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.     

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.     

High-resolution synthetic monitoring by a 4-dimensional variational data assimilation system in the northwestern North Pacific

A data assimilation system is applied to the integrated monitoring of oceanic states in the northwestern North Pacific by combining a high resolution ocean general circulation model with an adjoint method. A comparison of assimilation results with observations shows that the system is better able to represent synoptic features of ocean circulation than do models or data alone. Furthermore, meso-scale features associated with frontal structures and eddies, which are often seen in the Kuroshio and Oyashio extension regions and the Sea of Japan, are better defined in the assimilation results. These features suggest that our 4D-VAR high-resolution data assimilation system is capable of providing time series data which satisfy the model physics and fit the observations, and hence the ocean state derived from our system has greater information content than that obtained from earlier methods.     

Data assimilation into a Princeton Ocean Model of the Mediterranean Sea using advanced Kalman filters

This study investigates the effectiveness of the Singular Evolutive Extended Kalman filter (SEEK) and its variants (SEIK and SFEK filters) for data assimilation into a Princeton Ocean Model (POM) of the Mediterranean Sea. The SEEK filters are sub-optimal Kalman filters based on the approximation of the filter's error covariance matrices by singular low-rank matrices, reducing in this way extensive computational burden. At the initialization, the filters error covariance matrix is parameterized by a set of multivariate empirical orthogonal functions (EOFs) which describe the dominant modes of the system's variability. The Mediterranean model is implemented on a 1/4° × 1/4° horizontal grid with 25 sigma levels and is forced with 6-hour ECMWF re-analysis atmospheric data. Several twin experiments, in which pseudo-observations of altimetric data and/or data profiles were assimilated, were first performed to evaluate the filters performances and to study their sensitivities to different parameters and setups. The results of these experiments were very encouraging and helped in setting up an effective configuration for the assimilation of real data in near-real time situation. In the hindcast experiments, Topex/Poseidon and ERS weekly sea level anomaly data were first assimilated during 1993 and the filters solution was evaluated against independent Reynolds sea surface temperature (SST) analysis. The assimilation system was able to significantly enhance the consistency between the model and the assimilated data, although the improvement with respect to independent SST data was significantly less pronounced. The model SST was only improved after including SST data in the assimilation system.     

Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo

This study considers advanced statistical approaches for sequential data assimilation. These are explored in the context of nowcasting and forecasting using nonlinear differential equation based marine ecosystem models assimilating sparse and noisy non-Gaussian multivariate observations. The statistical framework uses a state space model with the goal of estimating the time evolving probability distribution of the ecosystem state. Assimilation of observations relies on stochastic dynamic prediction and Bayesian principles. In this study, a new sequential data assimilation approach is introduced based on Markov Chain Monte Carlo (MCMC). The ecosystem state is represented by an ensemble, or sample, from which distributional properties, or summary statistical measures, can be derived. The Metropolis-Hastings based MCMC approach is compared and contrasted with two other sequential data assimilation approaches: sequential importance resampling, and the (approximate) ensemble Kalman filter (including computational comparisons). A simple illustrative application is provided based on a 0-D nonlinear plankton ecosystem model with multivariate non-Gaussian observations of the ecosystem state from a coastal ocean observatory. The MCMC approach is shown to be straightforward to implement and to effectively characterize the non-Gaussian ecosystem state in both nowcast and forecast experiments. Results are reported which illustrate how non-Gaussian information originates, and how it can be used to characterize ecosystem properties.