Dmitri A. Nechaev

On the zonal and meridional circulation and ocean transports between Tasmania and Antarctica

The large scale circulation of the WOCE hydrographic section SR3 between Tasmania and Antarctica is studied through inversion of hydrographic, wind stress and current meter data acquired between 1993 and 1996. These data are assimilated within the framework of a steady state model that is based on hydrostatics, geostrophy, tracer, and potential vorticity conservation. Posterior variances of the major current systems are estimated via the implicit inversion of the Hessian matrix, associated with the assimilation scheme. Analysis of the residuals shows that averaged water mass properties are conserved and that most of the adjustment by the solution is through the uniform vertical displacement of density surfaces within the water column. The inclusion of the tracer and potential vorticity constraints allows parts of the large-scale vertical and meridional circulation to be determined. The upwelling over the Antarctic Divergence is driven mainly by the winds, while the downwelling in the Sub-antarctic Front (SAF) is shown to result from the meridional gradients of the density field caused by the mean Antarctic Circumpolar Current. The shallow meridional and vertical circulation in the SAF is along density surfaces and follows the salinity minimum waters to a depth of 500 dbar. This result suggests a possible mechanism for ventilation of Antarctic Intermediate Water. The total volume transport between Tasmania and Antarctica is estimated as 151±50 Sv, with variations between repeat measurements for this section of about 10 Sv. The cross-section circulation pattern can be qualitatively subdivided into five persistent features and their transports and errors are given.

A Diagnostic Stabilized Finite-Element Ocean Circulation Model

Abstract A stabilized finite-element (FE) algorithm for the solution of oceanic large scale circulation equations and optimization of the solutions is presented. Pseudo-residual-free bubble function (RFBF) stabilization technique is utilized to enforce robustness of the numerics and override limitations imposed by the Babuska–Brezzi condition on the choice of functional spaces. The numerical scheme is formulated on an unstructured tetrahedral 3d grid in velocity–pressure variables defined as piecewise linear continuous functions. The model is equipped with a standard variational data assimilation scheme, capable to perform optimization of the solutions with respect to open lateral boundary conditions and external forcing imposed at the ocean surface. We demonstrate the model performance in applications to idealized and realistic basin-scale flows. Using the adjoint method, the code is tested against a synthetic climatological data set for the South Atlantic ocean which includes hydrology, fluxes at the ocean surface and satellite altimetry. The optimized solution proves to be consistent with all these data sets, fitting them within the error bars. The presented diagnostic tool retains the advantages of existing FE ocean circulation models and in addition (1) improves resolution of the bottom boundary layer due to employment of the 3d tetrahedral elements; (2) enforces numerical robustness through utilization of the RFBF stabilization, and (3) provides an opportunity to optimize the solutions by means of 3d variational data assimilation. Numerical efficiency of the code makes this a desirable tool for dynamically constrained analyses of large datasets.

Reconstruction of summer Barents Sea circulation from climatological data

Abstract An estimate of the summer Barents Sea circulation is constructed as a four‐dimensional variational inverse of the monthly hydrographic and atmospheric climatologies. The reconstructed evolution of temperature, salinity, and velocity fields provides the best fit to climatological data and satisfies dynamical and kinematic constraints of a primitive equation ocean circulation model. The data‐optimized Barents Sea state is in general agreement ‐with the existing schemes of circulation in the region. The circulation is characterized by the 3.2 Sv inflow from the Norwegian Sea with the Norwegian Atlantic Current. Approximately 1.5 Sv of this inflow recirculates along the northern flank of Bear Island Trough, while the major branch of the current crosses the Barents Sea and outflows through Franz Josef Land—Novaya Zemliya and the Kara Gate straits with transports of 1.1 Sv and 0.6 Sv, respectively. The data assimilation reveals an eastward current between the Great and Central banks and cyclonic circulation in the region between Central Bank and Novaya Zemliya. These two circulation feature s have recently been confirmed in a number of publications. The reconstructed surface heat and salt fluxes are in qualitative and quantitative agreement with the known observational estimates. The posterior error analysis and sensitivity experiments provide additional arguments in support of the reliability of the data assimilation results.

A Method of Successive Corrections of the Control Subspace in the Reduced-Order Variational Data Assimilation*

A version of the reduced control space four-dimensional variational method (R4DVAR) of data assimilation into numerical models is proposed. In contrast to the conventional 4DVAR schemes, the method does not require development of the tangent linear and adjoint codes for implementation. The proposed R4DVAR technique is based on minimization of the cost function in a sequence of low-dimensional subspaces of the control space. Performance of the method is demonstrated in a series of twin-data assimilation experiments into a nonlinear quasigeostrophic model utilized as a strong constraint. When the adjoint code is stable, R4DVAR’s convergence rate is comparable to that of the standard 4DVAR algorithm. In the presence of strong instabilities in the direct model, R4DVAR works better than 4DVAR whose performance is deteriorated because of the breakdown of the tangent linear approximation. Comparison of the 4DVAR and R4DVAR also shows that R4DVAR becomes advantageous when observations are sparse and noisy.

Large scale circulation in the Bellingshausen and Amundsen seas as a variational inverse of climatological data

Atmospheric and oceanic climatological data are combined with the World Ocean Circulation Experiment S4 section hydrology in the framework of a variational data assimilation scheme into a steady state nonlinear model of the large-scale circulation. The reconstructed fields of density and three-dimensional velocity are dynamically balanced and provide qualitative and quantitative estimates of the circulation features of the Amundsen and Bellingshausen seas. Natural assumptions on the spatial structure of the density covariance matrices enable us to obtain realistic coastal currents near the continental slopes of Antarctica within the framework of model equations. The horizontal circulation pattern reveals along shore westward current with typical velocities of 1 cm s -1 and cyclonic gyres in the Amundsen and Bellingshausen seas transporting 2 and 0.5 Sv, respectively. Three eastward branches of the Antarctic Circumpolar Current are observed in offshore regions. Their transports are diagnosed as 19, 12, and 6 Sv. The lower layer is characterized by westward countercurrent in the northwestern part of the basin with the transport of 8 Sv. Average Ekman upwelling rate in the major part of the basin amounts to 20-25 m yr -1 . Downwelling in the shelf regions of the Bellingshausen and Amundsen seas is estimated as 250-350 m yr -1 .

Seasonal variation of the North Atlantic Current

The seasonal circulation of the upper 1000 m of the North Atlantic between 408-558N and 208 -4 08W is calculated using the traditional dynamic method and a circulation model with a density field that evolves with the flow. The model is of finite difference form and is based on dynamics that describe the nonlinear evolution of the ocean at low Rossby number. The model is controlled by initial and boundary conditions that include air-sea buoyancy and momentum fluxes. The model is run in two ways: with controls specified directly from observations and with controls inferred by the assimilation of all available data. These data include surface drifter trajectories, sea levels from the TOPEX/Poseidon altimeter, Bunker air-sea fluxes, and the Levitus climatological monthly means of temperature and salinity. We conclude that the North Atlantic Current transport is 40 6 18 Sv with seasonal variations of the order of 2 Sv. The mean vertical transport out of the region is 2 6 9 Sv and is subject to seasonal variations of 2 Sv. Overall, these estimates are in good agreement with integral North Atlantic Current features derived from independent long-term measurements made in the region over the past decade. The optimal ocean state has a volume transport across the western boundary of 51 6 3 Sv with a maximum transport of 61 6 5 Sv in April-May and a minimum of 42 6 3S v in October-November. This western inflow is compensated by mean outflows of 28 6 2 (east), 16 6 2 (north), 5 6 2 (south), and 1.8 6 0.4 Sv out of the domain at 1000 m. Sensitivity studies show that nonlinear mixing and seasonality are important in determining the overall circulation. Specifically, steady boundary forcing leads to annual mean transports that are 15-25% smaller than transports obtained with seasonal forcing. Winter convection is also shown to play a significant role in determining the overall circulation pattern.

Variational Assimilation of Glider Data in Monterey Bay

Abstract : Temperature and salinity profiles observed by gliders in the Monterey Bay in August 2003 are assimilated into NCOM model in the framework of a 3dVar scheme with a hybrid background error covariance (BEC) representation. The model performance is validated against independent mooring observations for the assimilation runs with I-hour analysis cycle In the first experiment the background error statistics was estimated using the ensemble of model states spanning the entire observation period, whereas in the second experiment the BEC information was acquired by averaging over the 3day floating temporal window (FTW) centered at the analysis time. It is found that the FTW scheme provides lower discrepancy between the values of temperature, salinity and velocity predicted by the model and observed at the moorings. The improvement becomes more clearly visible during the upwelling and relaxations events, associated with intermittent wind forcing. During these periods the FTW scheme provides a significantly (2-3 times) better fit to the mooring data.

A Hybrid Background Error Covariance Model for Assimilating Glider Data into a Coastal Ocean Model

AbstractA hybrid background error covariance (BEC) model for three-dimensional variational data assimilation of glider data into the Navy Coastal Ocean Model (NCOM) is introduced. Similar to existing atmospheric hybrid BEC models, the proposed model combines low-rank ensemble covariances with the heuristic Gaussian-shaped covariances to estimate forecast error statistics. The distinctive features of the proposed BEC model are the following: (i) formulation in terms of inverse error covariances, (ii) adaptive determination of the rank m of with information criterion based on the innovation error statistics, (iii) restriction of the heuristic covariance operator to the null space of , and (iv) definition of the BEC magnitudes through separate analyses of the innovation error statistics in the state space and the null space of .The BEC model is validated by assimilation experiments with simulated and real data obtained during a glider survey of the Monterey Bay in August 2003. It is shown that the proposed h...

Evaluation of the Northern Gulf of Mexico Littoral Initiative Model Based On the Observed Temperature and Salinity In the Mississippi Bight

Temperature and salinity measurements from the Northern Gulf of Mexico Littoral Initiative (NGLI) survey during August 30 - September 14, 2000 reveal a high level of temporal and spatial variability in the Mississippi Bight. To support scientific studies using a numerical model, a three-dimensional hydrodynamic Estuarine and Coastal Ocean Model (ECOM) is implemented in the Mississippi Bight. The ECOM is run with realistic topography, stratification and meteorological forcing to hindcast circulation on a shallow and highly variable shelf of the Mississippi Bight. The results of the model are compared with observation to evaluate the ECOM performance on different temporal scales. Based on the area oceanography and data availability, three temporal scales are chosen for model/data comparison: fine scale (less than an hour), diurnal, and large scale (a two-week period). Limitations of the ECOM application on each scale are discussed. The model is capable to reproduce observed water masses, describe spatial distribution of water properties, and simulate areas with high horizontal gradient such as freshwater plumes. However, delayed response to meteorological forcing, overestimated mixing rates and uncertainties in computation of river discharges result in statistically significant bias in the simulations. Along with traditional linear correlations from all observational points and spectral analysis over the diurnal cycle, a new technique of model validation is introduced. The technique is a new application of an existing variational interpolation method. Detailed description of the method and numerical procedure allow one to apply this technique to any oceanographic data with prescribed data variances for model/data comparison.

On the time-splitting scheme used in the Princeton Ocean Model

The analysis of the time-splitting procedure implemented in the Princeton Ocean Model (POM) is presented. The time-splitting procedure uses different time steps to describe the evolution of interacting fast and slow propagating modes. In the general case the exact separation of the fast and slow modes is not possible. The main idea of the analyzed procedure is to split the system of primitive equations into two systems of equations for interacting external and internal modes. By definition, the internal mode varies slowly and the crux of the problem is to determine the proper filter, which excludes the fast component of the external mode variables in the relevant equations. The objective of this paper is to examine properties of the POM time-splitting procedure applied to equations governing the simplest linear non-rotating two-layer model of constant depth. The simplicity of the model makes it possible to study these properties analytically. First, the time-split system of differential equations is examined for two types of the determination of the slow component based on an asymptotic approach or time-averaging. Second, the differential-difference scheme is developed and some criteria of its stability are discussed for centered, forward, or backward time-averaging of the external mode variables. Finally, the stability of the POM time-splitting schemes with centered and forward time-averaging is analyzed. The effect of the Asselin filter on solutions of the considered schemes is studied. It is assumed that questions arising in the analysis of the simplest model are inherent in the general model as well.