RAnGO combines a regional model of the Antarctic ice sheet with a global ocean model. The coupled system consists of a global configuration of FESOM (Timmermann et al., 2012), and a regional setup of the Revised Ice Model Based on frAnk pattYn (RIMBAY; Thoma et al., 2014). While the FESOM domain covers the world ocean including the sub-ice-shelf cavities in the Southern Ocean, the RIMBAY setup comprises the FRIS and the relevant catchment basin up to the ice divides. The interface between the two models is the FRIS base (Fig. ). All other ice shelves are modelled with fixed geometry. As for the stand-alone model runs of Hellmer et al. (2012), the coupled model is forced by atmospheric output from the HadCM3 climate model.

FESOM is a primitive-equation hydrostatic ocean model that is solved on a horizontally unstructured mesh (Wang et al., 2014). It comprises a dynamic–thermodynamic sea ice model (Danilov et al., 2015). The ice-shelf component (Timmermann et al., 2012) goes back to the Hellmer and Olbers (1989) three-equation model of ice-shelf–ocean interaction with a velocity-dependent parameterization of boundary layer heat and salt fluxes according to Holland and Jenkins (1999).

The model is run on a global mesh with a horizontal resolution varying from 1 km along the FRIS grounding line to 340 km in the deep Atlantic and Pacific basins (Fig. ). It uses a hybrid vertical coordinate with 22 sigma levels south of the 2500 m isobath surrounding the Antarctic continent and up to 36 z levels outside this domain. Antarctic sub-ice-shelf cavities are thus all inside the sigma domain, which allows for a smooth representation of the ice-shelf base. The ice-shelf front is approximated by a ramp-like shape; with a horizontal resolution between 10 and 16 km in this area, the deviation from the true geometry is mostly confined to 50 (100) km inwards of the Filchner (Ronne) ice-shelf front. We apply a minimum water column thickness of 50 m for all sub-ice cavities.

An early version of RTopo-2 (Schaffer et al., 2016) has been used to derive ocean bathymetry and the ice-shelf draft and grounding lines for all cavities with fixed geometry. With the present-day ice-shelf configuration for FRIS, the FESOM mesh comprises a total of ≈2.6×106 nodes, 1.1×105 of which are surface nodes (where the term surface equally refers to open ocean and ice-shelf base). The model is run with a default time step of 90 s owing to the very fine horizontal resolution along the FRIS grounding line and a minimum sigma layer thickness of just over 2 m. For several situations with eddies running into shallow sections of the FRIS cavity, it turned out to be necessary to decrease the ocean model time step to 4 s.

RIMBAY (Thoma et al., 2014) is a three-dimensional thermomechanical multi-approximation ice-shelf/sheet model going back to the ice flow model of Pattyn (2003). Within the RAnGO experiments, the ice model domain comprises the FRIS and its upstream catchment area of grounded ice, confined by the surrounding ice divides (Fig. ). Ice velocities are calculated following the hybrid approach which combines the shallow-ice and the shallow-shelf approximations. A basal friction correction at the grounding line after Feldmann et al. (2014) ensures a smooth transition between grounded and floating ice and thus a realistic grounding line migration.

The ice model is run at a horizontal resolution of 10 km with 41 terrain-following sigma layers and a time step of 0.1 years. Bedmap2 (Fretwell et al., 2013) data are used for bedrock topography and initial ice thickness. Since Bedmap2 is also the source for the Antarctic ice and bedrock relief in RTopo-2, all topographies are fully consistent within RAnGO.

First, we perform a 1000-year stand-alone RIMBAY simulation. This ice model spinup is forced by present-day surface temperatures (Comiso, 2000), accumulation rates (Arthern et al., 2006) and geothermal heat flux (Shapiro and Ritzwoller, 2004). Basal melt rates are parameterized according to Beckmann and Goose (2003). As a result, ice dynamics are in a quasi-stationary steady state and ice thickness, ice velocity, and grounding line position match current observations very well. Additional figures and a thorough discussion of the ice model spinup are presented in our companion paper (Part II: the ice perspective; Goeller and Timmermann, 2017).

With this RIMBAY present-day cavity geometry, we integrate FESOM for 21 years (1930–1950) using atmospheric forcing from the 20th-century simulation of the HadCM3 climate model. Annual mean basal melt rates for FRIS from the last year (1950) are then transferred back to RIMBAY, which starts the RAnGO coupled model loop (Fig. ).

For each of the cycles within the coupled RAnGO system, FRIS basal melt rates averaged over year N are obtained from FESOM and passed to RIMBAY, which is then stepped forward for that same year N. From the simulated ice draft and grounding line location at the end of RIMBAY year N, a new cavity geometry is derived and an updated FESOM mesh is generated. FESOM's prognostic variables are projected onto the new mesh (details below), and FESOM is then integrated over year N+1. Basal melt rates are averaged over FESOM year N+1 and passed to RIMBAY, and the cycle repeats itself with RIMBAY running year N+1.

A 1-year coupling time step is long compared to the relevant timescales in the ocean but short compared to the typical timescales for ice dynamics or the ice mass budget. The fact that variations of RIMBAY ice thickness distribution, grounding line location, and melt rate patterns are small for each coupling time step indicates that this coupling strategy is adequate.

Adjustment of the model domain to a varying ice-shelf geometry is a natural part of RIMBAY and is rather straightforward to implement for a finite-difference ocean model with a land–sea mask. For FESOM, the computational mesh only exists in the ocean and has to satisfy certain criteria in order to ensure numeric stability and efficiency. For stand-alone FESOM applications (e.g. Timmermann et al., 2012) we use an iterative method to generate surface meshes in which the size of triangles smoothly varies according to the desired resolution, while at the same time triangles approximate the ideal of being equilateral as well as possible. For a mesh with about 105 surface nodes, the algorithm takes about 2 days to converge – which clearly prevents it from being used as part of a coupling interface.

To reduce the mesh generation overhead, we generated an initial surface grid that covers the full RTopo-2 ocean (blue and green triangles in Fig. ) plus all ice around FRIS that is grounded on bedrock deeper than 100 m below sea level (red triangles in Fig. ). This criterion to define the “potentially ungrounding” area adjacent to the currently floating ice shelf proves to be well on the safe side for any grounding line movement in our coupled model runs. Mesh resolution along the present-day grounding line and in the potentially ungrounding area is about 1 km to describe grounding line migration as smoothly as possible. For each topography/cavity geometry to be run with RAnGO, the coupler removes all grid nodes that are covered by grounded ice. The remaining ocean grid nodes are renumbered consecutively. The full three-dimensional grid is then created from this new surface mesh, with the terrain-following vertical coordinate easily adjusting to any change in water column thickness due to a varying ice-shelf draft.

During this procedure, the vast majority of finite element mesh nodes keep their position (despite being renumbered), so that no horizontal interpolation is necessary for the ocean state variables outside the immediate vicinity of the grounding line. This makes it much easier to ensure the conservation of heat and salt. Wherever new ocean (i.e. cavity) nodes are created, ocean temperature, salinity, and sea surface height are taken from the nearest existing neighbour grid node. Again, the small variations per coupling step make this simple “no-flux” approach justified.

Coupling has been implemented in an “offline” way with RIMBAY and the RAnGO coupler running on local servers and FESOM relying on a massively parallel supercomputing system. Given that (1) model output is in any case transferred to local disks for postprocessing and analysis and that (2) the updated mesh configuration files are comparatively small, the overhead arising from the file transfer necessary in our offline approach is negligible.

To run a typical model year with the current configuration of RAnGO requires about 7 h on 528 CPUs for FESOM, less than 10 min for RIMBAY, and almost 2.5 h for the coupling procedures. Within the coupler, more than 90 % of the time is spent on the construction of the three-dimensional, tetrahedral mesh from the updated surface grid. A more efficient algorithm that starts from the existing three-dimensional mesh and only applies corrections where necessary is currently being developed.

As stated in Sect. , 1951 is the first year of the coupled RAnGO simulation. We integrated the coupled model until 1999 using atmospheric output (10 m wind speed, 1.5 m air temperature, 1.5 m specific humidity, surface moisture flux, downward long- and shortwave radiation, total precipitation) from the HadCM3 20th-century simulation. This experiment is referred to as the RAnGO 20C simulation. HadCM3 data for the A1B scenario have been used to conduct the RAnGO A1B simulation for the period 2000–2199. The suite of the RAnGO 20C (1950–1999) + A1B (2000–2199) model runs serves as the reference simulation for analysis in this paper. A control run with present-day climate (RAnGO CTRL) has been performed twice repeating the HadCM3 1900–1999 forcing.

Next to the coupled RAnGO simulation launched from the end of 1950, an uncoupled FESOM experiment with the RIMBAY present-day cavity geometry prescribed has been conducted. Like its RAnGO counterpart, this experiment starts with a FESOM 20C simulation and splits into a FESOM A1B and a FESOM CTRL branch at the beginning of the 21st century.

As has been discussed in Sect. , simulated basal melt rates increase by roughly a factor of 6 between the 1990s and the 2190s in the RAnGO A1B and FESOM A1B simulations. Taking a more quantitative view, we find an increase factor of 6.1 for RAnGO A1B vs. only 5.4 for FESOM A1B. We also note that the area-mean melt rate in RAnGO A1B is always higher than in FESOM A1B (Fig. ). Given that a reducing ice draft implies a rising in situ freezing temperature and thus a reducing melt potential for any warm water mass flowing into the cavity, this is not necessarily an obvious result – instead it would have appeared plausible to assume that a reducing ice thickness would reduce (not increase) the basal melt rate in a warming scenario like the one discussed in this study. In this section, we will therefore look into the processes that lead to an increased melt for a thinning ice shelf.

From the RAnGO and FESOM melt rate maps for the 2190s (Fig. b, c) a systematic change introduced by the transition from a fixed geometry to a coupled model is not obvious. A map of the difference between the two fields (Fig. , panel a) reveals that in many places with a retreating grounding line, an increased melt in newly ungrounded areas is at least partly compensated by reduced melt in areas along the old grounding line location. Even in this warm-water-inflow scenario, ice-shelf–ocean interaction in many places still appears to fully extract the heat content of water getting in touch with the ice base near the grounding line, so that a shift in the grounding line position merely shifts the location of melt rate maxima, but does not increase total melt.

A more substantial and largely unbalanced melt rate increase is found (1) along the ice-shelf front and (2) at locations with a substantial increase in water column thickness. Along the ice-shelf front, increasing melt rates in the A1B scenario lead to a reduction of thickness (only) in the coupled model, reducing its function as a dynamic barrier. Second, reducing ice draft close to the grounding lines leads to an increasing water column thickness below still deep-drafted ice, even if the grounding line position remains unchanged or grounding line migration is very small. In several locations that have already been under the floating ice shelf in the present-day situation, up to 90 % of the water column thickness found at the end of the RAnGO A1B simulation are due to ice-shelf thinning (Fig. , panel b). Even though the water mass properties change only very little between FESOM A1B and RAnGO A1B (Fig. ), the increased water column thickness in the coupled model allows for a transport of warm water to the deepest parts of the cavity more easily. This is most notable at the estuaries of the Recovery and Support Force glaciers, but also to the north of Bailey Ice Stream. At Support Force Glacier, the increasing melt rates in the A1B scenario lead to a reduced ice-shelf thickness and an increased slope of the ice-shelf base directly off the grounding line (Fig. ). The latter causes 2195 annual mean along-slope ocean current velocities at the ice-shelf base to increase from about 5 cm s-1 in FESOM A1B to a maximum of 15 cm s-1 in RAnGO A1B, reinforcing stronger melt rates in this area and thus forming a positive feedback loop. Some of this increased melting is compensated by a reduced melting in adjacent areas, but the residual remains positive, so that together with the increased melting along the ice front, total ice-shelf basal mass loss in the coupled model increases slightly more than in the fixed-geometry case.

A striking feature in the time series of Fig.  is the sudden reduction of FRIS mass and area from 1950 to 1951, i.e. with the first coupling step. What appears as a big discontinuity merely represents 2.7 % of the original ice-shelf mass and 1.0 % of ice-shelf area. Nevertheless, this event deserves a closer look.

While 1950 is the last year in which RIMBAY was run with parameterized melt rates, 1951 is the first year of RAnGO, i.e. the first year in which RIMBAY is forced with basal melt rates from FESOM. The top left panel in Fig.  thus shows the FRIS thickness distribution at the end of the 1000-year RIMBAY spinup with Beckmann and Goose (2003) melt rates, representing the RIMBAY present-day geometry introduced above. Using this ice thickness distribution, FESOM has been integrated with a fixed cavity geometry for 21 years. Annual-mean melt rates from the last year of this simulation (Fig. , bottom left panel) are fed back to RIMBAY as part of the first communication step of the coupled model. Ice thickness distribution after this first RAnGO year (Fig. , top right panel) shows that compared to the RIMBAY present-day geometry, ice thickness has reduced mainly in the area south of Berkner Island, i.e. between the Support Force Glacier and the Foundation Ice Stream. The time series of floating ice area (Fig. , bottom panel) indicates that some previously floating ice has now become grounded, but grounding line migration is very small. FESOM basal melt rates obtained with this updated ice draft distribution (Fig. , bottom right panel) differ only very little from the result of the previous year. We conclude that variations in basal melting affect the ice-shelf thickness distribution quickly and substantially, while the feedback from a perturbed ice thickness distribution on simulated basal melt rates is much weaker.