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120
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 408 (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 169 (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...
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
Ensemble Square Root Filters
, 2003
"... Ensemble data assimilation methods assimilate observations using statespace estimation methods and lowrank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics ..."
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Cited by 115 (7 self)
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Ensemble data assimilation methods assimilate observations using statespace estimation methods and lowrank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics. This transformation may be performed stochastically by treating observations as random variables, or deterministically by requiring that the updated analysis perturbations satisfy the Kalman filter analysis error covariance equation. Deterministic analysis ensemble updates are implementations of Kalman square root filters. The nonuniqueness of the deterministic transformation used in square root Kalman filters provides a framework to compare three recently proposed ensemble data assimilation methods.
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.
Mapping tropical Pacific sea level: Data assimilation via a reduced state space Kalman
, 1996
"... Abstract. The wellknown fact that tropical sea level can be usefully simulated by linear wind driven models recommends it as a realistic test problem for data assimilation schemes. Here we report on an assimilation of monthly data for the period 19751992 from 34 tropical Pacific tide gauges into s ..."
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Cited by 75 (11 self)
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Abstract. The wellknown fact that tropical sea level can be usefully simulated by linear wind driven models recommends it as a realistic test problem for data assimilation schemes. Here we report on an assimilation of monthly data for the period 19751992 from 34 tropical Pacific tide gauges into such a model using a Kalman filter. We present an approach to the Kalman filter that uses a reduced state space representation for the required error covariance matrices. This reduction makes the calculation highly feasible. We argue that a more complete representation will be of no value in typical oceanographic practice, that in principle it is unlikely to be helpful, and that it may even be harmful if the data coverage is sparse, the usual case in oceanography. This is in part a consequence of ignorance of the correct error statistics for the data and model, but only in part. The reduced state space is obtained from a truncated set of multivariate empirical orthogonal functions (EOFs) derived from a long model run without assimilation. The reduced state space filter is compared with a full grid point Kalman filter using the same dynamical model for the period 19791985, assimilating eight tide gauge stations and using an additional seven for verification [Miller et al., 1995]. Results are not inferior to the full grid point filter, even when the reduced filter retains only nine EOFs. Five sets of reduced space filter assimilations are run with all tide gauge data for the period 19751992. In each set a different number of EOFs is
Practical and Theoretical Aspects of Adjoint Parameter Estimation and Identifiability in . . .
, 1997
"... The present paper has two aims. One is to survey briefly the state of the art of parameter estimation in meteorology and oceanography in view of applications of 4D variational data assimilation techniques to inverse parameter estimation problems, which bear promise of serious positive impact on imp ..."
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Cited by 73 (6 self)
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The present paper has two aims. One is to survey briefly the state of the art of parameter estimation in meteorology and oceanography in view of applications of 4D variational data assimilation techniques to inverse parameter estimation problems, which bear promise of serious positive impact on improving model prediction. The other aim is to present crucial aspects of identifiability and stability essential for validating results of optimal parameter estimation and which have not been addressed so far in either the meteorological or the oceanographic literature. As noted by Yeh (1986, Water Resour. Res. 22, 95108) in the context of ground water flow parameter estimation the inverse or parameter estimation problem is often illposed and beset by instability and nonuniqueness, particularly if one seeks parameters distributed in spacetime domain. This approach will allow one to assess and rigorously validate results of parameter estimation, i.e. do they indeed represent a real identification of physical model parameters or just compensate model errors? A brief survey of other approaches for solving the problem of optimal parameter estimation in meteorology and oceanography is finally presented. 1997 Elsevier Science B.V.
Which is better, an ensemble of positivenegative pairs or a centered spherical simplex ensemble? Monthly Weather Rev
, 2004
"... New methods to center the initial ensemble perturbations on the analysis are introduced and compared with the commonly used centering method of positive–negative paired perturbations. In the new method, one linearly dependent perturbation is added to a set of linearly independent initial perturbatio ..."
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Cited by 61 (1 self)
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New methods to center the initial ensemble perturbations on the analysis are introduced and compared with the commonly used centering method of positive–negative paired perturbations. In the new method, one linearly dependent perturbation is added to a set of linearly independent initial perturbations to ensure that the sum of the new initial perturbations equals zero; the covariance calculated from the new initial perturbations is equal to the analysis error covariance estimated by the independent initial perturbations, and all of the new initial perturbations are equally likely. The new method is illustrated by applying it to the ensemble transform Kalman filter (ETKF) ensemble forecast scheme, and the resulting ensemble is called the spherical simplex ETKF ensemble. It is shown from a multidimensional Taylor expansion that the symmetric positive–negative paired centering would yield a more accurate forecast ensemble mean and covariance than the spherical simplex centering if the ensemble were large enough to span all initial uncertain directions and thus the analysis error covariance was modeled precisely. However, when the number of uncertain directions is larger than the ensemble size, the spherical simplex centering has the advantage of allowing almost twice as many uncertain directions to be spanned as the symmetric positive–negative paired centering. The performances of the spherical simplex ETKF and symmetric positive–negative paired ETKF ensembles are compared by using the Community Climate Model
An Adaptive Ensemble Kalman Filter
, 2000
"... To the extent that model error is nonnegligible in numerical models of the atmosphere, it must be accounted for in 4D atmospheric data assimilation systems. In this study, a method of estimating and accounting for model error in the context of an ensemble Kalman filter technique is developed. The ..."
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Cited by 54 (0 self)
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To the extent that model error is nonnegligible in numerical models of the atmosphere, it must be accounted for in 4D atmospheric data assimilation systems. In this study, a method of estimating and accounting for model error in the context of an ensemble Kalman filter technique is developed. The method involves parameterizing the model error and using innovations to estimate the modelerror parameters. The estimation algorithm is based on a maximum likelihood approach and the study is performed in an idealized environment using a threelevel, quasigeostrophic, T21 model and simulated observations and model error. The use of a
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 singlemoment ice microphysics schemes using radar observations is investigated for a modelsimulated supercell storm by examining parameter sensitivity and identifiability. These parameters include the intercept parameters for rain, sn ..."
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Cited by 48 (25 self)
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The possibility of estimating fundamental parameters common in singlemoment ice microphysics schemes using radar observations is investigated for a modelsimulated 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 5min intervals for parameter estimation. The response functions calculated from ensemble mean forecasts for all five individual parameters show concave shapes, with unique