J.-F. Müller and T. StavrakouIASB-BIRA

Avenue Circulaire 3, 1180 Brussels

jfm@aeronomie.be

Seminar at Harvard University, June 2nd, 2006

Inverse modelling of emissions based on the adjoint model

technique

Short introduction on carbon monoxide

Adjoint-based inverse modeling: methodology

The IMAGES model used in two inversion exercises constrained by:

A) 1997 CMDL data & GOME NO2 columns B) the 2000-2001 MOPITT CO columns

Big-region vs. grid-based inversion approach

Related work at IASB-BIRA: satellite retrievals of tropospheric gases, chemistry of terpenes

Conclusions and perspectives

Outline

COCO2 CH2O CH4

OH OH, hv OH

1100 570 360

85 30

deposition deposition

NMVOC (non-methane volatile organic compounds)

700100

50

200

80250

OH,O3

100340

deposition

SOA= Secondary

OrganicAerosols

CO2

(units: Tg C/year)

410

???

Carbon monoxide: sources and sinks

Inversion methodology and setup

m

jj txtxG

10 ),(),(

m

jjjj txfftxG

1

),()exp(),,(

The a priori emission distributions for a given species can be expressed as :

where j runs over the base functions. The posterior flux estimate is given by

where f is a vector of dimensionless control parameters to be optimized, so that the posterior fluxes are close enough to the prior bottom-up fluxes and the resulting abundances exhibit minimal deviation from the observed concentrations.

The solution of this problem corresponds to the minimum of the cost function.

Cost function:

measures the bias between the model and the observations

J(f)=½Σi (Hi(f)-yi)T E-1(Hi(f)-yi) + ½ (f-fB)TB-1(f-fB)

Model operator acting on the

control parameters

observations

1st guess values of the control parameters

Matrix of errors on the observations

Matrix of errors on the control parameters

Vector of the control parameters

For what values of f is the cost function minimal?

Inversion methodology and setup

Gradient of the cost function

Calculation of new parameters f with a descent algorithm Minimum of J(f) ?

Observations

Forward CTM Integration from t0 to t

Transport

Chemistry

Cost function J(f)

Adjoint model Integration from t to t0

Adjoint transport

Adjoint chemistry

Adjoint cost function

Checkpointing

Control variables f

yes

no

Optimized control parameters

Minimizing the cost

Calculated derivatives are exact

Non-linearities (chemical feedbacks) are taken into account

The emissions of different compounds can be optimized simultaneously, their chemical interactions being taken into account

Computational time not dependent on the number of control variables grid-based inversions can be addressed

High computational cost: calculation of derivatives requires 3 times more CPU time than a forward model run, and on the order of 20-50 iterations are needed to attain convergence (reduction of gradient by a factor >1000)

The exact estimation of posterior error is not possible within this framework; instead, iterative approximations of the inverse Hessian can be used

Adjoint modelling: pros and cons

60 chemical compounds, 5°x5° resolution, 25 σ levels (Müller and Brasseur, 1995)

Use monthly averaged meteorological fields from ECMWF analyses, impact of wind variability represented as horizontal diffusion

Semi-lagrangian transport Anthropogenic emissions : 1997 EDGAR v3 Biomass burning emissions : GFED (Van der Werf et al., 2003) or the

POET inventory (Olivier et al., 2003) Biogenic emissions for isoprene and monoterpenes from Guenther

et al., 1995, and for CO from Müller and Brasseur, 1995 Two main modes: (A) with or (B) without diurnal cycle calculations Mode B (Δt=1 day) uses info. on diurnal profiles of chemical species

calculated in mode A (Δt=20 min) to correct the kinetic rate constants and photorates

Inverse modeling: only in mode B (emission updates not expected to affect the diurnal behavior of chemical compounds)

16 months simulations, including spin-up of 4 months

The IMAGES model

The inversion is constrained by:

NOAA/CMDL CO mixing ratios

Ground-based FTIR CO vertical column abundances

GOME tropospheric NO2 columns

Simultaneous optimization of the

total annual CO & NOx emissions

over large regions (39 flux parameters)

chemical feedbacks via the adjoint

constant seasonality of the sources

B is assumed diagonal

Müller and Stavrakou, ACP, 2005

A. Big-region inversion of the 1997 CO emissions

Impact of emission changes on OH

Comparison to aircraft observations

Direct calculation of the Hessian matrix using finite differences on the adjoint model

Use of the inverse BFGS formula and the output of the minimization algorithm at each iteration

Use of the DFP update formula

Estimation of posterior errors

The inversion is constrained by the MOPITT daytime CO columns from May 2000 to April 2001

The columns and averaging kernels are binned onto the IMAGES grid and monthly averaged total : ~ 6000 observations

Error on the column is assumed 50% of the observed value

« Big-region approach »: optimize the global CO fluxes over large regions as in case A (18 variables)

« Grid-based » inversion: optimize the fluxes emitted from every model grid cell by month ( ~30000 param.) seasonality and geographical

distribution varied source-specific correlations

among prior errors on the flux parameters B non-diagonal

In both cases,

distinguish between anthropogenic, biomass burning and biogenic emissions

Stavrakou and Müller, JGR, in press

B. Big-region vs. Grid-based inversion for optimizing CO&VOC emissions

Spatial correlations for anthrop. emissions

En = total emission of country n, σ En = standard error

din = fraction emitted by the country n in the ith grid cell

φi = total flux emitted by the cell i

En = total emission of country n, σ En = standard error

din = fraction emitted by the country n in the ith grid cell

φi = total flux emitted by the cell i

= fraction of the flux emitted by the cell i and country n

m

Em

n

En

mn

mj

ni

nmnmijij EE

xxACB

,

σEn / En = 0.6, 0.35 for industrialized countries

Anm = 1, when n=m, 0.3 if n,m belong to the same big region, 0 otherwise

Cijnm = 0.7, 0.85 when n,m belong to the industrialized countries, 1 when i=j

i

nnin

i

Edx

n

nnii Ed

Correlation setup for pyrogenic and biogenic emissions

Spatial correlations :

Based on the geographical distance dij between the grid cells i and j

Relative error on the flux : 0.7 for pyrogenic / 0.6 for biogenic

Decorrelation length : 2000 km for pyrogenic / 6000 km for biogenic

ein : fraction of the flux emitted by the cell i and ecosystem n (n=2 for

pyrogenic, 40 for biogenic emissions)

Cnm : 1 or 0.5 depending on whether the same or different ecosystems occupy the grid cells i and j

Temporal correlations : linearly varying between 0 and 0.5 for pyrogenic

emissions, between 0.7 and 0.9 for biogenic emissions

)/)(/)(/exp(,

jjiiijmj

mn

ni

nmij deeCB

• Both solutions succeed in reducing the model/MOPITT bias over most regions

• Larger cost reduction in the grid-based case (4.6) as compared to the big-region setup (2.2)

Big-region setup Grid-based setup

MOPITT column

Optimization results

Evolution of the cost and its gradient throughout the minimization

The gradient is 10 times smaller than its initial value after 6 iterations

The gradient is 100 times smaller than its initial value after 24 iterations

The gradient is 1000 times smaller than its initial value after 42 iterations

0

50

100

150

200

250

N.Am. S.Am. Africa Europe Far East S.Asia

A priori

Big-region

Grid-based

Anthropogenic emissions by region

Big-region setup

Grid-based setup

prior GFEDprior POETbig-region GFEDgrid-based GFEDgrid-based POET

Remarkable convergence of optimizations using either GFED or POET prior emissions

Important changes in seasonality of biomass burning emissions

Increased S. African emissions in September, reduction in June when using GFED

Vegetation fire emission updates

Seasonal variation

Global enhancement of biogenic VOC emissions (~ +15%)

Higher NMVOCs oxidation source by 10%

grid-based inversion

prior

big-region

grid-based

Biogenic emission updates Seasonal variation

priorbig-regiongrid-based

Comparison to independent data

(CMDL, FTIR, aircraft campaigns)

prior

Anthro-pogenic sources

Tropical forest fires

Savanna fires

Extra-tropical

fires

Biogenic sources

Photo-chemical source

Total

priorprior 571571 170170 268268 2929 160160 15301530 27482748

standard grid-basedstandard grid-based 664664 162162 257257 3131 199199 15741574 29072907

errors on control variables doubled 620 144 268 27 221 1600 2900

errors on control variables halved 672 170 262 32 185 1556 2897

decorrelation lengths doubled 667 161 258 29 202 1592 2909

decorrelation lengths halved 677 166 257 32 192 1570 2914

lower temporal anthropogenic correlations

705 156 250 29 193 1567 2920

halved spatial correlations for anthrop. sources

653 163 257 31 200 1576 2900

constant biog. fluxes 760 187 260 43 160 1532 2942

Sensitivity inversions

2200

2400

2600

2800

3000

3200

Global annual in Tg CO

Bergamaschi et al.,2000

Pétron et al., 2002

Arellano et al., 2004

Müller&Stavrakou,2005

Stavrakou&Müller,2006

600

700

800

900

1000

Anthropogenic emissions

Comparison of our results to past inverse modelling studies

020406080

100120140160180200220240260

East Asian FF+BF

Heald et al., 2004

Pétron et al., 2004

Arellano et al., 2004

Wang et al. 2004

Stavrakou&Müller 2006

Streets et al., 2003

Edgar v3

East Asian anthropogenic emissions

After 6 iterations (grad./10)

After 42 iterations (grad./1000)

After 24 iterations (grad./100)

Biogenic emissions error reduction

After 6 iterations (grad./10) After 24 iterations (grad./100)

After 42 iterations (grad./1000)

Anthropogenic emissions error reduction

Regions Anthropogenic Pyrogenic Biogenic

N. America 1.2 1 1.5

S. America 1 1.2 2.3

N. Africa 1.1 1.1 2

S.Africa 1.1 2.3 2.1

Europe 1.2 1.1 1.9

Far East 1.7 1 1.7

Former S. U. 1.3 1 2.4

S. Asia 1.3 1.1 2

Oceania 1 1 1.6

Tropics (25 N-25 S) 1.3 1.4 3.9

Extratropics 1.8 1 2.7

Error reduction factors over large regions (estimated using the DFP-based update)

Sigma-pressure coordinate system, 40 levels Use of ECMWF analyses for convective fluxes, PBL

diffusion clouds washout/rainout KPP as alternative chemical solver (not in adjoint

model calculations - well for diurnal cycle calculations)

MEGAN model for BVOC emissions Treatment of diurnal cycle NMVOC chemical mechanisms Optimize horizontal diffusion coefficients using

adjoint technique and output using varying winds OR get rid of these coefficients and use varying winds

done

IMAGES model updates (in progress)

in progress future

In collaboration with KNMI, determination of NO2 tropospheric columns from satellites (AMFs, stratosphere from KNMI model)

Retrieval of CH2O columns from GOME using IMAGES profiles

Related work at IASB-BIRA : satellite retrievals (M. Van Roozendael et al.)

(Courtesy of I. De Smet & M. Van Roozendael)

GOME-IMAGES CH2O : 1997-2001

State-of-the-art mechanism development for α-pinene, based on theoretical work of J. Peeters and co-workers (Uni. Leuven)

Mechanism validation by simulations of laboratory experiments using a box model

SOA parameterization based on original vapor pressure prediction method

Reduced mechanism (~30 compounds) (work in progress)

Future: ozonolysis of α-pinene and sesquiterpenes

Related work at IASB-BIRA: chemistry of terpenes

Alpha-pinene + OH quasi-explicit mechanism :

Peeters et al. (2001), Fantechi et al. (2002), Vereecken and Peeters (2004), Capouet et al.

(2005)

OH

OH

O2

OH

O

OHO

O

O

OH

OO

OH

OO

OH

O

OH

OH

OHO

OH

OH

O

O

O2

OH

O

O

OH

O

OH

OO2 OHOH

O2

OHO

OO

O2

OHO

OOH

OH

O

OOH

OHO

O

+~9 %

~44 %~44 %

H-abstraction

OH-addition

Pinonaldehyde

40 % syn 60 % anti

1,5 H shift

.

R1

.

.

.

+ O2 / NO

.

.

+ O2

stabilization

+ NO

.

.

+ O2

+ NO.

ring closure

50 %

50 %

1,5 H-shift+ ring closure

acetone

R8

R9O

.

.+ O2

.

+ NO

.

+ HCOOH+ CH3COOH

decomp.

decomp.

.

1,7 H-shiftdecomp

.

.

.

+ O2 / NO

+ O2 / NO.

.

decomp.

Pinonaldehyde

decomp.

stabilization.

.

.

*

*

*

Very exotic chemistry(ring closure, isomeri-sations, peroxy radical decomposition, etc.)

800 species, 2400 reactions (ozonolysis included)

Capouet et al., 2005

Lamp spectra

Model simulation of laboratory experiments

CO CH2O+OH

Hermans et al., 2004; 2005 :

+HO2

CH2OHO2 +NO

HCOOH+HO2

+hv

Also for acetone and other carbonyls!

J. Phys Chem. A (May 2005)

Related work at IASB-BIRA : unexpected reaction sequences in the UT/LS

Feasibility of multi-compound and grid-based inversions

Comparable results of big-region and grid-based approaches when averaged over large regions

Importance of the error correlation setup for grid-based inversions -- further work needed to better quantify the correlations

Posterior uncertainty analysis made possible by the DFP approximation, shows important error reductions for large-scale fluxes (e.g. Chinese anthropogenic emissions, African biomass burning), small error reductions for individual grid cells

Synergetic use of different datasets is required to better quantify emissions, in particular the CO production from the NMVOCs

CH2O from satellites promising in that perspective, but large differences between retrievals by different groups intercomparisons are mandatory

Also, large differences between inversion studies based on same data but different models

Conclusions and perspectives