Daniel M. Matross University of California Berkeley

1. Lessons from forward and inverse modeling of Northeast regional CO2 fluxes using airborne and tower data Daniel M. Matross University of California Berkeley With help from Steven C. Wofsy, Scot M. Miller, Marcos Longo, and others A view from the trenches NCAR ASP regional methods in biogeochemistry colloquium; Boulder, CO; 14-June-2007

2. COBRA-Maine & STILT+VPRM • An integrated atmospheric field campaign and top-down data assimilation scheme “I am always ready to learn although I do not always like being taught.” –W.C.

3. COBRA-Maine Flight Strategy • 2004 • Build flights around surface anchor points of collaborators • Maximize vertical coverage • Two phases: Early season (May 15th – June 15th) & Later season (July 15th to August 15th)

4. Argyle Chebogue Point Fluxnet Canada EOBS Harvard Forest Howland Forest

5. Regional CO2 exchange from ModelData Fusion Atmospheric Data Tower or Airborne Atmospheric representation + Model Concentrations Surface Flux Model Built from the bottom up Environmental Drivers λ, α, dk Adjustable Parameters

6. Receptor Oriented Modeling Framework X Instead of modeling concentrations everywhere at all times… …pick a point in space and time and run transport backwards… upwind influence backwards “Receptor point” …points chosen are associated with actual observations

7. STILT: Stochastic Time Inverted Lagrangian Transport Model Assimilated meteorology… …drives particles released from receptor point… …which determine upstream surface influence function

8. STILT+VPRM Receptor Oriented Modeling Framework Fossil fuel inventory VPRM Tracer boundary condition Vegetation Fluxes Influence function STILT Model Concentrations

9. II. Regionally representative data “Difficulties mastered are opportunities won.” – W.C.

10. High Frequency Variations Contain Information about the regional signal Observations are influenced by fluxes at all spatial scales, including the near field and the global field, and everything in between.

11. Vertical Profiles over Argyle Tower 30-July-2004 Taken during COBRA-Maine Upper level CO2 concentrations influenced very little by continental exchange—indicative of oceanic background Gorgeous residual layer contains information about uptake the day before Stable nocturnal boundary layer is prominent in the morning

12. Temporal correlations determined by modeling data as first order Markov process and fitting an AR(1) model to afternoon average concentration data at WLEF (WLEF data courtesy K. Davis and colleagues) Spatial correlations via an exponential variogram fit of COBRA-Maine airborne data

13. III. Forward model runs and their importance “However beautiful the strategy, you should occasionally look at the results.” – W. C.

14. The model works…depending on the boundary condition

15. Vertical Profiles over Argyle Tower 30-July-2004

16. Some situations are difficult for the transport model to represent

17. Errors in VPRM driver fields cause errors in concentration calculation Most NWP products under-predict non-precipitating clouds, and thus over-predict CO2 uptake.

18. Why this is difficult: • Inverse methods conflate errors or corrections for sources with errors in transport and drivers, because only the source model can be optimized • Errors are taken up by the parameters of the source model! How to deal with it: • Know the forward model • Incorporate all the knowledge possible into the inversion

19. IV. A short look at inverse results “Now this is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning.”—W. C.

20. What do you learn about surface fluxes from different types of observations? Results from a Bayesian inversion study of data from tall and short towers, plus intensive aircraft measurements (200 hours of 1s data over 6 weeks). Marginal cost of constraint is high! One tower gives lots of constraint, but a second one provides an order of magnitude less additional constraint. Information within multiple towers is redundant. Airborne data and tower data are strongly complementary. A surface network and a single tower + airplane supply similar constraint. Towers give temporal coverage, aircraft give spatial coverage, plus potentially boundary information Total DF equals the number of parameters and are split between those contributing information (signal) about the data and those contributing no information (noise). A higher signal value indicates the data places more constraint on the parameters in the inversion. N refers to afternoon hours of tower data or sub-sampled 20-second averages of airborne data. Maximal constraint requires surpisingly large number of observations

21. VPRM NE/Quebec (41-52˚N, 67-80˚W) Carbon Budget (NEE in tons/ha) But what uncertainty?

22. Take home lessons from down in the trenches Getting optimal regional-scale CO2 fluxes requires: • Collecting lots of targeted data • Spatial correlations reduce degrees of freedom • Qualitative assessment of information important • 2) Characterizing the forward model • Transport, driver errors get conflated surface flux function • Case studies • 3) Quantitatively connect data and model in inversion • Error correlations, transport errors MUST be quantitatively incorporated • garbage in = garbage out “If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time-a tremendous whack.” – W.C.

23. END OF PRESENTATION “I'm just preparing my impromptu remarks.” – W. C.

24. SLIDES NOT IN USE

25. Bayesian Inversion • Probabilistic combination of prior model & associated error estimates with observations & associated uncertainty estimates Observations Optimum posterior solution uncertainty estimates Prior model posterior error estimates error estimates Bayesian Inversion Assumes model errors and measurement uncertainties are Gaussian

26. CO STILT/BRAMS r2=0.56 30 CO (ppb) 10 03 08 13 18 June 2004 June 12 16 Background subtracted

27. Top-down models are usually thought to have very limited need for a detailed bottom-up model fluxes—large areas are typically aggregated in global inverse models, while a variety of simple surface flux models are used for more regional studies. This represents a false dichotomy between top-down and bottom-up models. Since top-down models are under-constrained, information from the assumed pattern of fluxes survives into the final budget estimates. Thus top-down models require very careful design of the surface flux field to be optimized against data. The underlying reason is that observations are influenced by fluxes at all spatial scales, including the near field and the global field, and everything in between. There are many other features and design elements of top-down models that can affect the results…

28. Water, ice, urban, other Grassland Cropland Savanna Shrubland Mixed Forest Deciduous Forest Subtropical evergreen Dry temperate evergreen Wet temperate evergreen Boreal evergreen

29. Regional CO2 exchange from ModelData Fusion Atmospheric Data Tower or Airborne STILT Atmospheric transport model ? How well do these match up before optimization? + Model Concentrations Surface Flux Model Built from the bottom up VPRM

30. Explaining Argyle Transport Problems The Coastal Domain 89% (median by receptor—hour) of the particles that reached Argyle in June/July 2004 entered the coastal domain (East of the red points) during their transit!

31. All top-down models : • use the same types of inputs, including drivers for photosynthesis and a model for transport that connects fluxes and concentrations. • assimilate measurements that are discrete, partial representations of the whole field; • separate contributions from vegetation vs. combustion, (derived from inventories); • produce predicted CO2 and CH4 in the domain for comparison with observations. Some: • use a Lagrangian approach (e.g. STILT/VPRM – Matross poster) to map sources into atmospheric concentrations, others use Eulerian models (more comprehensive, but having more spatial averaging) • use minimal remote-sensing driven models to give a priori fluxes, others use sophisticated bottom-up models, with the full range in between. • are global (lack resolution), others regional (need boundary conditions) • All: • Conflate errors or corrections for sources with errors in transport and drivers, because only the source model can be optimized; • Errors are taken up by the parameters of the source model!

32. Bayesian Inversion • We define error covariance matrix as much as possible from data, including uncertainty from: • Off-diagonal elements defined with exponentially decaying correlation Instruments Fossil fuel inventory VPRM fitting Unresolved eddies Neglecting ocean fluxes Boundary condition Aggregation Random particle statistics Mixed layer height Example B: Time constant for correlation of tower data from AR(1) model (WLEF shown here) Example A: Length constant for spatial correlation of airborne data from spatial variogram

33. However beautiful the strategy, you should occasionally look at the results. A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty. He has all of the virtues I dislike and none of the vices I admire Difficulties mastered are opportunities won. Although personally I am quite content with existing explosives, I feel we must not stand in the path of improvement. Criticism may not be agreeable, but it is necessary. It fulfils the same function as pain in the human body. It calls attention to an unhealthy state of things. We must beware of needless innovations, especially when guided by logic I am always ready to learn although I do not always like being taught. Now this is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning. I am easily satisfied with the very best. I'm just preparing my impromptu remarks. Success is going from failure to failure without losing enthusiasm If you are going through hell, keep going. If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time-a tremendous whack. In war as in life, it is often necessary when some cherished scheme has failed, to take up the best alternative open, and if so, it is folly not to work for it with all your might. It is a mistake to look too far ahead. Only one link of the chain of destiny can be handled at a time.