Post on 04-Jan-2016
description
FastOpt
A prototype Global Carbon Cycle Data Assimilation
System (CCDAS)
Marko Scholze1, Wolfgang Knorr2, Peter Rayner3,Thomas Kaminski4, Ralf Giering4
1 2 3 4
FastOpt
Overview
• Top-down vs. bottom-up
• Gradient method and optimisation
• Results: Optimal fluxes
• Uncertainties in parameters + results
• Uncertainties in fluxes + results
• Possible assimilation of flux data
• Conclusions and Outlook
FastOpt
Top-down / Bottom-upatm. CO2 data
inverseatmospheric
transportmodelling
net CO2fluxes at the
surface
processmodel
climate and other driving data
FastOpt
Carbon Cycle Data Assimilation
Biosphere Model: BETHY
Atmospheric Transport Model: TM2
Misfit to Observations
Parameters: 58
Fluxes: 800,000
Station Conc. 6,500
Misfit 1 Forward modelling:
Parameters –> Misfit
Adjoint or Tangent linear model:
Misfit / ∂ Parameters
parameter optimization
FastOpt
Figure taken from Tarantola '87
Space of m (model parameters)
First derivative (Gradient) of J(m) w.r.t. m (model parameters) :
–∂J(m)/∂m yields direction of steepest
descent
Gradient Method
Cost Function J(m)
FastOpt
Carbon Cycle Data Assimilation System (CCDAS)
CCDAS Step 2BETHY+TM2
only Photosynthesis, Energy&Carbon Balance
CO2
+ Uncert.
Optimized Params + Uncert.
Diagnostics + Uncert.
veg. indexsatellite +Uncert.
CCDAS Step 1full BETHY
PhenologyHydrology
AssimilatedPrescribedAssimilated
BackgroundCO2 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)
FastOpt
BETHY(Biosphere Energy-Transfer-Hydrology Scheme)
• GPP:
C3 photosynthesis – Farquhar et al. (1980)
C4 photosynthesis – Collatz et al. (1992)
stomata – Knorr (1997)
• Raut:
maintenance respiration = f(Nleaf, T) – Farquhar, Ryan (1991)
growth respiration ~ NPP – Ryan (1991)
• Rhet:
fast/slow pool resp. = wQ10 T/10 C fast/slow / fast/slow
slow –> infin.
average NPP = average Rhet (at each grid point)
<1: source>1: sink
t=1h
t=1h
t=1day
lat, lon = 2 deg
FastOpt
Optimisation
FastOpt
Optimised fluxes (1)
global fluxes
Major El Niño events
Major La Niña event
Post Pinatubo Period
FastOpt
Optimised fluxes (2)normalized CO2 flux and ENSO
ENSO and terr. biosph. CO2:correlation seems strong
lag correlation(low-pass filtered)
correlation between Niño-3 SST anomaly and net CO2 flux shows maximum at 4 months lag, forboth El Niño and La Niña states
FastOpt
net CO2 flux to atm.gC / (m2 month)
during El Niño (>+1)
Optimised fluxes (3)
lagged correlationat 99% significance
-0.8 -0.4 0 0.4 0.8
flux sites?
FastOpt
Figure taken from Tarantola '87
J(x)
Second Derivative (Hessian) of J(m):
∂2J(m)/∂m2 yields curvature of J,provides estimateduncertainty in m
opt
Error Covariances in Parameters
Space of m (model parameters)
FastOpt
Error Covariances in Parameters
first guess optimized prior unc. opt.unc. Vm(TrEv) Vm(EvCn) Vm(C3Gr) Vm(Crop)
µmol/m2s µmol/m2s % %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:
Cost function (misift):
J(
m ) 1
2[m
m 0]Cm0-1 [
m
m 0] 1
2[y (
m )
y 0]Cy-1 [
y (
m )
y 0 ]
model diagnostics
error covariance matrixof measurements
measurements
assumedmodel parameters
a priori covariance matrixof parameter + model errora priori
parameter values
Error covariance of parametersafter optimisation:
Cm 2J
mi, j2
1
= inverse Hessian
FastOpt
Relative Error Reduction
FastOpt
Error Covariances in Diagnostics
Error covariance of diagnostics, y,after optimisation (e.g. CO2 fluxes):
Cy(m opt)
yi(m opt)
m j
Cm
y i(m opt)
m j
T
error covarianceof parameters
adjoint ortangent linear
model
FastOpt
Regional Net Carbon Balance and Uncertainties
FastOpt
Comparison shows impact of a (pseudo) flux measurement in the broadleaf evergreen biome on Q10 estimated by an inversion of SDBM:
Upper panel: only concentration data
Lower panel: concentration data +pseudo flux measurement(mean: as predicted sigma: 10gC/m^2/year)
Details:Kaminski et al., GBC, 2001
a posteriori mean/uncertaintiesa priori mean/uncertainties
FastOpt
• CCDAS with 58 parameters can already fit 20 years
of CO2 concentration data
• Sizeable reduction of uncertainty for ~13 parameters
• terr. biosphere response to climate fluctuations
dominated by ENSO
• System can test model with uncertain parameters,
and deliver a posteriori uncertainties on parameters,
fluxes
Conclusions
FastOpt
• explore more parameter configurations• include fire as a process with uncertainties• need more constraints, e.g. eddy fluxes –>
reduce uncertainties• however: needs to solve scaling problem
(satellites?)• approach can be regionalized easily• extend approach to ocean carbon cycle• projection of uncertainties into future
Outlook