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Controlling overestimation of error covariance in ensemble Kalman filters with sparse observations: A variance limiting Kalman filter. Monthly Weather Review 139(8
, 2011
"... Abstract We consider the problem of an ensemble Kalman filter when only partial observations are available. In particular we consider the situation where the observational space consists of variables which are directly observable with known observational error, and of variables of which only their ..."
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Abstract We consider the problem of an ensemble Kalman filter when only partial observations are available. In particular we consider the situation where the observational space consists of variables which are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. To limit the variance of the latter poorly resolved variables we derive a variance limiting Kalman filter (VLKF) in a variational setting. We analyze the variance limiting Kalman filter for a simple linear toy model and determine its range of optimal performance. We explore the variance limiting Kalman filter in an ensemble transform setting for the Lorenz96 system, and show that incorporating the information on the variance on some unobservable variables can improve the skill and also increase the stability of the data assimilation procedure.
A Comparison of the Hybrid and EnSRF Analysis Schemes in the Presence of Model Errors due to Unresolved Scales
, 2009
"... A hybrid analysis scheme is compared with an ensemble square root filter (EnSRF) analysis scheme in the presence of model errors as a followup to a previous perfectmodel comparison. In the hybrid scheme, the ensemble perturbations are updated by the ensemble transform Kalman filter (ETKF) and the ..."
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A hybrid analysis scheme is compared with an ensemble square root filter (EnSRF) analysis scheme in the presence of model errors as a followup to a previous perfectmodel comparison. In the hybrid scheme, the ensemble perturbations are updated by the ensemble transform Kalman filter (ETKF) and the ensemble mean is updated with a hybrid ensemble and static backgrounderror covariance. The experiments were conducted with a twolayer primitive equation model. The true state was a T127 simulation. Data assimilation experiments were conducted at T31 resolution (3168 complex spectral coefficients), assimilating imperfect observations drawn from the T127 nature run. By design, the magnitude of the truncation error was large, which provided a test on the ability of both schemes to deal with model error. Additive noise was used to parameterize model errors in the background ensemble for both schemes. In the first set of experiments, additive noise was drawn from a large inventory of historical forecast errors; in the second set of experiments, additive noise was drawn from a large inventory of differences between forecasts and analyses. The static covariance was computed correspondingly from the two inventories. The hybrid analysis was statistically significantly more accurate than the EnSRF analysis. The improvement of the hybrid over the EnSRF was smaller when differences of forecasts and analyses were used to form the random noise and the static covariance. The EnSRF analysis was more sensitive to the size of the ensemble than the hybrid. A series of tests was conducted to understand why the EnSRF performed worse than the hybrid. It was shown that the inferior performance of the EnSRF was likely due to the sampling error in the estimation of the modelerror covariance in the mean update and the lessbalanced EnSRF initial conditions resulting from the extra localizations used in the EnSRF. 1.
Evolved and random perturbation methods for calculating model sensitivities and covariances
"... Different ways of perturbing the initial condition of an ensemble of forecasts for the purpose of calculating sensitivity or covariance fields of model variables are examined. The three methods considered are: random perturbations at each gridpoint, smoothed random perturbations, and perturbations ..."
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Different ways of perturbing the initial condition of an ensemble of forecasts for the purpose of calculating sensitivity or covariance fields of model variables are examined. The three methods considered are: random perturbations at each gridpoint, smoothed random perturbations, and perturbations that are evolved by the model through time from an earlier set of perturbations. A very large ensemble of model runs using spatially discrete perturbations is also compared for validation purposes. An ensemble size of 2000 members is used so as to reduce the noise in sensitivity fields. Covariances found from the three methods are highly accurate and nearly identical for any perturbation method. The calculation of sensitivity fields, however, is more dependent on the perturbation method. For the cases of evolved or smoothed perturbations, the spatial correlation of the perturbations leads to an inherent smoothing of the sensitivity fields. Sensitivity structures of scales smaller than the perturbation correlation distance can not be found. This is a particular problem for the evolved perturbations in the boundary layer. Furthermore, the spatial correlation of initial perturbations makes the calculation of sensitivity values inaccurate unless the complicated problem of separating the combined effects of correlated perturbations on the forecast is dealt with. Consequently, mathematically correct sensitivity values are only found by using initial perturbation fields that are spatially completely random.
Surf zone bathymetry and circulation predictions via data assimilation of
"... remote sensing observations ..."
Assimilating synthetic CryoSat sea ice thickness in a coupled iceocean model
"... [1] Simulated CryoSat ice thickness measurements have been assimilated into a coupled iceocean model to examine the impact in Arctic ocean prediction systems. The model system is based on the HYbrid Coordinate Ocean Model (HYCOM) and the EVP ice rheology, and the data assimilation method is the Ens ..."
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[1] Simulated CryoSat ice thickness measurements have been assimilated into a coupled iceocean model to examine the impact in Arctic ocean prediction systems. The model system is based on the HYbrid Coordinate Ocean Model (HYCOM) and the EVP ice rheology, and the data assimilation method is the Ensemble Kalman Filter (EnKF). It is shown how ocean salinity, surface temperature, and ice concentration fields are affected by the ice thickness assimilation, and how these fields are improved relative to a freerun experiment of the model. The ice thickness assimilation primarily affects the surface properties of the ocean. By running two different assimilation experiments, it is shown how the choice of stochastic forcing is crucial to the performance of the assimilation. Specifically, it is shown how stochastic wind forcing is important to correctly describe model prediction errors, which are important for the data assimilation step. The assimilation experiments illustrate how the ice thickness observations can have a strong impact on the ice thickness estimates of the model system. The manner in which the EnKF forcing is set up is crucial, but with the correct setup, the assimilation of ice thickness measurements could have a beneficial effect on the modeled ice thickness and ocean fields. Citation: Lisæter, K. A., G. Evensen, and S. Laxon (2007), Assimilating synthetic CryoSat sea ice thickness in a coupled iceocean model, J. Geophys. Res., 112, C07023, doi:10.1029/2006JC003786. 1.
Data Assimilation for Atmospheric CO2: Towards Improved Estimates of CO2 Concentrations and Fluxes
, 2012
"... ii ACKNOWLEDGEMENTS The variations in data assimilation branch out so quickly that it is impossible to cover them all. On more than one occasion, I have succumbed to this tree of variations and consequently, ended up in a muddled and chaotic state of mind that would simply refuse to clear. Such mome ..."
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ii ACKNOWLEDGEMENTS The variations in data assimilation branch out so quickly that it is impossible to cover them all. On more than one occasion, I have succumbed to this tree of variations and consequently, ended up in a muddled and chaotic state of mind that would simply refuse to clear. Such moments are best summarized by Mikhail Tal’s statement“Oh, what a task so harsh / To drag a hippo from a marsh!”* I am indebted to my advisor Anna Michalak for repeatedly dragging my mind out of the marsh, and making the science clearer and simpler. It would have been hopeless, quite frankly impossible, to put together any semblance of this work without Anna’s guidance and insights into the science questions. Over the last six years, I have received an abundance of ideas, mathematical knowledge and insightful criticisms from her. Anna’s chief forte (among her many other strengths!) is her perseverance and passion in doing research. Ultimately, this has always been, and shall be a huge source of inspiration to me. I am thankful to her for introducing me to her science community, and also in helping me get started during the early stages of my graduate
INFORMATION SYNTHESIS ACROSS SCALES IN ATMOSPHERIC STATE ESTIMATION: THEORY AND NUMERICAL EXPERIMENTS
, 2015
"... This thesis studies the benefits of simultaneously considering system information from different sources when performing ensemble data assimilation. In particular, in Chapter 2 we consider ensemble data assimilation using both a global dynamical model and climatological forecast error information, ..."
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This thesis studies the benefits of simultaneously considering system information from different sources when performing ensemble data assimilation. In particular, in Chapter 2 we consider ensemble data assimilation using both a global dynamical model and climatological forecast error information, and, in Chapters 3 and 4, using both a global dynamical model and at least one higherresolution limitedarea dynamical model. Focus is given to applying data assimilation for atmospheric state estimation. Introductory material on ensemble forecasting is given in Chapter 1. In Chapter 2, I first investigate how the forecast backgrounderror climatology can be used to help improve state estimates, and subsequent forecasts initialized from those state estimates. “Climatological perturbations ” derived from an estimate of the backgrounderror covariance matrix are added to the dynamic ensemble that has been forecasted from the previous analysis time, enlarging the space of possible analysis increments. Numerical experiments on a onedimensional toy model test this method and illustrate that climatologically augmenting the dynamical forecast
Evaluation of Stochastic Kinetic Energy Backscatter  in the GME Ensemble Prediction System
, 2013
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SYNCHRONIZATION IN CHAOTIC SYSTEMS: COUPLING OF CHAOTIC MAPS, DATA ASSIMILATION, AND WEATHER FORECASTING
, 2007
"... The theme of this thesis is the synchronization of coupled chaotic systems. Background and introductory material are presented in Chapter 1. In Chapter 2, we study the transition to coherence of ensembles of globally coupled chaotic maps allowing for ensembles of nonidentical maps and for noise. Th ..."
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The theme of this thesis is the synchronization of coupled chaotic systems. Background and introductory material are presented in Chapter 1. In Chapter 2, we study the transition to coherence of ensembles of globally coupled chaotic maps allowing for ensembles of nonidentical maps and for noise. The transition coupling strength is determined from a transfer function of the perturbation evolution. Analytical results are presented and tested using numerical experiments. One of our examples suggests that the validity of the perturbation theory approach can be problematic for an ensemble of noiseless identical ‘nonhyperbolic’ maps, but can be restored by noise and/or parameter spread. The problem of estimating the state of a large evolving spatiotemporally chaotic system from noisy observations and a model of the system dynamics is studied in Chapters 3 – 5. This problem, refered to as ‘data assimilation’, can be thought of as a synchorization problem where one attempts to synchronize the model state to the system state by using incoming data to correct synchronization error. In Chapter 3, using a simple data assimilation technique, we show the possible