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495
Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter
- Physica D
, 2007
"... Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become availab ..."
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Cited by 152 (11 self)
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Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to “forecast ” the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, I describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of “Ensemble Kalman Filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. I discuss both the mathematical basis of this approach and its implementation; my primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble Kalman filtering. 1
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 130 (79 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 multi-class 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 multi-class 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
Sampling strategies and square root analysis schemes for the EnKF
"... this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a signific ..."
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Cited by 89 (2 self)
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this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a significant improvement in the EnKF results, using the same number of members in the ensemble
Four-dimensional ensemble Kalman filtering
- Tellus
, 2004
"... Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible an additional benefit: the timing of observations, ..."
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Cited by 52 (15 self)
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Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible an additional benefit: the timing of observations,
Simultaneous Estimation of Microphysical Parameters and Atmospheric State with Simulated Radar Data and Ensemble Square Root Kalman Filter. Part I: Sensitivity Analysis and Parameter Identifiability
- 1630 MONTHLY WEATHER REVIEW VOLUME
, 2008
"... The possibility of estimating fundamental parameters common in single-moment ice microphysics schemes using radar observations is investigated for a model-simulated supercell storm by examining parameter sensitivity and identifiability. These parameters include the intercept parameters for rain, sn ..."
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Cited by 50 (26 self)
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The possibility of estimating fundamental parameters common in single-moment ice microphysics schemes using radar observations is investigated for a model-simulated supercell storm by examining parameter sensitivity and identifiability. These parameters include the intercept parameters for rain, snow, and hail/graupel, and the bulk densities of snow and hail/graupel. These parameters are closely involved in the definition of drop/particle size distributions of microphysical species but often assume highly uncertain specified values. The sensitivity of model forecast within data assimilation cycles to the parameter values, and the issue of solution uniqueness of the estimation problem, are examined. The ensemble square root filter (EnSRF) is employed for model state estimation. Sensitivity experiments show that the errors in the microphysical parameters have a larger impact on model microphysical fields than on wind fields; radar reflectivity observations are therefore preferred over those of radial velocity for microphysical parameter estimation. The model response time to errors in individual parameters are also investigated. The results suggest that radar data should be used at about 5-min intervals for parameter estimation. The response functions calculated from ensemble mean forecasts for all five individual parameters show concave shapes, with unique
Ensemble data assimilation with the ncep global forecast system
, 2007
"... Real-data 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 50 (7 self)
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Real-data 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 real-time NCEP operational runs (triangular truncation at wavenumber 254 with 64 levels). The ensemble data assimilation system outperformed the reduced-resolution version of the NCEP three-dimensional variational data assimilation system (3DVAR), with the biggest improvement in data-sparse regions. Ensemble data assimilation analyses yielded a 24-h improvement in forecast skill in the Southern Hemisphere extratropics relative to the NCEP 3DVAR system (the 48-h forecast from the ensemble data assimilation system was as accurate as the 24-h forecast from the 3DVAR system). Improvements in the data-rich 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
Assimilation of Simulated Polarimetric Radar Data for a Convective Storm Using the Ensemble Kalman Filter. Part I: Observation Operators for Reflectivity and Polarimetric Variables // [Mon.
, 2008
"... Abstract A data assimilation system based on the ensemble square-root Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables. It is used to assess the impact of simulating additional polarimetric observations on convective storm analysis ..."
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Cited by 44 (31 self)
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Abstract A data assimilation system based on the ensemble square-root Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables. It is used to assess the impact of simulating additional polarimetric observations on convective storm analysis in an OSSE (Observing System Simulation Experiment) framework. The polarimetric variables considered include differential reflectivity Z DR , reflectivity difference Z dp , and specific differential phase K DP . To simulate the observational data more realistically, a new error model is introduced for characterizing the errors of the non-polarimetric and polarimetric radar variables. The error model includes both correlated and uncorrelated error components for reflectivities at horizontal and vertical polarizations (Z H and Z V ). It is shown that the storm analysis is improved when polarimetric variables are assimilated in addition to Z H or in addition to both Z H and radial velocity V r . Positive impact is largest when Z DR , Z dp , and K DP are assimilated all together. Improvement is generally larger in vertical velocity, water vapor and rainwater mixing ratios. The rain water field benefits the most while the impacts on horizontal wind components and snow mixing ratios are smaller. Improvement is found at all model levels even though the polarimetric data, after the application of thresholds, are mostly limited to the lower levels. Among Z DR , Z dp , and K DP , Z DR is found to produce the largest positive impact on the analysis. It is suggested that Z DR provides more independent information than the other variables. The impact of polarimetric data is also expected to be larger when they are used to retrieve drop size distribution parameters. This study is believed to be the first to directly assimilate (simulated) polarimetric data into a numerical model. 1
4D-Var or Ensemble Kalman Filter?
- TELLUS
, 2007
"... We consider the relative advantages of two advanced data assimilation systems, 4-D-Var and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation. With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation wi ..."
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Cited by 42 (5 self)
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We consider the relative advantages of two advanced data assimilation systems, 4-D-Var and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation. With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4-D-Var, variance inflation in EnKF, and the effect of model errors and reduced observation coverage. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4-D-Var. For infrequent observations, when ensemble perturbations grow non-linearly and become non-Gaussian, 4-D-Var attains lower errors than EnKF. If the model is imperfect, the 4-D-Var with long windows requires weak constraint. Similar results are obtained with a quasi-geostrophic channel model. EnKF experiments made with the primitive equations SPEEDY model provide comparisons with 3-D-Var and guidance on model error and ‘observation localization’. Results obtained using operational models and both simulated and real observations indicate that currently EnKF is becoming competitive with 4-D-Var, and that the experience acquired with each of these methods can be used to improve the other. A table summarizes the pros and cons of the two methods.
MATHEMATICAL STRATEGIES FOR FILTERING TURBULENT DYNAMICAL SYSTEMS
"... Abstract. The modus operandi of modern applied mathematics in developing very recent mathematical strategies for filtering turbulent dynamical systems is emphasized here. The approach involves the synergy of rigorous mathematical guidelines, exactly solvable nonlinear models with physical insight, a ..."
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Cited by 32 (15 self)
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Abstract. The modus operandi of modern applied mathematics in developing very recent mathematical strategies for filtering turbulent dynamical systems is emphasized here. The approach involves the synergy of rigorous mathematical guidelines, exactly solvable nonlinear models with physical insight, and novel cheap algorithms with judicious model errors to filter turbulent signals with many degrees of freedom. A large number of new theoretical and computational phenomena such as “catastrophic filter divergence ” in finite ensemble filters are reviewed here with the intention to introduce mathematicians, applied mathematicians, and scientists to this remarkable emerging scientific discipline with increasing practical importance. 1. Introduction. Filtering
Sampling the posterior: An approach to non-gaussian data assimilation
, 2006
"... The viewpoint taken in this paper is that data assimilation is fundamentally a statistical problem and that this problem should be cast in a Bayesian framework. In the absence of model error, the correct solution to the data assimilation problem is to find the posterior distribution implied by this ..."
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Cited by 30 (10 self)
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The viewpoint taken in this paper is that data assimilation is fundamentally a statistical problem and that this problem should be cast in a Bayesian framework. In the absence of model error, the correct solution to the data assimilation problem is to find the posterior distribution implied by this Bayesian setting. Methods for dealing with data assimilation should then be judged by their ability to probe this distribution. In this paper we propose a range of techniques for probing the posterior distribution, based around the Langevin equation; and we compare these new techniques with existing methods. When the underlying dynamics is deterministic, the posterior distribution is on the space of initial conditions leading to a sampling problem over this space. When the underlying dynamics is stochastic the posterior distribution is on the space of continuous time paths. By writing down a density, and conditioning on observations, it is possible to define