Spatial Processes and Landatmosphere Flux

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Spatial Processes andLand-atmosphere Flux

• Constraining regional
• ecosystem models with
• flux tower data assimilation

Flux Measurements and Advanced Modeling, 23 July
2009 CU Mountain Research Station, Ned,
Colorado Ankur R 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 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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Discrepancies
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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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For the concrete minded

• MCMC is an method to minimize model-data mismatch
• Quasi-random walk through parameter space
  (Metropolis-Hastings)
• Prior parameters distribution needed
• Start at many random places (chains)
• 1. Randomly change parameter from current to a
  nearby value
• Use simulated annealing to tune how far you move
  from current spot
• 2. Move downhill to maximize a likelihood in
  model-data error
• Avoid local minima by occasionally performing
  uphill moves in proportion to maximum
  likelihood of accepted point
• 3. End chain when accepted reaches a threshold,
  or back to 1
• 4. Pick best chain and continue space exploration
• Save parameter sets after a burn-in period
• End result best parameter set and confidence
  intervals
• Any sort of observations could be used, but need
  a fast model and many iterations

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Some case studies

• Interannual variability
• Regional scaling

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Interannual Variability
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Ricciuto et al.
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Ricciuto et al.
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Regional coherence
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IAV

• Does growing season timing 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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Simple model

• Twice daily model, annually resetting pools
• Driven by PAR, Air and Soil T, VPD
• LUE based GPP model f(PAR,T,VPD)
• Three respiration pools f(Air T, Soil T, GPP)
• Model 1. NOLEAF
• Constant leaf on and leaf off days
• Model 2. LEAF (Phenology)
• Sigmoidal Threshold GDD (base 10) function for
  leaf on
• Sigmoidal Threshold Daily Mean Soil Temp function
  for leaf off
• 17 parameters, 3 are fixed
• Output NEE, ER, GPP, LAI

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Cost function

• Original log likelihood computes sum of squared
  difference at hourly
• Maybe it overfits hourly data at expense of
  slower variations?
• What if we also added some information about
  longer time scale differences to this likelihood?

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New cost function
HALF-DAILY
IAV
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Experiment Design

• HN Half-daily cost function, No-Leaf model
• HL Half-daily cost function, Leaf model
• IN Interannual cost function, No-Leaf model
• IL Interannual cost function, Leaf model
• Same number of parameters in each, so no need to
  compare BIC, AIC, or DIC sizes

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Half-Daily
HN
HL
IL
IN
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Interannual
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Parameters
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Controls
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Future Idea

• Cost functions for multiple kinds of data with
  differing time steps

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Regional Scaling
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Our tower is bigger
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Is this the regional flux?
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Not quite
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Lots of variability
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So many towers
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Can we use these data?
Desai et al, 2008, Ag For Met
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Regional flux

• 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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Heterogeneous footprint
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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 simple model

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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 regional climate data
• Scale to region by cover/age class

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Hardwood
Conifer
Shrub
Mixed Forest
Crop
Grassland
Herbaceous wetland
Forested wetland
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Scaling evaluation

• Black upscaled towers, Gray forest inventory
  model, Triangle inverse model, Square
  boundary layer budget

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Regional IAV
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Controls on regional IAV
Water Table
CO2
Autumn SoilT
Spring PAR
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Building a better model
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Back to the tall tower

• Wang et al., 2006

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Towers vs Tower!
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Future Idea

• Create a joint cost function for multiple site
  assimilation

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Enough?
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What did we learn?

• Spatial prediction, scaling, parameterization all
  benefit from data assimilation
• Interannual variability has interesting spatial
  attributes that are hard to model
• You cant build infinite towers, or even a
  sufficient number
• Use data assim. to discover optimal design?
• Spatial covariate and uncertainty information
  needs to be considered in data assimilation
• "The only thing that makes life possible is
  permanent, intolerable uncertainty not knowing
  what comes next. -- Ursula K. LeGuin

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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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Todays lab

• Sipnet at flux towers
• Parameter estimation with MCMC
• Group projects

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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
• Zobitz et al., 2008
• Moore et al., 2008
• Hu et al., 2009

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Thanks

• Ankur R Desai
• desai_at_aos.wisc.edu
• http//flux.aos.wisc.edu
• Position available in Desai lab Rocky Mountain
  carbon cycle post-doc, see website for more info