Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Challenges simulating the AMOC in climate models

Laura C. Jackson

Laura C. Jackson

Met Office, Exeter, UK

[email protected]

Contribution: Conceptualization, Formal analysis, Investigation, Visualization, Writing – original draft, Writing – review & editing

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Helene T. Hewitt

Helene T. Hewitt

Met Office, Exeter, UK

Contribution: Conceptualization, Methodology, Supervision, Writing – original draft, Writing – review & editing

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Diego Bruciaferri

Diego Bruciaferri

Met Office, Exeter, UK

Contribution: Visualization, Writing – review & editing

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Daley Calvert

Daley Calvert

Met Office, Exeter, UK

Contribution: Writing – review & editing

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Tim Graham

Tim Graham

Met Office, Exeter, UK

Contribution: Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing

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Catherine Guiavarc’h

Catherine Guiavarc’h

Met Office, Exeter, UK

Contribution: Writing – review & editing

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Matthew B. Menary

Matthew B. Menary

Met Office, Exeter, UK

Contribution: Investigation, Visualization, Writing – review & editing

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Adrian L. New

Adrian L. New

National Oceanography Centre, Southampton, UK

Contribution: Supervision, Writing – review & editing

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Malcolm Roberts

Malcolm Roberts

Met Office, Exeter, UK

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David Storkey

David Storkey

Met Office, Exeter, UK

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    Abstract

    The latest assessment report from the Intergovernmental Panel on Climate Change concluded that the Atlantic Meridional Overturning Circulation (AMOC) was very likely to decline over the twenty-first century under all emissions scenarios; however, there was low confidence in the magnitude of the decline. Recent research has highlighted that model biases in the mean climate state can affect the AMOC in its mean state, variability and its response to climate change. Hence, understanding and reducing these model biases is critical for reducing uncertainty in the future changes of the AMOC and in its impacts on the wider climate. We discuss how model biases, in particular salinity biases, influence the AMOC and deep convection. We then focus on biases in the UK HadGEM3-GC3-1 climate model and how these biases change with resolution. We also discuss ongoing model development activities that affect these biases, and highlight priorities for improved representation of processes, such as the position of the North Atlantic Current, transports in narrow boundary current, resolution (or improved parameterization) of eddies and spurious numerical mixing in overflows.

    This article is part of a discussion meeting issue ‘Atlantic overturning: new observations and challenges’.

    1. Introduction

    The Atlantic Meridional Overturning Circulation (AMOC) plays a critical role in the climate system through its northwards transport of heat in the Atlantic. Many studies have shown that a weakening of the AMOC, whether through natural variability or anthropogenic forcing, would have a significant impact on atmosphere and ocean temperatures, subsequently impacting other aspects of climate such as precipitation, sea levels, storm tracks and atmospheric circulation [13].

    The increase in greenhouse gases through anthropogenic activities is expected to weaken the AMOC through warming and freshening the surface waters in the subpolar North Atlantic (SPNA), both of which reduce densities and inhibit deep water formation [4]. The latest IPCC report concluded that the AMOC was very likely to weaken by 2100 [5]. However, there is a large range of model projections of AMOC weakening, leading to substantial uncertainties in the magnitudes and rates of future weakening [57]. This uncertainty is important since it has been shown that the magnitude of AMOC weakening affects projections of temperature change, precipitation and North Atlantic storm tracks [2,8,9]. One way to reduce uncertainties is to constrain projections through understanding relationships between the projections and observable quantities. One such relationship is between AMOC mean strength and weakening: those models with a stronger AMOC tend to have a greater weakening under anthropogenic climate change [4,6,1012]. Relationships have also been shown between AMOC weakening and other aspects of the mean climate state such as salinity, sea ice extent and locations of deep convection [12,13]. Hence, biases in the climate state can affect projections of AMOC weakening.

    Our knowledge of the AMOC has improved significantly over the last couple of decades through various observational campaigns. The longest continuous dataset has come from the RAPID array at 26.5° N [14], which has provided invaluable data for testing ocean and climate models. Climate models have a wide range of AMOC strengths at 26.5° N, but common biases have been shown of a too shallow overturning [6,15,16] and too strong transports in the western boundary current, offset by too strong recirculation in the upper mid ocean [17]. Observations of heat transports at the RAPID array have also shown that many climate models have biases in heat transports associated with the AMOC because of biases in the temperature difference between upper and lower Atlantic waters [15,18]. The long time series at RAPID has also provided an understanding of AMOC variability. This has been useful in showing that climate models underestimate interannual and decadal variability of the AMOC [19,20]. More recent observations further north from the OSNAP array [21] have also been useful for assessing climate models. Observations have shown that most of the overturning takes place in the east section. A comparison of CMIP6 models has found that they generally agree with the overturning strength in the east of the OSNAP array, but have a wide range of overturning strengths in the western section, with some models having essentially no mean overturning there and some models having much too strong overturning [22].

    Since the overturning circulation of the AMOC is the net result of many processes, some of which are not resolved, there are challenges in representing the AMOC in models. The northwards transport of the upper limb of the AMOC is calculated as the zonal total of meridional velocities and obscures many details such as transports in narrow boundary currents, gyre recirculations (which are partly driven by winds), transports by eddies and steering of currents by bathymetry [23]. As warm, saline subtropical waters travel northwards into the SPNA and Greenland-Iceland-Norwegian (GIN) seas, there is transformation (mainly by heat loss) of surface waters, leading to the formation of dense waters [12,24]. There are also fresh, cold waters which are exported from the Arctic in the East and West Greenland currents, and in narrow boundary currents [25,26]. Mixing of these subtropical and Arctic water masses is achieved through eddies, influencing water mass transformation and the stratification [2729]. The presence of relatively dense surface waters reduces the stratification in the Labrador Sea, Irminger Sea and GIN seas, preconditioning the ocean for wintertime deep convection. This deep convection mixes water through the column, resulting in more heat loss and the formation of deep water masses. These processes change densities and hence density gradients which drive sinking along the coasts where friction can overcome geostrophic balance [30,31]. Deep water masses that are formed in the GIN seas flow southwards at depth into the SPNA in overflows across the Greenland–Scotland ridge [32,33]. These overflows contain dense waters that flow down the topography, mixing with overlying waters. This water is advected into the Irminger and Labrador seas at depth, where it also has an impact on stratification, which can affect deep convection there. Deep convection is also affected by submesoscale eddies, which restratify the water column after a convective event. The deep waters formed in the GIN seas and west SPNA move southwards at depth in the deep western boundary current and via interior pathways. This water is eventually upwelled to the surface via winds in the Southern Ocean and via internal mixing [34].

    Many of these processes are challenging to simulate, particularly in global climate models where resolution is limited [35], in particular: narrow boundary currents, mesoscale and submesoscale eddies are not resolved [36]; there is too much numerical mixing in overflows in the majority of ocean models (which use z-level coordinates) [35,37]; locations of sinking are adversely affected by resolution [30]; steering of currents can be affected by numerical discretization and representation of bathymetry [38]; interior mixing is poorly represented and affected by numerics [35]. This has led to common biases in climate models such as overly deep wintertime convection in the SPNA [39,40] and an overly shallow AMOC [6]. There is also uncertainty around the complex interactions between dense water formation, convection and sinking, and whether they are correctly captured by climate models [21].

    In this article, we focus on the processes affecting the overturning within the North Atlantic in climate models. We firstly discuss how mean climate biases are important for AMOC projections. We then focus on a group of climate models (HadGEM3-GC3-1) at three different resolutions. We discuss the assessment of various processes affecting the AMOC and the model development efforts to improve these processes.

    2. Models and methods

    (a) HadGEM3-GC3-1

    We focus on HadGEM3-GC3-1, which is a coupled climate model, comprising the UM atmospheric model, the NEMO ocean model, the JULES land surface model and the CICE sea ice model [41,42]. In particular, we make use of the configuration with three different ocean resolutions that were used for the HighResMIP project (see [43] for model details). The different horizontal resolutions are nominally 1° (ML), 1/4° (MM) and 1/12° (MH), with all having 75 layers in depth. The configurations also differ in that only ML uses the Gent–McWilliams (GM) [44] parameterization of eddy mixing, while the other resolutions rely on their limited resolution of eddy processes. These configurations all have the same atmospheric resolution of 60 km. However, the biases shown are similar with other atmospheric resolutions, i.e. biases of ML are similar to the LL model (which has the same ocean as ML but a coarser atmospheric resolution), and the biases of MH are similar to the HH model (which has the same ocean as MH but a finer atmospheric resolution) [43]. Biases are also similar in the low- and medium-resolution configurations of HadGEM3-GC3-1 submitted to CMIP6 (referred to here as CMIP6-LL and CMIP6-MM) which uses a more complex atmospheric aerosol scheme [45]. All versions of HadGEM3-GC3-1 used in this article are shown in table 1.

    Table 1. HadGEM3-GC3-1 models and their nominal resolution in the ocean and atmosphere. The last columns indicate the aerosol scheme and the model reference.

    name ocean res (degrees (km)) atmos res (km) aerosol scheme reference
    LL 1 (100) 250 simplified [43]
    ML 1 (100) 100 simplified [43]
    MM 1/4 (25) 100 simplified [43]
    MH 1/12 (8) 100 simplified [43]
    HH 1/12 (8) 50 simplified [43]
    CMIP6-LL 1 (100) 250 full [42]
    CMIP6-MM 1/4 (25) 100 full [41]

    The experiments analysed are control experiments with constant 1950s forcings [43]. There was a spin up of 30 years after initialization from a common initial condition taken from the EN4 ocean analysis [46], followed by a control experiment with constant 1950s forcings. We use an average of years 50–100 of this control to allow for some additional spin up; however, the surface biases shown evolve over the first few years-decades.

    (b) CMIP6 models

    In §3, we use data from a subset of CMIP6 models to get a broader understanding of how salinity affects the AMOC in a multi-model context. In particular, we use the preindustrial control experiments and the experiments with 1% increase in CO2 (1pctCO2) from ACCESS-CM2 [47,48], CanESM5 [49,50], CESM2 [51,52], EC-Earth3 [53,54], E3SM-1-0 [55,56], GFDL-ESM4 [57,58], GISS-E2-2-G [59,60], HadGEM3-GC3-1LL [61,62], HadGEM3-GC3-1MM [63,64], INM-CM5-0 [65,66], IPSL-CM6A-LR [67,68], MIROC6 [69,70], MPI-ESM1-2-LR [71,72], MRI-ESM2-0 [73,74] and NorESM2-MM [75,76]. Where there are multiple ensemble members, we use the first one only. We use a time-mean of the first 100 years of the preindustrial control and take the AMOC trend in the 1pctCO2 experiment over the first 140 years. We measure the AMOC strength as the maximum in depth of the Atlantic overturning streamfunction at 26.5° N.

    (c) Downstream relaxation experiments

    In §4d, we present results from relaxing water mass properties downstream of the overflows from the GIN seas into the SPNA. These were carried out using the coupled model HadGEM3-GC1 [77], which is an earlier version of HadGEM3-GC3-1 which uses an earlier NEMO version at 1/4° ocean resolution, but with a coarser atmosphere model than used in MM.

    The experiment uses Newtonian damping of the temperature and salinity to the EN3 analysis [78] and is compared with a control simulation. A 6-hour restoration timescale is used to relax the waters downstream of the overflows to the seasonal climatology of the EN3 analysis. The damping is applied in the Irminger sea and Icelandic basin below a depth of 1000 m. The aim of this experiment is to try to remove biases in subsurface eastern SPNA to examine the impact on the Labrador sea. Biases in this region can be caused by the model’s inability to correctly simulate the overflows from the GIN seas, which would have an impact at the depth of overflow waters and also on waters above due to mixing. Biases can also be related to the advection into the eastern SPNA of waters originating in the subtropical North Atlantic, or of waters recirculating in the subpolar gyre.

    The ocean is initialized from rest with temperature and salinity taken from the EN3 analysis and the simulation is 100 years long, with results averaged over the last 40 years of the experiment.

    3. Biases

    (a) Relationship of biases with the AMOC

    Previous research has shown that biases in the mean climate can affect AMOC mean strength, variability and response to external forcings. Biases in salinity in the western SPNA (consisting of the Labrador and Irminger seas) have particularly been highlighted.

    Several studies have shown relationships between salinity in the western SPNA and the mean AMOC strength across various ensembles of climate models [12,13,40,7981]. One in particular [80] also showed the wider relationship between salinity patterns and mean AMOC strength across CMIP5 models. They showed that models with a stronger AMOC had more saline waters in the upper SPNA and Arctic, and in deep Atlantic waters, but fresher waters outside the Atlantic. They attributed this to models with a stronger AMOC having greater transport of salt to the SPNA and Arctic, and more salt transported to the deep Atlantic. They concluded that the fresh surface waters outside the Atlantic were a result of models with a stronger AMOC having greater heat transport, and hence warmer subtropical waters, greater evaporation and hence greater atmospheric moisture transport to the Pacific. Correlations of sea surface salinity (SSS) in the North Atlantic with the AMOC across several CMIP6 models show similar findings (figure 1a). A recent study [13] has also shown that other aspects of the mean state in the Labrador sea are related to AMOC strength: those models participating in CMIP6 that have a stronger mean AMOC strength have a warmer, more saline Labrador sea, with weaker stratification and less sea ice extent. However, it is not clear what the causality of the biases is, since a model with a stronger AMOC might be expected to have a greater northwards transport of heat and salt, resulting in a warmer and more saline Labrador sea, and hence less sea ice and a weaker stratification with deeper convection. These then enable greater heat loss, which would encourage a stronger AMOC.

    Figure 1.

    Figure 1. (a) Correlation between time-mean AMOC strength and SSS across CMIP6 models in the preindustrial control experiments. (b) Correlation of AMOC trend in the 1pctCO2 CMIP6 experiments against the time-mean SSS in the preindustrial control experiments. Correlations smaller than 0.48 (grey) are not significant at the 0.05 level. Bottom line shows scatter plots between (c) the time and area-mean SSS in the Labrador Sea (52–62° N, 45–60° W) and the time-mean AMOC strength in the preindustial control experiments; (d) the time and area-mean SSS in the Labrador Sea and the AMOC trend in the 1pctCO2 experiment; (e) the time-mean AMOC strength in the preindustial control and the AMOC trend in the 1pctCO2 experiment.

    Biases also can have an impact on variability of the ocean circulation. CMIP6 models with a more saline Labrador sea have been shown to not only have more dense water formation there but also to have greater variability of that formation and a stronger correlation between the AMOC variability further south and dense water formation in the Labrador sea [81]. Another study by [82] showed that biases in temperature and salinity have an impact on how temperature and salinity anomalies impact densities because of nonlinearities in the equation of state. Both these studies show that biases can impact which mechanisms are dominant in driving variability in different models.

    Many studies have shown that the mean AMOC strength can have an impact on the magnitude of AMOC weakening as a response to increased greenhouse gases, with those models that have a stronger AMOC strength also having a greater AMOC weakening [4,1012]. However, the larger multi-model studies of CMIP5 and CMIP6 models found that in some scenarios there was no significant relationship between AMOC strength and weakening, or that the relationship was obscured by outliers [6,10]. Hence, the relationship may not always hold when considering a diversity of models and scenarios. There have also been mixed results when correlating mean AMOC strength with percentage (rather than absolute) AMOC weakening.

    The magnitude of AMOC weakening in response to increased greenhouse gases has also been shown to be related to other aspects of the mean climate state. One study [12] examined the AMOC weakening in a scenario where the CO2 increases by 1% per year using an ensemble of models of varying resolution. They found that those models with a higher horizontal ocean resolution had a more saline western SPNA and more dense water formation and deeper convection in the Labrador and Irminger seas rather than the GIN seas. They showed that the location of dense water formation is important since that in the Labrador and Irminger seas is more sensitive to changes in a warming climate than that in the GIN seas. This results in those models with more saline surface waters and more dense water formation in the western SPNA having a stronger AMOC weakening when CO2 increases. However, the influence of resolution on the mean state might be model dependent since the study primarily uses models with the same ocean model component. Other studies have found that models with higher horizontal ocean resolution can have stronger [15,43,8385] or weaker [11,86,87] AMOC strengths.

    The mean state in the Labrador sea has also been shown to have a strong influence on AMOC projections in CMIP6 models [13], with those models with a strong AMOC weakening having a stronger mean AMOC and a warmer, more saline Labrador sea, with weaker stratification and less sea ice extent than those models with less AMOC weakening. Parallel analysis of CMIP6 models here also shows correlations between salinity in the Labrador sea and both AMOC mean strength and the AMOC weakening trend in the 1pctCO2 experiments (figure 1c,d). Both correlations are significant (0.71 and 0.58 with 15 models, 0.57 and 0.59 with 14 models) even when excluding the very fresh outlier (model E3SM-1-0). There is no significant correlation between the mean AMOC and the trend (figure 1e), excluding the possibility that the relationship found between the AMOC trend and Labrador sea salinity is caused by a relationship of both with the AMOC mean strength. There is also no significant relationship with the percentage weakening (not shown). Figure 1b shows that the relationship between AMOC trend and salinity in the control extends from the Labrador sea across the SPNA and is actually stronger in the eastern SPNA. Hence, the relationships between salinity and other biases and the AMOC may not be limited to the Labrador sea.

    One important mechanism controlling AMOC weakening proposed previously by [88] and supported by [13] involves sea ice: models with a greater sea ice extent have greater sea ice retreat as the climate warms and a hence greater increase in area exposed to the atmosphere. This enables more heat loss from the ocean, offsetting the reduction in heat loss from atmospheric warming which is driving the AMOC weakening. An additional mechanism is also proposed by [13], who show that those models with stronger AMOC weakening not only have warmer surface temperatures with less sea ice but also have more saline surface waters with weaker stratification. With a weaker stratification and deeper convection, there is a greater penetration of the warming signal to depth, and hence a stronger impact on AMOC weakening. They are not able to point to which mechanism may be dominant.

    (b) Biases in Met Office climate models

    To understand in more detail some of the biases affecting the AMOC, we will concentrate on one group of climate models: those from the Met Office family of models HadGEM3-GC3-1 (§2a). Before discussing the representation of important processes in these models, we first assess the large-scale biases in the AMOC and their dependence on resolution.

    Figure 2 shows the AMOC streamfunctions for the three models ML, MM and MH. AMOC strengths (as measured at 26.5° N), respectively, are 15.6, 17.9 and 19.8 Sv (Sverdrup, 1Sv=1×106m3s1). In agreement with other studies of these experiments and of the equivalent forced ocean models, we see an increase of AMOC strength with resolution [15,43,83]. However, the relationship of AMOC strength to resolution may be model dependent, since some climate models using non-NEMO ocean components find different results [11,86,87].

    Figure 2.

    Figure 2. The AMOC streamfunction (panels a-c; Sv) and March MLD (panels d-f) for the three resolution models ML (a, d), MM (b, e) and MH (c, f). Black lines in the bottom panels show the March sea ice extent.

    Consistent with having a stronger AMOC, the higher resolution models also have deeper and more widespread convection (as indicated by March mixed layer depth [MLD]), particularly in the Labrador Sea (figure 2). This increase of deep convection with resolution is found in other climate models, particularly those using the NEMO ocean model [15,89]. Observations suggest that the MM and MH models have too much deep convection in common with many other climate models [39,40].

    The higher resolution models also tend to have a warmer and more saline surface SPNA (figure 3). It might be expected that models with a stronger AMOC would have a stronger heat and salt transport, and hence, a warmer and more saline SPNA, which (since the high SSS in the Labrador sea leads to denser waters there) is consistent with those models also having deeper convection. Although the mechanistic links between the AMOC and deep convection are complex [30,31], increased deep convection is associated with a stronger AMOC [15,39,79,90]. Hence, the source of the biases is difficult to identify.

    Figure 3.

    Figure 3. The bias in SST (panels a-c, °C) and SSS (panels d-f, PSU) for the three resolution models ML (a, d), MM (b, e) and MH (c, f). Biases are with respect to the EN4 observational analysis over the period 1950–1980.

    In comparison with observations, the ML model has a large cold and fresh bias over much of the SPNA. This bias is also seen in the similar low-resolution model CMIP6-LL [12] and the equivalent low-resolution forced ocean model [91]. Despite this bias, the salinity in the Labrador sea itself is only slightly fresher than the observations. MM and MH have smaller biases across the central SPNA; however, the Labrador sea is too warm and saline, particularly in MH. It is interesting to note that good agreement with Labrador sea salinities does not necessarily imply good agreement with deep convection or AMOC strength or that good agreement of the AMOC strength with observations does not necessarily imply good agreement of deep convection, despite significant correlations. This mismatch has been seen in previous multi-model studies [15,79,89] and suggests that there may be multiple sources of biases. For instance, it is possible that temperature and salinity biases affect the stratification and hence influence the deep convection and water mass transformation that affect the AMOC, while inaccurate representations of subgridscale eddy processes or deep water masses from the overflows can separately affect the deep convection and AMOC.

    4. Assessing and improving model biases and processes

    (a) Transports

    One major influence on salinity biases in the Labrador sea and SPNA is the transport of saline subtropical waters and fresh Arctic waters into the region. In examining the development of biases in four forced ocean models with different ocean components (one of which uses NEMO), it was found that all experiments developed a saline bias in the Labrador sea [92]. This was attributed to erroneous transports rather than surface fluxes or vertical mixing.

    A dominant pathway of water entering the SPNA is that of subtropical waters travelling northwards via the Gulf Stream and then the North Atlantic Current (NAC). Figure 4 shows the position of the NAC in ML, MM and MH models, along with the EN4 observational analysis [46]. These results agree with previous studies that have shown that the NAC is too far south and east in lower resolution models, but better at higher resolutions in NEMO-based models [12,91,93,94]. However, these higher resolution models may then have too much of this warm, saline water reaching the western SPNA instead of travelling northwards into the GIN seas. One study showed that their higher resolution model developed a shortcut from the NAC to the Irminger sea [94], while another pointed to the strong transports westwards across the Reykjanes ridge [92].

    Figure 4.

    Figure 4. North Atlantic current position assessed as the 10°C isotherm at 50 m depth in ML (blue), MM (yellow), MH (magenta) and the EN4 observational analysis (black). Filled contours show the 50 m temperature from EN4.

    The SPNA is also fed by cold, fresh waters exiting the Arctic via the East Greenland Current to the West Greenland Current, and through the Canadian archipelago to the Labrador Current. Since these transports are in narrow coastal and boundary currents, they are better represented at higher resolutions [91,94,95]. However, their strengths can still be adversely affected due to problems with representation of shallow topography and near shore density gradients [92]. Even if the strengths of the boundary currents are well represented, their fresh water transports may not be if models are unable to capture very fresh conditions near the coast, e.g. from lack of representation of glacial melt [92] or reduced sea ice extent [94]. However, a couple of studies [26,94] have found through various methods that increasing freshwater export from the Arctic did not have a large impact on the salinity of the Labrador sea.

    (b) Water mass transformation

    As water masses travel from the subtropics to the SPNA, they become more dense as heat is lost to the atmosphere. This water mass transformation can be related to the AMOC in density space: in steady state, the circulation of lighter waters transported northwards and dense deep waters southwards is balanced by the water mass transformation between the two [96,97]. Much of this transformation occurs due to surface buoyancy forcing (mainly not only from surface heat fluxes but also from surface freshwater fluxes), though mixing also has a contribution [12,24,98,99].

    Observations show that most of the water mass transformation associated with the AMOC occurs in the eastern SPNA (Icelandic basin and Irminger Sea), with the densest waters formed in the GIN seas and in the Labrador Sea [21,100102]. While climate models mostly agree with observations about the dominance of the eastern SPNA for the mean state, there are large differences across models in the amount of water mass transformation in the Labrador Sea [81,103105]. In particular, those models that have a more saline Labrador Sea have greater water mass transformation there [81].

    The water mass transformation has been examined previously in related HadGEM3-GC3-1 models. In the CMIP6-LL and MM models, they agree with observations that the water mass transformation is dominated by that in the east SPNA, with transformation in the Labrador Sea being small. However, in CMIP6-LL, it is slightly too small, and in CMIP6-MM, it is slightly too large [12,81]. Similar results are found in the LL, MM and HH models where the water mass transformation in the Labrador Sea increases with resolution [106]. This increase with resolution is attributed to the higher resolution models having a warmer, more saline Labrador sea with less sea ice, resulting in a greater ice-free area for transformation and a shift of the locations of outcropping isopycnals.

    (c) Labrador Sea convection and eddies

    The magnitude and location of deep convection in climate models can have a significant impact on water mass properties and the strength of the AMOC. Biases in MLD have been noted by a number of authors [39,40,89]. In particular, as noted in §3b, MM and MH models have deeper Labrador Sea MLD than the ML model (figure 2). This suggests that the magnitude of Labrador Sea convection may be linked to the model representation of the ocean mesoscale. However, it is also possible that the deeper MLD is a result of the warmer, more saline Labrador sea surface waters, since these biases have been suggested to affect the MLD [13]. The background stratification (and hence MLD) can also be affected by biases in the subsurface waters advected into the Labrador Sea from the Irminger Sea. In an experiment using an earlier Met Office climate model (see §2c), where the water mass properties in the Irminger Sea and Icelandic basin were relaxed towards climatology, convection in the Labrador Sea was reduced (figure 6). Hence, Labrador Sea convection could be affected by biases in the eastern SPNA, which is fed by the NAC and can be impacted by spurious mixing from the North Atlantic overflows (§4d).

    Eddies are known to play an important role in mixing in the Labrador Sea [27,107]. In the Met Office climate models at 1 resolution, eddies are parameterized by GM, while at higher resolutions, they currently are not. This is in spite of the fact that even 1/12 is insufficient to resolve the Rossby radius at the latitude of the Labrador Sea [108]. A scale-aware eddy parameterization is being implemented in the 1/4 resolution as part of work to reduce biases in the Southern Ocean [109]. Figure 5 shows that this has a notable impact on the strength of Labrador Sea convection with a decline in the Labrador Sea and a shift of deep convection into the Irminger Sea. Further analysis is required to assess to what extent this is due to improved representation of eddy processes in the boundary currents or due to changes to the magnitude or steering of the currents themselves.

    Figure 5.

    Figure 5. Impact of including GM parameterization at high latitudes [109] on March MLD (m). Plotted is the difference in MLD when including the GM parameterization in MM in comparison with that in the standard model.

    Figure 6.

    Figure 6. Impact of relaxing water mass properties on MLD. Shown is the March MLD (m) in (a) the control experiment and (b) the experiment where subsurface temperature and salinity properties are relaxed towards observations over the region shown by the white contour. Experiments are described in §2c.

    This result suggests that further consideration of model parameterizations are needed even at resolutions that might be considered to be (mesoscale) ‘eddy resolving’ or ‘eddy rich’. There is also a need to consider the representation of the ocean submesoscale. Submesoscale eddies have been shown to play an important role in restratifying the Labrador Sea [110] and reducing deep convection. Explicit representation of the submesoscale is currently beyond the resolution of climate models and therefore inclusion of a parameterization scheme such as that in [111] is needed. Work to implement such a scheme in climate models has demonstrated that it also has an impact on Labrador Sea convection [29,111,112].

    (d) Overflows

    The deep North Atlantic is linked to the shallower GIN seas via two main overflow choke points: the Denmark Straits and the Faroe-Shetland channel. The water masses originating from these overflows contribute to the southward return flow of the AMOC [33]. There is some evidence that overflow waters may influence Labrador Sea convection, which would increase their importance in the returning branch of the AMOC (§4c). Representation of overflow waters has also been shown to impact currents in the North Atlantic, including the separation of the Gulf Stream and the path of the NAC [113,114].

    Representation of overflow processes and the resulting water masses has been a long-standing issue in climate models [35,37,115] with a number of different approaches investigated in an attempt to improve this. In z-level models, the issue with representation of the overflows is that excessive mixing occurs between levels as the overflow water moves downslope leading to erroneous water mass properties and a weak flow. One of the most promising approaches has been the use of terrain-following coordinates, which allows the water masses to maintain their properties as they move downwards and southwards. However, terrain-following coordinates are typically not appropriate for global models because they can introduce large errors in the calculation of the pressure gradient [116]. To overcome this, a vertical grid was proposed where computational surfaces are terrain-following only in the proximity of the Greenland–Scotland ridge while they revert to geopotential levels in the rest of the model domain [117,118]. This idea was combined with the multi-envelope (ME) approach to vertical coordinates by [119] to develop a generalized method to change the vertical coordinate system within the domain of quasi-Eulerian ocean models. This new approach has been tested in the Nordic overflows region with promising results [120], with the model using ME terrain-following levels preserving more of the dense waters downstream of the overflows (figure 7).

    Figure 7.

    Figure 7. Impact of vertical coordinate systems on overflows [119,120]. (a) Map showing positions of the sections. Plotted is the potential density (kgm3) along the M82/1 section in the Irminger Sea [121] for (b) the observations, (c) the model using z-coordinates with partial steps (zps) and (d) the model with localized multi-envelope terrain-following coordinates (MEs). Also shown is the potential density (kg m-3) along the extended Ellett line in the Icelandic basin [122] for (e) the observations and the models using zps (f) or localized MEs (g) computational levels. The red contour shows the 27.85 isopycnal contour.

    (e) Sinking

    The northwards transport of upper waters and southwards transport of deep waters in the AMOC must be balanced by a net downwards mass flux in the northern North Atlantic. This is not achieved by convection (which transfers temperature and salinity anomalies, but does not involve a net mass flux) and cannot occur in the ocean interior without overcoming constraints by vorticity conservation [31,123,124]. Sinking is thought to instead occur along coastal boundaries where friction is important. In low-resolution ocean and climate models, however, viscous dissipation can be larger in the interior leading to more widespread patterns of sinking [30].

    Analysis of sinking at different ocean resolutions in a NEMO-based forced ocean model shows that at the resolution used by MM (1/4° resolution), the sinking agrees with theoretical models of sinking along the boundary driven by density gradients. However, at lower resolutions, such as those used for ML (1° resolution), the sinking is spread over a wider boundary region and the agreement with the theory is poor [30]. Analysis of the CMIP6-LL and MM versions of HadGEM3-GC3-1 shows similar resolution dependence in their patterns of sinking [103].

    (f) Influence of numerics and bathymetry

    The representation of bathymetry has been discussed in the context of the overflows in §4d. However, interactions of the flow with bathymetry is not limited to the overflows. Flow-topography interactions play a key role for simulating a realistic western North Atlantic circulation [125127]. Experiments with the MM and MH models have shown that resolution sets the separation of the Gulf Stream, but bathymetry determines the steering, particularly for the NAC (P Mathiot, personal communication). In addition, ongoing investigations with the MM model employing localized ME terrain-following levels only in the proximity of the shelf and the continental slope of the subpolar gyre highlighted the impact of model bathymetry on the simulated circulation, especially for the case of the DWBC at depth (not shown).

    As noted in §4d, a terrain-following coordinate system can improve aspects of the interaction between the bathymetry and the flow. However, the pressure gradient errors associated with this coordinate system have inhibited its use in global climate models. For geopotential coordinates, still widely used in climate models, ocean model numerics are not straightforward in the presence of bathymetry. Different choices can be made about how grid points are treated near bathymetry, and this can have an impact on the subsequent evolution of the ocean model dynamics [38,125,128,129]. This is also the case in the Met Office climate models where the choice of numerical scheme near bathymetry can change the steering of the NAC and the integrity of the southward flowing deep western boundary current (not shown).

    5. Summary and pathways forward

    We have discussed how model biases in the ocean climate state can impact the AMOC, in its mean strength, but also in terms of its variability and response to future projections of climate change. In particular, biases in the Labrador Sea and SPNA seem to have an important role. Since there is large uncertainty in the magnitudes of AMOC weakening in future projections [5,6], reducing these biases could reduce uncertainty in future projections.

    We discuss the evaluation and model development activities taking place for some of these processes. Although we have focused on the Met Office climate model HadGEM3-GC3-1, many of the processes are common to other climate models [35]. Some important processes for the North Atlantic that we find are misrepresented: pathways of water masses including the NAC; narrow boundary currents importing fresh Arctic water to the Atlantic; lack of eddies, which are important for mixing and restratification; numerical mixing in overflows; and locations of sinking. Some of these processes improve with resolution, for instance at medium and high resolutions (1/4° and 1/12°), the path of the NAC improves (solving the cold, fresh bias off Newfoundland), and sinking is more confined to the boundary. However, eddies are still not sufficiently resolved, particularly at submesoscale.

    There are ongoing efforts to address these biases. These efforts include increasing resolution and improved parameterization. As discussed in [130], increasing ocean model horizontal resolution has lagged behind in the development of climate models. In the low-resolution models, the biggest problem is the large cold and fresh bias off Newfoundland caused by errors in the path of the North Atlantic Current. Increasing standard resolution of ocean models towards 1/10° or 1/12° is high priority and would address this issue described here as well as improve the representation of the boundary currents transporting Arctic water [131]. Resolutions of 1/10° are often described as ‘eddy-resolving’ but is really the first frontier in horizontal resolution, and there is a push towards the kilometre scale [130], which would further improve representation of both mesoscale eddies and boundary currents, particularly at high latitudes. However, while scientifically desirable, computational costs currently slow the push to high horizontal resolution and enhanced resolution in limited areas may be a good compromise given sufficient scientific insight to choose regions appropriately. This approach is addressed in a number of other ocean modelling systems [132134].

    Increasing horizontal resolution on its own remains insufficient to solve some problems, for example in representing overflows. We have demonstrated that terrain-following vertical coordinates show promise in reducing the spurious numerical mixing in overflows. This supports other findings that have shown improvements that can be made using isopycnal coordinates, e.g. [37,114]. One of the novel developments described here in the context of the NEMO ocean model is the ability to limit terrain-following coordinates to local areas. This is advantageous as it reduces errors associated with the horizontal pressure gradient. While this is the approach in the NEMO ocean model, other model families have different approaches to vertical coordinates, including the generalized arbitrary Lagrangian–Eulerian coordinates of the MOM6 model [135,136]. Given a diversity of approaches in vertical coordinates, a broader model intercomparison studying the impact of the choice of vertical coordinates on overflow representation could be a fruitful way to better understand the key processes.

    Other issues may also require improved parameterization. There are arguments for using higher resolution models to improve parameterizations for lower resolution models, reducing computational overheads and allowing larger ensembles of longer simulations. In this article, we have described two examples of the use of parameterization: the implementation of the GM mesoscale eddy parameterization at high latitudes for the medium-resolution models (where eddies are not properly resolved), and the development of submesoscale eddy parameterizations to reduce the overly deep convection in the Labrador Sea.

    Some of the biases described here may be model dependent, for instance the biases in the Labrador Sea. In the medium- and high-resolution models with NEMO, we find that the key biases are that the Labrador Sea region is too warm and saline, with too deep a mixed layer; however, in some models, the Labrador Sea is too cold and fresh [22]. Further analysis is required to understand the source of these biases; Lagrangian diagnostics may be useful to understand impacts of different pathways on the Labrador Sea. While other models may not experience exactly the same biases, the development of novel analysis techniques will be of broader benefit. In addition, community agreement on a set of common benchmarking metrics for North Atlantic simulations in ocean and climate models would enable model intercomparison and support efforts such as CMIP [137]. New efforts to make comparisons of the AMOC between observations and models more comparable will make assessments easier to do [138].

    Observations play a key role in assessing climate models driving model improvements. Continued observations of the AMOC will help us to assess models’ abilities to represent variability and trends, aiding our ability to assess likely rates of anthropogenic weakening. Observations of processes related to the AMOC are also very important for assessing models and for developing new parameterizations, as are very high-resolution modelling studies aimed at understanding specific processes.

    In this article, we have looked at a number of different processes that can influence the representation of the AMOC and North Atlantic in global climate models. Reducing climate model biases can take many years and require a number of different approaches to be investigated (e.g. [139] demonstrates this for the Southern Ocean). The improved representation of many of the processes outlined here, continue to be topics for active research in the modelling community. Our approach to leveraging developments to improve the Met Office climate model is to work in a coordinated manner to assess the impacts of developments in combination and to take advantage of the existence of a hierarchy of models at different resolutions. This approach is similar to the Climate Process Teams that have delivered success in US climate models through bringing together climate model developers with observationalists and process experts [140]. We propose that this coordinated approach is the best way forward to target improvements in specific areas of climate models.

    Data accessibility

    Data used for the figures in this paper are available via https://doi.org/10.5281/zenodo.7717335 [141] and https://doi.org/10.5281/zenodo.7764694 [142]. More extensive data are available for CMIP6 models (including CMIP-LL and CMIP6-MM) and from the HighResMIP experiments LL, MM, HH and MH from the CMIP6 Earth System Grid Federation.

    Authors' contributions

    L.C.J.: conceptualization, formal analysis, investigation, visualization, writing—original draft and writing—review and editing; H.T.H.: conceptualization, methodology, supervision, writing—original draft and writing—review and editing; D.B.: visualization and writing—review and editing; D.C.: writing—review and editing; T.G.: formal analysis, investigation, methodology, writing—original draft and writing—review and editing; C.G.: writing—review and editing; M.B.M.: investigation, visualization and writing—review and editing; A.L.N.: supervision and writing—review and editing; M.R.: resources and writing—review and editing; D.S.: visualization and writing—review and editing.

    All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

    Conflict of interest declaration

    We declare we have no competing interests.

    Funding

    This work was supported by the Met Office Hadley Centre Climate Programme funded by BEIS and Defra.

    Footnotes

    One contribution of 13 to a discussion meeting issue ‘Atlantic overturning: new observations and challenges’.

    Published by the Royal Society. All rights reserved.