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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
A Study of the predictability of tropical Pacific SST in a coupled atmosphere–ocean model using singular vector analysis: The role of the annual cycle and the ENSO cycle
 Mon. Wea. Rev
, 1997
"... The authors examine the sensitivity of the Battisti coupled atmosphere–ocean model—considered as a forecast model for the El Niño–Southern Oscillation (ENSO)—to perturbations in the sea surface temperature (SST) field applied at the beginning of a model integration. The spatial structures of the fa ..."
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Cited by 26 (5 self)
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The authors examine the sensitivity of the Battisti coupled atmosphere–ocean model—considered as a forecast model for the El Niño–Southern Oscillation (ENSO)—to perturbations in the sea surface temperature (SST) field applied at the beginning of a model integration. The spatial structures of the fastest growing SST perturbations are determined by singular vector analysis of an approximation to the propagator for the linearized system. Perturbation growth about the following four reference trajectories is considered: (i) the annual cycle, (ii) a freely evolving model ENSO cycle with an annual cycle in the basic state, (iii) the annual mean basic state, and (iv) a freely evolving model ENSO cycle with an annual mean basic state. Singular vectors with optimal growth over periods of 3, 6, and 9 months are computed. The magnitude of maximum perturbation growth is highly dependent on both the phase of the seasonal cycle and the phase of the ENSO cycle at which the perturbation is applied and on the duration over which perturbations are allowed to evolve. However, the spatial structure of the optimal perturbation is remarkably insensitive to these factors. The structure of the optimal perturbation consists of an east–west dipole spanning the entire tropical Pacific basin superimposed on a north–south dipole in the eastern tropical Pacific. A simple physical interpretation for the optimal pattern is provided. In most cases investigated, there is only one structure that exhibits growth.
Analysis of the singular vectors of the fullphysics FSU Global Spectral Model
 Tellus A
, 2005
"... Analysis of singular vectors (SV) is performed on the Florida State University Global Spectral Model (FSUGSM) which includes linearized full physics of the atmosphere. ..."
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Cited by 6 (1 self)
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Analysis of singular vectors (SV) is performed on the Florida State University Global Spectral Model (FSUGSM) which includes linearized full physics of the atmosphere.
Upper bounds for the solution of the discrete algebraic Lyapunov equation
 Automatica
, 1999
"... Introduction The discrete algebraic Lyapunov equation (DALE) is P = APA T + Q; A; Q 2 R n\Thetan ; Q = Q T ? 0 ; (1) where all the eigenvalues of A lie inside the unit circle; ( T ) and (? 0) denote transpose and positive definiteness, respectively; P = P T ? 0 is the solution. The 1 Cor ..."
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Cited by 6 (1 self)
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Introduction The discrete algebraic Lyapunov equation (DALE) is P = APA T + Q; A; Q 2 R n\Thetan ; Q = Q T ? 0 ; (1) where all the eigenvalues of A lie inside the unit circle; ( T ) and (? 0) denote transpose and positive definiteness, respectively; P = P T ? 0 is the solution. The 1 Corresponding author: Prof. Dan Marchesin, Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460320 Rio de Janeiro, RJ, Brazil; fax: 55215295075; email: marchesi@fluid.impa.br Preprint submitted to Automatica 25 January 1999 matrix P is the steadystate covariance of a discretetime, stochastically forced, stable linear system,<F
2007: Comparing adjoint and ensemble sensitivity analysis with applications to observation targeting
"... The sensitivity of numerical weather forecasts to small changes in initial conditions is estimated using ensemble samples of analysis and forecast errors. Ensemble sensitivity is defined here by linear regression of analysis errors onto a given forecast metric. We show that ensemble sensitivity is p ..."
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Cited by 1 (0 self)
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The sensitivity of numerical weather forecasts to small changes in initial conditions is estimated using ensemble samples of analysis and forecast errors. Ensemble sensitivity is defined here by linear regression of analysis errors onto a given forecast metric. We show that ensemble sensitivity is proportional to the projection of the analysiserror covariance onto the adjoint sensitivity field. Furthermore, the ensemble sensitivity approach proposed here involves a small calculation that is easy to implement. Ensemble and adjointbased sensitivity fields are compared for a representative wintertime flow pattern near the West Coast of North America for a 90member ensemble of independent initial conditions derived from an ensemble Kalman filter. The forecast metric is taken for simplicity to be the 24hr forecast of sealevel pressure at a single point in western Washington state. Results show that adjoint and ensemble sensitivities are very different in terms of location, scale, and magnitude. Adjoint sensitivity fields reveal mesoscale lowertropospheric structures that tilt strongly upshear, whereas ensemble sensitivity fields emphasize synopticscale features that tilt modestly throughout the troposphere and are associated with significant weather features at the initial time. Optimal locations for targeting can easily be determined from ensemble sensitivity, and results indicate that the primary targeting locations are located away from regions of greatest adjoint and ensemble sensitivity. We show that this method of targeting is similar to previous ensemblebased methods that estimate forecasterror variance reduction, but easily allows for the application of statistical confidence measures to deal with sampling error. 1 1.
unknown title
, 2003
"... Analysis of singular vectors (SVs) is performed on the Florida State University Global Spectral Model, which includes linearized full physics of the atmosphere. It is demonstrated that the physical processes, especially precipitation, fundamentally affect the leading SVs. When the SVs are coupled w ..."
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Analysis of singular vectors (SVs) is performed on the Florida State University Global Spectral Model, which includes linearized full physics of the atmosphere. It is demonstrated that the physical processes, especially precipitation, fundamentally affect the leading SVs. When the SVs are coupled with the precipitation geographically, their growth rates increase substantially and their structures change significantly. The physical processes however have little impact on growth rates or structures of the SVs that are geographically independent of precipitation. Furthermore, it is shown that spatial filtering along with the projection operator that projects the flow winds to the rotational wind (designed as a simple initialization process) improves the structural features of SVs and is found to mitigate spurious modes. 1.