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

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:10.1029/2006JG000367, 2007. CSIRO. Calibration of land surface models

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

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

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

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

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

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

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

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

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