The degree of freedom for signal assessment of measurement networks for joint chemical state and emission analysis

Abstract. The Degree of Freedom for Signal (DFS) is generalized and applied to estimate the potential observability of observation networks for augmented model state and parameter estimations. The control of predictive geophysical model systems by measurements is dependent on a sufficient observational basis. Control parameters may include prognostic state variables, mostly the initial values, and insufficiently known model parameters, to which the simulation is sensitive. As for chemistry-transport models, emission rates are at least as important as initial values for model evolution control. Extending the optimisation parameter set must be met by observation networks, which allows for controlling the entire optimisation task. In this paper, we introduce a DFS based approach with respect to address both, emission rates and initial value observability. By applying a Kalman smoother, a quantitative assessment method on the efficiency of observation configurations is developed based on the singular value decomposition. For practical reasons an ensemble based version is derived for covariance modelling. The observability analysis tool can be generalized to additional model parameters.

[1]  Birgit Jacob,et al.  Optimal Control and Observation Locations for Time-Varying Systems on a Finite-Time Horizon , 2016, SIAM J. Control. Optim..

[2]  E. Kostelich,et al.  Kalman filter data assimilation: targeting observations and parameter estimation. , 2014, Chaos.

[3]  Zifeng Wang,et al.  Inversion of CO emissions over Beijing and its surrounding areas with ensemble Kalman filter , 2013 .

[4]  Marc Bocquet,et al.  Joint state and parameter estimation with an iterative ensemble Kalman smoother , 2013 .

[5]  Adrian Sandu,et al.  An optimization framework to improve 4D-Var data assimilation system performance , 2013, J. Comput. Phys..

[6]  Adrian Sandu,et al.  Low-rank approximations for computing observation impact in 4D-Var data assimilation , 2013, Comput. Math. Appl..

[7]  Henk Eskes,et al.  Simultaneous assimilation of satellite NO 2 , O 3 , CO, and HNO 3 data for the analysis of tropospheric chemical composition and emissions , 2012 .

[8]  Liang Xu,et al.  Optimal placement of mobile sensors for data assimilations , 2012 .

[9]  Marc Bocquet,et al.  Parameter‐field estimation for atmospheric dispersion: application to the Chernobyl accident using 4D‐Var , 2012 .

[10]  Xiao Tang,et al.  Improvement of ozone forecast over Beijing based on ensemble Kalman filter with simultaneous adjustment of initial conditions and emissions , 2011 .

[11]  Adrian Sandu,et al.  A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation , 2011, SIAM/ASA J. Uncertain. Quantification.

[12]  N. Goris,et al.  Singular vector decomposition for sensitivity analyses of tropospheric chemical scenarios , 2011 .

[13]  Marion Schroedter-Homscheidt,et al.  Understanding the aerosol information content in multi-spectral reflectance measurements using a synergetic retrieval algorithm , 2010 .

[14]  Takemasa Miyoshi,et al.  Analysis sensitivity calculation in an ensemble Kalman filter , 2009 .

[15]  Christopher M. Danforth,et al.  Accounting for Model Errors in Ensemble Data Assimilation , 2009 .

[16]  D. Daescu.  On the Sensitivity Equations of Four-Dimensional Variational (4D-Var) Data Assimilation , 2008 .

[17]  E. Kalnay,et al.  Estimating observation impact without adjoint model in an ensemble Kalman filter , 2008 .

[18]  Yoram J. Kaufman,et al.  Retrieving global aerosol sources from satellites using inverse modeling , 2008 .

[19]  Hendrik Elbern,et al.  Emission rate and chemical state estimation by 4-dimensional variational inversion , 2007 .

[20]  Roger Daley,et al.  Observation and background adjoint sensitivity in the adaptive observation‐targeting problem , 2007 .

[21]  Y. Trémolet.  Model‐error estimation in 4D‐Var , 2007 .

[22]  Dusanka Zupanski,et al.  Applications of information theory in ensemble data assimilation , 2007 .

[23]  B. De Moor,et al.  Model error estimation in ensemble data assimilation , 2007 .

[24]  Adrian Sandu,et al.  Singular Vector Analysis for Atmospheric Chemical Transport Models , 2006 .

[25]  Dusanka Zupanski,et al.  An ensemble data assimilation system to estimate CO2 surface fluxes from atmospheric trace gas observations , 2005 .

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

[27]  Dacian N. Daescu,et al.  Adaptive observations in the context of 4D-Var data assimilation , 2004 .

[28]  M. Leutbecher.  A Reduced Rank Estimate of Forecast Error Variance Changes due to Intermittent Modifications of the Observing Network. , 2003 .

[29]  Istvan Szunyogh,et al.  Propagation of the effect of targeted observations: The 2000 Winter Storm Reconnaissance program , 2002 .

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

[31]  O. Talagrand,et al.  4D-variational data assimilation with an adjoint air quality model for emission analysis , 2000, Environ. Model. Softw..

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

[33]  David S. Richardson,et al.  Current status and future developments of the ECMWF Ensemble Prediction System , 2000 .

[34]  Ronald Gelaro,et al.  Targeted observations in FASTEX: Adjoint‐based targeting procedures and data impact experiments in IOP17 and IOP18 , 1999 .

[35]  Chris Snyder,et al.  Ensemble‐based targeting experiments during FASTEX: The effect of dropsonde data from the lear jet , 1999 .

[36]  Roberto Buizza,et al.  Targeting Observations Using Singular Vectors , 1999 .

[37]  Hauke Schmidt,et al.  A four-dimensional variational chemistry data assimilation scheme for Eulerian chemistry transport modeling , 1999 .

[38]  John C. Gille,et al.  Assimilation of photochemically active species and a case analysis of UARS data , 1999 .

[39]  Chris Snyder,et al.  Statistical Design for Adaptive Weather Observations , 1999 .

[40]  Craig H. Bishop,et al.  Ensemble Transformation and Adaptive Observations , 1999 .

[41]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[42]  J. Barkmeijer,et al.  Singular vectors and estimates of the analysis‐error covariance metric , 1998 .

[43]  Roberto Buizza,et al.  The Singular-Vector Structure of the Atmospheric Global Circulation , 1995 .

[44]  R. Buizza.  Localization of optimal perturbations using a projection operator , 1994 .

[45]  D. Catlin.  Estimation, Control, and the Discrete Kalman Filter , 1988 .

[46]  F. Ham,et al.  Observability, Eigenvalues, and Kalman Filtering , 1983, IEEE Transactions on Aerospace and Electronic Systems.

[47]  M. Sain.  Finite dimensional linear systems , 1972 .

[48]  E. Lorenz.  A study of the predictability of a 28-variable atmospheric model , 1965 .

[49]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[50]  Marc Bocquet,et al.  Estimation of the caesium-137 source term from the Fukushima Daiichi nuclear power plant using a consistent joint assimilation of air concentration and deposition observations , 2014 .

[51]  Adrian Sandu,et al.  Dynamic Sensor Network Configuration in InfoSymbiotic Systems Using Model Singular Vectors , 2013, ICCS.

[52]  Sarah L. Dance,et al.  Data assimilation for state and parameter estimation: application to morphodynamic modelling , 2013 .

[53]  Adrian Sandu,et al.  International Conference on Computational Science , ICCS 2012 Information Theoretic Metrics to Characterize Observations in Variational Data Assimilation , 2013 .

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

[55]  Christine Johnson,et al.  Information Content of Observations in Variational Data Assimilation , 2003 .

[56]  Jean-Noël Thépaut,et al.  390 Validation of the NESDIS Near Real Time AIRS channel selection , 2002 .

[57]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[58]  Ionel M. Navon,et al.  Optimality of variational data assimilation and its relationship with the Kalman filter and smoother , 2001 .

[59]  Ionel Michael Navon,et al.  Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography , 1998 .

[60]  J. R. Eyre,et al.  The information content of data from satellite sounding systems: A simulation study , 1990 .