1. Data assimilation as a tool for biogeochemical studies Mathew Williams University of Edinburgh

2. The carbon problem  Friedlingstein P., et al. 2006. Journal of Climate. – 11 coupled climate-carbon models predicted very different future C dynamics  Conclusion – our models are flawed  Solution – better model testing against data, and better use of multiple data sets to test the representation of process interactions

3. Talk outline  Assimilating C flux and stocks data to improve analyses of C dynamics  Assimilating reflectance data  Assimilating latent energy flux data to deconvolve net carbon fluxes

4. 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

5. Time update “predict” Measurement update “correct” A prediction-correction system Initial conditions

6. 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 Ensemble Kalman Filter Drivers

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

8. GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D C = carbon pools A = allocation L = litter fall R = respiration (auto- & heterotrophic)

9. GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Temperature controlled 6 model pools 10 model fluxes 9 parameters 10 data time series R total & Net Ecosystem Exchange of CO 2 C = carbon pools A = allocation L = litter fall R = respiration (auto- & heterotrophic)

10. Time (days since 1 Jan 2000) Williams et al (2005)

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

12. Time (days since 1 Jan 2000) Williams et al (2005)

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

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

15. Assimilating EO reflectance data DALEC AtAt F t+1 Reflectance t +1 Radiative transfer A t+1 MODIS t+1 DA

16. Model only Assimilating MODIS NDVI EO assimilation to improve photosynthesis predictions  = observation — = mean analysis | = SD of the analysis Quaife et al. (RSE in press)

17. CfCf CrCr CwCw ClCl C som GPP W S1 W S2 W S3 ET Ppt RhRh CarbonHydrology RaRa Constraining the C cycle via hydrology

18. Deconvolving net C fluxes  NEE = R eco – GPP  Eddy flux towers also measure LE  LE  GPP (some complications…)  Use a model of coupled C-water fluxes…  Assimilate LE and NEE data, and use LE to constrain GPP  Improved flux deconvolution  Improved model diagnosis and prognosis

19. Demonstration study  Generate a “true” system with a complex model  Sample the “truth” and generate observations (with errors)  Attempt to reconstruct the truth through assimilating the observations into a simple model  Experiment with NEE data alone, and NEE + LE data

20. Fluxes Truth Obs. Analysis

21. Residuals Obs. Truth

22. Stocks Truth Obs. Analysis

23. Summary  Data assimilation techniques are powerful tools for ecological research  Time series data are most useful  For improved predictions, better constraints on long time constant processes are required  Error characterisation is vital  EO data can be assimilated  Hydrological assimilation can decompose net C fluxes into components.

24. Thank you Acknowledgements: Bev Law Tris Quaife