On the Approximation of the Coriolis Terms in C-grid Models

A new representation of the Coriolis terms on the Arakawa C grid is proposed. The approximation dumps the grid-scale noise that arises because of spatial averaging of the Coriolis terms when the grid spacing is larger than the deformation radius. The proposed approximation can also be applied in C-grid schemes with semi-implicit treatment of the Coriolis terms. The new scheme is analyzed in the context of the linear inertial-gravity waves and its advantageous behavior is demonstrated with respect to the conventional technique

Simulations of Quasigeostrophic Currents Derived From Satellite Altimetry and Acoustic Tomography of an Open Ocean Region

Acoustic tomography (AT) and satellite altimetry (SA) measure properties of the ocean state with high temporal resolution. That makes these data suitable for long-term monitoring of mesoscale features in the open ocean regions, where the open boundaries are the major sources of model forecast uncertainties on timescales larger than 1 week. In this paper, a finite-difference quasigeostrophic model of an open ocean region is considered as a possible tool for interpolating AT-SA data in space and time. The assimilation algorithm is based upon the 4D variational data assimilation scheme controlled by the initial and boundary conditions of the model. The model configuration used in the simulations corresponds to the AT array deployed by the Japan Marine Science and Technology Center (JAMSTEC) in the region of the Kuroshio Extension in 1997. Twin data experiments show that mesoscale features in an area of 1000 km x 1000 km can be effectively monitored by five acoustic transceivers, measuring reciprocal travel times. The quality of assimilation is studied as a function of the position of the transceivers in the vertical and the effective number of monitored rays. It is shown that reciprocal travel time observations (differential tomography) in combination with SA provide a significant improvement of the quality of assimilation

Decadal Variability of Circulation in the Arctic Ocean Retrieved From Climatological Data by a Variational Method

[1] An inverse 3D finite-element ocean circulation model has been designed and used to study variability of the Arctic Ocean circulation in the last 4 decades. We obtained stationary model solutions with the temperature and salinity fields close to the ones given by the Environmental Working Group (EWG) [1998] atlas. Transports at the open boundaries, wind forcing and hydrographic fields are treated as unknowns, which are varied to minimize a quadratic cost function subject to model constraints. The inverse problem is solved for 10 gridded hydrographic data sets that were obtained as winter and summer averages of EWG data over each of the 4 decades (1950s to 1980s) and over the whole period of observations (1948-1993) documented in the atlas. The results show that Arctic circulation in the last 4 decades has undergone significant changes, which manifest themselves in (1) 10% reduction of the ventilation rate in the Atlantic sector of the Arctic Ocean; (2) substantial decrease of the advective heat and freshwater import at the lateral boundaries; (3) spinning down of the cyclonic gyre in the northern Greenland sea, which is partly driven by deep convection; and (4) 3400 km(3) increase of the net fresh water storage, with 75% taking place in the Atlantic sector of the Arctic Ocean. Most of these changes are similar to the ones observed on seasonal transition from winter to summer climatologies, and indicate that the Arctic Ocean is experiencing a shift toward a warmer state

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

A 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 B(m) with the heuristic Gaussian-shaped covariances B(0) 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 B(m) with information criterion based on the innovation error statistics, (iii) restriction of the heuristic covariance operator B(0) to the null space of B(m), and (iv) definition of the BEC magnitudes through separate analyses of the innovation error statistics in the state space and the null space of B(0). 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 hybrid scheme substantially improves the forecast skill of the heuristic covariance model

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\u27s 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

Seasonal Variation of the North Atlantic Current

The seasonal circulation of the upper 1000 m of the North Atlantic between 40 degrees -55 degreesN and 20 degrees -40 degreesW 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 +/- 18 Sv with seasonal variations of the order of 2 Sv. The mean vertical transport out of the region is 2 +/- 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 +/- 3 Sv with a maximum transport of 61 +/- 5 Sv in April-May and a minimum of 42 +/- 3 Sv in October-November, This western inflow is compensated by mean outflows of 28 +/- 2 (east), 16 +/- 2 (north), 5 +/- 2 (south), and 1.8 +/- 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

Summer Transport Estimates of the Kamchatka Current Derived As a Variational Inverse of Hydrophysical and Surface Drifter Data

The quasistationary summer Bering Sea circulation is reconstructed as a variational inverse of the hydrographic and atmospheric climatologies, transport estimates through the Bering Strait, and surface drifter data. Our results indicate the splitting of the Kamchatka Current in the vicinity of the Shirshov Ridge. This branching is in agreement with independent ARGO drifter observations. It was also found, that transport of the Kamchatka Current gradually increases downstream from 14 Sv in the Olyutorsky Gulf to 24 Sv in the Kamchatka Strait, which is twice higher than previous estimates

Investigation of the Summer Kara Sea Circulation Employing a Variational Data Assimilation Technique

[ 1] The summer circulations and hydrographic fields of the Kara Sea are reconstructed for mean, positive and negative Arctic Oscillation regimes employing a variational data assimilation technique which provides the best fit of reconstructed fields to climatological data and satisfies dynamical and kinematic constraints of a quasi-stationary primitive equation ocean circulation model. The reconstructed circulations agree well with the measurements and are characterized by inflow of 0.63, 0.8, 0.51 Sv through Kara Gate and 1.18, 1.1, 1.12 Sv between Novaya Zemlya and Franz Josef Land, for mean climatologic conditions, positive and negative AO indexes, respectively. The major regions of water outflow for these regimes are the St. Anna Trough (1.17, 1.21, 1.34 Sv) and Vilkitsky/ Shokalsky Straits (0.52, 0.7, 0.51 Sv). The optimized velocity pattern for the mean climatological summer reveals a strong anticyclonic circulation in the central part of the Kara Sea ( Region of Fresh Water Inflow, ROFI zone) and is confirmed by ADCP surveys and laboratory modeling. This circulation is well pronounced for both high and low AO phases, but in the positive AO phase it is shifted approximately 200 km west relatively to its climatological center. During the negative AO phase the ROFI locaion is close to its climatological position. The results of the variational data assimilation approach were compared with the simulated data from the Hamburg Shelf Ocean Model (HAMSOM) and Naval Postgraduate School 18 km resolution (NPS-18) model to validate these models

Reconstruction and Analysis of the Chukchi Sea Circulation in 1990-1991

The Chukchi Sea (CS) circulation reconstructed for September 1990 to October 1991 from sea ice and ocean data is presented and analyzed. The core of the observational data used in this study comprises the records from 12 moorings deployed in 1990 and 1991 in U. S. and Russian waters and two hydrographic surveys conducted in the region in the fall of 1990 and 1991. The observations are processed by a two-step data assimilation procedure involving the Pan-Arctic Ice-Ocean Modeling and Assimilation System (employing a nudging algorithm for sea ice data assimilation) and the Semi-implicit Ocean Model [utilizing a conventional four-dimensional variational (4D-var) assimilation technique]. The reconstructed CS circulation is studied to identify pathways and assess residence times of Pacific water in the region; quantify the balances of volume, freshwater, and heat content; and determine the leading dynamical factors configuring the CS circulation. It is found that in 1990-1991 (high AO index and a cyclonic circulation regime) Pacific water transiting the CS toward the Canada basin followed two major pathways, namely via Herald Canyon (Herald branch of circulation, 0.23 Sv) and between Herald Shoal and Cape Lisburne (central branch of circulation and Alaskan Coastal Current, 0.32 Sv). The annual mean flow through Long Strait was negligible (0.01 Sv). Typical residence time of Pacific water in the region varied between 150 days for waters entering the CS in September and 270 days for waters entering in February/March. Momentum balance analysis reveals that geostrophic balance between barotropic pressure gradient and Coriolis force dominated for most of the year. Baroclinic effects were important for circulation only in the regions with large horizontal salinity gradients associated with the fresh Alaskan and Siberian coastal currents and the Cape Lisburne and Great Siberian polynyas. In the polynyas, the baroclinic effects were due to strong salinification and convection processes associated with sea ice formation

Summer Transport Estimates of the Kamchatka Current Derived As a Variational Inverse of Hydrophysical and Surface Drifter Data

The quasistationary summer Bering Sea circulation is reconstructed as a variational inverse of the hydrographic and atmospheric climatologies, transport estimates through the Bering Strait, and surface drifter data. Our results indicate the splitting of the Kamchatka Current in the vicinity of the Shirshov Ridge. This branching is in agreement with independent ARGO drifter observations. It was also found, that transport of the Kamchatka Current gradually increases downstream from 14 Sv in the Olyutorsky Gulf to 24 Sv in the Kamchatka Strait, which is twice higher than previous estimates