Most of Antarctica's coastline is comprised of floating ice shelves where glaciers of the Antarctic Ice Sheet drain into the surrounding Southern Ocean. Mass loss of these ice shelves occurs through ocean-induced melting at their base and calving of icebergs which both contribute about the same amount . Observations show that ice shelf–ocean interaction has been the main driver for mass loss of the West Antarctic Ice Sheet for the past 25 years . Ocean forcing has also been identified as playing a major role in past changes of the Antarctic Ice Sheet. Evidence that the Holocene retreat of the West Antarctic Ice Sheet was driven by warm water intrusions onto the continental shelf was provided by the palaeo-proxy data analysis of and supported by ensemble modelling for the Ross Embayment . Ice sheets respond to changing oceanic and atmospheric conditions, but they also feed back to the Earth's climate in various ways, including through meltwater input into the oceans, sea level change, or change in atmospheric circulation and precipitation patterns resulting from changes in orography and albedo . To study interactions and feedbacks between the Antarctic Ice Sheet and the ocean, such as through melt-induced freshwater input into the ocean, numerical models are an important tool. As the large ice sheets have long response timescales, coupled simulations over millennia are necessary to capture long-term effects. Such coupled simulations are also useful to study the long-term past or future evolution of ice sheets and oceans. This, together with the advantage of using ensemble simulations to constrain uncertainty in parameterized processes, makes computational efficiency a key requirement for such coupled models.

Existing land ice–ocean modelling approaches can be classified in five major categories which will be briefly introduced below:

global ocean and/or atmosphere models with fixed ice sheets;

The standard set of experiments for the Coupled Model Intercomparison Projects (CMIPs) are performed by atmosphere–ocean general circulation models which use fixed, non-dynamic ice sheet configurations and, therefore, only have a limited representation of the aforementioned interactions and feedbacks category 1; e.g.. CMIP-style models are computationally demanding which usually limits their application to centennial timescales . For transient runs beyond the 21st century, however, fixed ice sheets would be an unrealistic assumption.

Ice dynamics missing in stand-alone climate models are traditionally computed by stand-alone ice sheet models (category 2), as ice dynamics typically respond on centennial to millennial timescales. These simulations rely on external forcing, most notably for atmospheric and oceanic boundary conditions. Ocean forcing is applied either through prescribed melt rates or through parameterizations of various complexity based on temperature, salinity, or pressure (see e.g. , for a more in-depth discussion). The latter approach is used, for instance, in the Ice Sheet Model Intercomparison Project for CMIP6 ISMIP6;, where stand-alone ice sheet models are forced by atmospheric and oceanic boundary conditions from CMIP5 to constrain Antarctic mass loss and sea level rise until the end of the century.

The low computational cost of melt parameterizations for stand-alone ice sheet models allows experiments to be integrated on multi-millennial timescales. However, this comes with uncertainties in oceanic boundary conditions not only due to the absence of a dynamic ocean but also due to missing feedbacks between ice and ocean.

A much more detailed representation of the ice–ocean boundary layer processes is achieved with high-resolution, cavity-resolving ocean models (category 3). Usually, this model type simulates the ice shelf geometry as static but thermodynamically active e.g.. Their application ranges from idealized-geometry set-ups to specific regions like the Weddell or Amundsen seas and even circum-Antarctic set-ups. High-resolution ocean modelling (horizontal resolution of the order of 1–10 km) is needed to capture the complex processes determining the water masses that access the ice shelf cavities and the amount of heat that is available for melting the ice. A detailed discussion of these processes including a list of available models is given in .

Closely related to ice shelf cavity-resolving ocean models are coupled ice–ocean high-resolution models (category 4), which include an additional representation of grounded and floating ice dynamics. These models have been applied to idealized geometries e.g. or regional set-ups e.g.. They can also be used to assess simple melt parameterizations from category 2 (e.g. ).

While the detailed representation of sub-shelf processes is important for realistic estimates of melt rates, these highly resolved configurations are, because of their computational demand, not practical to examine long-term and global effects of ice–ocean interaction.

This is, however, crucial because including freshwater fluxes from the Antarctic Ice Sheet in simulations of global circulation models has been shown to influence global ocean temperatures and their variability, to impact precipitation patterns, and to increase Antarctic ice loss through trapping warm water below the sea surface . To study these effects on long timescales, a relatively new type of model is useful: large-scale ice–ocean models coupled via simplified melt parameterizations (category 5). Examples of global ocean-ice sheet coupling approaches are given in and . Both of the above-mentioned studies use melt parameterizations that describe the melt process directly at the ice–ocean interface . In addition to the melting at the ice–ocean interface, the Potsdam Ice-shelf Cavity mOdel PICO; mimics the large-scale overturning circulation in ice shelf cavities. PICO can model melt rates in accordance with observations : while average melt rates in cold cavities, such as underneath Filchner–Ronne Ice Shelf, are of the order of 1 m a-1, melt rates in warm cavities, such as those found in the Amundsen Sea, are of the order of 10 m a-1. At the same time PICO is computationally efficient compared with high-resolution, cavity-resolving ocean models. So far PICO has been used for stand-alone ice sheet modelling (category 2 from above e.g. in , and ); however, as PICO is driven by far-field ocean temperature and salinity in front of the ice shelf cavities, it can also act as a coupler between non-cavity-resolving ocean models and ice sheet models.

To study the ice sheet and ocean system on a global and multi-millennial scale, we present a category 5 framework for the dynamical coupling of the Parallel Ice Sheet Model PISM; and a coarse-resolution configuration of the Modular Ocean Model MOM5; using PICO. The design of the presented framework follows three criteria: (1) mass and energy conservation needs to be ensured over both ocean and ice sheet component domains, (2) the coupling framework should not introduce a performance bottleneck to the existing stand-alone models, and (3) the framework should follow a generic and flexible design independent of specific grid resolutions or number of deployed CPUs.

In the following, we introduce the ice sheet and ocean components in use, including their grid definitions (Sect. ). The framework design including the variables that are exchanged between the components is discussed in Sect. , followed by a detailed description of inter-component data processing in Sect. . The framework's computational performance, conservation of mass and energy, and results of coupled simulations for present-day conditions are evaluated in Section , followed by a discussion (Sect. ) and conclusions (Sect. ).

The following paragraphs introduce the PISM ice sheet model including its sub-shelf cavity model PICO and the MOM5 ocean model, which are coupled as components into the framework.

The design of the coupling between the PISM ice sheet component and the MOM5 ocean component is shown in Fig. , including the exchanged variables. PICO uses two-dimensional (horizontal) input fields, namely temperature and salinity of water masses that access the ice shelf cavities, to calculate melting and refreezing at the ice–ocean interface, as illustrated in Fig. . Fluxes describing basal melt, surface runoff, and calving in the ice component are used to determine the mass as well as energy fluxes received by the ocean component.

The timescales of physical processes as well as the numerical time steps in MOM5 (hours) and PISM (years) differ by several orders of magnitude. This is one motivation among others to use an offline sequential coupling approach to exchange the fields between the two components. In this case, both components are run in alternating order for the same model time, which will be referred to as the coupling time step. This technical procedure is illustrated in Fig. . An alternative online coupling approach is discussed in Sect. . In the offline coupling procedure, one component is first run for the period of a coupling time step. The output is then processed and provided as input or a boundary condition to the other component. Using the modified input, the components are restarted from their previous computed state. For example, MOM5 runs for 10 years and writes annual mean diagnostics fields of temperature and salinity. PISM receives the temporal average of these fields over the coupling time step as boundary conditions for PICO and is then integrated for the same 10-year period. Melt water and energy fluxes derived from PISM output are aggregated over the coupling time step. The resulting fluxes are then added as external fluxes to the ocean over the course of the next integration period. To avoid shocks in the forcing, they are distributed uniformly over the entire coupling time step.

The coupling framework consists of a Bash script that implements the coupling procedure indicated in Fig. , making use of the Climate Data Operator CDO; and netCDF Operator NCO; software tools. The output processing between the different component executions is implemented in Python scripts. Their functionality will be explained in the next section. The code is made available in a public archive (10.5281/zenodo.4692679, ), and the reader is referred to the “Code and data availability” section for further information.

To make the output of the ocean component compatible with the input requirements of the ice component and vice versa, processing of data output fields, like regridding, adjustment of dimensions, unit conversion, or filling of missing values, is required, which is described in this section.

The ice and ocean components operate on independent, non-complementary computational grids. The inset of Fig.  shows that there are both spatial gaps and overlaps between the ocean grid cells and the ice extent represented by PISM. As the ocean grid is much coarser than the ice grid and MOM5 cells are either defined entirely as land or ocean (no mixed cells allowed), inconsistencies in the exchange of quantities between the two grids are unavoidable, requiring careful consideration of data regridding.

The grid remapping mechanisms presented in the following sections are independent of the used grid resolutions.

In this section, the coupling set-up will be evaluated on the basis of runtime performance and numerical accuracy. Physical evaluation of the coupled set-up is provided for present-day conditions. Further validation and implications in terms of possible feedback mechanisms will be studied in detail in a separate article.

The framework presented here to couple the PISM ice component to the MOM5 ocean component via PICO fulfils all three goals stated in Sect. 1: (1) mass and energy conservation across both component domains and (2) an efficient as well as (3) generic and flexible coupling framework design:

As described in Sect. , mass conservation across both component domains can be assured. Furthermore, the remapping scheme for energy fluxes is conservative as well. Compared with the required run time of MOM5, the framework routines are very efficient when choosing a coupling time step of 10 years. More frequent coupling causes a larger overhead, as reading and writing the complete model state of PISM to and from files is relatively expensive for very short simulation times. However, an increased ocean to ice forcing of 1 year does not affect the equilibrium state of the coupled system as shown in Sect. . The third criterion is fulfilled by the chosen offline coupling approach, which provides a generic and flexible design by making use of the component-related flexibility concerning grid resolution and degree of parallelization. This does not easily apply to the alternative approach of online coupling, which will be discussed below.

The chosen offline coupling framework executes the two different components alternately and independently, and manages the redistribution of the input and output files across the components as explained in Sect. . However, it is also conceivable to adopt an online coupling approach (also called synchronous coupling), where the ice and ocean component code are consolidated into one code structure. The exchange of variables between both components can subsequently take place through access to the same shared memory instead of writing the required variables to disc and reading from there again, as is done in offline coupling. This approach is used in studies such as . A comprehensive framework for online coupling of ocean and ice components is described in . This coupling approach is especially powerful for high-resolution, cavity-resolving ice–ocean coupling, where frequent updates of the ice shelf cavity geometries and corresponding melt rates are important. However, a prerequisite for online coupling is the adaptation of the stand-alone models for interactive execution of subroutines through a defined (external) interface. In the given case of coupling PISM and MOM5, this means that at least one of the two programs' code structure needs major modifications and modularization to equip the individual component parts, like initialization, time stepping routine, disc I/O (input and output), and stock checking, with suitable interfaces. This is independent of the chosen online coupling design (incorporating one code structure into the other or creating a new master program that governs both components). Synchronization of the PISM adaptive time step and the fixed ocean component time step would be a further issue, also keeping in mind that the comparably small ocean time step of a few hours is not applicable for the ice component: PISM can have a time step of around 0.5 years close to equilibrium with 16 km resolution due to the longer characteristic timescales of ice dynamics. The fact that both components are written in different programming languages (C++ and Fortran) imposes its own (although minor) barriers. A possible benefit of the described online coupling is less disc I/O overhead, which is especially relevant for small coupling time steps in the offline coupling approach (see Sect. ); however, that does not outweigh the high initial and ongoing development effort which arises through writing and maintaining modified versions of the main component versions. Offline coupling comes with the advantage that only very minimal modifications of the existing components' source code are necessary. This makes it fairly easy to even replace the ice or ocean components in use with similar existing models, like using MOM5's successor MOM6. A further benefit of the offline coupling approach is that running several independent instances of PISM (e.g. for Antarctica and Greenland) at the same time can be easily implemented.

The coupling implementation exhibits certain simplifications that can be subject of future improvements. As described in Sect. , the mass and energy fluxes computed from PISM output are given as input to the ocean surface rather than being distributed throughout the water column – a limitation of MOM5's simplified treatment of all land-derived mass fluxes, including those from ice sheets. This simplification may affect vertical heat distribution and local sea ice formation as near-surface input generally makes the vertical column more stratified, whereas input below the mixed layer destabilizes the water column, thereby enhancing vertical mixing and extending the mixed layer depth . A more realistic input depth into the ocean would be the lower edge of the ice shelf front see start of upper green arrow in Fig. ; which could be determined as the average ice shelf depth of the last PICO box.

Mass and energy fluxes are composed of basal melting, surface runoff, and calving and are provided as input to the southernmost ocean cells (see Sect. ). Icebergs can, however, travel substantial distances before they are completely melted and, thus, continuously distribute mass and energy fluxes into the ocean . The resulting spatial distribution of iceberg fluxes can introduce biases in sea ice formation, ocean temperatures, and salinities around Antarctica . Currently this is not considered in our framework and may be simulated by an additional iceberg component as described in in the future.

Another simplification is contained in the energy flux description from ice to ocean. As explained in Sect. , the flux is calculated as the energy transferred through phase change from frozen ice to liquid water. Diffusion of heat through the ice and energy required to warm up melt water to ambient ocean temperatures are currently not considered as they are estimated to be comparably small .

The waxing and waning of ice sheets on glacial–interglacial timescales causes the transfer of large amounts of water between the oceans and land ice sheets. Significant changes in sea level (120–135 m below present during the last glacial maximum; ) have large impacts on coastline positions. The response of the solid Earth component to changes in ice sheet mass has a similar effect. During long simulations the land–ocean mask needs to be adapted accordingly. As MOM5 cannot handle mixed ocean–land cells, which would allow for a smooth adaption of a changing coastline, major changes in the land–ocean mask need to be performed during a transient simulation. This requires careful considerations like the initialization of newly flooded cells and implications concerning mass and energy conservation as well as model stability. The development of a sea-level-based dynamic ocean domain adaptation which applies the described changes to new ocean restart conditions is currently under way and will be incorporated in the described coupled set-up in the future.

In this study, we focus on the technical implementation of the coupling framework and evaluate it in a transient simulation under constant present-day climate forcing. As the ocean component has warm biases at intermediate depth around the Antarctic margin, we apply an anomaly approach to avoid unrealistic high melting and obtain physically meaningful simulations of the coupled system. We add anomalies from the ocean model component to observed temperatures, similar to the approach in ISMIP6 . The difficulties to accurately simulate Antarctic shelf dynamics and deep water formation in the Southern Ocean with ocean general circulation models is a long-standing issue for the ocean modelling community, with almost no models of the CMIP5 generation able to do this successfully . The improvement of these biases is the subject of ongoing work via the implementation and tuning of the new MOM6 ocean model. While the anomaly approach is appropriate for present-day simulations, for which we have observations, it is as yet unclear how these biases might be addressed for transient simulations on multi-millennial timescales. In the transient simulations, the effect of using a 10-yearly coupling time step was tested in a simulation with the variable 10-year ocean forcing being applied to the ice sheet instead of the 10-year average. We find that this variability has no effect in a steady-state simulation. These open issues, including the choice of the coupling time step under physical aspects, will be considered in a future study.

The presented coupling framework is characterized by a reduced-complexity approach. This is reflected, for instance, in the basin-wide averaging of PICO input which does not account for horizontal differences such as cavity in- and outflow regions or modification of water masses on the continental shelf. Similarly, the complex processes determining whether upwelling Antarctic Circumpolar Deep Water reaches the continental shelf and the grounding lines can only be partly represented due to the coarse bathymetric features of the MOM5 grid (see also Fig. b). However, the intermediate complexity of the coupled system enables ocean simulations on a global domain, opening possibilities to study interactions, feedbacks, and possible tipping behaviour on millennial timescales. Overall, despite the limitations discussed above, the coarse grid set-up of MOM5 in combination with the representation of the ice pump mechanism in PICO makes large-scale and long-term ice–ocean coupling possible at an intermediate level of complexity.

In this study, we focus on the technical approach and conservation aspects of coupling a large-scale configuration of the PISM ice sheet model and a coarse-grid-resolution set-up of the MOM5 ocean model via the PICO cavity model. This approach makes it possible to capture the typical overturning circulation in ice shelf cavities that cannot be modelled in global stand-alone ocean models. We can assure that conservation of mass and energy is obtained in the coupler between the ocean and land ice components while having a computationally efficient and flexible coupling set-up. Using this framework, which is openly available and can also be transferred to other ice sheet and ocean general circulation model components, feedbacks between the ice and ocean can be analysed in large-scale or long-term modelling studies. In future work, the physical processes and feedbacks between ice sheet, ice shelves, and ocean will be further analysed, and the interaction strengths can be evaluated on various timescales, from decades to multi-millennial simulations.