Comparison of reduced-order, sequential and variational data assimilation methods in the tropical Pacific Ocean

This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the Tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasi-linear regime, both methods produce similarly good results. However the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more non-linear regime, when Tropical Instability Waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error

Reduced-order 4D-Var: a preconditioner for the Incremental 4D-Var data assimilation method

This study demonstrates how the incremental 4D-Var data assimilation method can be applied efficiently preconditione d in an application to an oceanographic problem. The approach consists in performing a few iterations of the reduced-order 4D-Var prior to the incremental 4D-Var in the full space in order to achieve faster convergence. An application performed in the tropical Pacific Ocean, with assimilation of TAO temperature data, shows the method to be both feasible and efficient. It allows the global cost of the assimilation to be reduced by a factor of 2 without affecting the quality of the solution

Assessment of the ocean circulation in the Azores region as predicted by a numerical model assimilating altimeter data from Topex/Poseidon and ERS-1 satellites

International audienceTwo years of altimetric data from Topex/Poseidon (October 1992-September 1994) and ERS-1 (October 1992-December 1993) were assimilated into a numerical model of the North Atlantic. The results of these simulations are analysed in the Azores region to assess the performance of our model in this particular region. Maps of instantaneous dynamic topography and transports show that the model performs well in reproducing the velocities and transports of the Azores Front. Drifter data from the Semaphore experiment are also used to study the correlation between the drifter velocities and the corresponding model velocities. Some interesting oceanographic results are also obtained by examining the seasonal and interannual variability of the circulation and the influence of bathymetry on the variability of the Azores Front. Thus, on the basis of our two year experiment, it is possible to confirm the circulation patterns proposed by previous studies regarding the seasonal variations in the origin of the Azores Current. Moreover, it is shown that the Azores Current is quite narrow in the first year of assimilation (1992-1993), but becomes much wider in the second year (1993-1994). The role of the bathymetry appears important in this area since the mesoscale activity is shown to be strongly related to the presence of topographic slopes. Finally, spectral analyses of sea-level changes over time and space are used to identify two types of wave already noticed in other studies: a wave with (300 km)-1 wave number and (120 days)-1 frequency, which is characteristic of mesoscale undulation, and a wave with (600 km)-1 wave number and (250 days)-1 frequency which probably corresponds to a Rossby wave generated in the east of the basin

Dynamical evolution of the error statistics with the SEEK filter to assimilate altimetric data in eddy-resolving ocean models

ISSN 0035 - 9009International audienceThe Singular Evolutive Extended Kalman (SEEK) filter introduced by Pham et al. is applied to a primitive‐equation model in order to reconstruct the mesoscale circulation typical of the mid‐latitude ocean from altimetric data. The SEEK filter is a variant of the Kalman‐filter algorithm based on two concepts: the order reduction of the initial‐error covariance matrix, and the dynamical evolution of the reduced‐order basis. This makes the method potentially suitable for problems with a high number of degrees of freedom.Previous work has shown the ability of a steady version of the filter to improve the vertical structure of the ocean thermocline in the case of the quasi‐linear dynamics associated with the equatorial tropical Pacific Ocean, and the need to combine the dynamical evolution of the basis with an adaptive scheme in a mid‐latitude ocean model of the Gulf Stream region.This work examines the potential advantages of the dynamical evolution of the basis functions with simple assimilation experiments. It demonstrates the ability of the method to propagate in time the statistical properties of the system when the filter is initialized properly. However, the lack of robustness of the filter is investigated theoretically and experimentally, showing the need to consider variants of the method when the filter is not properly initialized

Vortex merger in surface quasi-geostrophy

The merger of two identical surface temperature vortices is studied in the surface quasi- geostrophic model. The motivation for this study is the observation of the merger of sub- mesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incom- pressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and sym- metric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vor- tex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.PostprintPeer reviewe

Thermocline Circulation in the Solomon Sea: A Modeling Study

International audienceIn the southwest Pacific, thermocline waters connecting the tropics to the equator via western boundary currents (WBCs) transit through the Solomon Sea. Despite its importance in feeding the Equatorial Undercurrent (EUC) and its related potential influence on the low-frequency modulation of ENSO, the circulation inside the Solomon Sea is poorly documented. A model has been implemented to analyze the mean and the seasonal variability of the Solomon Sea thermocline circulation. The circulation involves an inflow from the open southern Solomon Sea, which is distributed via WBCs between the three north exiting straits of the semiclosed Solomon Sea. The system of WBCs is found to be complex. Its main feature, the New Guinea Coastal Undercurrent, splits in two branches: one flowing through Vitiaz Strait and the other one, the New Britain Coastal Undercurrent (NBCU), exiting at Solomon Strait. East of the Solomon Sea, the encounter of the South Equatorial Current (SEC) with the Solomon Islands forms a previously unknown current, which the authors call the Solomon Islands Coastal Undercurrent (SICU). The NBCU, SEC, and SICU participate in the feeding of the New Ireland Coastal Undercurrent (NICU), which retroflects to the Equatorial Undercurrent, providing the most direct western boundary EUC connection, which is particularly active in June-August. The Solomon Sea WBC seasonal variability results from the combination of equatorial dynamics, remotely forced Rossby waves north of 10°S, and the spinup and spindown of the subtropical gyre as a response of Rossby waves forced south of 10°S

Динамика бароклинных вихрей с нулевой суммарной интенсивностью (хетонов)

Приводится обзор работ, посвященных изучению свойств вихревых движений в устойчиво стратифицированной быстро вращающейся жидкости и описываемых уравнением эволюции потенциального вихря в квазигеострофическом приближении. Основное внимание уделено вихрям с нулевой суммарной циркуляцией — так называемым хетонам. Рассматриваются задачи самодвижения дискретных хетонов, устойчивости единичного распределенного хетона, взаимодействия двух хетонов конечных размеров. Приводятся также новые решения задач о трех и более дискретных вихрях хетонной структуры. Даются примеры возникновения хаотических режимов. Обсуждаются область применимости хетонной теории и перспективыее возможных приложений, в частности, — для анализа динамической стадии развития глубокой конвекции в океане

4D-Var/SEEK : A Consistent Hybrid Variational-Smoothing Data Assimilation Method

A mixed variational-smoothing data assimilation method is derived under the perfect-model hypothesis. An incremental 4D-Var analysis scheme is supplemented with a low-rank approximation of its equivalent Kalman smoother, under the perfect-model assumption. A consistent method results, where the analysis and forecast error covariances provided by the smoother part describe the errors performed respectively during the incremental 4D-Var analysis and the model prediction phases. This is because the whole method is built around a low-rank approximation of the forecast error covariance matrix, and different hypotheses for the computation of the analysis and that of its error covariances are avoided. The method provides both flow-depen- dent analysis and forecast error covariances. In addition, most current developments for pre-operational or operational variational data assimilation systems are either already embedded within the method or may be straightforwar- dly included to it

Comparative assimilation of Topex/poseidon and ERS altimetric data and of TAO temperature data in the tropical Pacific Ocean during 1994-1998, and the mean sea-surface height issue

International audienceFive years of Topex/Poseidon (T/P) and ERS sea level anomaly (SLA) data (1994–1998) are assimilated every 10 days into a primitive equation model of the tropical Pacific ocean. The data assimilation technique used here is a reduced-order Kalman filter derived from the Singular Evolutive Extended Kalman (SEEK) filter [J. Mar. Syst. 16(3–4) (1998) 323] with an error covariance matrix parameterised by a subset of multivariate 3D global empirical orthogonal functions (EOFs). The assimilation run is compared to the free run and to independent data from the TAO network. The impact of sea-surface height (SSH) assimilation on surface and subsurface temperature and currents is estimated in the equatorial band. In a second stage, temperature data from the TAO array are assimilated in the same conditions as in the first stage. The comparison between the results of the two assimilation experiments is made mainly with a view to gaining insights into the mean sea-surface height (MSSH) for the assimilation of altimeter data, and more generally, into the question of biases. XBT observations and TAO array data are then used to build a physically more consistent mean sea-surface height for assimilation of SLA data. Results from the assimilation of altimeter data referenced to this new MSSH show significant improvements