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66
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Wellknown numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computati...
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...
Analysis Scheme in the Ensemble Kalman Filter
, 1998
"... This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct st ..."
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Cited by 141 (1 self)
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This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low. This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.
Using Bayesian model averaging to calibrate forecast ensembles
 MONTHLY WEATHER REVIEW 133
, 2005
"... Ensembles used for probabilistic weather forecasting often exhibit a spreaderror correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distr ..."
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Cited by 139 (34 self)
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Ensembles used for probabilistic weather forecasting often exhibit a spreaderror correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distributions from different sources. The BMA predictive probability density function (PDF) of any quantity of interest is a weighted average of PDFs centered on the individual biascorrected forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts and reflect the models ’ relative contributions to predictive skill over the training period. The BMA weights can be used to assess the usefulness of ensemble members, and this can be used as a basis for selecting ensemble members; this can be useful given the cost of running large ensembles. The BMA PDF can be represented as an unweighted ensemble of any desired size, by simulating from the BMA predictive distribution. The BMA predictive variance can be decomposed into two components, one corresponding to the betweenforecast variability, and the second to the withinforecast variability. Predictive PDFs or intervals based solely on the ensemble spread incorporate the first component but not the second. Thus BMA provides a theoretical explanation of the tendency of ensembles to exhibit a spreaderror correlation but yet
Ensemble Kalman Filter Assimilation of Doppler Radar Data with a Compressible Nonhydrostatic Model: OSS Experiments
, 2004
"... A Doppler radar data assimilation system is developed based on ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, we assume the forward models are perfect and radar data are sampled at the analysis grid points. A general pur ..."
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Cited by 127 (78 self)
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A Doppler radar data assimilation system is developed based on ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, we assume the forward models are perfect and radar data are sampled at the analysis grid points. A general purpose nonhydrostatic compressible model is used with the inclusion of complex multiclass ice microphysics. New aspects compared to previous studies include the demonstration of the ability of EnKF method in retrieving multiple microphysical species associated with a multiclass ice microphysics scheme, and in accurately retrieving the wind and thermodynamic variables. Also new are the inclusion of reflectivity observations and the determination of the relative role of radial velocity and reflectivity data as well as their spatial coverage in recovering the full flow and cloud fields. In general, the system is able to reestablish the model storm extremely well after a number of assimilation cycles, and best results are obtained when both radial velocity and reflectivity data, including reflectivity information outside precipitation regions, are used. Significant positive impact of the reflectivity assimilation
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...
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 58 (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...
Using ensembles for shortrange forecasting
 Mon. Wea. Rev
, 1999
"... Numerical forecasts from a pilot program on shortrange ensemble forecasting at the National Centers for Environmental Prediction are examined. The ensemble consists of 10 forecasts made using the 80km Eta Model and 5 forecasts from the regional spectral model. Results indicate that the accuracy of ..."
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Cited by 51 (3 self)
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Numerical forecasts from a pilot program on shortrange ensemble forecasting at the National Centers for Environmental Prediction are examined. The ensemble consists of 10 forecasts made using the 80km Eta Model and 5 forecasts from the regional spectral model. Results indicate that the accuracy of the ensemble mean is comparable to that from the 29km Meso Eta Model for both mandatory level data and the 36h forecast cyclone position. Calculations of spread indicate that at 36 and 48 h the spread from initial conditions created using the breeding of growing modes technique is larger than the spread from initial conditions created using different analyses. However, the accuracy of the forecast cyclone position from these two initialization techniques is nearly identical. Results further indicate that using two different numerical models assists in increasing the ensemble spread significantly. There is little correlation between the spread in the ensemble members and the accuracy of the ensemble mean for the prediction of cyclone location. Since information on forecast uncertainty is needed in many applications, and is one of the reasons to use an ensemble approach, the lack of a correlation between spread and forecast uncertainty presents a challenge to the production of shortrange ensemble forecasts. Even though the ensemble dispersion is not found to be an indication of forecast uncertainty, significant spread can occur within the forecasts over a relatively short time period. Examples are shown to illustrate how small uncertainties in the model initial conditions can lead to large differences in numerical forecasts from an identical numerical model. 1.
Evaluation of a shortrange multimodel ensemble system
, 2001
"... Forecasts from the National Centers for Environmental Prediction’s experimental shortrange ensemble system are examined and compared with a single run from a higherresolution model using similar computational resources. The ensemble consists of five members from the Regional Spectral Model and 10 ..."
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Cited by 43 (4 self)
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Forecasts from the National Centers for Environmental Prediction’s experimental shortrange ensemble system are examined and compared with a single run from a higherresolution model using similar computational resources. The ensemble consists of five members from the Regional Spectral Model and 10 members from the 80km Eta Model, with both inhouse analyses and bred perturbations used as initial conditions. This configuration allows for a comparison of the two models and the two perturbation strategies, as well as a preliminary investigation of the relative merits of mixedmodel, mixedperturbation ensemble systems. The ensemble is also used to estimate the shortrange predictability limits of forecasts of precipitation and fields relevant to the forecast of precipitation. Whereas error growth curves for the ensemble and its subgroups are in relative agreement with previous work for largescale fields such as 500mb heights, little or no error growth is found for fields of mesoscale interest, such as convective indices and precipitation. The difference in growth rates among the ensemble subgroups illustrates the role of both initial perturbation strategy and model formulation in creating ensemble dispersion. However, increase spread per se is not necessarily beneficial, as is indicated by the fact that the ensemble subgroup with the greatest spread is less skillful than the subgroup with the least spread. Further examination into the skill of the ensemble system for forecasts of precipitation shows the advantage gained from a mixedmodel strategy, such that even the inclusion of the less skillful Regional Spectral Model members improves ensemble performance. For some aspects of forecast performance, even ensemble configurations with as few as five members are shown to significantly outperform the 29km MesoEta Model. 1.