BRINGING BIOGEOCHEMICAL MODELS and DATA TOGETHER through data assimilation

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BRINGING BIOGEOCHEMICALMODELS and DATA
TOGETHER(through data assimilation)
Marjorie Friedrichs Virginia Institute of Marine
Science College of William and Mary
Acknowledgments Larry Anderson, Rob Armstrong,
Fei Chai, Jim Christian, Scott Doney, John Dunne,
Jeff Dusenberry, Masahiko Fujii, Raleigh Hood,
Keith Moore, Dennis McGillicuddy, Markus
Schartau,Yvette Spitz, Jerry Wiggert, Raghu
Murtugudde, Vince Saba, Wayne Luo, Hugh Ducklow
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Hofmann and the USECoS team, Oceanography, March
2008
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Hofmann and the USECoS team, Oceanography, March
2008
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Hofmann and the USECoS team, Oceanography, March
2008
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Hofmann and the USECoS team, Oceanography, March
2008
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Hofmann and the USECoS team, Oceanography, March
2008
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Biogeochemical Data Assimilation
DA can be used to

• Combine data collected on different scales
• Improve model skill Gain information on poorly
  known parameters necessary for bgc models (
  uncertainties)
• Assess/compare model skill Identify which model
  structures and/or formulations best fit
  available data
• Computationally intensive
• Requires knowledge of data/model uncertainties

Additional issues
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Outline

• How much complexity is required for a given
  model?
• Which model formulations produce the greatest
  skill?
• What are the effects of assimilating different
  satellite products?
• What can PP estimates derived from assimilative
  models tell us?

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Outline

• How much complexity is required for a given
  model?
• Which model formulations produce the greatest
  skill?
• What are the effects of assimilating different
  satellite products?
• What can PP estimates derived from assimilative
  (SeaWiFS in situ) models tell us?

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Complexity advantage or liability?
NEMURO model (Kishi et al., 2004)
P
grazing
production
Z
N
death
death
remin
D
excretion
Goal To objectively compare the skill of
ecosystem models characterized by varying levels
of complexity
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How can we objectively compare model skill?

• Provide a framework for quantitatively comparing
  different ecosystem models, which includes
• 1-D (vertical) numerical framework
• Physical forcing fields
• from 3-D circulation model or data
• T, MLD, light, vertical velocity, kz,
  horiz advection
• Biogeochemical data
• Assimilation/optimization framework

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Methods Ecosystem Model Descriptions

• Simplest Models (single P compartments)
• Model 1 N, P, Z, D (McCreary)
• Model 2 N, P, Z, D, DON (Hood)
• Model 3 N, P, Z, D, chl, T (CCCMA/Christian)
• Model 4 N, P, Z, D, chl, NH4 (Anderson/McGillicu
  ddy)
• Model 5 N, P, Z, D, chl, NH4, DOM, T, C
  (Schartau)

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Methods Ecosystem Model Descriptions

• More Complex Models (multiple P compartments)
• Model 6 N, NH4, Fe, 2P, 2Z, 2D, chl (Christian)
• Model 7 N, NH4, Fe, 2P, 2Z, 2D, chl (Wiggert)
• Model 8 N, NH4, Si, 2P, 2Z, 2D (Chai)
• Model 9 N, 2P, 4Z, D, DOM, B (Laws)
• Model 10 N, NH4, Si, 2P, 3Z, 2D, chl, DOM
  (Fujii)
• Model 11 N, PO, NH4, Si, Fe, 3P, 0Z, D, chl, DOM
  (Dunne)
• Model 12 N, PO, NH4, Si, Fe, 3P, Z, 2D, chl, DOM
  (Dusenberry)

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Biogeochemical data
Cruise observations nitrate chlorophyll pro
duction Sediment trap 1 year time series
Arabian Sea
Equatorial Pacific
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Model-data comparison
cost function measure of model-data misfit
data
sites types Nij
cost function ? ? ? Wij (Xdat-Xmod)2
i j n
N number of observations W weight
(inversely proportional to square of
uncertainty) Xdat Data (PP, chl, NO3, or
export) Xmod Model equivalents of the data
Normalize model cost to cost of the mean of the
data Means (over depth and time) are computed
for each type of data Compute cost assuming Xmod
equals mean at all times and depths
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Pre-assimilation skill comparison
Worse than mean
Better than mean
Without data assimilation, only one model does
better than meanGeneral improvement with
increasing complexityAre we comparing model
structure, or degree of tuning?
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Variational Adjoint Method
Nonlinear weighted least squares parameter
optimization method Minimize cost function by
systematically and iteratively adjusting values
of a subset of model parameters Key selection
of appropriate subset of model parameters 1.
sensitivity of cost function 2. parameter
correlations Three to four parameters can be
optimized
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Variational Adjoint Method
Expt. 1 Expt. 2 Expt. 3
AS EP data data AS
EP params params AS
EP output output
Individual cost Simultaneous cost
Cross validation cost
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Experiment 1
Expt. 1 Expt. 2 Expt. 3
AS EP data data AS
EP params params AS
EP output output
Individual cost Simultaneous cost
Cross validation cost
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Expt. 1 Individual Assimilation
No Assim
Indiv Assim
Most models do better than mean of
observationsNo improvement with additional
complexity
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Experiment 2
Expt. 1 Expt. 2 Expt. 3
AS EP data data AS
EP params params AS
EP output output
Individual cost Simultaneous cost
Cross validation cost
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Expt. 2 Simultaneous Assimilation
Indiv Assim
Simul Assim
More complex (multi-P) models can fit data at
both locations simultaneously better than
simpler models
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Experiment 3
Expt. 1 Expt. 2 Expt. 3
AS EP data data AS
EP params params AS
EP output output
Individual cost Simultaneous cost
Cross validation cost
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Expt. 3 Cross Validation
Worse than mean
Better than mean
Only five models do better than meanMore complex
(multi-P) models do better in cross validation,
i.e. are more portable
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Outline

• How much complexity is required for a given
  model?
• Which model formulations produce the greatest
  skill?
• What are the effects of assimilating different
  satellite products?
• What can PP estimates derived from assimilative
  models tell us?

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Community comparison exercise
Advantages Large number of widely varying
participating models Useful to assess the
relative skill of models currently in use in
the community Group dynamics large of people
dealing with same issues regarding model skill
assessment Disadvantages Participating models
vary in many different ways Difficult to draw
conclusions about the relative skill of
specific model structures/parameterizations Ne
xt approach Systematically change individual
model structures
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Which changes in parameterizations affect model
skill?
Cross Validation Results
Model 6
No Fe
1 PZD
No NH4
Z2 mort.
No Nitrif.
Mean Model
Const ?,Pmax
NH4 inhib.
No T dep.
Const Cchl
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Outline

• How much complexity is required for a given
  model?
• Which model formulations produce the greatest
  skill?
• What are the effects of assimilating different
  satellite products (POC vs. chl)?
• What can PP estimates derived from assimilative
  models tell us?

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Identical Twin Experiment
large phytoplankton mortality rate (initial
1.0 actual 2.0)
normalized parameter value
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Zl grazing
normalized parameter value
Zs mortality
satellite-derived POC constrains model better
than chlorophyll
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Outline

• How much complexity is required for a given
  model?
• Which model formulations produce the greatest
  skill?
• What are the effects of assimilating different
  satellite products?
• What can PP estimates derived from assimilative
  models tell us?

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Microbial dynamics model Luo Ducklow
Equatorial Pacific Arabian Sea Hawaii Ocean
Time- series (HOT)
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HOT PP
2001 assimilation
2001 mean
Luo assimilates in situ chl, PP, NO3, export
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HOT PP
2001 assimilation
2001 mean
Luo assimilates 2001 in situ chl, PP, NO3, export
SeaWiFS chl
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Summary

• DA techniques can be used to quantitatively
• Compare the skill of ecosystem models
  characterized by varying levels of complexity
• Simple models can fit data well at individual
  sites
• Multiple-P models are best able to fit data
  simultaneously at both sites if tuned to one
  site, may perform well in another ecosystem as
  well
• Assess the skill of different model structures
  and formulations

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Summary (cont.)

• DA techniques can be used to
• Improve productivity estimates
• Highlight climate-related ecosystem changes
• Compare the effects of assimilating various
  satellite products
• Satellite POC data constrained the models much
  better than chlorophyll
• New satellite products may be better able to
  constrain coupled biogeochemical models!