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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
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
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
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.
Path planning of autonomous underwater vehicles (AUVs) for adaptive sampling
, 2005
"... Abstract—The goal of adaptive sampling in the ocean is to predict the types and locations of additional ocean measurements that would be most useful to collect. Quantitatively, what is most useful is defined by an objective function and the goal is then to optimize this objective under the constrain ..."
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Cited by 22 (4 self)
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Abstract—The goal of adaptive sampling in the ocean is to predict the types and locations of additional ocean measurements that would be most useful to collect. Quantitatively, what is most useful is defined by an objective function and the goal is then to optimize this objective under the constraints of the available observing network. Examples of objectives are better oceanic understanding, to improve forecast quality, or to sample regions of high interest. This work provides a new pathplanning scheme for the adaptive sampling problem. We define the pathplanning problem in terms of an optimization framework and propose a method based on mixed integer linear programming (MILP). The mathematical goal is to find the vehicle path that maximizes the line integral of the uncertainty of field estimates along this path. Sampling this path can improve the accuracy of the field estimates the most. While achieving this objective, several constraints must be satisfied and are implemented. They relate to vehicle motion, intervehicle coordination, communication, collision avoidance, etc. The MILP formulation is quite powerful to handle different problem constraints and flexible enough to allow easy extensions of the problem. The formulation covers single and multiplevehicle cases as well as singleand multipleday formulations. The need for a multipleday formulation arises when the ocean sampling mission is optimized for several days ahead. We first introduce the details of the formulation, then elaborate on the objective function and constraints, and finally, present a varied set of examples to illustrate the applicability of the proposed method. Index Terms—Adaptive sampling, Autonomous Ocean Sampling Network (AOSN), autonomous underwater vehicle (AUV), data
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
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 (4 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...
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 16 (9 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
 J. Atmos. Sci
, 2003
"... The spatiotemporal distribution of the 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 assi ..."
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Cited by 14 (2 self)
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The spatiotemporal distribution of the 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 with the case of multiple observations are addressed and it is shown that using the adjoint modeling an efficient implementation may be achieved. Computational and practical aspects are discussed and our analysis indicate that it is feasible to implement the proposed method for comprehensive air quality models. Numerical experiments performed with a two dimensional test model show promising results. 1 1
Applications of information theory in ensemble data assimilation
 Quarterly Journal of the Royal Meteorological Society
, 2007
"... Application of information theory in ensemble ..."