1. Forest Research, 20 February 2009 Understanding the carbon cycle of forest ecosystems: a model-data fusion approach Mathew Williams School of GeoSciences, University of Edinburgh

2. Overview  Problems with assessing forest C dynamics  Model-data fusion – Process dynamics – Spatial variability and scaling

3. Soil chamber Eddy fluxes Litterfall Autotrophic Respiration Photosynthesis Soil biota Decomposition CO 2 ATMOSPHERE Heterotrophic respiration Litter Soil organic matter Leaves Roots Stems Translocation Carbon flow Litter traps Leaf chamber

4. GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Modelling C exchanges

5. GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Photosynthesis & plant respiration Phenology & allocation Senescence & disturbance Microbial & soil processes Climate drivers Non linear functions of temperature Simple linear functions Feedback from C f

6. Improving estimates of C dynamics MODELS OBSERVATIONS FUSION ANALYSIS MODELS + Capable of interpolation & forecasts - Subjective & inaccurate? OBSERVATIONS +Clear confidence limits - Incomplete, patchy - Net fluxes ANALYSIS + Complete + Clear confidence limits + Capable of forecasts

7. Combining models and observations  Are observations consistent among themselves and with the model?  What processes are constrained by observations?  Can multiple constraints improve analyses? 1.State estimation with EnKF 2.REFLEX experiment

8. MDF: The Kalman Filter MODEL AtAt F t+1 F´ t+1 OPERATOR A t+1 D t+1 Assimilation Initial stateForecast Observations Predictions Analysis P Drivers

9. Observations – Ponderosa Pine, OR (Bev Law) Flux tower (2000-2) Sap flow Soil/stem/leaf respiration LAI, stem, root biomass Litter fall measurements

10. Time (days since 1 Jan 2000) Williams et al GCB (2005)  = observation — = mean analysis | = SD of the analysis

11. Time (days since 1 Jan 2000) Williams et al GCB (2005) = observation — = mean analysis | = SD of the analysis

12. Data brings confidence Williams et al, GCB (2005)  = observation — = mean analysis | = SD of the analysis

13. Outstanding questions  Are the confidence intervals generated by MDF reliable?  How do different MDF approaches compare?  How can model error be characterised?  Can MDF produce reliable estimates of model parameters consistent with observations?

14. Reflex experiment  Objectives: To compare the strengths and weaknesses of various model-data fusion techniques for estimating carbon model parameters and predicting carbon fluxes.  Real and synthetic observations from evergreen and deciduous ecosystems  Evergreen and deciduous models  Multiple MDF techniques www.carbonfusion.org

15. A tolab GPP CrCr CwCw CfCf C lit C SOM RaRa AfAf ArAr AwAw LfLf LrLr LwLw R h1 D C lab A fromlab R h2 Model and parameters

16. Parameter constraint Consistency among methods Confidence intervals constrained by the data Consistent with known “truth” “truth”

17. Testing algorithms

18. Parameter summary  Parameters closely associated with foliage and gas exchange are better constrained  Parameters for wood and roots poorly constrained and even biased  Similar parameter consistency values for synthetic and true data  Correlated parameters were neither better nor worse constrained

20. Testing algorithms – synthetic data Synthetic data Fraction of successful annual flux tests (3 years x 2 sites, n=6) Confidence interval (gC m -2 yr -1 ) GPP ReRe NEE

21. Problems with soil organic matter…

22. And with woody C

23. State retrieval summary  Confidence interval estimates differed widely  Some techniques balanced success with narrow confidence intervals  Some techniques allowed large slow pools to diverge unrealistically  Decomposition of NEE into GPP/R e was generally successful using daily data  Model error = 88%  Prediction error = 31%

25. (Van Wijk & Williams 2005)

27. 0.2 m 0.5 m 1.0 m 1.5 m 2.0 m 3.0 m 0.1 m0.75 m1.5 m2.35 m3.0 m4.5 m Height of sensor and field of view

28. A multiscale experimental design Distance (m) (Williams et al. 2008) macroscalemicroscale

29. Linear averaged Skye NDVIs (collected at 0.2 x 02 m resolution with diffuser off) versus measured NDVIs at coarser spatial scales with diffuser on

30. Relationships between estimated LAI (using both Skye NDVI and LI-COR LAI-2000 observations at 0.2 m resolution, linearly averaged for upscaling) versus Skye NDVI at different spatial scales.

31. Frequency histograms for LAI estimates in the microscale site at a range of resolutions. (Williams et al. 2008)

33. A significant but poor correlation with LandSat data

34. Error (Williams et al. 2008) Ground EO Ground + EO

35. Spatial analysis summary  Scale invariance in LAI-NDVI relationships at scales > vegetation patches  However spatial variability is high so Kriging has limited usefulness  Over scales >50 m interpolation error was of similar magnitude to the uncertainty in the Landsat NDVI calibration to LAI  Characterisation of spatial LAI errors provides key data for spatial data assimilation

36. Conclusions  Model data fusion provides insights into information retrieval from noisy and incomplete observations  Challenges and opportunities: – Linking to observations of C pools, tree rings, inventory – Linking other biogeochemical cycles – Designing optimal sensor networks – Linking to earth observation data

37. Thank you Acknowledgements: Andrew Fox, Andrew Richardson, and REFLEX team Bev Law, James Irvine Mark Van Wijk, Rob Bell, Luke Spadavecchia, Lorna Street