Application of a dual unscented Kalman filter for simultaneous state and parameter estimation in problems of surface‐atmosphere exchange

A dual unscented Kalman filter (UKF) was used to assimilate net CO2 exchange (NEE) data measured over a spruce-hemlock forest at the Howland AmeriFlux site in Maine, USA, into a simple physiological model for the purpose of filling gaps in an eddy flux time series. In addition to filling gaps in the measurement record, the UKF approach provides continuous estimates of model parameters and uncertainty.

[1]  N. F. Toda,et al.  Divergence in the Kalman Filter , 1967 .

[2]  D. Fraser,et al.  The optimum linear smoother as a combination of two optimum linear filters , 1969 .

[3]  Andrew H. Jazwinski,et al.  Adaptive filtering , 1969, Autom..

[4]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[5]  A.H. Haddad,et al.  Applied optimal estimation , 1976, Proceedings of the IEEE.

[6]  R. Shumway,et al.  AN APPROACH TO TIME SERIES SMOOTHING AND FORECASTING USING THE EM ALGORITHM , 1982 .

[7]  Richard M. Stanley.  Optimal Estimation With an Introduction to Stochastic Control , 1988 .

[8]  James D. Hamilton.  9 Estimation, inference and forecasting of time series subject to changes in regime , 1993 .

[9]  F. W. Cathey,et al.  The iterated Kalman filter update as a Gauss-Newton method , 1993, IEEE Trans. Autom. Control..

[10]  J. Lloyd,et al.  On the temperature dependence of soil respiration , 1994 .

[11]  D. Hollinger,et al.  External and internal factors regulating photosynthesis , 1995 .

[12]  J. William Munger,et al.  Exchange of Carbon Dioxide by a Deciduous Forest: Response to Interannual Climate Variability , 1996, Science.

[13]  J. William Munger,et al.  Measurements of carbon sequestration by long‐term eddy covariance: methods and a critical evaluation of accuracy , 1996 .

[14]  Jeffrey K. Uhlmann,et al.  A consistent, debiased method for converting between polar and Cartesian coordinate systems , 1997 .

[15]  Keith Beven,et al.  On the sensitivity of soil-vegetation-atmosphere transfer (SVAT) schemes: equifinality and the problem of robust calibration , 1997 .

[16]  P. Reich,et al.  Photosynthesis and respiration rates depend on leaf and root morphology and nitrogen concentration in nine boreal tree species differing in relative growth rate , 1998 .

[17]  Willem Bouten,et al.  Water and carbon fluxes above European coniferous forests modelled with artificial neural networks , 1999 .

[18]  James F. Reynolds,et al.  VALIDITY OF EXTRAPOLATING FIELD CO2 EXPERIMENTS TO PREDICT CARBON SEQUESTRATION IN NATURAL ECOSYSTEMS , 1999 .

[19]  Genshiro Kitagawa.  Processing of Missing Observations and Outliers in Time Series , 1999 .

[20]  E. Davidson,et al.  Seasonal patterns and environmental control of carbon dioxide and water vapour exchange in an ecotonal boreal forest , 1999 .

[21]  P. Young,et al.  Stochastic, Dynamic Modelling and Signal Processing: Time Variable and State Dependent Parameter Estimation , 2000 .

[22]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .

[23]  Eric A. Wan,et al.  Nonlinear estimation and modeling of noisy time series by dual kalman filtering methods , 2000 .

[24]  Kazufumi Ito,et al.  Gaussian filters for nonlinear filtering problems , 2000, IEEE Trans. Autom. Control..

[25]  Niels Kjølstad Poulsen,et al.  New developments in state estimation for nonlinear systems , 2000, Autom..

[26]  Ü. Rannik,et al.  Gap filling strategies for defensible annual sums of net ecosystem exchange , 2001 .

[27]  Keith Beven,et al.  The Predictive Uncertainty of Land Surface Fluxes in Response to Increasing Ambient Carbon Dioxide , 2001 .

[28]  Andrew E. Suyker,et al.  Gap filling strategies for long term energy flux data sets , 2001 .

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

[30]  N. Buchmann,et al.  Large-scale forest girdling shows that current photosynthesis drives soil respiration , 2001, Nature.

[31]  Thomas S. Huang,et al.  Parametric contour tracking using unscented Kalman filter , 2002, Proceedings. International Conference on Image Processing.

[32]  Simon J. Julier,et al.  The scaled unscented transformation , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[33]  J Kurths,et al.  Estimation of parameters and unobserved components for nonlinear systems from noisy time series. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  W. Massman,et al.  Eddy covariance flux corrections and uncertainties in long-term studies of carbon and energy exchanges , 2002 .

[35]  Rudolph van der Merwe,et al.  The Unscented Kalman Filter , 2002 .

[36]  Eric A. Wan,et al.  Dual Extended Kalman Filter Methods , 2002 .

[37]  Andrew Harvey,et al.  Forecasting, structural time series models and the Kalman filter: Selected answers to exercises , 1990 .

[38]  W. Bouten,et al.  Simulating Daily and Half-Hourly Fluxes of Forest Carbon Dioxide and Water Vapor Exchange with a Simple Model of Light and Water Use , 2002, Ecosystems.

[39]  T. A. Black,et al.  Ecophysiological controls on the carbon balances of three southern boreal forests , 2003 .

[40]  T. Singh,et al.  The higher order unscented filter , 2003, Proceedings of the 2003 American Control Conference, 2003..

[41]  Kuo-Chu Chang,et al.  Comparison of nonlinear estimation for ballistic missile tracking , 2003, SPIE Defense + Commercial Sensing.

[42]  F. Markley,et al.  Unscented Filtering for Spacecraft Attitude Estimation , 2003 .

[43]  D. Baldocchi.  Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future , 2003 .

[44]  T. Griffisa,et al.  Ecophysiological controls on the carbon balances of three southern boreal forests , 2003 .

[45]  J. Tenhunen,et al.  Inverse modeling of seasonal drought effects on canopy CO2/H2O exchange in three Mediterranean ecosystems , 2003 .

[46]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[47]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[48]  Kuo-Chu Chang,et al.  Nonlinear estimation comparison for ballistic missile tracking , 2004 .

[49]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[50]  Peter C. Young,et al.  The seasonal temperature dependency of photosynthesis and respiration in two deciduous forests , 2004 .

[51]  T. Vesala,et al.  Simulation and scaling of temporal variation in gross primary production for coniferous and deciduous temperate forests , 2004 .

[52]  M. C. VanDyke,et al.  UNSCENTED KALMAN FILTERING FOR SPACECRAFT ATTITUDE STATE AND PARAMETER ESTIMATION , 2004 .

[53]  Rudolph van der Merwe,et al.  Sigma-Point Kalman Filters for Integrated Navigation , 2004 .

[54]  E. Davidson,et al.  Spatial and temporal variability in forest–atmosphere CO2 exchange , 2004 .

[55]  M. R. R A U Pa C H,et al.  Model – data synthesis in terrestrial carbon observation : methods , data requirements and data uncertainty specifications , 2005 .

[56]  D. Hollinger,et al.  Uncertainty in eddy covariance measurements and its application to physiological models. , 2005, Tree physiology.

[57]  B. Law,et al.  An improved analysis of forest carbon dynamics using data assimilation , 2005 .

[58]  D. Hollinger,et al.  Statistical modeling of ecosystem respiration using eddy covariance data: Maximum likelihood parameter estimation, and Monte Carlo simulation of model and parameter uncertainty, applied to three simple models , 2005 .

[59]  K. Davis,et al.  A multi-site analysis of random error in tower-based measurements of carbon and energy fluxes , 2006 .

[60]  J. Gove,et al.  Monitoring the growth of American beech affected by beech bark disease in Maine using the Kalman filter , 1996, Environmental and Ecological Statistics.

[61]  K. E. S AVAGE,et al.  A distinct seasonal pattern of the ratio of soil respiration to total ecosystem respiration in a spruce-dominated forest , 2006 .