data assimilation in marko scholze. strictly speaking, there are so far no da activities in quest,...
DESCRIPTION
A Carbon Cycle Data Assimilation System (CCDAS) 2 FastOpt 3 1 Wolfgang Knorr and Marko Scholze in collaboration with Peter Rayner 1, Heinrich Widmann 2, Thomas Kaminski 3 & Ralf Giering 3TRANSCRIPT
Data assimilation in
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Marko Scholze
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)
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
A Carbon Cycle Data Assimilation System (CCDAS)
2FastOpt
31
Wolfgang Knorr and Marko Scholze
in collaboration withPeter Rayner1, Heinrich Widmann2, Thomas Kaminski3
& Ralf Giering3
Carbon Cycle Data Assimilation System (CCDAS) current form
BETHY+TM2only Photosynthesis,
Energy&Carbon Balance+Adjoint and Hessian code
Globalview CO2
+ Uncert.
Optimised Parameters + Uncert.
Diagnostics + Uncert.
Assimilation Step 2 (calibration) + Diagnostic Step
Background CO2 fluxes:ocean: Takahashi et al. (1999), LeQuere et al. (2000)emissions: Marland et al. (2001), Andres et al. (1996)
land use: Houghton et al. (1990)
veg. Index (AVHRR) + Uncert.
full BETHY
PhenologyHydrology
Assimilation Step1
Parameter Priors + Uncert.
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
€
J(r p ) =1
2r p −
r p 0[ ]
T Cp 0
-1 r p −
r p 0[ ] + 1
2
r M (
r p ) −
r D [ ]
T CD
-1 r
M (r p ) −
r D [ ]
covariance of uncertainty in measurements + modelcovariance of uncertainty
in priors for parameters
priors for parameters
observed concentrations
• Terrestrial biosphere model BETHY (Knorr 97)delivers CO2 fluxes to atmosphere
• Uncertainty in process parameters from laboratory measurements
• Global atmospheric network provides additional constraint
Gradient of J(p) providessearch directions for
minimisation.Second Derivative (Hessian)
of J(p) yields curvature of J,provides estimateduncertainty in popt
Figure taken from Tarantola '87
J(p)Minimisation and Parameter-Uncertainties
Space of p (model parameters)
€
Cp ≈ ∂ 2J(popt)∂pi, j
2
⎧ ⎨ ⎩
⎫ ⎬ ⎭
−1
Optimisation(BFGS+ adjoint gradient)
Posterior uncertainties on parameters
f ir st guess opt im ized pr ior unc. opt . unc. Vm ( Tr Ev) Vm ( EvCn) Vm ( C3G r) Vm ( Cr op)
µmol/m 2s µmol/m 2s % %Vm(TrEv) 60.0 43.2 20.0 10.5 0.28 0.02 -0.02 0.05Vm(EvCn) 29.0 32.6 20.0 16.2 0.02 0.65 -0.10 0.08Vm(C3Gr) 42.0 18.0 20.0 16.9 -0.02 -0.10 0.71 -0.31Vm(Crop) 117.0 45.4 20.0 17.8 0.05 0.08 -0.31 0.80
error covarianceexamples:
€
Cm ≈∂2J popt( )
∂pi, j2
⎧ ⎨ ⎪
⎩ ⎪
⎫ ⎬ ⎪
⎭ ⎪
−1Use inverse Hessian of objective function to
approximate posterior uncertainties
Relative reduction of uncertainties
Observations resolve about 10-15 directions in parameter space
CCDAS diagnostic stepGlobal fluxes and their uncertainties
• Examples for diagnostics:• Long term mean fluxes to atmosphere
(gC/m2/year) and uncertainties• Regional means
Extension of concept1. More processes/components
• Have tested a version extended by an extremely simplified form of an ocean model:flux(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 model:include state as unknown with prior uncertainty estimated from model error
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 ...
Extension of concept2. Adding more observations
Flux Data
•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), ...
Inventories
AtmosphericIsotope Ratios
Atmospheric Concentrations (could also be column integrated)
Earth-System Predictions
• to build an adequate Earth System Model that is computationally efficient QUEST’s 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
• 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).
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 uncertainty
What 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 ...)
BETHY(Biosphere Energy-Transfer-Hydrology
Scheme)• 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)<1: source>1: sink
t=1h
t=1h
t=1day
lat, lon = 2 deg
Seasonal cycleBarrow Niwot Ridge
observed seasonal cycleoptimised modeled seasonal cycle
Parameters I• 3 PFT specific parameters (Jmax, Jmax/Vmax and b)• 18 global parameters• 57 parameters in all plus 1 initial value (offset)
Param Initial Predicted Prior unc. (%) Unc. Reduction (%)
fautleafc-costQ10 (slow)
(fast)
0.41.251.51.5
0.241.271.351.62
2.50.57075
3917278
(TrEv) (TrDec) (TmpDec) (EvCn) (DecCn) (C4Gr) (Crop)
1.01.01.01.01.01.01.0
1.440.352.480.920.731.563.36
25252525252525
7895629591901
Some values of global fluxes
1980-2000 (prior)
1980-2000
1980-1990
1990-2000
GPPGrowth resp.Maint. resp.NPP
135.723.544.0468.18
134.822.3572.740.55
134.322.3172.1340.63
135.322.3973.2840.46
Fast soil resp.Slow soil resp.NEP
53.8314.46-0.11
27.410.692.453
27.610.712.318
27.2110.672.587
Value Gt C/yr
Global Growth Rate
Calculated as:
observed growth rateoptimised modeled growth rate
Atmospheric CO2 growth rate
MLOSPOGLOB CCC 75.025.0 +=
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
Including the oceanSeasonality at MLOGlobal land flux
Observations
Low-res incl. ocean basis functions Low resolution model
High resolution standard model