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254
Data Assimilation Using an Ensemble Kalman Filter Technique
, 1998
"... The possibility of performing data assimilation using the flowdependent statistics calculated from an ensemble of shortrange forecasts (a technique referred to as ensemble Kalman filtering) is examined in an idealized environment. Using a threelevel, quasigeostrophic, T21 model and simulated ob ..."
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Cited by 411 (5 self)
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The possibility of performing data assimilation using the flowdependent statistics calculated from an ensemble of shortrange forecasts (a technique referred to as ensemble Kalman filtering) is examined in an idealized environment. Using a threelevel, quasigeostrophic, T21 model and simulated observations, experiments are performed in a perfectmodel context. By using forward interpolation operators from the model state to the observations, the ensemble Kalman filter is able to utilize nonconventional observations. In order to
An Introduction to Estimation Theory
 OFFICE NOTE SERIES ON GLOBAL MODELING AND DATA ASSIMILATION
, 1997
"... Despite the explosive growth of activity in the field of Earth System data assimilation over the past decade or so, there remains a substantial gap between theory and practice. The present article attempts to bridge this gap by exposing some of the central concepts of estimation theory and connectin ..."
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Cited by 166 (7 self)
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Despite the explosive growth of activity in the field of Earth System data assimilation over the past decade or so, there remains a substantial gap between theory and practice. The present article attempts to bridge this gap by exposing some of the central concepts of estimation theory and connecting them with current and future data assimilation approaches. Estimation theory provides a broad and natural mathematical foundation for data assimilation science. Stochasticdynamic modeling and stochastic observation modeling are described first. Optimality criteria for linear and nonlinear state estimation problems are then explored, leading to conditionalmean estimation procedures such as the Kalman filter and some of its generalizations, and to conditionalmode estimation procedures such as variational methods. A detailed derivation of the Kalman filter is given to illustrate the role of key probabilistic concepts and assumptions. Extensions of the Kalman filter to nonlinear observat...
Unified Notation for Data Assimilation: Operational, Sequential and Variational
, 1997
"... The need for unified notation in atmospheric and oceanic data assimilation arises from the field's rapid theoretical expansion and the desire to translate it into practical applications. Selfconsistent notation is proposed that bridges sequential and variational methods, on the one hand, and o ..."
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Cited by 163 (9 self)
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The need for unified notation in atmospheric and oceanic data assimilation arises from the field's rapid theoretical expansion and the desire to translate it into practical applications. Selfconsistent notation is proposed that bridges sequential and variational methods, on the one hand, and operational usage, on the other. Over various other mottoes for this risky endeavor, the authors selected: "When I use a word," Humpty Dumpty said, in rather a scornful voice tone, "it means just what I choose it to mean  neither more nor less." Lewis
A Hybrid Ensemble Kalman Filter / 3DVariational Analysis Scheme
"... A hybrid 3dimensional variational (3DVar) / ensemble Kalman filter analysis scheme is demonstrated using a quasigeostrophic model under perfectmodel assumptions. Four networks with differing observational densities are tested, including one network with a data void. The hybrid scheme operates by ..."
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Cited by 123 (18 self)
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A hybrid 3dimensional variational (3DVar) / ensemble Kalman filter analysis scheme is demonstrated using a quasigeostrophic model under perfectmodel assumptions. Four networks with differing observational densities are tested, including one network with a data void. The hybrid scheme operates by computing a set of parallel data assimilation cycles, with each member of the set receiving unique perturbed observations. The perturbed observations are generated by adding random noise consistent with observation error statistics to the control set of observations. Background error statistics for the data assimilation are estimated from a linear combination of timeinvariant 3DVar covariances and flowdependent covariances developed from the ensemble of shortrange forecasts. The hybrid scheme allows the user to weight the relative contributions of the 3DVar and ensemblebased background covariances. The analysis scheme was cycled for 90 days, with new observations assimilated every 12 h...
OnLine Estimation of Error Covariance Parameters for Atmospheric Data Assimilation
, 1994
"... We present a simple scheme for online estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximumlikelihoodapproach in which estimates are produced on the basis of a single batch of simultaneous observations. Singlesample covariance estimation is ..."
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Cited by 122 (10 self)
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We present a simple scheme for online estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximumlikelihoodapproach in which estimates are produced on the basis of a single batch of simultaneous observations. Singlesample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the singlesample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: timedependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be th...
The operational CMCMRB Global Environmental Multiscale (GEM) model: Part I  Design considerations and formulation. Monthly Weather Review 126
, 1998
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2004: A ThreeDimensional Variational Data Assimilation System for MM5: Implementation and Initial Results Mon
 Wea. Rev
, 2004
"... A limitedarea threedimensional variational data assimilation (3DVAR) system applicable to both synoptic and mesoscale numerical weather prediction is described. The system is designed for use in timecritical realtime applications and is freely available to the data assimilation community for gene ..."
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Cited by 69 (7 self)
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A limitedarea threedimensional variational data assimilation (3DVAR) system applicable to both synoptic and mesoscale numerical weather prediction is described. The system is designed for use in timecritical realtime applications and is freely available to the data assimilation community for general research. The unique features of this implementation of 3DVAR include (a) an analysis space represented by recursive filters and truncated eigenmodes of the background error covariance matrix, (b) the inclusion of a cyclostrophic term in 3DVAR’s explicit mass–wind balance equation, and (c) the use of the software architecture of the Weather Research and Forecast (WRF) model to permit efficient performance on distributedmemory platforms. The 3DVAR system is applied to a multiresolution, nesteddomain forecast system. Resolution and seasonaldependent background error statistics are presented. A typhoon bogusing case study is performed to illustrate the 3DVAR response to a single surface pressure observation and its subsequent impact on numerical forecasts of the fifthgeneration Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). Results are also presented from an initial realtime MM5based application of 3DVAR. 1.
2004: A threedimensional variational data analysis method with recursive filter for Doppler radars
 J. Atmos. Ocean. Tech
"... In this paper, a new method of dualDoppler radar wind analysis based on a threedimensional variational data assimilation (3DVAR) approach is proposed. In it, a cost function, including background term and radial observation term, is minimized through a limited memory, quasiNewton conjugategradie ..."
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Cited by 64 (37 self)
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In this paper, a new method of dualDoppler radar wind analysis based on a threedimensional variational data assimilation (3DVAR) approach is proposed. In it, a cost function, including background term and radial observation term, is minimized through a limited memory, quasiNewton conjugategradient algorithm with the mass continuity equation imposed as a weak constraint. In the method, the background error covariance matrix, though simple in this case, is modeled by a recursive filter. Furthermore, the square root of this matrix is used to precondition the minimization problem. The current method is applied to Doppler radar observation of a supercell storm, and the analysis results are compared to a conceptual model and previous research. It is shown that the horizontal circulations, both within and around the storms, as well as the strong updraft and the associated downdraft, are well analyzed. Because no explicit integration of the anelastic mass continuity equation is involved, error accumulation associated with such integration is avoided. As a result, the method is less sensitive to the vertical boundary uncertainties. 1.
Ensemble data assimilation with the ncep global forecast system
, 2007
"... Realdata experiments with an ensemble data assimilation system using the NCEP Global Forecast System model were performed and compared with the NCEP Global Data Assimilation System (GDAS). All observations in the operational data stream were assimilated for the period 1 January–10 February 2004, ex ..."
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Cited by 51 (7 self)
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Realdata experiments with an ensemble data assimilation system using the NCEP Global Forecast System model were performed and compared with the NCEP Global Data Assimilation System (GDAS). All observations in the operational data stream were assimilated for the period 1 January–10 February 2004, except satellite radiances. Because of computational resource limitations, the comparison was done at lower resolution (triangular truncation at wavenumber 62 with 28 levels) than the GDAS realtime NCEP operational runs (triangular truncation at wavenumber 254 with 64 levels). The ensemble data assimilation system outperformed the reducedresolution version of the NCEP threedimensional variational data assimilation system (3DVAR), with the biggest improvement in datasparse regions. Ensemble data assimilation analyses yielded a 24h improvement in forecast skill in the Southern Hemisphere extratropics relative to the NCEP 3DVAR system (the 48h forecast from the ensemble data assimilation system was as accurate as the 24h forecast from the 3DVAR system). Improvements in the datarich Northern Hemisphere, while still statistically significant, were more modest. It remains to be seen whether the improvements seen in the Southern Hemisphere will be retained when satellite radiances are assimilated. Three different parameterizations of background errors unaccounted for in the data assimilation system (including
Assessing the effects of data selection with the DAO Physicalspace Statistical Analysis System
 Mon. Wea. Rev
, 1998
"... Conventional optimal interpolation (OI) analysis systems solve the standard statistical analysis equations approximately, by invoking a local approximation and a data selection procedure. Although solution of the analysis equations is essentially exact in the recent generation of global spectral var ..."
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Cited by 49 (9 self)
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Conventional optimal interpolation (OI) analysis systems solve the standard statistical analysis equations approximately, by invoking a local approximation and a data selection procedure. Although solution of the analysis equations is essentially exact in the recent generation of global spectral variational analysis systems, these new systems also include substantial changes in error covariance modeling, making it difficult to discern whether improvements in analysis and forecast quality are due to exact, global solution of the analysis equations, or to changes in error covariance modeling. The formulation and implementation of a new type of global analysis system at the Data Assimilation Office, termed the Physicalspace Statistical Analysis System (PSAS), is described in this article. Since this system operates directly in physical space, it is capable of employing error covariance models identical to those of the predecessor OI system, as well as more advanced models. To focus strictly on the effect of global versus local solution of the analysis equations, a comparison between PSAS and OI analyses is carried out with both systems using identical error covariance models and identical data. Spectral decomposition of the analysis increments reveals that, relative to the PSAS increments, the OI increments have too little power at large horizontal scales and excessive power at small horizontal scales. The OI increments also display an unrealistically large ratio of divergence to vorticity. Dynamical imbalances in the OIanalyzed state can therefore be attributed in part to the approximate local method of solution, and are not entirely due to the simple geostrophic constraint built into the forecast error covariance model. Rootmeansquare observation minus 6h forecast errors in the zonal wind component are substantially smaller for the PSAS system than for the OI system. 1.