Max Yaremchuk

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 .

Filtering Drifter Trajectories Sampled at Submesoscale Resolution

In this paper, a variational method for removing positioning errors (PEs) from drifter trajectories is proposed. The technique is based on the assumption of statistical independence of the PEs and drifter accelerations. The method provides a realistic approximation to the probability density function of the accelerations while keeping the difference between the filtered and observed trajectories within the error bars of the positioning noise. Performance of the method is demonstrated in application to real data acquired during the Grand Lagrangian Deployment (GLAD) experiment in the Northern Gulf of Mexico in 2012.

Background Error Correlation Modeling with Diffusion Operators

Many background error correlation (BEC) models in data assimilation are formulated in terms of a positive-definite smoothing operator B that is employed to simulate the action of correlation matrix on a vector in state space. In this chapter, a general procedure for constructing a BEC model as a rational function of the diffusion operator D is presented and analytic expressions for the respective correlation functions in the homogeneous case are obtained. It is shown that this class of BEC models can describe multi-scale stochastic fields whose characteristic scales can be expressed in terms of the polynomial coefficients of the model. In particular, the connection between the inverse binomial model and the well-known Gaussian model \(\mathbf{\mathsf{B}}_{g} =\exp \mathbf{\mathsf{D}}\) is established and the relationships between the respective decorrelation scales are derived.By its definition, the BEC operator has to have a unit diagonal and requires appropriate renormalization by rescaling. The exact computation of the rescaling factors (diagonal elements of B) is a computationally expensive procedure, therefore an efficient numerical approximation is needed. Under the assumption of local homogeneity of D, a heuristic method for computing the diagonal elements of B is proposed. It is shown that the method is sufficiently accurate for realistic applications, and requires 102 times less computational resources than other methods of diagonal estimation that do not take into account prior information on the structure of B.

An inverse modeling study of circulation in the Eastern Bering Sea during 2007-2010

A two-way nested 4d-variational data assimilation system is implemented in the Eastern Bering Sea (EBS) to investigate changes in circulation and thermodynamic state for a 3.8-year period. Assimilated observations include data from 19 moorings deployed on the shelf and in the Bering Strait, 1705 hydrographic stations occupied during eight surveys, and remotely sensed sea surface temperature and sea surface height (SSH) data. Validation of the presented 4dVar reanalysis against the output of two sequential data-assimilative systems (the Bering Ecosystem Study ice-ocean Modeling and Assimilation System (BESTMAS) and the Arctic Cap Nowcast-Forecast System (ACNFS)) has shown that the product is more consistent with the observed transports in the Bering Strait and in the EBS interior both in terms of their magnitude and time variability. Analysis of the data-optimized solution quantifies a sequence of wind-forced events that resulted in the anomalous heat and freshwater transports through the Bering Strait, including a 28-day long flow reversal that occurred in November of 2009 and carried Siberian Coastal Current water down to the Gulf of Anadyr. Lagrangian study of the Arctic-bound Pacific waters indicates the extreme importance of the cross-shelf exchange along the path of the Bering Slope Current and quantifies the spectrum of residence times for the waters entering EBS through Unimak Pass and through Aleutian passages. Residence times in the EBS cold pool are diagnosed to be 2-3 times longer than those in the surrounding waters. This article is protected by copyright. All rights reserved.