Understanding Differences in North Atlantic Poleward Ocean Heat Transport and Its Variability in Global Climate Models

The ocean heat transport from the North Atlantic to the Barents Sea impacts the sea ice extent and the energy budget of the Arctic. The analyzed climate models from the fifth (CMIP5) and sixth (CMIP6) phases of the Coupled Model Intercomparison Project show large intermodel differences in the ocean heat transport with biases of several Terawatts at the Iceland‐Scotland Ridge and Barents Sea Opening (BSO). While both model generations show a large spread in mean volume transports, in CMIP6 temperatures are more homogeneous and realistic, yielding heat transports closer to observations. On all time scales, changes in heat transport reflect changes in volume transport, while temperature changes affect the heat transport variability on longer time scales, especially at the BSO. The temporal variability of heat and volume transports is linked to wind forcing south of Iceland and along the Norwegian coast in all models but has different magnitudes.

The OHT depends on the amount of transported water (i.e., the ocean volume transport, OVT) and its temperature (Buckley & Marshall, 2016;Orvik & Skagseth, 2005). The same OHT can result from the transport of a large volume of relatively cold water, or a small volume of relatively warm water. The relative importance of these two components (OVT and temperature) for the OHT depends on the considered time scale and location. Observations at the BSO indicate that the OVT dominates the OHT signal on shorter time scales, while on longer time scales water temperature is also important (Orvik & Skagseth, 2005). At the Fram Strait, modeled long-term OHT variability is dominated by variations in temperature (Muilwijk et al., 2018). Therefore, to better understand why climate models have so different OHT it is key to consider both components of the OHT at different time scales.
Finally, OHT is linked to ocean currents that are forced by the atmosphere (Lien et al., 2017;Orvik & Skagseth, 2003;Richter et al., 2009;Sandø et al., 2012;Sandø & Furevik, 2008;Serra et al., 2010), so OHT differences in models could also result from differences in wind forcing (Muilwijk et al., 2018(Muilwijk et al., , 2019. Since the representation of the jet stream and the storm tracks over the North Atlantic is often too zonal in CMIP5 and CMIP6 (Harvey et al., 2020;Oudar et al., 2020;Priestley et al., 2020;Zappa et al., 2014), these biases can have implications for the representation of the wind stress curl and ocean circulation.
To understand present and future changes in the Arctic regions, it is crucial to investigate what controls the OHT and its variability, as this has an impact on the poleward energy transport and sea ice extent. In this study, we consider the OHT into the Nordic and Barents Seas across 15 CMIP5 and 9 CMIP6 models. We focus on the ISR and BSO only, on the one hand, because the Fram Strait transports are strongly influenced by eddy-driven variability (Muilwijk et al., 2018), which cannot be realistically reproduced in the low-resolution global models. On the other hand, to compare models and observations, continuous measurements are needed and are available for these two sections for more than two decades. The goal of the study is to understand which factors account for the intermodel differences in the OHT mean state and variability. We consider the water temperature and OVT, as well as the atmospheric wind forcing, which is expected to influence the OVT.

Observations and Reanalyses
The observation-based numbers are combinations of different observational time series and estimates. The net OHT and OVT at the BSO consist of combined estimates for different water masses based on the inflow of Atlantic Water (Ingvaldsen et al., 2004;Skagseth, 2008) and Norwegian Coastal Current water (Skagseth et al., 2011) from the Norwegian Marine Data Center (NMDC, 2020) from 1998 to 2016. The OHT and OVT at the ISR are based on the inflow of Atlantic Water (Berx et al., 2013;Hansen & Østerhus, 2000) and outflow of deep waters (Hansen & Østerhus, 2000(Hansen & Østerhus, , 2007 at the Iceland-Faroe Ridge (IFR) and Faroe-Shetland Channel (FSC) from AtlantOS (OceanSITES, 2020) from 1993. These estimates are available at a monthly resolution. Time series of annual temperatures representing northward-flowing Atlantic Water (i.e., the upper 200 meters) are taken from the ICES Report on Ocean Climate (ICES, 2020). For comparison with model data, we use values only until 2005, and the climatological means are reported in Table S1.
For the atmospheric forcing, we use the zonal wind (U) at 850 hPa from the twentieth-century atmospheric reanalysis (ERA-20C) of the European Center for Medium-Range Weather Forecasts (Poli et al., 2016) available for 1900-2010.

CMIP5 and CMIP6 Model Data
Modeled data from CMIP5 (Taylor et al., 2012) and CMIP6 (Eyring et al., 2016) is downloaded from the Earth System Grid Federation (ESGF; Cinquini et al., 2014). The analysis is based on monthly outputs over the periods 1850-2005 (or 1986-2005 when comparing to observations) with ensemble members r1i1p1 and r1i1p1f1 from 15 CMIP5 and 9 CMIP6 models, respectively. Only models that provide variables for both heat (hfx, hfy) and mass (umo, vmo) transports per month are included. Thereby, hfx and hfy (umo and vmo) contain all contributions to x-and y-ward heat (mass) transport from resolved and parameterized processes. Volume transports are calculated from mass transports assuming a density of water of 1000 kg m −3 . This assumption can lead to a slight ( 3%) overestimation of OVT but it does not affect its variability (not shown). In addition, we consider monthly ocean temperatures (thetao) at 100 m depth and zonal wind (U) at 850 hPa. Sea level height (zos) and ocean surface velocity (uo and vo components) are used to illustrate circulation differences in Figure 1.

Calculation of the Ocean Heat and Volume Transports
The OHT through a section S depends on the amount of transported water and its temperature. Following Orvik and Skagseth (2005) it is defined as where, c p is the specific heat capacity of water, ρ the density of seawater, v the velocity of the water perpendicular to section S, and T the temperature of the water relative to a reference temperature of 0°C. The term ∫ S vdS represents the OVT.
We calculate monthly OHT and OVT from the model outputs, and consider two sections shown in Figure 1: the Iceland-Scotland Ridge (ISR), which encompasses the Iceland-Faroe Ridge and the Faroe-Scotland Channel, and the BSO, from southern Svalbard to the Norwegian coast. For each section, we first find grid indices that are closest to specific longitude and latitude positions at each end of the section. We also check that the endpoints are on land as the resolution and the corresponding bathymetry differ from model to model. Thereafter, we find the grid indices and corresponding x and y transport components for each grid cell along a line between the two endpoints to calculate the total OHT and OVT across the considered sections.
For each model, we use the temperature at 100 m depth as an estimation for the Atlantic water core temperature, and calculate temperatures along the same sections as for OHT and OVT.

Mean Properties, Seasonal Cycle, Decadal Variability
The mean properties are calculated for the period 1986-2005 for both CMIP5 and CMIP6 models to cover a similar period as in the observational estimates. The amplitude of the seasonal cycle is defined as the difference between the lowest and the highest monthly mean values of the considered time series. We also estimate the range of decadal variability by computing a set of 10-year means for different periods using the 150 available years (starting with 1996-2005 going backward, i.e., 1986-1995, 1976-1985. 1856-1865, for a total of 15 periods). We refer to "decadal variability" as the range between the lowest and highest value.

Ocean Mean State and Variability
The mean OHT and its variability at different time scales are differently represented in CMIP models. Figures 2a-2c show the monthly time series of OHT (thin lines) for three different models (cf. Figure S1 for all models). While the MPI-ESM-MR and IPSL-CM6A-LR models have comparable magnitudes of mean OHT at the ISR (values of 346 and 309 TW, respectively, in blue) and BSO (132 and 93 TW, respectively, in gray), the IPSL-CM5A-LR model has much lower values at both locations (57 and 3 TW). On decadal time scales (i.e., applying a running mean of 10 years, thick lines) the models' variability reveals remarkable differences; for example, the MPI-ESM-MR model shows large fluctuations and an increase in OHT between 1940 and 1970 that is not visible in the other models in any periods. The co-variability on decadal (monthly, in brackets) time scales between OHT at the ISR and BSO is for most models positive (cf. Figures 2a-2c with Figure S1) but varies largely in strength. In addition, correlations between decadal temperature and OVT (r_T100) at the ISR (blue) and BSO (gray) are displayed in (g)-(i), and in brackets using monthly data.
Large differences are also evident in the seasonal cycle and decadal variability of OHT across CMIP models. Figure 3 (and Table S1) summarizes the mean properties (bar height), and the seasonal cycle (color shading) for 1986-2005, and the decadal variability (black segments) for 1850-2005 for all considered models, except CMCC-CESM, which is not displayed due to the unrealistic large values of OHT at the ISR. The estimates from observations are shown as gray horizontal lines and are reported in the corner of each panel. There is a large spread across models, where the OHT at the ISR (Figure 3a) spans from 30 to 400 TW. Compared to the observed OHT of 231 TW, several models overestimate the OHT by almost 100 TW. This overestimation is still present if we take into account decadal variability (black segments). The models also have very different seasonal cycles that vary from practically 0 to more than 150 TW. Large differences in the OHT climatologies (ranging from 0 to 120 TW), decadal variability (0-50 TW), and seasonal cycles (0-80 TW) are also observed at the BSO (Figure 3b). Positive and negative biases of OHT at the BSO are observed for both CMIP generations. However, taking into account the decadal variability, the OHT for the considered CMIP6 models falls within the observed range.
Observations show that the ratio between the OHT at the ISR and the BSO is about 3 (Table S1). This ratio is for most models (17 out of 24) higher than 3.5, meaning that most models lose more heat on their way northward than observed. Hence not all models with positive OHT biases at the ISR also have excessive OHT at the BSO. For example, the GFDL-CM3 and the EC-Earth models have a positive bias in OHT at the ISR and a ratio of 5.3 and 4.2, respectively, but show OHT values within the observed range at the BSO.
Since the volume of transported water, together with the water temperature, contribute to the OHT (Equation 1), we want to examine whether there is already a large intermodel spread in the OVT. At the ISR the OVT ranges from less than 1 to 10 Sv, while at the BSO it ranges from −1 Sv (i.e., a net transport of water out from the Barents Sea) to ∼5 Sv (Figures 3c and 3d and Table S1). About half of the models simulate an OVT within the observed range at the ISR, but there are several models that largely overestimate the flow. Most models yield OVT values close to the observed range at the BSO, especially if decadal variability is taken into account (black segments, Figures 2d-2f and Figure S2). For both sections, a diversity of OVT seasonality ranges are visible.
Differences in the mean temperature of the Atlantic water (i.e., at 100 m) can also lead to discrepancies in the mean OHT. Among the analyzed models, CMIP6 models have temperatures close to observations at the ISR (∼9°C) and BSO (∼6°C), while CMIP5 models show mostly cold biases at both sections (Figures 3e and 3f). The decadal variation of water temperatures is comparable between models (see also Figures 2g-2i and S3). The seasonal changes of the water temperature at 100 m are for most models and sections in the order of magnitudes of a few degrees.

Lag Correlation of OHT, OVT, and Temperatures
To investigate how OHT is linked to OVT and temperatures (at 100 m) at different time scales, time series for both sections have been correlated with and without running mean (rm) filters. The non-filtered time series (rm = 1) represent the monthly variability, while the time series filtered by a running mean of 48 months (rm = 48) represent multi-annual variability. The correlations are performed at different lags, with negative lags defined such that OHT anomalies lead OVT/temperature anomalies.
The OVT dominates the OHT on monthly time scales at both sections (Figures 4a and 4b, black lines), with correlations close to 1 at lag 0. Compared to monthly time scales, the correlation between temperatures and OHT increases at all lags on longer time scales (multi-annual, Figures 4c and 4d, gray lines). The multi-annual correlations of OHT with OVT and temperature are similar at the BSO, while OHT shows lower correlations with temperature at the ISR (gray line). The correlation between OHT and OVT maximizes at lag 0, while the correlation between OHT and temperature maximizes at negative lags, especially on monthly time scales (Figures 4a  and 4b), suggesting that the OHT leads temperature changes by some months. These conclusions hold for both CMIP5 and CMIP6 models ( Figures S4 and S5, in blue and orange, respectively), even though there is a large spread in the strength of the correlations.

Atmospheric Mean State and Variability
The large differences in OVT could be linked to differences in wind forcing. We first regress for each model zonal wind at 850 hPa on the OVT at each section and calculate the multi-model mean of the regressions ( Figure 5) to identify the region where winds have the strongest influence on OVT. The jet stream location over the North Atlantic (green contours in Figure 5 and S6) is relatively similar in most models, which compared to observations is too zonal, strong, and extending toward Europe, a typical bias of climate models (i.e., Harvey et al., 2020;Oudar et al., 2020). The regression patterns indicate that when the zonal wind is particularly strong on the poleward side of the jet south of Iceland (positive regression values in the black box, Figure 5a), the volume of water  (d) show the correlation between temperature and OHT for each model at lag 0 and the colors indicate the correlations between temperature and OVT; red for strong positive correlations (r > 0.5), gray for weak positive correlations (0 < r < 0.5) and blue for negative correlations (r < 0). The significance levels (horizontal *) are based on the method described in Chelton (1983). Negative lags mean that OHT leads OVT/temperatures changes.  Table S1) using detrended and deseasonalised monthly means and then averaged (multi-model mean). Dots show regions where the sign of the regression is not the same for all models. Green contours show the zonal wind at 850 hPa (4 and 8 m s −1 ) from the multi-model mean . Black lines show the location of the sections used for calculating the OVT. The dashed box shows the region used to compute the mean zonal wind (U) reported in Table S1.
flowing through the ISR is enhanced. Strong winds in the same region and also further downstream have similar effects on the OVT at the BSO (Figure 5b).
To verify if differences in winds are linked to biases in OVT, we calculate the climatological area-averaged zonal wind in the box south of Iceland for every model and compare it to ERA-20C (Table S1). Models with stronger winds south of Iceland (arranged from low to high in Figure 3) are not systematically the models with larger OVT at the ISR. For example, GFDL-ESM2M has a climatological wind lower than MPI-ESM-MR (4.0 vs. 4.4 m s −1 , respectively) while the mean OVT at the ISR is much higher (9.9 vs. 6.3 Sv, Table S1 and Figure 3c). Likewise, the strength of the climatological wind is also not linked to the climatological OVT at the BSO, and similar conclusions hold when considering wind forcing in a box located further downstream, closer to the BSO, or if other variables (e.g., wind stress curl or mean sea level pressure) are regressed on the OVT (not shown).

Discussion
In general, from the analyzed models, there is an overall improvement and reduction in the inter-model spread from CMIP5 to CMIP6, especially with respect to temperature (Figure 3). For CMIP5, the inter-model differences in OHT are caused by both OVT and temperature differences, on the contrary to CMIP6 where they are mainly caused by differences in OVT. Since not all models provide OVT for CMIP5 and CMIP6, a direct comparison between the new generation of the same model is possible only for the three pairs IPSL-CM5A-LR/ IPSL-CM6A-LR, MPI-ESM-LR/MPI-ESM1-2-LR, NorESM1-M/NorESM2-LM. For both sections, the OVT in the NorESM and MPI-ESM models remain almost unchanged, while it increases considerably and assumes more realistic values in the IPSL-CM6A-LR model (Figure 3). The IPSL-CM5A-LR model has an elevated sea level height in the Arctic, similar to some other CMIP5 models (Richter et al., 2017), and the water is flowing from the Barents Sea toward the Nordic Seas and the North Atlantic (arrows in Figure 1b), leading to negative OVT. The reduced sea level height in the Barents Sea in the IPSL-CM6A-LR model (Figure 1a) leads to an improvement in the representation of the currents, OHT, OVT, and temperatures (see also Boucher et al., 2020).
Some studies have shown that the ocean resolution can improve the OVT, but the improvements might depend on the considered section and model (e.g., Docquier et al., 2020;Heuzé & Årthun, 2019;Olsen et al., 2016). Our results are not straightforward but show that the resolution alone can not explain the inter-model difference in OVT, as models with higher resolution do not have systematically higher or more realistic OVT through both sections ( Figure 3).
Observations indicate that the Atlantic Water entering the Barents Sea has warmed over the past decades (Skagseth et al., 2020;Yashayaev & Seidov, 2015). We analyzed temperature only till 2005, but also looked for the considered CMIP6 models at the temperature evolution at the BSO until 2014 ( Figure S8). Apart from EC-Earth3, changes in temperature during the last decades are overlaid by large interannual variability.
On multi-annual time scale, OHT correlated well (r > 0.8) with both OVT and temperatures at the BSO, in agreement with observations (Orvik & Skagseth, 2005), but less at the ISR, where the correlation between OHT and temperature is low (r ∼ 0.5, Figure 4c, gray line). To understand the different behaviors at the two sections, we color-coded the correlation between OHT and 100 m temperature based on the correlation values between OVT and 100 m temperature at lag 0 (in red/gray/blue for strong/weak/negative correlations, respectively). At the BSO, most models have high positive correlations between OHT and temperature as well as between OVT and temperature (red triangles, Figure 4d). This might offer an explanation for the good correlations of OHT with both OVT and temperature. At the ISR, however, we observe a large spread in correlations between OHT and temperature, and only a few models show that OVT and temperature anomalies are in phase (few red triangles, Figure 4c). As a result, the multi-model mean correlation between OHT and temperature at the ISR is lower than the one at the BSO. It is still unclear why the models behave so differently, and further studies are needed to clarify it.
The winds south of Iceland and along the Norwegian coast are also important for the OVT variability. When regressing the zonal wind at 850 hPa on OVT at the ISR and BSO, similar patterns emerge in all CMIP models (non-dotted regions in Figure 5), although the strength of the regression varies between models ( Figures S6  and S7). This means, for example, that at the BSO a change of one standard deviation of OVT is associated with a change of wind speed at the BSO of ∼0.5 m s −1 in the GFDL-ESM2G model and of ∼1.5 m s −1 in the 9 of 11 GFDL-ESM2M model ( Figure S7). Similar results are obtained if the wind is regressed on OHT ( Figure S9), as on shorter time scales the OHT reflects the variability in OVT. Winds south of Iceland affect the ocean circulation in terms of barotropic ocean circulation anomalies in the North Atlantic-Nordic Seas exchanges (Sandø et al., 2012), while changes in the strength of the North Atlantic subpolar gyre are mostly responsible for hydrographic anomalies in the inflow region to Nordic Seas (Asbjørnsen et al., 2019;Hátún, Sandø, Drange, Hansen, & Valdimarsson, 2005;Langehaug et al., 2019). The wind regression pattern at the ISR (Figure 5a) resembles the Iceland-Azores dipole of the North Atlantic Oscillation (Woollings et al., 2015), while positive regression values extend further east at the BSO (Figure 5b), indicating that winds along the Norwegian coast are important for OVT into the Barents Sea.

Conclusion
We analyzed how coupled climate models represent mean and variability of the poleward OHT, as it plays an important role in the energy budget of the Arctic and the sea ice extent therein. Based on the subgroup of CMIP models analyzed here, CMIP6 models have less inter-model spread and OHT mean values closer to observations compared to CMIP5 models, which show biases of several Terawatts at the ISR and BSO (Figure 3). When accounting for decadal variability, at the BSO, CMIP6 models reproduce OHT values comparable to observations and the spread in OHT across CMIP6 models arises mostly from differences in OVT.
OHT variability is strongly controlled by OVT on shorter and longer time scales at both sections ( Figure 4). On longer time scales temperature correlations with OHT become as strong as OVT correlations at the BSO, while they are weaker at the ISR, as the variations of OVT and temperature are not necessarily in phase.
Winds south of Iceland and along the Norwegian coast drive much of the OVT variability at the ISR and BSO, respectively ( Figure 5). The strength of this link varies across models especially at the BSO, indicating different magnitude in the responses of the ocean circulation to atmospheric forcing. The reason for the differences should be further investigated as they have a direct impact on the OHT variability, which at the BSO is key for the sea ice variability of the Barents Sea (Årthun et al., 2019).