Parameter estimation of forest carbon dynamics using Kalman Filter methods –Preliminary results
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Parameter estimation of forest carbon dynamics using Kalman Filter met Parameter estimation of forest carbon dynamics using Kalman Filter met hods –Preliminary results hods –Preliminary results Chao Gao, 1 Han Wang, 2 S Lakshmivarahan, 3 Ensheng Weng, 1 Yanfen Zhang, 4 and Yiqi Luo 1 1 Department of Botany and Microbiology, 2 Department of Electric Engineering, 3 Department of Computer Science, 4 Department of Petroleum, University of Oklahoma Email address: [email protected] Kalman Filter (KF) is a sequential data assimilation technique, first used in weather forecasting and curren tly widely used in other disciplines (e.g., Hydrology a nd Petroleum). Estimates of carbon (C) transfer coefficients is crit ical to the understanding of carbon turnover time and e cosystem C sequestration. However, in the previous study, number of parameters t hat can be constrained is limited and the efficiency is relatively low (e.g., MCMC). In this study, Kalman Filter approaches (Linear, Nonli near, and Ensemble) were applied to a terrestrial ecosy stem C dynamic model for optimal estimation of paramete rs at each step (daily) during a 9-year period in Duke forest FACE site . Introductio n Method 1. Create initial 1. Create initial ensemble ensemble 2. Propagate the state vector and its 2. Propagate the state vector and its covariance matrix forward in time covariance matrix forward in time 3. Update the state vector and its 3. Update the state vector and its covariance matrix using the new data covariance matrix using the new data ) ( 0 0 ) ( i i n s y y ) , 2 , 1 ( ) ( 1 , , e e k j f k j N j y y ) , 2 , 1 ( ) ( , , , , , , e f k j k k j obs k e f k j e k j N j y H z K y y ] [ 2 1 Ne j y y y y Y 1 , , , , ) ( k d T k f k e k T k f k e k e R H P H H P K e N j T f k j f k j f k j f k j e f k e y y y y N P 1 , , , , , ) )( ( 1 1 Implementation of Implementation of EnKF EnKF Nc k k k k k c c c c c ) ( ) ( ) ( ) ( 1 3 1 2 1 1 1 1 Nf k k k k k c f c f c f c f c f ) ( ) ( ) ( ) ( ) ( 1 3 1 2 1 1 1 1 Nz k k k k k c Z c Z c Z c Z c Z ) ( ) ( ) ( ) ( ) ( 1 3 1 2 1 1 1 1 State State vector vector Results Discuss ion No M noise Real case Estimation usi ng EnKF C=[1.946×10 -3 2.734×10 -3 2.303×10 -4 1.383×10 -2 9.475×10 -5 4.992×10 -3 1.572×10 -4 8.0985×1 0 -6 ] Given C=[2.106×10 -3 2.515×1 0 -3 1.269×1 0 -4 1.438×1 0 -2 8.952×1 0 -5 5.073×1 0 -3 1.670×1 0 -4 8.905×1 0 -6 ] 1.38% Conclusion 1) Reliability of the model Using the simulated results from a given set of par ameters as input in the Kalman Filter model, the es timated parameters were very close to the given one s. 2) Comparison of observations with simulation results 3) Comparison of results from different kinds of KF 1) Estimated results using EnKF The last step The last step parameter value parameter value 2) High-precision measurements will reduce quantity of observations needed for parameter constraint Test model: The simulated results were used as the observed values for inverse analysis. 1) EnKF, which is another widely used data ass imilation technique, is efficient to estimate parameters in forest ecosystem C dynamics. 2) High-precision measurements provide strong constraints for parameter estimations with a reduced number of observations needed. 3) Recovery rates of parameter estimates are v ery high when we used model output as virtual data in parameter estimation. ) ( ) ( ) ( ) ( t BU t ACX t dt t dX ) ( ) ( ) ( ) ( t BU t ACX t dt t dX Soil respiration, Plant bioma ss, Litterfall, Micro biomass, S oil carbon, Forest floor carbon, Wood biomass, Foliage and Root ( together). Acknowledgem ent Model strutu re Data Data source source Fig. 5 Recovery test estimation Fig. 6 Estimates of transfer coefficients using simulation results (a) and observed data (b). Fig. 3 Comparison between observed and modeled data Fig. 2 Estimates of eight transfer coefficients with each time step Fig.1 Schematic diagram of eight carbon pool model Fig. 4 Estimated result s using linear KF (a), nonlinear KF (b), and E nKF (c). We thank US DOE (DE-FG03-99R62800) for financial support difference — scaling function, AC — transfer efficient, X — carbon pool, BU — photosynthesis input ) ( t a . c . b . a . b . C=[2.106×10 - 3 2.515× 10 -3 1.269× 10 -4 1.438× 10 -2 8.952× 10 -5 5.073× 10 -3 1.670× 10 -4 8.905× 10 -6 ] — observations simulati on
description
No M noise. Real case. Fig. 4 Estimated results using linear KF (a), nonlinear KF (b), and EnKF (c). Parameter estimation of forest carbon dynamics using Kalman Filter methods –Preliminary results Chao Gao, 1 Han Wang, 2 S Lakshmivarahan, 3 Ensheng Weng, 1 Yanfen Zhang, 4 and Yiqi Luo 1 - PowerPoint PPT Presentation
Transcript of Parameter estimation of forest carbon dynamics using Kalman Filter methods –Preliminary results
Parameter estimation of forest carbon dynamics using Kalman Filter methods –Preliminary resultsParameter estimation of forest carbon dynamics using Kalman Filter methods –Preliminary resultsChao Gao,1 Han Wang,2 S Lakshmivarahan,3 Ensheng Weng,1 Yanfen Zhang,4 and Yiqi Luo1
1 Department of Botany and Microbiology, 2Department of Electric Engineering, 3 Department of Computer Science, 4 Department of Petroleum, University of OklahomaEmail address: [email protected]
Kalman Filter (KF) is a sequential data assimilation technique, first used in weather forecasting and currently widely used in other disciplines (e.g., Hydrology and Petroleum).
Estimates of carbon (C) transfer coefficients is critical to the understanding of carbon turnover time and ecosystem C sequestration.
However, in the previous study, number of parameters that can be constrained is limited and the efficiency is relatively low (e.g., MCMC).
In this study, Kalman Filter approaches (Linear, Nonlinear, and Ensemble) were applied to a terrestrial ecosystem C dynamic model for optimal estimation of parameters at each step (daily) during a 9-year period in Duke forest FACE site .
Introduction
Method
1. Create initial ensemble1. Create initial ensemble
2. Propagate the state vector and its covariance 2. Propagate the state vector and its covariance matrix forward in timematrix forward in time
3. Update the state vector and its covariance matrix 3. Update the state vector and its covariance matrix using the new datausing the new data
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Results Discussion
No M noise Real case
Estimation using EnKFC=[1.946×10-3
2.734×10-3
2.303×10-4
1.383×10-2
9.475×10-5
4.992×10-3
1.572×10-4
8.0985×10-6]
Given
C=[2.106×10-3
2.515×10-3
1.269×10-4
1.438×10-2
8.952×10-5
5.073×10-3
1.670×10-4
8.905×10-6]
1.38%
Conclusion
1) Reliability of the model
Using the simulated results from a given set of parameters as input in the Kalman Filter model, the estimated parameters were very close to the given ones.
2) Comparison of observations with simulation results
3) Comparison of results from different kinds of KF
1) Estimated results using EnKF
The last step The last step parameter valueparameter value
2) High-precision measurements will reduce quantity of observations needed for parameter constraint
Test model: The simulated results were used as the observed values for inverse analysis.
1) EnKF, which is another widely used data assimilation technique, is efficient to estimate parameters in forest ecosystem C dynamics.
2) High-precision measurements provide strong constraints for parameter estimations with a reduced number of observations needed.
3) Recovery rates of parameter estimates are very high when we used model output as virtual data in parameter estimation.
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Soil respiration, Plant biomass, Litterfall, Micro biomass, Soil carbon, Forest floor carbon, Wood biomass, Foliage and Root (together).
Acknowledgement
Model struture
Data sourceData source
Fig. 5 Recovery test estimation
Fig. 6 Estimates of transfer coefficients using simulation results (a) and observed data (b).
Fig. 3 Comparison between observed and modeled data
Fig. 2 Estimates of eight transfer coefficients with each time step
Fig.1 Schematic diagram of eight carbon pool model
Fig. 4 Estimated results using linear KF (a), nonlinear KF (b), and EnKF (c).
We thank US DOE (DE-FG03-99R62800) for financial support
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— scaling function, AC — transfer efficient, X — carbon pool, BU — photosynthesis input
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C=[2.106×10-3
2.515×10-3
1.269×10-4
1.438×10-2
8.952×10-5
5.073×10-3
1.670×10-4
8.905×10-6]
—
observations
simulation
