Regional Flux Estimation using the Ring of Towers

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Regional Flux Estimation using the Ring of Towers

• Scott Denning, Ken Davis, Scott Richardson,
  Marek Uliasz, Dusanka Zupanski, Kathy Corbin,
  Andrew Schuh, Nick Parazoo, Ian Baker, Tasha
  Miles, and Peter Rayner

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Regional Fluxes are Hard!

• Eddy covariance flux footprint is only a few
  hundred meters upwind
• Heterogeneity of fluxes too fine-grained to be
  captured, even by many flux towers
• Temporal variations hours to days
• Spatial variations in annual mean
• Some have tried to paint by numbers,
• measure flux in a few places and then apply
  everywhere else using remote sensing
• Annual source/sink isnt a result of vegetation
  type or LAI, but rather a complex mix of
  management history, soils, nutrients, topography
  not seen by RS

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Temporal Variations in NEE
NEE _at_ WLEF

• Flux is nothing like a constant value to be
  estimated!
• Coherent diurnal cycles?, but
• Day-to-day variability of factor of 2 due to
  passing weather disturbances

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Pesky Variability in the Real World
High-Frequency Variations in Space

• Managed forests, variable soils, suburban
  landscapes, urban parks
• Disturbance and succession fires, harvest, etc
• Crops Wheat vs Corn vs Soybeans
• Irrigation, fertilization, tillage practice
• Wisconsin (ChEAS) flux towers Attempt to
  upscale annual NEE over 40 km
• WLEF a1 WC a2 LC,
• but only if a2 lt 0
• decorrelation length scale is very small on
  annual NEE!

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What Causes Long-Term Model Bias?

• Parameters (maybe, but more likely to control
  variability than bias)
• State!
• Respiration soil carbon, coarse woody debris
• GPP stand age, nutrient availability, management
• Missing equations!
• Physiology is easier to model than site history
  and management

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Our Strategy

• Divide carbon balance into fast processes that
  we know how to model, and slow processes that
  we dont
• Use coupled model to simulate fluxes and
  resulting atmospheric CO2
• Measure real CO2 variations
• Figure out where the air has been
• Use mismatch between simulated and observed CO2
  to correct model biases for slow BGC
• GOAL Time-varying maps of sources/sinks
  consistent with observed vegetation, fluxes, and
  CO2 as well as process knowledge

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Observational Constraints

• Satellite imagery veg maps
• spatial and seasonal variations
• Flux towers
• Ecosystem physiology for different veg types
• GPP, Resp, stomates, drought response
• Atmospheric CO2
• Average source/sink over large upstream area

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Continental NEE and CO2

• Variance dominated by diurnal and seasonal
  cycles, but target is source/sink processes on
  interannual to decadal time scales
• Diurnal variations controlled locally by
  nocturnal stability (ecosystem resp is
  secondary!)
• Seasonal variations controlled hemispherically by
  phenology
• Synoptic variations controlled regionally, over
  scales of 100 - 1000 km. Target these.

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Seasonal and Synoptic Variations
Daily min CO2, 2004

• Strong coherent seasonal cycle across stations
• SGP shows earlier drawdown (winter wheat), then
  relaxes to hemispheric signal
• Synoptic variance of 10-20 ppm, strongest in
  summer
• Events can be traced across multiple sites
• What causes these huge coherent changes?

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Lateral Boundary Forcing

• Flask sampling shows N-S gradients of 5-10 ppm in
  CO2 over Atlantic and Pacific
• Synoptic waves (weather) drive quasi-periodic
  reversals in meridional (v) wind with 5 day
  frequency
• Expect synoptic variations of 5 ppm over North
  America, unrelated to NEE!
• Regional inversions must specify correct
  time-varying lateral boundary conditions

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Modeling Analysis Tools(alphabet soup)

• Ecosystem model (Simple Biosphere, SiB)
• Weather and atmospheric transport (Regional
  Atmospheric Modeling System, RAMS)
• Large-scale inflow (Parameterized Chemical
  Transport Model, PCTM)
• Airmass trajectories(Lagrangian Particle
  Dispersion Model, LPDM)
• Optimization procedure to estimate persistent
  model biases upstream (Maximum Likelihood
  Ensemble Filter, MLEF)

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Frontal Composites of Weather
Oklahoma
Wisconsin
Alberta
Frontal Locator Function

• The time at which magnitude of gradient of
  density (?) changes the most rapidly defines the
  trough (minimum GG ?, cold front) and ridge
  (maximum GG?)

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Frontal CO2 Climatology

• Multiple cold fronts averaged together (diurnal
  seasonal cycle removed)
• Some sites show frontal drop in CO2, some show
  frontal rise controls?
• Simulated shape and phase similar to observations
• What causes these?

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Deformational Flow
gradient strength

• shear
• deformation
• tracer field
• rotated by
• shear vorticity

• stretching
• deformation
• tracer field
• deformed
• by stretching

• Anomalies organize along cold front
• dC/dx 15ppm/3-5

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Ring of Towers

• inexpensive instruments deployed on six 75-m
  towers in 2004
• 200 km radius
• 1-minute data May-August

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Ring of Towers Datamid-day only June 9- July 5,
2004
5 ppm over 200 km u 10 m/s ?z 1500 m 13
?mol m-2 s-1
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Coupled Model SiB-RAMS-LPDM

• SiB3 Simple Biosphere Model Sellers et al.,
  1996
• Calculates the transfer of energy, water, and
  carbon between the atmosphere and the vegetated
  surface of the earth
• Photosynthesis model of Farquhar et al. 1980
  and stomatal model of Collatz et al 1991, 1992
• Ecosystem respiration depends on soil
  temperature, water, FPAR, with pool size chosen
  to enforce annual carbon balance
• Parameters specified from MODIS Vegetation
  imagery (1 km)
• RAMS5 Regional Atmospheric Modeling System
• Comprehensive mesoscale meteorological modeling
  system (Cotton et al., 2002), with telescoping,
  nested grid scheme
• Bulk cloud microphysics parameterization
• Meteorological fields initialized and lateral
  boundaries nudged using the NCEP mesoscale Eta
  analysis (?x 40 km)
• Deep cumulus after Grell (1995) Shallow cloud
  transports after Freitas (2001)
• Lateral CO2 boundary condition from global
  SiB-PCTM analysis
• LPDM - Lagrangian Particle Dispersion Model
• Backward-in time particle trajectories from
  receptors
• Driven from 15-minute RAMS output

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SiB-RAMS Simulated Net Ecosystem Exchange (NEE)
Average NEE
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Back-trajectory Analysis

• Release imaginary particles every hour from
  each tower receptor
• Trace them backward in time, upstream, using flow
  fields saved from RAMS
• Count up where particles have been that reached
  receptor at each obs time
• Shows quantitatively how much each upstream grid
  cell contributed to observed CO2
• Partial derivative of CO2 at each tower and time
  with respect to fluxes at each grid cell and time

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Treatment of Variations for Inversion

• Fine-scale variations (hourly, 20-km pixels) from
  weather forcing and satellite vegetation data as
  processed by forward model logic (SiB-RAMS)
• Multiplicative biases (caused by slow BGC
  thats not in the model) derived by from observed
  hourly CO2

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Maximum Likelihood Ensemble Filter (MLEF)

• Closely related to Ensemble Kalman Filter
• No adjoint, forward modeling of ensemble of
  perturbed states or parameters
• Propagate estimates of ?GPP(x,y) and ?Resp(x,y)
  along with (sample of) full covariance matrix
• Model learns about parameters, state variables,
  and covariance structure over each data
  assimilation cycle
• Explain on whiteboard?

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Pseudodata Ring Inversions

• 6 short towers plus 396 m at WLEF
• 2-hour averaged data (from 1 min)
• SiB-RAMS nest at ?x10 km
• LPDM on RAMS output, convolve with GPP and Resp,
  influence functions integrated for 10 days
• Add Gaussian noise to initial ?s and obs
• Estimate ?GPP and ?Resp for 30x30 grid boxes
  centered at WLEF at ?x20 km
• Nunk 30 x 30 x 2 1800

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Synthetic Ring Experiment MLEF

• Solve??for ?(x,y) on a 20-km grid
• Truth divided in half (E vs W)
• Noise added at different scales (8?x N vs 4?x S)
• Prior ? 0.75
• Prior smoothing 6?x solve

6 towers, obs every 2 hours
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MLEF Result after 70 Days

• Easily finds E-W diffs
• Some skill locating anomalies
• Better N-S diff in covariance than prior
• No flux over lakes, so no skill there!

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NACP Mid-Continent Intensive (2007)
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31 Towers in 2007
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Next Step Predict ?

• If we had a deterministic equation that predict
  the next ? from the current ???we could improve
  our estimates over time
• Fold ? into model state, not parameters
• Spatial covariance would be based on model
  physics rather than an assumed exponential
  decorrelation length
• Assimilation would progressively learn about
  both fluxes and covariance structure

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Coupled Modeling and Assimilation System

• Add C allocation and biogeochemistry to SiB-RAMS
• Parameterize using eddy covariance and satellite
  data
• Optimize model state variables, not parameters or
  unpredictable biases
• Propagate flux covariance using BGC instead of a
  persistence forecast