Download - J.-F. Müller and T. Stavrakou IASB-BIRA Avenue Circulaire 3, 1180 Brussels [email protected]
J.-F. Müller and T. StavrakouIASB-BIRA
Avenue Circulaire 3, 1180 Brussels
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