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254
Gaussian process approximation of stochastic differential equations
 Journal of Machine Learning Research, Workshop and Conference Proceedings
, 2007
"... Some of the most complex models routinely run are numerical weather prediction models. These models are based on a discretisation of a coupled set of partial differential equations (the dynamics) which govern the time evolution of the atmosphere, described in terms of temperature, pressure, velocity ..."
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Cited by 45 (10 self)
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Some of the most complex models routinely run are numerical weather prediction models. These models are based on a discretisation of a coupled set of partial differential equations (the dynamics) which govern the time evolution of the atmosphere, described in terms of temperature, pressure, velocity,
Ensemblebased atmospheric data assimilation
, 2004
"... Ensemblebased data assimilation techniques are being explored as possible alternatives to current operational analysis techniques such as 3 or 4dimensional variational assimilation. Ensemblebased assimilation techniques utilize an ensemble of parallel data assimilation and forecast cycles. The ..."
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Cited by 42 (2 self)
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Ensemblebased data assimilation techniques are being explored as possible alternatives to current operational analysis techniques such as 3 or 4dimensional variational assimilation. Ensemblebased assimilation techniques utilize an ensemble of parallel data assimilation and forecast cycles. The backgrounderror covariances are estimated using the forecast ensemble and are used to produce an ensemble of analyses. The backgrounderror covariances are flow dependent and often have very complicated structure, providing a very different adjustment to the observations than are seen from methods such as 3 dimensional variational assimilation. Though computationally expensive, ensemblebased techniques are relatively easy to code, since no adjoint nor tangentlinear models are required, and previous tests in simple models suggest that dramatic improvements over existing operational methods may be possible. A review of the ensemblebased assimilation is provided here, starting from the basic concepts of Bayesian assimilation. Without some simplification, full Bayesian assimilation is computationally impossible for model states of large dimension. Assuming normality of error statistics and linearity of error growth, the state and its error covariance may be predicted optimally using Kalman filter (KF) techniques. The ensemble Kalman filter (EnKF) is then described. The EnKF is an approximation to the KF in that backgrounderror covariances are estimated from a finite ensemble of forecasts. However, no assumptions about linearity of error growth are made. Recent algorithmic variants on the standard EnKF are also described, as well as methods for simplifying the computations and increasing the accuracy. Examples of ensemblebased assimilations are provided in simple and more realistic dynamical systems.
Accounting for the Error due to Unresolved Scales in Ensemble Data Assimilation: A Comparison of Different Approaches
 3132 MONTHLY WEATHER REVIEW VOLUME
, 2005
"... Insufficient model resolution is one source of model error in numerical weather predictions. Methods for parameterizing this error in ensemble data assimilations are explored here. Experiments were conducted with a twolayer primitive equation model, where the assumed true state was a T127 forecast ..."
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Cited by 42 (4 self)
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Insufficient model resolution is one source of model error in numerical weather predictions. Methods for parameterizing this error in ensemble data assimilations are explored here. Experiments were conducted with a twolayer primitive equation model, where the assumed true state was a T127 forecast simulation. Ensemble data assimilations were performed with the same model at T31 resolution, assimilating imperfect observations drawn from the T127 forecast. By design, the magnitude of errors due to model truncation was much larger than the error growth due to initial condition uncertainty, making this a stringent test of the ability of an ensemblebased data assimilation to deal with model error. Two general methods, “covariance inflation ” and “additive error, ” were considered for parameterizing the model error at the resolved scales (T31 and larger) due to interaction with the unresolved scales (T32 to T127). Covariance inflation expanded the background forecast members ’ deviations about the ensemble mean, while additive error added specially structured noise to each ensemble member forecast before the update step. The method of parameterizing this model error had a substantial effect on the accuracy of the ensemble data assimilation. Covariance inflation produced ensembles with analysis errors that were no lower than the analysis errors from threedimensional variational (3DVar) assimilation, and for the method to avoid filter
Adaptive Tuning of Numerical Weather Prediction Models: Simultaneous Estimation of Weighting, Smoothing and Physical Parameters
, 1996
"... In Wahba et al (1995) it was shown how the randomized trace method could be used to adaptively tune numerical weather prediction models via generalized cross validation (GCV ) and related methods. In this paper a `toy' four dimensional data assimilation model is developed (actually one space an ..."
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Cited by 33 (10 self)
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In Wahba et al (1995) it was shown how the randomized trace method could be used to adaptively tune numerical weather prediction models via generalized cross validation (GCV ) and related methods. In this paper a `toy' four dimensional data assimilation model is developed (actually one space and one time variable), consisting of an equivalent barotropic vorticity equation on a latitude circle, and used to demonstrate how this technique may be used to simultaneously tune weighting, smoothing and physical parameters. Analyses both with the model as a strong constraint (corresponding to the usual 4DVar approach) and as a weak constraint (corresponding theoretically to a fixedinterval Kalman smoother) are carried out. The conclusions are limited to the particular toy problem considered but it can be seen how more elaborate experiments could be carried out, as well as how the method might be applied in practice. We have considered five adjustable parameters, two related to a distributed c...
Global ensemble predictions of 2009’s tropical cyclones initialized with an ensemble Kalman filter
 WEATHER REV
, 2011
"... Verification was performed on ensemble forecasts of 2009 Northern Hemisphere summer tropical cyclones (TCs) from two experimental global numerical weather prediction ensemble prediction systems (EPSs). The first model was a highresolution version (T382L64) of the National Centers for Environmental ..."
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Cited by 29 (4 self)
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Verification was performed on ensemble forecasts of 2009 Northern Hemisphere summer tropical cyclones (TCs) from two experimental global numerical weather prediction ensemble prediction systems (EPSs). The first model was a highresolution version (T382L64) of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS). The secondmodel was a 30km version of the experimental NOAA/ Earth System Research Laboratory’s Flowfollowing finitevolume Icosahedral Model (FIM). Both models were initialized with the first 20 members of a 60member ensemble Kalman filter (EnKF) using the T382L64 GFS. The GFS–EnKF assimilated the full observational data stream that was normally assimilated into the NCEP operational Global Statistical Interpolation (GSI) data assimilation, plus humansynthesized ‘‘observations’ ’ of tropical cyclone central pressure and position produced at the National Hurricane Center and the Joint Typhoon Warning Center. The forecasts from the two experimental ensembles were compared against four operational EPSs from the European Centre for MediumRangeWeather Forecasts (ECMWF), NCEP, the Canadian Meteorological Centre (CMC), and the Met Office (UKMO). The errors of GFS–EnKF ensemble track forecasts were competitive with those from the ECMWF ensemble system, and the overall spread of the ensemble tracks was consistent inmagnitudewith the track error.
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.
Estimating atmospheric CO2 from advanced infrared satellite radiances within an operational 4DVar data assimilation system: Methodology and first results
 J. Geophys. Res
, 2004
"... satellite radiances within an operational fourdimensional variational (4DVar) data assimilation system: Results and validation ..."
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Cited by 25 (3 self)
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satellite radiances within an operational fourdimensional variational (4DVar) data assimilation system: Results and validation
A comparative study of 4DVAR and a 4D ensemble Kalman filter: perfect model simulations with Lorenz96, Tellus A 59 (2007
"... We formulate a four dimensional Ensemble Kalman Filter (4DLETKF) that minimizes a cost function similar to that in a 4DVAR method. Using perfect model experiments with the Lorenz96 model, we compare assimilation of simulated asynchronous observations with 4DVAR and 4DLETKF. We find that both s ..."
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Cited by 24 (3 self)
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We formulate a four dimensional Ensemble Kalman Filter (4DLETKF) that minimizes a cost function similar to that in a 4DVAR method. Using perfect model experiments with the Lorenz96 model, we compare assimilation of simulated asynchronous observations with 4DVAR and 4DLETKF. We find that both schemes have comparable error when 4DLETKF is performed sufficiently frequently and when 4DVAR is performed over a sufficiently long analysis time window. We explore how the error depends on the time between analyses for 4DLETKF and the analysis time window for 4DVAR. 1
Circumventing Storage Limitations in Variational Data Assimilation Studies
 SIAM J. Sci. Comput
, 1995
"... . An application of Pontryagin's Maximum Principle, data assimilation is used to blend possibly incomplete or nonuniformly distributed spatiotemporal observational data into geophysical models. Used extensively in engineering control theory applications, data assimilation has relatively recent ..."
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Cited by 22 (3 self)
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. An application of Pontryagin's Maximum Principle, data assimilation is used to blend possibly incomplete or nonuniformly distributed spatiotemporal observational data into geophysical models. Used extensively in engineering control theory applications, data assimilation has relatively recently been introduced into meteorological forecasting, naturalresource recovery modeling, and climate dynamics. Variational data assimilation is a promising assimilation technique in which it is assumed that the optimal state of the system is an extrema of a carefully chosen cost function. Provided that an adjoint model is available, the required model gradient can be computed by integrating the model forward and its adjoint backward. The gradient is then used to extremize the cost function with a suitable iterative or conjugate gradient solver. The problem addressed in this study is the explosive growth in both online computer memory and remote storage requirements of computing the gradient by ...