ORAS5 uses the same ocean model and spatial configuration as ORAP5 (Table ). The NEMO ocean model version 3.4.1 has been used for ORAS5 in a global configuration ORCA025.L75 , a tripolar grid which allows eddies to be represented approximately between 50${}^{\circ }$ S and 50${}^{\circ }$ N . Model horizontal resolution is approximately 25 $\mathrm{km}$ in the tropics and increases to 9 $\mathrm{km}$ in the Arctic. There are 75 vertical levels, with level spacing increasing from 1 m at the surface to 200 m in the deep ocean. NEMO is coupled to the Louvain-la-Neuve sea-ice model version 2 (LIM2; see ) implemented with the viscous-plastic (VP) rheology. The wave effects introduced since ORAP5 were also implemented in ORAS5, with updated ocean mixing terms for wind. Given that the wave field is not defined under sea ice, the wave impact in the turbulent kinetic energy (TKE) scheme is not used under sea ice. Instead, a constant value of 20 is used under sea ice as coefficient of the surface input of TKE in ORAS5.

The reanalysis is conducted with NEMOVAR in its 3D-Var FGAT (first guess at appropriate time) configuration. NEMOVAR is used to assimilate subsurface temperature, salinity, sea-ice concentration and sea-level anomalies (SLAs), using a 5 d assimilation window with a model time step of 1200 $\mathrm{s}$. The observational information is also used via an adaptive bias correction scheme , which will be explained in Sect. .

A schematic diagram of the ORAS5 system can be found in Fig . The analysis cycle consists of one outer iteration of 3D-Var FGAT with observational QC (quality control) and bias correction steps. In the first step (also called the first outer loop), the NEMO model is integrated forward and used for calculation of the model equivalent of each available observation at the time step closest to the observation time, after which the QC of the observations is performed. The quality-controlled observations and model background state are passed to the so-called inner loop, where the 3D-Var FGAT method minimizes the linearized cost function to produce the assimilation increment. The increment is applied during a second forward integration of the model (the second outer loop) using the incremental analysis updates method with constant weights (IAU; ). Both SIC and other observations are assimilated using a 5 d assimilation cycle in ORAS5 and share the outer loop model integrations.

As in ORAP5, assimilation of SIC data is also included in ORAS5. The background state of ocean and sea ice is produced from a coupled NEMO-LIM2 run, but the minimization of the SIC cost function is separated from the minimization of the cost function for all other ocean state variables. The separation of the sea-ice minimization assumes that there are no covariances between SIC and other variables. Variables which are physically related are divided into balanced and unbalanced components. The balanced components are linearly dependent (related by the multivariate relationships), while the unbalanced components are independent and uncorrelated with other variables. The ORAS5 balance relations are the same as for ORAS4 and ORAP5. The observation and background error specifications are the same as in ORAP5 , except for sea level (see Sect. ).

The sea-level anomaly observations produced by AVISO (Archiving, Validation and Interpretation of Satellite Oceanographic data) DUACS (Data Unification and Altimeter Combination System) has been updated to the latest version DT2014 in ORAS5 for both filtered along-track and gridded SLA data. Compared to the previous version DT2010 that has been used in ORAS4 and ORAP5 reanalyses, the DT2014 data set has received a series of major upgrades, including a new 20-year altimeter reference period (1993–2012) and increased spatial resolution (14 $\mathrm{km}$ in low latitudes), among others. Another important change in ORAS5 with respect to ORAS4 and ORAP5 is that SLA thinning is now done by stratified random sampling instead of creating superobbing SLA observations, as a method to account for observation representativeness errors from along-track SLA data. As a result, ORAS5 ingests SLA observations with increased local variability but reduced observation error standard deviations (OBE STDs). Compared to ORAS4, the SLA OBE STD in ORAS5 is reduced by approximately 20 % in the tropics due to increased spatial resolution of the DT2014 data set. ORAS5 also assimilates more along-track SLA data whenever newly available satellite missions (i.e. GeoSat Follow-On, Haiyang-2A, Jason-1 Geodetic, Saral/AltiKa) are available in DT2014. Other parts of the scheme, e.g. a reduced-grid construction (typical 1${}^{\circ }$ by 1${}^{\circ }$ in latitude–longitude) and a method for diagnosing OBE STD , remain unchanged. SLA observation has not been assimilated in ORAS5 outside the latitudinal band from 50${}^{\circ }$ S to 50${}^{\circ }$ N or in regions shallower than 500 $\mathrm{m}$. Assessment of this change in SLA assimilation can be found in Sect. .

A reference mean dynamic topography (MDT) is required in order to assimilate SLA along-track data in an ocean general circulation model. This is necessary because altimeter measurement and the state variable in the ocean model are with respect to different reference surfaces. There are several approaches to tackle this problem. One approach consists of using an external MDT , which is further corrected by using cumulative SLA innovation terms . This is the approach followed in the Met Office's global Forecasting Ocean Assimilation Model (FOAM, ) and in the CMEMS global ocean monitoring and forecasting system . A different approach is used at ECMWF and consists of estimating the MDT from a multi-year pre-reanalysis run assimilating $T/S$ observations; this is the so-called model MDT approach, and it is described in . The MDT in ORAS5 follows this model MDT approach, except that the pre-reanalysis run, which assimilates only in situ observations and with bias correction, was produced using two parallel streams instead of one sequential integration, in order to accelerate the process of computing the MDT. The MDT was then constructed by averaging the resulting sea surface height over a reference period 1996–2012, with an additional correction term to account for the different averaging period with respect to the DT2014 data set as done in ORAP5 . In this way, the assimilation of SLA constrains the temporal variability of the reanalysis without affecting the reanalysis mean state. However, it also means that the assimilation of SLAs will not further correct the model mean state. The difference in MDT used by ORAS5 and by the FOAM system is shown in Fig. . Large differences can be found in regions with strong mesoscale eddy activities (e.g. along the western boundary currents and the ACC currents) and along the Antarctic coasts. A dipole of positive–negative MDT departures along the Gulf Stream and its extensions is of particular interest. This is consistent with the estimated a priori temperature and salinity biases in ORAS5 (Fig.), suggesting some model and/or forcing errors in this regions.

Prior to 1993, mass variation that contributes to the change in Global Mean Sea Level (GMSL) in ORAS5 was constrained using the GRACE-derived climatology. The total GMSL was then constrained by assimilating altimeter-derived GMSL after 1993. This is the same as in ORAP5 . The GMSL was derived from altimeter observations, firstly using reprocessed DT2014 gridded SLA data up to 2014 and then using the AVISO NRT gridded SLA from 2015 onwards. A systematic offset of GMSL between these two data sets is expected, due to slightly different data processing methods (e.g. multi-mission and mapping method). This offset is corrected for, in order to avoid introducing spurious GMSL discontinuities in the system. Assuming that sources of error do not change over time, this GMSL offset between delayed and NRT gridded SLA products can be derived using the GMSL difference averaged over their overlapping period. This period covers from May to November 2014 at the time of ORAS5 production. This value was then added for bias correction of GMSL derived from NRT data from 2015 onwards.

A new generic ensemble generation scheme developed by perturbing both observations and surface forcings has been implemented in ORAS5. Here, we give a brief summary of the scheme. Preliminary assessments of ORAS5 temperature and salinity ensemble spread are also presented here. The reader should refer to for details about this ensemble generation scheme.

ORAS5 has employed a stratified random sampling method for preprocessing of both surface and subsurface observations. As a result, the different members of the ensemble see different observations. This is a way to optimize the number of the observations, since more observations are used in the ensemble. The in situ observation profiles are perturbed in ORAS5 in two ways: by perturbing the longitude–latitude locations, and vertical perturbation by applying vertical stratified random thinning. The latitude–longitude locations of ocean in situ profiles are perturbed so that the resulting locations are uniformly distributed within a circle of radius 50 $\mathrm{km}$ around the original location. This radius is chosen primarily considering observation representativeness error with respect to model horizontal resolution. The vertical thinning is applied by assuming a uniform distribution of possible observation location within any given vertical range, and a maximum of two observations within each model level, if available, are then randomly selected for data assimilation. A similar stratified random thinning method is also applied to perturbing ORAS5 surface observations (SIC and SLA). In all cases some predefined reduced grids are constructed in order to carry out thinning, where observations within a given stencil in the reduced grid are randomly selected. As a result, each ensemble member assimilates slightly different observations. For SIC observation, this reduced grid is constructed with a length scale of approximately 30 $\mathrm{km}$ in the Arctic region. For SLA observation, this reduced grid is constructed with a length scale of approximately 100 $\mathrm{km}$ in the tropics. These values were chosen to ensure a reasonable sample size within the reduced grid. Altimeter observations from different satellite missions are treated separately. This method ensures that the number of observation assimilated in each of the perturbed ORAS5 members is comparable to that in the unperturbed member.

A new method has also been developed to perturb surface forcing fields used to drive ORAS5. This method preserves the multivariate relationship between different surface flux components and has been used to perturb SST, SIC, wind stress, net precipitation (precipitation minus evaporation) and solar radiation. ORAS5 forcing perturbation takes into account both structural errors, which are derived from differences between separate analyses data sets (e.g. wind stress differences between NCEP and ERA-40); and analysis errors, which are derived from differences between ensemble members within the same ensemble analysis (e.g. the 10 ensemble members of ERA20C; ). The forcing in the ORAS5 control member remains unperturbed.

Assessment of the ORAS5 temperature and salinity ensemble spreads has been carried out with respect to specified model background error (BGE) standard deviation (${\mathit{\sigma }}_{\mathrm{b}}^{\mathrm{s}}$) and the BGE standard deviation diagnosed with the Desroziers method (${\mathit{\sigma }}_{\mathrm{b}}^{\mathrm{d}}$), following the same procedure described in . Readers are reminded that the salinity ${\mathit{\sigma }}_{\mathrm{b}}^{\mathrm{s}}$ shown here is for unbalance component only. Figure  shows a spatial map of these diagnosed values at 100 $\mathrm{m}$ depth, after binning and averaging in $\mathrm{5}{}^{\circ }\times \mathrm{5}{}^{\circ }$ long–lat boxes. Here, the ORAS5 temperature ensemble spread (Fig. a) shows a spatial pattern that is very similar to the diagnosed value using the Desroziers method (Fig. e), except its amplitude is weaker, especially in the tropics. The salinity ensemble spread in ORAS5 (Fig. b) is in general under-dispersive when verified against diagnosed ${\mathit{\sigma }}_{\mathrm{b}}^{\mathrm{d}}$ (Fig. f). The spatial patterns between salinity ensemble spread and diagnosed ${\mathit{\sigma }}_{\mathrm{b}}^{\mathrm{d}}$ are reasonably consistent. On the contrary, the specified ${\mathit{\sigma }}_{\mathrm{b}}^{\mathrm{s}}$ values in ORAS5 are clearly overestimated almost everywhere for both temperature and salinity (Fig. c, d), suggesting that the current method of specifying temperature and salinity background error standard deviations using analytical functions may be suboptimal, especially for the tropical regions. Fig.  shows the tropical averaged vertical profile of the same variables. Specified values for temperature and salinity (grey shaded area in Figure a, b) are both larger than those of diagnosed ${\mathit{\sigma }}_{\mathrm{b}}^{\mathrm{d}}$ (cyan dashed) values from surface to 2000 $\mathrm{m}$. Estimations from ORAS5 ensemble spread (red solid), on the other hand, are more consistent with ${\mathit{\sigma }}_{\mathrm{b}}^{\mathrm{d}}$ profiles, except for the upper 300 $\mathrm{m}$ where ensemble spreads are underestimated by a factor of approximately 2. In order to assess impact of model resolution, we include here results from a ORAS5-equivalent low-resolution experiment (O5-LR; see Table ) as well. The ensemble spreads in O5-LR (green solid) are almost always smaller than those of ORAS5. However, there are noticeable variations in that difference depending on region and depth range.

Despite the fact that ORAS5 does not include stochastic model perturbations and has a small ensemble of only five members, its ensemble spread is still considered to be a better estimation of BGE than the specified values used in the current ocean analysis system. This indicates that specified model background error standard deviation can be improved by including this ensemble information, possibly in a hybrid way, in order to achieve better statistical consistency. This would also introduce a flow-dependent component into the NEMOVAR BGE covariances matrix through combing the ensemble-based and climatological estimation of BGE covariances.

Additional experiments have been conducted within the ORAS5 framework to help with assessment of different system components. These include sensitivities to SST nudging, bias correction, and assimilation of in situ and satellite altimeter data. Studies of other system parameters, e.g. sensitivity to OBE STD specification, have been carried out but are not discussed here for the sake of conciseness. A summary of system configurations of these sensitivity experiments can be found in Table . All sensitivity experiments cover the period 1979–2015 and are driven by the same surface forcing fields from ERA-Interim. For all experiments except CTL-NoSST, SSTs are nudged to the HadISST2 product before 2008 and OSTIA operational analysis after 2008 (see Fig. ). All diagnostics presented in this section focus on the unperturbed member only, and ORAS5 always refers to the unperturbed member of the reanalysis in all of the following discussions.

Assessment of ORAS5 performance in observation space is carried out using model background errors with respect to all assimilated observations. We compute the model RMSE based on discrepancy between model background and observation for ORAS5 and all sensitivity experiments in Table . This approach allows us to assess contributions from different system components and the performance of ORAS5 as an integrated reanalysis system. The reader should note that error statistics in CTL-NoSST and CTL-HadIS were computed in an observation space slightly differently (without vertical thinning of in situ profiles) from other assimilation runs (ORAS5, O5-NoAlt, O5-NoBias). Assuming that there is no significant change in model error characteristics within some small vertical depth range (e.g. within 100 m), then this comparison between control runs and assimilation runs is still valid. Time series of global mean RMSE in temperature and salinity from different sensitivity experiments are shown in Fig. , together with the total number of assimilated observations of various types shown with the right $y$ axis. Mean vertical profiles of these model RMSEs can be found in Fig. , after being temporally averaged over a period (2005–2014) with near-homogeneous global Argo distribution.

Overall, all components of the ocean reanalysis system (SST nudging, bias correction, assimilation of in situ observation and altimeter data) contribute to reducing the model error, both in temperature (Fig. a) and salinity (Fig. b). However, by construction, some components have a more profound impact on the improvement of the ocean state, e.g. the assimilation of in situ observations. The magnitude of RMSE reduction due to direct $T/S$ assimilation can be derived from departure between O5-NoBias (red lines) and CTL-HadIS (green lines). The error reduction due to assimilation of in situ data varies over time and is loosely proportional to the total number of observations assimilated. Over the Argo period 2005–2014, assimilation of in situ data accounts for 65 % of total RMSE reduction in temperature and for nearly 90 % of total RMSE reduction in salinity. These values are normalized against the total RMSE reductions derived from departures between ORAS5 (black lines) and CTL-NoSST (blue lines). Note that CTL-NoSST also shows a declining trend in its fit-to-observation errors, especially following the introduction of the Argo floats (Fig. ). It is important to point out that this trend in CTL-NoSST does not represent a change in model errors over time but is mainly a result of the evolving GOOS. For instance, most southern extra-tropical ocean regions are only sampled with Argo floats after 2005. Therefore, global mean RMSE reduces after including these extra regions, because (a) by construction, observation errors are larger near the coast than in the open ocean (see ), and (b) there is much less land in the Southern than in the Northern Hemisphere. As a result, observations were given more weight in these regions. The readers should note that results in Fig.  are also subject to changes in the surface driving forcings; e.g. improvement in ERA-Interim forcings over time due to better atmospheric observation coverage could result in reduced CTL-NoSST error as well.

After 2015 a noticeable drop in the available Argo observations is due to switching from reprocessed EN4 to the NRT GTS data stream, leading to small rise in ORAS5 temperature and salinity RMSEs in Fig. . A disruption in TAO/TRITON mooring array between 2012 and 2014 is also visible in Fig. a, which caused slightly increased ORAS5 RMSE in the tropics during this period (not shown).

Differences between the CTL-NoSST and CTL-HadIS in Figs.  and give an estimate of surface SST nudging contributions. This component contributes about 18 % to the global temperature error reduction (Fig. a). However, it leads to an increase in salinity errors between 1985 and 2005 (Fig. b). This deterioration can be as large as 10 % in the mid 1990s. SST nudging is the dominant term in temperature error reduction for the upper 200 $\mathrm{m}$ in the northern extra-tropics (Fig. b) but also leads to a slightly increased temperature error in the tropics below 300 $\mathrm{m}$ (Fig. a). This degradation may be linked with the inappropriate partition of surface non-solar heat fluxes above and below the tropical thermocline, which is normally shallower than 200 $\mathrm{m}$. During the Argo period, SST nudging also reduces the salinity RMSE for the upper 1000 $\mathrm{m}$ in the southern extra-tropics (Fig. f). For the upper 200 $\mathrm{m}$ of the southern extra-tropics, SST nudging accounts for nearly 40 % (0.05 psu) of salinity RMSE reduction. This suggests that some unstable vertical density structures could persist in the model background for this region.

Contribution of the multi-scale bias correction implemented in ORAS5 can be derived from differences between O5-NoBias and ORAS5. This component plays an important role in correcting model errors, especially for the extra-tropical regions where the online bias term is applied as a direct correction to the $T/S$ fields (Fig. b, c, e, f). In the global ocean, this bias correction contributes to the total RMSE reduction with about 14 % for temperature and about 10 % for salinity, averaged for the upper 1000 m. This bias correction contribution is also relatively stable over time and less susceptible to the evolving GOOS (Fig. ).

Other system components, like the assimilation of the altimeter data, lead to marginal improvements in global temperature (ca. 3 %) and have a mostly neutral impact on the model salinity errors (not shown). One possible reason for this relatively small impact from assimilation of altimeter data is that, by construction, the assimilation of SLAs does not correct mean model biases but only affects the temporal variability of reanalysis. In addition, the altimeter data in the ECMWF reanalyses are perhaps given a weak weight compared with mesoscale applications of ocean data assimilation, as to avoid spurious circulations and degradation of the deep ocean . This result is very similar to ORAP5, which indicates that the new SLA thinning scheme in ORAS5 is as effective as the superobbing scheme in representing the observation representativeness error. Overall, we conclude that all components of the ORAS5 ocean data assimilation contribute to an improved ocean analysis state when verified against in situ observations.

The ESA SST CCI (SST_cci) long-term analysis provides daily surface temperature of the global ocean over the period 1992–2010. Unlike the HadISST2 and OSTIA SST analyses, both of which are bias-corrected against in situ observations (e.g. drifting buoys), ESA SST_cci only uses satellite observations (AVHRR and ATSR). Therefore, it provides a reference SST data set of a quality that is suitable for climate research. The latest version 1.1 of the ESA SST_cci data set (referred to as SST_cci1.1 hereafter) has been used here for verification of the performance of ORAS5 at the sea surface. The SST_cci1.1 data set is an update of version 1.0, described by .

Figure c and d show the mean bias and normalized RMSE of ORAS5 SST with respect to SST_cci1.1 for the 1993–2010 period. For intercomparison, results from ORAS4 and two other sensitivity experiments are also included here. Compared to ORAS4 (Fig. a), ORAS5 SST has reduced warm bias in extra-tropics, especially in the northern North Pacific, the Norwegian sea, the Southern Ocean and in the Brazil–Malvinas current regions. A dipole of positive–negative bias patterns in the Gulf Stream and its extension is still visible in ORAS5, though it has a reduced magnitude compared to ORAS4. This suggests that the pathway of Gulf Stream extensions may be misrepresented in ORAS5. Spatial patterns of SST bias and RMSE in ORAS5 (Fig. c, d) are consistent with those derived from the difference of HadISST2 and SST_cci1.1 (Fig. a, b), with large RMSE normally in regions with strong eddy kinetic energy (EKE). These are also regions where ORAS5 SST has a large ensemble spread ($>\mathrm{0.5}$ K in Fig. ). In general, the SST RMSE in ORAS5 is reduced with respect to ORAS4 (Fig. b), e.g. in the southern Indian, the South and western North Pacific, and southern South Atlantic Ocean. Readers are reminded that mean differences between ocean syntheses and SST_cci1.1 have been removed before computing RMSE in Fig. b, d, f and h. Compared to ORAS4, the global averaged RMSE is reduced by about 10 % (30 % if taking the mean difference into account) in ORAS5.

It is worth pointing out that different SST data sets were used for constraining SST in these two ocean syntheses before 2008: ORAS4 used OSTIA, and ORAS5 uses HadISST2. However, this improvement in ORAS5 SST can not be attributed to the new HadISST2 data set. To the contrary, with respect to SST_cci1.1, SST in HadISST2 has a higher RMSE (by about 5 %) and increased warm bias than OSTIA in the extra-tropics (Fig. ). Therefore, improvements in ORAS5 SST should be attributed to increased model resolution and assimilation of updated EN4 in situ data with improved vertical resolution.

Differences between ORAS5 (Fig. c, d) and CTL-HadIS (Fig. e, f) are non-trivial, with largely reduced mean biases in ORAS5, especially for the Labrador Sea and east of Japan. These regions also have large SST RMSE due to misrepresentation of mixed layer depth in CTL-HadIS but are slightly improved in ORAS5 by assimilating in situ observations. As expected, CTL-NoSST (Fig. g, h) has the largest SST biases with respect to SST_cci1.1. These biases are associated with systematic model and/or forcing errors, e.g. underestimated upwelling west of South America and South Africa, misrepresentation of mixing in the Southern Ocean, or others. The difference between CTL-NoSST and CTL-HadIS highlights the fact that the SST nudging method is very effective in keeping SST close to observations in the reanalysis system. Further investigation on the poor performance in the Gulf Stream and its extension is ongoing at moment.

The ESA sea-level CCI (SL_cci) project provides long-term along-track and gridded sea-level products from satellites for climate applications. Here, we use the latest reprocessed version 2.0 data from SL_cci (hereafter called SL_cci2) for validation of ocean synthesis sea level. The SL_cci2 sea-level data are an update of version 1.1 and include data from additional altimeter missions (SARAL/AltiKa and CryoSat-2). Unlike the AVISO DT2014 product, which is dedicated to the best possible retrieval of mesoscale signals, SL_cci2 data focus on the homogeneity and stability of the sea-level record. It has been produced using a different processing chain, and it also uses new altimeter standards, including a new orbit solution, atmospheric corrections, wet troposphere corrections, and a new mean sea surface and ocean–tide model (see ). Therefore, it can be used here as a reference climate data set for validation of ocean syntheses in climate scale.

In order to evaluate the temporal variability of regional sea level in ocean synthesis, the temporal correlation between ORAS5 SLA and SL_cci2 gridded SLA data has been computed over the 2004–2013 period, with its result shown in Fig. c. In general, sea-level variation of ORAS5 is well reproduced in the tropics, with a temporal correlation normally higher than 0.9. Reduced correlation is visible along the North Equatorial Countercurrent in the Pacific and is related to the discrepancy between DT2014 and SL_cci2 data sets (Fig. a). Poor performance near the coast and in the extra-tropics could be attributed partly to no SLA assimilation in these regions. This is similar for ORAS4 (Fig. a), except that ORAS4 sea-level correlation is lower than ORAS5 almost everywhere, and especially in the tropical Indian, the tropical Atlantic and the Norwegian Sea. This difference can in large parts be attributed to the eddy-permitting model resolution of ORAS5, which accounts for most improvement in the extra-tropics, and the assimilation of the new AVISO DT2014 data set, which accounts for most improvement in the tropics.

As expected, removal of altimeter SLA data significantly degraded system performance, as demonstrated by the correlation difference between O5-NoAlt (Fig. e) and ORAS5. In addition, assimilation of ocean in situ observations further improves representation of sea level in the reanalysis due to better representation of mesoscale dynamics. This improvement is relatively homogeneous but is most pronounced in the extra-tropical Pacific, as demonstrated by differences between O5-NoAlt and CTL-HadIS (Fig. g). We would like to point out that both O5-NoAlt and CTL-HadI performed reasonably well in the tropical Pacific and Indian oceans, suggesting that these regions have the lowest model and/or forcing error. This result is consistent with the in situ observation OSE in Sect. .

For reference, the same diagnostics have been carried out for AVISO DT2014 data with respect to SL_cci2 (Fig. ). In general, the temporal correlation between DT2014 and SL_cci2 is very high, indicating excellent agreement of temporal variations between the two data sets. Regions with lower correlation are visible though, e.g. along the North Equatorial Countercurrent in the Pacific between 180 and 100${}^{\circ }$ W (Fig. a). This is likely associated with differences in the production chains between DT2014 and SL_cci2, which include different altimeter-mission-dependent orbit solutions and geophysical corrections and different filtering methods in processing along-track SLAs. This discrepancy between different observational data sets is also responsible for the low correlation between ORAS5 and SL_cci2 SLAs in the same region. Discrepancies in polar sea-level variances between DT2014 and SL_cci2 are likely associated with the new pole tide model used in SL_cci2.

In order to evaluate the magnitude of temporal SLA variance in ORAS5, we compute the ratio of SLA variance between ocean syntheses and SL_cci2 for the 2004–2013 period, with results shown in Fig. b, d, f and h. Compared to SL_cci2 data, both ORAS4 (Fig. b) and ORAS5 (Fig. d) underestimate SLA variance between 50${}^{\circ }$ S and 50${}^{\circ }$ N. The domain-averaged SLA variance in ORAS4 is about two-thirds of the SL_cci2 estimate, mostly because ORAS4 is incapable of resolving mesoscale activity and assimilates SLAs through a superobbing scheme. This problem has been alleviated by increasing the model resolution and using a new SLA thinning scheme in ORAS5 (see Sect. ). However, ORAS5 still underestimates SLA variance by approximately one quarter in the average grid cell. One important reason for this underestimation is that ORAS5 still uses a 1${}^{\circ }$ reduced grid when applying thinning for SLA observations, which may be suboptimal considering ORAS5 comprises a 0.25${}^{\circ }$ resolution ocean model. However, whether the assimilation should compensate for a deficiency that has its origin in the forward ocean model remains an open question. The CTL-HadIS experiment clearly exhibits this underestimation (Fig. h); it is likely related to the 0.25${}^{\circ }$ resolution still being insufficient. Some of this underestimation is also attributed to the assimilated DT2014 data set, which has about 10 % less variance than SL_cci2 in the average grid cell (see Fig. b). This difference between SL_cci2 and DT2014 is mostly due to different geophysical corrections used in production (Jean-François Legeais, personal communication, 2018). Removal of altimeter data (O5-NoAlt, Fig. f) and in situ data (CTL-HadIS, Fig. h) from the assimilation system further reduces simulated SLA variances, by approximately 3 % and 5 %, respectively. There are regions where ORAS5 has a larger SLA variance though, e.g. in the Baffin Bay, Hudson Bay and most areas in the Southern Ocean. The readers is referred to for a detailed evaluation about the ORAS5 sea-level trend and its decomposition with respect to AVISO DT2014 and other ESA Sea Level CCI products.

The ESA Sea Ice CCI (SI_cci) project has produced a long-term SIC data set based on satellite passive microwave radiances. The latest version 1.1 SIC data from SI_cci (hereafter SI_cci1.1) was produced using a sea-ice concentration algorithm and methodology developed by the EUMETSAT Ocean and Sea Ice Satellite Application Facility . This SI_cci1.1 data set is available from 1993 to 2008 in 25 km resolution and is used here for the evaluation of the ORAS5 sea ice.

Figure  shows maps of Arctic SIC RMSE based on departures between ocean syntheses and SI_cci1.1 data, averaged over the 1993–2008 period. Note that coastlines are not drawn on the map. ORAP5 is a pilot reanalysis before ORAS5, and its ability to represent Arctic sea ice has been documented to be reasonably good . Therefore, ORAP5 has been retained here as a reference data set. Overall, ORAS5 SIC (Fig. c, d) has the same error characteristics as ORAP5 (Fig. a, b), which has already been well documented in . The averaged SIC RMSE is normally less than 5 % in the Arctic, which is again comparable with ORAP5. The largest ORAS5 SIC RMSE (up to 20 %) appears in the Labrador Sea in Arctic winter (Fig. c), which is caused by a mean positive (negative) SIC bias in the western (eastern) part of Labrador Sea. High SIC RMSE is also visible in the east coast of Greenland in both Arctic winter and summer for ORAS5 (Fig. d) and is caused by a mean positive (negative) SIC bias in the East Greenland Current north (south) of Iceland. These are also regions identified with large model and/or forcing errors as shown in CTL-HadIS (Fig. e). Like in ORAP5, the visible SIC error along the Arctic coastal lines and in the Baltic Sea in ORAS5 can be attributed to observation errors in OSTIA SIC reanalysis. Assimilation of OSTIA SIC has greatly improved sea-ice performance in ORAS5. Compared to CTL-HadIS (Fig. e, f), ORAS5 has reduced SIC RMSE almost everywhere in Arctic summer (Fig. d). The largest improvement in Arctic winter is located at the east of Greenland along the south edge of the Arctic sea-ice outflow extension, which is associated with model errors in ocean current and/or sea-ice velocity. The SST nudging scheme also contributes to a reduction of SIC RMSE in the system (not shown). These improvements are mostly due to correction of thermodynamic errors in the model, which is common in Arctic summer for Arctic surface water but also in Arctic winter and in the Barents Seas.

For reference, the ensemble spreads of ORAS5 SIC are shown in Fig. , which are estimated using the same monthly mean SIC conditions from the five ensemble members of ORAS5. It is encouraging to see that the spatial patterns of ORAS5 SIC uncertainty match those of RMSE reasonably well, even though the ORAS5 is overconfident in the Labrador Sea and east coast of Greenland. ORAS5 sea-ice uncertainty has been tested by in two radiative transfer models to generate atmosphere brightness temperatures. In addition, an evaluation of ORAS5 sea-ice thickness in the Arctic has been carried out by with a focus on thin sea ice with respect to a data set derived from L-band radiances from the SMOS satellite. The interested reader is also referred to for a case study about extreme sea-ice conditions derived from ORAS5 in 2016 and possible causes for both the Arctic and Antarctic.