The Ensemble Kalman Filter:
|
|
- Tyler Baldwin
- 6 years ago
- Views:
Transcription
1 p.1 The Ensemble Kalman Filter: Theoretical formulation and practical implementation Geir Evensen Norsk Hydro Research Centre, Bergen, Norway Based on Evensen 23, Ocean Dynamics, Vol 53, No 4
2 p.2 The Ensemble Kalman Filter (EnKF) Represents error statistics using an ensemble of model states. Evolves error statistics by ensemble integrations. Variance minimizing analysis scheme operating on the ensemble. Monte Carlo, low rank, error subspace method. Converges to the Kalman Filter with increasing ensemble size. Fully nonlinear error evolution, contrary to EKF. Assumption of Gaussian statistics in analysis scheme.
3 p.3 The error covariance matrix Define ensemble covariances around the ensemble mean The ensemble mean is the bestguess. The ensemble spread defines the error variance. The covariance is determined by the smoothness of the ensemble members. A covariance matrix can be represented by an ensemble of model states (not unique).
4 p.4 Dynamical evolution of error statistics Each ensemble member evolve according to the model dynamics which is expressed by a stochastic differential equation d The probability density then evolve according to Kolmogorov s equation! This is the fundamental equation for evolution of error statistics and can be solved using Monte Carlo methods.
5 " # # # p.5 Analysis scheme (1) Given an ensemble of model forcasts, forecast error covariance, defining Create an ensemble of observations &% $# " " with, the real observations,, a vector of observation noise,. ' '
6 p.6 Analysis scheme (2) Update each ensemble member according to % " where + *) ' ( ( Thus the update of the mean becomes " The posterior error covariance becomes,
7 p.7 Example: Lorenz model Application with the chaotic Lorenz model Illustrates properties with higly nonlinear dynamical models. From Evensen (1997), MWR.
8 p.8 EnKF solution 2 EnKF: Estimate
9 p.9 EnKF error variance 3 EnKF: Error variance
10 p.1 EnKS solution 2 EnKS: Estimate
11 p.11 EnKS error variance 3 EnKS: Error variance
12 p.12 Summary: Lorenz model The EnKF and EnKS works well with highly nonlinear dynamical models. There is no linearization in the evolution of error statistics. Methods using tangent linear or adjoint operators have problems with the Lorenz equations: limited by the predictability time, limited by the validity time of tangent linear operator. Can we expect the same to be true for high resolution ocean and atmosphere models?
13 3 2 1 / % % 5 / / 3 1 / / p.13 Analysis equation (1) Define the ensemble matrix / +.% 67 ) The ensemble mean is (defining 4 / The ensemble perturbations become, becomes The ensemble covariance matrix 8 8
14 " 7 ; % % / " % < # % % 7 p.14 Analysis equation (2), define 19 Given a vector of measurements % :% $# " " stored in / 3 91 " % " +:% The ensemble perturbations are stored in / % 3 91 / # + % # thus, the measurement error covariance matrix becomes < < '
15 8 ) < < + p.15 Analysis equation (3) The analysis equation can now be written *) ' + Defining the innovations previous definitions: and using i.e., analysis expressed entirely in terms of the ensemble
16 Analysis equation (4) Define = 8 and > = = < <. Use 8, 4 /. Use 4 / = 5?. 8 = = = < < ) + 8, 4 / = >) + 8,, 4 / = >) + 8, = >) + 8 (1) p.16
17 = = p.17 Remarks on the analysis equation (1) Covariances only needed between observed variables at measurement locations ( ). 8 = never computed but indirectly used to determine. Analysis may be interpreted as: combination of forecast ensemble members, or, forecast pluss combination of covariance functions. Accuracy of analysis is determined by: the accuracy of, the properties of the ensemble error space.
18 p.18 Remarks on the analysis equation (2) For a linear model, any choice of will result in an analysis which is also a solution of the model. Filtering of covariance functions introduces nondynamical modes in the analysis.
19 p.19 Examples of ensemble statistics Taken from Haugen and Evensen (22), Ocean Dynamics. OGCM (MICOM) for the Indian Ocean. Assimilation of SST and SLA data.
20 Spatial correlations Latitude SSTDP(1) Latitude SSHDP(1) Longitude Longitude Latitude SSTSSH Latitude SSHUVEL Longitude Longitude p.2
21 Correlation functions SSH SSH SSH SST SSH DP SST SSH SST SST SST DP p.21
22 Correlation functions SSH SSH SSH SST SSH DP SST SSH SST SST SST DP p.22
23 Time Depth: Temperature 1 2 Depth 3 4 OBSERVED AND SIMULATED TEMPERATURE Days p.23
24 p.24 Ensemble Kalman Smoother (EnKS) Derived in Evensen and van Leeuwen (2), MWR. Starts with EnKF solution. Computes updates backward in time; sequentially for each measurement time, using covariances in time, no backward integrations. The analysis becomes for + ) C ML 8 KI E G 8 JI FEHG
25 + O V O S V O + p.25 Time correlated model noise Most schemes assume white model noise in time. Augment model state to include time correlations UTC ) + NC ) PRQ SNC C ) NC C White noise when and.
26 W Results ( ) Time p.26
27 W Results ( X) Time p.27
28 r r d r ^ r a p.28 Parameter and bias estimation in model Y C Introduces poorly known parameter d ]&c p:q b k gon d b\]&c `[`s Z[Z e `[` d ^ ]&c m\] l k ij e hij ^ ] e fg e _ ]&c Z[Z a `[` \] ^ ] _ ] Z[Z Two cases. ^ut. ^wv a poorly known parameter with 1. 2.
29 p.29 Estimate and model error, EnKF Time
30 p.3 Estimate and model error, EnKS Time
31 p.31 Estimate, model error and, EnKF Time
32 p.32 Estimate, model error and, EnKS Time
33 p.33 Estimated and std dev Time
34 p.34 Summary The EnKF and EnKS can handle time correlated model errors. The EnKF and EnKS can be used for parameter estimation by augmenting the model state with the unknown parameters.
35 p.35 Oil reservoar application The EnKF has been used to estimate permeability in a reservoar simulation model using production well data. The greatest uncertainty is the reservoar permeability and porosity. The well data consists of pressures and oil, gas and water production rates.
36 Estimated bias and std dev p.36
37 x y 7 p.37 Local analysis May be useful when is large or Analysis is computed grid point by grid point using only nearby measurements. Inverts many small matrices instead of one large. Different for each grid point, thus, allows us to reach a larger class of solutions. Suboptimal solution which introduces nondynamical modes..
38 z 8 + " 8 z ) < < 8 8 p.38 Nonlinear measurements Measurement equation # z Define ensemble of model prediction of the measurements / { % / % % The analysis then becomes { % { { { Analysis based on covariances between z and.
39 p.39 TOPAZ Operational ocean prediction system for the Atlantic and Arctic oceans. topaz.nersc.no Based on HYCOM State space is 26 5 unknowns. Ensemble size is 1. Assimilates SSH, SST, Ice concentration, and ARGO T&S profiles. Total of more than 1 measurements in each assimilation step. Uses local analysis as well as nonlinear measurements.
40 TOPAZ p.4
Ensemble Kalman Filter
Ensemble Kalman Filter Geir Evensen and Laurent Bertino Hydro Research Centre, Bergen, Norway, Nansen Environmental and Remote Sensing Center, Bergen, Norway The Ensemble Kalman Filter (EnKF) Represents
More informationThe Ensemble Kalman Filter:
p.1 The Ensemble Kalman Filter: Theoretical formulation and practical implementation Geir Evensen Norsk Hydro Research Centre, Bergen, Norway Based on Evensen, Ocean Dynamics, Vol 5, No p. The Ensemble
More information6 Sequential Data Assimilation for Nonlinear Dynamics: The Ensemble Kalman Filter
6 Sequential Data Assimilation for Nonlinear Dynamics: The Ensemble Kalman Filter GEIR EVENSEN Nansen Environmental and Remote Sensing Center, Bergen, Norway 6.1 Introduction Sequential data assimilation
More informationSmoothers: Types and Benchmarks
Smoothers: Types and Benchmarks Patrick N. Raanes Oxford University, NERSC 8th International EnKF Workshop May 27, 2013 Chris Farmer, Irene Moroz Laurent Bertino NERSC Geir Evensen Abstract Talk builds
More informationAnalysis Scheme in the Ensemble Kalman Filter
JUNE 1998 BURGERS ET AL. 1719 Analysis Scheme in the Ensemble Kalman Filter GERRIT BURGERS Royal Netherlands Meteorological Institute, De Bilt, the Netherlands PETER JAN VAN LEEUWEN Institute or Marine
More informationThe Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation
Noname manuscript No. (will be inserted by the editor) The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation Geir Evensen Nansen Environmental and Remote Sensing Center, Bergen
More informationThe Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation
The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation Geir Evensen Norsk Hydro, Oil and Energy Research Centre, Bergen PO Box 7190 - N 5020 Bergen, Norway Geir.Evensen@hydro.com
More informationNorwegian Climate Prediction Model (NorCPM) getting ready for CMIP6 DCPP
Norwegian Climate Prediction Model (NorCPM) getting ready for CMIP6 DCPP Francois Counillon, Noel Keenlyside, Mats Bentsen, Ingo Bethke, Laurent Bertino, Teferi Demissie, Tor Eldevik, Shunya Koseki, Camille
More informationAsynchronous data assimilation
Ensemble Kalman Filter, lecture 2 Asynchronous data assimilation Pavel Sakov Nansen Environmental and Remote Sensing Center, Norway This talk has been prepared in the course of evita-enkf project funded
More informationGaussian Filtering Strategies for Nonlinear Systems
Gaussian Filtering Strategies for Nonlinear Systems Canonical Nonlinear Filtering Problem ~u m+1 = ~ f (~u m )+~ m+1 ~v m+1 = ~g(~u m+1 )+~ o m+1 I ~ f and ~g are nonlinear & deterministic I Noise/Errors
More informationKalman Filter and Ensemble Kalman Filter
Kalman Filter and Ensemble Kalman Filter 1 Motivation Ensemble forecasting : Provides flow-dependent estimate of uncertainty of the forecast. Data assimilation : requires information about uncertainty
More informationA comparison of sequential data assimilation schemes for. Twin Experiments
A comparison of sequential data assimilation schemes for ocean prediction with HYCOM Twin Experiments A. Srinivasan, University of Miami, Miami, FL E. P. Chassignet, COAPS, Florida State University, Tallahassee,
More informationSPE History Matching Using the Ensemble Kalman Filter on a North Sea Field Case
SPE- 1243 History Matching Using the Ensemble Kalman Filter on a North Sea Field Case Vibeke Haugen, SPE, Statoil ASA, Lars-Jørgen Natvik, Statoil ASA, Geir Evensen, Hydro, Aina Berg, IRIS, Kristin Flornes,
More informationRelationship between Singular Vectors, Bred Vectors, 4D-Var and EnKF
Relationship between Singular Vectors, Bred Vectors, 4D-Var and EnKF Eugenia Kalnay and Shu-Chih Yang with Alberto Carrasi, Matteo Corazza and Takemasa Miyoshi 4th EnKF Workshop, April 2010 Relationship
More informationMethods of Data Assimilation and Comparisons for Lagrangian Data
Methods of Data Assimilation and Comparisons for Lagrangian Data Chris Jones, Warwick and UNC-CH Kayo Ide, UCLA Andrew Stuart, Jochen Voss, Warwick Guillaume Vernieres, UNC-CH Amarjit Budiraja, UNC-CH
More informationLagrangian Data Assimilation and Manifold Detection for a Point-Vortex Model. David Darmon, AMSC Kayo Ide, AOSC, IPST, CSCAMM, ESSIC
Lagrangian Data Assimilation and Manifold Detection for a Point-Vortex Model David Darmon, AMSC Kayo Ide, AOSC, IPST, CSCAMM, ESSIC Background Data Assimilation Iterative process Forecast Analysis Background
More informationA Note on the Particle Filter with Posterior Gaussian Resampling
Tellus (6), 8A, 46 46 Copyright C Blackwell Munksgaard, 6 Printed in Singapore. All rights reserved TELLUS A Note on the Particle Filter with Posterior Gaussian Resampling By X. XIONG 1,I.M.NAVON 1,2 and
More informationReservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter
SPE 84372 Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter Geir Nævdal, RF-Rogaland Research; Liv Merethe Johnsen, SPE, Norsk Hydro; Sigurd Ivar Aanonsen, SPE, Norsk Hydro;
More informationAspects of the practical application of ensemble-based Kalman filters
Aspects of the practical application of ensemble-based Kalman filters Lars Nerger Alfred Wegener Institute for Polar and Marine Research Bremerhaven, Germany and Bremen Supercomputing Competence Center
More informationEnsemble square-root filters
Ensemble square-root filters MICHAEL K. TIPPETT International Research Institute for climate prediction, Palisades, New Yor JEFFREY L. ANDERSON GFDL, Princeton, New Jersy CRAIG H. BISHOP Naval Research
More informationRelative Merits of 4D-Var and Ensemble Kalman Filter
Relative Merits of 4D-Var and Ensemble Kalman Filter Andrew Lorenc Met Office, Exeter International summer school on Atmospheric and Oceanic Sciences (ISSAOS) "Atmospheric Data Assimilation". August 29
More informationAutonomous Navigation for Flying Robots
Computer Vision Group Prof. Daniel Cremers Autonomous Navigation for Flying Robots Lecture 6.2: Kalman Filter Jürgen Sturm Technische Universität München Motivation Bayes filter is a useful tool for state
More informationRelationship between Singular Vectors, Bred Vectors, 4D-Var and EnKF
Relationship between Singular Vectors, Bred Vectors, 4D-Var and EnKF Eugenia Kalnay and Shu-Chih Yang with Alberto Carrasi, Matteo Corazza and Takemasa Miyoshi ECODYC10, Dresden 28 January 2010 Relationship
More informationState and Parameter Estimation in Stochastic Dynamical Models
State and Parameter Estimation in Stochastic Dynamical Models Timothy DelSole George Mason University, Fairfax, Va and Center for Ocean-Land-Atmosphere Studies, Calverton, MD June 21, 2011 1 1 collaboration
More informationAdaptive ensemble Kalman filtering of nonlinear systems
Adaptive ensemble Kalman filtering of nonlinear systems Tyrus Berry George Mason University June 12, 213 : Problem Setup We consider a system of the form: x k+1 = f (x k ) + ω k+1 ω N (, Q) y k+1 = h(x
More information4. DATA ASSIMILATION FUNDAMENTALS
4. DATA ASSIMILATION FUNDAMENTALS... [the atmosphere] "is a chaotic system in which errors introduced into the system can grow with time... As a consequence, data assimilation is a struggle between chaotic
More informationGaussian Process Approximations of Stochastic Differential Equations
Gaussian Process Approximations of Stochastic Differential Equations Cédric Archambeau Dan Cawford Manfred Opper John Shawe-Taylor May, 2006 1 Introduction Some of the most complex models routinely run
More informationData assimilation in high dimensions
Data assimilation in high dimensions David Kelly Courant Institute New York University New York NY www.dtbkelly.com February 12, 2015 Graduate seminar, CIMS David Kelly (CIMS) Data assimilation February
More informationConvective-scale data assimilation in the Weather Research and Forecasting model using a nonlinear ensemble filter
Convective-scale data assimilation in the Weather Research and Forecasting model using a nonlinear ensemble filter Jon Poterjoy, Ryan Sobash, and Jeffrey Anderson National Center for Atmospheric Research
More informationLagrangian Data Assimilation and Its Application to Geophysical Fluid Flows
Lagrangian Data Assimilation and Its Application to Geophysical Fluid Flows Laura Slivinski June, 3 Laura Slivinski (Brown University) Lagrangian Data Assimilation June, 3 / 3 Data Assimilation Setup:
More informationLocal Ensemble Transform Kalman Filter: An Efficient Scheme for Assimilating Atmospheric Data
Local Ensemble Transform Kalman Filter: An Efficient Scheme for Assimilating Atmospheric Data John Harlim and Brian R. Hunt Department of Mathematics and Institute for Physical Science and Technology University
More informationForecasting and data assimilation
Supported by the National Science Foundation DMS Forecasting and data assimilation Outline Numerical models Kalman Filter Ensembles Douglas Nychka, Thomas Bengtsson, Chris Snyder Geophysical Statistics
More informationData Assimilation with the Ensemble Kalman Filter and the SEIK Filter applied to a Finite Element Model of the North Atlantic
Data Assimilation with the Ensemble Kalman Filter and the SEIK Filter applied to a Finite Element Model of the North Atlantic L. Nerger S. Danilov, G. Kivman, W. Hiller, and J. Schröter Alfred Wegener
More informationThe Ensemble Kalman Filter: theoretical formulation and practical implementation
Ocean Dynamics (2003) 53: 343 367 DOI 10.1007/s10236-003-0036-9 Geir Evensen The Ensemble Kalman Filter: theoretical formulation and practical implementation Received: 16 December 2002 / Accepted: 7 May
More informationThe ECMWF Hybrid 4D-Var and Ensemble of Data Assimilations
The Hybrid 4D-Var and Ensemble of Data Assimilations Lars Isaksen, Massimo Bonavita and Elias Holm Data Assimilation Section lars.isaksen@ecmwf.int Acknowledgements to: Mike Fisher and Marta Janiskova
More informationThe Canadian approach to ensemble prediction
The Canadian approach to ensemble prediction ECMWF 2017 Annual seminar: Ensemble prediction : past, present and future. Pieter Houtekamer Montreal, Canada Overview. The Canadian approach. What are the
More informationComparison of of Assimilation Schemes for HYCOM
Comparison of of Assimilation Schemes for HYCOM Ashwanth Srinivasan, C. Thacker, Z. Garraffo, E. P. Chassignet, O. M. Smedstad, J. Cummings, F. Counillon, L. Bertino, T. M. Chin, P. Brasseur and C. Lozano
More informationHandling nonlinearity in Ensemble Kalman Filter: Experiments with the three-variable Lorenz model
Handling nonlinearity in Ensemble Kalman Filter: Experiments with the three-variable Lorenz model Shu-Chih Yang 1*, Eugenia Kalnay, and Brian Hunt 1. Department of Atmospheric Sciences, National Central
More informationAn Efficient Ensemble Data Assimilation Approach To Deal With Range Limited Observation
An Efficient Ensemble Data Assimilation Approach To Deal With Range Limited Observation A. Shah 1,2, M. E. Gharamti 1, L. Bertino 1 1 Nansen Environmental and Remote Sensing Center 2 University of Bergen
More informationData assimilation in the geosciences An overview
Data assimilation in the geosciences An overview Alberto Carrassi 1, Olivier Talagrand 2, Marc Bocquet 3 (1) NERSC, Bergen, Norway (2) LMD, École Normale Supérieure, IPSL, France (3) CEREA, joint lab École
More informationFour-Dimensional Ensemble Kalman Filtering
Four-Dimensional Ensemble Kalman Filtering B.R. Hunt, E. Kalnay, E.J. Kostelich, E. Ott, D.J. Patil, T. Sauer, I. Szunyogh, J.A. Yorke, A.V. Zimin University of Maryland, College Park, MD 20742, USA Ensemble
More informationOOPC-GODAE workshop on OSE/OSSEs Paris, IOCUNESCO, November 5-7, 2007
OOPC-GODAE workshop on OSE/OSSEs Paris, IOCUNESCO, November 5-7, 2007 Design of ocean observing systems: strengths and weaknesses of approaches based on assimilative systems Pierre Brasseur CNRS / LEGI
More informationAn Ensemble Kalman Smoother for Nonlinear Dynamics
1852 MONTHLY WEATHER REVIEW VOLUME 128 An Ensemble Kalman Smoother or Nonlinear Dynamics GEIR EVENSEN Nansen Environmental and Remote Sensing Center, Bergen, Norway PETER JAN VAN LEEUWEN Institute or Marine
More informationFour-dimensional ensemble Kalman filtering
Tellus (24), 56A, 273 277 Copyright C Blackwell Munksgaard, 24 Printed in UK. All rights reserved TELLUS Four-dimensional ensemble Kalman filtering By B. R. HUNT 1, E. KALNAY 1, E. J. KOSTELICH 2,E.OTT
More informationOrganization. I MCMC discussion. I project talks. I Lecture.
Organization I MCMC discussion I project talks. I Lecture. Content I Uncertainty Propagation Overview I Forward-Backward with an Ensemble I Model Reduction (Intro) Uncertainty Propagation in Causal Systems
More informationGeir Evensen Data Assimilation
Geir Evensen Data Assimilation Geir Evensen Data Assimilation The Ensemble Kalman Filter With 63 Figures PROF.GEIR EVENSEN Hydro Research Centre, Bergen PO Box 7190 N 5020 Bergen Norway and Mohn-Sverdrup
More informationA Stochastic Collocation based. for Data Assimilation
A Stochastic Collocation based Kalman Filter (SCKF) for Data Assimilation Lingzao Zeng and Dongxiao Zhang University of Southern California August 11, 2009 Los Angeles Outline Introduction SCKF Algorithm
More informationRobust Ensemble Filtering With Improved Storm Surge Forecasting
Robust Ensemble Filtering With Improved Storm Surge Forecasting U. Altaf, T. Buttler, X. Luo, C. Dawson, T. Mao, I.Hoteit Meteo France, Toulouse, Nov 13, 2012 Project Ensemble data assimilation for storm
More informationStability of Ensemble Kalman Filters
Stability of Ensemble Kalman Filters Idrissa S. Amour, Zubeda Mussa, Alexander Bibov, Antti Solonen, John Bardsley, Heikki Haario and Tuomo Kauranne Lappeenranta University of Technology University of
More informationDemonstration and Comparison of of Sequential Approaches for Altimeter Data Assimilation in in HYCOM
Demonstration and Comparison of of Sequential Approaches for Altimeter Data Assimilation in in HYCOM A. Srinivasan, E. P. Chassignet, O. M. Smedstad, C. Thacker, L. Bertino, P. Brasseur, T. M. Chin,, F.
More informationAdaptive Observation Strategies for Forecast Error Minimization
Adaptive Observation Strategies for Forecast Error Minimization Nicholas Roy 1, Han-Lim Choi 2, Daniel Gombos 3, James Hansen 4, Jonathan How 2, and Sooho Park 1 1 Computer Science and Artificial Intelligence
More informationLocalization and Correlation in Ensemble Kalman Filters
Localization and Correlation in Ensemble Kalman Filters Jeff Anderson NCAR Data Assimilation Research Section The National Center for Atmospheric Research is sponsored by the National Science Foundation.
More informationA demonstration of ensemble-based assimilation methods with a layered OGCM from the perspective of operational ocean forecasting systems
Journal of Marine Systems 40 41 (2003) 253 289 www.elsevier.com/locate/jmarsys A demonstration of ensemble-based assimilation methods with a layered OGCM from the perspective of operational ocean forecasting
More informationErgodicity in data assimilation methods
Ergodicity in data assimilation methods David Kelly Andy Majda Xin Tong Courant Institute New York University New York NY www.dtbkelly.com April 15, 2016 ETH Zurich David Kelly (CIMS) Data assimilation
More informationData assimilation in high dimensions
Data assimilation in high dimensions David Kelly Kody Law Andy Majda Andrew Stuart Xin Tong Courant Institute New York University New York NY www.dtbkelly.com February 3, 2016 DPMMS, University of Cambridge
More informationShort tutorial on data assimilation
Mitglied der Helmholtz-Gemeinschaft Short tutorial on data assimilation 23 June 2015 Wolfgang Kurtz & Harrie-Jan Hendricks Franssen Institute of Bio- and Geosciences IBG-3 (Agrosphere), Forschungszentrum
More informationAbstract 2. ENSEMBLE KALMAN FILTERS 1. INTRODUCTION
J5.4 4D ENSEMBLE KALMAN FILTERING FOR ASSIMILATION OF ASYNCHRONOUS OBSERVATIONS T. Sauer George Mason University, Fairfax, VA 22030 B.R. Hunt, J.A. Yorke, A.V. Zimin, E. Ott, E.J. Kostelich, I. Szunyogh,
More informationPreliminary Test of Glider Data Assimilation Along the Labrador Sea Shelf Break
Preliminary Test of Glider Data Assimilation Along the Labrador Sea Shelf Break Third Annual VITALS Science Meeting October 19, 2015 Changheng Chen, K. Andrea Scott Department of Systems Design Engineering
More informationEnvironment Canada s Regional Ensemble Kalman Filter
Environment Canada s Regional Ensemble Kalman Filter May 19, 2014 Seung-Jong Baek, Luc Fillion, Kao-Shen Chung, and Peter Houtekamer Meteorological Research Division, Environment Canada, Dorval, Quebec
More informationRevision of TR-09-25: A Hybrid Variational/Ensemble Filter Approach to Data Assimilation
Revision of TR-9-25: A Hybrid Variational/Ensemble ilter Approach to Data Assimilation Adrian Sandu 1 and Haiyan Cheng 1 Computational Science Laboratory Department of Computer Science Virginia Polytechnic
More informationAn Iterative EnKF for Strongly Nonlinear Systems
1988 M O N T H L Y W E A T H E R R E V I E W VOLUME 140 An Iterative EnKF for Strongly Nonlinear Systems PAVEL SAKOV Nansen Environmental and Remote Sensing Center, Bergen, Norway DEAN S. OLIVER Uni Centre
More informationStochastic Collocation Methods for Polynomial Chaos: Analysis and Applications
Stochastic Collocation Methods for Polynomial Chaos: Analysis and Applications Dongbin Xiu Department of Mathematics, Purdue University Support: AFOSR FA955-8-1-353 (Computational Math) SF CAREER DMS-64535
More informationGeir Evensen Data Assimilation
Geir Evensen Data Assimilation Geir Evensen Data Assimilation The Ensemble Kalman Filter With 63 Figures PROF.GEIR EVENSEN Hydro Research Centre, Bergen PO Box 7190 N 5020 Bergen Norway and Mohn-Sverdrup
More informationEnsembles and Particle Filters for Ocean Data Assimilation
DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Ensembles and Particle Filters for Ocean Data Assimilation Robert N. Miller College of Oceanic and Atmospheric Sciences
More informationNonlinear and/or Non-normal Filtering. Jesús Fernández-Villaverde University of Pennsylvania
Nonlinear and/or Non-normal Filtering Jesús Fernández-Villaverde University of Pennsylvania 1 Motivation Nonlinear and/or non-gaussian filtering, smoothing, and forecasting (NLGF) problems are pervasive
More informationLocal Ensemble Transform Kalman Filter
Local Ensemble Transform Kalman Filter Brian Hunt 11 June 2013 Review of Notation Forecast model: a known function M on a vector space of model states. Truth: an unknown sequence {x n } of model states
More informationEnsemble Data Assimilation and Uncertainty Quantification
Ensemble Data Assimilation and Uncertainty Quantification Jeff Anderson National Center for Atmospheric Research pg 1 What is Data Assimilation? Observations combined with a Model forecast + to produce
More informationA Dressed Ensemble Kalman Filter Using the Hybrid Coordinate Ocean Model in the Pacific
ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 26, NO. 5, 2009, 1042 1052 A Dressed Ensemble Kalman Filter Using the Hybrid Coordinate Ocean Model in the Pacific WAN Liying 1 (!"#), ZHU Jiang 2 ($%), WANG Hui
More informationAssimilating Altimetry Data into a HYCOM Model of the Pacific: Ensemble Optimal Interpolation versus Ensemble Kalman Filter
APRIL 2010 W A N E T A L. 753 Assimilating Altimetry Data into a HYCOM Model of the Pacific: Ensemble Optimal Interpolation versus Ensemble Kalman Filter LIYING WAN National Marine Environmental Forecasting
More informationAdaptive ensemble Kalman filtering of nonlinear systems. Tyrus Berry and Timothy Sauer George Mason University, Fairfax, VA 22030
Generated using V3.2 of the official AMS LATEX template journal page layout FOR AUTHOR USE ONLY, NOT FOR SUBMISSION! Adaptive ensemble Kalman filtering of nonlinear systems Tyrus Berry and Timothy Sauer
More informationFundamentals of Data Assimilation
National Center for Atmospheric Research, Boulder, CO USA GSI Data Assimilation Tutorial - June 28-30, 2010 Acknowledgments and References WRFDA Overview (WRF Tutorial Lectures, H. Huang and D. Barker)
More informationData assimilation with and without a model
Data assimilation with and without a model Tim Sauer George Mason University Parameter estimation and UQ U. Pittsburgh Mar. 5, 2017 Partially supported by NSF Most of this work is due to: Tyrus Berry,
More informationData Assimilation: Finding the Initial Conditions in Large Dynamical Systems. Eric Kostelich Data Mining Seminar, Feb. 6, 2006
Data Assimilation: Finding the Initial Conditions in Large Dynamical Systems Eric Kostelich Data Mining Seminar, Feb. 6, 2006 kostelich@asu.edu Co-Workers Istvan Szunyogh, Gyorgyi Gyarmati, Ed Ott, Brian
More informationOn the convergence of (ensemble) Kalman filters and smoothers onto the unstable subspace
On the convergence of (ensemble) Kalman filters and smoothers onto the unstable subspace Marc Bocquet CEREA, joint lab École des Ponts ParisTech and EdF R&D, Université Paris-Est, France Institut Pierre-Simon
More informationPar$cle Filters Part I: Theory. Peter Jan van Leeuwen Data- Assimila$on Research Centre DARC University of Reading
Par$cle Filters Part I: Theory Peter Jan van Leeuwen Data- Assimila$on Research Centre DARC University of Reading Reading July 2013 Why Data Assimila$on Predic$on Model improvement: - Parameter es$ma$on
More informationEnsemble Kalman Filtering for State and Parameter Estimation on a Reservoir Model
Ensemble Kalman Filtering for State and Parameter Estimation on a Reservoir Model John Petter Jensen Master of Science in Engineering Cybernetics Submission date: June 27 Supervisor: Bjarne Anton Foss,
More informationEnsemble variational assimilation as a probabilistic estimator Part 1: The linear and weak non-linear case
Nonlin. Processes Geophys., 25, 565 587, 28 https://doi.org/.594/npg-25-565-28 Author(s) 28. This work is distributed under the Creative Commons Attribution 4. License. Ensemble variational assimilation
More informationSequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 99, NO. C, PAGES,143,162, MAY, 1994 Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics Geir
More informationEnsemble Kalman filters, Sequential Importance Resampling and beyond
Ensemble Kalman filters, Sequential Importance Resampling and beyond Peter Jan van Leeuwen Institute for Marine and Atmospheric research Utrecht (IMAU) Utrecht University, P.O.Box 80005, 3508 TA Utrecht,
More informationarxiv: v1 [physics.ao-ph] 23 Jan 2009
A Brief Tutorial on the Ensemble Kalman Filter Jan Mandel arxiv:0901.3725v1 [physics.ao-ph] 23 Jan 2009 February 2007, updated January 2009 Abstract The ensemble Kalman filter EnKF) is a recursive filter
More informationR. E. Petrie and R. N. Bannister. Department of Meteorology, Earley Gate, University of Reading, Reading, RG6 6BB, United Kingdom
A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation R. E. Petrie and R. N. Bannister Department
More informationBayes Filter Reminder. Kalman Filter Localization. Properties of Gaussians. Gaussians. Prediction. Correction. σ 2. Univariate. 1 2πσ e.
Kalman Filter Localization Bayes Filter Reminder Prediction Correction Gaussians p(x) ~ N(µ,σ 2 ) : Properties of Gaussians Univariate p(x) = 1 1 2πσ e 2 (x µ) 2 σ 2 µ Univariate -σ σ Multivariate µ Multivariate
More informationGaussian anamorphosis extension of the DEnKF for combined state and parameter estimation: application to a 1D ocean ecosystem model.
Gaussian anamorphosis extension of the DEnKF for combined state and parameter estimation: application to a D ocean ecosystem model. Ehouarn Simon a,, Laurent Bertino a a Nansen Environmental and Remote
More informationDART_LAB Tutorial Section 2: How should observations impact an unobserved state variable? Multivariate assimilation.
DART_LAB Tutorial Section 2: How should observations impact an unobserved state variable? Multivariate assimilation. UCAR 2014 The National Center for Atmospheric Research is sponsored by the National
More informationEnKF Review. P.L. Houtekamer 7th EnKF workshop Introduction to the EnKF. Challenges. The ultimate global EnKF algorithm
Overview 1 2 3 Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation 6th EnKF Purpose EnKF equations localization After the 6th EnKF (2014), I decided with Prof. Zhang to summarize progress
More informationApplication of the Ensemble Kalman Filter to History Matching
Application of the Ensemble Kalman Filter to History Matching Presented at Texas A&M, November 16,2010 Outline Philosophy EnKF for Data Assimilation Field History Match Using EnKF with Covariance Localization
More informationA Comparison of Error Subspace Kalman Filters
Tellus 000, 000 000 (0000) Printed 4 February 2005 (Tellus LATEX style file v2.2) A Comparison of Error Subspace Kalman Filters By LARS NERGER, WOLFGANG HILLER and JENS SCHRÖTER Alfred Wegener Institute
More informationEstimation of positive sum-to-one constrained parameters with ensemble-based Kalman filters: application to an ocean ecosystem model
Estimation of positive sum-to-one constrained parameters with ensemble-based Kalman filters: application to an ocean ecosystem model Ehouarn Simon 1, Annette Samuelsen 1, Laurent Bertino 1 Dany Dumont
More informationA data-driven method for improving the correlation estimation in serial ensemble Kalman filter
A data-driven method for improving the correlation estimation in serial ensemble Kalman filter Michèle De La Chevrotière, 1 John Harlim 2 1 Department of Mathematics, Penn State University, 2 Department
More informationFundamentals of Data Assimila1on
014 GSI Community Tutorial NCAR Foothills Campus, Boulder, CO July 14-16, 014 Fundamentals of Data Assimila1on Milija Zupanski Cooperative Institute for Research in the Atmosphere Colorado State University
More informationBayesian Statistics and Data Assimilation. Jonathan Stroud. Department of Statistics The George Washington University
Bayesian Statistics and Data Assimilation Jonathan Stroud Department of Statistics The George Washington University 1 Outline Motivation Bayesian Statistics Parameter Estimation in Data Assimilation Combined
More informationSome Applications of WRF/DART
Some Applications of WRF/DART Chris Snyder, National Center for Atmospheric Research Mesoscale and Microscale Meteorology Division (MMM), and Institue for Mathematics Applied to Geoscience (IMAGe) WRF/DART
More informationA data assimilation approach for reconstructing sea ice volume in the Southern Hemisphere
Harmony on Ice 2 meeting Paris, 28-29 Nov. 2011 A data assimilation approach for reconstructing sea ice volume in the Southern Hemisphere F. Massonnet, P. Mathiot, T. Fichefet, H. Goosse, C. König Beatty,
More informationEnhancing information transfer from observations to unobserved state variables for mesoscale radar data assimilation
Enhancing information transfer from observations to unobserved state variables for mesoscale radar data assimilation Weiguang Chang and Isztar Zawadzki Department of Atmospheric and Oceanic Sciences Faculty
More informationRepresentation of inhomogeneous, non-separable covariances by sparse wavelet-transformed matrices
Representation of inhomogeneous, non-separable covariances by sparse wavelet-transformed matrices Andreas Rhodin, Harald Anlauf German Weather Service (DWD) Workshop on Flow-dependent aspects of data assimilation,
More informationZentrum für Technomathematik
Zentrum für Technomathematik Fachbereich 3 Mathematik und Informatik On the influence of model nonlinearity and localization on ensemble Kalman smoothing Lars Nerger Svenja Schulte Angelika Bunse-Gerstner
More informationBayesian Inverse problem, Data assimilation and Localization
Bayesian Inverse problem, Data assimilation and Localization Xin T Tong National University of Singapore ICIP, Singapore 2018 X.Tong Localization 1 / 37 Content What is Bayesian inverse problem? What is
More informationAssimilation des Observations et Traitement des Incertitudes en Météorologie
Assimilation des Observations et Traitement des Incertitudes en Météorologie Olivier Talagrand Laboratoire de Météorologie Dynamique, Paris 4èmes Rencontres Météo/MathAppli Météo-France, Toulouse, 25 Mars
More informationGaussian Process Approximations of Stochastic Differential Equations
Gaussian Process Approximations of Stochastic Differential Equations Cédric Archambeau Centre for Computational Statistics and Machine Learning University College London c.archambeau@cs.ucl.ac.uk CSML
More informationMaximum Likelihood Ensemble Filter Applied to Multisensor Systems
Maximum Likelihood Ensemble Filter Applied to Multisensor Systems Arif R. Albayrak a, Milija Zupanski b and Dusanka Zupanski c abc Colorado State University (CIRA), 137 Campus Delivery Fort Collins, CO
More information