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53
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
An Ensemble Adjustment Kalman Filter for Data Assimilation
, 2001
"... A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear ..."
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Cited by 283 (12 self)
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A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear
Ensemble forecasting at NCEP and the breeding method
 Mon. Wea. Rev
, 1997
"... The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In ..."
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Cited by 193 (16 self)
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The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 independent global forecasts valid for two weeks every day. For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. It is shown that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the firstguess forecasts, is ‘‘scaled down’ ’ at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth. The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred vectors are superpositions of the leading local (timedependent)
A comparison of probabilistic forecasts from bred, singularvector, and perturbation observation ensembles
 MON. WEA. REV
, 2000
"... The statistical properties of analysis and forecast errors from commonly used ensemble perturbation methodologies are explored. A quasigeostrophic channel model is used, coupled with a 3Dvariational data assimilation scheme. A perfect model is assumed. Three perturbation methodologies are considere ..."
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Cited by 55 (7 self)
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The statistical properties of analysis and forecast errors from commonly used ensemble perturbation methodologies are explored. A quasigeostrophic channel model is used, coupled with a 3Dvariational data assimilation scheme. A perfect model is assumed. Three perturbation methodologies are considered. The breeding and singularvector (SV) methods approximate the strategies currently used at operational centers in the United States and Europe, respectively. The perturbed observation (PO) methodology approximates a random sample from the analysis probability density function (pdf) and is similar to the method performed at the Canadian Meteorological Centre. Initial conditions for the PO ensemble are analyses from independent, parallel data assimilation cycles. Each assimilation cycle utilizes observations perturbed by random noise whose statistics are consistent with observational error covariances. Each member’s assimilation/forecast cycle is also started from a distinct initial condition. Relative to breeding and SV, the PO method here produced analyses and forecasts with desirable statistical characteristics. These include consistent rank histogram uniformity for all variables at all lead times, high spread/ skill correlations, and calibrated, reducederror probabilistic forecasts. It achieved these improvements primarily because 1) the ensemble mean of the PO initial conditions was more accurate than the mean of the bred or
Statistical Design for Adaptive Weather Observations
 J. Atmos. Sci
, 1999
"... Suppose that we have the freedom to adapt the observational network by choosing the times and locations of observations. Which choices would yield the best analysis of the atmospheric state or the best subsequent forecast? Here, this problem of "adaptive observations" is formulated as a pr ..."
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Cited by 32 (2 self)
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Suppose that we have the freedom to adapt the observational network by choosing the times and locations of observations. Which choices would yield the best analysis of the atmospheric state or the best subsequent forecast? Here, this problem of "adaptive observations" is formulated as a problem in statistical design. The statistical framework provides a rigorous mathematical statement of the adaptive observations problem and indicates where the uncertainty of the current analysis, the dynamics of error evolution, the form and errors of observations, and data assimilation each enter the calculation. The statistical formulation of the problem also makes clear the importance of the optimality criteria (for instance, one might choose to minimize the total error variance in a given forecast) and identifies approximations that make calculation of optimal solutions feasible in principle. Optimal solutions are discussed and interpreted for a variety of cases. Selected approaches to the adaptiv...
2003: Ensemble forecasts and the properties of flowdependent analysis error covariance singular vectors
 Mon. Wea. Rev
"... Approximations to flowdependent analysiserror covariance singular vectors (AEC SVs) were calculated in a dry, T31 L15 primitiveequation global model. Sets of 400member ensembles of analyses were generated by an ensemblebased data assimilation system. A sparse network of simulated rawinsonde obs ..."
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Cited by 17 (3 self)
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Approximations to flowdependent analysiserror covariance singular vectors (AEC SVs) were calculated in a dry, T31 L15 primitiveequation global model. Sets of 400member ensembles of analyses were generated by an ensemblebased data assimilation system. A sparse network of simulated rawinsonde observations were assimilated, and a perfect model was assumed. Ensembles of 48h forecasts were also generated from these analyses. The structure of evolved singular vectors was determined by finding the linear combination of the forecast ensemble members that resulted in the largest forecasterror variance, here measured in a totalenergy norm north of 20�N latitude. The same linear combination of analyses specifies the initialtime structure that should evolve to the forecast singular vector under assumptions of linearity of error growth. The structures of these AEC SVs are important because they represent the analysiserror structures associated with the largest forecast errors. If singular vectors using other initial norms have very different structures, this indicates that these structures may be statistically unlikely to occur. The European Centre for MediumRange Weather Forecasts currently uses singular vectors using an initial totalenergy norm [‘‘totalenergy singular vectors’ ’ or (TE SVs)] to generate perturbations to initialize their ensemble forecasts. Approximate TE SVs were also calculated by drawing an initial random ensemble with perturbations that were white in total energy and
Singular vector perturbation growth in a primitive equation model with moist physics
 J. Atmos. Sci
, 1999
"... Finitetime growth of perturbations in the presence of moist physics (specifically, precipitation) is investigated using singular vectors (SVs) in the context of a primitive equation regional model. Two difficulties appear in the explicit consideration of the effect of moist physics when studying su ..."
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Cited by 16 (0 self)
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Finitetime growth of perturbations in the presence of moist physics (specifically, precipitation) is investigated using singular vectors (SVs) in the context of a primitive equation regional model. Two difficulties appear in the explicit consideration of the effect of moist physics when studying such optimal growth. First, the tangentlinear description of moist physics may not be as straightforward and accurate as for dryadiabatic processes; second, because of the consideration of moisture, the design of an appropriate measure of growth (i.e., norm) is subject to even more ambiguity than in the dry situation. In this study both of these problems are addressed in the context of the moist version of the National Center for Atmospheric Research Mesoscale Adjoint Modeling System, version 2, with emphasis on the second problem. Leading SVs are computed in an iterative fashion, using a Lanczos algorithm, for three norms over an optimization interval of 24 h; these norms are based on an expression related to (total) perturbation energy. The properties of these SVs are studied for a case of explosive cyclogenesis and a case of summer convection. The consideration of moisture leads to faster growth of perturbations than in the dry situation, as well as to the appearance of new growing structures. Apparently, moist processes provide for new mechanisms of error growth and do not simply lead to a modulation of SVs obtained with the dry version of the model. Consequently, consideration of the linearized moist processes is essential for revealing all structures that might potentially grow in a moist primitive equation model. In the context of this investigation growth rates depend more on the choice of the basic state and linearized model (moist vs dry) than on the choice of the norm (moist vs dry total energy norm). A reference is cited that supports the validity of the moist tangentlinear SV perturbation growth studied here in the nonlinear regime. 1.
Monte Carlo Based Ensemble Forecasting
 Statistics and Computing
, 1998
"... Ensemble forecasting involves the use of several integrations of a numerical model. Even if this model is assumed to be known, ensembles are needed due to uncertainty in initial conditions. The ideas discussed in this paper incorporate aspects of both analytic model approximations and Monte Carlo ar ..."
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Cited by 12 (0 self)
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Ensemble forecasting involves the use of several integrations of a numerical model. Even if this model is assumed to be known, ensembles are needed due to uncertainty in initial conditions. The ideas discussed in this paper incorporate aspects of both analytic model approximations and Monte Carlo arguments to gain some efficiency in the generation and use of ensembles. Efficiency is gained through the use of importance sampling Monte Carlo. Once ensemble members are generated, suggestions for their use, involving both approximation and statistical notions such as kernel density estimation and mixture modeling are discussed. Fully deterministic procedures derived from the Monte Carlo analysis are also described. Examples using the threedimensional Lorenz system are described. Address: Mark Berliner Department of Statistics Ohio State University 1958 Neil Ave. Columbus, OH 432101247 USA email: mb@stat.ohiostate.edu Keywords and Phrases: Chaos, Importance sampling, Kernel density es...