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A parametric and process-oriented view of the carbon
system
The challenge: explain the controls over the system’s response
Carbon emissions and uptakes since 1800 (Gt C)
180
110
115
265
140Land use change
Fossil emissions
Atmosphere
Oceans
Terrestrial
Expanding the model:
A model for (Fba-Fab)
Fab = G(Di, pi, S i) = photosynthesisFba = G(Di, pi, S i) = respiration and fire
A Hierarchical view of the carbon system
Drivers (weather, nutrients, fires)
Fluxes
ConcentrationsInverse models do something is this
direction
Causation goes in this direction
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 parameterizedNEE = 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.
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)
Some key model equations
NEE = Ra +Rh - GPP
GPPmax = AamaxAd+Rleaf
GPPpot = GPPmaxDtempDvpdDlight
Rh = CsKhQ10sTsoil/10(W/Wc)
GPP = canopy photosynthesis, R denotes respiration, Amax = max
leaf-level carbon assimilation, Ds are scalars for environmental factors, Ad, a scaling factor over time, Cs = substrate, K, rate
constant, Q10 the temperature scalar and W, water scalars.
Estimation
(zj - H(Fapj,Fpaj))tR-j1 (zj - H(Fapj,Fpaj))/2 +
(pj - Pj)tR-j1 (pj - Pj) /2
The rubber bands are the prior estimates of parameters
Assimilation of fluxes provides consistency between priorknowledge and observed carbon exchange
Control variables
• Temperature• Soil moisture• Nutrient availability• Fire regime• Light interception• Land management
• Atmospheric CO2
• etc
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
Get closer to the answer: measure fluxes
Tower-based measurements
FLUXNET
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More gadgets
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My little flux tower….
More gadgets
CO2, H2O T, u,v,w
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w
Time-scale character of carbon modeling
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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
Observed variability of fluxes
Analyzed variability of processes
Analysis of controls
Warm springs accelerategrowth but also evaporation.Despite the overall positive response shown earlier, the annual relationship of flux to temperature is negative
Self-consistent parameter sets
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J F M A M J J A S O N D
NEE (g C m
-2 day
-1)
Modeled DaytimeObserved DaytimeModeled NighttimeObserved NighttimeModeled TotalObserved Total
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J F M A M J J A S O N D
NEE (g C m
-2 day
-1)
Modeled DaytimeObserved DaytimeModeled NighttimeObserved NighttimeModeled TotalObserved Total
Fit to the diurnal cycle (~12 hour time steps)
Fit to daily data: 24 hour time steps
Assimilating water and carbon
Just water
Carbon only or carbon plus water
Adding water doesn’t help carbon, but it helps water
Carbon only
Carbon and water
Evaluation against an independent water flux measurement
Normal Model Parameterization Method
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Step 2…..
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Self-consistent parameter sets
CS,0 (g m-2)
KH (g g-1 y-1)
Range from priorknowledge
First p
ara
me
ter
Validate-tune
Second parameter dictated
Analysis of controls
The emergentRelationship of temperature and carbon uptake.
Note the multipleRegimes. The lower lines are the water-limited response
Realized T response, dry
Realized T response wet
What does this type of local study contribute to global
modeling?
We can use this to understand the information in different types of
observation
Carbon from space
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OCO uses reflected sunlight to make measurements during the day
Day and Night
Remember, we’ve shown a huge loss of process information without diurnal information
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J F M A M J J A S O N D
NEE (g C m
-2 day
-1)
Modeled DaytimeObserved DaytimeModeled NighttimeObserved NighttimeModeled TotalObserved Total
Future active CO2 experiments make day and
night observations
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LIDAR
Process priors for global models
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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)
The global scale is very distant from processes
Distributed local measurements and innovative measurement
approaches can bridge the gap
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ACME prepares for its first flight
Vertical profiles and CO2 “lakes”
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Carbon data assimilation
Carbon data assimilation and parametric estimation are fast-moving fields
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)