Toward a global ocean data assimilation system based on ensemble optimum interpolation: altimetry data assimilation experiment

A global ocean data assimilation system based on the ensemble optimum interpolation (EnOI) has been under development as the Chinese contribution to the Global Ocean Data Assimilation Experiment. The system uses a global ocean general circulation model, which is eddy permitting, developed by the Institute of Atmospheric Physics of the Chinese Academy of Sciences. In this paper, the implementation of the system is described in detail. We describe the sampling strategy to generate the stationary ensembles for EnOI. In addition, technical methods are introduced to deal with the requirement of massive memory space to hold the stationary ensembles of the global ocean. The system can assimilate observations such as satellite altimetry, sea surface temperature (SST), in situ temperature and salinity from Argo, XBT, Tropical Atmosphere Ocean (TAO), and other sources in a straightforward way. As a first step, an assimilation experiment from 1997 to 2001 is carried out by assimilating the sea level anomaly (SLA) data from TOPEX/Poseidon. We evaluate the performance of the system by comparing the results with various types of observations. We find that SLA assimilation shows very positive impact on the modeled fields. The SST and sea surface height fields are clearly improved in terms of both the standard deviation and the root mean square difference. In addition, the assimilation produces some improvements in regions where mesoscale processes cannot be resolved with the horizontal resolution of this model. Comparisons with TAO profiles in the Pacific show that the temperature and salinity fields have been improved to varying degrees in the upper ocean. The biases with respect to the independent TAO profiles are reduced with a maximum magnitude of about 0.25°C and 0.1 psu for the time-averaged temperature and salinity. The improvements on temperature and salinity also lead to positive impact on the subsurface currents. The equatorial under current is enhanced in the Pacific although it is still underestimated after the assimilation.     

Argo data assimilation in ocean general circulation model of Northwest Pacific Ocean

The Argo temperature and salinity profiles in 2005–2009 are assimilated into a coastal ocean general circulation model of the Northwest Pacific Ocean using the ensemble adjustment Kalman filter (EAKF). Three numerical tests, including the control run (CTL) (without data assimilation, which serves as the reference experiment), ensemble free run (EnFR) (without data assimilation), and EAKF experiment (with Argo data assimilation using EAKF), are carried out to examine the performance of this system. Using the restarts of different years as the initial conditions of the ensemble integrations, the ensemble spreads from EnFR and EAKF are all kept at a finite value after a sharp decreasing in the first few months because of the sensitive of the model to the initial conditions, and the reducing of the ensemble spread due to Argo data assimilation is not much. The ensemble samples obtained in this way can well represent the probabilities of the real ocean states, and no ensemble inflation is necessary for this EAKF experiment. Different experiment results are compared with satellite sea surface temperature (SST) data and the Global Temperature-Salinity Profile Program (GTSPP) data. The comparison of SST shows that modeled SST errors are reduced after data assimilation; the error reduction percentage after assimilating the Argo profiles is about 10?% on average. The comparison against the GTSPP profiles, which are independent of the Argo profiles, shows improvements in both temperature and salinity. The comparison results indicated a great error reduction in all vertical layers relative to CTL and the ensemble mean of EnFR; the maximum value for temperature and salinity reaches to 85?% and 80?%, respectively. The standard deviations of sea surface height are employed to examine the simulation ability, and it is shown that the mesoscale variability is improved after Argo data assimilation, especially in the Kuroshio extension area and along the section of 10°N. All these results suggest that this system is potentially useful for improving the simulation ability of oceanic numerical models.     

Correcting surface winds by assimilating high-frequency radar surface currents in the German Bight

Surface winds are crucial for accurately modeling the surface circulation in the coastal ocean. In the present work, high-frequency radar surface currents are assimilated using an ensemble scheme which aims to obtain improved surface winds taking into account European Centre for Medium-Range Weather Forecasts winds as a first guess and surface current measurements. The objective of this study is to show that wind forcing can be improved using an approach similar to parameter estimation in ensemble data assimilation. Like variational assimilation schemes, the method provides an improved wind field based on surface current measurements. However, the technique does not require an adjoint, and it is thus easier to implement. In addition, it does not rely on a linearization of the model dynamics. The method is validated directly by comparing the analyzed wind speed to independent in situ measurements and indirectly by assessing the impact of the corrected winds on model sea surface temperature (SST) relative to satellite SST.     

Using ensemble adjustment Kalman filter to assimilate Argo profiles in a global OGCM

An ensemble adjustment Kalman filter (EAKF) is used to assimilate Argo profiles of 2008 in a global version of the Modular Ocean Model version 4. Four assimilation experiments are carried out to compare with the simulation without data assimilation, which serves as the control experiment. All experiment results are compared with dataset of Global Temperature–Salinity Profile Program and satellite sea surface temperature (SST). The first experiment (Exp 1) is implemented by perturbing temperature of upper layers in the initial conditions (ICs) with an amplitude of 1.0°C and no ensemble inflation. The results from Exp 1 show that the simulated temperature (salinity) deviation in the upper 400 m (500 m) is reduced through Argo data assimilation; however, these deviations are increased in deeper layers. The error reduction in SST is much greater during January to June than during the rest of the year. Three more experiments are designed to understand the responses in different layers and months. Two of them test model sensitivities to ICs by perturbing them vertically: one over the vertical extent of the whole water column (Exp 2) and the other employs smaller perturbation amplitude of 0.1°C (Exp 3). Exp 2 shows that the simulated temperature and salinity deviations are systematically improved in the whole water column. Comparison between Exps 2 and 3 suggests that perturbation amplitude is important. Exp 4 tests the influence of the optimal inflation factor of 5%, which is determined by other set of numerical tests. Exp 4 improves assimilation performance much more than the other three experiments without inflation. Therefore, we conclude that the perturbation should be introduced to all model layers, proper perturbation amplitude is important for Ocean data assimilation using EAKF, and the ensemble inflation by an optimal inflation is critical to improve the skill of the EAKF analysis.     

Coupled assimilation for an intermediated coupled ENSO prediction model

The value of coupled assimilation is discussed using an intermediate coupled model in which the wind stress is the only atmospheric state which is slavery to model sea surface temperature (SST). In the coupled assimilation analysis, based on the coupled wind–ocean state covariance calculated from the coupled state ensemble, the ocean state is adjusted by assimilating wind data using the ensemble Kalman filter. As revealed by a series of assimilation experiments using simulated observations, the coupled assimilation of wind observations yields better results than the assimilation of SST observations. Specifically, the coupled assimilation of wind observations can help to improve the accuracy of the surface and subsurface currents because the correlation between the wind and ocean currents is stronger than that between SST and ocean currents in the equatorial Pacific. Thus, the coupled assimilation of wind data can decrease the initial condition errors in the surface/subsurface currents that can significantly contribute to SST forecast errors. The value of the coupled assimilation of wind observations is further demonstrated by comparing the prediction skills of three 12-year (1997–2008) hindcast experiments initialized by the ocean-only assimilation scheme that assimilates SST observations, the coupled assimilation scheme that assimilates wind observations, and a nudging scheme that nudges the observed wind stress data, respectively. The prediction skills of two assimilation schemes are significantly better than those of the nudging scheme. The prediction skills of assimilating wind observations are better than assimilating SST observations. Assimilating wind observations for the 2007/2008 La Niña event triggers better predictions, while assimilating SST observations fails to provide an early warning for that event.     

Assimilating along-track SLA data using the EnOI in an eddy resolving model of the Agulhas system

The greater Agulhas Current is one of the most energetic current systems in the global ocean. It plays a fundamental role in determining the mean state and variability of the regional marine environment, affecting its resources and ecosystem, the regional weather and the global climate on a broad range of temporal and spatial scales. In the absence of a coherent in-situ and satellite-based observing system in the region, modelling and data assimilation techniques play a crucial role in both furthering the quantitative understanding and providing better forecasts of this complicated western boundary current system. In this study, we use a regional implementation of the Hybrid Coordinate Ocean Model and assimilate along-track satellite sea level anomaly (SLA) data using the Ensemble Optimal Interpolation (EnOI) data assimilation scheme. This study lays the foundation towards the development of a regional prediction system for the greater Agulhas Current system. Comparisons to independent in-situ drifter observations show that data assimilation reduces the error compared to a free model run over a 2-year period. Mesoscale features are placed in more consistent agreement with the drifter trajectories and surface velocity errors are reduced. While the model-based forecasts of surface velocities are not as accurate as persistence forecasts derived from satellite altimeter observations, the error calculated from the drifter measurements for eddy kinetic energy is significantly lower in the assimilation system compared to the persistence forecast. While the assimilation of along-track SLA data introduces a small bias in sea surface temperatures, the representation of water mass properties and deep current velocities in the Agulhas system is improved.     

OpenDA-NEMO framework for ocean data assimilation

Data assimilation methods provide a means to handle the modeling errors and uncertainties in sophisticated ocean models. In this study, we have created an OpenDA-NEMO framework unlocking the data assimilation tools available in OpenDA for use with NEMO models. This includes data assimilation methods, automatic parallelization, and a recently implemented automatic localization algorithm that removes spurious correlations in the model based on uncertainties in the computed Kalman gain matrix. We have set up a twin experiment where we assimilate sea surface height (SSH) satellite measurements. From the experiments, we can conclude that the OpenDA-NEMO framework performs as expected and that the automatic localization significantly improves the performance of the data assimilation algorithm by successfully removing spurious correlations. Based on these results, it looks promising to extend the framework with new kinds of observations and work on improving the computational speed of the automatic localization technique such that it becomes feasible to include large number of observations.     

Assimilation of sea surface temperature into CECOM by flux correction

Sea surface temperature (SST) from a near real-time data set produced from satellites data has been assimilated into a coupled ice–ocean forecasting model (Canadian East Coast Ocean Model) using an efficient data assimilation method. The method is based on an optimal interpolation scheme by which SST is melded into the model through the adjustment of surface heat flux. The magnitude and space–time variation of the adjustment depend on the depth of heat diffusion into the water column in response to changes in surface flux, the correlation time scale of the data, and model and data errors. The diffusion depth is scaled by the eddy diffusivity for temperature. The ratio of the model and data errors is treated as an adjustable parameter. To evaluate the quality of the assimilation, the results from the model with and without assimilation are compared to independent ship data from the Atlantic Zone Monitoring Program and the World Ocean Circulation Experiment. It is shown that the assimilation has a significant impact on the modeled SST, reducing the root mean square difference (RMSD) between the model SST and the ship SST by 0.63°C or 37%. The RMSD of the assimilated SST is smaller than that of the satellite SST by 0.23°C. This suggests that model simulations or predictions with data assimilation can provide the best estimate of the true SST. A sensitivity study is performed to examine the change of the model RMSD with the adjustable parameter in the assimilation equation. The results show that there is an optimal value of the parameter and the model SST is not very sensitive to the parameter.     

A dual-pass data assimilation scheme for estimating surface fluxes with FY3A-VIRR land surface temperature

In this work, a dual-pass data assimilation scheme is developed to improve predictions of surface flux. Pass 1 of the dual-pass data assimilation scheme optimizes the model vegetation parameters at the weekly temporal scale, and Pass 2 optimizes the soil moisture at the daily temporal scale. Based on ensemble Kalman filter(EnKF), the land surface temperature(LST) data derived from the new generation of Chinese meteorology satellite(FY3A-VIRR) are assimilated into common land model(CoLM) for the first time. Six sites, Daman, Guantao, Arou, BJ, Miyun and Jiyuan, are selected for the data assimilation experiments and include different climatological conditions. The results are compared with those from a dataset generated by a multi-scale surface flux observation system that includes an automatic weather station(AWS), eddy covariance(EC) and large aperture scintillometer(LAS). The results indicate that the dual-pass data assimilation scheme is able to reduce model uncertainties and improve predictions of surface flux with the assimilation of FY3A-VIRR LST data.     

Validation and application of an ensemble Kalman filter in the Selat Pauh of Singapore

The effectiveness of an ensemble Kalman filter (EnKF) is assessed in the Selat Pauh of Singapore using observing system simulation experiment. Perfect model experiments are first considered. The perfect model experiments examine the EnKF in reducing the initial perturbations with no further errors than those in the initial conditions. Current velocity at 15 observational sites from the true ocean is assimilated every hour into the false ocean. While EnKF reduces the initial velocity error during the first few hours, it fails after one tidal cycle (approximately 12 h) due to the rapid convergence of the ensemble members. Successively, errors are introduced in the surface wind forcing. A random perturbation ε is applied independently to each ensemble member to maintain the ensemble spread. The assimilation results showed that the success of EnKF depends critically on the presence of ε, yet it is not sensitive to the magnitude of ε, at least in the range of weak to moderate perturbations. Although all experiments were made with EnKF only, the results could be applicable in general to all other ensemble-based data assimilation methods.     

A three-dimensional variational ocean data assimilation system:Scheme and preliminary results

A new 3DVAR-based Ocean Variational Analysis System (OVALS) is developed. OVALS is capable of assimilating in situ sea water temperature and salinity observations and satellite altimetry data. As a component of OVALS, a new variational scheme is proposed to assimilate the sea surface height data. This scheme considers both the vertical correlation of background errors and the nonlinear temperature-salinity relationship which is derived from the generalization of the linear balance constraints to the nonlinear in the 3DVAR. By this scheme, the model temperature and salinity fields are directly adjusted from the altimetry data. Additionally, OVALS can assimilate the temperature and salinity profiles from the ARGO floats which have been implemented in recent years and some temperature and salinity data such as from expendable bathythermograph, moored ocean buoys, etc. A 21-year assimilation experiment is carried out by using OVALS and the Tropical Pacific circulation model. The results show that the assimilation system may effectively improve the estimations of temperature and salinity by assimilating all kinds of observations. Moreover, the root mean square errors of temperature and salinity in the upper depth less than 420 m reach 0.63℃ and 0.34 psu.     

Evaluation on surface current observing network of high frequency ground wave radars in the Gulf of Thailand

Due to the high cost of ocean observation system, the scientific design of observation network becomes much important. The current network of the high frequency radar system in the Gulf of Thailand has been studied using a three-dimensional coastal ocean model. At first, the observations from current radars have been assimilated into this coastal model and the forecast results have improved due to the data assimilation. But the results also show that further optimization of the observing network is necessary. And then, a series of experiments were carried out to assess the performance of the existing high frequency ground wave radar surface current observation system. The simulated surface current data in three regions were assimilated sequentially using an efficient ensemble Kalman filter data assimilation scheme. The experimental results showed that the coastal surface current observation system plays a positive role in improving the numerical simulation of the currents. Compared with the control experiment without assimilation, the simulation precision of surface and subsurface current had been improved after assimilated the surface currents observed at current networks. However, the improvement for three observing regions was quite different and current observing network in the Gulf of Thailand is not effective and a further optimization is required. Based on these evaluations, a manual scheme has been designed by discarding the redundant and inefficient locations and adding new stations where the performance after data assimilation is still low. For comparison, an objective scheme based on the idea of data assimilation has been obtained. Results show that all the two schemes of observing network perform better than the original network and optimal scheme-based data assimilation is much superior to the manual scheme that based on the evaluation of original observing network in the Gulf of Thailand. The distributions of the optimal network of radars could be a useful guidance for future design of observing system in this region.     

Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea

Coastal management and maritime safety strongly rely on accurate representations of the sea state. Both dynamical models and observations provide abundant pieces of information. However, none of them provides the complete picture. The assimilation of observations into models is one way to improve our knowledge of the ocean state. Its application in coastal models remains challenging because of the wide range of temporal and spatial variabilities of the processes involved. This study investigates the assimilation of temperature profiles with the ensemble Kalman filter in 3-D North Sea simulations. The model error is represented by the standard deviation of an ensemble of model states. Parameters’ values for the ensemble generation are first computed from the misfit between the data and the model results without assimilation. Then, two square root algorithms are applied to assimilate the data. The impact of data assimilation on the simulated temperature is assessed. Results show that the ensemble Kalman filter is adequate for improving temperature forecasts in coastal areas, under adequate model error specification.     

GRACE terrestrial water storage data assimilation based on the ensemble four-dimensional variational method PODEn4DVar:Method and validation

Seasonal and interannual changes in the Earth's gravity field are mainly due to mass exchange among the atmosphere,ocean,and continental water sources.The terrestrial water storage changes,detected as gravity changes by the Gravity Recovery and Climate Experiment(GRACE) satellites,are mainly caused by precipitation,evapotranspiration,river transportation and downward infiltration processes.In this study,a land data assimilation system LDAS-G was developed to assimilate the GRACE terrestrial water storage(TWS) data into the Community Land Model(CLM3.5) using the POD-based ensemble four-dimensional variational assimilation method PODEn4 DVar,disaggregating the GRACE large-scale terrestrial water storage changes vertically and in time,and placing constraints on the simulation of vertical hydrological variables to improve land surface hydrological simulations.The ideal experiments conducted at a single point and assimilation experiments carried out over China by the LDAS-G data assimilation system showed that the system developed in this study improved the simulation of land surface hydrological variables,indicating the potential of GRACE data assimilation in large-scale land surface hydrological research and applications.     

Assimilation of SLA and SST data into an OGCM for the Indian Ocean

 Remotely sensed observations of sea-level anomaly and sea-surface temperature have been assimilated into an implementation of the Miami Isopycnic Coordinate Ocean Model (MICOM) for the Indian Ocean using the Ensemble Kalman Filter (EnKF). The system has been applied in a hindcast validation experiment to examine the properties of the assimilation scheme when used with a full ocean general circulation model and real observations. This work is considered as a first step towards an operational ocean monitoring and forecasting system for the Indian Ocean. The assimilation of real data has demonstrated that the sequential EnKF can efficiently control the model evolution in time. The use of data assimilation requires a significant amount of additional processing and computational resources. However, we have tried to justify the cost of using a sophisticated assimilation scheme by demonstrating strong regional and temporal dependencies of the covariance statistics, which include highly anisotropic and flow-dependent correlation functions. In particular, we observed a marked difference between error statistics in the equatorial region and at off-equatorial latitudes. We have also demonstrated how the assimilation of SLA and SST improves the model fields with respect to real observations. Independent in situ temperature profiles have been used to examine the impact of assimilating the remotely sensed observations. These intercomparisons have shown that the model temperature and salinity fields better resemble in situ observations in the assimilation experiment than in a model free-run case. On the other hand, it is also expected that assimilation of in situ profiles is needed to properly control the deep ocean circulation. Received: 8 January 2002 / Accepted: 8 April 2002     

Benchmarking the mesoscale variability in global ocean eddy-permitting numerical systems

The role of data assimilation procedures on representing ocean mesoscale variability is assessed by applying eddy statistics to a state-of-the-art global ocean reanalysis (C-GLORS), a free global ocean simulation (performed with the NEMO system) and an observation-based dataset (ARMOR3D) used as an independent benchmark. Numerical results are computed on a 1/4 ^° horizontal grid (ORCA025) and share the same resolution with ARMOR3D dataset. This “eddy-permitting” resolution is sufficient to allow ocean eddies to form. Further to assessing the eddy statistics from three different datasets, a global three-dimensional eddy detection system is implemented in order to bypass the need of regional-dependent definition of thresholds, typical of commonly adopted eddy detection algorithms. It thus provides full three-dimensional eddy statistics segmenting vertical profiles from local rotational velocities. This criterion is crucial for discerning real eddies from transient surface noise that inevitably affects any two-dimensional algorithm. Data assimilation enhances and corrects mesoscale variability on a wide range of features that cannot be well reproduced otherwise. The free simulation fairly reproduces eddies emerging from western boundary currents and deep baroclinic instabilities, while underestimates shallower vortexes that populate the full basin. The ocean reanalysis recovers most of the missing turbulence, shown by satellite products , that is not generated by the model itself and consistently projects surface variability deep into the water column. The comparison with the statistically reconstructed vertical profiles from ARMOR3D show that ocean data assimilation is able to embed variability into the model dynamics, constraining eddies with in situ and altimetry observation and generating them consistently with local environment.     

Joint altimetric and in-situ data assimilation using the GRACE mean dynamic topography: a 1993–1998 hindcast experiment in the Tropical Pacific Ocean

The altimetric satellite signal is the sum of the geoid and the dynamic topography, but only the latter is relevant to oceanographic applications. Poor knowledge of the geoid has prevented oceanographers from fully exploiting altimetric measurements through its absolute component, and applications have concentrated on ocean variability through analyses of sea level anomalies. Recent geodetic missions like CHAMP, GRACE and the forthcoming GOCE are changing this perspective. In this study, data assimilation is used to reconstruct the Tropical Pacific Ocean circulation during the 1993–1996 period. Multivariate observations are assimilated into a primitive equation ocean model (OPA) using a reduced order Kalman filter (the Singular Evolutive Extended Kalman filter). A 6-year (1993–1998) hindcast experiment is analyzed and validated by comparison with observations. In this experiment, the new capability offered by an observed absolute dynamic topography (built using the GRACE geoid to reference the altimetric data) is used to assimilate, in an efficient way, the in-situ temperature profiles from the TAO/TRITON moorings together with the T/P and ERS1&2 altimetric signal. GRACE data improves compatibility between both observation data sets. The difficulties encountered in this regard in previous studies such as Parent et al. (J Mar Syst 40–41:381–401, 2003) are now circumvented. This improvement helps provide more efficient data assimilation, as evidenced, by assessing the results against independent data. This leads in particular to significantly more realistic currents and vertical thermal structures.     

Application of altimetry data assimilation on mesoscale eddies simulation

Mesoscale eddy plays an important role in the ocean circulation. In order to improve the simulation accuracy of the mesoscale eddies, a three-dimensional variation (3DVAR) data assimilation system called Ocean Variational Analysis System (OVALS) is coupled with a POM model to simulate the mesoscale eddies in the Northwest Pacific Ocean. In this system, the sea surface height anomaly (SSHA) data by satellite altimeters are assimilated and translated into pseudo temperature and salinity (T-S) profile data. Then, these profile data are taken as observation data to be assimilated again and produce the three-dimensional analysis T-S field. According to the characteristics of mesoscale eddy, the most appropriate assimilation parameters are set up and testified in this system. A ten years mesoscale eddies simulation and comparison experiment is made, which includes two schemes: assimilation and non-assimilation. The results of comparison between two schemes and the observation show that the simulation accuracy of the assimilation scheme is much better than that of non-assimilation, which verified that the altimetry data assimilation method can improve the simulation accuracy of the mesoscale dramatically and indicates that it is possible to use this system on the forecast of mesoscale eddies in the future.     

Calibration/Data Assimilation Approach for Integrating GRACE Data into the WaterGAP Global Hydrology Model (WGHM) Using an Ensemble Kalman Filter: First Results

We introduce a new ensemble-based Kalman filter approach to assimilate GRACE satellite gravity data into the WaterGAP Global Hydrology Model. The approach (1) enables the use of the spatial resolution provided by GRACE by including the satellite observations as a gridded data product, (2) accounts for the complex spatial GRACE error correlation pattern by rigorous error propagation from the monthly GRACE solutions, and (3) allows us to integrate model parameter calibration and data assimilation within a unified framework. We investigate the formal contribution of GRACE observations to the Kalman filter update by analysis of the Kalman gain matrix. We then present first model runs, calibrated via data assimilation, for two different experiments: the first one assimilates GRACE basin averages of total water storage and the second one introduces gridded GRACE data at \(5^\circ\) resolution into the assimilation. We finally validate the assimilated model by running it in free mode (i.e., without adding any further GRACE information) for a period of 3 years following the assimilation phase and comparing the results to the GRACE observations available for this period.     

An Assessment of Two-Dimensional Past Sea Level Reconstructions Over 1950–2009 Based on Tide-Gauge Data and Different Input Sea Level Grids

We compare different past sea level reconstructions over the 1950–2009 time span using the Empirical Orthogonal Function (EOF) approach. The reconstructions are based on 91 long (up to 60?years) but sparsely distributed tide-gauge records and gridded sea level data from two numerical ocean models over 1958–2007 (the DRAKKAR/NEMO model without data assimilation and the simple ocean data assimilation ocean reanalysis-SODA-) and satellite altimetry data over 1993–2009. We find that the reconstructed global mean sea level computed over the?~60-year-long time span little depends on the input spatial grids. This is unlike the regional variability maps that appear very sensitive to the considered input spatial grids. Using the DRAKKAR/NEMO model, we test the influence of the period covered by the input spatial grids and the number of EOFs modes used to reconstruct sea level. Comparing with tide-gauge records not used in the reconstruction, we determine optimal values for these two parameters. As suggested by previous studies, the longer the time span covered by the spatial grids, the better the fit with unused tide gauges. Comparison of the reconstructed regional trends over 1950–2009 based on the two ocean models and satellite altimetry grids shows good agreement in the tropics and substantial differences in the mid and high latitude regions, and in western boundary current areas as well. The reconstructed spatial variability seems very sensitive to the input spatial information. No clear best case emerges. Thus, using the longest available model-based spatial functions will not necessarily give the most realistic results as it will be much dependent on the quality of the model (and its associated forcing). Altimetry-based reconstructions (with 17-year long input grids) give results somewhat similar to cases with longer model grids. It is likely that better representation of the sea level regional variability by satellite altimetry compensates the shorter input grids length. While waiting for much longer altimetry records, improved past sea level reconstructions may be obtained by averaging an ensemble of different model-based reconstructions, as classically done in climate modelling. Here, we present such a ‘mean’ reconstruction (with associated uncertainty) based on averaging the three individual reconstructions discussed above.