2. A parametric and process- oriented view of the carbon system

3. The challenge: explain the controls over the system’s response

4. Carbon emissions and uptakes since 1800 (Gt C)

5. Expanding the model: A model for (F ba -F ab ) F ab =  G(D i, p i, S i ) = photosynthesis F ba =  G(D i, p i, S i ) = respiration and fire

6. A Hierarchical view of the carbon system Drivers (weather, nutrients, fires) Fluxes Concentrations Inverse models do something is this direction Causation goes in this direction

7. A-R: A key feature of the system What we measure: Net Ecosystem Exchange (the flux of CO2 across an imaginary plane above the canopy) But: NEE cannot be directly parameterized NEE = Photosynthesis - Respiration The model (or observation equation) must “transform” the observation (NEE) into physically modeling components. This is neglecting complex but different processes such as fire and forest harvest.

8. Ecosystem Model Structure Plant Carbon Soil CarbonSoil Moisture Drainage Precip. Transpiration Photosynthesis (Phenology,Soil Moisture, Tair, VPD, PAR) Plant Respiration (Plant C, Tair) Litterfall (Plant C, Phenology) Soil Respiration (Soil C, Soil Moisture, Tsoil)

9. Some key model equations NEE = R a +R h - GPP GPP max = A amax A d +R leaf GPP pot = GPP max D temp D vpd D light R h = C s K h Q 10s Tsoil/10 (W/W c ) GPP = canopy photosynthesis, R denotes respiration, A max = max leaf-level carbon assimilation, Ds are scalars for environmental factors, A d, a scaling factor over time, C s = substrate, K, rate constant, Q 10 the temperature scalar and W, water scalars.

10. Estimation (z j - H(Fap j,Fpa j )) t R - j 1 (z j - H(Fap j,Fpa j ))/2 + (p j - P j ) t R - j 1 (p j - P j ) /2 The rubber bands are the prior estimates of parameters

11. Assimilation of fluxes provides consistency between prior knowledge and observed carbon exchange

12. Control variables Temperature Soil moisture Nutrient availability Fire regime Light interception Land management Atmospheric CO 2 etc

13. Concentrations have less information about processes and parameters than do fluxes Why? They are “one step more removed” (by transport) That step includes “invertible” (advective) processes and irreversible (diffusive) processes There is information loss along the chain of causation

14. Get closer to the answer: measure fluxes Tower-based measurements

15. FLUXNET

17. More gadgets My little flux tower….

18. More gadgets CO 2, H 2 O T, u,v,w w

20. Time-scale character of carbon modeling Diurnal Seasonal 1.Variability is at a maximum on the strongly forced time scales 2.They have an annual sum of ~0 3.Modeling the carbon storage time scales (years) is the goal

21. Observed variability of fluxes

22. Analyzed variability of processes

23. Analysis of controls Warm springs accelerate growth but also evaporation. Despite the overall positive response shown earlier, the annual relationship of flux to temperature is negative

24. Self-consistent parameter sets Fit to the diurnal cycle (~12 hour time steps) Fit to daily data: 24 hour time steps

25. Assimilating water and carbon Just water Carbon only or carbon plus water

26. Adding water doesn’t help carbon, but it helps water Carbon only Carbon and water

27. Evaluation against an independent water flux measurement

28. Normal Model Parameterization Method

29. Step 2…..

30. Self-consistent parameter sets C S,0 (g m -2 ) K H (g g -1 y -1 ) Range from prior knowledge First parameter Validate-tune Second parameter dictated

31. Analysis of controls The emergent Relationship of temperature and carbon uptake. Note the multiple Regimes. The lower lines are the water-limited response Realized T response, dry Realized T response wet

32. What does this type of local study contribute to global modeling? We can use this to understand the information in different types of observation

33. Carbon from space OCO uses reflected sunlight to make measurements during the day

34. Day and Night Remember, we’ve shown a huge loss of process information without diurnal information

35. Future active CO 2 experiments make day and night observations LIDAR

36. Process priors for global models Tower-based estimates of parameters can be used as priors to invert global concentration data to estimate parameters controlling fluxes instead of fluxes (Knorr, Wofsy, Rayner)

37. The global scale is very distant from processes Distributed local measurements and innovative measurement approaches can bridge the gap

40. ACME prepares for its first flight

41. Vertical profiles and CO 2 “lakes”

42. Carbon data assimilation Carbon data assimilation and parametric estimation are fast- moving fields

43. A few references Vukicevic, T., B.H. Braswell and D.S. Schimel. 2001. A diagnostic study of temperature controls on global terrestrial carbon exchange. Tellus (B) 53:150-170. (variational) Braswell, B.H., W.J. Sacks, E. Linder and D.S. Schimel. 2004. Estimating ecosystem process parameters by assimilation of eddy flux observations of NEE. Global Change Biol. 11:335-355 (MCMC) Williams, M. Schwarz, B.E. Law, J. Irvine, and M.R. Kurpius. 2005. An improved analysis of forest carbon dynamics using data assimilation. Glov=bal Change Biol. 11:85-105 (EKF) Wang, Y-P. and D Barrett. 2003. stimating regional terrestrial carbon fluxes for the Australian continent using a multiple- constraint approach. I. Using remotely sensed data and ecological observations of net primary production. Tellus (B) 55:270-289 (Synthesis inversion)