The Southern Ocean Freshwater Input from Antarctica (SOFIA) Initiative: scientific objectives and experimental design

Abstract

As the climate warms, the grounded ice sheet and floating ice shelves surrounding Antarctica are melting and releasing additional freshwater into the Southern Ocean. Nonetheless, almost all existing coupled climate models have fixed ice sheets and lack the physics required to represent the dominant sources of Antarctic melt. These missing ice dynamics represent a key uncertainty that is typically unaccounted for in current global climate change projections. Previous modelling studies that have imposed additional Antarctic meltwater have demonstrated regional impacts on Southern Ocean stratification, circulation, and sea ice, as well as remote changes in atmospheric circulation, tropical precipitation, and global temperature. However, these previous studies have used widely varying rates of freshwater forcing, have been conducted using different climate models and configurations, and have reached differing conclusions on the magnitude of meltwater–climate feedbacks. The Southern Ocean Freshwater Input from Antarctica (SOFIA) initiative brings together a team of scientists to quantify the climate system response to Antarctic meltwater input along with key aspects of the uncertainty. In this paper, we summarize the state of knowledge on meltwater discharge from the Antarctic ice sheet and ice shelves to the Southern Ocean and explain the scientific objectives of our initiative. We propose a series of coupled and ocean–sea ice model experiments, including idealized meltwater experiments, historical experiments with observationally consistent meltwater input, and future scenarios driven by meltwater inputs derived from stand-alone ice sheet models. Through coordinating a multi-model ensemble of simulations using a common experimental design, open data archiving, and facilitating scientific collaboration, SOFIA aims to move the community toward better constraining our understanding of the climate system response to Antarctic melt.

1 Introduction

As the largest relative contributor to the oceanic sink of both anthropogenic heat and carbon, processes at work in the Southern Ocean directly modulate the rate of global change . The Southern Ocean also exerts a direct influence on sea level rise, as interactions with the warming ocean are the primary driver of the observed melting of ice shelves around West Antarctica that in turn leads to mass loss from the grounded Antarctic ice sheet (AIS) . Observations over recent decades show that mass loss from Antarctica is accelerating in regions of rapid ice shelf melt . Standalone ice sheet models project that this mass loss will continue to accelerate in the future, with the resulting freshwater input to the Southern Ocean becoming a primary contributor to global sea level rise in coming decades and centuries . This freshwater input from melting of the grounded ice sheet and the fringing floating ice shelves is expected to have significant impacts that feedback onto the global climate system and influence the trajectory of global climate change . However, interactive ice sheets and shelves have generally not been included in coupled climate model simulations, including those used in the latest generation of the Coupled Model Intercomparison Project CMIP6;. Thus, any feedbacks between ice sheets, ice shelves, and the global climate system are unaccounted for in CMIP6. This lack of inclusion of ice–climate feedbacks in CMIP coupled climate simulations represents a major source of uncertainty in future climate projections .

Previous studies have attempted to quantify the impacts of Antarctic meltwater on the global climate system through the use of idealized freshwater perturbation experiments in which additional freshwater is imposed in a coupled climate model or ocean–sea ice simulation (Table ). However, these previous studies have used widely varying experimental designs, including differing magnitudes and spatiotemporal distributions of freshwater forcing, and differing methods to impose freshwater and heat fluxes associated with the melting ice. These studies have also been conducted using various model configurations including intermediate-complexity models, CMIP-class coupled atmosphere–ocean models with varying horizontal resolutions (typically 1${}^{\circ }$), and finer-resolution ocean–sea ice simulations ($<\mathrm{0.25}$${}^{\circ }$). The results have revealed some model responses that appear to be qualitatively robust to additional freshening in the Southern Ocean, such as cooling of Southern Hemisphere sea surface and surface air temperatures, Antarctic sea ice expansion, accumulation of oceanic heat at depth, and a reduction in Antarctic Bottom Water (AABW) formation. However, these studies often disagree on the magnitude of the response and in some cases have reached opposing conclusions, for example regarding subsurface thermal changes on the continental shelf and the magnitude of the meltwater impact on historical sea ice trends e.g..

Table 1

Survey of recent studies inserting freshwater forcing into coupled or ocean-only models. Model refers to atmosphere–ocean coupled (C), intermediate-complexity (I), or ocean-only (O) models. Function is the freshwater forcing function with time, either constant (C), linear (L), exponential (E), or variable (V). Depth is the depth of freshwater input being at the surface (S; $<\mathrm{50}$ m), with a uniform distribution (U) or a realistic distribution (R), and the maximum freshwater input applied in the study is given in both Gt yr${}^{-\mathrm{1}}$ and Sv. Where values were not clear, they were left blank. The list of studies in this table is not exhaustive but covers the range of forcing used in previous work. The value marked with an asterisk (*) was derived from the literature, and the other value was computed using 1 Sv $=$ $\mathrm{3.154}\times {\mathrm{10}}^{\mathrm{4}}$ Gt yr${}^{-\mathrm{1}}$, and all are reported to two places to facilitate comparison.

Study	Model	Function	Depth	Max input	Max input
			m	$\times {\mathrm{10}}^{\mathrm{3}}$ Gt yr${}^{-\mathrm{1}}$	Sv
	C	E	S	9.46 to 255.47	0.30 to 8.10*
	C	V	S	25.23, 78.85	0.80, 2.50*
	C	C	S	31.54	1.00*
	C	C	S	31.54	1.00*
	C	V	S	18.92	0.60*
	C	E	R	17.71*	0.56
	C	L	S	4.81 to 16.65	0.15 to 0.53
	C	V	S	5.05*	0.16
	C	E	S	5.05*	0.16
	C	C	U	0.50, 2.0, 5.0*	0.02, 0.06, 0.16
	C	C	S	2.18 to 6.59	0.07 to 0.21*
	C	L	R	4.10*	0.13
	C	V	R	4.02	0.13
	C	C	S	3.15	0.10*
	C	C	S	3.15	0.10*
	C	C	S	1.58, 3.15	0.05, 0.10*
	C	C	U	0.74*	0.02
	C	C	S	0.25*	0.01
	C	C	R	0.17 to 3.00*	0.01 to 0.10
	C	C	S	0.01 to 0.12*	$<\mathrm{0.01}$
	I	C	S	3.15 to 63.08	0.1 to 2.00*
	I	L	S	31.54	1*
	I	C	S	0.13, 12.62	$<$0.01, 0.40*
	I	C, L	S	5.68, 11.04	0.18, 0.35*
	I	L	S	0.09 to 0.95	$<$0.01 to 0.03*
	O	E	S	3.15	1.00
	O	C	S	1.32, 5.05	0.04, 0.16*
	O	L	S	2.52	0.08*
	O	C	R	0.28*	$<$0.01
	O	C	S	0.38 to 1.89	0.01 to 0.06*
	O	C	U	0.84	0.03*

The inconsistency in experimental design across previous studies inhibits our ability to constrain the climate impacts of Antarctic mass loss and the uncertainties associated with not accounting for this forcing in climate projections. Since virtually all existing Southern Ocean hosing experiments have each used only a single model, the role of model uncertainty in response to freshwater is unknown. Understanding the climate system feedbacks to meltwater is important context as coupled climate models evolve to include more comprehensive representations of ice sheet–ocean interactions e.g.. Understanding the future evolution of the real climate system and its impact on society requires better quantification of the important feedbacks associated with meltwater-derived freshwater input to the ocean e.g.. A large body of ice sheet modelling literature exists that explores the response and feedbacks of ice sheet dynamics to changing climate, such as the Ice Sheet Model Intercomparison Project or the Marine Ice Sheet–Ocean Model Intercomparison Project . However, there has not yet been a comprehensive effort to assess the response in other components of the climate system to ice sheet driven freshwater input from Antarctica (i.e. ocean, sea ice, and atmospheric changes) and particularly the role of model uncertainty in that response.

The SOFIA initiative aims to advance our understanding of the climate response to Antarctic freshwater input through coordinating a model intercomparison and by facilitating open and collaborative research. This effort builds off of established model intercomparison projects (MIPs), including the Flux-Anomaly-Forced Model Intercomparison Project , that are designed to document the climate system response to specific forcings across an ensemble of models. Here, we summarize the state of knowledge on meltwater discharge from the Antarctic ice sheet and ice shelves to the Southern Ocean, explain the key scientific objectives of our initiative, and describe the design of a coordinated set of experiments that allows the consistent quantification of the impact of Antarctic meltwater on climate simulations across multiple models and some key uncertainties.

2 Mass balance of Antarctic ice sheet and ice shelves

This section provides an overview of ice mass balance in the observations and in coupled models, as well as projections of future changes in mass balance. The goal of this section is to provide context for scientific objectives and experiments proposed by SOFIA in the following sections.

2.1 The observed mass balance

provide a detailed explanation of the Antarctic ice mass budget as it relates to freshwater forcing supplied to the ocean, which we briefly summarize here. The total budget comprises two components: the first is for the grounded ice mass ($M$) and the second for the floating ice shelves ($m$). Only the grounded ice is relevant to sea level rise. In steady state, the total grounded ice mass budget represents a balance between surface mass transports (${\dot{M}}_{\mathrm{SM}}$) and mass transports across the grounding line (${\dot{M}}_{\mathrm{GL}}$) meaning that the general mass imbalance is as follows (${\dot{M}}_{\mathrm{imb}}$ would equal zero; Fig. a):

1$${\dot{M}}_{\mathrm{SM}}+{\dot{M}}_{\mathrm{GL}}={\dot{M}}_{\mathrm{imb}},$$ where positive tendencies lead to mass gain for the ice sheet. Runoff is considered a result of the local surface mass balance and thus already lost to the ice sheet mass. In a changing climate, the grounded mass can be altered via changes in the surface mass balance or via changes in transport across the grounding line. Observations suggest that the grounded ice sheet has lost a total of $\mathrm{2720}\pm \mathrm{1390}$ Gt between 1992 and 2017 . This mass loss from the grounded ice sheet is rapidly accelerating, increasing from $\mathrm{49}\pm \mathrm{67}$ Gt yr${}^{-\mathrm{1}}$ over 1992 to 1997 to $\mathrm{219}\pm \mathrm{43}$ Gt yr${}^{-\mathrm{1}}$ over 2012 to 2017 .

Figure 1

A schematic showing the key components of the Antarctic ice mass budget in (a) the real world and (b) the representation of the budget in typical CMIP6-class coupled climate models. In reality, the total ice mass consists of grounded ice ($M$) and floating ice shelves ($m$). Mass change over time is noted as $\dot{M}$ or $\dot{m}$ and considered positive for mass gain. Red arrows indicate transport directions associated with a negative sign in the respective mass budget. In contrast, most models only consider a snow–water equivalent layer of limited mass $M_{\mathrm{swe}}$ for surface mass balance and runoff calculations. Some models distinguish between liquid and solid runoff (snow), albeit with the latter often denoted as discharge. After , their Fig. 1.

[Figure omitted. See PDF]

The second component of the mass budget is associated with floating ice shelves (Fig. a). The ice shelves receive mass from the grounded ice via transport across the grounding line (${\dot{M}}_{\mathrm{GL}}$), exchange mass with the atmosphere via their surface (${\dot{m}}_{\mathrm{SM}}$), and lose mass via basal melt (${\dot{m}}_{\mathrm{BM}}$) and calving of icebergs (${\dot{m}}_{\mathrm{C}}$). 2$${\dot{m}}_{\mathrm{SM}}+{\dot{m}}_{\mathrm{BM}}+{\dot{m}}_{\mathrm{C}}-{\dot{M}}_{\mathrm{GL}}={\dot{m}}_{\mathrm{imb}}$$ Here, the grounding line transport is considered negative in the predominant case of ice sheet mass loss and ice shelf mass gain. Climatologically, calving and basal melt are roughly equivalent in magnitude . It is important to note that while changes in the mass balance of floating ice shelves do not affect sea level rise directly, they do affect the liquid freshwater input to the Southern Ocean and thus ocean circulation and climate. Furthermore, through their mechanical coupling to the grounded ice (buttressing), ice shelf thinning is believed to accelerate the mass transport across the grounding line . Observational studies show that overall the Antarctic ice shelves have been losing mass since the early 1990s when suitable satellite observations began . found mass loss due to ice shelf thinning by basal melt was small between 1994 and 2003 but increased to $\mathrm{288}\pm \mathrm{69}$ Gt yr${}^{-\mathrm{1}}$ ($\sim \mathrm{0.009}$ Sv) between 2003 and 2012. More recent satellite data revealed that mass loss from the ice shelves due to basal melt slowed down in the 2010s relative to the previous decade and that the excess meltwater transport over the longer period 1994 to 2018 was about $\mathrm{161}\pm \mathrm{147}$ Gt yr${}^{-\mathrm{1}}$ ($\sim \mathrm{0.005}$ Sv) . Net mass loss due to calving has increased in recent decades, reaching $\mathrm{250}\pm \mathrm{68}$ Gt yr${}^{-\mathrm{1}}$ in the 2010s .

To estimate the additional freshwater input to the Southern Ocean, the net mass loss from grounded ice and floating ice shelves has to be added. For the decade of the 2010s, give a total mass loss rate of $\mathrm{509}\pm \mathrm{186}$ Gt yr${}^{-\mathrm{1}}$ ($\mathrm{0.017}\pm \mathrm{0.006}$ Sv; see Fig. b). Summing the grounded and floating ice shelf numbers of and provides a comparable estimate. This additional freshwater transport entering the Southern Ocean over recent decades can be regarded as the transport that is unaccounted for by CMIP6 models, assuming approximate mass balance before this time see below. We use these numbers to inform the freshwater input in our historical experiments described in Sect. . Note that the time at which the net ice mass balance left its presumable pre-industrial steady state and mass loss began is not precisely known. In addition, the influence of long-term natural variability in the observed estimates is also not known, but it likely contributes to, for example, differences in reported ice shelf thinning . From trends in available observations and the rate of known anthropogenic warming in the climate system, we infer that forced net mass loss around Antarctica before 1970 was likely negligible.

2.2 Antarctic meltwater discharge in coupled climate models

Coupled climate models represent many significant sources of freshwater forcing to the Southern Ocean, including that from net precipitation (precipitation–evaporation; $P$-$E$), surface runoff ($R$), and in some configurations iceberg calving (typically with a fixed, prescribed calving flux). Some models distinguish between liquid and solid (snow) runoff where the latter could serve as input mass transport to an interactive iceberg module . There is also freshwater redistribution via sea ice formation, transport and melt, with dynamic–thermodynamic interactive sea ice components being state-of-the-art examples in such models. In a limited number of dedicated studies, interactive ice sheet components fully coupled to atmosphere–ocean climate models have been applied for Greenland e.g. and Antarctica e.g.. However, due to their large computational expense, long timescales, and sensitivity to background climate, fully interactive ice sheet and ice shelf components, or even ice shelf cavities for the surrounding ocean, have generally not been included in coupled climate models, particularly those participating in CMIP6 .

In these CMIP-class coupled models, ice sheet coverage is typically prescribed as fixed, with any imbalances in surface mass balance carried to the ocean via runoff, although the exact details vary see Fig. b; e.g.. This runoff implicitly represents the calving and basal melt transport, which balances the accumulation of ice mass over land resulting from positive net precipitation (some models have explicit calving instead of pure runoff). The instantaneous runoff may respond to future changes in surface mass balance on timescales very different from those of the real ice sheet. In fact, liquid runoff from the Antarctic ice sheet is insignificant (due to low atmospheric temperatures year-round), while most of the snow that is deposited will remain on the continent for centuries or even millennia and become part of the glaciological cycle, before being discharged at the coast. Interactions between the Antarctic ice sheet and the ocean and dynamical ice sheet changes remain unaccounted for despite these processes being the primary drivers of Antarctic mass loss in the real world . For example, increasing basal melt and acceleration of mass transport across the grounding line are not represented in CMIP6 models. Owing to their highly simplified ice sheet physics, CMIP6 class climate models are thus missing an important feedback associated with the growing source of meltwater input into the Southern Ocean. The SOFIA project aims to systematically test the climate effect of including this missing freshwater forcing using the coordinated experiments described in Sect.  below.

2.3 Projected changes in future ice sheet mass

Integrating ice sheet models directly into coupled climate simulations is challenging; hence, the primary approach to date has been to take ocean and atmospheric climate fields from climate models and using these to force stand-alone ice sheet models to produce future projections of ice mass , in some cases allowing for an offline single-step coupling back to the ocean to explore feedback between the ice sheet and the climate system or in some very recent studies using full inline coupling between the ice sheet and climate models .

The magnitude of future mass loss projected by ice sheet models is highly uncertain, due to both uncertainties in the input climate scenarios and potential dynamic instabilities in the ice sheet response to this forcing . The latter notably arises from major uncertainties relating to marine ice sheet and ice cliff instability . As a result, a large range of excess freshwater input rates have been used in previous coupled modelling studies (Table ). As increasing Antarctic meltwater enters the Southern Ocean, its potential to feedback onto the global climate system is a compounding uncertainty . There are some emerging coupled modelling systems that include key ice sheet processes e.g., but these are not yet widely employed. The approach we take in Appendix  is to obtain future freshwater forcing from an ensemble of ice sheet models run under two different scenarios spanning the broad uncertainty range in future climate forcing and applying this forcing to coupled climate or ocean/sea-ice models.

3 Scientific objectives

This section describes the key scientific objectives of SOFIA and links these objectives to the experiments proposed in Appendix .

3.1 The climate response to freshwater forcing

A major objective of SOFIA is to quantify the pattern and magnitude of the climate system response to freshwater input associated with melt of the Antarctic ice sheet (see Fig. ). Previous studies have shown that freshwater input affects ocean stratification and the thermohaline structure; large-scale ocean circulation, including the Antarctic Circumpolar Current (ACC) and the Atlantic Meridional Overturning Circulation (AMOC); and circulation regimes along the Antarctic continental shelves . A key area of scientific interest is the impact of meltwater on sea ice extent and trends, which is an area of particular disagreement in previous literature . Furthermore, feedbacks have been hypothesized, where increased meltwater input further enhances on-shore ocean heat transport through different processes in different regions and with impacts on the ice sheet mass loss . Some of these feedbacks have been assessed more carefully in regional or process-oriented contexts, while other studies delineate larger-scale effects . However, a systematic assessment of the response of on-shore heat transport to increased freshwater input from Antarctica across state-of-the-art climate models is still lacking, and is subject to resolution and other uncertainties in the models.

Responses to meltwater input are not confined to the Southern Ocean but are also known to impact, for example, global surface air temperature . Indeed, meltwater addition can reduce the climate sensitivity, making it a key process to include in future climate projections . Beyond temperatures, meltwater addition can influence precipitation, both regionally and remotely through shifts in the Intertropical Convergence Zone (ITCZ) . Teleconnections between freshwater-induced Southern Ocean change and remote parts of the climate system are of key interest and can be formed through both oceanic and atmospheric pathways . We also note that while the SOFIA experiments and models are not designed to quantify total eustatic sea-level rise, the meltwater impact on the steric sea level component could be assessed. Southern Ocean freshwater input will also likely have an influence on biological production, ocean carbon uptake, and ocean acidification in this key region that connects the atmosphere to the deep ocean .

Figure 2

A schematic showing the key impacts of Antarctic ice sheet meltwater forcing on the climate system. Relevant changes in ocean circulation are highlighted, including changes in the Antarctic Slope Current (ASC), Antarctic Coastal Current (AcOc), Antarctic Circumpolar Current (ACC), Dense Shelf Water (DSW), and Antarctic Bottom Water (AABW) formation.

[Figure omitted. See PDF]

The model experiments described in Appendix  are intended to enable quantification of these key impacts of Antarctic meltwater on the climate system. We have structured the experimental design as follows. The idealized tier 1 antwater experiment adds 0.1 Sv of meltwater at the surface evenly around Antarctica and is intended to quantify the basic climate response to meltwater forcing alone. The meltwater impact in the antwater experiment can be derived by comparison with each model's piControl simulation. The tier 2 experiments are designed to test plausible historical and future rates of meltwater input in combination with other climate forcing, such as increasing greenhouse gas concentrations, again using idealized horizontal distributions. We have selected to use plausible rates of meltwater and other climate forcing (as opposed to idealized forcing), as we aim to understand how existing historical simulations and future projections from these coupled models are influenced by the inclusion of meltwater. These tier 2 experiments will be compared with each other and also used in reference to each model's historical or scenario simulations without meltwater. Tier 3 experiments test the sensitivity of the climate response to the distribution of meltwater input and the associated latent heat of melt. Central to the SOFIA effort is improved quantification of key uncertainties in the climate response to Antarctic meltwater forcing, which we expand on more below following the uncertainty breakdown of .

3.2 Quantifying uncertainty

3.2.1 Model uncertainty

Since virtually all existing Southern Ocean hosing experiments have used only one model each, the role of model uncertainty in response to freshwater is unknown. Running the coordinated suite of simulations proposed by SOFIA across a diversity of models will allow us to address how the response to Southern Ocean freshwater release depends on differing model physics and numerics. The models that have completed the tier 1 experiment at the time of writing are listed in Table . We invite additional models to participate, and indeed the intention of this paper is to formalize the experiments to encourage broad and diverse participation.

The models participating so far have differing horizontal and vertical resolutions, ocean vertical coordinates, parameterization schemes to represent sub-grid-scale processes, numerics, and underlying mean state model biases. Of particular relevance is whether models exhibit deep open-ocean convection or not . Other relevant processes that may impact a model's response to Antarctic meltwater include the underlying thermal state and stratification of the Southern Ocean and the mechanisms of dense water formation, such as whether Antarctic Bottom Water (AABW) is formed realistically as Dense Shelf Water (DSW) or though open-ocean convection . Sampling across a range of models that have different representations of such processes will enable quantification of differing responses to Antarctic meltwater due to model uncertainty.

Table 2

Models that have submitted data for the SOFIA antwater experiment at the time of writing. Resolution refers to the nominal horizontal resolution of the model component. A contact person for the simulations and model reference paper are also provided.

Type	Model	Resolution	Contact	Reference
		(ocn/atm, lat $\times$ long, ${}^{\circ }$)
Coupled	ACCESS-ESM1-5	1/$\mathrm{1.875}\times \mathrm{1.25}$	Ariaan Purich
	AWI-ESM-1-REcoM	1/1.8	Christopher Danek
	CanESM5	1/3	Neil Swart
	CESM2	1/$\mathrm{0.9}\times \mathrm{1.25}$	Andrew Pauling
	EC-Earth3	1/1	André Jüling
	FOCI	0.5/1.9	Torge Martin
	GFDL-CM4	0.25/1	Stephen Griffies
	GFDL-ESM4	0.50/1	Stephen Griffies
	GISS-E2-1-G	$\mathrm{1}\times \mathrm{1.25}$/$\mathrm{2}\times \mathrm{2.5}$	Qian Li
	HadGEM3-GC3.1-LL	1/1	Max Thomas
	NorESM2-MM	1/1	Tore Hattermann
Ocean	MOM5	1	Riccardo Farneti

3.2.2 Internal variability

Internal climate variability is significant in the Southern Ocean and has the potential to influence the climate system response to Antarctic melt . To quantify the impact of internal variability on the forced response, the experimental design proposed by SOFIA encourages the production of multiple ensemble members. Of particular note are the large, multi-decadal- to centennial-scale oscillations in Southern Ocean properties known to exist in many CMIP-class climate models due to open-ocean deep convective events . We aim to enable an understanding of how the magnitude and patterns of the forced response depend on the phase of these internal oscillations, with more detailed description for generating the ensemble members given in Appendix 3.

3.2.3 Forcing uncertainty

Section  described the uncertainties in both historical and future rates of Antarctic meltwater forcing. In the experimental design described below (Appendix ), we include multiple experiments over the historical period and aim to capture the uncertainty represented in the observational estimate. Similarly, for future projections, we use two scenarios – one with large increases in anthropogenic forcing and meltwater and another with smaller changes to broadly bracket possible future combinations of forcing. There are also uncertainties in both the horizontal and vertical distribution of freshwater input to the ocean, as discussed, for example, in . We include multiple tier 3 experiments, which test the sensitivity to different vertical and horizontal distributions of freshwater forcing in an idealized way. Whether the latent heat required to melt the ice resulting in freshwater input is extracted from the ocean or not is a further uncertainty , and we include tier 3 experiments to test this sensitivity. Finally, because there might be interactions between freshwater forcing and other climate forcings such as greenhouse gases, we aim to test the impact of freshwater forcing both alone (e.g. under piControl conditions) and in combination with other forcings (e.g. under historical and Shared Socioeconomic Pathways (SSP) conditions). We note that our experiments do not comprehensively test all the uncertainties in the meltwater forcing, but they are designed to span the largest known uncertainties at leading order.

4 Interpreting SOFIA results

Our experiments are best interpreted as tests of the impact of adding meltwater into coupled atmosphere-ocean or ocean only models, and for understanding how excluding this meltwater has influenced existing climate change projections, such as those from CMIP6. When interpreting results from SOFIA, and in particular the tier 2 historical and future scenario simulations, users should bear in mind the idealized nature of the horizontal and vertical distributions of meltwater input and the absence of latent heat of melt associated with this water. While the tier 2 experiments aim to use realistic meltwater inputs, there are large uncertainties in these historical and future meltwater input rates. We encourage users to make use of the various tier 2 and tier 3 experiments that have different magnitudes and distributions of forcing, and the inclusion or not of latent heat of melt, in order to understand the sensitivity of their results to these choices.

Beyond the simplifications in the SOFIA forcing protocol, users of the data should also remain aware of the limitations of the models used to run the experiments. For example, many of the models participating in SOFIA so far are CMIP6-class coupled climate models, that do not directly resolve mesoscale and submesoscale dynamics, the continental slope current, Dense Shelf Water overflows, etc. Nonetheless, such coupled models remain the best available tools for understanding future climate change, including the impact of meltwater that we examine here. Higher-resolution models (particularly ocean-only models) that participate in the future may better resolve these dynamics. Despite the simplification in the meltwater forcing protocol and the limitations of the models, we believe that the SOFIA results can be used to help inform the next generation of Earth system models, as well as helping us to understand the possible impact of meltwater on the real climate system.

5 Ongoing work and activities

The immediate goal of SOFIA is to encourage the participation of a wide and diverse group of models in the experiments described here. The larger and more diverse the participating ensemble, the more robust our quantification of the climate response to freshwater forcing and its uncertainty will be. The initial group of participating models is starting to archive data for the antwater experiment. SOFIA also advances research by facilitating collaboration across an international team of researchers through regular meetings and online communications portals (see https://sofiamip.github.io/, last access: 11 December 2023). A series of analysis papers are being prepared, one on the general climate response to freshwater forcing, and several papers focused on particularly noteworthy aspects of the response, including the effect on deep convection and bottom water formation and Southern Ocean circulation. We anticipate that results from the historical experiments will allow us to study important questions surrounding detection and attribution of climate changes to freshwater forcing, such as for Antarctic sea ice. Through analysis of the SOFIA future scenario runs with freshwater forcing, we aim to quantify the impact of this missing climate feedback in the CMIP6 model projections. Moreover, we aim to provide information for modelling centres trying to determine the relative importance of including ice–ocean interactions in future generations of coupled climate models, such as those being prepared for CMIP7. We invite the broader community to propose additional studies and to make use of the SOFIA data archive (Appendix ) to advance our collective understanding of the role of Antarctic meltwater on the climate system.

Appendix A Experimental design

A1 Overall philosophy

The experimental suite designed by SOFIA builds off the CMIP6 framework for organizing our experiments and data request . A tiered hierarchy of experiments is proposed to allow basic quantification of meltwater impacts in idealized and more realistic settings (Table ). The idealized experiments provide a low barrier to entry for participants, whereas higher-tier experiments explore more realistic scenarios and sensitivities. In the following sections we provide details on the model setup and realizations, the details of each experiment, and the data request.

Table A1

SOFIA experiment name, branch year from the standard CMIP6 run, the amount or increasing rate of freshwater (FW) forcing starting from the branch year, simulation year, and other external forcing. For all experiments, besides where explicitly noted, the freshwater is added in the circumpolar adjacent distribution.

Name	FW perturbation	Branch year	Time span	Other forcing
	(Sv)		(year)
Tier 1
piControl	None	N/A	$\ge \mathrm{100}$	Fixed pre-industrial
antwater	Fixed 0.1	Model year	$\ge \mathrm{100}$	Fixed pre-industrial
Tier 2
hist-antwater-70-01	Increasing by 0.1 ($\times {\mathrm{10}}^{-\mathrm{3}}$ Sv yr${}^{-\mathrm{1}}$)	1970	1970–2020	Historical
hist-antwater-70-03	Increasing by 0.3 ($\times {\mathrm{10}}^{-\mathrm{3}}$ Sv yr${}^{-\mathrm{1}}$)	1970	1970–2020	Historical
hist-antwater-70-05	Increasing by 0.5 ($\times {\mathrm{10}}^{-\mathrm{3}}$ Sv yr${}^{-\mathrm{1}}$)	1970	1970–2020	Historical
hist-antwater-92-11	Increasing by 1.1 ($\times {\mathrm{10}}^{-\mathrm{3}}$ Sv yr${}^{-\mathrm{1}}$)	1992	1992–2020	Historical
ssp126-ismip6-water	Fixed 0.015	2015	2015–2100	SSP126 scenario
ssp585-ismip6-water	Increasing nonlinearly; maximum 0.196	2015	2015–2100	SSP585 scenario
Tier 3
antwater-60S	Fixed 0.1${}^{\mathrm{a}}$	Model year	$\ge \mathrm{100}$	Fixed pre-industrial
antwater-lh	Fixed 0.1${}^{\mathrm{b}}$	Model year	$\ge \mathrm{100}$	Fixed pre-industrial
antwater-ambe	Fixed 0.1${}^{\mathrm{c}}$	Model year	$\ge \mathrm{100}$	Fixed pre-industrial
antwater-depth	Fixed 0.1${}^{\mathrm{d}}$	Model year	$\ge \mathrm{100}$	Fixed pre-industrial
antwater-depth-lh	Fixed 0.1${}^{\mathrm{b},\mathrm{d}}$	Model year	$\ge \mathrm{100}$	Fixed pre-industrial
antwater-ambe-depth-lh	Fixed 0.1${}^{\mathrm{b},\mathrm{c},\mathrm{d}}$	Model year	$\ge \mathrm{100}$	Fixed pre-industrial

${}^{\mathrm{a}}$ Freshwater added south of 60${}^{\circ }$ S. ${}^{\mathrm{b}}$ Ocean cooling imposed to extract latent heat required to melt equivalent freshwater. ${}^{\mathrm{c}}$ Freshwater added exclusively to the Amundsen and Bellingshausen seas (210 to 290${}^{\circ }$ E). ${}^{\mathrm{d}}$ Freshwater added uniformly from the surface to the continental shelf base.

A2 Model configurations and forcings

SOFIA welcomes contributions from fully coupled and ocean–sea ice models. Many of our objectives (Sect. ) relate to the broader climate system and require coupled atmosphere–ocean models to fully address. However, additional information relating to the ocean response may also be gained by examining the response of forced ocean–sea ice models, as done in the CMIP6 OMIP exercise . Models that already include interactive representations of ocean–ice shelf interactions should not be used for SOFIA experiments, as they already include the freshwater forcing that we represent with our protocol.

In all cases, we encourage groups to use well-known and documented versions of their models. In particular, for models that participated in CMIP6, we suggest using the same configuration as used in CMIP6 for SOFIA. The same model configuration should be used for all SOFIA experiments labelled with the same name, with only the forcing changing between experiments (if multiple physical variants are submitted, they should be clearly labelled). The SOFIA experiments build on the protocols for the CMIP6 DECK and ScenarioMIP experiments . Besides the specified freshwater flux anomalies, all forcing prescriptions follow the relevant CMIP6 design.

A2.1 Distribution of freshwater anomalies

In the experiments below, three spatial (horizontal) distributions are defined for the implementation of freshwater anomalies. By default, in all tier 1 and tier 2 cases, the freshwater anomaly is applied at the ocean surface, which is equivalent to an adjustment in $E$-$P$-$R$. The Antarctic-adjacent distribution applies the freshwater anomaly directly around the Antarctic coastline (Fig. a). For simplicity, the anomalies are by default applied uniformly in the model grid cell immediately adjacent to the Antarctic coast. This means that models with different horizontal resolutions will spread the anomalies over different areas, but the area-integrated anomalies will be the same across models. Models may choose, at their discretion, to distribute the anomalies over a slightly broader area immediately adjacent to the Antarctic coast. However, we recommend all anomalies are constrained within 100 km of the coastline as far as practically possible.

In reality, some meltwater is distributed northward by iceberg transport, and over the observational period most Antarctic mass loss has occurred in the Amundsen region and at depth . To examine the impact of the idealized horizontal distribution of freshwater (Antarctic adjacent) and the surface distribution of freshwater anomalies in tier 1 and 2 experiments, additional distributions of freshwater anomalies are proposed in tier 3 experiments. Specifically, we propose a combination of experiments applying freshwater in the grid cells adjacent to the coast in the Amundsen and Bellingshausen seas only, applying vertically distributed freshwater anomalies, and distributing freshwater input uniformly south of 60${}^{\circ }$ S (see tier 3 below for details).

A3 Initial conditions and ensemble members

For all experiments, participants are encouraged to run as many ensemble members as they can afford to help quantify internal variability. We identify between 3 and 10 members per model and experiment as likely optimal. For SOFIA experiments that start from the piControl (Table ), the recommended method for spawning ensemble members is to launch the SOFIA experiments from restarts of substantially different years in the control simulation. Using this macro-initialization approach allows for sampling over decadal or longer timescale ocean variability. Micro-initialization approaches, which typically add round-off-level perturbations to model fields, cannot properly sample over such ocean variability and thus are discouraged. We leave it to each participating model to decide the strategy and restart time spacing to optimally sample variability in their model, factoring in the timescales of the dominant modes of decadal climate variability.

We also invite participating models to submit variants with alternative process representation of their models, using different parameters or parameter tunings, which might reveal different but plausible responses to freshwater input. When using different variants with different model physics, participants need to clearly identify this as a different model configuration in their output. In the CMIP6 naming convention, this is typically done using either a different “source_id” or a different “p” number in the model variant label.

A4 Experiments

Beyond the freshwater forcing, the experimental design below provides details of the forcing to be used in coupled models. Ocean/sea-ice modellers may apply the SOFIA freshwater perturbations in their own forcing frameworks, however, we recommend the CMIP6 OMIP-1 or OMIP-2 experiment and protocol as a logical common choice for other forcing fields (see Appendix ).

A4.1 piControl

The piControl simulation provides the model baseline state against which the Antarctic freshwater forcing simulations will be compared. For coupled models, the SOFIA piControl experiment is equivalent to the CMIP6 piControl experiment. For models that participated in CMIP6, the published piControl may be used. If a model has changed its configuration since CMIP6 or did not participate in CMIP6, then it should run a simulation conforming to the CMIP6 piControl experimental design for at least 100 years and preferably 500 or more years.

A4.2 antwater

The aim of the idealized antwater experiment is to assess the climate response to an applied Antarctic freshwater forcing anomaly in the participating models. The antwater experiment is branched off the piControl simulation, with all other forcings the same as in piControl. On top of this, a freshwater flux anomaly is applied at the ocean surface in the Antarctic-adjacent distribution, which when area integrated represents a constant freshwater transport of 0.1 Sv (1 Sv $=$ $\mathrm{3.15}\times {\mathrm{10}}^{\mathrm{4}}$ Gt yr${}^{-\mathrm{1}}$). The simulation is run for a minimum of 100 years. The SOFIA antwater experiment is closely related to the CMIP6 FAFMIP experiment faf-antwater-stress . The only difference in SOFIA antwater relative to faf-antwater-stress is that no wind stress anomaly is applied. We note that the perturbation applied in antwater is substantially larger then current observational estimates and the SOFIA historical experiments (Sect. ). However, the magnitude of freshwater forcing in antwater is used to produce a clear signal for the purposes of comparing model responses, is well within the range of previous studies (Table ), and is comparable to forcing magnitudes expected in the 21st century, such as those in the SOFIA future scenario experiments (Sect. ; Fig. c).

Figure A1

SOFIA forcing. (a) The horizontal distribution of freshwater inputs and (b) rate of freshwater input in historical experiments and (c) in future scenario experiments. In (c), the idealized fits to the forcing described in the text are shown as dashed lines, and the rates of input in historical experiments in 2014 are shown by crosses. The lighter red lines show the basal melt rate simulated by individual ISMIP6 models multiplied by $\mathrm{1}/\mathrm{0.55}$ to account for calving. In (b) the central black dots and error bars represent the summed ice shelf plus Antarctic grounded ice loss estimates from . In (b) and (c) we show both units of Gt yr${}^{-\mathrm{1}}$ (with lines computed using the equations in the text) and Sv using the conversion 1 Sv $=$ $\mathrm{3.154}\times {\mathrm{10}}^{\mathrm{4}}$ Gt yr${}^{-\mathrm{1}}$.

[Figure omitted. See PDF]

A4.3 Historical experiments

The aim of the SOFIA hist-antwater simulations is to assess the impact of plausible rates of historical Antarctic freshwater input, in conjunction with and relative to other realistically evolving climate forcings. The hist-antwater experiments are branched off an existing CMIP6 or CMIP6-like historical experiment in the year 1970 or 1992, and run to 2020. A regular historical experiment (without additional freshwater), conforming to the CMIP6 standard, is the reference against which this is to be compared and should be submitted by models that did not publish historical experiment data for CMIP6. We intentionally keep the simulations short to make the experiment more computationally affordable. Two different start dates are used because the exact point at which Antarctic mass loss began is not precisely known, although it was likely weak prior to 1970 and is only observationally constrained since the early 1990s (Sect. ). All forcings and protocols from the CMIP6 historical experiment apply from January 1970 to December 2014, and from January 2015 to December 2020 the ssp585 forcings are used. Since all forcing scenarios are very similar over 2015 to 2020, which scenario is used is arbitrary, and such extensions are commonly used e.g.. Extending the historical experiments to 2020 will allow for a more comprehensive comparison with observations and will provide overlap with the future scenario runs. Models without existing historical simulations can branch off the control experiment in 1850 and run under CMIP6 historical forcings. For ocean and sea ice simulations, participating models can use the JRA55-do surface forcing dataset from 1958 to 2020 following the OMIP-2 framework .

Four separate historical experiments with additional meltwater forcing are proposed to span the uncertainty range in historical freshwater input (Fig. b). In each experiment, additional freshwater input before the branch date is zero. From the branch date onwards, a freshwater transport anomaly is applied over the Antarctic-adjacent distribution, with a linearly increasing rate, according to Table . The linear rates of increase in Table  are given in Sv yr${}^{-\mathrm{1}}$, and the intention is that the input would increase linearly over the course of the year, starting on 1 January of the branch year and increasing by the annual increment by 31 December. How exactly modelling centres implement the increase (e.g. as monthly means or at the time step level) could slightly influence the amount of input, but this method-based variance is small compared to the annual amount of freshwater being added. The span of freshwater input magnitudes across the experiments will allow us to quantify how uncertainty in historical rates of ice sheet melt affect the climate response.

In these experiments, the cumulative freshwater input ranges from 4101 Gt in the hist-antwater-70-01 experiment to 20 506 Gt in the hist-antwater-70-05 experiment. In the hist-antwater-92-11 experiment, the cumulative input amounts to 14 587 Gt, and the average transport is 0.0165 Sv (521 Gt yr${}^{-\mathrm{1}}$). Both measures in this experiment agree closely with the current best estimate of the observed combined changes in the grounded ice sheet and the floating ice shelves (Sect. ). The maximum input of about 0.03 Sv by the end of the historical experiment is at the lower end of the maximum input applied in previous modelling experiments (Table ).

A4.4 Future scenarios

The aim of the SOFIA future scenario simulations is to assess the impact of possible rates of future Antarctic freshwater input in conjunction with and relative to other evolving climate forcings. As climate forcings, we use one low-end (SSP126) and one high-end (SSP585) emission scenario from CMIP6 ScenarioMIP . To these we add freshwater forcing, which is derived from the basal melt rates generated by offline ice sheet models participating in the Ice Sheet Model Intercomparison for CMIP6 (ISMIP6) under the equivalent CMIP5 climate forcings RCP2.6 and RCP8.5, respectively;. Basal melt rates for ISMIP6 were obtained from projected ocean temperatures and time-varying ice geometry, intended to provide boundary conditions for the ice sheet simulations to quantify the mass flux across the grounding line , which is relevant for assessing sea level contributions from Antarctica. Although iceberg calving is a by-product of many of the ISMIP6 models, its reliability was not systematically assessed, and the intercomparison does not make any statements about the partitioning of the total freshwater flux between basal melting and iceberg calving in future scenarios. Hence, to account for additional iceberg calving, we divide the ISMIP6 basal melting rate by a factor of $\mathrm{0.55}$, following the fraction of basal melt to calving given in . Our approach is similar to that applied in .

The SOFIA scenario experiments are branched off a regular CMIP6 or CMIP6-like historical experiment instead of the hist-antwater experiments. Branching from a standard historical run makes the experiments more modular – groups could run only future scenarios if they choose. Further, in the high-end warming scenario (SSP585) the freshwater forcing in the future is considerably stronger than the historical freshwater forcing, implying that starting from a zero freshwater transport anomaly in 2015 is a reasonable approximation given the scale of the future freshwater increase. Figure c shows the SOFIA scenario freshwater input rates, along with idealized fits described below.

A4.5 ssp126-ismip6-water

The ssp126-ismip6-water experiment is branched off a CMIP6 or CMIP6-like historical experiment and runs for at least 86 years from 2015 to at least 2100. In coupled models, all forcings and protocols from the CMIP6 ssp126 experiment apply. In addition to this, a freshwater transport anomaly is applied over the Antarctic-adjacent distribution at a rate which is determined from the ensemble mean basal melt rate from ISMIP6 under RCP26 forcing . This rate is then multiplied by $\mathrm{1}/\mathrm{0.55}$ to account for calving fluxes, following the basal melt to calving ratios in . For simplicity, this total forcing can be approximated by a constant input of 0.015 Sv (475 Gt yr${}^{-\mathrm{1}}$, Fig. c, dashed blue line), which approximately matches the current observed rate (Sect. ) and the rate of the historical experiments (Sect. ; crosses in Fig. c).

A4.6 ssp585-ismip6-water

The ssp585-ismip6-water experiment is branched off a CMIP6 or CMIP6-like historical experiment and runs for 86 years from 2015 to 2100. If possible, we encourage modellers to extend their simulations to 2300, as some impacts of the strong ramp-up in freshwater input in this scenario might have long timescale responses. If extending beyond 2100, all forcings, including freshwater, should be held constant at 2100 levels. In coupled models, all forcings and protocols from the CMIP6 ssp585 experiment apply. In addition to this, a freshwater transport anomaly is applied over the Antarctic-adjacent distribution at a rate which is determined from the ensemble mean basal melt rate from ismip6 under RCP85 forcing. As for ssp126-ismip6-water, this rate is then multiplied by $\mathrm{1}/\mathrm{0.55}$ to account for additional calving fluxes.

For convenience in applying the forcing in models, we have produced a generalized logistic fit for the total freshwater forcing (Fig. c, dashed red line). This fit is given by

A1$$y\left(t\right)={\displaystyle \frac{\mathrm{1}}{\mathrm{0.55}}}\left(A+{\displaystyle \frac{K-A}{(\mathrm{1}+Q\cdot e^{-Bt}{)}^{\mathrm{1}/v}}}\right),$$ where the coefficients are given in Table  and $t$ is the number of years since 2015 (with $t$ starting at 0 in 2015).

Table A2

Coefficients of the generalized logistic fit from Eq. () to the freshwater forcing to be applied in the SOFIA ssp585-ismip6-water experiment.

Coefficient	Value	Units
$A$	$\mathrm{5.18}\times {\mathrm{10}}^{\mathrm{2}}$	Gt yr${}^{-\mathrm{1}}$
$K$	$\mathrm{3.41}\times {\mathrm{10}}^{\mathrm{3}}$	Gt yr${}^{-\mathrm{1}}$
$B$	$\mathrm{0.21}$	yr${}^{-\mathrm{1}}$
$v$	$\mathrm{3.85}\times {\mathrm{10}}^{-\mathrm{5}}$
$Q$	$\mathrm{1.48}\times {\mathrm{10}}^{\mathrm{1}}$

All models undertaking the SOFIA scenario simulations should also make available standard CMIP6-conforming ssp126 and ssp585 experiments against which the SOFIA experiments can be compared (again this could be via the CMIP6 data archive for those models who participated).

A4.7 Idealized sensitivity tests

Idealized sensitivity tests are proposed as tier 3 to help with the interpretation of tier 1 and 2 data. The experiments are designed to test the consequences of four key simplifying assumptions in the tier 1 and 2 freshwater distribution: (1) coastal input, (2) surface input, (3) uniform input around the coast, and (4) input without extracting latent heat. These tier 3 experiments require additional technical work to implement and may require significant modifications to the model, particularly for depth distribution changes. Even a small subset of models submitting tier 3 runs would help us to identify the likely consequences of our simplified freshwater input protocol.

A4.8 antwater-60S

The antwater-60S experiment is identical to antwater, except for the horizontal distribution of the freshwater anomalies. In antwater-60S, the freshwater flux anomaly is applied at the ocean surface uniformly south of 60${}^{\circ }$ S, with an area-integrated constant rate of 0.1 Sv (blue area in Fig. a). Freshwater is added at the surface and latent heat is not extracted. The intention of this experiment is to test the sensitivity of the horizontal distribution of freshwater input, and in particular as a crude representation of the effect that northward distribution by icebergs might have on the climate. It will also facilitate comparison with previous studies using a broader distribution of freshwater e.g.. Subtracting antwater from antwater-60S gives the impact of confining freshwater inputs to the coast.

A4.9 antwater-lh

The antwater-lh experiment is identical to antwater, except that in addition to the freshwater anomaly applied to the ocean surface, the latent heat of melt required to melt 0.1 Sv is also extracted from the ocean surface, uniformly with the Antarctic adjacent distribution. In reality, latent heat is extracted from the ocean to induce basal melt of ice shelves and icebergs; however, this latent heat forcing is often neglected in the literature , and indeed in all the experiments described above it has been excluded for simplicity. The aim of this experiment is to quantify the additional effect of including the latent heat of melt on the climate response. We do not include the heat required to bring the ice from its ambient temperature to the freezing point, as this is generally much smaller than the latent heat of melt . Subtracting antwater from antwater-lh gives the impact of neglecting ocean cooling from latent heat extraction.

A4.10 antwater-ambe

The antwater-ambe experiment is identical to antwater, except that the entire 0.1 Sv perturbation is confined to the Amundsen and Bellingshausen seas (210 to 290${}^{\circ }$ E). Freshwater is added at the surface, and latent heat is not extracted. This experiment tests the impact of the lateral distribution of freshwater input. The Amundsen and Bellingshausen seas are a major source of freshwater in the present . Subtracting antwater from antwater-ambe tests the sensitivity of freshwater-induced anomalies to changes in lateral input distribution.

A4.11 antwater-depth

The antwater-depth experiment is identical to antwater, except that the freshwater perturbation is spread uniformly from the surface to the continental shelf base for each coastal location. Latent heat is not extracted. This experiment tests the impact of different vertical freshwater input distributions. In reality, we expect basal shelf melt to be input at depth. Subtracting antwater from antwater-depth gives the impact of confining freshwater inputs to the surface.

A4.12 antwater-depth-lh

The antwater-depth-lh experiment is identical to antwater-depth, except that the latent heat of melt requires to melt 0.1 Sv is extracted from the corresponding ocean. In reality, we expect the basal melting of ice shelves to cool the ocean at depth from latent heat extraction. Subtracting antwater-depth from antwater-depth-lh tests the sensitivity of freshwater-induced anomalies to extraction of latent heat at depth.

A4.13 antwater-ambe-depth-lh

The antwater-ambe-depth-lh provides an extreme counter-example to antwater, where the simplifying assumptions of a uniform, surface freshwater input with no latent heat extraction have all been removed. Subtracting antwater from antwater-ambe-depth-lh gives an upper limit on the impact of our simplifying assumptions.

A5 Using ocean–sea ice models

Performing forced global ocean–sea ice simulations requires the use of sea surface salinity (SSS) or water restoring. Surface restoring is not physical, and its required strength is sensitive to the model and configuration used. However, it is necessary in order to prevent long-term salinity drifts due to uncertainties in the prescribed surface forcing . When performing surface flux perturbations, such as the idealized meltwater experiments proposed in SOFIA, surface restoring would inevitably affect the perturbation-induced response in both the surface and interior of the ocean. A methodology proposed for carrying out SOFIA experiments in forced ocean–sea ice mode is detailed next, with recommendations on how to obtain stable control solutions without applying any surface restoring.

Table A3

SOFIA data request. For more details, see the OMIP data request specified in .

Category	CMIP6 name	Units	Time	Shape	CF standard name
Ocean 1D	zostoga	m	month	0	global_average_thermosteric_sea_level_change
Ocean 2D	mlotst	m	month	XY	ocean_mixed_layer_thickness_defined_by_sigma_t
	hfds	W m${}^{-\mathrm{2}}$	month	XY	surface_downward_heat_flux_in_sea_water
	wfo	kg (m${}^{\mathrm{2}}$ s)${}^{-\mathrm{1}}$	month	XY	water_flux_into_sea_water
	friver	kg (m${}^{\mathrm{2}}$ s)${}^{-\mathrm{1}}$	month	XYZ	water_flux_into_sea_water_from_rivers
	ficeberg	kg (m${}^{\mathrm{2}}$ s)${}^{-\mathrm{1}}$	month	XYZ	water_flux_into_sea_water_from_icebergs
	zos	m	month	XY	sea_surface_height_above_geoid
	msftmyz	kg s${}^{-\mathrm{1}}$	month	YZ-basin	ocean_meridional_overturning_mass_streamfunction
Ocean 3D	thetao	${}^{\circ }$C	month	XYZ	sea_water_potential_temperature
	so	1e-3	month	XYZ	sea_water_salinity
	uo	m s${}^{-\mathrm{1}}$	month	XYZ	sea_water_x_velocity
	vo	m s${}^{-\mathrm{1}}$	month	XYZ	sea_water_y_velocity
	wo	m s${}^{-\mathrm{1}}$	month	XYZ	upward_sea_water_velocity
Sea-ice 2D	siconc	%	month	XY	sea_ice_area_fraction
	sithick	m	month	XY	sea_ice_thickness
	sivol	m	month	XY	sea_ice_volume
	siu	m s${}^{-\mathrm{1}}$	month	XY	sea_ice_x_velocity
	siv	m s${}^{-\mathrm{1}}$	month	XY	sea_ice_y_velocity
	sidmassgrowthbot	kg (m${}^{\mathrm{2}}$ s)${}^{-\mathrm{1}}$	month	XY	tendency_of_sea_ice_amount_due_to_congelation_ice_accumulation
	sidmassmeltbot	kg (m${}^{\mathrm{2}}$ s)${}^{-\mathrm{1}}$	month	XY	tendency_of_sea_ice_amount_due_to_basal_melting
Atmos 2D	tas	K	month	XY	air_temperature
	pr	kg (m${}^{\mathrm{2}}$ s)${}^{-\mathrm{1}}$	month	XY	precipitation_flux
	psl	Pa	month	XY	air_pressure_at_mean_sea_level
	evspsbl	kg (m${}^{\mathrm{2}}$ s)${}^{-\mathrm{1}}$	month	XY	water_evapotranspiration_flux
	uas	m s${}^{-\mathrm{1}}$	month	XY	eastward_wind
	vas	m s${}^{-\mathrm{1}}$	month	XY	northward_wind
	clt	%	month	XY	cloud_area_fraction
Atmos 3D	ta	K	month	XY-plev19	air_temperature
	ua	m s${}^{-\mathrm{1}}$	month	XY-plev19	northward_wind
	va	m s${}^{-\mathrm{1}}$	month	XY-plev19	eastward_wind
Static-o	areacello	m${}^{\mathrm{2}}$		XY	cell_area
	thkcello	m		XYZ	cell_thickness
	volcello	m${}^{\mathrm{3}}$		XYZ	ocean_volume
	sftof	%		XY	sea_area_fraction
Static-a	areacella	m${}^{\mathrm{2}}$		XY	cell_area
	sftlf	%		XY	land_area_fraction

First, and after a sufficiently long spin-up, a multi-century-long control experiment is completed using SSS restoring. The restoring timescale is subject to the model but it is recommended to be as weak as possible. Also, no SSS restoring is applied under sea ice. Models transporting water across the ocean surface, such as MOM, add or subtract freshwater impacting the ocean volume. For this reason, a global normalization is applied at each time step at the surface so that the net water input is set to zero. We chose to force the model with the Coordinated Ocean-Ice Reference Experiment (CORE) repeating Normal Year Forcing (NYF); see , where the atmospheric dataset is used to compute idealized repeating annual cycles for heat, moisture, and momentum. An alternative approach could use the JRA55-do 1984–1985 Repeat Year Forcing RYF;. In both cases, air–sea fluxes are diagnosed through bulk formulae.

During the last 100 years of the control simulation, SSS restoring-induced surface freshwater fluxes are saved with a recommended frequency of 6 h, as daily fluxes have been proven to be not sufficient to reproduce a stable solution. Then, a twin control is performed, reproducing the last 100 years of the control simulation, but with SSS restoring deactivated and adding as salt correction the 6-hourly SSS fluxes from the restoring simulation. Hence, following the method described in , in this case no SSS restoring is applied, and only the restoring-induced fluxes are prescribed to the ocean and sea ice model. Imposing 6-hourly SSS restoring-induced fluxes results in negligible changes in globally averaged sea surface temperature (SST), SSS, and volume-average temperature and salinity. Standard metrics such as the ACC and AMOC strength present a stable behaviour during the entire length of both controls, with no significant modifications in transports.

Now that a control simulation without SSS restoring is available, serving the same purpose as a piControl experiment for coupled models (Sect. ), the idealized antwater experiment (Sect. ) can be carried out by adding to the SSS restoring-induced fluxes the SOFIA freshwater perturbations during the entire 100-year period. Given the deterministic behaviour within a forced ocean–sea ice simulation and the limited spread achieved by perturbing the initial conditions, we recommend exploring the response within the parameter space of the freshwater anomalies instead of producing an ensemble of simulations.

For historical experiments (Sect. ), the same protocol is followed with an ocean–sea ice model forced by either the interannual CORE-II atmospheric state as in OMIP-1; or the interannually varying JRA55-do surface atmospheric dataset as in OMIP-2;.

A6 Data request

A6.1 Requested variables and format

We request a subset of the full CMIP6 data request to enable us to address our core scientific objectives, while limiting the burden on modellers and disc archives. The list of requested variables, using CMIP6 standard nomenclature, is provided in Table . Output according to CMIP6 standards and conventions (i.e. Coupled Model Output Rewriter; CMOR) is preferred. However, in the interest of a low bar for participating in SOFIA, netCDF formatted data not conforming with CMIP6 naming and metadata requirements will be accepted. In this case, models must provide sufficient information for users to interpret their data and specifically the mapping between CMIP6 names and units and their model names and units.

A6.2 Data sharing and usage policy

A common archive of key variables is housed at http://crd-data-donnees-rdc.ec.gc.ca/CCCMA/SOFIA/ (last access: 11 December 2023). Each modelling group may provide more complete output using a service of their choice. Significant effort has been invested by the SOFIA team to design the experiments, the modellers to run the experiments, and the project coordinators to house the data in an open common archive. These efforts should be recognized. We request that this experimental design paper should be cited whenever the SOFIA data are used in publication. We also suggest that users of the data contact us (https://sofiamip.github.io/, last access: 11 December 2023) for input on appropriate use of the data and attribution, as well as collaboration on addressing scientific questions.

Code and data availability

SOFIA data will be provided at http://crd-data-donnees-rdc.ec.gc.ca/CCCMA/SOFIA/ – see Sect. 

Author contributions

NCS coordinated the authors, wrote much of the original text, made Fig. , and managed the common data archive. TM coordinated author meetings and produced Fig. . RB created Fig. . All authors contributed to the discussion of the experimental design and the editing of the text. Various authors ran and contributed model results or acted as points of contact for their model output (Table ).

Competing interests

At least one of the (co-)authors is a member of the editorial board of Geoscientific Model Development. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.

Disclaimer

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

Acknowledgements

The authors thank Nicholas Golledge, Karen J. Heywood, Paul Holland, Katherine Turner, and an anonymous reviewer for their valuable comments helping to improve the manuscript and the experimental design.

Financial support

Matthew H. England and Ariaan Purich are funded by the Australian Research Council Special Research Initiative as part of the Antarctic Science scheme (grant nos. SR200100008 and SR200100005). Tore Hattermann and Morven Muilwijk received funding from the European Union's Horizon 2020 Research and Innovation Programme (grant no. 101003826) via project CRiceS. F. Alexander Haumann was supported by NASA (grant no. 80NSSC19K1115), the European Union (ERC, VERTEXSO, grant no. 101041743), and the Initiative and Networking Fund of the Helmholtz Association (grant no. VH-NG-19-33). Qian Li and John Marshall are supported by the NASA MAP program 19-MAP19-0011 and the MIT-GISS cooperative agreement. The model simulations and analysis were conducted on the NASA High-End Computing (HEC) Program through the NASA Center for Climate Simulation (NCCS) at Goddard Space Flight Center. Torge Martin received funding from the German Federal Ministry of Education and Research (BMBF) through project PalMod: From the Last Interglacial to the Anthropocene – Modeling a Complete Glacial Cycle, WP1.4.3 (FKZ: 01LP1918C). Andrew G. Pauling, Max Thomas, and Inga J. Smith were supported by the Deep South National Science Challenge (MBIE C01X1412) and the Antarctic Science Platform (University of Otago subcontract 19424 from VUW's ASP Project 4 contract with Antarctica New Zealand through MBIE SSIF Programmes Investment ANTA1801).

Review statement

This paper was edited by Philippe Huybrechts and reviewed by Nicholas Golledge and one anonymous referee.