The ISOMIP+ bed topography and ice shelf draft (Fig. ) are idealised geometric configurations that overlap with the MISMIP+ and MISOMIP1 domain. The domain has size 480 and 80 km in the x and y directions, respectively, though part of this domain (x<400 km) contains only grounded ice and is therefore not included in our figures. The x direction aligns with the direction of the ice flow, towards the calving front. This choice does not affect the ocean circulation, since the participating models use the f-plane approximation (referenced to 75° S latitude). The bed topography is the same as MISMIP+ and the ice shelf draft for Ocean0 and Ocean1 is a steady state ice shelf configuration computed with the BISICLES model with the MISMIP+ Ice1 parameters , and computed similarly for Ocean2 with MISMIP+ Ice1r parameters. The BISICLES geometry includes a steep calving front located at x=640 km. The bed topography also provided as an analytic expression; and ice shelf draft were provided on a 1 km horizontal resolution grid. Participants then interpolated and smoothed the bed topography and ice shelf draft using different methods to achieve a horizontal grid resolution of 2 km (details are in Sect. ; see Figs. S11, S12 in the Supplement). However, where interpolation results in an ice shelf thickness less than 100 m, the thickness is set to zero to represent a steep calving front, except where smoothing of the calving front was required for model stability. Models are configured with 36 vertical levels, spread over the 720 m maximum depth in different ways depending on the vertical coordinate used, resulting in varying vertical resolution beneath the ice shelf. All z-level models use a vertical grid size of 20 m with differing partial cell choices. In the Ocean0-2 experiments discussed in this paper, the ice shelf draft is fixed and does not change in time.

The initial conditions for the experiments are either a “warm” or “cold” profile (Fig. d–g). Potential temperature (referred to as temperature in the remainder of this manuscript) and practical salinity (noting that we use the PSS-78 salinity scale, so values do not have units) vary linearly with depth. For the cold profile (qualitatively representative of the Ross or Weddell Seas), the temperature is a constant -1.9 °C and salinity varies linearly between 33.8 at the surface (0 m depth) to 34.55 at the bottom (720 m). For the warm profile qualitatively representative of the Amundsen and Bellingshausen Seas, with warm, salty Circumpolar Deep Water intrusions at depth, e.g.,, the temperature and salinity varies from -1.9°C and 33.8 at the surface to +1 °C and 34.7 at the seafloor. By making use of the experiment's linear equation of state, the cold and warm profiles are designed to have the same density profile Fig. 6 from to reduce convective instabilities. Having the same density profile also means that density variations are solely created by ice shelf meltwater, not by the boundary . However, the salinity stratification of the cold profile is stronger than the conditions observed in cold Antarctic ice shelf cavities e.g.. In all experiments, the ocean begins at rest.

The boundaries on all side walls use no-slip conditions whilst top and bottom boundaries employ a quadratic drag with drag coefficient CD. Additionally, the temperature and salinity are forced using a restoring sponge at the “northern” x boundary. This sponge is applied over the entire ocean depth and y direction, and linearly increases in restoring strength from no restoring at x=790 km to full restoring at x=800 km, with a restoring timescale of 0.1 d (i.e. 2.4 h) towards either the warm or cold profile. To avoid sea level rise over the course of the simulation, sea level may also be restored if melting is implemented as a volume flux using surface mass fluxes in the sponge restoring region; otherwise, there are no open ocean surface fluxes (unless specified in Sect. , see also the Meltwater addition column of Table ).

The experiment protocol prescribes a linear equation of state given by 1ρ=ρref1-α(T-Tref)+β(S-Sref), where the reference density, temperature and salinity are ρref, Tref and Sref, and the thermal expansion and haline contraction coefficients are α and β. Numerical values are presented in Table .

Ice shelf basal melt rates are calculated using the three-equation parameterisation with a linear dependence of the freezing temperature on pressure and salinity and constant transfer coefficients : 2Tzd=λ1Szd+λ2+λ3pzd3ρfwmwL=-ρswcwu*ΓT(Tzd-Tw)4ρfwmwSzd=-ρswu*ΓS(Szd-Sw)5u*2=CDuw2+utidal2. All parameters are described in Table . Here, the liquidus slope is λ1, intercept λ2 and pressure coefficient λ3. The melt rate mw is expressed as a freshwater flow rate (m s⁻¹), which is solved by the equations along with the temperature and salinity at the ice–ocean interface Tzd and Szd. The temperature Tw, salinity Sw and velocity uw represent the ocean properties outside of the turbulent ice-ocean boundary layer and can be determined by models in different ways, but are generally taken as the surface mixed layer properties or properties averaged over a constant distance from the ice. Salt and freshwater densities are ρsw and ρfw. The latent heat of fusion is L and the specific heat capacity of water is cw. The drag coefficient CD for determining the friction velocity is the same as the dynamic drag boundary condition at the top and bottom boundaries.

Here, the prescribed tidal velocity utidal is used to account for the additional ocean motion (ostensibly due to tides) in the friction velocity (u*). Without this prescribed velocity, no melt would occur when the ocean is at rest, even when heat is available for melting, contradicting our expectations from both theory and observations. It is worth noting that there are more complex and accurate methods to include the effect of tidal motion . The transfer coefficients ΓT and ΓS=ΓT/35 are tuned constants (see Sect. ). Using constant transfer coefficients is an approximation that does not hold in the real world, and models may use variable transfer coefficients e.g.. Furthermore, the ice is considered to be perfectly insulating without any conductive heat flux at the ice–ocean interface. For a review on melt parameterisations in ice shelf–ocean models, see and .

demonstrate with the ISOMIP+ setup that melt rates are impacted by both the distance across which the ocean properties subscript w are sampled (tracer sampling distance, TSD) and the distance across which the meltwater is distributed (flux mixing thickness, FMT). The ISOMIP+ model contributions vary in their sampling and distribution methods (Table ); these are described further in Sect. . Additionally, models vary in their addition of freshwater, either as a volume or virtual salt flux (Table ).

The mixing of momentum and tracers in vertical and horizontal directions is parameterised using a Laplacian (harmonic) operator with constant coefficients (values are prescribed in Table ). Vertical (or more precisely, between model layers) diffusivity is κstab, except when there is locally unstable stratification, where it increases to account for convective instability (to κunstab) or using a model-dependent convective adjustment scheme described in Sect. . Similarly, the vertical viscosity νstab in the interior also increases with unstable local stratification to νunstab. Horizontal diffusivity and viscosity are κH and νH, respectively, though numerical mixing may also be significant. Mixing also occurs implicitly via the distribution of meltwater: typically, z-coordinate models use a -style scheme where meltwater is distributed evenly over a fixed distance from the ice. This distance is usually the z-coordinate thickness, which usually covers multiple grid cells if partial cells are used. Other models may distribute meltwater only in the uppermost cell, thereby removing the implicit mixing due to meltwater distribution (details in Sect. ).

The Ocean0 tuning experiment uses the warm initial conditions and warm northern boundary sponge forcing with the ice draft of Fig. b. This allows a quasi-equilibrium, warm-shelf melt rate and circulation to be attained quickly. For the COM experiments, participants were requested to modify ΓT (and consequently ΓS=ΓT/35 also varies) to achieve a target area-averaged melt rate at depth (z<-300 m) of 30±2 m yr⁻¹. This tuning involved running multiple Ocean0 configurations to sample various ΓT until the target melt rate was achieved, with larger ΓT producing more melt via Eqs. ()–(). The Ocean0 simulations use these optimal transfer coefficients and were run for 1 year, or longer if quasi-equilibrium was not achieved within 6 months.

Ocean1 and Ocean2 use the same optimally tuned transfer coefficients as Ocean0 but with different restoring forcing, initial conditions and/or ice draft. Ocean1 begins with cold initial conditions but a warm restoring boundary (Fig. d) and same ice draft as Ocean0 (Fig. b), whereas Ocean2 begins with warm initial conditions and a cold restoring boundary (Fig. f) and a different ice draft (Fig. c), consisting of a steeper ice base slope over a narrower x-axis extent compared to Ocean1. Both experiments are run for 20 years to investigate the timescales and ocean states during the transition between warm and cold states of an ice shelf cavity.

In their typical usage (for both realistic and idealised simulations), ice shelf–ocean model configurations generally differ from the prescribed ISOMIP+ protocol. For example, they may employ different mixing schemes, horizontal resolutions, or ice shelf melt parameterisations e.g.. The typical “TYP” simulations submitted by participants use the same geometry and boundary conditions as the Ocean0-2 COM experiments but with other parameters, resolutions, or physics schemes configured per participant choices for more conventional use, with these settings often taken from previous simulations. Since ice shelf melt parameterisations may have been modified, most TYP experiments do not use a tuned transfer coefficient to achieve the COM Ocean0 target melt rate. The TYP experiments provide an additional measure of variability between models, which are compared in Sect. . Any differences between models' TYP and COM configurations are described in Appendix . Since participants were asked to prioritise COM simulations, not all participants submitted TYP experiments (Table ).

One submission is based on COCO version 4.9 , using the ice shelf component described in . The horizontal direction uses an Arakawa B-Grid. The vertical direction employs a hybrid coordinate system consisting of sigma layers in the near-surface and z-coordinate layers below. The ice shelf component is only activated in the z-coordinate layers. The configuration uses a second-order centred scheme for momentum advection and the UTOPIA/QUICKEST scheme for horizontal and vertical tracer advection . The melt rate is calculated by sampling the temperature, salinity, and velocity in the uppermost grid cell under the ice shelf. Meltwater is also distributed on the uppermost grid cell under the ice shelf. The mean sea level is maintained by removing the mean sea level anomaly in the open water area at each time step. The land mask is generated by designating areas where the water column thickness is less than 40 m (i.e. 2-grid cells) as land grid points. The ice draft is also manually filled in at the sides to create a smoother geometry (e.g. Figs. , S11, S12). The COCO submission uses partial cells to represent the bed topography better in the z-coordinate model , with an accuracy of 10 % of the grid cell thickness (i.e. 2 m). For the ice shelf draft, a full step representation is used to reduce grid size noise in the velocity field see for further explanation.

One submission uses the version of the unstructured grid Finite Volume Community Ocean Model (FVCOM) that resolves ice shelf cavities . FVCOM solves the governing equations in integral form by computing fluxes between non-overlapping horizontal triangular control volumes using generalized terrain-following coordinates. In the COM submission, the model setup uses a horizontal grid mesh composed of equilateral triangles of sidelength 2 km, and 35 terrain-following vertical layers with slightly increasing resolution towards the bottom. Both momentum and tracers are horizontally advected using a second-order upwind scheme. For the vertical advection of tracers, the second-order Multidimensional Positive Definite Advection Transport Algorithm is used . To address unstable vertical mixing, salinity and temperature values in the two layers are averaged if the upper layer's density is greater than that of the lower layer. The melt rate is calculated by sampling the temperature, salinity, and velocity in the uppermost grid cell under the ice shelf. The ice shelf draft is linearly smoothed within 20 km of the ice front (Fig. b). The minimum water column thickness is 30 m. In addition, the bed topography in Ocean2 (seen in Fig. b) is further adjusted according to the water column thickness output from the ROMS model, which was first smoothed using a mean filter over a square of size 10 km side length. It was not possible to reach the target melt rate of 30±2 m yr⁻¹ below 300 m depth in FVCOM during the tuning stage in Ocean0 as melt rates saturated with high transfer coefficient values. Instead, the large value of ΓT=0.2 chosen resulted in an equilibrium melt rate of 18.9 m yr⁻¹ in Ocean0.

Three submissions are based on the Massachusetts Institute of Technology general circulation model MITgcm;, from Jet Propulsion Laboratory (hereafter MITgcm-JPL), the British Antarctic Survey (MITgcm-BAS) and a second configuration from the British Antarctic Survey that uses the coupled ice–ocean framework as described in (MITgcm-BAS-Coupled). The implementation of ice shelf cavities in MITgcm is described in . MITgcm is a finite volume model. The configurations used here employ an Arakawa C-grid and a z-level vertical coordinate. Momentum is advected using a second-order centered scheme, while tracers are advected using a third-order Direct Space-Time (DST) flux limiter scheme (note this scheme was later found to cause some spurious behaviour, see Sect. ). Differing from the COM protocol, unstable vertical mixing is parameterised with the convection scheme of , which instantaneously mixes the unstable density gradients, and is applied every time step. The melt rate is calculated by sampling the temperature, salinity, and velocity within a fixed 20 m boundary layer beneath the ice. Melt fluxes are also distributed over a 20 m layer beneath the ice.

The major difference between the three MITgcm COM submissions is the choice of heat and salt transfer coefficients at the ice–ocean interface (Table ), the minimum water column thickness and the limit on the size of partial grid cells at the ice–ocean boundary. MITgcm-BAS uses a minimum water column thickness of 40 m, which is maintained by excavating the ice draft while keeping the bed topography and grounding line fixed. MITgcm-BAS-Coupled imposes a minimum water column thickness of 0.5 m for consistency with the Ocean3-4 and MISOMIP1 experiments, where the minimum water column thickness is required , with minimal effect on melt rates. The minimum size of partial cells is 25 % of a regular cell for MITgcm-JPL and 20 % for MITgcm-BAS and MITgcm-BAS-Coupled. All three configurations achieved similar, but not identical, melt rates at depth during the tuning experiment that fell within the target error margin, explained by their use of similar but not equal heat transfer coefficients and partial cell limits. The MITgcm-BAS-Coupled setup requires the use of a small (of the order of 0.05 m) minimum water column under all grounded ice in the domain (seen in Fig. d) to represent grounding-line retreat when used in coupled mode .

Heat transfer coefficients ΓT for MITgcm-BAS and MITgcm-BAS-Coupled were initially reported as 0.019 and 0.021 respectively. However, subsequent analyses verifying the melt parameterisation (Sect. ) revealed inconsistencies between the quoted transfer coefficients and the model output. These analyses suggested that MITgcm-BAS-Coupled used a transfer coefficient of 0.0135, and MITgcm-BAS used 0.011 in the Ocean1 experiment and 0.036 in the Ocean2 experiment (Table ). Due to a lack of model data traceability during the intervening years, we are unable to verify which transfer coefficients these experiments used. It is hence possible that the experimental protocol was not completely followed, particularly for the MITgcm-BAS Ocean2 experiment (in the MITgcm-BAS Ocean1 experiment we can verify it achieved the tuned melt rate of 30 m yr⁻¹ averaged below 300 m depth at steady state, see Sect. ). For MITgcm-BAS-Coupled we are reasonably confident that the value 0.0135 was used because we have found ISOMIP+ Ocean3 and Ocean4 simulations using that value.

Two submissions are based on the Modular Ocean Model version 6 MOM6;. MOM6 is a finite volume model, uses the Arakawa C-grid and is formulated in a generalised vertical coordinate form. Momentum is advected using a second-order centred scheme, while tracers are advected using a piecewise linear method. Vertical mixing due to shear instabilities and convection is represented using the scheme, with the critical Richardson number set to 0.25. The minimum vertical viscosity within the surface boundary layer is 10-2 m² s⁻¹. Melting is set to zero when the total water column thickness is less than 10 m, and meltwater is added as a volume flux. The differences between the two MOM6 COM submissions are described below.

One submission uses the Model for Prediction Across Scales Ocean MPAS-Ocean; version 6.1. MPAS-Ocean uses finite volume methods on an Arakawa C-grid. The configuration has an Arbitrary Lagrangian-Eulerian (ALE) vertical coordinate, which smoothly transitions from z* in the open ocean (with 36 vertical layers of 20 m resolution) to a terrain-following top coordinate under ice shelves. The coordinate under ice shelves constrains layer thicknesses such that the local Haney number rx1; does not exceed a maximum value of 5. This prevents large horizontal pressure gradient errors due to the tilted vertical coordinate. Momentum is advected using a second-order, kinetic-energy-conserving scheme and tracers are advected with a third-order, flux-corrected transport (FCT) scheme . MPAS-Ocean's melt parameterisation uses temperature and salinity that are averaged within 10 m of the ice draft. The far-field ocean speed |uw|=2EK is computed from kinetic energy EK at cell centres in the layer closest to the interface, and is not averaged vertically over multiple layers. Melt fluxes (heat and freshwater) are distributed based on an exponentially decaying transmission function T=e−(z−zd)/D, where zd is the ice draft and the length scale of decay D=10 m. Sea level is approximately maintained, for all but the Ocean0 experiment, using negative freshwater fluxes applied in the northern restoring region. These fluxes are adjusted monthly, using a 3-month running mean of the meltwater flux, which was implemented offline via simple “evaporative” freshwater flux, heat flux and salt flux adjustments rather than modifying MPAS-Ocean code. The 3-month averaging window was chosen so that the lagged sea-level adjustment would not over-react to monthly fluctuations in the melt rates, though in retrospect this was likely not needed for the ISOMIP+ experiments. The provided ISOMIP+ topography was modified by smoothing with a Gaussian filter with a half-width of 2 km before interpolating to the 2 km grid. A minimum thickness of 3 layers was maintained by deepening bed topography near the grounding line.

Two submissions are based on NEMO, the Nucleus for European Modelling of the Ocean : a version used at the French National Centre for Scientific Research (CNRS) e.g., and a version used in the UK Earth System Model UKESM, . The NEMO-CNRS configuration is based on a post-v3.6 release of NEMO that is described as the “COM” configuration in , with details on the model parameters in . The NEMO-UKESM1is configuration is the “GO7” version described in . Both configurations use finite-difference methods on an Arakawa C-grid . A z* coordinate is used with a nominal uniform vertical resolution of 20 m. For a better representation of the topography, partial cells are used in the lowest and uppermost grid cells . NEMO-CNRS makes use of the third-order Upstream Biased Scheme (UBS) scheme for momentum advection (flux form) and for horizontal tracer advection , and a second-order flux corrected transport scheme is used for vertical tracer advection. In NEMO-UKESM1is, momentum is advected in a vector invariant form, and tracers are advected with a Lax-Wendroff Total Variance Dissipation (TVD) scheme. Vertical mixing in NEMO-CNRS follows the ISOMIP+ protocol, while NEMO-UKESM1is uses a different “TKE scheme” , in which the background viscosity is set to the recommended stable vertical eddy viscosity and diffusivity (Table ), with double diffusion mixing for tracers. The melt rates are calculated using temperature, salinity and velocity averaged over the top 20 m of the water column. The ice shelf meltwater and associated heat are also spread uniformly over the top 20 m. To maintain the mean sea level, ice shelf melting in NEMO-CNRS is compensated by a uniform water flux correction applied at the open ocean surface at each time step, with no associated latent heat and salt flux as described in equations 34–36 of . In NEMO-UKESM1is, this correction was incorrectly allowed to affect the salinity of the remaining surface water. For cases of significant ice shelf melting, this issue leads to salinification of the open ocean surface and unwanted convective mixing, cooling the interior of the domain (e.g. Fig. j). As NEMO needs at least two vertical cells to resolve a water column, the topography is adjusted by “digging” into the ice in NEMO-UKESM1is, and equally into the ice shelf draft and the bed topography in NEMO-CNRS. Water columns of only one grid cell width in either x or y directions are also removed.

One submission uses the Parallel Ocean Program 2 eXtended (POP2x), a version of POP2 that includes ice shelf cavities . POP2x uses finite-difference methods on an Arakawa B-grid. It has a z-level vertical coordinate with 20 m vertical resolution and partial top and bottom cells to represent the topography with higher fidelity. Momentum is advected using a second-order, centred scheme and tracers are advected with a flux-limited Lax-Wendroff scheme . POP2x's melt parameterisation uses far-field temperature and salinity, averaged over the top 20 m – from the top of the first partial cell down to the remaining required fraction of the second vertical layer. The far-field ocean velocity used in the melt parameterisation is averaged over the four neighbouring B-grid points only in the upper vertical layer. Melt fluxes (heat and freshwater) are distributed over the upper 20 m. After interpolation and removing ice thinner than 100 m, the topography is modified by (1) smoothing with a Gaussian filter with half-width of 2 km, (2) deepening bed topography near the grounding line to maintain a minimum water column thickness of 40 m, (3) either thickening or removing partial top cells thinner than 5 m, and (4) adjusting the ice draft and bed topography to ensure horizontal connectivity between neighbouring cells.

One submission is based on the Regional Ocean Modeling System ROMS;, adapted to include ice shelf cavities . ROMS is a finite volume model that uses an Arakawa C-grid and a terrain-following vertical coordinate system. Only 21 vertical layers are used in the ROMS configuration, with a higher resolution near the surface and bottom. The mean top layer thickness is 0.5 m near the grounding line, 3 m at the mid-ice shelf, and 5 m near the ice front. Momentum is advected using a 3rd order upstream scheme (fourth-order centred for the barotropic momentum), and all tracers are advected using a third-order upstream scheme in the horizontal direction and a fourth-order centred scheme in the vertical. Horizontal mixing is along geopotential (i.e. horizontal, not the model terrain following) surfaces. Basal melting and freezing are computed using temperature, salinity and velocity from the top vertical layer. Heat and meltwater fluxes are distributed at the surface of the top layer only. The topography was smoothed with a 4th-order Shapiro filter to lower the maximum “slope parameter” to 0.1. A minimum water column depth of 20 m is used. It was not possible to reach the target melt rate of 30±2 m yr⁻¹ below 300 m depth in ROMS during the tuning stage in Ocean0, as melt rates saturated with high transfer coefficient values. Instead, the chosen value of ΓT=0.05 results in an equilibrium melt rate of 14 m yr⁻¹.

In this section, we present the spun-up temperature and salinity profiles and melt rate spatial distributions at the end of the Ocean1 and Ocean2 COM experiments. We take results from the average of the final year (year 20). By then, Ocean1 melt rates are approximately constant and at steady-state, but Ocean2 is still evolving and therefore still exhibits a small amount of transient adjustment (see Sect.  for further details).

Temperature and salinity distributions at year 20 of the Ocean1 and Ocean2 COM simulations at the y= 40 km transect show similarities between models (Figs. ,  for temperature and Figs. , S8 for salinity, noting that salinity variations control the density stratification). Though Ocean1 is initialised with cold conditions, the temperature inside the cavity resembles the warm restoring conditions at the end of the simulation, with an additional cold boundary layer near the ice. Similarly, Ocean2, which is initialised with warm conditions, ends up resembling the cold restoring conditions. However, there are differences between the models; in Ocean1, NEMO-UKESM1is has a relatively colder interior (Fig. j), and POP2x has a colder boundary layer (Fig. k, see also Fig. k) than most other models. The cold interior of NEMO-UKESM1is can be explained by spurious convection arising from the incorrect water flux correction, as discussed in Sect. . In Ocean2, temperatures are more uniform within the domain, matching the uniform -1.9 °C sponge forcing, but MITgcm-BAS-Coupled, MITgcm-JPL and NEMO-CNRS have a warmer interior of the cavity with temperatures reaching -1.6 °C (note the different colourbar to Ocean1, which emphasises these features). This warm interior may be associated with remnant warm water from the Ocean2 warm initial conditions that have not been circulated out of the domain by the boundary forcing; that is, Ocean2 is not yet at a steady state after 20 years (see Sect. ), or may indicate spurious model behaviour. These three models' counterparts MITgcm-BAS and NEMO-UKESM1is are much colder, but also have known inconsistencies with the experimental protocol (Sect. , ). The coldest temperatures in all simulations range between -2.3 to -2.0 °C, lower than the coldest -1.9 °C sponge forcing temperature. These cold temperatures are generated by the melt parameterisation and occur at depth where the freezing temperature is depressed below the surface freezing point.

In the open ocean, Ocean1 temperature stratification (Fig. ) and salinity stratification (Fig. ) have distinct column-like features that are associated with barotropic gyres, discussed in Sect. . There is a front with a horizontal gradient in temperature below the calving front, and for some models, there is an additional front at approximately x=720 km, indicating the presence of one or two gyres.

Salinity transects in both experiments approximately indicate the density and stratification (Figs. , S8), which are important controllers of ocean circulation. The fresh salinity near the ice shelf–ocean boundary layer of the Ocean1 experiment indicates meltwater stratification, further highlighted by the increased density of the salinity contours near the ice. Stratification of the Ocean2 experiment (Fig. S8) is dominated by the far-field restoring forcing rather than meltwater effects, with relatively flat salinity contours. The density of the initial conditions and far-field forcings is the same for both cold and warm profiles, indicating that gradients of density are only due to meltwater interactions.

Melt rate spatial distributions in year 20 of the warm Ocean1 and cold Ocean2 COM simulations also show similarities between models (Figs. , ). Melt in both experiments is enhanced at depth and near the grounding line (Fig. ), where the thermal driving is larger. This enhancement is particularly pronounced for Ocean2, which has a steep ice shelf draft near the grounding line (Fig. c). Comparing Ocean1 models, the spatial distribution of melt varies, with MOM6-LAYER, MPAS-Ocean and NEMO-UKESM1is having enhanced melt at the deepest grounding line (Fig. a). In contrast, COCO, MITgcm-BAS-Coupled and MOM6-SIGMA-ZSTAR have enhanced melt at the cavity sidewalls (Fig. ). FVCOM has a region of freezing on the +y side wall. Additionally, POP2x has a pronounced checker-board melt pattern. This striped pattern is also visible to a lesser extent in the other z-level coordinate models COCO, MITgcm and NEMO. For Ocean2, melt rates away from the deepest grounding line are small but COCO and FVCOM simulate significant freezing at the side walls (Fig. ). COCO and FVCOM also have larger melting at depth near the grounding line (Fig. b) and also have cold temperatures near the ice base of the y=40 km transect (Fig. ). Other models (e.g. MITgcm-BAS, MOM6-LAYER, NEMO-UKESM1is, POP2x, ROMS) also have cold temperature transects (i.e. lack the warm temperatures remnant from the spin-down observed in some models, Fig. ) and no such freezing, however, the temperature transects do not sample the sidewall region where freezing occurs. These variations demonstrate that models can achieve similar cavity-averaged melt rates (the tuning target melt rate below 300 m is achieved by all models except ROMS and FVCOM) with very different spatial distributions of melting. These differences in melt rate patterns, particularly near the grounding line and side walls, are likely to be at least partly associated with differences in representations of bed topography and ice shelf draft between models that are enhanced near the side walls, grounding line and ice front (Figs. S11, S12). Differences in spatial distributions of melting have implications for ice sheet evolution in coupled ice sheet–ocean models as the ice thickness and therefore the buttressing effect may evolve differently depending on the location of melt.

We present the overturning and barotropic streamfunctions for the Ocean1 and then Ocean2 COM experiments during year 20, where models are spun up. Ocean1 is approximately at steady state, but Ocean2 still exhibits some transient adjustment. Further calculation details are in . The overturning streamfunction is presented in x–depth coordinates due to model data availability: using density coordinates may have allowed better quantification of water mass transformations in the ice shelf cavity , but circulations are qualitatively similar see, e.g. Fig. 4 inbut note they use smaller transfer coefficients and have lower melt rates than the ISOMIP+ protocol. Future model intercomparisons should consider including the density-coordinate overturning streamfunction as a required diagnostic, and may also consider diagnosing adiabatic and diabatic contributions to heat transport.

The overturning circulations in year 20 of the warm Ocean1 experiments show common features across models (Fig. ), with upwelling occurring in the ice shelf cavity and downwelling near the northern boundary. The strength of the overturning varies between models, with most models showing maximum streamfunction values of 0.20–0.25 Sv. COCO demonstrates the strongest overturning streamfunction, with a peak value of 0.39 Sv, whilst ROMS and FVCOM have weaker circulation which is likely attributed to lower melt rates (Fig. , see also Fig. ). The structure of the overturning streamfunction also varies, with some models displaying two distinct peaks, one within the ice shelf cavity and another near the “northern” (x= 800 km) boundary (e.g., MITgcm-BAS-Coupled, MITgcm-JPL, NEMO-CNRS), and others exhibit a single peak near the northern boundary (e.g., FVCOM, MITgcm-BAS, MPAS-Ocean, POP2x, ROMS). Varying bed topography and ice geometry in both x and y-direction (Fig. ) results in the streamfunction, which is computed by averaging velocities over the y-direction, being nonzero in (x,z) coordinates that are not simulated as ocean in the y=40 km transect (e.g. Fig. ).

The barotropic streamfunctions in year 20 of the warm Ocean1 experiments reveal similar circulation patterns across most models within the ice shelf cavity, with the exception of COCO (Fig.  in the ice shelf cavity and see Fig. S5 for the full domain). The typical pattern involves a boundary-intensified (y>50 km) clockwise, cyclonic circulation within the cavity, with a maximum barotropic streamfunction of 0.26 ± 0.17 Sv in this region (y>50 km, x<640 km). The circulation feature varies in shape, with some models having strongly boundary-intensified circulation (e.g. MITgcm-BAS) while others are centred further away from the boundary (e.g. MOM6-SIGMA-ZSTAR), and the extent that the circulation penetrates towards the grounding line also differs between models. However, COCO deviates from this pattern, with only a weak boundary flow and instead a strong counterclockwise circulation within the ice shelf cavity. This circulation is potentially linked to a spatial pattern of ice shelf melt with peaks along the “eastern” (y<30 km) boundary of the ice shelf cavity, in contrast to many other models (Fig. ). In this eastern region of the ice shelf cavity, there are differences in circulation between all models (e.g. differences in location of the grey, solid 0 Sv line in Fig. ), and in particular, the MOM6 models display a large counterclockwise circulation. Variation in circulation between models may be associated with the different interpolation and smoothing choices of the bed topography and ice shelf draft, particularly near the side walls, grounding line and ice front (Sect. , Figs. S11, S12) and are likely also related to the different melt rate spatial distributions (Figs. , , ).

Moving further towards the open ocean, the warm Ocean1 barotropic streamfunctions show a clockwise inflow and outflow of water crossing beneath the ice shelf calving front at x= 640 km. This flow, quantified by the maximum barotropic streamfunction near the ice front (630 km <x< 650 km), varies in magnitude (0.41 ± 0.27 Sv), with models with higher barotropic streamfunctions also typically having higher overturning streamfunctions. Despite the general similarity in ocean circulation within the ice shelf cavity, the ocean circulation outside the ice shelf cavity shows significant variability among the models, and is generally stronger in magnitude (Fig. S5). Some models have two open ocean gyres, with no consistent rotation direction between models, whilst other models (e.g. FVCOM, MOM6-SIGMA-ZSTAR) have just one gyre (and the number of gyres can vary with time). These open ocean gyres are sensitive to the discretisation of the ice shelf geometry in the MISOMIP1 configuration and may also be sensitive to the model implementation of the northern boundary restoring region.

In the cold and steep ice base Ocean2 experiments at year 20, the overturning circulation consists of an opposing two-cell structure across most models, with a clockwise, cyclonic circulation at deeper levels and a counterclockwise circulation at shallower depths (Fig. ). This circulation can be explained by a buoyant meltwater current that rises beneath the steep ice base near the grounding line until it reaches its neutral buoyancy and separates from the ice shelf . Return flow above and below this depth is created by the modifications made by the restoring forcing to the fluid's buoyancy at the x=800 km wall boundary and is constrained by conservation of volume. The similar cell separation height across models (grey solid line in Fig. ) suggests that the neutral buoyancy depth places a strong constraint on the vertical overturning structure, especially since the salinity stratification is strong (Fig. S8). Typical circulation strengths are 8.2±2.4 mSv for the deep clockwise circulation and -7.6±2.4 mSv for the shallower counterclockwise circulation for all models except COCO and FVCOM. COCO and FVCOM show overturning strengths about 14 and 3 times larger than the other models, respectively. The separation of the meltwater current from the ice draft at its neutral buoyancy depth also explains the lack of freezing in the models (Fig. ). Note that the simulated shallow counterclockwise circulation is likely related to density gradients in the domain that develop in response to the boundary restoring to the salinity-stratified cold profile, in combination with the steep ice base geometry, rather than local buoyancy fluxes (which are small due to the low melting at shallow depths, Fig. ). The circulation is a feature of our model setup, noting the unrealistically strong stratification and that reversed overturning cells of this extent have not been observed in Antarctic ice shelf cavities (to our knowledge). However, the counterclockwise circulation may not be completely unrealistic since mixed-source circulation and a surface inflow of shelf water have been observed at cold cavity ice fronts and observations of large-scale currents beneath Antarctic ice shelves remain limited.

The barotropic streamfunction in the cavity (Fig. ; see Fig. S6 for the full domain) at year 20 of the cold Ocean2 experiments generally shows a similar circulation pattern across models, except for COCO. Most models exhibit weak clockwise circulation near the grounding line (maximum streamfunction for x< 460 km is 47 ± 42 mSv) and counterclockwise circulation in the outer ice shelf cavity (minimum negative streamfunction inside the cavity for x> 460 km is -75 ± 43 mSv), though circulation patterns differ. In contrast, circulation in COCO once again differs significantly from other models, consisting of two strong clockwise circulations within the ice shelf cavity. These circulations have peaks in both the inner and outer cavity, showing circulation strengths of 0.29 and 1.2 Sv, respectively. Despite the similarities in simulated ocean circulation within the ice shelf cavities, the circulation patterns outside the ice shelf cavity differ significantly (Fig. S6), consistent with the findings from the Ocean1 experiment.

The circulation results for both the Ocean1 and Ocean2 experiments suggest that (a) most ISOMIP+ ocean models are capable of simulating similar ocean circulation structures within the ice shelf cavity, which are only weakly influenced by the off-shelf ocean circulation, underscoring the robustness of these models, and (b) differences in the treatment of ocean boundaries and sponge layers among the models and model geometries may contribute to the observed discrepancies.

In this section, we explore the transient nature of the ISOMIP+ Ocean1 and Ocean2 COM ice shelf cavity experiments where the ocean's initial conditions adjust to the forcing at the northern boundary. The melt rate changes as temperature and salinity changes are advected into the cavity, and there are feedback mechanisms between melting and the barotropic and overturning circulation.

The area-averaged melt rates over the entire ice shelf for the Ocean1 and Ocean2 experiments as a function of time demonstrate the dependence of melt rate on ocean conditions and circulation (Fig. ). The Ocean1 melt rate increases from its low baseline created by the cold initial conditions as the warm boundary forcing penetrates the cavity. Melt rates approach a constant value for all models by year 14, except for ROMS which is still increasing in year 20 (Fig. a). The quasi-steady mean melt rates vary significantly across models (4–12 m yr⁻¹) and some models (COCO, MITgcm-BAS, NEMO-UKESM1is and MPAS-Ocean) show larger temporal variability in melt rate with ∼ 1 m yr⁻¹ variation in the monthly averaged data. These maximum area-averaged melt rates are lower than the target 30 m yr⁻¹ of the Ocean0 tuning experiment, which matches the steady state Ocean1 conditions, because the Ocean0 tuning only considers the ice shelf cavity regions deeper than 300 m (recall that all models except FVCOM and ROMS achieved the Ocean0 target melt rate). The large variation in the final ice shelf cavity-averaged melt rate highlights the importance of the spatial distribution of melt (Fig. a), particularly as a function of depth (Fig. ). Additionally, the time taken for the model spin-up to reach a steady state varies between the models, with COCO reaching steady melt rates within 5 years but ROMS still increasing in melt at year 20. However, after an initial spin-up phase, most models show a similar transition time during which the melt rates increase in response to the warming cavity, as demonstrated in Fig. c. Here, the melt rates are normalised by their maximum value and shifted by the earliest time they achieve a melt rate of half their maximum melt rate. The models merge into one sigmoid-like profile with an approximate width of 5 years, except for ROMS. This similarity indicates that differences in spin-up time are more likely to be associated with the timescales for which the boundary forcing propagates into the ice shelf cavity rather than different circulation responses to changing melt rates.

The Ocean2 melt rates decrease from relatively high values, due to the warm initial conditions, towards melt rates of less than 2 m yr⁻¹ within 2 years, in response to the advection of the colder water from the restoring into the cavity (Fig. b). The logarithmic scale inset demonstrates that the resultant melt rates at 20 years still vary by an order of magnitude between 0.01–0.2 m yr⁻¹, and additionally that many of the models have not yet reached steady state, a possible explanation for the remnant warm temperatures in some of the year 20 temperature transects (Fig. ). When scaled and shifted in time (Fig. d), the models are similarly described by a sigmoid-like profile, though there are some exceptions with a rebound in melt rate in MITgcm-BAS-Coupled and MITgcm-JPL after ∼ 2 years, possibly related to the development of a melt-circulation feedback or a result of the advection scheme producing spuriously warm water (Sect. ).

The different initial (slower) spin-up and (faster) spin-down timescales in the Ocean1 and Ocean2 experiments, respectively (Fig. ), can be explained by the timescales of advection of temperature anomalies by the overturning circulation, as well as the differing ice geometries in the two experiments. Since the boundary conditions and initial conditions have the same density stratification Fig. 6 of , the only source of density variations is ice shelf melting , which is guided by the temperature of the cavity. In the Ocean1 simulation, warm water is slowly advected from the boundary to the base of the initially cold Ocean1 ice shelf by the weak cold cavity state circulation, leading to low melt rates for ∼ 5 years for most models. Once warm intrusions arrive at the ice shelf base, they drive increased melt and buoyancy-driven overturning, which advects warm boundary water into the cavity more quickly in a feedback mechanism that further spins up the circulation. The colder-restoring Ocean2 begins with a fast warm cavity state circulation, rapidly slowed by the cold temperature intrusion as the melting drops, to become a weak circulation. The flow also separates from the ice at mid-depth (Fig. ), further reducing melt and circulation. The slower circulation in Ocean2 therefore increases the time required to “flush” the cavity with the boundary conditions and equilibrate, explaining why most models have reached a steady state by the end of Ocean1, but not Ocean2. Additionally, the difference in ice base geometries between Ocean1 and Ocean2 (Fig. ) likely contributes to this asymmetric behaviour. However, similar asymmetries in warming and cooling transient melt rate responses are seen in fixed geometry simulations with an oscillating far-field forcing, such as in the Ocean1 domain and in wedge-like ice shelf setups .

We also compare the relationship between ocean temperatures and melting. For the Ocean2 experiments, area-averaged melt rates scale approximately quadratically with ocean temperatures near the front of the cavity (or more specifically, the thermal forcing at the front of the cavity, taken as the difference between the ocean temperature and a reference freezing point at depth of -2.1 °C, has a log-log best-fit power-law exponent with melt of n≈2 on average in Fig. S1b). This relationship is consistent with the quadratic equilibrium response of the melt rate to thermal forcing shown in and . The Ocean1 simulations have a different scaling (close to linear with n≈1.3, see Fig. S1a) associated with the cavity being in a transient state. This transient state can be explained by the observed delay in spin-up due to weak circulation despite warming ocean temperatures near the front of the cavity. The deviation from the quadratic scaling is consistent with , who show that warm-to-cold transitions (i.e. Ocean2) better match the equilibrium response (a quadratic melt rate–thermal driving relationship) compared with cold-to-warm transitions (i.e. Ocean1).

The ISOMIP+ experiments demonstrate a strong relationship between melt rate and circulation across models and forcings. Fig.  shows the barotropic and overturning circulation strength, calculated from the difference between maximum and minimum streamfunction amplitudes within the ice shelf cavity, as a function of area-averaged melt rate for each month of the Ocean1 and Ocean2 simulations. Most models follow shared linear relationships between melt rate and overturning and barotropic streamfunctions for both the Ocean1 and Ocean2 experiments. Consistent with previous circulation metrics (Figs.  and ), the COCO barotropic streamfunction is abnormally strong in both experiments, suggesting the influence of a circulation source other than melting. Deviation from the linear relationship between melt and circulation strength may be explained by the circulation being influenced by the restoring at the boundary in addition to the expected buoyancy forcing from melting. If the ice shelf cavity flow is driven only by buoyancy, the magnitude of melt would be expected to be proportional to the near-ice velocity, which in turn should scale (to first-order) with overturning circulation strength e.g., noting that melt rate feedbacks on stratification would modify this relationship. In this buoyancy-driven flow regime, the barotropic ice shelf cavity flow is mostly geostrophic and driven by the density difference between the buoyant meltwater and deep ocean restoring water properties, therefore, barotropic flow would also scale linearly with melt e.g.. However, note that geostrophy does not hold near boundaries due to the presence of boundary drag, but the boundaries of the ice shelf cavity contain regions with significant melt (e.g. y>60 km in Fig. ). Understanding the ocean dynamics involved in the coupled melt rate–circulation relationship requires further experiments not performed here.

Despite both Ocean1 and Ocean2 having linear circulation–melt relationships, correlations are weaker in Ocean2 (Fig. b, d). The overturning metric in Ocean2 quantifies the speed of the mid-depth flow away from the ice shelf as the meltwater flow separates from the ice (Fig. ), and is therefore less tightly coupled to the melt rate averaged across the whole ice shelf than in Ocean1. Additionally, the reduction in the strength of the correlation between melt and circulation in Ocean2 may be due to weaker circulation strength, which would increase the importance of boundary layer temperature and salinity properties that change with melting. The prescribed tidal friction velocity (acting to increase the melt compared to that expected by the boundary layer velocity) may contribute to the non-zero intercepts of the circulation–melt relationships, which is more prominent in the slower Ocean2 experiments (Fig. ).

Despite the deviations in some models from the linear circulation–melt relationship, Fig.  demonstrates agreement in the circulation–melt relationship amongst the models. This model agreement is promising, showing reliability in simulated ocean-ice interactions and feedback processes between circulation and melt. The circulation–melt relationship is thus an important metric for model comparison, where models display agreement despite individual melt rate or temperature distributions.

Many of these differences in melt rate between models can be understood by considering the driving factors of ice shelf basal melt. Much of these differences can be attributed to (a) the differences in the representation of the temperature and salinity properties in the boundary layer region, and (b) model choices of calculating the thermal and haline driving and the distribution of heat and meltwater fluxes.

The representation of the ice shelf–ocean boundary layer in the Ocean1 COM models at year 20 is shown in Fig. , when the cavity is in a warm state. Here, we show the potential temperature in the upper ice shelf cavity, where the vertical coordinate is the distance from the ice shelf basal surface. This remapping produces the jagged features of Fig. : model output is remapped onto a discrete grid with 5 m vertical spacing, relative to 0 m depth, whereas the ice draft used in each model can vary continuously. Therefore, the distance from the ice (the difference in depth, i.e. the difference between ice draft crosses and 5 m output in Fig. S13) has both discrete and continuous components and is jagged in shape. Additionally, the distance can be negative if the depth to which the ocean model output is remapped is shallower than the ice draft (e.g. MITgcm-BAS-Coupled, Fig. S13d).

Comparing boundary layer temperature profiles, most Ocean1 models show warmer water at depth away from the ice base (Fig. ). Conditions are particularly warm (greater than 0.5 °C) near the ice base in the deeper portions of the cavity (e.g. x-coordinate of 450–500 km), but models show different widths in the x-direction of this warmer water band. Upslope of this warm region (x>500 km), there is a transition to cooler temperatures (∼ -1.1 to -0.025 °C). Above this, and directly below the ice shelf, there is a cold layer (the ice shelf meltwater; approximately <-1.7 °C, shown in white contours in Fig. ). All the Ocean1 COM models simulate these features but with different horizontal and vertical scales. Ice shelf–ocean boundary layers in the cold Ocean2 COM models are colder and thicker than Ocean1, but also exhibit inter-model variation (Fig. S2) and may be associated with the models not yet reaching equilibrium (Figs. , ).

Focusing on the meltwater layer closest to the ice shelf–ocean boundary, Ocean1 COM models have different temperature profiles (Fig. ; see Fig. S2 for Ocean2 COM results). Some models have a thin, cold layer that transitions smoothly and relatively rapidly into warmer water below, e.g. FVCOM, MITgcm-JPL, MOM6-SIGMA-ZSTAR, MOM6-LAYER and ROMS: mostly the terrain-following and isopycnal coordinate models (note the 5 m resolution output may also hide part of the thin, cold boundary layers in ROMS and FVCOM, e.g. ROMS has top layer thicknesses less than 5 m). Some models have a cold layer but with a thicker extent (MITgcm-BAS, MITgcm-BAS-Coupled, MPAS-Ocean, NEMO-CNRS and NEMO-UKESM1is). Sharp differences in temperature along the meltwater layer suggest that the z-coordinate resolution and its step-like boundary are partially responsible. Lastly, some other models have a largely unique representation of the boundary layer, being much thicker than the other models (COCO and NEMO-UKESM1is, the latter of which has known erroneous surface cooling). POP2x also has a very cold boundary layer, which explains why it requires such a large melt rate transfer coefficient (Table ) compared to other z-coordinate models to achieve the same target melt rate, and may indicate numerical inaccuracies. Boundary layer representations are therefore dependent on the vertical coordinate, with terrain-following coordinates tending to have thinner boundary layers, likely due to their higher vertical resolution beneath the ice shelf and reduced implicit mixing (in models that distribute meltwater over only the uppermost layer). Meltwater fluxes stably stratify the water column, hence thin, stratified boundary layers have potential feedback effects on melt rate. However, other model-specific numerics may also play a role, noting significant differences in boundary layer representation even between z-coordinate models with the same vertical resolution. These differences may be associated with different implementations of the -style sampling and meltwater distribution layer, as well as partial cell thicknesses. The simplified, prescribed diffusivities of the ISOMIP+ COM protocol may also be an important controller of boundary layer representation compared to model mixing parameterisations used in typical realistic model configurations (equivalent results for TYP configurations shown in Figs. S9, S10). In summary, Fig.  demonstrates that the ice–ocean boundary temperature profile is a key metric of variability between models.

Ice shelf–ocean boundary layer temperature is one controller of melting that differs between models. However, the strength of the friction velocity is also included in the basal melt parameterisation, as are the transfer coefficients. Fig.  shows the distribution of thermal driving (defined as the difference between the far-field and boundary layer temperature in the melt parameterisation; Tw-Tzd in Eq. ), friction velocity and melt over the cavity averaged over year 20, noting that the product of thermal driving and friction velocity is scaled by the transfer coefficients (which differ between models) and other constants to determine melt. Thermal driving in Ocean1 is generally larger in the models with thicker boundary layers, mostly z-level models that use a 20 m layer to sample temperature and salinity that may extend deeper into the warm cavity interior than the meltwater layer (e.g. COCO, MITgcm-BAS, MITgcm-BAS-Coupled, MITgcm-JPL and NEMO-CNRS). z-level models also tend to have slightly larger friction velocities, possibly also associated with a deeper sampling depth. The spatial distribution of melt rates with depth (Fig. ) is associated with both thermal driving and friction velocity distributions, where model variation in the location of peak melt rate is associated with the friction velocity (and therefore circulation) as well as increasing thermal driving with depth. In Ocean2, there are large differences in the distribution of thermal driving, whereas friction velocities are small and for all but COCO (which has an anomalously strong barotropic circulation, Sect. ) display a nearly spatially uniform friction velocity of 5×10-4 m s⁻¹, which is the minimum prescribed tidal velocity scaled by the drag coefficient. Fig. b also highlights the significant portions of the COCO, FVCOM, ROMS and MITgcm-BAS-Coupled cavities that are freezing at the ice shelf-ocean interface rather than melting.

One of the key parameters in the experiment is the heat and salt transfer coefficients of the three-equation parameterisation, which control the melt rate and, therefore, circulation. To verify the implementation of the basal melt parameterisation, diagnosed melt rates (and hence applied meltwater fluxes) are compared with the product of the diagnosed thermal driving and friction velocity in the Ocean1 and Ocean2 COM models (Fig. S3). The melt rate is scaled by constants in Eq. (), including model-dependent transfer coefficients (Table ). POP2x shows some deviations from the diagonal 1:1 line, possibly indicating transient numerical inaccuracies. The MITgcm-BAS-Coupled simulation has a slope of 1 only if a readjusted transfer coefficient is used rather than the value initially reported (see Sect.  for more details), as does the Ocean1 simulation of MITgcm-BAS, which has a systematically different slope from the Ocean2 simulation. As discussed in Sect. , the transfer coefficients used may have differed from the reported values, or there was a diagnostics error. Nevertheless, the z-level models tend to have similar thermal transfer coefficients between 0.0135 and 0.0325 (Table ) with some exceptions: NEMO-UKESM1is requires a larger coefficient to offset its erroneous cooling, MITgcm-BAS has inconsistent transfer coefficients, and POP2x has an anomalously large transfer coefficient that we do not have an explanation for. The other z-level model configuration transfer coefficients are generally smaller than that for the terrain-following, ALE and isopycnal coordinates (Table ). z-level models are expected to require smaller transfer coefficients to achieve the same tuned melt rate, since the lower vertical resolution near the ice implies greater thermal driving sampling and freshwater flux distribution distances. z-level models therefore tend to have larger melt rates compared with higher resolution terrain-following configurations when the same transfer coefficient is used .

To verify the simulated representation of ice–ocean thermodynamics in the models, we assess the water mass evolution in the warming Ocean1 experiment (Fig. ). In the absence of other heat and freshwater sources, water mass properties should eventually be confined between the restoring conditions and the meltwater mixing line , along which a given water mass will cool and freshen at a constant ratio when interacting with the ice shelf at different depths. Neglecting heat conduction into the ice, as in the experimental protocol , the slope of these characteristic lines in temperature–salinity (T–S) space are given by 6∂T∂S=Tw-Tf+L/cwS0, . Here, the specific heat capacity of seawater cw and latent heat of fusion L are presented in Table . The salinity S0 of the seawater in contact with the ice is taken as a constant Sref=34.2 for simplicity, but with insignificant impact on the results. Tw is the temperature of the source water, taken to be the warmest water of the warm restoring condition, and Tf, the boundary layer freezing point, is taken to be the freezing point at the reference salinity and a depth of 360 m. Temperature and salinity data are taken from the cross-section of the model results at y=40 km, the most complete available datasets for this analysis. Fig.  shows that most models produce water masses within the expected range that is spanned by the restoring conditions and modification by ice shelf melting: T–S properties in all models deviate along the meltwater mixing line from the cold restoring properties (that were used as model initial conditions, blue line) to lower temperatures during the first month of the simulation, confirming the consumption of heat by basal melting of ice at greater pressure in the cold cavity. At the end of the simulation, this cold and saline water mass has been eroded by the warmer Ocean1 forcing, with most models featuring a T–S distribution in the last year (year 20, yellow colours) of the simulation that is bounded by the warm restoring conditions (red line), and the meltwater mixing line originating from the warmest water mass in the domain (black thick line), indicating mixing between these water masses. The absence of significantly colder temperatures than the 100 m melting point in most models at the end of the Ocean1 experiment is consistent with the paradigm of a warm ice shelf cavity circulation, where melt rates are limited by the fluxes across the ice-ocean boundary layer and a significant fraction of the available heat for melting is advected out of the cavity by the cavity circulation.

Some models show T–S properties at year 20 “to the right” of the warm restoring conditions (compare yellow and red colours in MITgm-BAS, MITgcm-JPL and NEMO-UKESM1is in Fig. ). This feature could originate either from remnants of the initial conditions (unlikely, since models are well spun up; Fig. ), or spurious salinification. The latter is known to have occurred in the imperfect application of the sea level restoring in NEMO-UKESM1is. Additionally, T–S properties “to the left” of the meltwater mixing line (MITgcm-BAS and MITgcm-JPL) indicate spurious freshwater. Both the spuriously fresh and saline features in these two models were found to be caused by the MITgcm advection scheme (https://mitgcm.readthedocs.io/en/latest/algorithm/adv-schemes.html, last access: 1 April 2026) used, the third-order DST flux limiter option 33 (and can be resolved with alternative advection schemes e.g. the second-order flux limiter option 77). Lower ocean temperatures than the freezing point at 720 m depth (the deepest ice in the domain) may indicate unphysical heat loss in two other models (POP2x and MOM6-SIGMA-ZSTAR, the latter found to be likely caused by diagnostic interpolation errors). T–S properties in ROMS lie below the warm restoring line, likely caused by a combination of the 5 m vertical resolution processed model output not capturing the cold, top boundary layer that is thinner than 5 m (the raw model data has water masses colder and fresher than the warm restoring line, not shown), and also that melting is driven by this cold boundary layer rather than warm restoring conditions, shifting the location of the Gade line. The latter highlights that differences in the water masses that drive melt (either through model differences, boundary layer and mixing choices) create different signatures in T–S space (Fig. ).

For Ocean2, the water mass evolution reverses (Fig. S4), confirming a transition from a warm cavity into a cold cavity circulation paradigm. However, in some models (MITgcm-BAS-Coupled, MITgcm-JPL and NEMO-CNRS) there is less Ice Shelf Water (water masses colder than the surface freezing point, similar to the dotted line) present in the last year of the Ocean2 experiment compared to the first month of the Ocean1 experiment. These are the same models with a relatively warm interior in Fig. . The lack of Ice Shelf Water may be because these Ocean2 models have not yet reached their “cold” steady state (Figs. , ) or a numerical issue, perhaps a consequence of the advection scheme issue noted in the Ocean1 analysis for the MITgcm models. The different ice base geometries between Ocean1 and Ocean2 may also affect the comparison between the first month of Ocean1 and last of Ocean2. The T–S space results indicate that water mass analysis is effective for model verification.

The TYP set of experiments noted in Sect.  repeated the geometries and forcing used in Ocean1 and Ocean2 but allowed groups to configure their models as they would choose to do for a typical simulation, relaxing the stricter requirements of resolution, physics and parameter choices required for the COM experiments. COM simulations were the priority in ISOMIP+, and not all groups chose to conduct TYP simulations (Table ). TYP configuration choices are described in Appendix .

There are a wide variety of differences between the COM and TYP configurations across the models so it is challenging to find simple explanations when comparing results between the two sets of experiments. It is generally true that a group's TYP model configuration produces less melt in response to the warm ocean forcing than using the idealised COM protocol (Fig. a, b), but this primarily reflects differences in resolution and parameterizations rather than the COM target melt rate being unrealistically high. Comparing melt below 300 m, which is the calibration depth used for setting each model's transfer coefficient values in Ocean0, the only model with a higher melt rate in its TYP configuration is FVCOM, which achieves this benchmark with the Ocean1 TYP configuration but not with COM, likely because of the use of different vertical mixing schemes. This lowering of melt rates and a marked increase in the variety of melt responses to warming suggests that the COM protocol was quite different to what model groups typically use, but succeeded in creating a common ground on which very different models could be compared. Although TYP models generally do not show more melt than COM, there is no consistent picture when comparing the rate at which the circulation spins up in the Ocean1 experiment. Temporal variability is similar in most TYP models compared to their Ocean1 COM counterparts, except for NEMO-UKESM1is, which has less temporal variability, and the ROMS model equipped with semidiurnal tides, which develops a clear periodic signal (likely showing resonance or aliasing in the monthly output).

There is less variation between COM and TYP in the Ocean2 experiment, with the models generally reducing their melt rates below 300 m at a similar rate (Fig. b, d). MPAS-Ocean has a higher final melt rate in TYP than COM in Ocean2 despite having a significantly lower melt rate in TYP compared to COM in Ocean1, and FVCOM shows the opposite behaviour, with more TYP melt in Ocean1 and less in Ocean2 compared to COM. This difference may be associated with changes in the depth at which the buoyant meltwater current separates from the ice. The two TYP variants of NEMO-CNRS achieve the same mean melt rate as each other in Ocean1 but with different timescales (possibly associated with different lateral momentum boundary conditions, vertical resolutions and melt distributions), and in Ocean2, after 20 years, they have spun down towards different area-average melt rates. As in COM, few of the Ocean2 TYP models have fully equilibrated melt rates at the end of the 20 years.

Even where TYP configurations produce similar melt rates to COM in response to the boundary forcing, similar melt rates can result from a different balance of physical processes (friction velocity and thermal driving) in the cavity (Fig. S7) and are also complicated by varying melt parameterisation choices. Generally, TYP models use smaller transfer coefficients than their COM counterparts (except for the NEMO simulations which tuned their melt rates to 30 m yr⁻¹, see Table  vs. Appendix. , ), and are closer to those suggested by observations e.g. Cd1/2ΓT=1.1×10-3 suggested byin comparison to an average Cd1/2ΓT of 3.0×10-3 across the COM models. However, note that transfer coefficients vary with ice shelf melt regimes and may not be constant in reality . FVCOM TYP uses a smaller transfer coefficient than its COM counterpart but has a higher melt rate (Fig. b), likely explained by its more realistic vertical mixing scheme (Appendix ), highlighting the importance of interior mixing choices on melt rates. Additionally, boundary layer temperature profiles of TYP configurations are also diverse and likely related to varying melt rate parameterisation and mixing choices (Figs. S9, S10).

In summary, the TYP experiments demonstrate how the COM experimental protocol moved many models away from their typical behaviour. There is significant variation in the simulated melt, melt drivers and circulation when models use their typical model parameters and resolution. However, untangling mechanisms and causes of model differences amongst the TYP models is challenging and emphasises the success of the COM experiments in providing a consistent common ground from which models can be compared.