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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
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.
2004: Resilience of hybrid ensemble/3DVAR analysis schemes to model error and ensemble covariance error
 Mon. Wea. Rev
"... Previous idealized numerical experiments have shown that a straightforward augmentation of an isotropic error correlation matrix with an ensemblebased error correlation matrix yields an improved data assimilation scheme under certain conditions. Those conditions are (a) the forecast model is perfec ..."
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Cited by 30 (3 self)
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Previous idealized numerical experiments have shown that a straightforward augmentation of an isotropic error correlation matrix with an ensemblebased error correlation matrix yields an improved data assimilation scheme under certain conditions. Those conditions are (a) the forecast model is perfect and (b) the ensemble accurately samples the probability distribution function of forecast errors. Such schemes blend characteristics of ensemble Kalman filter analysis schemes with threedimensional variational data assimilation (3DVAR) analysis schemes and are called hybrid schemes. Here, we test the robustness of hybrid schemes to model error and ensemble inaccuracy in the context of a numerically simulated twodimensional turbulent flow. The turbulence is produced by a doubly periodic barotropic vorticity equation model that is constantly relaxing to a barotropically unstable state. The types of forecast models considered include a perfect model, a model with a resolution error, and a model with a parameterization error. The ensemble generation schemes considered include the breeding scheme, the singular vector scheme, the perturbed observations system simulation scheme, a gridpoint noise scheme, and a scheme based on the ensemble transform Kalman filter (ETKF). For all combinations examined, it is found that the hybrid schemes outperform the 3DVAR scheme. In the presence of model error a perturbed observations hybrid and a singular vector hybrid perform best, though the ETKF ensemble is competitive. 1.
Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation
 MONTHLY WEATHER REVIEW
, 2008
"... The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upperocean model a ..."
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Cited by 22 (7 self)
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The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upperocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identicaltwin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Modelgenerated oceanic datasets are assimilated to produce a timecontinuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean
Assimilation of Surface Pressure Observations using an Ensemble Filter in an Idealized Global Atmospheric Prediction System
, 2005
"... An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held–Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model’s state at all levels when only observations of surface pressure (PS) are avail ..."
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Cited by 17 (2 self)
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An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held–Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model’s state at all levels when only observations of surface pressure (PS) are available. The impacts of varying the spatial density and temporal frequency of PS observations are examined. The error of the ensemble mean assimilation prior estimate appears to saturate at some point as the number of PS observations available once every 24 h is increased. However, increasing the frequency with which PS observations are available from a fixed network of 1800 randomly located stations results in an apparently unbounded decrease in the assimilation’s prior error for both PS and all other model state variables. The error reduces smoothly as a function of observation frequency except for a band with observation periods around 4 h. Assimilated states are found to display enhanced amplitude highfrequency gravity wave oscillations when observations are taken once every few hours, and this adversely impacts the assimilation quality. Assimilations of only surface temperature and only surface wind components are also examined. The results indicate that, in a perfect model context, ensemble filters are able to extract surprising amounts of information from observations of only a small portion of a model’s spatial domain. This suggests
EnsembleBased Simultaneous State and Parameter Estimation in a TwoDimensional SeaBreeze Model
, 2005
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2007: A data assimilation case study using a limitedarea ensemble Kalman filter
"... Ensemble Kalman filter (EnKF) data assimilation experiments are conducted on a limitedarea domain over the Pacific Northwest region of the United States, using the Weather Research and Forecasting model. Idealized surface pressure, radiosoundings, and aircraft observations are assimilated every 6 h ..."
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Cited by 9 (2 self)
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Ensemble Kalman filter (EnKF) data assimilation experiments are conducted on a limitedarea domain over the Pacific Northwest region of the United States, using the Weather Research and Forecasting model. Idealized surface pressure, radiosoundings, and aircraft observations are assimilated every 6 h for a 7day period in January 2004. The objectives here are to study the performance of the filter in constraining analysis errors with a relatively inhomogeneous, sparseobservation network and to explore the potential for such a network to serve as the basis for a realtime EnKF system dedicated to the Pacific Northwest region of the United States. When only a single observation type is assimilated, results show that the ensemblemean analysis error and ensemble spread (standard deviation) are significantly reduced compared to a control ensemble without assimilation for both observed and unobserved variables. Analysis errors are smaller than background errors over nearly the entire domain when averaged over the 7day period. Moreover, comparisons of background errors and observation increments at each assimilation step suggest that the flowdependent filter corrections are accurate in both scale and amplitude. An illustrative example concerns a misspecified mesoscale 500hPa shortwave trough moving along the British Columbia coast, which is corrected by surface pressure observations alone. The relative impact of each observation type upon different variables and vertical levels is also discussed. 1.
Data Assimilation for Geophysical Fluids
"... The ultimate purpose of environmental studies is the forecast of its natural evolution. A prerequisite before a prediction is to retrieve at best the state of the environment. Data assimilation is the ensemble of techniques which, starting from heterogeneous information, permit to retrieve the initi ..."
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Cited by 8 (1 self)
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The ultimate purpose of environmental studies is the forecast of its natural evolution. A prerequisite before a prediction is to retrieve at best the state of the environment. Data assimilation is the ensemble of techniques which, starting from heterogeneous information, permit to retrieve the initial state of a flow. In the first part, the mathematical models governing geophysical flows are presented together with the networks of observations of the atmosphere and of the ocean. In variational methods, we seek for the minimum of a functional estimating the discrepancy between the solution of the model and the observation. The derivation of the optimality system, using the adjoint state, permits to compute a gradient which is used in the optimization. The definition of the cost function permits to take into account the available statistical information through the choice of metrics in the space of observation and in the space of the initial condition. Some examples are presented on simplified models, especially an application in oceanography. Among the tools of optimal control, the adjoint model permits to carry out sensitivity studies, but if we look for the sensitivity of the prediction with respect to the observations, then a secondorder analysis should be considered. One of the first methods used for assimilating data in oceanography is the nudging method, adding a forcing term in the equations. A variational variant of nudging method is described and also a socalled Computational Methods for the Atmosphere and the Oceans
Ensemble Kalman Filter: Current Status and Potential
 P. SAKOV AND P. OKE, “IMPLICATIONS OF THE FORM OF THE ENSEMBLE TRANSFORMATION IN THE ENSEMBLE SQUARE ROOT FILTERS” MON.WEA.REV.,136
, 2008
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2007: Numerical prediction of highimpact local weather: A driver for petascale computing
 Petascale Computing: Algorithms and Applications, Taylor & Francis Group, LLC
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