fast opt

A global Carbon Cycle Data Assimilation System (CCDAS) to infer atmosphere-biosphere CO2

exchanges and their uncertainties

Marko Scholze1, Peter Rayner2, Wolfgang Knorr1, Thomas Kaminski3, Ralf Giering3 & Heinrich

Widmann1

TransCom Tsukuba, 2004 FastOpt1 2 3

Overview

• CCDAS set-up• Calculation and propagation of

uncertainties• Data fit• Global results• New developments• Conclusions and outlook

Combined ‘top-down’/’bottom-up’ Method

CCDAS – Carbon Cycle Data Assimilation System

CO2 stationconcentration

Biosphere Model:BETHY

Atmospheric Transport Model: TM2

Misfit to observations

Model parameter

Fluxes

Misfit 1 Forward Modeling:

Parameters –> Misfit

Inverse Modeling:

Parameter optimization

CCDAS set-up

2-stage-assimilation:

1. AVHRR data(Knorr, 2000)

2. Atm. CO2 data

Background fluxes:1. Fossil emissions (Marland et al., 2001 und Andres et al., 1996)2. Ocean CO2 (Takahashi et al., 1999 und Le Quéré et al., 2000)3. Land-use (Houghton et al., 1990)

Transport Model TM2 (Heimann, 1995)

Station network

41 stations from Globalview (2001), no gap-filling, monthly values

1979-1999.

Annual uncertainty values from Globalview (2001).

Terminology

GPP Gross primary productivity (photosynthesis)NPP Net primary productivity (plant growth)NEP Net ecosystem productivity (undisturbed C storage)NBP Net biome productivity (C storage)

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 dependent

• Carbon balance:average NPP = average soil resp. (at each grid point)

<1: source>1: sink

t=1h

t=1h

t=1day

lat, lon = 2 deg

Calibration Step

Flow of information in CCDAS. Oval boxes represent the various quantities. Rectangular boxes denote mappings between these fields.

Prognostic Step

Oval boxes represent the various quantities. Rectangular boxes denote mappings between these fields.

Methodology

Minimize cost function such as (Bayesian form):

DpMDpMpp pppJ D

T

pT

)()()( 2

1

2

1 10

10 0

-- C C

where- is a model mapping parameters to observable quantities- is a set of observations- error covariance matrixC

DM

p

need of (adjoint of the model)Jp

Calculation of uncertainties

• Error covariance of parameters1

2

2

ji,

p pJ

C = inverse Hessian

T

pX p)p(X

p)p(X

CC

• Covariance (uncertainties) of prognostic quantities

• Adjoint, Hessian, and Jacobian code generated automatically from model code by TAF

Figure from Tarantola, 1987

Gradient Method

1st derivative (gradient) ofJ (p) to model parameters p:

yields direction of steepest descent.

p

p

ppJ

)(

cost function J (p) p

Model parameter space (p)p

2nd derivative (Hessian)of J (p):

yields curvature of J.Approximates covariance ofparameters.

p

22 ppJ

)(

Data fit

Seasonal cycle

Barrow Niwot Ridge

observed seasonal cycle

optimised modeled seasonal cycle

Global Growth Rate

Calculated as:

observed growth rate

optimised modeled growth rate

Atmospheric CO2 growth rate

MLOSPOGLOB CCC 75.025.0

Parameters I

• 3 PFT specific parameters (Jmax, Jmax/Vmax and )

• 18 global parameters• 57 parameters in all plus 1 initial value (offset)

Param InitialPredicted

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

Parameters II

Relative Error Reduction

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

Carbon Balance

latitude N*from Valentini et al. (2000) and others

Euroflux (1-26) and othereddy covariance sites*

net carbon flux 1980-2000gC / (m2 year)

Uncertainty in net flux

Uncertainty in net carbon flux 1980-200gC / (m2 year)

Uncertainty in prior net flux

Uncertainty in net carbon flux from prior values 1980-2000gC / (m2 year)

NEP anomalies: global and tropical

global flux anomalies

tropical (20S to 20N) flux anomalies

IAV and processes

Major El Niño events

Major La Niña event

Post Pinatubo period

Interannual Variability I

Normalized CO2 flux and ENSO

Lag correlation(low-pass filtered)

ENSO and terr. biosph. CO2:Correlations seems strong with a maximum at ~4 months lag,for both El Niño and La Niña states.

Interannual Variabiliy II

Lagged correlation on grid-cell basis at 99% significance

correlation coefficient

Low-resolution CCDAS

• A fully functional low resolution version of CCDAS, BETHY runs on the TM2 grid (appr. 10° x 7.8°)

• 506 vegetation points compared to 8776 (high-res.)• About a factor of 20 faster than high-res. Version -> ideal

for developing, testing and debugging• On a global scale results are comparable (can be used

for pre-optimising)

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

Seasonality at MLOGlobal land flux

Observations

Low-res incl. ocean basis functions Low resolution model

High resolution standard model

Conclusions

• CCDAS with 58 parameters can fit 20 years of CO2 concentration data; ~15 directions can be resolved

• Terr. biosphere response to climate fluctuations dominated by El Nino.

• A tool to test model with uncertain parameters and to deliver a posterior uncertainties on parameters and prognostics.

• With the ability of including ocean basis functions in the optimisation procedure CCDAS comprises a ‘normal’ atmospheric inversion.

Future

• Explore more parameter configurations.• Include missing processes (e.g. fire).• Upgrade transport model and extend data.• Include more data constraints (eddy fluxes,

isotopes, high frequency data, satellites) -> scaling issue.

• Projections of prognostics and uncertainties into future.

• Extend approach to a prognostic ocean carbon cycle model.

Visit:

http://www.ccdas.org