Calibration of land surface models

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Calibration of land surface models

• Cathy Trudinger
• CSIRO Marine and Atmospheric Research
• Aspendale, Australia

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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)
  doi10.1029/2006JG000367, 2007.

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Optic model
whereF(t) forcing (log-Markovian i.e. log of
forcing is Markovian) x1 fast storex2 slow
storep1, p2 scales for effect of x1 and x2
limitation of productionk1, k2 decay rates for
poolss0 seed production (constant value to
prevent collapse)
(p1 and p2 colinear)
Estimate parameters p1, p2, k1, k2
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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)
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Parameter estimates
p1
p2
k1
k2
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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

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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/dt0
• 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/dt0 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.

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Extended Kalman filter

• Estimating parameters in the Optic model

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Parameter estimation with the Kalman filter
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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

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Thank you