Dr. Yiqi Luo Botany and microbiology department University of Oklahoma, USA

1. Parameter identifiability, constraints, and equifinality in data assimilation with ecosystem models (Luo et al. Ecol Appl. In press) Dr. Yiqi Luo Botany and microbiology department University of Oklahoma, USA Land surface models and FluxNET data Edinburgh, 4-6 June 2008

2. Parameter identifiability Prior knowledge Posterior distribution Constrained Inverse model Edge-hitting Observed Data Equifinality

3. Identiable parameters • Wang et al. (2001) ------ a maximum of 3 or 4 parameters can be determined. • Braswell et al. (2005) ------ 13 out of 23 parameters were well-constrained. • Xu et al. (2006) ------ 4 or 3 out of 7 parameters can be constrained, respectively under ambient and elevated CO2.

4. Three methods to examine parameter identifiability • Search method • Model structure • Data variability

5. Harvard Forest EMS-Tower Eddy flux data

6. Eddy flux technology • CO2 flux • H2O flux • Wind speed • Temperature • PAR • Relative humidity Hourly or half-hourly

7. Model Leaf-level Photosynthesis Sub-model Canopy-level Photosynthesis Sub-model System-level C balance Sub-model

8. Table 1 Parameters information

9. Bayesian inversion • Develop prior distribution • Apply Metropolis-Hasting algorithm a) generate candidate p from sample space b) input to model and calculate cost function c) select according to decision criterion d) repeat • Construct posterior distribution

12. Bayesian inversion Conditional Bayesian inversion Bayesian inversion Bayesian inversion Bayesian inversion

14. Fig. 2 Decrease of cost function with each step of conditional inversion

16. Conclusions • Conditional inversion can substantially increase the number of constrained parameters. • Cost function and information loss decrease with each step of conditional inversion.

17. Measurement errors and parameter identifiability

18. GPP Leaves X1 Woody X2 Fine Roots X3 Metabolic Litter X4 Structural Litter X5 Microbes X6 Slow SOM X7 Passive SOM X8 TECO – biogeochemical model

19. No. of parameter 8 12 8 3

20. Exit rates

21. Transfer coefficients

22. Initial values

23. Pool sizes without data

24. Pool sizes with data and different SD

25. Conclusion Magnitudes of measurement errors do not affect parameter identifiability but influence relative constraints of parameters

26. GPP Leaves X1 Stems X2 Roots X3 Metabolic L. X4 Struct. L. X5 Microbes X6 Slow SOM X7 Passive SOM X8 Base model

27. GPP GPP CO2 CO2 Plant C Plant C Litter C Litter C O Soil C Soil C Miner. C Simplified models 3P model 4P model

28. GPP GPP Leaves X1 Leaves X1 Stems X2 Stems X2 Roots X3 Roots X3 Metabolic L. X4 Litter X4 Struct. L. X5 Slow C X5 Microbes X6 Miner. Soil C X6 Soil C X7 Simplified models 6P model 7P model

29. 3P model-parameter constraints Plant C Litter C Soil C

30. 4P model-parameter constraints Plant C Litter C Slow Soil C Passive Soil C

31. 6P model-parameter constraints Foliage Woody Fine roots Litter C Slow Soil C Passive Soil C

32. 7PM model-parameter constraints Foliage Woody Fine roots Metabolic L. C Structure L. C Microbes C Soil C

33. 8P model-parameter constraints

34. Conclusion Differences in model structure are corresponding to different sets of parameters. The number of constrained parameters varies with data availability