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106
Adaptive Sampling With the Ensemble Transform . . .
, 2001
"... A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filt ..."
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Cited by 321 (19 self)
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A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filters in that it uses ensemble transformation and a normalization to rapidly obtain the prediction error covariance matrix associated with a particular deployment of observational resources. This rapidity enables it to quickly assess the ability of a large number of future feasible sequences of observational networks to reduce forecast error variance. The ET KF was used by the National Centers for Environmental Prediction in the Winter Storm Reconnaissance missions of 1999 and 2000 to determine where aircraft should deploy dropwindsondes in order to improve 2472h forecasts over the continental United States. The ET KF may be applied to any wellconstructed set of ensemble perturbations. The ET KF
Assessing the effects of data selection with the DAO Physicalspace Statistical Analysis System
 Mon. Wea. Rev
, 1998
"... Conventional optimal interpolation (OI) analysis systems solve the standard statistical analysis equations approximately, by invoking a local approximation and a data selection procedure. Although solution of the analysis equations is essentially exact in the recent generation of global spectral var ..."
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Cited by 49 (9 self)
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Conventional optimal interpolation (OI) analysis systems solve the standard statistical analysis equations approximately, by invoking a local approximation and a data selection procedure. Although solution of the analysis equations is essentially exact in the recent generation of global spectral variational analysis systems, these new systems also include substantial changes in error covariance modeling, making it difficult to discern whether improvements in analysis and forecast quality are due to exact, global solution of the analysis equations, or to changes in error covariance modeling. The formulation and implementation of a new type of global analysis system at the Data Assimilation Office, termed the Physicalspace Statistical Analysis System (PSAS), is described in this article. Since this system operates directly in physical space, it is capable of employing error covariance models identical to those of the predecessor OI system, as well as more advanced models. To focus strictly on the effect of global versus local solution of the analysis equations, a comparison between PSAS and OI analyses is carried out with both systems using identical error covariance models and identical data. Spectral decomposition of the analysis increments reveals that, relative to the PSAS increments, the OI increments have too little power at large horizontal scales and excessive power at small horizontal scales. The OI increments also display an unrealistically large ratio of divergence to vorticity. Dynamical imbalances in the OIanalyzed state can therefore be attributed in part to the approximate local method of solution, and are not entirely due to the simple geostrophic constraint built into the forecast error covariance model. Rootmeansquare observation minus 6h forecast errors in the zonal wind component are substantially smaller for the PSAS system than for the OI system. 1.
A Review of Current Methodologies for Regional Evapotranspiration Estimation from Remotely Sensed Data
, 2009
"... sensors ..."
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.
2008b), ‘Data assimilation: Mathematical and statistical perspectives
 Internat. J. Numer. Methods Fluids
"... The bulk of this paper contains a concise mathematical overview of the subject of data assimilation, highlighting three primary ideas: (i) the standard optimization approaches of 3DVAR, 4DVAR and weak constraint 4DVAR are described and their interrelations explained; (ii) statistical analogues of th ..."
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Cited by 26 (8 self)
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The bulk of this paper contains a concise mathematical overview of the subject of data assimilation, highlighting three primary ideas: (i) the standard optimization approaches of 3DVAR, 4DVAR and weak constraint 4DVAR are described and their interrelations explained; (ii) statistical analogues of these approaches are then introduced, leading to filtering (generalizing 3DVAR) and a form of smoothing (generalizing 4DVAR and weak constraint 4DVAR) and the optimization methods are shown to be maximum a posteriori estimators for the probability distributions implied by these statistical approaches; and (iii) by taking a general dynamical systems perspective on the subject it is shown that the incorporation of Lagrangian data can be handled by a straightforward extension of the preceding concepts. We argue that the smoothing approach to data assimilation, based on statistical analogues of 4DVAR and weak constraint 4DVAR, provides the optimal solution to the assimilation of space–time distributed data into a model. The optimal solution obtained is a probability distribution on the relevant class of functions (initial conditions or timedependent solutions). The approach is a useful one in the first instance because it clarifies the notion of what is the optimal solution, thereby providing a benchmark against which existing approaches can be evaluated. In the longer term it also provides the potential for new methods to create ensembles of solutions to the model, incorporating the available data in an optimal
A comparison of hybrid ensemble transform Kalman filterOptimum Interpolation and ensemble squareroot filter analysis schemes
, 2007
"... A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A twolayer primitive equation model was used under perfectmodel assumptions. A simplified observation network was used ..."
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Cited by 21 (6 self)
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A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A twolayer primitive equation model was used under perfectmodel assumptions. A simplified observation network was used, and the OI method utilized a static background error covariance constructed from a large inventory of historical forecast errors. The hybrid scheme updated the ensemble mean using a hybridized ensemble and static backgrounderror covariance. The ensemble perturbations in the hybrid scheme were updated by the ETKF scheme. The EnSRF ran parallel data assimilation cycles for each member and serially assimilated the observations. The EnSRF backgrounderror covariance was estimated fully from the ensemble. For 50member ensembles, the analyses from the hybrid scheme were as accurate or nearly as accurate as those from the EnSRF, depending on the norm. For 20member ensembles, the analyses from the hybrid scheme were more accurate than analyses from the EnSRF under certain norms. Both hybrid and EnSRF analyses were more accurate than the analyses from the OI. Further reducing the ensemble size to five members, the EnSRF exhibited filter divergence, whereas the analyses from the hybrid scheme were still better than those updated by the OI. Additionally, the hybrid scheme was less prone to spurious gravity
Sequential Data Assimilation Techniques in Oceanography
, 2003
"... this article, we will focus on sequential DA methods that constitute the second class. These methods use a probabilistic framework and give estimates of the whole system state sequentially by propagating information only forward in time. This avoids deriving an inverse or an adjoint model and theref ..."
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Cited by 19 (3 self)
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this article, we will focus on sequential DA methods that constitute the second class. These methods use a probabilistic framework and give estimates of the whole system state sequentially by propagating information only forward in time. This avoids deriving an inverse or an adjoint model and therefore makes sequential methods easier to adapt for all models. Further, the probabilistic framework is more convenient for error estimation and further stochastic analysis such as threshold characterization
2006: Numerical forecasts of the 1516 June 2002 Southern Plains severe MCS: Impact of mesoscale data and cloud
"... Highresolution explicit forecasts using the Advanced Regional Prediction System (ARPS) of the 15–16 June 2002 mesoscale convective system (MCS) that occurred over the U.S. central and southern plains ..."
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Cited by 16 (10 self)
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Highresolution explicit forecasts using the Advanced Regional Prediction System (ARPS) of the 15–16 June 2002 mesoscale convective system (MCS) that occurred over the U.S. central and southern plains
On the mapping of multivariate geophysical fields: sensitivity to size, scales and dynamics
 J
, 2002
"... The effects of a priori parameters on the error subspace estimation and mapping methodology introduced by P. F. J. Lermusiaux et al. is investigated. The approach is threedimensional, multivariate, and multiscale. The sensitivities of the subspace and a posteriori fields to the size of the subspace ..."
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Cited by 16 (3 self)
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The effects of a priori parameters on the error subspace estimation and mapping methodology introduced by P. F. J. Lermusiaux et al. is investigated. The approach is threedimensional, multivariate, and multiscale. The sensitivities of the subspace and a posteriori fields to the size of the subspace, scales considered, and nonlinearities in the dynamical adjustments are studied. Applications focus on the mesoscale to subbasinscale physics in the northwestern Levantine Sea during 10 February–15 March and 19 March–16 April 1995. Forecasts generated from various analyzed fields are compared to in situ and satellite data. The sensitivities to size show that the truncation to a subspace is efficient. The use of criteria to determine adequate sizes is emphasized and a backoftheenvelope rule is outlined. The sensitivities to scales confirm that, for a given region, smaller scales usually require larger subspaces because of spectral redness. However, synoptic conditions are also shown to strongly influence the ordering of scales. The sensitivities to the dynamical adjustment reveal that nonlinearities can modify the variability decomposition, especially the dominant eigenvectors, and that changes are largest for the features and regions with high shears. Based on the estimated variability variance fields, eigenvalue spectra, multivariate eigenvectors and (cross)covariance functions, dominant dynamical balances and the spatial distribution of hydrographic and velocity characteristic scales are obtained for primary regional features. In particular, the Ierapetra Eddy is found to be close to gradientwind balance and coastaltrapped waves are anticipated to occur along the northern escarpment of the basin. 1.