Data assimilation in

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Data assimilation in
Marko Scholze
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Strictly speaking, there are so far no DA
activities in QUEST, but

• CCDAS (as part of core team activities)
• CPDAS and C4DAS (in the planning stage)

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A Carbon Cycle Data Assimilation System (CCDAS)
Wolfgang Knorr and Marko Scholze in
collaboration with Peter Rayner1, Heinrich
Widmann2, Thomas Kaminski3 Ralf Giering3
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Carbon Cycle Data Assimilation System (CCDAS)
current form
Assimilation Step 2 (calibration) Diagnostic
Step
Assimilation Step1
veg. Index (AVHRR) Uncert.
Parameter Priors Uncert.
Globalview CO2 Uncert.
BETHYTM2 only Photosynthesis, EnergyCarbon
Balance Adjoint and Hessian code
full BETHY
Background CO2 fluxesocean Takahashi et al.
(1999), LeQuere et al. (2000)emissions Marland
et al. (2001), Andres et al. (1996)land use
Houghton et al. (1990)
Phenology Hydrology
Optimised Parameters Uncert.
Diagnostics Uncert.
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CCDAS calibration step

• Terrestrial biosphere model BETHY (Knorr
  97)delivers CO2 fluxes to atmosphere
• Uncertainty in process parameters from laboratory
  measurements
• Global atmospheric network provides additional
  constraint

• Terrestrial biosphere model BETHY (Knorr
  97)delivers CO2 fluxes to atmosphere
• Uncertainty in process parameters from laboratory
  measurements
• Global atmospheric network provides additional
  constraint

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Minimisation and Parameter-Uncertainties
Figure taken from Tarantola '87
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Optimisation(BFGS adjoint gradient)
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Posterior uncertainties on parameters
Use inverse Hessian of objective function to
approximate posterior uncertainties
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CCDAS diagnostic stepGlobal fluxes and their
uncertainties

• Examples for diagnostics
• Long term mean fluxes to atmosphere (gC/m2/year)
  and uncertainties
• Regional means

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Extension of concept1. More processes/components

• Have tested a version extended by an extremely
  simplified form of an ocean modelflux(x,t) ?
  coefficient(i) pattern(i,x,t)
• Optimising coefficients for biosphere
  patternswould allow the optimisation to
  compensate for errors (e.g. missing processes) in
  biosphere model (weak constraint 4DVar, see
  ,e.g., Zupanski (1993))
• But it is always preferable to include a process
  model, e.g for fire, marine biogeochemistry
• Can also extend to weak constraint formulation
  for state of biosphere modelinclude state as
  unknown with prior uncertainty estimated from
  model error

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Extension of concept2. Adding more observations
Atmospheric Concentrations (could also be column
integrated)
J(p) ½ (p-p0)T Cp-1(p-p0) ½
(cmod(p)- cobs) T Cc-1(cmod(p)- cobs)
½ (fmod(p)- fobs)T Cf-1(fmod(p)- fobs)
½ (Imod(p)- Iobs)T
CI-1(Imod(p)- Iobs) ½ (Rmod(p)-
Robs)T CR-1(Rmod(p)- Robs) etc ...
Flux Data
Inventories
AtmosphericIsotope Ratios

• Can add further constraints on any quantity that
  can be extracted from the model (possibly after
  extensions/modifications of model)
• Covariance matrices are crucial Determine
  relative weights!
• Uses Gaussian assumption can also use logarithm
  of quantity (lognormal distribution), ...

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Earth-System Predictions

• to build an adequate Earth System Model that is
  computationally efficient ? QUESTs Earth System
  Modelling Strategy
• to develop a tool that allows the assimilation of
  observations of various kinds that relate to the
  various Earth System components, such as climate
  variables, atmospheric tracers, vegetation, ice
  extent, etc. ? CPDAS C4DAS

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• Climate Prediction Data Assimilation System
  (CPDAS) Assimilate climate variables of the past
  100 years to constrain predictions of the next
  100 years, including error bars.
• Coupled Climate C-Cycle Data Assimilation System
  (C4DAS) Assimilate carbon cycle observations of
  the past 20 (flask network) and 100 years (ice
  core data), to constrain coupled climate-carbon
  cycle predictions of the next 100 years,
  including error bars.
• Step-wise approach, building on and enhancing
  existing activities such as CCDAS, C4MIP,
  QUEST-ESM (FAMOUS), GENIEfy, QUMP and possibly
  Paleo-QUMP.
• Using the adjoint (and Hessian, relying on
  automatic differentiation techniques) which
  allows for the first time to optimize
  parameters comprehensively in a climate or earth
  system model before making climate predictions.
• Scoping study to start next month (pot. users
  meeting).

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CCDAS methodological aspects

• remarks
• CCDAS tests a given combination of observational
  data plus model formulation with uncertain
  parameters
• CCDAS delivers optimal parameters,
  diagnostics/prognostics, and their a posteriori
  uncertainties
• all derivative code (adjoint, Hessian, Jacobian)
  generated automatically from model code by
  compiler tool TAF quick updates of CCDAS after
  change of model formulation
• derivative code is highly efficient
• CCDAS posterior flux field consistent with
  trajectory of process model rather than linear
  combination of prescribed flux patterns (as
  transport inversion)
• CCDAS includes a prognostic mode (unlike
  transport inversion)
• some of the difficulties/problems
• Prognostic uncertainty (error bars) only reflect
  parameter uncertaintyWhat about uncertainty in
  model formulation, driving fields?
• Uncertainty propagation only for means and
  covariances (specific PDFs), and only with a
  linearised model
• Result depends on a priori information on
  parameters
• Result depends on a single model
• Two step assimilation procedure sub optimal
• lots of other technical issues (bounds on
  parameters, driving data, Eigenvalues of Hessian
  ...)

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BETHY(Biosphere Energy-Transfer-Hydrology Scheme)
?lat, ?lon 2 deg

• GPP
• C3 photosynthesis Farquhar et al. (1980)
• C4 photosynthesis Collatz et al. (1992)
• stomata Knorr (1997)
• Plant respiration
• maintenance resp. f(Nleaf, T) Farquhar, Ryan
  (1991)
• growth resp. NPP Ryan (1991)
• Soil respiration
• fast/slow pool resp., temperature (Q10
  formulation) and soil moisture
  dependant
• Carbon balance
• average NPP b average soil resp. (at each grid
  point)

?t1h
?t1h
?t1day
blt1 source bgt1 sink
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Seasonal cycle
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Parameters I

• 3 PFT specific parameters (Jmax, Jmax/Vmax and b)
• 18 global parameters
• 57 parameters in all plus 1 initial value
  (offset)

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Some values of global fluxes
Value Gt C/yr
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Global Growth Rate
Atmospheric CO2 growth rate
Calculated as
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Including the ocean

• A 1 GtC/month pulse lasting for three months is
  used as a basis function for the optimisation
• Oceans are divided into the 11 TransCom-3 regions
• That means 11 regions 12 months 21 yr / 3
  months 924 additional parameters
• Test case
• all 924 parameters have a prior of 0. (assuming
  that our background ocean flux is correct)
• each pulse has an uncertainty of 0.1 GtC/month
  giving an annual uncertainty of 2 GtC for the
  total ocean flux

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Including the ocean
High resolution standard model
Low resolution model
Low-res incl. ocean basis functions