1. Using data assimilation to improve understanding and forecasts of the terrestrial carbon cycle Mathew Williams School of GeoSciences, University of Edinburgh And National Centre for Earth Observation

2. Source: CD Keeling, NOAA/ESRL Sampling at 3397 meters, well mixed free troposphere

3. 60 90 650 120 GPP R H 60 o R A 0.1 0.4 Source: Schlesinger (1997), Schimel et al. (1995), Reeburgh (1997) THE BIOLOGICAL GLOBAL CARBON CYCLE (1750) Pools (billions of tonnes C) & fluxes ( billions of tonnes C yr -1 ) Soils 1580 Atmosphere 540 Deep ocean DOC 700 DIC 38000 Surface DOC 40 POC 7 Sediments 75,000,000

4. 6 60 92 90 600 120? GPP R H 1.4 60 Net destruction of vegetation R A 0.1 0.4 Source: Schlesinger (1997), Schimel et al. (1995), Reeburgh (1997) THE MODERN GLOBAL CARBON CYCLE (2000) Pools (billions of tonnes C) & fluxes ( billions of tonnes C yr -1 ) Soils 1580 Atmosphere 720 (+3.2/yr) Unattributed C sink 1.6 Deep ocean DOC 700 DIC 38000 Surface DOC 40 POC 7 Sediments 75,000,000

5. Friedlingstein et al 2006: C4MIP Intercomparison of 11 coupled carbon climate models

6. Problems with models Poor parameterisation Inaccurate initial conditions Missing processes Solution: make and break models with observations?

7. Space (km) time s hr day month yr dec 0.11.010100100010000 Flask Site Time and space scales in ecological processes Physiology Climate change Succession Growth and phenology Adaptation Disturbance Photosynthesis and respiration Climate variability

8. OCO Space (km) time s hr day month yr dec 0.11.010100100010000 Flux Tower Aircraft Flask Site Flask Site Field Studies MODIS Time and space scales in ecological observations Tall tower

9. Observing networks: Flask [CO 2 ]

10. Observing networks: CO 2 Fluxes FluxNet - ~200 eddy covariance systems

11. Source: Wofsy et al, Harvard Forest LTER Hourly data ~5 m above canopy

12. Tall Tower ‘Angus’ CO 2 CH 4 N 2 O SF 6 CO H 2 222 Rn at 222 m at 50 m  T and RH at 220,100, 50 and 5 m agl  P, u and wind direction at 5 m agl  Li-7000  Agilent 6890 FID & ECD  TGA3  ANSTO Radon Photo: T Hill & T Wade

13. Landscape and regional ecology

14. Barkley et al, [2006] SCIAMACHY CO 2 [P Monks] MODIS EVI [NASA] Airborne LIDAR biomass [C Nichol] A range of Earth observation data

15. 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

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

18. 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

19. Exploring model behaviour  Sensitivity to initial conditions  Parameter sensitivity  Steady state solutions  A master’s study by Tom Ilett – Supported by Sarah Dance, Jon Pitchford, Nancy Nichols

20. Sensitivity of pools and NEE to altered initial conditions of C f

21. C r - roots C w - wood C lit - litterC som – soil organic matter NEE sensitivity to varying initial conditions over 3 years

22. Parameter details Parameter sensitivity

23. The steady state solution For  C f = 0 The equilibria for the other stocks are linear functions of G and C f Assume climate inputs are constants

24. There are three fixed points for GPP and C f, for C f  0; 50; 450.

25. Equilibrated values of other C stocks Equilibrium value (gC m -2 ) Time to equilibrium (yrs) G*10.8 gC m -2 d -1 C f* 450<12 C r* 290<12 C w* 37,000250 C lit* 210<12 C som* 230,0002000

26. NEE trajectories 12 yrs250 yrs2000 yrs Evolution of NEE  0, time constant depends on stabilisation of C som

28. Relationship between GPP, C f and time – an indicator of phenology?

29. Convergence to attracting orbit for a 15 year projection. Trajectories become darker as time progresses – final year is a black line

30. Combining models and observations  Are observations consistent among themselves and with the model?  What processes are constrained by observations?

31. 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

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

33. 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

35. ParticipantName – type of methodology CodePriorInitial poolsConvergence tests Number of parameter sets produced Number of model iterations Programming language E1 (stage 1) MCMC Metropolis, then EnKF UniformParameters to be estimated Gelman and Rubin (1992) ~400000~1000000Fortran E1 (stage 2) Evensen (2003) PDFs from stage 1 n/aState only8000Fortran E2Ensemble Kalman filter Evensen (2003) gaussian Cr=Cfmax, Clit=0.5Cfmax, Clab=0.5Cfmax n/a - ran EnKF 2 times with reinitialisation ~2000800Fortran90 U1Unscented Kalman filter Gove & Hollinger (2006) gaussian From M3n/a R G1Genetic algorithmBased on Haupt and Haupt (2004) uniform Tuned with parameters n/a ~100000Fortran90 M1MCMC – Metropolis Included in calibration visual 300000 Fortran M2MCMC – MetropolisMCMC1uniform Parameters to be estimated Visual comparison of parameter PDFs from 2 chains 1000000 Fortran M3Simulated annealing-Metropolis SAMuniform Parameters to be estimated none1000~250000Fortran M4MCMC – MetropolisMCMC3uniform Spinup to equilibrium of total C Heidelberger and Welch (1983) 80000~300000R M5Multiple complex MCMC – Metropolis SCEMuniform Parameters to be estimated Gelman and Rubin (1992) ~500000150000Matlab Algorithms in the Reflex Experiment

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

37. Parameter retrieval for EV ID Paramd1d2d3DRankBias p1T d 0.260.360.750.87111 p2F g 0.300.410.020.5163B p3F nf 0.070.490.000.5054A p4F nrr 0.240.650.310.7691 p5T f 0.060.200.030.2114A p6T w 0.220.400.690.83100* p7T r 0.270.520.030.5984 p8T l 0.070.220.030.2323 p9T s 0.050.160.210.2740* p10E t 0.040.240.000.2434 p11P r 0.210.470.150.5472B Mean0.160.380.200.51 d1.Consistency among methods:  (m 1,…,m 9 )/(p max -p min ) d2. CIs constrained by the data:  (CI 1,…,CI 9 )/(p max -p min ) d3.Consistent with truth:|t-  (m 1,…,m 9 )|/(p max -p min ) m i =estimate by method i, p=prior, t=truth. D =  (d 1,d 2,d 3 ). A, B indicate correlations

38. 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 D values for synthetic and true data  Correlated parameters were neither better nor worse constrained

40. Testing algorithms & their confidence Fraction of successful annual flux tests (3 years x 2 sites, n=6) Confidence interval (gC m -2 yr -1 ) GPP ReRe NEE

41. Problems with soil organic matter…

42. And with woody C

43. 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

44. Conclusions  Attractor analysis is a useful technique for understanding C models  Model data fusion provides insights into information retrieval from noisy and incomplete observations  Challenges and opportunities: – introducing stochastic forcing – Linking other biogeochemical cycles – Designing optimal sensor networks – Theoretical understanding of plant process

45. Thank you

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

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