Spatial Processes and Land-atmosphere Flux

Spatial Processes andSpatial Processes andLand-atmosphere FluxLand-atmosphere Flux

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

assimilationassimilation

Flux Measurements and Advanced Modeling, 22 July 2008CU Mountain Research Station, “Ned”, Colorado

Ankur DesaiAtmospheric & Oceanic Sciences, University of Wisconsin-Madison

Let’s get spacey…

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And regional

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

Why regional?

• NEP (=-NEE) at 13 sites

• Stand age matters

• Ecosystem type matters

• Is interannual variability coherent?

• Are we sampling sufficient land cover types”?

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

Why data assimilation?

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

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

Back to those stats…

[A|B] = [AB] / [B]

[P|D] = ( [D|P] [P] ) / [D]

(parameters given data) = [ (data given parameters)× (parameters) ] / (data)

Posterior = (Likelihood x Prior) / Normalizing Constraint

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

Regional Prediction

Our tower is bigger…

Is there a prediction signal?

Sipnet

• A “simplified” model of ecosystem carbon / water and land-atmosphere interaction– Minimal number of

parameters– Driven by meteorological

forcing

• Still has >60 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 (<10 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)

Goldilocks effect…

2 years = 7 years

1997 1998 1999 2000 2001 2002 2003 2004 2005

Regional futures

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Regional futures

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Upscaling and Downscaling

So many towers…

…so much variability

Simple comparisons…

Desai et al, 2008, Ag For Met

…don’t work

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?

• 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

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

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

Top down and bottom up

IAV not modeled well

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Region Interannual variability

Ricciuto et al.

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

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

History of land use

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?

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 can’t 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

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

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

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

Enough!

• Time for a beer?