1. Calibration of land surface models
Cathy Trudinger
CSIRO Marine and Atmospheric Research
Aspendale, Australia

2. 1. OptIC project OptIC – Optimisation Intercomparison project
Pseudo-data generated with a simple test model + noise
Participants estimated 4 model parameters
Methods used:
Down-gradient (Levenberg-Marquardt, adjoint)
Sequential (Extended Kalman filter, Ensemble Kalman filter)
Global search (Markov-Chain Monte Carlo, genetic algorithm).
Trudinger, C. M., Raupach, M. R., Rayner, P. J., Kattge, J., Liu, Q., Pak, B. C., Reichstein, M., Renzullo, L., Richardson, A. D., Roxburgh, S. H., Styles, J., Wang, Y. P., Briggs, P. R., Barrett, D., and Nikolova, S. OptIC project: An intercomparison of optimization techniques for parameter estimation in terrestrial biogeochemical models. Journal of Geophysical Research - Biogeosciences, 112 (G2, G02027): doi: /2006JG000367, 2007.
CSIRO. Calibration of land surface models

3. Optic model
where F(t) – forcing (log-Markovian i.e. log of forcing is Markovian) x1 – fast store x2 – slow store p1, p2 – scales for effect of x1 and x2 limitation of production k1, k2 – decay rates for pools s0 – seed production (constant value to prevent collapse)
(p1 and p2 colinear)
Estimate parameters p1, p2, k1, k2
CSIRO. Calibration of land surface models

4. Noisy pseudo-observations
T1: Gaussian (G)
T4: Gaussian but noise in x2 correlated with noise in x1 (GC)
T6: Gaussian with 99% of x2 data missing (GM)
T2: Log-normal (L)
T3: Gaussian + temporally correlated (Markov) (GT)
T5: Gaussian + drifts (GD)
CSIRO. Calibration of land surface models

5. Parameter estimates p1 p2 k1 k2
CSIRO. Calibration of land surface models

6. OptIC project Findings
Largest variation in results arose from the choice of the cost function, not the choice of optimisation method.
Relatively poor results were obtained when the model-data mismatch in the cost function included weights that were instantaneously dependent on noisy observations.
All methods gave biased results when the noise was temporally correlated or non-Gaussian, or when incorrect model forcing was used.
The results indicate the need for care in choosing the error model in any optimisation
CSIRO. Calibration of land surface models

7. 2. Parameter estimation with the Kalman filter
The Kalman filter is a sequential data assimilation method
Can include parameters in the state vector (joint estimation)
Evolution of parameters dp/dt=0
No observations of the parameter, information comes from observations of the variables via the state error covariance matrix
Parameter estimate (and associated uncertainty) vary with time
If model error for parameters Qparam = 0 then uncertainty in estimated parameters decreases as observations are assimilated
Should constant parameters have a stochastic component, i.e. Q? Probably not, as evolution model dp/dt=0 is perfect, and do not want error covariance to increase from prior
Trudinger, C. M., Raupach, M. R., Rayner and I. G. Enting. Using the Kalman filter for parameter estimation in biogeochemical models, Environmetrics, in press.
CSIRO. Calibration of land surface models

8. Extended Kalman filter
Estimating parameters in the Optic model
CSIRO. Calibration of land surface models

9. Parameter estimation with the Kalman filter
CSIRO. Calibration of land surface models

10. Parameter estimation with the Kalman filter
The Kalman filter is generally successful at retrieving model parameters for this simple model
Results can vary with choice of model and observation error
Including model error for parameters was not particularly successful
The best parameters were obtained with overstated observation uncertainties
CSIRO. Calibration of land surface models

11. Thank you