Data assimilation with the Ensemble Kalman Filter and the SEIK filter applied to a finite element model of the North Atlantic

Currently there are different approaches to filter algorithms based on the Kalman filter. One of the most used filter algorithms is the Ensemble Kalman Filter (EnKF). It uses a Monte Carlo approach to the filtering problem. Another approach is given by the Singular Evolutive Extended Kalman (SEEK) and Singular Evolutive Interpolated Kalman (SEIK) filters. These filters operate explicitly on a low-dimensional error space which is represented by an ensemble of model states. The EnKF and the SEIK filter have been implemented within a parallel data assimilation framework in the Finite Element Ocean Model FEOM. In order to compare the filter performances of the algorithms, several data assimilation experiments are performed. The filter algorithms have been applied with a model configuration of FEOM for the North Atlantic to assimilate the sea surface height in twin experiments. The dependence of the filter estimates on the represented error subspace is discussed. In the experiments the SEIK algorithm provides better estimates than the EnKF. Furthermore, the SEIK filter is much cheaper in terms of computing time.     

Multigrid state vector for data assimilation in a two-way nested model of the Ligurian Sea

A system of two nested models composed by a coarse resolution model of the Mediterranean Sea, an intermediate resolution model of the Provençal Basin and a high resolution model of the Ligurian Sea is coupled with a Kalman-filter based assimilation method. The state vector for the data assimilation is composed by the temperature, salinity and elevation of the three models. The forecast error is estimated by an ensemble run of 200 members by perturbing initial condition and atmospheric forcings. The 50 dominant empirical orthogonal functions (EOF) are taken as the error covariance of the model forecast. This error covariance is assumed to be constant in time. Sea surface temperature (SST) and sea surface height (SSH) are assimilated in this system.     

Validation of a hybrid optimal interpolation and Kalman filter scheme for sea surface temperature assimilation

A hybrid data assimilation scheme designed for operational assimilation of satellite sea surface temperatures (SST) into an ocean model has been developed and validated against in-situ observations. The scheme consists of an optimal interpolation (OI) part and a greatly simplified Kalman filter (KF) part.The OI is performed only in the longitudinal and latitudinal directions. A climatological field is used as a background field for the interpolation. It is constructed by fitting daily averages of satellite SST to the annual mean, annual, and semiannual harmonics in a 20 km by 20 km grid. The background error covariance is approximated by a spatially varying two-dimensional exponential covariance model. The parameters of the covariance model are fitted to the deviations of the satellite data from the background field using data from a full year.The simplified KF uses ocean model forecasts as a background field. It is based on the assumption that it is possible to neglect horizontal SST covariances in the filter and that the typical time scale for vertical mixing in the mixed layer is much shorter than the average time between observations. We therefore assume that the error variance in a column of water is evenly spread out throughout the mixed layer. The result of these simplifications is a computationally very efficient KF.A one year validation of the scheme is performed for year 2001 using an operational eddy resolving ocean model covering the North Sea and the Baltic Sea. It is found that assimilation of sea surface temperature data reduces the model root mean square error from 1.13 °C to 0.70 °C. The hybrid scheme is found to reduce the root mean square error slightly more than the simplified KF without OI to 0.66 °C. The inclusion of spatially varying satellite error variances does not improve the performance of the scheme significantly.     

Application of a SEEK filter to a 1D biogeochemical model of the Ligurian Sea: Twin experiments and real in-situ data assimilation

The Singular Evolutive Extended Kalman (SEEK) filter has been implemented to assimilate in-situ data in a 1D coupled physical-ecosystem model of the Ligurian Sea. The biogeochemical model describes the partly decoupled nitrogen and carbon cycles of the pelagic food web. The GHER hydrodynamic model (1D version) is used to represent the physical forcings. The data assimilation scheme (SEEK filter) parameterizes the error statistics by means of a set of empirical orthogonal functions (EOFs). Twin experiments are first performed with the aim to choose the suitable experimental protocol (observation and estimation vectors, number of EOFs, frequency of the assimilation,…) and to assess the SEEK filter performances. This protocol is then applied to perform real data assimilation experiments using the DYFAMED data base. By assimilating phytoplankton observations, the method has allowed to improve not only the representation of the phytoplankton community, but also of other variables such as zooplankton and bacteria that evolve with model dynamics and that are not corrected by the data assimilation scheme. The validation of the assimilation method and the improvement of model results are studied by means of suitable error measurements.     

Assimilation of altimetric data in the mid-latitude oceans using the Singular Evolutive Extended Kalman filter with an eddy-resolving, primitive equation model

A new data assimilation scheme has been elaborated for ocean circulation models based on the concept of an evolutive, reduced-order Kalman filter. The dimension of the assimilation problem is reduced by expressing the initial error covariance matrix as a truncated series of orthogonal perturbations. This error sub-space evolves during the assimilation so as to capture the growing modes of the estimation error. The algorithm has been formulated in quite a general fashion to make it tractable with a large variety of ocean models and measurement types. In the present paper, we have examined three possible strategies to compute the evolution of the error subspace in the so-called Singular Evolutive Extended Kalman (SEEK) filter: the steady filter considers a time-independent error sub-space, the apprentice filter progressively enriches the error sub-space with the information learned from the innovation vector after each analysis step, and the dynamical filter updates the error sub-space according to the model dynamics. The SEEK filter has been implemented to assimilate synthetic observations of the surface topography in a non-linear, primitive equation model that uses density as vertical coordinate. A simplified box configuration has been adopted to simulate a Gulf Stream-like current and its associated eddies and gyres with a resolution of 20 km in the horizontal, and 4 levels in the vertical. The concept of twin experiments is used to demonstrate that the conventional SEEK filter must be complemented by a learning mechanism in order to model the misrepresented tail of the error covariance matrix. An approach based on the vertical physics of the isopycnal model, is shown particularly robust to control the velocity field in deep layers with surface observations only. The cost of the method makes it a suitable candidate for large-size assimilation problems and operational applications.     

Improving the physics of a coupled physical–biogeochemical model of the North Atlantic through data assimilation: Impact on the ecosystem

Several studies on coupled physical–biogeochemical models have shown that major deficiencies in the biogeochemical fields arise from the deficiencies in the physical flow fields. This paper examines the improvement of the physics through data assimilation, and the subsequent impact on the ecosystem response in a coupled model of the North Atlantic. Sea surface temperature and sea surface height data are assimilated with a sequential method based on the SEEK filter adapted to the coupling needs. The model domain covers the Atlantic from 20°S to 70°N at eddy-permitting resolution. The biogeochemical model is a NPZD-DOM model based on the P3ZD formulation. The results of an annual assimilated simulation are compared with an annual free simulation.With assimilation, the representation of the mixed layer depth is significantly improved in mid latitudes, even though the mixed layer depth is generally overestimated compared to the observations. The representation of the mean and variance of the currents is also significantly improved.The nutrient input in the euphotic zone is used to assess the data assimilation impact on the ecosystem. Data assimilation results in a 50% reduction of the input due to vertical mixing in mid-latitudes, and in a four- to six-fold increase of the advective fluxes in mid-latitudes and subtropics. Averaged zonally, the net impact is a threefold increase for the subtropical gyre, and a moderate (20–30%) decrease at mid and high latitudes.Surface chlorophyll concentration increases along the subtropical gyre borders, but little changes are detected at mid and high latitudes. An increase of the primary production appears along the Gulf Stream path, but it represents only 12% on average for mid and high latitudes. In the subtropical gyre centre, primary production is augmented but stays underestimated (20% of observations). These experiments show the benefits of physical data assimilation in coupled physical–biogeochemical applications.     

Application of an Ensemble Kalman filter to a 1-D coupled hydrodynamic-ecosystem model of the Ligurian Sea

The Ensemble Kalman filter (EnKF) has been applied to a 1-D complex ecosystem model coupled with a hydrodynamic model of the Ligurian Sea. In order to improve the performance of the EnKF, an ensemble subsampling strategy has been used to better represent the covariance matrices and a pre-analysis step for correcting the non-normality of the members distribution has been implemented. Twin experiments have been realized to assess the performance of the developed tool and a real data assimilation experiment has been conducted to hindcast the ecosystem at the Dyfamed site during the year 2000. Finally the performance of the EnKF has been compared with a Singular Evolutive Extended Kalman (SEEK) filter with a fixed basis. We conclude that, on one hand, there is a benefit in using the subsampling strategy and the lognormal transformation with the EnKF, and on the other hand, this filter presents better performance than the fixed basis version of the SEEK filter. However, it also incurs a large computational cost.     

Improving assimilation of SeaWiFS data by the application of bias correction with a local SEIK filter

Ocean-biogeochemical models show typically significant errors in the representation of chlorophyll concentrations. The model state can be improved by the assimilation of satellite chlorophyll data with algorithms based on the Kalman filter. However, these algorithms do usually not account for the possibility that the model prediction contains systematic errors in the form of model bias. Accounting explicitly for model biases can improve the assimilation performance. To study the effect of bias estimation on the estimation of surface chlorophyll concentrations, chlorophyll data from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) are assimilated on a daily basis into the NASA Ocean Biogeochemical Model (NOBM). The assimilation is performed by the ensemble-based SEIK filter combined with an online bias correction scheme. The SEIK filter is simplified here by the use of a static error covariance matrix. The performance of the filter algorithm is assessed by comparison with independent in situ data over the 7-year period 1998–2004. The bias correction results in significant improvements of the surface chlorophyll concentrations compared to the assimilation without bias estimation. With bias estimation, the daily surface chlorophyll estimates from the assimilation show about 3.3% lower error than SeaWiFS data. In contrast, the error in the global surface chlorophyll estimate without bias estimation is 10.9% larger than the error of SeaWiFS data.     

Forecast verification of a 3D model of the Mediterranean Sea. The use of discrete wavelet transforms and EOFs in the skill assessment of spatial forecasts

The quality assessment of a nested model system of the Mediterranean Sea is realised. The model has two zooms in the Provençal Basin and in the Ligurian Sea, realised with a two-way nesting approach. The experiment lasts for nine weeks, and at each week sea surface temperature (SST) and sea level anomaly are assimilated. The quality assessment of the surface temperature is done in a spatio-temporal approach, to take into account the high complexity of the SST distribution. We focus on the multi-scale nature of oceanic processes using two powerful tools for spatio-temporal analysis, wavelets and Empirical Orthogonal Functions (EOFs). We apply two-dimensional wavelets to decompose the high-resolution model and observed SST into different spatial scales. The Ligurian Sea model results are compared to observations at each of those spatial scales, with special attention on how the assimilation affects the model behaviour. We also use EOFs to assess the similarities between the Mediterranean Sea model and the observed SST. The results show that the assimilation mainly affects the model large-scale features, whereas the small scales show little or no improvement and sometimes, even a decrease in their skill. The multiresolution analysis reveals the connection between large- and small-scale errors, and how the choice of the maximum correlation length of the assimilation scheme affects the distribution of the model error among the different spatial scales.     

On the key role of nutrient data to constrain a coupled physical–biogeochemical assimilative model of the North Atlantic Ocean

A sequential assimilative system has been implemented into a coupled physical–biogeochemical model (CPBM) of the North Atlantic basin at eddy-permitting resolution (1/4°), with the long-term goal of estimating the basin scale patterns of the oceanic primary production and their seasonal variability. The assimilation system, which is based on the SEEK filter [Brasseur, P., Verron, J., 2006. The SEEK filter method for data assimilation in oceanography: a synthesis. Ocean Dynamics. doi: 10.1007/s10236-006-0080-3], has been adapted to this CPBM in order to control the physical and biogeochemical components of the coupled model separately or in combination. The assimilated data are the satellite Topex/Poseidon and ERS altimetric data, the AVHRR Sea Surface Temperature observations, and the Levitus climatology for salinity, temperature and nitrate.In the present study, different assimilation experiments are conducted to assess the relative usefulness of the assimilated data to improve the representation of the primary production by the CPBM. Consistently with the results obtained by Berline et al. [Berline, L., Brankart, J-M., Brasseur, P., Ourmières, Y., Verron, J., 2007. Improving the physics of a coupled physical–biogeochemical model of the North Atlantic through data assimilation: impact on the ecosystem. J. Mar. Syst. 64 (1–4), 153–172] with a comparable assimilative model, it is shown that the assimilation of physical data alone can improve the representation of the mixed layer depth, but the impact on the ecosystem is rather weak. In some situations, the physical data assimilation can even worsen the ecosystem response for areas where the prior nutrient distribution is significantly incorrect. However, these experiments also show that the combined assimilation of physical and nutrient data has a positive impact on the phytoplankton patterns by comparison with SeaWiFS ocean colour data, demonstrating the good complementarity between SST, altimetry and in situ nutrient data. These results suggest that more intensive in situ measurements of biogeochemical nutrients are urgently needed at basin scale to initiate a permanent monitoring of oceanic ecosystems.     

Wave data assimilation with the Kalman filter

A new data assimilation method for ocean waves is presented, based on an efficient low-rank approximation to the Kalman filter. Both the extended Kalman filter and a truncated second-order filter are implemented. In order to explicitly estimate past wind corrections based on current wave measurements, the filter is extended to a fixed-lag Kalman smoother for the wind fields. The filter is tested in a number of synthetic experiments with simple geometries. Propagation experiments with errors in the boundary condition showed that the KF was able to accurately propagate forecast errors, resulting in spatially varying error correlations, which would be impossible to model with time-independent assimilation methods like OI. An explicit comparison with an OI assimilation scheme showed that the KF also is superior in estimating the sea state at some distance from the observations. In experiments with errors in the driving wind, the modeled error estimates were also in agreement with the actual forecast errors. The bias in the state estimate, which is introduced through the nonlinear dependence of the waves on the driving wind field, was largely removed by the second-order filter, even without actually assimilating data. Assimilation of wave observations resulted in an improved wave analysis and in correction of past wind fields. The accuracy of this wind correction depends strongly on the actual place and time of wave generation, which is correctly modeled by the error estimate supplied by the Kalman filter. In summary, the KF approach is shown to be a reliable assimilation scheme in these simple experiments, and has the advantage over other assimilation methods that it supplies explicit dynamical error estimates.     

Assessment of sea surface temperature observational networks in the Baltic Sea and North Sea

The satellite and in situ Sea Surface Temperature (SST) observational networks in the Baltic Sea and North Sea are evaluated based on the quality of the gridded SST products generated from the networks. A multi-indicator approach is applied in the assessment. It includes evaluation of data quality, effective data coverage, field reconstruction error and model nowcast error. The results show that the best available full-coverage SST product is generated by assimilating the SST observations to obtain a yearly mean model bias of 0.07 °C and RMSE of 0.64 °C. The effective data coverage rate is 31% by using AVHRR (Advanced Very High Resolution Radiometer) data from NOAA (National Ocean and Atmosphere Administration) satellites 12, 14 and 16. The data redundancy increases rapidly with the number of infrared sensors. Using either NOAA satellite 12 or all 3 satellites makes a small difference with regard to derived effective coverage and the ocean model nowcast error. The influence of using the in situ SST observations in the SST field reconstruction is negligibly small. Instead, the major role of in situ SST observations is in calibrating the satellite observations. To study the relative importance of data quality and data coverage, an assessment is done for two satellite products: one product is based entirely on NOAA 12 data and has larger coverage but lower quality. The other product is a subset of the SAF products (derived from NOAA 14 and 16) and has lower coverage but higher quality. Based on current monitoring, modelling and assimilation technology, the results suggest that the data quality is an important factor in further improving the quality of the gridded SST products. Recommendations are made for possible further improvements of the existing SST observational networks.     

1/32° real-time global ocean prediction and value-added over 1/16° resolution

A 1/32° global ocean nowcast/forecast system has been developed by the Naval Research Laboratory at the Stennis Space Center. It started running at the Naval Oceanographic Office in near real-time on 1 Nov. 2003 and has been running daily in real-time since 1 Mar. 2005. It became an operational system on 6 March 2006, replacing the existing 1/16° system which ceased operation on 12 March 2006. Both systems use the NRL Layered Ocean Model (NLOM) with assimilation of sea surface height from satellite altimeters and sea surface temperature from multi-channel satellite infrared radiometers. Real-time and archived results are available online at http://www.ocean.nrlssc.navy.mil/global_nlom. The 1/32° system has improvements over the earlier system that can be grouped into two categories: (1) better resolution and representation of dynamical processes and (2) design modifications. The design modifications are the result of accrued knowledge since the development of the earlier 1/16° system. The improved horizontal resolution of the 1/32° system has significant dynamical benefits which increase the ability of the model to accurately nowcast and skillfully forecast. At the finer resolution, current pathways and their transports become more accurate, the sea surface height (SSH) variability increases and becomes more realistic and even the global ocean circulation experiences some changes (including inter-basin exchange). These improvements make the 1/32° system a better dynamical interpolator of assimilated satellite altimeter track data, using a one-day model forecast as the first guess. The result is quantitatively more accurate nowcasts, as is illustrated by several model-data comparisons. Based on comparisons with ocean color imagery in the northwestern Arabian Sea and the Gulf of Oman, the 1/32° system has even demonstrated the ability to map small eddies, 25–75 km in diameter, with 70% reliability and a median eddy center location error of 22.5 km, a surprising and unanticipated result from assimilation of altimeter track data. For all of the eddies (50% small eddies), the reliability was 80% and the median eddy center location error was 29 km. The 1/32° system also exhibits improved forecast skill in relation to the 1/16° system. This is due to (a) a more accurate initial condition for the forecast and (b) better resolution and representation of critical dynamical processes (such as upper ocean – topographic coupling via mesoscale flow instabilities) which allow the model to more accurately evolve these features in time while running in forecast mode (forecast atmospheric forcing for the first 5 days, then gradually reverting toward climatology for the remainder of the 30-day forecast period). At 1/32° resolution, forecast SSH generally compares better with unassimilated observations and the anomaly correlation of the forecast SSH exceeds that from persistence by a larger amount than found in the 1/16° system.     

Multivariate assimilation in MERCATOR project: New statistical parameters from forecast error estimation

The new operational prototype of Mercator (french Global Ocean Data Assimilation Experiment contribution) is composed of a North Atlantic primitive equation ocean model OPA (Ocean Parallel Algorithm between 20°S and 70°N, [Madec, G., P. Delecluse, M. Imbard and C. Lévy (1998). OPA8.1 ocean general circulation model reference manuel. Notes du pôle de modélisation IPSL. n°11: 91p]) and of a multivariate and multidata assimilation scheme [De Mey, P. and M. Benkiran (2002). “A multivariate reduced-order optimal interpolation method and its application in Mediterranean basin-scale circulation.” Ocean Forecasting : Conceptual basis and application, Pinardi, N., Springer Verlag.] This system has already given some significant improvements from previous Mercator configurations (M. Benkiran, personal communication). However some biases on ocean state still remain in the tropics where the reduced-order optimal interpolation scheme is suspected to be ill-parameted in the model forecast error. Indeed the guess error covariance matrix is decomposed into an error variance value and a spatio-temporal correlation function which are assumed to have some “good” properties (spatial homogeneity of the correlation function, constant ratio between signal and error variance). This study shows how we can use ensemble methods to validate these assumptions. We can see that the correlation function can reach negative values locally, mostly in regions of high variability contradictory with the homogeneous hypothesis. The reduced space used in the operational configuration is based on the signal seasonal Empirical Orthogonal Functions (EOFs). An empirical relationship between signal and error variance has been set and the correlation function is the same on every dimension of the reduced space. By projection of the estimated guess error variance onto the reduced space, we find a repartition of this quantity quite different to what was set in the system. The error statistics is found to be inhomogeneous compared to hypothesis made in the assimilation scheme. These two new parameters tested separately in the assimilation scheme gives significant improvements of the forecast and analysis results. This is particularly obvious in the tropics. But relationship between signal and error statistics (as assumed in the optimal interpolation) is found to be complex.     

Using data assimilation in laboratory experiments of geophysical flows

Data assimilation is used in numerical simulations of laboratory experiments in a stratified, rotating fluid. The experiments are performed on the large Coriolis turntable (Grenoble, France), which achieves a high degree of similarity with the ocean, and the simulations are performed with a two-layer shallow water model, using the SEEK method for data assimilation. Since the flow is measured with a high level of precision and resolution, a detailed analysis of a forecasting system is feasible. The procedure is tested for the baroclinic instability of a two-layer vortex. It is shown that the method of data assimilation properly captures the details of the initial flow perturbation. Then it is shown by sensitivity studies that an error of the model, attributed to small non-hydrostatic effects, can be distinguished from the error growth associated with the intrinsic instability of the system. Finally, it is experimentally demonstrated that the velocity field in the lower layer can be well controlled by data assimilation limited to the top layer.     

Altimeter assimilation in the OCCAM global model: Part I: A twin experiment

An altimeter data assimilation scheme has been tested in the OCCAM (Ocean Circulation and Climate Advanced Modelling) global 1/4°, 36-level model using a twin experiment format. The Cooper and Haines displacement scheme is used. The method works well in most regions and depths. Currents and densities in the top 1000 m generally improve by over 50–70% after 5 months of sea level assimilation every 15 days. Below 1000 m, an error reduction of up to 50% is achieved. The errors remain low during a further 60-day run without assimilation. Diagnostics for the North Atlantic, the Tropical Pacific and the Antarctic Circumpolar Current are shown alongside the global averages.The main problems encountered were in weakly stratified regions of the Antarctic and Arctic seas. A scale selective filter is developed to avoid assimilating scales much larger than the local deformation radius, and this avoids the adverse assimilation effects in the southern oceans. A companion paper uses this scheme to assimilate TOPEX and ERS-1 altimeter maps.     

Seasonal variability in sea surface oceanographic conditions in the Aegean Sea (Eastern Mediterranean): an overview

Seasonal variability and the spatial distribution of sea surface temperatures (SST) and salinities (SSS) are reviewed, in relation to the prevailing climatological conditions, heat fluxes, water budget and general water circulation patterns. Within this context, consideration is given to: sea surface temperatures; air temperatures; precipitation; evaporation; wind speeds and directions; freshwater (mainly riverine) discharges throughout the Aegean; and the exchange of water masses with the Black Sea and eastern Mediterranean Sea. The investigation of satellite images, covering a 6-yr period (1988–1994), has enabled a synthesis of the monthly sea surface thermal distribution to be established.The climate of the Aegean Sea is characterised by annual air temperatures of 16–19.5°C, precipitation of about 500 mm yr⁻¹ and evaporation of some 4 mm d⁻¹. The Aegean has a negative heat budget (approximately −25 W m⁻²) and positive water balance (+ 1.0 m yr⁻¹), when inflow from the Black Sea is considered. During the summer, the (northerly) Etesians are the dominant winds over the Sea.Mean monthly sea surface temperatures (SST) vary from 8°C in the north during winter, up to 26°C in the south during summer. SST depends mainly upon air temperature; there is a month's delay between the former and latter maxima. The sea surface salinity (SSS) varies also spatially and seasonally, ranging from less than 31 psu, in the north, to more than 39 psu, in the southeast; lower values (< 25 psu) occur adjacent to the river mouths. SSSs present their maximum differences during summer, whilst during winter and autumn the distribution of SSS is more uniform. The overall spatial SST and SSS distribution pattern is controlled by: distribution of the (colder) Black Sea Waters; advection of the (warmer) Levantine Waters, from the southeastern part of the Aegean; upwelling and downwelling; and, to a lesser extent, but locally important, freshwater riverine inflows.     

The Mercator global ocean operational analysis system: Assessment and validation of an 11-year reanalysis

This paper presents Prototype Système 2 Global (PSY2G), the first Mercator global Ocean General Circulation Model (OGCM) to assimilate along-track sea level anomaly (SLA) satellite data. Based on a coarse resolution ocean model, this system was developed mainly for climatic purposes and will provide, for example, initial oceanic states for coupled ocean-atmosphere seasonal predictions. It has been operational since 3 September 2003 and produces an analysis and a two-week forecast for the global ocean every week. The PSY2G system uses an incremental assimilation scheme based on the Cooper and Haines [Cooper, M., Haines, K., 1996. Data assimilation with water property conservation. J. Geophys. Res., 101, 1059-1077.] lifting–lowering of isopycnals. The SLA increment is obtained using an optimal interpolation method then the correction is partitioned into baroclinic and barotropic contributions. The baroclinic ocean state correction consists of temperature, salinity and geostrophic velocity increments and the barotropic correction is a barotropic velocity increment. A reanalysis (1993–2003) was carried out that enabled the PSY2G system to perform its first operational cycle. All available SLA data sets (TOPEX/Poséïdon, ERS2, Geosat-Follow-On, Jason1 and Envisat) were assimilated for the 1993–2003 period. The major objective of this study is to assess the reanalysis from both an assimilation and a thermodynamic point of view in order to evaluate its realism, especially in the tropical band which is a key region for climatic studies. Although the system is also able to deliver forecasts, we have mainly focused on analysis. These results are useful because they give an a priori estimation of the qualities and capabilities of the operational ocean analysis system that has been implemented. In particular, the reanalysis identifies some regional biases in sea level variability such as near the Antarctic Circumpolar Current, in the eastern Equatorial Pacific and in the Norwegian Sea (generally less than 1 cm) with a small seasonal cycle. This is attributed to changes in mean circulation and vertical stratification caused by the assimilation methodology. But the model's low resolution, inaccurate physical parameterisations (especially for ocean–ice interactions) and surface atmospheric forcing also contribute to the occurrence of the SLA biases. A detailed analysis of the thermohaline structure of the ocean reveals that the isopycnal lifting–lowering tends to diffuse vertically the main thermocline. The impact on temperature is that the surface layer (0–200 m) becomes cooler whereas in deeper waters (from 500 to 1500 m), the ocean becomes slightly warmer. This is particularly true in the tropics, between 30°N and 30°S. However it can be demonstrated that the assimilation improves the variability in both surface currents and sub-surface temperature in the Equatorial Pacific Ocean.     

Measurement of ocean temperatures using instruments carried by Antarctic fur seals

The study aimed to test the utility of instruments deployed on marine mammals for measuring physical oceanographic variation and, using this method, to examine temperature variation in the coastal waters around South Georgia. There was a significant correlation between temperature measurements made using a towed undulating oceanographic recorder (UOR) and concurrent measurements from time-depth recorders (TDRs) fitted to lactating Antarctic fur seals foraging from the coast of South Georgia. Congruence was found at horizontal spatial scales from 0.01°×0.01° to 0.5°×0.5° (degrees of latitude and longitude), and at a vertical scale of 10 m. However, there was no significant correlation between temperature measured by TDRs in the top 5 m and sea surface temperature (SST) measured by satellite remote sensing. TDR data provided information about temperature variation vertically through the water column, and through time. The UOR data were used to recalibrate the TDR data in order to correct for the slow response time of the TDR thermistor relative to the speed of seal movements through the water column. Seasonal temperature variation was apparent, and temperatures also varied between regions, and with bathymetry. These results were consistent with the current interpretation of the coastal oceanography around South Georgia. In particular, the relationship between on- and off-shelf waters showed larger amounts of warmer surface water in a region in which more run-off was to be expected. The study also showed that Antarctic fur seals concentrate their activity in regions of colder, and presumably oceanic, water. Such instrumented animals could provide near real time data for assimilation into ocean models.     

Gaussian anamorphosis extension of the DEnKF for combined state parameter estimation: Application to a 1D ocean ecosystem model

We consider the problem of combined state-parameter estimations in biased nonlinear models with non-Gaussian extensions of the Deterministic Ensemble Kalman Filter (DEnKF). We focus on the particular framework of ocean ecosystem models. Such models present important obstacles to the use of data assimilation methods based on Kalman filtering due to the non-linearity of the models, the constraints of positiveness that apply to the variables and parameters, and the non-Gaussian distribution of the variables in which they result.We present extensions of the DEnKF dealing with these difficulties by introducing a nonlinear change of variables (anamorphosis function) in order to execute the analysis step with Gaussian transformed variables and parameters. Several strategies to build the anamorphosis functions are investigated and compared within the framework of twin experiments realized in a simple 1D ocean ecosystem model. A solution to the problem of the specification of the observation error for transformed observations is suggested. The study highlights the inability of the plain DEnKF with a simple post-processing of the negative values to properly estimate parameters when constraints of positiveness apply to the variables. It goes on to show that the introduction of the Gaussian anamorphosis can remedy these assimilation biases.