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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 328 (20 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 295 (13 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
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 23 (1 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.
The Role of Operational Constraints in Selecting Supplementary Observations
 J. Atmos. Sci
, 2000
"... Adaptive observation strategies in numerical weather prediction aim to improve forecasts by exploiting additional observations at locations that are themselves optimized with respect to the current state of the atmosphere. The role played by an inexact estimate of the current state of the atmosphe ..."
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Cited by 21 (3 self)
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Adaptive observation strategies in numerical weather prediction aim to improve forecasts by exploiting additional observations at locations that are themselves optimized with respect to the current state of the atmosphere. The role played by an inexact estimate of the current state of the atmosphere (i.e., error in the "analysis") in restricting adaptive observation strategies is investigated; necessary conditions valid across a broad class of modeling strategies are identified for strategies based on linearized model dynamics to be productive. It is demonstrated that the assimilation scheme, or more precisely, the magnitude of the analysis error is crucial in limiting the applicability of dynamically based strategies. In short, strategies based on linearized dynamics require that analysis error is sufficiently small so that the model linearization about the analysis is relevant to linearized dynamics of the full system about the true system state. Inasmuch as the analysis erro...
Ensemblebased sensitivity analysis
 MON. WEA. REV
, 2008
"... The sensitivity of forecasts to observations is evaluated using an ensemble approach with data drawn from a pseudooperational ensemble Kalman filter. For Gaussian statistics and a forecast metric defined as a scalar function of the forecast variables, the effect of observations on the forecast metr ..."
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Cited by 16 (1 self)
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The sensitivity of forecasts to observations is evaluated using an ensemble approach with data drawn from a pseudooperational ensemble Kalman filter. For Gaussian statistics and a forecast metric defined as a scalar function of the forecast variables, the effect of observations on the forecast metric is quantified by changes in the metric mean and variance. For a single observation, expressions for these changes involve a product of scalar quantities, which can be rapidly evaluated for large numbers of observations. This technique is applied to determining climatological forecast sensitivity and predicting the impact of observations on sea level pressure and precipitation forecast metrics. The climatological 24h forecast sensitivity of the average pressure over western Washington State shows a region of maximum sensitivity to the west of the region, which tilts gently westward with height. The accuracy of ensemble sensitivity predictions is tested by withholding a single buoy pressure observation from this region and comparing this perturbed forecast with the control case where the buoy is assimilated. For 30 cases, there is excellent agreement between these forecast differences and the ensemble predictions, as measured by the forecast metric. This agreement decreases for increasing numbers of observations. Nevertheless, by using statistical confidence tests to address sampling error, the impact of thousands of observations on forecastmetric variance is shown to be well estimated by a subset of the O(100) most significant observations.
Assimilation of Standard and Targeted Observations within the Unstable Subspace of the ObservationAnalysisForecast Cycle System
 J. Atmos. Sci
"... In this paper it is shown that the flowdependent instabilities that develop within an observation–analysis– forecast (OAF) cycle and that are responsible for the background error can be exploited in a very simple way to assimilate observations. The basic idea is that, in order to minimize the analy ..."
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Cited by 15 (8 self)
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In this paper it is shown that the flowdependent instabilities that develop within an observation–analysis– forecast (OAF) cycle and that are responsible for the background error can be exploited in a very simple way to assimilate observations. The basic idea is that, in order to minimize the analysis and forecast errors, the analysis increment must be confined to the unstable subspace of the OAF cycle solution. The analysis solution here formally coincides with that of the classical threedimensional variational solution with the background error covariance matrix estimated in the unstable subspace. The unstable directions of the OAF system solution are obtained by breeding initially random perturbations of the analysis but letting the perturbed trajectories undergo the same process as the control solution, including assimilation of all the available observations. The unstable vectors are then used both to target observations and for the assimilation design. The approach is demonstrated in an idealized environment using a simple model, simulated standard observations over land with a single adaptive observation over the ocean. In the application a simplified form is adopted of the analysis solution and a single unstable vector at each analysis time whose amplitude is determined by means of the adaptive observation. The remarkable reduction of the analysis and forecast error obtained by
An adjoint sensitivity method for the adaptive location of the observations in air quality modeling
 Journal of Atmospheric Sciences
"... ABSTRACT The spatiotemporal distribution of observations plays an essential role in the data assimilation process. An adjoint sensitivity method is applied to the problem of adaptive location of the observational system for a nonlinear transportchemistry model in the context of 4D variational data ..."
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Cited by 13 (2 self)
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ABSTRACT The spatiotemporal distribution of observations plays an essential role in the data assimilation process. An adjoint sensitivity method is applied to the problem of adaptive location of the observational system for a nonlinear transportchemistry model in the context of 4D variational data assimilation. The method is presented in a general framework and it is shown that in addition to the initial state of the model, sensitivity with respect to emission and deposition rates and certain types of boundary values may be obtained at a minimal additional cost. The adjoint modeling is used to evaluate the influence function and to identify the domain of influence associated with the observations. These essential tools are further used to develop a novel algorithm for targeting observations that takes into account the interaction among observations at different instants in time and spatial locations. Issues related to the case of multiple observations are addressed and it is shown that by using the adjoint modeling an efficient implementation may be achieved. Computational and practical aspects are discussed and this analysis indicates that it is feasible to implement the proposed method for comprehensive air quality models. Numerical experiments performed with a twodimensional test model show promising results.
Data Assimilation for Numerical Weather Prediction: A Review
"... Abstract During the last 20 years data assimilation has gradually reached a mature center stage position at both Numerical Weather Prediction centers as well as being at the center of activities at many federal research institutes as well as at many universities. The research encompasses now activit ..."
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Cited by 13 (0 self)
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Abstract During the last 20 years data assimilation has gradually reached a mature center stage position at both Numerical Weather Prediction centers as well as being at the center of activities at many federal research institutes as well as at many universities. The research encompasses now activities which involve, beside meteorologists and oceanographers at operational centers or federal research facilities, many in the applied and computational mathematical research communities. Data assimilation or 4D VAR extends now also to other geosciences fields such as hydrology and geology and results in the publication of an ever increasing number of books and monographs related to the topic. In this short survey article we provide a brief introduction providing some historical perspective and background, a survey of data assimilation prior to 4D VAR and basic concepts of data assimilation. I first proceed to outline the early 4D VAR stages (1980–1990) and addresses in a succinct manner the period of the 1990s that saw the major developments and the flourishing of all aspects of 4D VAR both at operational centers and at research Universities and Federal Laboratories. Computational aspects of 4D Var data assimilation addressing computational burdens as well as ways to alleviate them are briefly outlined. Brief interludes are provided for each period surveyed allowing the reader to have a better perspective A brief survey of different topics related to state of the art 4D Var today is then presented and we conclude with what we perceive to be main directions of research and the future of data assimilation and some open problems. We will strive to use the unified notation of Ide et al. (J Meteor Soc Japan 75:181–189,
Learning
"... covariance dynamics for path planning of UAV sensors in a largescale dynamic environment ..."
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Cited by 7 (0 self)
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covariance dynamics for path planning of UAV sensors in a largescale dynamic environment
Dynamic design of ecological monitoring networks for nonGaussian spatiotemporal data
 P05FQM00990 of the Andalusian CICYE and MTM200508597 of the DGI
, 2005
"... Many ecological processes exhibit spatial structure that changes over time in a coherent, dynamical fashion. This dynamical component is often ignored in the design of spatial monitoring networks. Furthermore, ecological variables related to processes such as habitat are often nonGaussian (e.g., P ..."
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Cited by 3 (0 self)
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Many ecological processes exhibit spatial structure that changes over time in a coherent, dynamical fashion. This dynamical component is often ignored in the design of spatial monitoring networks. Furthermore, ecological variables related to processes such as habitat are often nonGaussian (e.g., Poisson or lognormal). We demonstrate that a simulationbased design approach can be used in settings where the data distribution is from a spatiotemporal exponential family. The key random component in the conditional mean function from this distribution is then a spatiotemporal dynamic process. Given the computational burden of estimating the expected utility of various designs in this setting, we utilize an extended Kalman filter approximation to facilitate implementation. The approach is motivated by, and demonstrated on, the problem of selecting sampling locations to estimate July brood counts in the prairie pothole region of the U.S.