Transcript Document

Data assimilation in
Marko Scholze
Quic kT ime™ and a
T IFF (Uncompres sed) decompres sor
are needed to s ee this pict ure.
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)
Quic kT ime™ and a
T IFF (Uncompres sed) decompres sor
are needed to s ee this pict ure.
A Carbon Cycle Data Assimilation System
(CCDAS)
Wolfgang Knorr and Marko Scholze
in collaboration with
Peter Rayner1, Heinrich Widmann2, Thomas Kaminski3
& Ralf Giering3
1
2
3
FastOpt
Carbon Cycle Data Assimilation System
(CCDAS) current form
Assimilation Step1
veg. Index (AVHRR)
+ Uncert.
full BETHY
Assimilation Step 2 (calibration) + Diagnostic Step
Parameter Priors
+ Uncert.
BETHY+TM2
only Photosynthesis,
Energy&Carbon Balance
+Adjoint and Hessian code
Globalview CO2
+ Uncert.
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)
Phenology
Hydrology
Optimised Parameters
+ Uncert.
Diagnostics
+ 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
covariance of uncertainty
in priors for parameters
covariance of uncertainty in
measurements + model
priors for parameters
observed concentrations

T
1
1
-1
J (p )  p  p 0  C p 0 p  p 0  M (p )  D
2
2

T

C-1D M (p )  D

Minimisation and Parameter-Uncertainties
J(p)
Gradient of J(p) provides
search directions for
minimisation.
Second Derivative (Hessian)
of J(p)
yields curvature of J,
provides estimated
uncertainty in popt
1
 2 J( popt ) 
Cp  

2
 pi, j 
Figure taken from Tarantola '87
Space of p (model parameters)
Optimisation
(BFGS+ adjoint gradient)
Posterior uncertainties on
parameters
1
2

 J popt 

Cm   2 

 pi, j 

Use inverse Hessian of objective function to
approximate posterior uncertainties
examples:
Vm(TrEv)
Vm(EvCn)
Vm(C3Gr)
Vm(Crop)
first guess
µmol/m
2
s
60.0
29.0
42.0
117.0
optimized
µmol/m
Relative reduction of uncertainties
2
s
43.2
32.6
18.0
45.4
prior unc.
opt.unc.
%
%
20.0
20.0
20.0
20.0
Vm(TrEv)
10.5
16.2
16.9
17.8
0.28
0.02
-0.02
0.05
Vm(EvCn)
Vm(C3Gr)
error covariance
0.02
0.65
-0.10
0.08
-0.02
-0.10
0.71
-0.31

Observations resolve about 10-15 directions in parameter space
Vm(Crop)
0.05
0.08
-0.31
0.80
CCDAS diagnostic step
Global fluxes and their uncertainties
•
Examples for diagnostics:
•
Long term mean fluxes to atmosphere
(gC/m2/year) and uncertainties
•
Regional means
Extension of concept
1. 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 patterns
would 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
Extension of concept
2. 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)
Flux Data
+ 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 ...
Inventories
Atmospheric
Isotope 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), ...
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)
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
moisture dependant
Carbon balance:
average NPP = b average soil resp. (at each grid point)
t=1h
t=1h
t=1day
soil
b<1: source
b>1: sink
Seasonal cycle
Barrow
Niwot Ridge
observed seasonal cycle
optimised 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 (%)
fautleaf
c-cost
Q10 (slow)
t (fast)
0.4
1.25
1.5
1.5
0.24
1.27
1.35
1.62
2.5
0.5
70
75
39
1
72
78
b (TrEv)
b (TrDec)
b (TmpDec)
b (EvCn)
b (DecCn)
b (C4Gr)
b (Crop)
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.44
0.35
2.48
0.92
0.73
1.56
3.36
25
25
25
25
25
25
25
78
95
62
95
91
90
1
Some values of global fluxes
Value Gt C/yr
1980-2000
(prior)
1980-2000
19801990
19902000
GPP
Growth resp.
Maint. resp.
NPP
135.7
23.5
44.04
68.18
134.8
22.35
72.7
40.55
134.3
22.31
72.13
40.63
135.3
22.39
73.28
40.46
Fast soil resp.
Slow soil resp.
NEP
53.83
14.46
-0.11
27.4
10.69
2.453
27.6
10.71
2.318
27.21
10.67
2.587
Global Growth Rate
Atmospheric CO2 growth rate
Calculated as:
C GLO B  0.25C SPO  0.75C MLO
observed growth rate
optimised modeled growth rate
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 ocean
Global land flux
Seasonality at MLO
Observations
High resolution standard model
Low resolution model
Low-res incl. ocean basis functions