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This study demonstrates that assimilating SST with an advanced data assimilation method yields prediction skill level with the best state-of-the-art systems. We employ the Norwegian Climate Prediction Model (NorCPM)—a fully-coupled forecasting system—to assimilate SST observations with the ensemble Kalman filter. Predictions of NorCPM are compared to predictions from the North American Multimodel Ensemble (NMME) project. The global prediction skill of NorCPM at 6- and 12-month lead times is higher than the averaged skill of the NMME. A new metric is introduced for ranking model skill. According to the metric, NorCPM is one of the most skilful systems among the NMME in predicting SST in most regions. Confronting the skill to a large historical ensemble without assimilation, shows that the skill is largely derived from the initialisation rather than from the external forcing. NorCPM achieves good skill in predicting El Niño–Southern Oscillation (ENSO) up to 12 months ahead and achieves skill over land via teleconnections. However, NorCPM has a more pronounced reduction in skill in May than the NMME systems. An analysis of ENSO dynamics indicates that the skill reduction is mainly caused by model deficiencies in representing the thermocline feedback in February and March. We also show that NorCPM has skill in predicting sea ice extent at the Arctic entrance adjacent to the north Atlantic; this skill is highly related to the initialisation of upper ocean heat content. publishedVersion

The Norwegian Climate Prediction Model version 1 (NorCPM1) is a new research tool for performing climate reanalyses and seasonal-to-decadal climate predictions. It combines the Norwegian Earth System Model version 1 (NorESM1) – which features interactive aerosol–cloud schemes and an isopycnic-coordinate ocean component with biogeochemistry – with anomaly assimilation of sea surface temperature (SST) and T/S-profile observations using the ensemble Kalman filter (EnKF). We describe the Earth system component and the data assimilation (DA) scheme, highlighting implementation of new forcings, bug fixes, retuning and DA innovations. Notably, NorCPM1 uses two anomaly assimilation variants to assess the impact of sea ice initialization and climatological reference period: the first (i1) uses a 1980–2010 reference climatology for computing anomalies and the DA only updates the physical ocean state; the second (i2) uses a 1950–2010 reference climatology and additionally updates the sea ice state via strongly coupled DA of ocean observations. We assess the baseline, reanalysis and prediction performance with output contributed to the Decadal Climate Prediction Project (DCPP) as part of the sixth Coupled Model Intercomparison Project (CMIP6). The NorESM1 simulations exhibit a moderate historical global surface temperature evolution and tropical climate variability characteristics that compare favourably with observations. The climate biases of NorESM1 using CMIP6 external forcings are comparable to, or slightly larger than those of, the original NorESM1 CMIP5 model, with positive biases in Atlantic meridional overturning circulation (AMOC) strength and Arctic sea ice thickness, too-cold subtropical oceans and northern continents, and a too-warm North Atlantic and Southern Ocean. The biases in the assimilation experiments are mostly unchanged, except for a reduced sea ice thickness bias in i2 caused by the assimilation update of sea ice, generally confirming that the anomaly assimilation synchronizes variability without changing the climatology. The i1 and i2 reanalysis/hindcast products overall show comparable performance. The benefits of DA-assisted initialization are seen globally in the first year of the prediction over a range of variables, also in the atmosphere and over land. External forcings are the primary source of multiyear skills, while added benefit from initialization is demonstrated for the subpolar North Atlantic (SPNA) and its extension to the Arctic, and also for temperature over land if the forced signal is removed. Both products show limited success in constraining and predicting unforced surface ocean biogeochemistry variability. However, observational uncertainties and short temporal coverage make biogeochemistry evaluation uncertain, and potential predictability is found to be high. For physical climate prediction, i2 performs marginally better than i1 for a range of variables, especially in the SPNA and in the vicinity of sea ice, with notably improved sea level variability of the Southern Ocean. Despite similar skills, i1 and i2 feature very different drift behaviours, mainly due to their use of different climatologies in DA; i2 exhibits an anomalously strong AMOC that leads to forecast drift with unrealistic warming in the SPNA, whereas i1 exhibits a weaker AMOC that leads to unrealistic cooling. In polar regions, the reduction in climatological ice thickness in i2 causes additional forecast drift as the ice grows back. Posteriori lead-dependent drift correction removes most hindcast differences; applications should therefore benefit from combining the two products. The results confirm that the large-scale ocean circulation exerts strong control on North Atlantic temperature variability, implying predictive potential from better synchronization of circulation variability. Future development will therefore focus on improving the representation of mean state and variability of AMOC and its initialization, in addition to upgrades of the atmospheric component. Other efforts will be directed to refining the anomaly assimilation scheme – to better separate internal and forced signals, to include land and atmosphere initialization and new observational types – and improving biogeochemistry prediction capability. Combined with other systems, NorCPM1 may already contribute to skilful multiyear climate prediction that benefits society.

Recent developments of the explicit elastic-viscous-plastic (EVP) solvers call for a new comparison with implicit solvers for the equations of viscous-plastic sea ice dynamics. In Arctic sea ice simulations, the modified and the adaptive EVP solvers, and the implicit Jacobian–free Newton–Krylov (JFNK) solver are compared against each other. The adaptive EVP method shows convergence rates that are generally similar or even better than those of the modified EVP method, but the convergence of the EVP methods is found to depend dramatically on the use of the replacement pressure (RP). Apparently, using the RP can affect the pseudo-elastic waves in the EVP methods by introducing extra non-physical oscillations so that, in the extreme case, convergence to the VP solution can be lost altogether. The JFNK solver also suffers from higher failure rates with RP implying that with RP the momentum equations are stiffer and more difficult to solve. For practical purposes, both EVP methods can be used efficiently with an unexpectedly low number of sub-cycling steps without compromising the solutions. The differences between the RP solutions and the NoRP solutions (when the RP is not being used) can be reduced with lower thresholds of viscous regularization at the cost of increasing stiffness of the equations, and hence the computational costs of solving them.

Stability and convergence of the modified EVP implementation of the visco-plastic sea ice rheology by Bouillon et al., Ocean Modell., 2013, is analyzed on B- and C-grids. It is shown that the implementation on a B-grid is less restrictive with respect to stability requirements than on a C-grid. On C-grids convergence is sensitive to the discretization of the viscosities. We suggest to adaptively vary the parameters of pseudotime subcycling of the modified EVP scheme in time and space to satisfy local stability constraints. This new approach generally improves the convergence of the modified EVP scheme and hence its numerical efficiency. The performance of the new “adaptive EVP” approach is illustrated in a series of experiments with the sea ice component of the MIT general circulation model (MITgcm) that is formulated on a C-grid.

There is a growing demand for skillful prediction systems in the Arctic. Using the Norwegian Climate Prediction Model that combines the fully coupled Norwegian Earth System Model and the Ensemble Kalman filter, we present a system that performs both, weakly coupled data assimilation (wCDA) when assimilating ocean hydrography (by updating the ocean alone) and strongly coupled data assimilation when assimilating sea ice concentration (SIC) (by jointly updating the sea ice and ocean). We assess the seasonal prediction skill of this version of the Norwegian Climate Prediction Model, the first climate prediction system using strongly coupled data assimilation, by performing retrospective predictions (hindcasts) for the period 1985 to 2010. To better understand the origins of the prediction skill of Arctic sea ice, we compare this version with a version that solely performs wCDA of ocean hydrography. The reanalysis that assimilates just ocean data exhibits skillful hydrography in the upper Arctic Ocean and features an improved sea ice state, such as improved summer SIC in the Barents Sea, or reduced biases in sea ice thickness. Skillful prediction of SIE up to 10–12 lead months are only found during winter in regions of a relatively deep ocean mixed layer outside the Arctic basin. Additional DA of SIC data notably further corrects the initial seaice state, confirming the applicability of the results of Kimmritz et al. (2018) in a historical setting. The resulting prediction skill of SIE is widely enhanced compared to predictions initialized through wCDA of only ocean data. Particularly high skill is found for July‐initialized autumn SIE predictions.

Most dynamic sea ice models for climate type simulations are based on the viscous-plastic (VP) rheology. The resulting stiff system of partial differential equations for ice velocity is either solved implicitly at great computational cost, or explicitly with added pseudo-elasticity (elastic-viscous-plastic, EVP). A recent modification of the EVP approach seeks to improve the convergence of the EVP method by re-interpreting it as a pseudotime VP solver. The question of convergence of this modified EVP method is revisited here and it is shown that convergence is reached provided the stability requirements are satisfied and the number of pseudotime iterations is sufficiently high. Only in this limit, the VP and the modified EVP solvers converge to the same solution. Related questions of the impact of mesh resolution and incomplete convergence are also addressed.

A data assimilation method capable of constraining the sea ice of an Earth system model in a dynamically consistent manner has the potential to enhance the accuracy of climate reconstructions and predictions. Finding such a method is challenging because the sea ice dynamics is highly non-linear, and sea ice variables are strongly non-Gaussian distributed and tightly coupled to the rest of the Earth system – particularly thermodynamically with the ocean. We investigate key practical implementations for assimilating sea ice concentration – the predominant source of observations in polar regions – with the Norwegian Climate Prediction Model that combines the Norwegian Earth System Model with the Ensemble Kalman Filter. The performances of the different configurations are investigated by conducting 10-year reanalyses in a perfect model framework. First, we find that with a flow-dependent assimilation method, strongly coupled ocean–sea ice assimilation outperforms weakly coupled (sea ice only) assimilation. An attempt to prescribe the covariance between the ocean temperature and the sea ice concentration performed poorly. Extending the ocean updates below the mixed layer is slightly beneficial for the Arctic hydrography. Second, we find that solving the analysis for the multicategory instead of the aggregated ice state variables greatly reduces the errors in the ice state. Updating the ice volumes induces a weak drift in the bias for the thick ice category that relates to the postprocessing of unphysical thicknesses. Preserving the ice thicknesses for each category during the assimilation mitigates the drift without degrading the performance. The robustness and reliability of the optimal setting is demonstrated for a 20-year reanalysis. The error of sea ice concentration reduces by 50% (65%), sea ice thickness by 25% (35%), sea surface temperature by 33% (23%) and sea surface salinity by 11% (25%) in the Arctic (Antarctic) compared to a reference run without assimilation.

The Finite-Element Sea Ice Model (FESIM), used as a component of the Finite-Element Sea ice Ocean Model, is presented. Version 2 includes the elastic-viscous-plastic (EVP) and viscous-plastic (VP) solvers and employs a flux corrected transport algorithm to advect the ice and snow mean thicknesses and concentration. The EVP part also includes a modified approach proposed recently by Bouillon et al. (2013), which is characterized by an improved stability compared to the standard EVP approach. The model is formulated on unstructured triangular meshes. It assumes a collocated placement of ice velocities, mean thicknesses and concentration at mesh vertices, and relies on piecewise-linear (P1) continuous elements. Simple tests for the modified EVP and VP solvers are presented to show that they may produce very close results provided the number of iterations is sufficiently high.

The version of the Norwegian Climate Prediction Model (NorCPM) that only assimilates sea surface temperature (SST) with the Ensemble Kalman Filter has been used to investigate the seasonal to decadal prediction skill of regional Arctic sea ice extent (SIE). Based on a suite of NorCPM retrospective forecasts, we show that seasonal prediction of pan-Arctic SIE is skillful at lead times up to 12 months, which outperforms the anomaly persistence forecast. The SIE skill varies seasonally and regionally. Among the five Arctic marginal seas, the Barents Sea has the highest SIE prediction skill, which is up to 10–11 lead months for winter target months. In the Barents Sea, the skill during summer is largely controlled by the variability of solar heat flux and the skill during winter is mostly constrained by the upper ocean heat content/SST and also related to the heat transport through the Barents Sea Opening. Compared with several state-of-the-art dynamical prediction systems, NorCPM has comparable regional SIE skill in winter due to the improved upper ocean heat content. The relatively low skill of summer SIE in NorCPM suggests that SST anomalies are not sufficient to constrain summer SIE variability and further assimilation of sea ice thickness or atmospheric data is expected to increase the skill.