Spatial Processes and Landatmosphere Flux

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Spatial Processes andLand-atmosphere Flux

• Constraining ecosystem models with regional flux
  tower data assimilation

Flux Measurements and Advanced Modeling, 22 July
2008 CU Mountain Research Station, Ned,
Colorado Ankur Desai Atmospheric Oceanic
Sciences, University of Wisconsin-Madison
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Lets get spacey
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And regional
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Why regional?

• Spatial interpolation/extrapolation
• Evaluation across scales
• Landscape level controls on biogeochem.
• Understand cause of spatial variability
• Emergent properties of landscapes

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Why regional?
Courtesy Nic Saliendra
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Why regional?

• NEP (-NEE) at 13 sites
• Stand age matters
• Ecosystem type matters
• Is interannual variability coherent?
• Are we sampling sufficient land cover types?

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Why data assimilation?

• Meteorological, ecosystem, and parameter
  variability hard to observe/model
• Data assimilation can help isolate model
  mechanisms responsible for spatial variability
• Optimization across multiple types of data
• Optimization across space

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Why data assimilation?

• Old way
• Make a model
• Guess some parameters
• Compare to data
• Publish the best comparisons
• Attribute discrepancies to error
• Be happy

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Why data assimilation?

• New way
• Constrain model(s) with observations
• Find where model or parameters cannot explain
  observations
• Learn something about fundamental interactions
• Publish the discrepancies and knowledge gained
• Work harder, be slightly less happy, but generate
  more knowledge

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Back to those stats

• AB AB / B
• PD ( DP P ) / D
• (parameters given data)
• (data given parameters) (parameters) /
  (data)
• Posterior
• (Likelihood x Prior) / Normalizing Constraint

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For the visually minded

• D Nychka, NCAR

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Some case studies

• Prediction
• Up and down scaling
• Regional evaluation
• Interannual variability
• Forest disturbance and succession

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Regional Prediction
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Our tower is bigger
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Is there a prediction signal?
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Sipnet

• A simplified model of ecosystem carbon / water
  and land-atmosphere interaction
• Minimal number of parameters
• Driven by meteorological forcing
• Still has gt60 parameters
• Braswell et al., 2005, GCB
• Sacks et al., 2006, GCB added snow
• Zobitz et al., 2008

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Parameter estimation

• MCMC is an optimizing method to minimize
  model-data mismatch
• Quasi-random walk through parameter space
  (Metropolis)
• Prior parameters distribution needed
• Start at many random places (Chains) in prior
  parameter space
• Move downhill to minima in model-data RMS by
  randomly changing a parameter from current value
  to a nearby value
• Avoid local minima by occasionally performing
  uphill moves in proportion to maximum
  likelihood of accepted point
• Use simulated annealing to tune parameter space
  exploration
• Pick best chain and continue space exploration
• Requires 500,000 model iterations (chain
  exploration, spin-up, sampling)
• End result best parameter set and confidence
  intervals (from all the iterations)
• NEE, Latent Heat Flux (LE), Sensible Heat Flux
  (H), soil moisture can all be used
• Nighttime NEE good measure of respiration, maybe
  H?
• Daytime NEE, LE good measures of photosynthesis
• SipNET is fast (lt10 ms year-1), so good for MCMC
  (4 hours for 7yr WLEF)
• Based on PNET ecosystem model
• Driven by climate, parameters and initial carbon
  pools
• Trivially parallelizable (needs to be done,
  though)

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Goldilocks effect
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2 years 7 years
1997
1998
1999
2000
2001
2002
2003
2004
2005
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Regional futures
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Regional futures
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Upscaling and Downscaling
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So many towers
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so much variability
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Simple comparisons
Desai et al, 2008, Ag For Met
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dont work
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We need to do better

• Lots of flux towers (how many?)
• Lots of cover types
• A very simple model
• Have to think about the tall tower flux, too
• What does it sample?

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• Multi-tower synthesis aggregation with large
  number of towers (12) in same climate space
• towers mapped to cover/age types
• parameter optimization with minimal 2 equation
  model

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Heterogeneous footprint
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Tall tower downscaling

• Wang et al., 2006

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Scaling evaluation

• Desai et al., 2008

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Scaling sensitivity
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Now we can wildly extrapolate

• Take 17 towers
• Fill the met data
• Use a simple model to estimate parameters for
  each tower using MCMC
• Apply parameters to other region meteorology data
• Scale to region by cover/age class

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Another simple(r) model

• No carbon pools
• GPP model driven by LAI, PAR, Air temp, VPD,
  Precip
• LAI model driven by GDD (leaf on) and soil temp
  (leaf off)
• 3 pool ER, driven by Soil temp and GPP
• 19 parameters, fix 3

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20 yr regional NEE

• Cover types
• Age structure
• Parameters
• Forcing for a lake organic carbon input model

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Regional scale evaluation
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Top down and bottom up
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IAV not modeled well
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Region Interannual variability
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Ricciuto et al.
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Ricciuto et al.
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IAV

• Does growing season start explain IAV?
• Can a very simple model be constructed to explain
  IAV?
• Hypothesis growing season length explains IAV
• Can we make a cost function more attuned to IAV?
• Hypothesis MCMC overfits to hourly data

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New cost function

• Original log likelihood computes sum of squared
  difference at hourly
• What if we also added monthly and annual squared
  differences to this likelihood?
• Have to scale these less frequent values

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Regional Succession
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History of land use
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Ecosystem Demography

• Moorcroft et al., 2001 Albani et al., 2006
  Desai et al., 2007
• Height and age structured statistical gap model
• Well suited to data assimilation of regional
  inventory data (e.g., USFS FIA)
• Use multiple FIA observation periods - estimate
  carbon pools by allometry, segregate by type,
  age, height classes
• Tune growth parameters until forest growth
  matches FIA growth

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Enough?
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What did we learn?

• Spatial prediction, scaling, parameterizing all
  benefit from data assimilation
• Interannual variability has interesting spatial
  attributes that are hard to model!
• Wetlands and land use history matter
• You cant build infinite towers, or even a
  sufficient number
• Use data assim to discover optimal design?
• Spatial covariate information needs a formal way
  to be used in data assimilation

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Where is your research headed?

• What questions do you have?
• Mechanisms, forcings, inference, evaluation,
  prediction, estimating error or uncertainty
• What kinds of data do you have, can get, can
  steal?
• Method-hopping
• A model can mean many things
• Data assimilation can be another tool in your
  toolbox to answer questions, discover new ones

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Data assimilation uses

• Not just limited to ecosystem carbon flux models
• E.g. estimating surface or boundary layer values
  (e.g., z0), advection, transpiration, data gaps,
  tracer transport
• Many kinds, for estimating state or parameters

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TOMORROW

• Lab - 6 hour tour
• Sipnet at Niwot Ridge
• Parameter estimation with MCMC
• Sipnet group projects
• Several ideas parameter sensitivity across
  sites, gap filling, prediction, regional
  extrapolation

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Enough!

• Time for a beer?