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773
Local low dimensionality of atmospheric dynamics
 Phys. Rev. Lett
, 2001
"... Recent studies (Patil et al. 2001, 2002) have shown that, when the Earthâ€™s surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector. In this paper ..."
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Cited by 53 (18 self)
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Recent studies (Patil et al. 2001, 2002) have shown that, when the Earthâ€™s surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector. In this paper we show how this finding can be exploited to formulate a potentially accurate and efficient data assimilation technique. The basic idea is that, since the expected forecast errors lie in a locally low dimensional subspace, the analysis resulting from the data assimilation should also lie in this subspace. This implies that operations only on relatively low dimensional matrices are required. The data assimilation analysis is done locally in a manner allowing massively parallel computation to be exploited. The local analyses are then used to construct global states for advancement to the next forecast time. Potential advantages of the method are discussed. 1
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 53 (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
Fourdimensional 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 51 (17 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,
Suboptimal Schemes for Atmospheric Data Assimilation Based on the Kalman Filter
, 1994
"... This work is directed toward approximating the evolution of forecast error covariances for data assimilation. We study the performance of different algorithms based on simplification of the standard Kalman filter (KF). These are suboptimal schemes (SOS's) when compared to the KF, which is optim ..."
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Cited by 50 (8 self)
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This work is directed toward approximating the evolution of forecast error covariances for data assimilation. We study the performance of different algorithms based on simplification of the standard Kalman filter (KF). These are suboptimal schemes (SOS's) when compared to the KF, which is optimal for linear problems with known statistics. The SOS's considered here are several versions of optimal interpolation (OI), a scheme for height error variance advection, and a simplified KF in which the full height error covariance is advected. In order to employ a methodology for exact comparison among these schemes we maintain a linear environment, choosing a betaplane shallow water model linearized about a constant zonal flow for the testbed dynamics. Our results show that constructing dynamicallybalanced forecast error covariances, rather than using conventional geostrophicallybalanced ones, is essential for successful performance of any SOS. A posteriori initialization of SOS's to comp...
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 49 (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
A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation
 IN REVIEW
, 2005
"... A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assump ..."
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Cited by 48 (4 self)
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A fourdimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloudresolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assumption of a perfect forecast model. Overall, both assimilation schemes perform well and are able to recover the supercell with comparable accuracy, given radialvelocity and reflectivity observations where rain was present. 4DVAR produces generally better analyses than the EnKF given observations limited to a period of 10 min (or three volume scans), particularly for the wind components. In contrast, the EnKF typically produces better analyses than 4DVAR after several assimilation cycles, especially for model variables not functionally related to the observations. The advantages of the EnKF in later cycles arise at least in part from the fact that the 4DVAR scheme implemented here does not use a forecast from a previous cycle as background or evolve its error covariance. Possible reasons for the initial advantage of 4DVAR are deficiencies in the initial ensemble used by the EnKF, the temporal smoothness constraint used in 4DVAR, and nonlinearities in the evolution of forecast errors over the assimilation window.
Toward a nonlinear ensemble filter for highdimensional systems
 J. Geophysical ResearchAtmospheres
, 2003
"... [1] Many geophysical problems are characterized by highdimensional, nonlinear systems and pose difficult challenges for realtime data assimilation (updating) and forecasting. The present work builds on the ensemble Kalman filter (EnsKF), with the goal of producing ensemble filtering techniques app ..."
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Cited by 47 (6 self)
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[1] Many geophysical problems are characterized by highdimensional, nonlinear systems and pose difficult challenges for realtime data assimilation (updating) and forecasting. The present work builds on the ensemble Kalman filter (EnsKF), with the goal of producing ensemble filtering techniques applicable to nonGaussian densities and highdimensional systems. Three filtering algorithms, based on representing the prior density as a Gaussian mixture, are presented. The first, referred to as a mixture ensemble Kalman filter (XEnsF), models local covariance structures adaptively using nearest neighbors. The XEnsF is effective in a threedimensional system, but the required ensemble grows rapidly with the dimension and, even in a 40dimensional system, we find the XEnsF to be unstable and inferior to the EnsKF for all computationally feasible ensemble sizes. A second algorithm, the locallocal ensemble filter (LLEnsF), combines localizations in physical as well as phase space, allowing the update step in highdimensional systems to be decomposed into a sequence of lowerdimensional updates tractable by the XEnsF. Given the same prior forecasts in a 40dimensional system, the LLEnsF update produces more accurate state estimates than the EnsKF if the forecast distributions are sufficiently
Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter
 Water Resour. Res. 2005
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Cited by 46 (5 self)
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Let us know how access to this document benefits you.
R.: Extended versus ensemble Kalman filtering for land data assimilation
 J. Hydrometeor
"... The performance of the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation. In a twin experiment for the southeastern United States synthetic observations of nearsurface soil moisture are assimilated once every 3 days, neglecting horizontal e ..."
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Cited by 46 (0 self)
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The performance of the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) are assessed for soil moisture estimation. In a twin experiment for the southeastern United States synthetic observations of nearsurface soil moisture are assimilated once every 3 days, neglecting horizontal error correlations and treating catchments independently. Both filters provide satisfactory estimates of soil moisture. The average actual estimation error in volumetric moisture content of the soil profile is 2.2 % for the EKF and 2.2 % (or 2.1%; or 2.0%) for the EnKF with 4 (or 10; or 500) ensemble members. Expected error covariances of both filters generally differ from actual estimation errors. Nevertheless, nonlinearities in soil processes are treated adequately by both filters. In the application presented herein the EKF and the EnKF with four ensemble members are equally accurate at comparable computational cost. Because of its flexibility and its performance in this study, the EnKF is a promising approach for soil moisture initialization problems. 1.
Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation
, 1996
"... The weak constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The wellknown result that for Gaussian error statistics the minimum of the weak constraint inverse is equal to the maximum likelihood estimate is rederived. Then several m ..."
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Cited by 44 (7 self)
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The weak constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The wellknown result that for Gaussian error statistics the minimum of the weak constraint inverse is equal to the maximum likelihood estimate is rederived. Then several methods based on ensemble statistics which can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. They also avoid iterative searches in an Hilbert space, and error estimates can be obtained without much additional computational effort. The feasibility of the new methods is illustrated in a twolayer quasigeostrophic ocean model.