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74
A Singular Evolutive Extended Kalman Filter For Data Assimilation In Oceanography
 Journal of Marine Systems
, 1996
"... In this work, we propose a modified form of the extended Kalman filter for assimilating oceanic data into numerical models. Its development consists essentially in approximating the error covariance matrix by a singular low rank matrix, which amounts in practice to making no correction in those dire ..."
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Cited by 107 (9 self)
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In this work, we propose a modified form of the extended Kalman filter for assimilating oceanic data into numerical models. Its development consists essentially in approximating the error covariance matrix by a singular low rank matrix, which amounts in practice to making no correction in those directions for which the error is attenuated by the system. This not only reduce the implementation cost to an acceptable level but may also improve the filter stability as well. The "directions of correction" of the filter evolve with time according to the model evolution, which is the most original feature of this filter, distinguishing it from other sequential assimilation methods based on the projection onto a fixed basis of functions. A method for initializing the filter based on the empirical orthogonal functions is also described. An example of assimilation based on the quasigeostrophic model for a square ocean domain with a certain wind stress forcing pattern, is given. Although this is ...
Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation
, 2010
"... This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The nonGaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspe ..."
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Cited by 47 (10 self)
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This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The nonGaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these nonGaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in highdimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on secondorder moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and nonGaussian effects remain. They essentially originate in the nonlinear models and in the nonGaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are
A DualWeighted Approach to Order Reduction in 4DVAR Data Assimilation
 MONTHLY WEATHER REVIEW VOLUME 136
, 2008
"... Strategies to achieve order reduction in fourdimensional variational data assimilation (4DVAR) search for an optimal lowrank state subspace for the analysis update. A common feature of the reduction methods proposed in atmospheric and oceanographic studies is that the identification of the basis f ..."
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Cited by 28 (12 self)
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Strategies to achieve order reduction in fourdimensional variational data assimilation (4DVAR) search for an optimal lowrank state subspace for the analysis update. A common feature of the reduction methods proposed in atmospheric and oceanographic studies is that the identification of the basis functions relies on the model dynamics only, without properly accounting for the specific details of the data assimilation system (DAS). In this study a general framework of the proper orthogonal decomposition (POD) method is considered and a costeffective approach is proposed to incorporate DAS information into the orderreduction procedure. The sensitivities of the cost functional in 4DVAR data assimilation with respect to the timevarying model state are obtained from a backward integration of the adjoint model. This information is further used to define appropriate weights and to implement a dualweighted proper orthogonal decomposition (DWPOD) method for order reduction. The use of a weighted ensemble data mean and weighted snapshots using the adjoint DAS is a novel element in reducedorder 4DVAR data assimilation. Numerical results are presented with a global shallowwater model based on the Lin–Rood fluxform semiLagrangian scheme. A simplified 4DVAR DAS is considered in the twinexperiment framework with initial conditions specified from the 40yr ECMWF ReAnalysis (ERA40) datasets. A comparative analysis with the standard
2006: Efficiency of reducedorder, timedependent adjoint data assimilation approaches
 J. Oceanogr
"... Applications of adjoint data assimilation, which is designed to bring an ocean circulation model into consistency with ocean observations, are computationally demanding. To improve the convergence rate of an optimization, reducedorder optimization methods that reduce the size of the control vector ..."
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Cited by 27 (0 self)
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Applications of adjoint data assimilation, which is designed to bring an ocean circulation model into consistency with ocean observations, are computationally demanding. To improve the convergence rate of an optimization, reducedorder optimization methods that reduce the size of the control vector by projecting it onto a limited number of basis functions were suggested. In this paper, we show that such order reduction can indeed speed up the initial convergence rate of an assimilation effort in the eastern subtropical North Atlantic using in situ and satellite data as constraints. However, an improved performance of the optimization was only obtained with a hybrid approach where the optimization is started in a reduced subspace but is continued subsequently using the full control space. In such an experiment about 50 % of the computational cost can be saved as compared to the optimization in the full control space. Although several orderreduction approaches seem feasible, the best result was obtained by projecting the control vector onto Empirical Orthogonal Functions (EOFs) computed from a set of adjusted control vectors estimated previously from an optimization using the same model configuration.
Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation
 MONTHLY WEATHER REVIEW
, 2008
"... The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upperocean model a ..."
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Cited by 21 (6 self)
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The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upperocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identicaltwin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Modelgenerated oceanic datasets are assimilated to produce a timecontinuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean
Sequential Data Assimilation Techniques in Oceanography
, 2003
"... this article, we will focus on sequential DA methods that constitute the second class. These methods use a probabilistic framework and give estimates of the whole system state sequentially by propagating information only forward in time. This avoids deriving an inverse or an adjoint model and theref ..."
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Cited by 19 (3 self)
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this article, we will focus on sequential DA methods that constitute the second class. These methods use a probabilistic framework and give estimates of the whole system state sequentially by propagating information only forward in time. This avoids deriving an inverse or an adjoint model and therefore makes sequential methods easier to adapt for all models. Further, the probabilistic framework is more convenient for error estimation and further stochastic analysis such as threshold characterization
2003: Assimilation of drifter observations for the reconstruction of the Eulerian circulation
"... [1] In light of the increasing number of drifting buoys in the ocean and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach ..."
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Cited by 17 (1 self)
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[1] In light of the increasing number of drifting buoys in the ocean and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach is developed based on optimal interpolation (OI) methods, which takes into account directly the Lagrangian nature of the observations. An idealized version of this general formulation is tested in the framework of identical twin experiments using a reduced gravity, quasigeostrophic model. An extensive study is conducted to quantify the effectiveness of Lagrangian data assimilation as a function of the number of drifters, the frequency of assimilation, and the uncertainties associated with the forcing functions driving the ocean model. The performance of the Lagrangian assimilation technique is also compared to that of conventional methods of assimilating drifters as moving current meters, and assimilation of Eulerian data, such as fixedpoint velocities. Overall, the results are very favorable for the assimilation of Lagrangian observations to improve the Eulerian velocity field in ocean models. The results of our assimilation twin experiments imply an optimal sampling frequency for oceanic Lagrangian instruments in
An optimized design for a moored instrument array in the tropical Atlantic
, 1998
"... Abstract. This paper presents a series of observing system simulation experiments (OSSEs) which are intended as a design study for a proposed array of instrumented moorings in the tropical Atlantic Ocean. Fields of TOPEX/Poseidon sea surface height anomalies are subsampled with the goal being recons ..."
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Cited by 15 (0 self)
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Abstract. This paper presents a series of observing system simulation experiments (OSSEs) which are intended as a design study for a proposed array of instrumented moorings in the tropical Atlantic Ocean. Fields of TOPEX/Poseidon sea surface height anomalies are subsampled with the goal being reconstruction of the original fields through the use of reducedspace Kalman filter data assimilation at a restricted number of locations. Our approach differs from typical identical and fraternal twin experiments in that real observed data (i.e., TOPEX/Poseidon data) are subsampled and used in place of synthetic data in all phases of the OSSEs. In this way the question of how closely a particular modelgenerated data set resembles nature is avoided. Several data assimilation runs are performed in order to optimize the location of a limited number of moorings for the proposed Pilot Research Moored Array in the Tropical Atlantic (PIRATA). Results of experiments in which data are assimilated at 2øN, 2øS and the equator and the longitude is systematically varied by 5 ø show that the greatest impact of the assimilated data occurs when the observations are taken between 15øW and 30øW. Next, a more systematic technique is presented which allows us to determine optimal points in an objective fashion
2008: A new approximate solution of the optimal nonlinear filter for data assimilation in meteorology and
"... This paper introduces a new approximate solution of the optimal nonlinear filter suitable for nonlinear oceanic and atmospheric data assimilation problems. The method is based on a local linearization in a lowrank kernel representation of the state’s probability density function. In the resulting l ..."
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Cited by 13 (4 self)
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This paper introduces a new approximate solution of the optimal nonlinear filter suitable for nonlinear oceanic and atmospheric data assimilation problems. The method is based on a local linearization in a lowrank kernel representation of the state’s probability density function. In the resulting lowrank kernel particle Kalman (LRKPK) filter, the standard (weight type) particle filter correction is complemented by a Kalmantype correction for each particle using the covariance matrix of the kernel mixture. The LRKPK filter’s solution is then obtained as the weighted average of several lowrank square root Kalman filters operating in parallel. The Kalmantype correction reduces the risk of ensemble degeneracy, which enables the filter to efficiently operate with fewer particles than the particle filter. Combined with the lowrank approximation, it allows the implementation of the LRKPK filter with highdimensional oceanic and atmospheric systems. The new filter is described and its relevance demonstrated through applications with the simple Lorenz model and a realistic configuration of the Princeton Ocean Model (POM) in the Mediterranean Sea. 1.
Globality and Optimality in Climate Field Reconstructions from Proxy Data
, 1999
"... A primary objective of paleoclimate research is the characterization of natural climate variability on time scales of years to millennia. We develop here a systematic methodology for the objective and verifiable reconstruction of climate fields from sparse observational networks of proxy data, using ..."
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Cited by 11 (4 self)
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A primary objective of paleoclimate research is the characterization of natural climate variability on time scales of years to millennia. We develop here a systematic methodology for the objective and verifiable reconstruction of climate fields from sparse observational networks of proxy data, using reduced space objective analysis. In this approach we seek to reconstruct only the leading modes of largescale variability which are observed in the modern climate and resolved in the proxy data. Given explicit assumptions, the analysis produces climate fields, indices, and their associated estimated errors. These may be subsequently checked for consistency with parameter choices and procedural assumptions by comparison with withheld data and results from benchmark experiments. The methodology is applied to the candidate tree ring indicator data set described by Villalba et al. (1999), for the reconstruction of gridded Pacific Ocean basin sea surface temperature (SST) over the interval 10...