International Conference on Computational Science , ICCS 2012 Information Theoretic Metrics to Characterize Observations in Variational Data Assimilation

Abstract Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different observation locations is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. This paper proposes a new approach to characterizes the usefulness of different observation in four dimensional variational (4D-Var) data assimilation. Metrics from information theory are used to quantify the contribution of observations to decreasing uncertainty with which the system state is known. We derive ensemble based, computationally feasible procedures to estimate the information content of various observations.

[1]  Adrian Sandu,et al.  Discrete second order adjoints in atmospheric chemical transport modeling , 2008, J. Comput. Phys..

[2]  Adrian Sandu,et al.  A hybrid approach to estimating error covariances in variational data assimilation , 2010 .

[3]  M. Fisher.  Estimation of Entropy Reduction and Degrees of Freedom for Signal for Large Variational Analysis Systems , 2003 .

[4]  Adrian Sandu,et al.  Adjoint sensitivity analysis of regional air quality models , 2005 .

[5]  Emil M. Constantinescu,et al.  Ensemble‐based chemical data assimilation. II: Covariance localization , 2007, Quarterly Journal of the Royal Meteorological Society.

[6]  Emil M. Constantinescu,et al.  Assessment of ensemble-based chemical data assimilation in an idealized setting , 2007 .

[7]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[8]  Emil M. Constantinescu,et al.  Autoregressive models of background errors for chemical data assimilation , 2007 .

[9]  Qin Xu,et al.  Measuring information content from observations for data assimilation: relative entropy versus shannon entropy difference , 2007 .

[10]  Clive D. Rodgers,et al.  Information content and optimisation of high spectral resolution remote measurements , 1998 .

[11]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[12]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[13]  Y. Sasaki,et al.  An ObJective Analysis Based on the Variational Method , 1958 .

[14]  Andrew J. Majda,et al.  Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows , 2006 .

[15]  Emil M. Constantinescu,et al.  Predicting air quality: Improvements through advanced methods to integrate models and measurements , 2008, J. Comput. Phys..

[16]  Adrian Sandu,et al.  Computational Aspects of Chemical Data Assimilation into Atmospheric Models , 2003, International Conference on Computational Science.

[17]  I. Yu. Gejadze,et al.  On Analysis Error Covariances in Variational Data Assimilation , 2008, SIAM J. Sci. Comput..

[18]  Adrian Sandu,et al.  Four-dimensional data assimilation experiments with International Consortium for Atmospheric Research on Transport and Transformation ozone measurements , 2007 .

[19]  Clive D Rodgers,et al.  Inverse Methods for Atmospheric Sounding: Theory and Practice , 2000 .

[20]  Dusanka Zupanski,et al.  Information Measures in Ensemble Data Assimilation , 2009 .

[21]  Emil M. Constantinescu,et al.  Ensemble‐based chemical data assimilation. I: General approach , 2007 .

[22]  Clive D. Rodgers.  Information content and optimization of high-spectral-resolution measurements , 1996, Optics + Photonics.

[23]  John R. Worden,et al.  Characterization of Atmospheric Profile Retrievals From Limb Sounding Observations of an Inhomogeneous Atmosphere , 2003 .

[24]  Erik Andersson,et al.  Influence‐matrix diagnostic of a data assimilation system , 2004 .

[25]  Andrew J. Majda,et al.  Quantifying Uncertainty for Non-Gaussian Ensembles in Complex Systems , 2005, SIAM J. Sci. Comput..

[26]  William Carlisle Thacker,et al.  The role of the Hessian matrix in fitting models to measurements , 1989 .

[27]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[28]  Nancy Nichols,et al.  Correlated observation errors in data assimilation , 2008 .

[29]  Florence Rabier,et al.  Channel selection methods for Infrared Atmospheric Sounding Interferometer radiances , 2002 .

[30]  Adrian Sandu,et al.  Chemical data assimilation of Transport and Chemical Evolution over the Pacific (TRACE-P) aircraft measurements , 2006 .

[31]  G. Carmichael,et al.  Adjoint Implementation of Rosenbrock Methods Applied to Variational Data Assimilation Problems , 2000, Journal of Computational Physics.

[32]  P. Courtier,et al.  Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. Ii: Numerical Results , 2007 .