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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
Adaptive Sampling With the Ensemble Transform . . .
, 2001
"... A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filt ..."
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Cited by 321 (19 self)
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A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filters in that it uses ensemble transformation and a normalization to rapidly obtain the prediction error covariance matrix associated with a particular deployment of observational resources. This rapidity enables it to quickly assess the ability of a large number of future feasible sequences of observational networks to reduce forecast error variance. The ET KF was used by the National Centers for Environmental Prediction in the Winter Storm Reconnaissance missions of 1999 and 2000 to determine where aircraft should deploy dropwindsondes in order to improve 2472h forecasts over the continental United States. The ET KF may be applied to any wellconstructed set of ensemble perturbations. The ET KF
Ensemble forecasting at NCEP and the breeding method
 Mon. Wea. Rev
, 1997
"... The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In ..."
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Cited by 193 (16 self)
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The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 independent global forecasts valid for two weeks every day. For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. It is shown that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the firstguess forecasts, is ‘‘scaled down’ ’ at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth. The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred vectors are superpositions of the leading local (timedependent)
DistanceDependent Filtering of Background Error Covariance Estimates in an Ensemble Kalman Filter
, 2001
"... The usefulness of a distancedependent reduction of background error covariance estimates in an ensemble Kalman filter is demonstrated. Covariances are reduced by performing an elementwise multiplication of the background error covariance matrix with a correlation function with local support. This ..."
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Cited by 189 (31 self)
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The usefulness of a distancedependent reduction of background error covariance estimates in an ensemble Kalman filter is demonstrated. Covariances are reduced by performing an elementwise multiplication of the background error covariance matrix with a correlation function with local support. This reduces noisiness and results in an improved background error covariance estimate, which generates a reducederror ensemble of model initial conditions. The benefits
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
2000: A simple ocean data assimilation analysis of the global upper ocean 1950–95. Part I: Method
 J. Phys. Oceanogr
"... The authors explore the accuracy of a comprehensive 46year retrospective analysis of upperocean temperature, salinity, and currents. The Simple Ocean Data Assimilation (SODA) analysis is global, spanning the latitude range 628S–628N. The SODA analysis has been constructed using optimal interpolat ..."
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Cited by 124 (11 self)
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The authors explore the accuracy of a comprehensive 46year retrospective analysis of upperocean temperature, salinity, and currents. The Simple Ocean Data Assimilation (SODA) analysis is global, spanning the latitude range 628S–628N. The SODA analysis has been constructed using optimal interpolation data assimilation combining numerical model forecasts with temperature and salinity profiles (MBT, XBT, CTD, and station), sea surface temperature, and altimeter sea level. To determine the accuracy of the analysis, the authors present a series of comparisons to independent observations at interannual and longer timescales and examine the structure of wellknown climate features such as the annual cycle, El Niño, and the Pacific–North American (PNA) anomaly pattern. A comparison to tidegauge time series records shows that 25%–35 % of the variance is explained by the analysis. Part of the variance that is not explained is due to unresolved mesoscale phenomena. Another part is due to errors in the rate of water mass formation and errors in salinity estimates. Comparisons are presented to altimeter sea level, WOCE global hydrographic sections, and to moored and surface drifter velocity. The results of these comparisons are quite encouraging. The differences are largest in the eddy production regions of the western boundary currents and the Antarctic Circumpolar Current. The differences are generally smaller in the
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...
Data assimilation via error subspace statistical estimation. Part I: Theory and schemes
, 1999
"... A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean–atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the const ..."
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Cited by 96 (15 self)
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A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean–atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the constraints and issues particular to ocean–atmosphere data assimilation are emphasized. An approximation to the optimal criterion satisfying the goals and addressing the issues is obtained using heuristic characteristics of geophysical measurements and models. This leads to the notion of an evolving error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. The concept of error subspace statistical estimation (ESSE) is defined. In the present minimum error variance approach, the suboptimal criterion is based on a continued and energetically optimal reduction of the dimension of error covariance matrices. The evolving error subspace is characterized by error singular vectors and values, or in other words, the error principal components and coefficients. Schemes for filtering and smoothing via ESSE are derived. The data–forecast melding minimizes variance in the error subspace. Nonlinear Monte Carlo forecasts integrate the error subspace in time. The smoothing is based on a statistical approximation approach. Comparisons with existing filtering and smoothing procedures
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 88 (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.