NorESM1-ME (Bentsen et al., 2013; Tjiputra et al., 2013) is based on the Community Earth System Model (CESM1.0.4; Hurrell et al., 2013). Its atmosphere component CAM4-OSLO replaces the original prescribed aerosol formulation of the Community Atmosphere Model (CAM4; Neale et al., 2010) with a prognostic aerosol life cycle formulation using emissions and new aerosol–cloud interaction schemes (Kirkevåg et al., 2013). It also uses a different ocean component – the Bergen Layered Ocean Model (BLOM, formerly NorESM-O; Bentsen et al., 2013; Danabasoglu et al., 2014) – that originates from the Miami Isopycnic Coordinate Ocean Model (MICOM; Bleck and Smith, 1990; Bleck et al., 1992). The vertical density coordinate of the ocean component minimizes spurious diapycnal mixing, improving conservation and transformation of tracers and water masses. BLOM transports biogeochemical tracers of the ocean carbon cycle component – the Hamburg Ocean Carbon Cycle model (HAMOCC; Maier-Reimer et al., 2005) – which has been coupled to the physical ocean model and optimized for the isopycnic-coordinate framework (Assmann et al., 2010; Tjiputra et al., 2013). The Community Land Model (CLM4; Lawrence et al., 2011) and the Los Alamos Sea Ice Model (CICE4; Bitz et al., 2012), with five thickness categories and the elastic–viscous–plastic rheology (Hunke and Dukowicz, 1997), are adopted from CESM in their original form.

The atmosphere and land components are configured on NCAR's finite-volume 2∘ grid (f19), which has a regular 1.9∘×2.5∘ latitude–longitude resolution. The atmospheric component comprises 26 hybrid sigma–pressure levels extending to 3 hPa. The ocean and sea ice components are configured on NCAR's gx1v6 horizontal grid, which is a curvilinear grid with the northern pole singularity shifted over Greenland and a nominal resolution of 1∘ that is enhanced meridionally towards the Equator and both zonally and meridionally towards the poles. The ocean component comprises a stack of 51 isopycnic layers, with a bulk mixed layer representation on top consisting of two layers with time-evolving thicknesses and densities.

This section details the CMIP6 external forcing implementation into NorCPM1. Special note is made where the model setup deviates from the CMIP6 protocol. The updates of external forcing from CMIP5 to CMIP6 are expected to moderately alter the model's climate mean state, variability and anthropogenic trends. A detailed assessment of the impacts of the individual forcing upgrades is beyond the scope of this overview paper and needs to be addressed in separate studies.

The update that most affects the anthropogenic climate trend in NorCPM1 compared to the original NorESM1-ME is likely the change in anthropogenic emissions of aerosols and aerosol precursors (see Sect. 2.1.1 in Kirkevåg et al., 2013, for details of NorESM1-ME's CMIP5 aerosol implementation and emission datasets). We updated the emissions of SO2, SO4, fossil fuel and biomass burning of black carbon (BC) and organic matter (OM) to the CMIP6 pre-industrial and historical forcing (Hoesly et al., 2018). We used the Shared Socioeconomic Pathway (SSP) 2-4.5 scenario forcing, i.e. the “middle-of-the-road” scenario of the SSP2 socioeconomic family, with an intermediate 4.5 W m-2 radiative forcing level by 2100 (Gidden et al., 2019) for the post-2014 period in accordance with the DCPP protocol (Boer et al., 2016). BC emissions from aviation, omitted in the CMIP5 implementation, are now included. The representations of natural aerosol emissions of biogenic OM and secondary organic aerosol (SOA) production, dimethyl sulfide (DMS), tropospheric background SO2 from volcanoes, mineral dust and sea salt are kept unchanged.

We updated prescribed atmospheric greenhouse gas concentrations (except ozone) to Meinshausen et al. (2017) for the pre-industrial and historical period and to SSP2-4.5 (Gidden et al., 2019) for the post-2014 period. We applied globally uniform concentrations of the five equivalent greenhouse gas species (CO2, NH4, N2O, CFC-11 and CFC-12). The forcing data are at annual resolution and linearly interpolated between years by the model. Due to a bug in the merging of historical and future scenario forcing, values for 2015 and 2016 were erroneously set to 2014 values, while from 2017 all values correctly follow the scenario forcing. This results in a CO2 concentration error of less than 4 ppm, which has a negligible impact on the radiative forcing evolution but may impact ocean–atmosphere CO2 flux prediction.

We updated prescribed atmospheric ozone concentrations to Hegglin et al. (2016) (see also Checa-Garcia et al., 2018) for the pre-industrial, historical and post-2014 periods. After most simulations had been completed, we discovered that the date in our historical and post-2014 ozone input files was erroneously shifted by 23 months (e.g. the January 2000 observation is applied in February 1998). As a result, the model anticipates anthropogenic ozone changes approximately 2 years too early. The 1-month shift in the seasonal cycle may have dynamical implications particularly for the stratosphere if compared against the pre-industrial simulation that does not contain the shift.

We updated the solar forcing to the CMIP6 product (Matthes et al., 2017) as well as the stratospheric volcanic forcing (Revell et al., 2017; Thomason et al., 2018). In NorESM1-ME used in CMIP5, stratospheric volcanic aerosol loadings were prescribed, and the model then computed the resulting radiative forcing assuming certain aerosol properties and particle growth. In CMIP6, pre-computed optical parameters are provided instead and prescribed directly to the radiation code of the models in order to reduce inter-model spread in responses. NorCPM1 prescribes a zonally uniform space–time-varying extinction coefficient, single scattering albedo and hemispheric asymmetry factor for 14 solar (i.e. shortwave covering infrared, visible and ultraviolet) and 16 terrestrial (i.e. thermal longwave) wavelength bands. Despite significant changes between volcanic forcing implementations, we found only minor differences when comparing the radiative forcing to the 1991 Mt. Pinatubo eruption, with the CMIP6 implementation producing a less distinct peak and a wider tail compared to the CMIP5 implementation (not shown). Additionally, the CMIP6 experimental protocol now requires the use of a stratospheric volcanic background forcing (monthly climatology computed from historical 1850–2000 volcanic forcing) during pre-industrial and future eras, whereas the use of such background forcing was optional in CMIP5 and not implemented in the original NorESM1-ME.

We updated the land surface types and transient land use to be consistent with the Land-Use Harmonization version 2 (LUH2) dataset (Lawrence et al., 2016). For the post-2014 period, NorCPM1 deviates from the DCPP protocol as it uses land-use data from SSP3-7.0 scenario (which were the only LUH2-version land-use scenario data for CLM4 available to us at that time) instead of the recommended SSP2-4.5. For CMIP6 DCPP, the main interest is in the historical period (1850–2014). From the future scenario, only the period prior to 2030 is of interest for DCPP decadal outlooks, during which time the differences between the SSP scenarios are still small. We expect this deviation to have a minimal impact on the outcomes of NorCPM1's near-future climate outlooks (note that the greenhouse gas concentrations still follow the SSP2-4.5 scenario). Data users who specifically investigate near-future land-use-related climate feedbacks are, however, advised to either exclude NorCPM1 from their analysis or take the land-use differences between SSP2-4.5 and SSP3-7.0 into consideration. A supporting simulation experiment revealed that the update to LUH2 caused an unrealistic land–cryosphere cooling trend over the historical period in NorCPM1 (Fig. S3, S4 and text in Sect. S1 in the Supplement). The cause and ramifications are subject to further investigation.

Other forcings not mentioned above (e.g. nitrogen deposition) are kept the same as in the CMIP5 model setup.

This section describes code changes unrelated to forcing upgrades and retuning of NorCPM1 relative to NorESM1-ME that was necessary due to forcing and code changes.

An error in the aerosol code that caused an overestimation of the BC load was identified in NorESM1-ME and a correction has been proposed (details in Graff et al., 2019). The correction of this error is applied in NorCPM1 and causes a slight cooling of the climate with a -0.5 ∘C difference in the Arctic (Fig. S4).

NorESM1-ME featured too-thick sea ice on the shelf seas of the eastern Eurasian Arctic due to spurious variability in ocean velocities enhancing ice formation in the region (Seland and Debernard, 2014; Graff et al., 2019). Increasing the built-in velocity damping applied to shallow ocean regions in MICOM reduces the regional thickness bias in NorCPM1.

NorESM1-ME's ocean biogeochemistry output has been subject to substantial grid noise. The noise was traced back to a local tracer mass correction that was applied because surface freshwater fluxes do not change the ocean column mass in the model. For instance, a positive surface freshwater flux into the ocean – assuming tracer concentrations of this flux to be zero – will reduce the ocean tracer concentrations. Without a compensating increase in column water mass, such a reduction in concentrations inevitably leads to a reduction (i.e. non-conservation) in column-integrated tracer mass. The correction in NorESM1-ME locally scales the tracer concentrations such that the column-integrated tracer mass is conserved for each grid cell. This correction scheme has the weakness that it produces considerable spatial noise at the surface and artificial temporal variability and trends in the deep ocean. These problems are mitigated in NorCPM1 by replacing the local scaling with a global scaling (i.e. the same correction scale factor is used for all grid cells) that enforces global instead of local tracer conservation.

Using the original parameter settings of NorESM1-ME, the surface climate of the physical component of NorCPM1 drifts towards an unrealistic cold state with exacerbated biases as a consequence of introducing stratospheric background volcanic forcing, changing the land surface boundary conditions and correcting the bug in the aerosol code. To avoid a deterioration of climate performance and to re-equilibrate the climate, we therefore retuned NorCPM1 relative to NorESM1-ME. Specifically, we increased the condensation threshold for low clouds (from 90.05 % to 90.08 %) and also decreased the snow albedo over sea ice by adjusting parameters that affect snow metamorphosis (from r_snw = 0, dt_mlt_in = 1.5, rsnw_mlt_in = 1500 to r_snw=-2, dt_mlt_in=2.0, rsnw_mlt_in = 2000).

After the retuning, NorCPM1 neither shows obvious climate improvements nor global-scale deterioration compared to NorESM1-ME, though some regional differences exist (see Sect. S1). Since the model characteristics did not substantially change, we performed only a short pre-industrial spin-up of 250 years for NorCPM1 – using the year-1000 state of NorESM1-ME's spin-up (corresponding to the year-100 state of its CMIP5 pre-industrial control simulation) as initial conditions – in order to allow the upper ocean, sea ice and land surface to equilibrate to the model code and forcing changes.

For the period 1950–2010, SST data are taken from the Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST2.1.0.0; John Kennedy, personal communication, 2015; and Nick Rayner, personal communication, 2015) that has also been utilized in the construction of the coupled reanalysis CERA-20C (Laloyaux et al., 2018). HadISST2 provides 10 realizations of monthly gridded SST over 1850–2010 with a 1∘ resolution. The spread between the realizations, which depends on time and space, is designed to reflect uncertainties in gridding and combining SST in situ observations, retrievals from AATSR (Advanced Along-Track Scanning Radiometer) reprocessing and AVHRR (Advanced Very High Resolution Radiometer) retrievals. We consider the average and variance of these 10 realizations as the observations and their error the variance. We use monthly SST data from the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation SST version 2 (OISSTV2; Reynolds et al., 2002) for the period 2011–2018, when HadISST2 data are not available. OISSTV2 provides weekly SST and weekly observation error variance, in addition to monthly SST. The observation error variance of the monthly data is estimated as the harmonic mean of weekly error variances provided by OISSTV2. We have confirmed through a separate reanalysis and set of hindcasts overlapping between 2006 and 2010 that the transition from HadISST2 to OISSTV2 does not cause discontinuities nor a significant change of prediction skill (not shown). SST data in the regions covered by sea ice are not assimilated; these regions are identified using the sea ice mask in HadISST2 or OISSTV2.

Subsurface ocean temperature and salinity hydrographic profile observations are taken from the EN4 dataset (EN4.2.1; Good et al., 2013). The EN4 dataset consists of profile data from all types of ocean profiling instruments, including those from the World Ocean Database, the Arctic Synoptic Basin Wide Oceanography project, the Global Temperature and Salinity Profile Program and Argo. The EN4 profile data are available from 1900 to the present, including data quality information and bias corrections (Gouretski and Reseghetti, 2010). Data that lie within the mixed layer of NorCPM's first ensemble member are not assimilated in order to maximize the impact of SST assimilation in the mixed layer. The uncertainty of observed hydrographic profiles is not available, and we have used the estimate provided by Levitus et al. (1994a, b) and Stammer et al. (2002).

The EnKF (Evensen, 2003) is an advanced, ensemble-based and recursive DA method. One advantage of the EnKF is its probabilistic nature that provides model uncertainty quantification through Monte Carlo ensembles (Fig. 1; red box). Moreover, the EnKF provides multivariate and flow-dependent updates, meaning that information is propagated from the observed variables to the unobserved variables dependent on the evolving state of the climate system; this is crucial to capture shifts in regimes (Counillon et al., 2016). To work efficiently, the EnKF needs an ensemble size sufficiently large to span the model subspace dimension (Natvik and Evensen, 2003; Sakov and Oke, 2008). Localization reduces the spatial domain of influence of observation which drastically reduces the need for a large ensemble size. With the recent improvements of high-performance computing, the use of the EnKF for seasonal-to-decadal climate prediction has emerged (Zhang et al., 2007; Karspeck et al., 2013; Counillon et al., 2014; Brune et al., 2015; Sandery et al., 2020). Because NorCPM1 performs monthly assimilation updates, the numerical cost for performing the updates is small compared to the cost of integrating the model.

NorCPM1 uses a deterministic variant of the EnKF (DEnKF; Sakov and Oke, 2008). The DEnKF updates the ensemble perturbations around the updated ensemble mean using an expansion of the expected correction to the forecast. This yields an approximate but deterministic form of the traditional stochastic EnKF that outperforms the latter, particularly for small ensembles (Sakov and Oke, 2008).

In order to generate the coupled reanalysis, we assimilate in the middle of the month all observations available during that month and update the instantaneous model state. Assimilation of monthly SST data implies that the innovation (i.e. observations minus model state) compares variability of an instantaneous model snapshot with that of monthly averaged observations. An alternative has been investigated, where data have been assimilated at the end of the month comparing the monthly averaged model output with the SST data. However, the latter approach shows poorer performance for reanalysis and no improvements during prediction (Billeau et al., 2016). This suggests that comparing model snapshots with monthly data is not a critical approximation for our system.

We perform anomaly assimilation in which the climatology of the observations is replaced by the model climatology. Considering the impact of the choice of the climatology reference period on the performance of reanalysis, NorCPM1 contributes two coupled reanalysis products to CMIP6 DCPP, labelled assim-i1 and assim-i2 (see Fig. 1; Sect. 2.3 for experiment overview). In assim-i1, the climatology is defined over the reference period (1980–2010) when assimilating EN4.2.1 hydrographic profile data and HadISST2 data, but over the period 1982–2010 when assimilating OISSTV2 data (i.e. beyond 2010) because OISSTV2 was not available before 1982. The model climatology is calculated from the ensemble mean of NorCPM1's 30-member no-assimilation historical experiment (Sect. 2.3). The observed climatology for assimilating hydrographic profile data is computed from EN4 objective analysis (Good et al., 2013). In assim-i2, the climatology reference period is 1950–2010. For the hydrographic profile and HadISST2 data, the climatology is computed for the longer reference period. However, the climatology for the OISSTV2 data (i.e. after 2010) is calculated from concatenated data of HadISST2 for 1950–1981 (when OISSTV2 is not available) and OISSTV2 for 1982–2010.

Together with changing the climatology reference period, we test two versions of the DA system. Time and resource constraints prevented us from testing these two aspects separately. In assim-i1, we only update the ocean state based on oceanic observations. In this case, the system belongs to the category of weakly coupled DA system (WCDA; Penny and Hamill, 2017), where the update in the ocean component of the system only influences the other components during model integration. In assim-i2, we allow the oceanic observations to update the ocean and the sea ice components. In this case, the system is a strongly coupled DA system (SCDA), where the oceanic observations influence the sea ice component of the system both at the DA step and during the model integration. To avoid confusion with atmosphere–ocean SCDA (e.g. Penny et al., 2019), we will refer to the assim-i2 approach as OSI-SCDA (where OSI stands for “ocean–sea ice”). The OSI-SCDA approach assures a more consistent initialization across components and exploits the longer temporal coverage of oceanic observations relative to sea ice observations (see also Appendix A). To update the sea ice state, we follow Kimmritz et al. (2018), where an optimal way to update the sea ice state was identified: the EnKF updates the sea ice concentrations of the individual thickness categories, while the other sea ice state variables (volume per thickness category, top surface temperature, snow and energy of melting) are post-processed to ensure physical consistency and maximize the benefit of the updates in the sea ice concentrations. In particular, the volume of the individual sea ice category is scaled proportionally to the updated individual concentration so that the prior individual category thickness is preserved. This approach ensures that the individual thickness values remain in their prescribed range but still allow a large reduction of total ice thickness error (Kimmritz et al., 2018).

The DA scheme updates all ocean physical state variables. In an isopycnal-coordinate ocean model, the layer thickness (a time-varying ocean state variable) is by definition always strictly positive. Due to normality assumptions, the linear analysis update of the EnKF may return unphysical (negative) values. To solve this issue, we use the aggregation method proposed by Wang et al. (2016), in which we iteratively aggregate layers in the vertical until no unphysical value is returned by the EnKF. This scheme does not significantly increase the computational cost of DA but avoids the drift in heat content, salt content and mass that would otherwise be caused.

The reanalysis system uses 30 ensemble members. The ensemble size is relatively small compared to the dimension of the system. In order to limit spurious correlation caused by sampling error, we use localization (Houtekamer and Mitchell, 1998). We use the local analysis framework (Evensen, 2003) in which DA is performed for each horizontal grid cell and that uses only observations around the targeted grid cell to limit spurious correlation as ocean covariance decays with distance. This also reduces the dimension of the problem. In order to avoid discontinuity in the increment at the edge of the local domain, we use the reciprocal of the Gaspari and Cohn function (a function of the distance between observation location and the target model grid; Gaspari and Cohn, 1999) to taper observation error variance (i.e. to reduce the influence of observations). We taper innovation and ensemble perturbations with the square root of the Gaspari and Cohn function, which is equivalent to the tapering of observation error variance. The localization radius used in NorCPM1 is a bimodal Gaussian function of latitude with a local minimum of 1500 km at the Equator where covariances become anisotropic, a maximum of 2300 km in the midlatitudes and another minimum in the high latitudes where the Rossby radius is small (Wang et al., 2017).

Observation errors are assumed to be uncorrelated. For the SST product, this assumption clearly fails because the SST data are the result of an analysis. We have therefore decided to only assimilate the nearest SST data. For the observed hydrographic profile, the independence of observation errors is more plausible. The observation error for the profile is considered to be the sum of the instrumental error (defined as in Levitus et al., 1994a, b, and Stammer et al., 2002) and the representativity error accounting for the model unresolved processes and scales. As detailed in Wang et al. (2017), the representativity error is estimated offline from the innovation and the ensemble spread of the 30-member historical experiment, to ensure that the reliability of the ensemble is preserved (i.e. the truth and the ensemble members can be considered to be drawn from the same underlying probability distribution function). The profile observation error is inflated by a factor of 3 in sea-ice-covered regions where the observation climatology critical for anomaly assimilation is highly uncertain because of the lack of observations. When there are several observations falling within the same grid cell, these observations are “superobed”: all observations falling within the same grid cell are averaged and the instrumental error variance is reduced as the harmonic sum of the individual instrumental error variances (Sakov et al., 2012). Note that the representativity error term mainly relates to the capability of the model to represent the truth and is thus not reduced by the superobed technique.

As further detailed in Sect. 2.3, the initial ensemble used at the start of the reanalyses (year 1950) is branched from a 30-member historical experiment. The historical experiment was initialized in 1850 from the end of a pre-industrial spin-up simulation (Sect. 2.1.3), with initial ensemble spread being generated by adding small random noise O(10-10 K) to the ocean temperatures and then integrated for 100 years, allowing the spread to grow. This approach ensures that the initial ensemble spans sufficient spread in the interior of the ocean needed for a well-calibrated EnKF and that each member is synchronized with respect to the timing of the external forcing. To avoid an abrupt start of the assimilation, the observation error variance is inflated by a factor of 8 during the first assimilation update; every two assimilation updates, the factor is decreased by one until it reaches 1, as suggested by Sakov et al. (2012). The ensemble spread is sustained during the reanalysis using the following inflation techniques. The DEnKF (Sect. 2.2.2) limits the need for inflation to some extent. We use the moderation technique of Sakov et al. (2012) – while the ensemble mean is updated with the observation error variance, the ensemble spread is updated with the observation error variance by a factor of 4. We also use pre-screening of the observation; i.e. the observation error variance is inflated so that the analysis remains within 2 standard deviations of the forecast error from the ensemble mean of the forecasts.

Fransner et al. (2020) showed with perfect model predictions using NorESM1-ME that the initial state of the biogeochemical tracers has a negligible impact on the predictability of ocean biogeochemistry beyond lead year 1. During the assimilation process, the thickness of the isopycnal layers changes, while the tracer concentrations on the layers remain unchanged, meaning that we allow assimilation to change the mass at every location. However, this does not introduce a drift as long as the analysis is unbiased (i.e. the assimilation does not systematically pull the model climate in one direction). This was verified with a 10-year long twin experiment where SST from a pre-industrial control run was assimilated every month into a run with 30 members. The total change in the biogeochemical tracer mass over this period was negligible; the largest drift was found for silicate that corresponded to 0.5 % of its global mass. With this approach, the global near-surface primary production approached that of the control run, showing that there is a good potential for constraining biogeochemical variability by assimilating SST only in our model setup. This might be improved by the additional assimilation of sea ice and temperature and salinity profiles. Other studies have shown that assimilation of ocean physics improves the representation of ocean biogeochemistry (e.g. Séférian et al., 2014; Li et al., 2016).

We use the innovation to monitor the performance of assimilation over time (Sakov et al., 2012; Counillon et al., 2016), which is defined as the ensemble mean of the model forecast state (at assimilation time on the observational grid) minus the observation. In combination with the ensemble spread and the observation error standard deviation, it can be used to assess the reliability of the ensemble system (Sakov et al., 2012). Ideally, the reliability is checked for each grid cell. Under an ergodicity assumption, we define global statistics based on innovation as follows: 1wi=ai∑jaj,2d‾=∑iwidi,3d^=∑iwidi2,4σf‾=∑iwidif,5σo‾=∑iwidif,6σt‾=σf‾2+σo‾2, where ai is the area of the model grid cell i where the gridded observation is located, wi is the area weight, di is the innovation, σif is the ensemble spread (standard deviation) of forecasts, and σio is the standard deviation of observation error at the grid cell i at a given time. The observations are binned onto the model grid and into 42 depth bins that are also used to bin the model data. In a perfectly reliable system, the RMSE d^ matches σt‾, i.e. the forecast ensemble spread combined with the observational error. Figure 2 shows the time evolution of the innovation statistics for SST, ocean temperature and salinity in assim-i1 (the evolution in assim-i2 is similar to that in assim-i1 and therefore not shown).

For SST (Fig. 2a), d^ is stable with an accuracy of approximately 0.5 K. The bias d‾ is stable as well, fluctuating around zero. This is expected as we use anomaly assimilation (with the bias estimated from the historical experiment that does not use assimilation). It also indicates that the assimilation with a monthly cycle largely eliminates the conditional bias, caused by model error in the sensitivity to the forcing and thus corrects the forced long-term trends. The ensemble spread σf‾ is also relatively stable. There is a drop in observation error standard deviation σo‾ in 1982 with the emergence of satellite measurements and in 2011 with the transition from HadISST2 to OISSTV2 (see Sect. 2.2.2). The reliability of the system is good until 1982 (compare blue and magenta curves), but then σt‾ drops slightly below d^ indicating that the introduction of satellite data overly reduces the observational error estimates applied during assimilation. When the observation error reduces, the model accuracy does not increase accordingly, most likely because the model fails to represent features seen in the observations. Adding a representativity error during the satellite era to improve the reliability should be explored in future development. For ocean temperature (Fig. 2b), the RMSE d^ decreases over time from 1.5 to 1.2 K. The bias d‾ is positive prior to 1970 but near zero afterwards. The distribution of the observations prior to 1970 is considerably uneven with a predominance in the North Atlantic region and the bias d‾ does not reflect the globally averaged bias. The total error standard deviation σt‾ is smaller than the RMSE, suggesting that the ensemble system overestimates its accuracy (i.e. the ensemble spread is too small). For ocean salinity (Fig. 2c), the RMSE d^ is stable prior to 2000 and after 2005. The decrease in the RMSE d^ in the period 2000–2005 is due to the introduction of Argo floats. There is a negative bias d‾ in salinity prior to 2000. The bias d‾ remains negative but is relatively small after 2000. As for ocean temperature, there is a mismatch between the RMSE d^ and total error standard deviation σt‾ indicating that the system is overconfident.

Anomaly assimilation should by design have a negligible effect on the climate mean state. Non-linear propagation of the assimilation updates between the assimilation updates can, however, yield a post-assimilation change in the mean state in regions where there are no observations. Furthermore, assim-i1 and assim-i2 are not using the same reference period (1980–2010 versus 1950–2010) and thus differences in the mean state can occur as because of different sampling of internal multidecadal climate variability in the observations and due to errors in the model's forced climate trend. Additionally, in the computation of observational profile anomalies, we subtracted the climatology of the objective EN4 analysis, which is inaccurate in regions with sparse data coverage. This can further impact mean states of the reanalyses.

We verify the effect of DA on the climatology by comparing mean state biases of our two assimilation products with those of the historical experiment (Fig. 3). The mean state changes due to assimilation in upper ocean temperature (T300) and salinity (S300) averaged over the top 300 m, sea surface height (SSH) and surface air temperature (SAT) are generally an order of magnitude smaller than the absolute biases of historical. The relative impact of DA on the biases is thus mostly below 10 % of its absolute magnitude. An exception is the Arctic, where the assim-i2 assimilation increases the S300 bias and decreases the SAT bias. This is consistent with that the assim-i2 assimilation tends to remove sea ice mass, leading to higher SAT because of the thinner ice and higher surface salinity because the model tries to grow back sea ice, ejecting salt during that process. Despite assimilating climate anomalies, the sea ice update in assim-i2 largely reduces the climatological sea ice thicknesses towards more realistic values, whereas the climatology of assim-i1 remains unchanged (Fig. 4). In a similar NorCPM version with climatologically too-thick Arctic sea ice, Kimmritz et al. (2019) found anomaly assimilation of observed sea ice concentration (updating the area in different thickness categories of the model using OSI-SCDA) to yield large reductions in total ice thickness error. Here, we show that similar bias reduction is achieved by a strongly coupled update of the sea ice states using ocean observations. The exact reason for this behaviour is subject to further investigation.

The effect the assimilation has on the mean state of nutrients was assessed by investigating the difference between the ensemble means of historical and assim-i1 (Fig. 5a–c, e–g). From previous studies (While et al., 2010; Park et al., 2018), we know that the equatorial regions are the most susceptible to errors originating from assimilation of physical variables. However, since sea ice, an efficient blocker of sunlight, is updated by weakly coupled DA, some differences in the polar region are also expected. There is indeed an increase in primary production in the polar regions in the respective summers of each hemisphere. On average, there is an increase in nutrients in the Arctic, indicating that part of the increase in productivity is caused by an increase in mixing as the ocean is exposed to the atmosphere. There are very small differences in the mean nutrients in the Southern Ocean.

Some impact of DA on the mean state of assim-i1 is also seen in the surface waters of the tropical oceans; these changes do not have a pronounced seasonal variation. The largest changes to the surface nitrate and phosphate occurred in the eastern Pacific, while for silicate there was also an increase in the concentration in the Bay of Bengal. The increase in silicate in the Bay of Bengal occurs throughout the water column; there is also a similar increase in the water column of the western Tropical Pacific. For nitrate and phosphate, the increase in concentration is confined to the upper 500–1000 m. At the surface and down to about 1000 m, all three nutrients have increased concentrations along the Equator. Below 1000 m, in the eastern equatorial Pacific nitrate has increased concentration, while silicate and phosphate have decreased concentrations compared to historical. An increase in nitrate with a simultaneous decrease in silicate indicates that there is some movement in the water masses that leads to decreased silicate and phosphate and at the same time an increase in oxygen in assim-i1 (Fig. 5d, h); this reduces the denitrification that occurs below the thermocline in the tropical Pacific. Furthermore, we compared the magnitude of the computed ensemble mean differences between assim-i1 and historical along the Equator with the variability of the historical ensemble. The changes are always within 1 standard deviation of the ensemble variability – i.e. small relative to the internal variability – except for oxygen in a small region at around 2000 m in the equatorial Atlantic where there is a large increase in oxygen. We therefore conclude that the changes to nutrients in assim-i1 are caused by changes to circulation and temperature and not by unphysical mixing caused by the assimilation.

We first evaluate the synchronization of physical ocean variability globally at grid scale interpolated to 5∘×5∘. Figure 6 shows ACCs for annual SST, T300, S300 and SSH for assim-i1 along with ΔACCs for assim-i1 – historical and assim-i2 – assim-i1. The ACCs for assim-i1 are high and statistically significant across variables in most regions. The ΔACCs for assim-i1 – historical show that the assimilation of ocean data significantly improves the synchronization of SST, T300 and S300 with observations in most regions. Significant improvements for T300 are in the Pacific and North Atlantic. The improvements for S300 are similarly high and largest in the Arctic, albeit showing localized degradation in some coastal regions. For SSH, ACCs are increased in the subpolar North Atlantic (SPNA), tropical Pacific and Indian oceans, but decreased in the South Atlantic due to the fact that the long-term trend is degraded by the weakly coupled DA in the assim-i1 system (not shown). Missing contributions from land ice in the model possibly play a role in the degradation. The small ΔACCs for assim-i2 – assim-i1 suggest that the choice of the climatology reference period does not play an important role for the overall performance of the reanalysis in terms of variability. Significant differences appear close to the sea-ice-covered areas and are thus likely related to the sea ice state updated via OSI-SCDA in assim-i2. However, we have limited confidence in the EN4 objective analysis that we used for validation in ice-covered regions where subsurface observations are sparse.

We evaluate the effect of assimilation on large-scale climate indices of leading modes of variability (Fig. 7). The North Atlantic subpolar gyre (SPG) circulation exerts strong control on subpolar North Atlantic (SPNA) temperature variations (e.g. Häkkinen and Rhines, 2004), affects the Atlantic meridional overturning circulation (AMOC) by regulating the poleward transport of Atlantic water (Hátún et al., 2005) and has a wide range of marine environmental impacts (e.g. Hátún et al., 2016). The SPG circulation index is here defined as the anomalous SSH averaged over the SPNA box (48–65∘ N, 60–15∘ W) (Lohmann et al., 2009). A positive (negative) SPG index reflects a weak (strong) barotropic mass transport in the SPNA region that usually coincides with a warm (cold) SPNA. We note that more elaborated index definitions based on principle component analysis of SSH and subsurface density are likely to capture circulation features and associated water mass variability better than our simple index (Koul et al., 2020). Figure 7a shows the SPG index over 1950–2018 in historical, assim-i1, assim-i2 and observations (altimetry data available from 1993). The observed SPG index exhibits an abrupt shift from a strong to a weak circulation around 1995, that has been linked to direct North Atlantic Oscillation (NAO) influence (Häkkinen and Rhines, 2004; Yeager and Robson, 2017) and NAO-related preconditioning of the ocean circulation state (e.g. Lohmann et al., 2009; Robson et al., 2012). The ensemble mean of the historical ensemble does not show the shift, but a slow long-term increase likely related to anthropogenic global sea level rise. The min–max range of the historical ensemble nevertheless bounds the observed SPG index, suggesting that the model range of variability is not inconsistent with the observed trajectory. The ensemble means of assim-i1 and assim-i2 show pronounced strong and weak SPG index phases and match well the observed SPG index changes during 1993–2018. Their simulated weak phase during 1950–1970 and strong phase during 1980–1997 are also in good agreement with other model studies (e.g. Msadek et al., 2014). The ensemble ranges of assim-i1 and assim-i2 are much smaller than that of historical, indicating the ensemble members are well synchronized by the assimilation. Despite showing similar decadal-scale variability, assim-i1 and assim-i2 have different means and long-term trends. The stronger SPG circulation of assim-i2 goes in tandem with a stronger AMOC, and it is likely that these two are related (Eden and Willebrand, 2001; Eden and Jung, 2001; Böning et al., 2006).

The strength of AMOC is measured continuously from April 2004 at 26.5∘ N by a joint US–UK Rapid Climate Change – Meridional Overturning Circulation and Heat flux Array (RAPID-MOCHA; Johns et al., 2011). Accordingly, we define the AMOC index as the yearly anomalies of overturning transport maximum at 26.5∘ N. Figure 7b shows the AMOC indices of historical, assim-i1 and assim-i2 and observations. The ensemble mean of historical, a measure for the simulated anthropogenic trend, rises before the mid-70s and then slowly declines. In contrast, the two assimilation products show a weakening before the mid-70s, followed by a strengthening that is consistent with a dominantly positive observed NAO during that period (Robson et al., 2012; Yeager and Robson, 2017; Zhang et al., 2019). The simulated AMOC strongly declines after 2005, though not as rapidly as in the observations, and flattens after 2010. Similar results have been shown in previous studies (e.g. Keenlyside et al., 2008; Karspeck et al., 2017). As for SPG circulation, assim-i1 and assim-i2 show similar multiyear AMOC variations but different long-term trends. Most notably, assim-i1 stays below the ensemble mean of historical over the entire period, while assim-i2 surpasses historical around 1990, which is more consistent with the anomalously strong AMOC during the mid-90s SPG shift. Results from a supporting experiment suggest that the stronger circulation in assim-i2 is primarily caused by the different climatological period but also partly by the OSI-SCDA update of sea ice (Fig. S8 and related text in Sect. S2).

The Atlantic Multidecadal Oscillation (AMO) – or Atlantic Multidecadal Variability – refers to large-scale, low-frequency SST variations in the North Atlantic, with linkages to AMOC variability (Keenlyside et al., 2015; Yeager and Robson, 2017). Following Enfield et al. (2001), we define the AMO index as the 10-year running mean of linearly detrended SSTs averaged over the entire North Atlantic (0–65∘ N, 0–80∘ W). Figure 7c shows the index in observations, historical, assim-i1 and assim-i2. In agreement with observations, the indices of all three experiments are in a warm phase during 1950–1965 and 1995–2018 and a cold phase during 1965–1995. However, the historical ensemble mean (representing the forced response of the model) underestimates the amplitude, exhibits a longer cold phase as well as an upward trend after 2010, when observations show a downward trend. As a result of assimilating SST observations, the AMO indices of assim-i1 and assim-i2 both follow the observed index with only minor departures. assim-i2 shows a slightly weaker post-2000 downward trend than assim-i1 and observations, either related to differing sea ice behaviour or differences in AMOC.

While ocean dynamics in the Atlantic basin give rise to multiyear climate predictability, ENSO variability is an important source for seasonal and interannual predictability. The ESM features realistic ENSO characteristics (Figs. S5, S6 and text in Sect. S1). But how well do monthly DA updates synchronize the model's ENSO variability with the observed one? Figure 7d shows the monthly Niño 3.4 – computed as the average of SST in the region 5∘ S–5∘ N, 120–170∘ W – for historical, assim-i1 and assim-i2 and HadISST. Both assim-i1 and assim-i2 accurately reproduce the observed index, showing a perfect match of the large 1998 event but slightly underestimate other peaks. We attribute the good performance to DA in NorCPM1 constraining well thermocline depth (equivalent to warm water volume) in the equatorial Pacific that is critical to develop ENSO events (Meinen and McPhaden, 2000; Wang et al., 2019). The Niño 3.4 indices of assim-i1 and assim-i2 are almost identical, meaning that the climatology reference period defined in anomaly assimilation and the jointly updated sea ice state have little impact on the equatorial Pacific. The ensemble mean of historical has a smaller amplitude and is only marginally correlated with the observed index (r=0.2, p=0.085, alpha = 0.1), suggesting a potential small contribution from external forcing.

Last, we consider the effect of assimilation on the global-mean SST representation. Figure 7e shows the anomalies of global-mean SST evolution for historical, assim-i1, assim-i2 and HadISST. historical captures the long-term warming trend and some shorter volcanic cooling events (e.g. after the 1963 Mt. Agung and 1991 Mt. Pinatubo eruptions). assim-i1 and assim-i2 additionally capture the high-frequency variability on top of the forced signal. The assimilation experiments show minor discrepancies with respect to observations, such as a too-weak post-eruption Mt. Pinatubo recovery and a seemingly underestimated 1998 El Niño imprint on global-mean SST. assim-i2 exhibits a slightly more positive trend after 2010 compared to assim-i1, which likely is the imprint of the more positive trend in AMO on global-mean SST. The behaviour of global-mean SAT (Fig. 7d) is similar to that of SST and will be further addressed in Sect. 3.1.6.

The correlation skills of annual-mean primary production (PP), pCO2 and air–sea CO2 fluxes for the assimilation experiments are shown in Fig. 8. For PP, the total skill (with contribution from external forcing) is high and field significant in the tropical Pacific and Indian oceans, with some skill in the subtropical oceans. The ΔACCs between assim-i1 and historical, measuring assimilation benefit, are not field significant and smaller in value than the ACCs of assim-i1, indicating that most skill comes from the external forcing. Still, large regions in the tropical Pacific and Indian oceans feature high ΔACCs that are locally significant. The ΔACCs between assim-i2 and assim-i1 are generally small. The largest differences are found in the polar regions, although precaution should be taken when evaluating the PP in these regions due to the low coverage of satellite data.

For the CO2 fluxes and pCO2 (linearly detrended), the total skill is high and field significant over the tropical and subtropical oceans. Exceptions are eastern part of the tropical Pacific, and the southern subtropical Pacific for the CO2 fluxes. For CO2 fluxes, there is also high skill in the southern part of the Southern Ocean and in the Nordic Seas. This is not the case for pCO2, which suggests that part of the CO2 flux skill might be related to successful synchronization of sea ice variability. As for PP, the ΔACCs relative to historical are considerably smaller than the ACCs of assim-i1, despite the linear detrending that was applied to the CO2 fields before the ACC computation. The ΔACCs remain field significant in parts of the subtropical and tropical oceans, although with a reduced westward extension of the skilful areas. Contrary to expectation, the SPNA shows little skill. As for PP, skill differences for CO2 fluxes and pCO2 are small between assim-i1 and assim-i2.

We evaluate the success of our assimilation in phasing sea ice variability. We use ACC maps of annual-mean sea ice concentration and HadISST (Rayner et al., 2003) data from 1950–2018 as a benchmark (Fig. 9).

Over the Arctic, assim-i1 features overall high skill. While much of this skill is from the externally forced trend, positive assim-i1 – historical ΔACCs show that ocean DA considerably improves the agreement in the marginal ice zones. Positive ΔACCs for assim-i2 – assim-i1 show that updating the sea ice state via OSI-SCDA of ocean observations further improves the agreement, including over the central Arctic.

Over the Antarctic, assim-i1 shows modest to high skill and only isolated negative ACCs. Strikingly, the assim-i1 – historical ΔACCs are as high or higher than the absolute ACCs of assim-i1. This means that assimilation corrects for the negative trend in the historical ensemble. OSI-SCDA again improves the skill (Fig. 9f), especially close to the coast where the ACCs of assim-i1 are low or negative (Fig. 9b).

Because our DA is weakly coupled with respect to the atmosphere, we expect a partial synchronization of atmospheric variability from the combined influence of the ocean surface–sea ice states and the external forcings. The reanalysis performance provides a hypothetical upper bound for the achievable atmospheric–land prediction skill with our system, assuming close-to-perfect prediction of ocean variability and skilful prediction of sea ice variability. We assess the synchronization of atmospheric variability with ACCs of annual-mean SAT, precipitation over land (PR), sea level pressure (SLP) and 500 hPa geopotential height (Z500) for assim-i1 (Fig. 10a–d). We also consider ΔACCs for assim-i1 – historical and assim-i2 – assim-i1 to isolate skill contribution from DA and skill differences between two reanalysis products.

For SAT, the ACCs of assim-i1 are high over both ocean and land. Most of the DA benefit is located over the oceans, as revealed by the ΔACCs for assim-i1 – historical, with benefits over land mainly found in the tropical regions and also over northwest North America, i.e. regions that are strongly affected by ENSO variability. assim-i2 does not show any significant skill improvement over assim-i1, despite the sizable improvements in sea ice variability when updating the sea ice state via OSI-SCDA. This is likely because the improvements in sea ice extent (Fig. 9) occur mostly during summer when they have little impact on surface temperatures (Deser et al., 2010). For global-scale SAT synchronization, the global warming hiatus at the beginning of the 21st century, which has been attributed to both internal variability and external forcing (e.g. Medhaug et al., 2017), makes an interesting test case. Figure 7f shows that global-mean SAT anomaly of assim-i1 reproduces well the flat post-2000 trend of the observations, while assim-i2 and historical continue to warm, consistent with their AMO and AMOC evolution. The better match of assim-i1 with observed global-mean SAT does not necessarily imply that assim-i1 is more correct than assim-i2. It is possible that assim-i1 makes up for a missing post-2000 cooling signal over the continents by an unrealistic low reduction of winter sea ice thickness during that period, something that warrants further investigation.

For PR over land, the ACCs of assim-i1 are overall positive. The ΔACCs for assim-i1 – historical show similar strength and pattern, indicating a limited contribution to the ACCs of assim-i1 from the anthropogenically driven spin-up of the hydrological cycle. The ΔACCs for assim-i2 – assim-i1 do not suggest statistically significant performance differences between the two products.

For SLP, the ACCs of assim-i1 are most positive over the low and high latitudes and less positive over the midlatitudes, with slightly negative values over the Southern Ocean and Eurasia. The ΔACCs for assim-i1 – historical suggest that a large portion of the positive skill can be attributed to DA, including benefits over the North Pacific that stretch over North America and also over the SPNA, consistent with ENSO influence. However, DA seems to cause degradation over the subtropical North Atlantic, central Europe, Siberia and East Asia. The ΔACCs for assim-i2 – assim-i1 reveal that updating sea ice improves SLP performance over the Arctic. DA also seems to partly mitigate the skill deficit over central Europe while degrading skill further east.

For Z500, the correlation skill of assim-i1 is virtually saturated over the tropics, decreases towards the midlatitudes and again slightly increases towards the poles. While modest ΔACCs for assim-i1 – historical indicate that external forcing contributes significantly to high tropical skill, DA leads to consistent skill enhancement in those regions. One should note that a change in correlation from 0.6 to 0.9 equates to more than doubling in explained variance from 36 % to 81 % (estimated by the square of the correlation). Hence, the benefit from DA is more substantial than the ΔACCs alone would suggest. Significant skill enhancement is also present over the mid-to-high latitudes, presumably related to ENSO influence on the extratropical atmospheric circulation. The ΔACCs for assim-i2 – assim-i1 indicate weak improvement over the polar regions, albeit not statistically significant, and no signs of degradation, as a consequence of updating the sea ice during DA.

SST prediction has the most direct application for near-term climate impact assessment. We evaluate NorCPM1's capability to predict interannual-to-multiyear SST variations with ACC skill maps for hindcast-i1 along with skill difference maps for hindcast-i1 – assim-i1, hindcast-i1 – persistence, hindcast-i1 – historical and hindcast-i2 – hindcast-i1 (Fig. 11). For LY1, hindcast-i1 exhibits generally positive ACCs, exceeding 0.8 over extended areas, that are both locally and field significant except for limited regions in the eastern Pacific and at high latitudes (Fig. 11a). The system loses information of the initial condition over time, resulting in notably smaller ACCs compared to the assim-i1 reanalysis (Fig. 11b). Significant benefits from initialization, as diagnosed from the ΔACC of hindcast-i1 – historical, are concentrated in the Pacific and Atlantic sectors of the tropics and Southern Ocean, and also in the subpolar North Atlantic (SPNA) and extending from there into the Eurasian Arctic (Fig. 11d). Consistent with other prediction systems (e.g. Yeager et al., 2018), the SPNA stands out as the region that benefits most from initialization. However, hindcast-i1 does not outperform persistence in the SPNA (Fig. 11c), indicating that the benefit of initialization primarily offsets poor performance of the uninitialized dynamical prediction of historical in that region. hindcast-i2 shows improved skill over hindcast-i1 in sea-ice-covered regions and in a small part of the SPNA (Fig. 11e). These skill differences are not field significant, but the fact that the two systems differ in their sea ice treatment adds confidence that skill improvements in the polar regions are real. Much of the LY1 skill, in particular in the tropics, is likely related to skilful initialization of ENSO in NorCPM (Fig. S9 and text in Sect. S2), which has been studied in detail using a similar model configuration (Wang et al., 2019).

The LY2–5 and LY6–9 multiyear SST skill patterns (Fig. 11, middle and right columns) resemble that of LY1 but with some notable differences. Large regions in the eastern central North Atlantic, tropical Indian Ocean and western Pacific show elevated skills that exceed 0.9. The same regions show, however, negligible gains relative to uninitialized prediction of historical (Fig. 11i, n). Thus, the skill increase relative to LY1 is likely due to the forced trend having more weight, as the 4-year averaging effectively filters out interannual internal variability, and less due to the presence of more predictable internal climate variability on multiyear timescales or forecast shock that more strongly impacts LY1. Despite limited initialization benefit, the initialized predictions globally outperform persistence except for in the Southern Ocean. Since we expect the persistence forecast to capture a linear trend, this may indicate a significant skill contribution from non-linearities in the forced trend. Also for multiyear prediction, the SPNA and its extension towards the Arctic stand out as the region benefiting most from initialization, although the benefit is somewhat reduced and less statistically robust than for LY1 (Fig. 11d). Over time, the impact of initializations in the SPNA diminishes and the system drifts back to the poorly performing simulated forced trend, causing skill deficit to emerge (Fig. 11f, k). This result stands in contrast to multi-model findings (that include NorCPM1) suggesting a positive contribution of the forced signal to SPNA temperature skill over a comparable period (Borchert et al., 2021). We suspect a problem with CMIP6 land use change specification (Fig. 13c and text in Sect. S1), leading to an unrealistic historical cooling trend over North America in NorCPM1. Via downstream effects, the continental cooling (likely an artefact) may contribute to the SPNA cooling trend shown after 1980, exacerbating the discrepancy between the observed and simulated SPNA temperature evolution. The eastern Pacific presents another region where the skill notably deteriorates over time. The historical simulations perform better here than for the SPNA (Fig. 11i, n), suggesting a detrimental effect of initialization on multiyear scales on Pacific SSTs notwithstanding the positive effect on LY1 prediction. Also for multiyear prediction, hindcast-i2 performs better than hindcast-i1 in the high-latitude regions, notably in the northwestern North Atlantic (Fig. 11j, o). However, the multiyear skill hindcast-i1 – historical and hindcast-i2 – hindcast-i1 differences are both not field significant, and we thus cannot exclude that they are a sampling artefact.

Skill patterns for the upper ocean temperature and salinity averaged over the top 300 m (Figs. S10, S11) and for sea surface height (Fig. S12) – a proxy for circulation and vertically integrated behaviour – largely reflect those for SST. Skill enhancement due to multiyear averaging is less apparent than for the surface state, presumably due to less presence of interannual climatic noise below the surface. Initialization benefit in the SPNA extends below the surface, across variables, and stands out as a robust feature.

Initialization of the large-scale ocean circulation and the associated meridional heat transport have been identified as essential for skilful prediction of SPNA climate (e.g. Yeager and Robson, 2017). We evaluate in more detail how well NorCPM1 represents mechanisms that give rise to North Atlantic decadal predictability. This evaluation provides additional forecast quality information and a better understanding of the hindcast-i2 – hindcast-i1 skill differences and of how well the predictive potential for North Atlantic SSTs is realized in the system.

The forced evolution of the AMOC strength shows a slight increase until 1980 and weakening thereafter (Fig. 12a, blue solid). assim-i1 initializes the circulation in an anomalous weak state prior to 1990, close to neutral between 1990 and 2010, and weak again thereafter (solid red), with the initial perturbations tending to be outside the internal variability range (blue shading). After initialization, the circulation (solid purple) rapidly relaxes towards the unperturbed ensemble-mean state evolution of historical (solid blue). Because ocean heat exchange between the subtropical and the SPNA covaries with the variability in AMOC strength (Fig. S13e–g), the anomalies of the northward heat transport at the time initialization (Fig. 12b, red solid) roughly resemble those of the circulation, mostly showing anomalously negative transports, except during the 1990s. The heat transport relaxes towards the ensemble-mean of historical during the hindcasts. assim-i2 shows generally stronger circulation and heat transports with weaker long-term decline than assim-i1 (Fig. 12d, e). These circulation and heat transport differences are key to explaining strikingly different SPNA temperature evolution in hindcast-i1 versus hindcast-i2 (Fig. 12c, f). hindcast-i1 and hindcast-i2 notably drift away from the observed SPNA-averaged temperature trajectory, suggesting that both configurations struggle to predict the observed decadal SPNA temperature trends. However, while hindcast-i1 exhibits drift behaviour towards cooling (most pronounced during 1960–1980 and after 2005), hindcast-i2 exhibits drift behaviour towards warming (most severe during 1980–2000).

Diagnosing the hindcast SPNA temperature evolution from the anomalous ocean heat transport across 48∘ N (Fig. S13a, c) or the regression of heat transport on AMOC (Fig. S13b, d) results in a very similar behaviour. The SPNA 0–2000 m heat content changes are well balanced by transport changes across 48∘ N and anomalous surface fluxes over the SPNA region (not shown). The latter mainly act to dampen the temperature signal, explaining the greater amplitude of the diagnosed temperature evolution. The resemblance of diagnosed and simulated hindcast evolution suggests that circulation exerts a strong control on the simulated SPNA temperature evolution and that poor SPNA prediction is largely a consequence of poor initialization of AMOC and associated poleward heat transport. Errors in the simulated externally forced AMOC trend and associated heat transport likely affect the skill as well.

How can hindcast-i1 and hindcast-i2 exhibit very different SPNA 0–2000 m temperature evolution but similar correlation skills? Applying lead-dependent drift correction largely removes the differences (Fig. 13a, c). Remaining differences hint at a slight time dependence, consistent with the somewhat different long-term trends in AMOC strength in assim-i1 and assim-i2 (Fig. 12a vs. d). In terms of ACC skill, hindcast-i2 performs marginally better than hindcast-i1 for long lead times but does not outperform persistence (Fig. 13e, g). The results for SPNA SST (Fig. 13b, d) generally resemble those for 0–2000 m temperature but look slightly more promising, with hindcast-i2 performing marginally better than persistence for long lead times (Fig. 13f, h).

We evaluated the performance of ocean biogeochemistry for PP and surface CO2 flux. Figure 14 shows maps of PP prediction skill for LY1, LY2–5 and LY6–9. While the results are patchy, some coherent patterns can be distinguished. For the total LY1 skill of hindcast-i1 (Fig. 14a), ACCs are relatively high and the field is significant over large parts of the tropical Pacific and tropical Indian oceans. The correlations stay relatively high for longer lead times (Fig. 14f, k), although their significance is reduced. When subtracting the skill of historical (Fig. 14d, i, n), the correlation is greatly reduced, showing that much of the total skill comes from external forcing. The only region with a coherent pattern of locally significant correlation differences is in the tropical Pacific (0–30∘ S, 120–150∘ W), which shows positive skill differences until LY2–5. For LY6–9, the correlation differences become statistically not significant, although the values stay relatively high. The ΔACCs for hindcast-i1 – assim-i1 (Fig. 14b, g, l) are negative over the tropical Indo-Pacific and large parts of the South Pacific and Southern Ocean, indicating information from initialization is lost over time, while they are positive over the tropical Atlantic, parts of the Atlantic subpolar gyre and most parts of the extratropical Indo-Pacific. Paradoxically, the analysis used to initialize the hindcasts does not consistently outperform the hindcasts. Improvement of the initialized dynamic predictions over persistence can be seen for LY2–5 and LY6–9, but not for LY1. Thus, temporal non-linearities in the externally forced climate trend are likely to contribute to skill, as persistence should capture any linear trends due to forcings and most of the skill comes from the external forcing. Differences between the two sets of hindcasts lack statistical robustness (Fig. 14e, j, o).

Using satellite chlorophyll measurements for model evaluation is subject to caveats. For example, temporal data coverage is relatively short and the spatial data coverage at high latitudes is poor due to cloudiness. Following Yeager et al. (2018), we therefore also analysed the model's ability to hindcast its own analysis over the period 1960–2018 (Fig. 15). We will refer to this as the potential predictability*, using the asterisk to indicate that it differs from more conventional potential predictability estimates based on self-prediction that typically utilize a pre-industrial control simulation (e.g. Collins et al., 2006). The results become less patchy, and the total skill stays field significant for large parts of the global ocean until LY6–9. Removing the skill of historical again reveals that there are regions where the skill is improved by initialization, notably the subtropical gyres and the Nordic Seas (Fig. 15d, i, n). Note that subtracting negative historical ACCs leads to ΔACCs higher than the absolute ACCs of hindcast-i1 itself. Therefore, a large skill benefit from initialization does not necessarily translate into a societally useful absolute skill. We analysed time series of region-averaged PP between 1970–2018 in regions of high skill, namely the subtropical gyres of the Pacific, Atlantic and Indian oceans, as well as the Nordic Seas (not shown). The Nordic Seas are the only region with a strong positive correlation between hindcast-i1 and historical (r=0.5 and 0.6 for single year and four-year means, respectively), indicating that there is a large contribution of the external forcing to the predictive skill. There, the correlation between the hindcast-i1 and assim-i1 is close to 0.75 for all lead year ranges, indicating an improvement with respect to historical, with the largest difference for LY1. For the other regions, there is considerable agreement between the hindcast-i1 and the assim-i1 for LY1, with correlations exceeding 0.7. For the subtropical gyres in the Pacific and South Atlantic, the agreement between the hindcasts and the analysis extends to LY2–5, while the skill in the Indian and North Atlantic oceans drops beyond LY1.

Despite the ambiguous results, the predictability of PP of a couple of years in the tropical/subtropical Pacific is in agreement with the results from perfect model experiments (Fransner et al., 2020) and Séférian et al. (2014), who found a predictability of 2–5 years when comparing with satellite-based PP in the same region. Also, Krumhardt et al. (2020) found a potential predictability of PP of a couple of years in tropical/subtropical regions when comparing to a reconstruction based on an ocean simulation forced with an atmospheric reanalysis. However, to remove the effect of external forcing, they performed a linear detrending. This partly removes the effect of climate change but not of other episodic external forcing such as volcanic eruptions. Frölicher et al. (2020) found a perfect model predictability of more than 10 years in some parts of the subtropical gyres in their perfect model study.

Studies have yet to report predictability of PP in high latitudes if compared to observational data. In these regions, the use of satellite observations is not reliable because of the lower data coverage and more variable chlorophyll-to-carbon ratio of phytoplankton (Frigstad et al., 2014). However, several recent perfect and potential predictability studies suggest that predictability of primary production in high latitudes is low or even non-existent on interannual-to-decadal timescales (Fransner et al., 2020; Frölicher et al., 2020; Krumhardt et al., 2020).

For CO2 fluxes (linearly detrended), a high total skill is found for all lead years but with initialization benefit limited to LY1 in the tropical Pacific, indicating that most skill stems from external forcing (Fig. S14 and text in Sect. S2). The modest benefit from initialization agrees with the findings of Lovenduski et al. (2019), who compared hindcasts of the CESM Decadal Prediction Large Ensemble (DPLE; Yeager et al., 2018) with the same observational dataset. However, other model systems (Li et al., 2016; Ilyina et al., 2020) and perfect model studies (Séférian et al., 2018; Fransner et al., 2020) have shown a predictability of unforced CO2 flux variability up to several years, particularly in the North Atlantic subpolar gyre, suggesting that there is room for improvement for the NorCPM1 decadal predictions.

Previous studies have found robust initialization benefits for sea ice prediction lasting for a couple of months (Guemas et al., 2016), with some re-emergence of skill during the second year (Day et al., 2014). While these studies reported strong seasonal dependencies, the evaluation here is limited to hindcasts initialized in November. We evaluate LY1 predictions of annual-mean sea ice concentration (SIC) against HadISST1 (Rayner et al., 2003) over the period 1960–2018 that includes historical observations as well as satellite estimates (Fig. 16). In the Arctic, the uninitialized predictions (historical) show externally forced skill in the Barents, Kara and Chukchi seas as well as the Canadian Archipelago (Fig. 16a). hindcast-i1 shows consistently higher ACCs than historical in these regions and additionally exhibits first-year skill in sub-Arctic regions, e.g. in the Bering and Greenland seas (Fig. 16b). hindcast-i2 benefits from a stronger constraint on the sea ice initial state compared to hindcast-i1, resulting in generally higher and more widespread skill (Fig. 16c). In the Antarctic, historical shows patches of both positive and negative ACC (Fig. 16d). There are nearly no regions where hindcast-i1 shows negative ACC, while regions with positive ACC are limited to the east Pacific sector of the Southern Ocean (Fig. 16e). hindcast-i2 shows even more positive skill, which extends into the Atlantic sector (Fig. 16f), but also some negative skill in the Pacific sector, albeit less negative than that in historical.

We address seasonal dependence and temporal forecast limit of sea ice prediction by computing the ACC of total Arctic and Antarctic sea ice area as a function of lead month after November initialization (Fig. 17a, c). The Arctic ACC of persistence drops rapidly and both hindcast-i1 and hindcast-i2 show comparable or higher skill during the first winter and into spring. From early summer, the ACCs of hindcast-i1 remain close to zero. In contrast, hindcast-i2 shows some re-emergence of skill from the first autumn extending into the second year. Performing 3-month pre-averaging makes the skill re-emergence for hindcast-i2 and improvements over hindcast-i1, persistence and historical clearer (Fig. 17b, d). The uninitialized prediction from historical shows some skill during autumn and winter but no skill during summer. For the Antarctic, both uninitialized and initialized predictions perform inferior to persistence, with hindcast-i1 performing worst (Fig. 17c, d). Nevertheless, assim-i1 and assim-i2, which provide the initial conditions for hindcast-i1 and hindcast-i2, outperform persistence during most of the year, except in austral winter when persistence shows re-emerging skill. This suggests that model errors are skill limiting rather than imperfect initialization in that region.

Since regional sea ice variability is not necessarily in phase with total hemispheric sea ice area, we define a hemispherically integrated skill score for predicting local (i.e. grid-cell scale) sea ice conditions (Fig. 18). We first interpolate observation and model data to a common 5∘×5∘ grid and then reduce the space and time dimensions to a vector that is used in the ACC computation. We apply square root grid-cell area weighting and only consider cells with non-zero temporal standard deviation. The squared score gives the fraction of predicted sea ice concentration variance. A theoretical score of one would imply perfect prediction in every location (note the score depends on the resolution of the common grid). In addition to monthly ACCs (Fig. 18a, c), we present 3-monthly ACCs (Fig. 18b, d) that are smoother. For the Arctic (Fig. 18a), the hindcast-i2 score reaches 0.4 during the first lead month, outperforming the sharply dropping persistence score (with 1-month e-folding scale) and remains significantly higher than the uninitialized historical score throughout winter and spring and marginally higher during the remainder of the two lead years. persistence shows a re-emergence of skill during summer and autumn that is present but weaker in hindcast-i2. hindcast-i1 shows a score below 0.3 for the first lead month and no initialization benefit after the first spring. Consistent with these differences in hindcast scores, assim-i2 features consistently higher scores than assim-i1. For the Antarctic (Fig. 18c), the initialized predictions do better than the uninitialized ones (with no or negative skill) but for the most part fall behind persistence. assim-i2 shows notably higher and more stable skill than assim-i1, explaining better performance of hindcast-i2 over hindcast-i1.

We have demonstrated initialization benefits for predicting sea ice up to two years ahead in NorCPM1, but can initialization improve prediction of decadal trends in Arctic sea ice decline? An analysis of Northern Hemisphere integrated sea ice volume (SIV) provides little evidence for that (Fig. S15). The initialized hindcasts have a tendency to simulate a flatter trend than the historical experiment over the last decade, which arguably can be interpreted as an improvement. Despite the lack of initialization benefit, the comparison between the two reanalysis products and their corresponding hindcasts is instructive and illustrates the importance of forecast drift correction. As mentioned in Sect. 3.1, the sea ice state update in assim-i2 overall reduces the simulated SIV to values closer to observations, whereas the climatology of assim-i1 remains unaffected. Once assimilation is stopped, the sea ice in hindcast-i2 grows back towards levels comparable to the no-assimilation historical experiment. As a result, the hindcast-i2 predictions all simulate strongly positive decadal SIV trends, whereas hindcast-i1 produces flat or negative trends more in line with observations. Adjusting for lead-dependent forecast drift largely eliminates differences in the decadal SIV trends between the two hindcast products.

Transfer of skill from the ocean to the atmosphere and over land is key to societally relevant climate prediction. We assess the extent such transfer is realized in NorCPM1 from ACCs of SAT, PR, 500 hPa geopotential height (Z500) and sea level pressure (SLP).

For SAT, hindcast-i1 shows considerable first-year and multiyear hindcast skill that exceeds persistence skill over most land areas, except over central South America and parts of Africa and South Asia (Fig. 19a, c). The LY1 initialization benefit (Fig. 19d) is highest over the subpolar North Atlantic, extending from there over Scandinavia and western Siberia. Siberia is also the only region where hindcast-i2 consistently shows higher skill than hindcast-i1 (Fig. 19e). While the ΔACCs are not field significant, it is plausible that differences in sea ice initialization impact skill over adjacent land (Ringgaard et al., 2020). For LY1, the ΔACCs relative to historical (Fig. 19d) hint ENSO-related initialization benefits over low-latitude coastal regions as well as over northwest North America. For LY2–5 and LY6–9, the difference maps indicate little initialization benefit, implying that most multiyear SAT skill over land stems from the externally forced trend in NorCPM1. However, this result can be sensitive to the ΔACC metric (Fig. S18 and related discussion in Sect. 4).

For PR, hindcast-i1 exhibits positive skill over most land regions for all lead ranges (Fig. 20a, f, k). For LY1 it is highest and field significant over the western tropical Pacific and Indonesian Archipelago (Fig. 20a). The LY1 skill difference to historical (Fig. 20d), a measure for the benefit from initialization, resembles the hindcast-i1 skill itself, suggesting only a small contribution from the externally forced trend to the first-year skill. For LY2–5 and LY6–9, the hindcast-i1 skill over the western tropical Pacific, Indonesian Archipelago and Australia is considerably reduced or disappears, whereas it is enhanced over north Africa, North America and northern Eurasia (Fig. 20f, k). It is plausible to assume that the bulk of the multiyear skill is driven by the externally forced changes in rainfall patterns and hydrological cycle (Dong and Sutton, 2015), which is evidently the case over north Africa where ΔACCs relative to historical are small or even negative (Fig. 20i, n). However, positive ΔACCs over western North America and northern Eurasia for all lead ranges suggest contributions from initialization. Most ΔACCs for precipitation are not field significant and we cannot preclude that they are a sampling artefact. This is in particular true for the hindcast-i2 and hindcast-i1 precipitation skill differences (Fig. 20e, j, o).

Initialization benefits for predicting atmospheric circulation variability, as diagnosed from Z500 (Fig. S16) and SLP (Fig. S17), are most robust for LY1 owing to the influence of ENSO. For SLP, some multiyear initialization benefits are also present – albeit not field significant – over the extratropical Atlantic Ocean and Indian Ocean as well as the North American and Eurasian continents. The DA update of sea ice in hindcast-i2 slightly improves the multiyear skill in the Arctic, though the differences are small and not field significant.

We globally summarize first-year and multiyear prediction skills by computing ACCs over time and space for the variables assessed in previous sections (Fig. 21). Skills are computed for LY1, LY2–5 and LY6–9 for the two analyses and hindcast products and benchmarked against the uninitialized historical predictions and persistence. The results are not particularly sensitive to grid-cell variance normalization and therefore similar to the globally averaged local (i.e. grid cell) ACC and also qualitatively similar to the mean-square skill score (not shown).

For SST (Fig. 21a), which is assimilated, the ACCs of assim-i1 and assim-i2 exceed 0.8 for all lead year ranges. After assimilation is discontinued, the values drop to 0.5 during the hindcasts. For LY1, this is still higher than and well separated from the 0.4 value of the historical experiment, suggesting statistically robust benefit from initialization for dynamical prediction with NorCPM1. Consistent with better first-year skill in ice-covered regions, hindcast-i2 performs slightly better than hindcast-i1, and both hindcast products exhibit marginally higher skill than persistence for LY1 (differences are not statistically significant). For LY2–5 and LY6–9, the ACCs of the two analyses and initialized hindcast products are very similar to or slightly higher than those for LY1. For multiyear prediction, the ACC of the historical experiment is on par with the initialized hindcast products, suggesting a major contribution from the externally forced trend and negligible initialization benefit. The fact that persistence scores lower than the uninitialized historical experiment reveals that the skill contribution from the externally forced trend is more than what could be expected from a linear anthropogenic climate trend. For T300 (Fig. 21b), the ACCs of the two analyses are 0.6–0.7, i.e. lower than for SST, presumably due to lower data coverage and higher observation error. Similar as for SST, a clear initialization benefit manifests for first-year prediction and only a hint of benefit for multiyear prediction. SSH (Fig. 21c) shows initialization benefit for first-year prediction but signs of detrimental initialization impact for multiyear prediction. The ACC estimates for SSH are more uncertain than for T300, partly owing to the shorter evaluation period.

Surface CO2 flux (Fig. 21d) and primary production (Fig. 21e) are poorly constrained by the assimilation with the two analyses exhibiting ACCs of 0.2 and below. It is therefore unsurprising that the initialized hindcasts are not skilful and at best show marginal initialization benefit over likewise unskilful uninitialized predictions of historical. However, Ilyina et al. (2020) found a predictability of the global air–sea CO2 fluxes of up to 6 years when combining the members of the two hindcast sets, suggesting considerable sensitivity to the chosen biogeochemistry skill metric, spatial averaging, evaluation period and ensemble size. In contrast to the hindcasts, the persistence skill for CO2 flux exceeds 0.6 for LY1 and 0.3 for LY2–5, and for PP is close to 0.3 for LY1. When using assim-i1 as observational truth for primary production (Fig. 21f), the system suggests initialization benefit for all lead years with hindcasts reaching ACCs close to 0.6 for LY1. Inherent issues in the marine ecosystem parameterization to represent realistic variability (Tjiputra et al., 2007; Gharamti et al., 2017) in combination with observational uncertainties are likely causing this discrepancy.

Assimilation in NorCPM1 updates the ocean and sea ice state but does not directly constrain the atmospheric and land states. Nevertheless, the assimilation can improve their prediction to the extent that SST and sea ice control the atmospheric state. The ACCs for SAT (Fig. 21g) resemble those for SST, but are lower, in particular for the two analyses. Land precipitation (PR) exhibits ACCs of 0.4 independent of lead year range for the two analyses, and 0.2 for the hindcasts for LY1, suggesting some success in initializing ENSO. Contrary to SAT, the historical experiment and persistence both exhibit zero skill for PR, both for annual means and multiyear means, despite anthropogenic spin-up of the hydrological cycle and other external influences. SLP (Fig. 21i) behaves differently in that the global ACCs of persistence, ranging between 0.3 and 0.5, are consistently higher than those of NorCPM1. Thus, the external forcing seems to have a significant influence on the observed SLP variability, but NorCPM1 fails to capture it. For LY1, the ACCs of the initialized hindcasts are slightly higher than those of the historical experiment, again suggesting skilful initialization of ENSO.

We finally evaluate how well the system constrains the temporal evolution of global means (Fig. 22). Especially in the context of climate change attribution, it is of interest whether DA leads to improved representation of global surface warming, global sea level change and strength of the global hydrological cycle. The initialized hindcasts outperform persistence and historical for SST and SAT for LY1. Beyond that, the results show little evidence of initialization benefit, except a marginal improvement of multiyear mean prediction for the oceanic CO2 flux and a sizable potential predictability* benefit for PP. While the initialized hindcasts performed as well as or better than historical for globally averaged skill of local SST, T300 and SAT (Fig. 21a, b, g), hindcast-i1 and hindcast-i2 show slightly poorer multiyear skill than historical in their global means (Fig. 22a, b, g). Except for SST, the reanalyses mostly outperform both persistence and historical but not as clearly as for the globally averaged skill. Interestingly the benefit from DA is considerably larger for global precipitation than for global-mean SST, possibly indicating a strong control of well constrained tropical – likely ENSO-related – SST variability on large-scale precipitation. DA does not improve the match with the 16-year short observational record of global sea level. Why exactly the globally averaged grid-cell skills (Fig. 21) show more benefit from DA than the skills of the global means (Fig. 22) is something that warrants further investigation.