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2008: A reanalysis of ocean climate using Simple Ocean Data Assimilation
"... This paper describes the Simple Ocean Data Assimilation (SODA) reanalysis of ocean climate variability. In the assimilation, a model forecast produced by an ocean general circulation model with an average resolution of 0.25 ° 0.4 ° 40 levels is continuously corrected by contemporaneous observati ..."
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Cited by 119 (9 self)
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This paper describes the Simple Ocean Data Assimilation (SODA) reanalysis of ocean climate variability. In the assimilation, a model forecast produced by an ocean general circulation model with an average resolution of 0.25 ° 0.4 ° 40 levels is continuously corrected by contemporaneous observations with corrections estimated every 10 days. The basic reanalysis, SODA 1.4.2, spans the 44yr period from 1958 to 2001, which complements the span of the 40yr European Centre for MediumRange Weather Forecasts (ECMWF) atmospheric reanalysis (ERA40). The observation set for this experiment includes the historical archive of hydrographic profiles supplemented by ship intake measurements, moored hydrographic observations, and remotely sensed SST. A parallel run, SODA 1.4.0, is forced with identical surface boundary conditions, but without data assimilation. The new reanalysis represents a significant improvement over a previously published version of the SODA algorithm. In particular, eddy kinetic energy and sea level variability are much larger than in previous versions and are more similar to estimates from independent observations. One issue addressed in this paper is the relative importance of the model forecast versus the observations for the analysis. The results show that at nearannual frequencies the forecast model has a strong influence, whereas at decadal frequencies the observations become increasingly dominant in the analysis. As a consequence, interannual variability in SODA 1.4.2 closely resembles interannual variability in SODA 1.4.0. However, decadal anomalies of the 0–700m heat content from SODA 1.4.2 more closely resemble heat content anomalies based on observations. 1.
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 ...
Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems
, 2001
"... This paper considers several filtering methods of stochastic nature, based on Monte Carlo drawing, for the sequential data assimilation in nonlinear models. They include some known methods such as the particle filter and the ensemble Kalman filter and some others introduced by the author: the seco ..."
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Cited by 98 (2 self)
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This paper considers several filtering methods of stochastic nature, based on Monte Carlo drawing, for the sequential data assimilation in nonlinear models. They include some known methods such as the particle filter and the ensemble Kalman filter and some others introduced by the author: the secondorder ensemble Kalman filter and the singular extended interpolated filter. The aim is to study their behavior in the simple nonlinear chaotic Lorenz system, in the hope of getting some insight into more complex models. It is seen that these filters perform satisfactory, but the new filters introduced have the advantage of being less costly. This is achieved through the concept of secondorderexact drawing and the selective error correction, parallel to the tangent space of the attractor of the system (which is of low dimension). Also introduced is the use of a forgetting factor, which could enhance significantly the filter stability in this nonlinear context.
Hydrologic Data Assimilation with the Ensemble Kalman Filter
, 2002
"... Soil moisture controls the partitioning of moisture and energy fluxes at the land surface and is a key variable in weather and climate prediction. The performance of the ensemble Kalman filter (EnKF) for soil moisture estimation is assessed by assimilating Lband (1.4 GHz) microwave radiobrightnes ..."
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Cited by 90 (7 self)
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Soil moisture controls the partitioning of moisture and energy fluxes at the land surface and is a key variable in weather and climate prediction. The performance of the ensemble Kalman filter (EnKF) for soil moisture estimation is assessed by assimilating Lband (1.4 GHz) microwave radiobrightness observations into a land surface model. An optimal smoother (a dynamic variational method) is used as a benchmark for evaluating the filter's performance. In a series of synthetic experiments the effect of ensemble size and nonGaussian forecast errors on the estimation accuracy of the EnKF is investigated. With a state vector dimension of 4608 and a relatively small ensemble size of 30 (or 100; or 500), the actual errors in surface soil moisture at the final update time are reduced by 55% (or 70%; or 80%) from the value obtained without assimilation (as compared to 84% for the optimal smoother). For robust error variance estimates, an ensemble of at least 500 members is needed.
A Local Least Squares Framework for Ensemble Filtering
, 2003
"... Many methods using ensemble integrations of prediction models as integral parts of data assimilation have appeared in the atmospheric and oceanic literature. In general, these methods have been derived from the Kalman filter and have been known as ensemble Kalman filters. A more general class of m ..."
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Cited by 89 (9 self)
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Many methods using ensemble integrations of prediction models as integral parts of data assimilation have appeared in the atmospheric and oceanic literature. In general, these methods have been derived from the Kalman filter and have been known as ensemble Kalman filters. A more general class of methods including these ensemble Kalman filter methods is derived starting from the nonlinear filtering problem. When working in a joint state observation space, many features of ensemble filtering algorithms are easier to derive and compare. The ensemble filter methods derived here make a (local) least squares assumption about the relation between prior distributions of an observation variable and model state variables. In this context, the update procedure applied when a new observation becomes available can be described in two parts. First, an update increment is computed for each prior ensemble estimate of the observation variable by applying a scalar ensemble filter. Second, a linear regression of the prior ensemble sample of each state variable on the observation variable is performed to compute update increments for each state variable ensemble member from corresponding observation variable increments. The regression can be applied globally or locally using Gaussian kernel methods.
Sampling strategies and square root analysis schemes for the EnKF
"... this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a signific ..."
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Cited by 89 (2 self)
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this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a significant improvement in the EnKF results, using the same number of members in the ensemble
Estimation of highdimensional prior and posterior covariance matrices in Kalman filter variants
 Journal of Multivariate Analysis
, 2007
"... This work studies the effect of using Monte Carlo based methods to estimate highdimensional systems. Recent focus in the geosciences has been on representing the atmospheric state using a probability density function, and, for extremely highdimensional systems, various sample based Kalman filter t ..."
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Cited by 83 (4 self)
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This work studies the effect of using Monte Carlo based methods to estimate highdimensional systems. Recent focus in the geosciences has been on representing the atmospheric state using a probability density function, and, for extremely highdimensional systems, various sample based Kalman filter techniques have been developed to address the problem of realtime assimilation of system information and observations. As the employed sample sizes are typically several orders of magnitude smaller than the system dimension, such sampling techniques inevitably induces considerable variability into the state estimate, primarily through prior and posterior sample covariance matrices. In this article we quantify this variability with mean squared error measures for two MonteCarlo based Kalman filter variants, the ensemble Kalman filter and the squareroot filter. Under weak assumptions, we derive exact expressions of the error measures. In other cases, we rely on matrix expansions and provide approximations. We show that covarianceshrinking (tapering) based on the Schur product of the prior sample covariance matrix and a positive definite function is a simple, computationally feasible, and very effective technique to reduce sample variability and to address rankdeficient sample covariances. We propose practical rules for obtaining optimally tapered sample covariance matrices. The theoretical results are verified and illustrated with extensive simulations.
The Maximum Likelihood Ensemble Filter as a . . .
, 2008
"... The Maximum Likelihood Ensemble Filter (MLEF) equations are derived without the differentiability requirement for the prediction model and for the observation operators. Derivation reveals that a new nondifferentiable minimization method can be defined as a generalization of the gradientbased un ..."
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Cited by 68 (18 self)
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The Maximum Likelihood Ensemble Filter (MLEF) equations are derived without the differentiability requirement for the prediction model and for the observation operators. Derivation reveals that a new nondifferentiable minimization method can be defined as a generalization of the gradientbased unconstrained methods, such as the preconditioned conjugategradient and quasiNewton methods. In the new minimization algorithm the vector of first order increments of the cost function is defined as a generalized gradient, while the symmetric matrix of second order increments of the cost function is defined as a generalized Hessian matrix. In the case of differentiable observation operators, the minimization algorithm reduces to the standard gradientbased form. The nondifferentiable aspect of the MLEF algorithm is illustrated in an example with onedimensional Burgers model and simulated observations. The MLEF algorithm has a robust performance, producing satisfactory results for tested nondifferentiable observation operators.
Advanced Data Assimilation for Strongly Nonlinear Dynamics.
, 1997
"... Advanced data assimilation methods becomes extremely complicated and challenging when used with strongly nonlinear models. Several previous works have reported various problems when applying existing popular data assimilation techniques with strongly nonlinear dynamics. Common for these techniques i ..."
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Cited by 62 (10 self)
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Advanced data assimilation methods becomes extremely complicated and challenging when used with strongly nonlinear models. Several previous works have reported various problems when applying existing popular data assimilation techniques with strongly nonlinear dynamics. Common for these techniques is that they can all be considered as extensions to methods which have proved to work well with linear dynamics. This paper examines the properties of three advanced data assimilation methods when used with the highly nonlinear Lorenz equations. The ensemble Kalman filter is used for sequential data assimilation and the recently proposed ensemble smoother method and a gradient descent method are used to minimize two different weak constraint formulations. The problems associated with the use of an approximate tangent linear model when solving the EulerLagrange equations, or when the extended Kalman filter is used, are eliminated when using these methods. All three methods give reasonable con...
Assimilation of Geosat Altimeter Data for the Agulhas Current using the Ensemble Kalman Filter with a QuasiGeostrophic Model
, 1996
"... The ringshedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate Geosat altimeter data into a two layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded ..."
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Cited by 60 (10 self)
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The ringshedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate Geosat altimeter data into a two layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded data. The Geosat data consist of 10 fields of gridded seasurface height anomalies separated 10 days apart which are added to a climatic mean field. This corresponds to a huge number of data values and a data reduction scheme must be applied to increase the efficiency of the analysis procedure. Further, it is illustrated how one can resolve the rank problem occurring when a too large data set or a small ensemble is used. 1 Introduction The Agulhas Current is a westernboundary current flowing along the east coast of South Africa. Its water originates from the Mozambique channel (see e.g. Saetre and da Silva, 1984) and from east of Madagascar (e.g. Lutjeharms et al., 1981) as part of the sub...