been created from various source data sets and subsequently merged into the existing fields. Interpolation from different projections to our geographic grid was based on Delaunay triangulation and subsequent linear interpolation. The regional “patches” have been blended into the existing fields using weight functions that – depending on the distance from the boundaries of the regional grids – vary between 0 and 1 and ensure a smooth transition between the two data sets without smoothing the topographies. As weight functions we used hyperbolic tangent functions with empirically derived length scales that have been cut off below values of 0.05 and above 0.95 to avoid overly long tails. This approach yields good results only when the two grids to be merged do not differ too strongly in the area of overlap, but with the data sets used here it was always possible to choose the location and width of the transition zone in a way that ensured a smooth blending.

For each of the newly incorporated regional grids, we had to ensure or enforce consistency with the existing topographies. The necessity for this step is quite obvious when independent data sets are combined; interpolation of discontinuous fields (an obvious example here is the discontinuity at ice shelf fronts) is another source for the creation of local inconsistencies that need to be cured. For RTopo-2, the term consistency implies that

ice thickness > 0 in the ice-covered region (with ice thickness = surface height minus lower ice topography);

According to , sub-ice bathymetry for Getz Ice Shelf cavity in Bedmap2 (Fig. a) has been derived from the topography grid of . While this data set provides an excellent bathymetry map for the open Amundsen Sea, it suffers from missing data for the sub-ice shelf cavities. As a result, Bedmap-2 suggests a very shallow water column in large parts of the cavity. For RTopo-2 (Fig. b), we decided to go back to the submarine trough structure that RTopo-1 inherited from ALBMAP . Upper and lower ice surface topographies and the surface type mask (locations of coast and grounding line) continue to be derived from Bedmap2. A smooth transition of sub-ice shelf bathymetry to the bedrock topography under grounded ice (from Bedmap2) and to open-ocean bathymetry (from IBCSO) is achieved using tanh functions in blending zones of ≈15 km width (Fig. c). As a result, water column thickness in the sub-ice cavity (Fig. d) features continuous troughs extending from the open-ocean continental shelf across the ice front towards the grounding line. The high basal melt rates suggested for Getz Ice Shelf (e.g. ) make the existence of such transport pathways for warm water seem plausible. A strict evaluation, however, is made very difficult by the lack of sub-ice bathymetry data, and there is no proof that the structures we suggest are correct.

A similar case can be made for Abbot Ice Shelf. For the eastern part of Abbot Ice Shelf, sub-ice bathymetry in Bedmap2 is derived from the data set, which incorporates ALBMAP bedrock topography in the sub-ice cavity. For the western part of the Abbot Ice Shelf, however, Bedmap2 utilizes the bathymetry map of , which again leads to a very small water column thickness with virtually no connection to the open ocean in this sector of the ice shelf. We decided to restore the structure of a sub-ice trough connected to the eastern Amundsen Sea from ALBMAP for the Abbot Ice Shelf cavity west of 98∘ W. Also here, it should be kept in mind that bathymetry under this ice shelf is only weakly constrained.

For Larsen C Ice Shelf cavity, Fig. 6 in indicates that bedrock topography was derived from RTopo-1. On a closer look, however, substantial differences between Bedmap2 and RTopo-1 can be seen in this area. Specifically, many of the deep troughs that had been inferred from ice draft at the grounding line in RTopo-1 have been removed (or are far less pronounced) in Bedmap2. Revisiting all the data sets in question here, we found that the RTopo-1 ice and bedrock topographies along the southern part of Larsen C grounding line imply an ice thickness maximum to be found not within the ice streams feeding the ice shelf but shortly downstream from where the ice comes afloat. This pattern is most obvious for the ice stream between the Joerg and Kenyon peninsulas in the southwestern corner of Larsen C Ice Shelf and not likely to be a good approximation to reality. Given that it can be safely assumed that the ice topographies in Bedmap2 are more reliable than the combination of data sets used in RTopo-1, we conclude that there is no sufficient evidence for the existence of the deep throughs suggested near the Larsen C grounding line in RTopo-1. RTopo-2 thus simply adopts the Larsen C cavity geometry from Bedmap2.

Bedmap2 bathymetry under the floating Fimbulisen is claimed to be derived from RTopo-1 but in fact deviates from the latter substantially. Specifically, the deep troughs between the islands (ice rises) in the eastern part of the cavity (i.e. between 1 and 5∘ E) that inferred from original seismic data are no longer there. We decided to go back to the / data set that was already incorporated in RTopo-1 for the Fimbulisen cavity between 1∘ and 5∘ E.

In August 1986, three giant icebergs (A-22, A-23, and A-24), each one between 3000 and 4000 km2 in area, calved from the Filchner Ice Shelf front and grounded at the eastern Berkner Bank. Iceberg A-24 came ungrounded in March 1990 and drifted northward through the Weddell and Scotia seas; icebergs A-22 and A-23 broke in two in 1994 and 1991, respectively. One of their remnants, A-23A, is still grounded on the eastern slope of Berkner Bank and continues to form a barrier to the sea ice drifting in this region, frequently creating a polynya in its lee . When modelling sea ice in this area, a comparison between modelled and observed (mostly remote sensing) data is strongly complicated if this effect is omitted in the model see e.g.. A similar case can be made for the iceberg's effect on the ocean currents on the continental shelf. Despite the fact that showed that iceberg calving and grounding does change the circulation and hydrography in the Filchner Ice Shelf–ocean system, it is not common for today's ocean models to take this into account.

To enable high-resolution modelers to do the model-to-data comparison in a more consistent way – especially given that data coverage is about to improve considerably in the framework of ongoing and planned field activities in the area – and to achieve a more realistic representation of the local ocean currents in hindcast simulations, we decided to include the signature of A-23A in RTopo-2. The area covered by the iceberg was picked from a composite of 2013 MODIS images and defined to be covered with grounded ice, i.e. ice with a lower surface topography identical to the ocean bathymetry (which clearly is only a schematic representation of the real situation). Freeboard of the iceberg is represented as a constant value in RTopo's surface height field; it is computed from Archimedes' principle assuming densities of ocean and ice to be 1028 and 910 kg m-3, respectively. Thickness of the iceberg in this equation is assumed to be such that its draft is equal to the minimum water depth in the area that is covered by the iceberg. Eventually, this procedure yields a freeboard (surface height) value of about 42 m over the iceberg area, which is consistent with the freeboard derived from SAR interferometry applied to TanDEM-X image pairs of June 2013 (M. Rankl, personal communication, 2016).

Note that the original bathymetry grid under the iceberg is fully preserved so that the whole feature can be removed without any loss of information in case this seems desirable in any particular application of the data set.

In addition to the maps of the bedrock and ice topographies we provide a global mask which distinguishes between open ocean, bare land, grounded ice, and floating ice (Fig. ).

On the polar continents, the mask largely follows M-2014 for Greenland and Bedmap2 for Antarctica. Ice caps not connected to the Antarctic ice sheet or Greenland mainland have been removed from the mask and classified as bare land. Ice surface height in these cases has been adopted as bedrock surface height. In contrast to RTopo-1, the surface type mask in RTopo-2 contains information about rock outcrops (surface type “bare land”) in Antarctica.

Lakes and enclosed seas outside Antarctica and Greenland are marked as bare land in the mask but are still present in the bathymetry data set adopted from GEBCO_2014. This was done to avoid the tedious procedure of manually removing features with a topography below sea level and no connection to the world ocean when setting up an ocean general circulation model.

For the Northeast Greenland continental shelf, the NEG_DBM bathymetry map provides bedrock elevation with a very high data coverage. We used this data set to adjust the surface type mask: grid points with an elevation > 0 were classified as bare land surface, and negative elevation obviously enforced a classification as ocean. Within the perimeter of the Greenland continent, the surface type mask remained being defined by M-2014.

In GEBCO_2014 approximately 18 % of the non-land grid cells are constrained by bathymetric control data, which consist of echo sounding data as well as pre-prepared bathymetric grids that may contain interpolated areas . In the current IBCAO version, the Arctic Ocean is mapped by multibeam surveys covering 11 % of the area and an additional vast amount of single beam data . In IBCSO around 17 % of grid cells in the Southern Ocean are directly constrained with data; 15.4 % of data points are from multibeam bathymetry . In areas with no direct measurements, the ocean bathymetry was interpolated between measurements and/or plausible bathymetry.

In general, the accuracy of echo sounding systems can be expected to be about one percent of the water depth. However, in the areas between the sounding tracks uncertainties can be much higher.

For ice surface heights of Greenland the overall root-mean-square deviation between the GIMP digital elevation model and ICESat elevation is ± 9.1 m . The deviation varies strongly with region (Fig. 6 in ).

The technical error of ice thicknesses derived from radio echo sounding depends mainly on the sampling interval and transmitted signal length, both of which vary from system to system. The vertical resolution in ice thickness of the various employed RES systems varies between 5.05 and 8.45 m; the sampling precision is higher, usually in the order of 1 m. Thus an uncertainty of about 15 to 35 m for the ice thickness is realistic. However, complex geometries and steep topography confining the investigated glaciers and ice tongues can cause side and multiple reflections which mask the subglacial reflections, especially in airborne measurements.

Ice thickness and ice draft mapped by are subject to errors of about 35 m for areas with a dense radar sounding coverage. In areas which are less well constrained, errors can exceed 50 m .

Ice thickness maps derived from the available observations for Nioghalvfjerdsfjorden Glacier and Zachariæ Isstrøm reveal distinct differences between data sets from different years. All data across Zachariæ Isstrøm are based on radar data from 2010 to 2014 (obtained from Operation Icebridge and AWI flights). Based on Landsat optical imagery, observed an accelerated retreat in the ice front position in 2013/14 and estimated a mass loss of 5 Gt yr-1. The extent of Zachariæ Isstrøm in RTopo-2 thus represents the state prior to its decay and not the present state.

Ice thickness data covering Nioghalvfjerdsfjorden Glacier include additionally a large number of radar tracks and seismic data obtained 10 years earlier in 1997/98 (DTU/) (see Fig. b). Data from the two time slices differ by about 50 m in several places, especially within 5 km from the grounding line where the floating ice tongue is subject to strong basal melt. The differences are in the same range as the along-track noise in some of the radar tracks (see above). Such discrepancies were smoothed out by our interpolation procedure.

Next to the uncertainties related to data interpretation and processing, the representation of the firn layer (“firn correction”) is an issue that requires serious attention. While in B-2013 a firn layer thickness of 10 m in all ablation regions around Greenland is assumed, there is no firn correction applied in M-2014. Snow depth varies strongly over the Greenland ice sheet and within the seasonal cycle , with most of the snow melting during the summer season close to the coast. A constant-value firn correction is therefore bound to be a rather crude approximation. We keep the M-2014 assumption of zero firn layer thickness and note that for determining a regionally varying firn correction the local depth–density relationship, respectively, the variation of the dielectric properties with depth needs to be known.