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119
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
Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model
, 1998
"... Anticipating the opportunity to make supplementary observations at locations that can depend upon the current weather situation, the question is posed as to what strategy should be adopted to select the locations, if the greatest improvement in analyses and forecasts is to be realized. To seek a p ..."
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Cited by 140 (1 self)
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Anticipating the opportunity to make supplementary observations at locations that can depend upon the current weather situation, the question is posed as to what strategy should be adopted to select the locations, if the greatest improvement in analyses and forecasts is to be realized. To seek a preliminary answer, the authors introduce a model consisting of 40 ordinary differential equations, with the dependent variables representing values of some atmospheric quantity at 40 sites spaced equally about a latitude circle. The equations contain quadratic, linear, and constant terms representing advection, dissipation, and external forcing. Numerical integration indicates that small errors (differences between solutions) tend to double in about 2 days. Localized errors tend to spread eastward as they grow, encircling the globe after about 14 days. In the
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
A Linear Stochastic Dynamical Model of ENSO. Part I: Model Development
 JOURNAL OF CLIMATE
, 2000
"... Singular vector analysis and Floquet analysis are carried out on a linearized variant of the Zebiak–Cane atmosphere–ocean model of El Niño–Southern Oscillation (ENSO), hereinafter called the nominal model. The Floquet analysis shows that the system has a single unstable mode. This mode has a shape a ..."
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Cited by 39 (3 self)
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Singular vector analysis and Floquet analysis are carried out on a linearized variant of the Zebiak–Cane atmosphere–ocean model of El Niño–Southern Oscillation (ENSO), hereinafter called the nominal model. The Floquet analysis shows that the system has a single unstable mode. This mode has a shape and frequency similar to ENSO and is well described by delayed oscillator physics. Singular vector analysis shows two interesting features. (i) For any starting month and time period of optimization the singular vector is shaped like one of two nearly orthogonal patterns. These two patterns correspond approximately to the real and imaginary parts of the adjoint of the ENSO mode for the timeinvariant basicstate version of the system that was calculated in previous work. (ii) Contour plots of the singular values as a function of starting month and period of optimization show a ridge along end times around December. This result along with a study of the time evolution of the associated singular vectors shows that the growth of the singular vectors has a strong tendency to peak in the boreal winter. For the case of a stochastically perturbed ENSO model, this result indicates that the annual cycle in the basic state of the ocean is sufficient to produce strong phase locking of ENSO to the annual cycle; it is not necessary to invoke either nonlinearity or an annual cycle in the structure of the noise. The structures of the ENSO mode, of the optimal vectors, and of the phase locking to the annual cycle are
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...
A conceptual framework for predictability studies
 J. Climate
, 1999
"... A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate tra ..."
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Cited by 28 (0 self)
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A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate transformations and applies to multivariate predictions irrespective of assumptions about the probability distribution of prediction errors. For univariate Gaussian predictions, the PP reduces to conventional predictability measures that are based upon the ratio of the rms error of a model prediction over the rms error of the climatological mean prediction. Since climatic variability on intraseasonal to interdecadal timescales follows an approximately Gaussian distribution, the emphasis of this paper is on multivariate Gaussian random variables. Predictable and unpredictable components of multivariate Gaussian systems can be distinguished by predictable component analysis, a procedure derived from discriminant analysis: seeking components with large PP leads to an eigenvalue problem, whose solution yields uncorrelated components that are ordered by PP from largest to smallest. In a discussion of the application of the PP and the predictable component analysis in different types of predictability studies, studies are considered that use either ensemble integrations of numerical models or autoregressive models fitted to observed or simulated data. An investigation of simulated multidecadal variability of the North Atlantic illustrates the proposed methodology. Reanalyzing an ensemble of integrations of the Geophysical Fluid Dynamics Laboratory coupled general circulation model confirms and refines earlier findings. With an autoregressive model fitted to a single integration of the same model, it is demonstrated that similar conclusions can be reached without resorting to computationally costly ensemble integrations. 1.
2004: Meteorological Research Needs for Improved Air Quality Forecasting
 Report of the 11th Prospectus Development Team of the U.S. Weather Research
"... *This is an abridged version of the final report of PDT11. The complete version can be found at ..."
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Cited by 27 (2 self)
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*This is an abridged version of the final report of PDT11. The complete version can be found at
2001: Idealized Adaptive Observation Strategies for Improving Numerical Weather Prediction
 J. Atmos. Sci
, 1998
"... Adaptive sampling uses information about individual atmospheric situations to identify regions where additional observations are likely to improve weather forecasts of interest. The observation network could be adapted for a wide range of forecasting goals, and it could be adapted either by allocat ..."
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Cited by 26 (2 self)
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Adaptive sampling uses information about individual atmospheric situations to identify regions where additional observations are likely to improve weather forecasts of interest. The observation network could be adapted for a wide range of forecasting goals, and it could be adapted either by allocating existing observations differently or by adding observations from programmable platforms to the existing network. In this study, observing strategies are explored in a simulated idealized system with a threedimensional quasigeostrophic model and a realistic data assimilation scheme. Using simple error norms, idealized adaptive observations are compared to nonadaptive observations for a range of observation densities. The results presented show that in this simulated system, the influence of both adaptive and nonadaptive observations depends strongly on the observation density. For sparse observation networks, the simple adaptive strategies tested are beneficial: adaptive observations can, on average, reduce analysis and forecast errors more than the same number of nonadaptive observations, and they can reduce errors by a given amount using fewer observational resources. In contrast, for dense observation networks it is much more difficult to benefit from adapting observations, at least for the data assimilation method used here. The results suggest that the adaptive strategies tested are most effective when the observations are adapted regularly and frequently, giving the data assimilation system as many opportunities as possible to reduce errors as they evolve. They also indicate that ensemblebased estimates of initial condition errors may be useful for adaptive observations. Further study is needed to understand the extent to which the results from this idealized study apply to more complex, more realistic systems. 1.
Evolving the subspace of the threedimensional multiscale ocean variability: Massachusetts Bay
 J. Marine Systems
, 2001
"... A data and dynamics driven approach to estimate, decompose, organize and analyze the evolving threedimensional variability of ocean fields is outlined. Variability refers here to the statistics of the differences between ocean states and a reference state. In general, these statistics evolve in tim ..."
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Cited by 25 (6 self)
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A data and dynamics driven approach to estimate, decompose, organize and analyze the evolving threedimensional variability of ocean fields is outlined. Variability refers here to the statistics of the differences between ocean states and a reference state. In general, these statistics evolve in time and space. For a first endeavor, the variability subspace defined by the dominant eigendecomposition of a normalized form of the variability covariance is evolved. A multiscale methodology for its initialization and forecast is outlined. It combines data and primitive equation dynamics within a MonteCarlo approach. The methodology is applied to part of a multidisciplinary experiment that occurred in Massachusetts Bay in late summer and early fall of 1998. For a 4day time period, the threedimensional and multivariate properties of the variability standard deviations and dominant eigenvectors are studied. Two variability patterns are discussed in detail. One relates to a displacement of the Gulf of Maine coastal current offshore from Cape Ann, with the creation of adjacent mesoscale recirculation cells. The other relates to a Baywide coastal upwelling mode from Barnstable Harbor to Gloucester in response to strong southerly winds. Snapshots and tendencies of physical fields and trajectories of simulated Lagrangian drifters are employed to diagnose and illustrate the use of the dominant variability covariance. The variability subspace is shown to guide the dynamical analysis of the physical fields. For the stratified conditions, it is found that strong wind events can alter the structures of the buoyancy flow and that circulation features are more variable than previously described, on multiple