INSPIRATION:

1
Retrieving global sources of aerosols from MODIS
by inverting GOCART model
INSPIRATION
INVERSION Oleg Dubovik1
Tatyana Lapyonok2 MODIS Yoram
Kaufman2, GOCART Mian Chin2
Paul Ginoux3
INSPIRATION
1- LOA/CNRS, University of Lille, France 2-
NASA/GSFC, Greenbelt, MD, USA 3 - NOAA/GFDL,
Princeton, NJ, USA
Yoram Kaufman2
Yoram J. Kaufman Symposium On Aerosols, Clouds
and Climate NASA/GSFC, , May 30, 31, and June 1,
2007
2
The idea of the approach

• GOCART
• meteorology
• transport
• chemistry
• removal
• emissions?

MODIS observations of ambient aerosol
INVERSION (e.g. via adjoint model)
Improved sources (location and strength)
Improved agreement of modeling with
observations Improved characterization of
climate, air quality, etc.
3
Basic principle of inversion
Forward Model
Matrix m -lines, n- columns
Least Square Method (mgtn)
Criterion of solution optimization
4
Vector of global aerosol mass
Vector elements - values of aerosol mass
Mpm(ti , xj , y k , zn)
(p 1, ., Np) Time and space coordinates
zn n ? ?z (n 1,,Nz) yk k ? ?y ( k
1,,Ny) xi j ? ?x ( j 1,,Nx ) ti
i ? ?t ( i 1,,Nt )

M
Index convention p (i-1) Nx Ny Nz (j-1) Ny
Nz (k-1) Nz n NpNt Nx Ny Nz
Z
m( t?t, x, y, z )
Z
m( t, x, y, z )
Y
?z
?y
X
?x
Y
Z
t
t
?z
Y
?y
X
X
?x
5
GOCART ModelGoddard Chemistry Aerosol Radiation
and Transport Model

• An atmospheric process model using assimilated
  meteorological fields from the Goddard Earth
  Observing System Data Assimilation System (GOES
  DAS)
• Including major types of aerosol, sulfate, dust,
  BC, OC, and sea-salt from both anthropogenic and
  natural sources
• Calculating aerosol composition, 4-D
  distributions, optical thickness, radiative
  forcing

(spatial resolution 20 x 2.50, time resolution 20
min)
6
Dimension of the Problem
Longitude Points (144) X Latitude Points
(91) X Vertical Layers (30) X Time
steps (12 days) 5,000,000
Longitude Points (144) X Latitude Points
(91) X Time steps (12 days) 200,000
5,000,000 X 200,000
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Transport Inversion
Transport Operator
Aerosol Mass
Source - Aerosol Emission
Least Square Method
Measured Aerosol Mass
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Steepest Descent Method
for p??, steepest descent method is equivalent
to LSM
???
It converges as
-has predominant diagonal due to
local character of aerosol
transport
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Transposed Adjoint Transport
Transport Model
?
- Adjoint (Transpose) Transport
For Transport -reversed order of time
integration -reversed order of component
processes (e.g., advection ? backward
advection, falling ? uplifting,
updraft ? falling)
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INPUT
Time Integration of Transport Model

initial mass m(t0,x)
emitted mass s(t,x) (t0 t tmax)
m(t1,x)T(t0,x)(m(t0,x)s(t0,x))?t
Ti - operators of isolated transport
processes - advection, -
diffusion, - convection, - wet
deposition, - dry deposition, etc.
m(t2,x)T(t1,x)(m(t1,x)s(t1,x))?t
t
m(t3,x)T(t2,x)(m(t2,x)s(t2,x))?t


m(t5,x)T(t1,x)(m(t1,x)s (t1,x))?t
m(t2,x)T(t1,x)(m(t1,x)s (t1,x))?t
m(t2,x)T(t1,x)(m(t1,x)s (t1,x))?t
ti1 ti?t
Matrix equivalent
OUTPUT
transported mass m(t,x) (t0 t tmax)
M - vector of global aerosol mass, M0 - vector of
global aerosol mass at t0, S - vector of global
aerosol emissions, T - matrix defining mass
transport
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Backward Time Integration of Adjoint Transport
Model
INPUT

Residual obtained using sp(t,x) ?p(t,x)
s-2 (t,x)(mp(t,x)- m(t,x)) (t0 t
tmax) mp(t,x) - mass simulated using
sp(t,x), m(t,x) - mass measurements
tn-1 tn- ?t
?sp(tn,x)T(tn,x)(?p(tn,x))?t
Ti - adjoint operators of isolated transport
processes - advection, -
diffusion, - convection, - wet
deposition, - dry deposition, etc.
?sp(tn-1,x) T(tn-1,x)(?sp(tn,x)?p(tn-1,x))?t
?sp(tn-2,x) T(tn-2,x)(?sp(tn-1,x)?p(tn-2,x))?t
(-t)




m(t2,x)T(t1,x)(m)s (t1, ?t
Matrix equivalent
OUTPUT
?Sp TTC-1 ? Mp
Solution Correction sp1(t,x) sp(t,x)-
?sp(t,x)
M0 - vector of global aerosol mass at t0, TT -
transpose of transport matrix T, C - measurement
covariance matrix, ? Mp - vector of residuals (?
Mp M(Sp)- M),
?sp(t,x) (t0. t tmax)
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Implementation of Steepest Descent Method via
Adjoint Modeling
Matrix Formulation
Time Integration of Transport Model
Time Integration of Transport Model
Initialization (p0)
m(t0,x)
mp(t,x)
p-th Approximation of Solution
sp(t,x)
sp0(t,x)
Residual calculation ?p(t,x) s-2
(t,x)(mp(t, x)- m(t,x))
yes
no
END
IF (p lt pmax)
Solution correction
Backward Time Integration of Adjoint
Transport Model ?sp(t,x)
Backward Time Integration of Adjoint Transport
Model
sp1(t,x) sp(t,x)- ?sp(t,x)
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Emission Sources
Testing of inversion
Testing of inversion
Assumed emission
Initial guess
Retrieved (40 iterations)
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inverting model output Black Carbon
August 28, 2000 (107 kg of mass/day) (two weeks
inversion)
Assumed Emission
Retrieved Emission
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Optical Thickness August 28, 2000
sfit lt 0.007 (for instantaneous t values)
?BC(0.55) simulated by GOCART using assumed
emission
?BC(0.55) simulated by GOCART using retrieved
emission
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Optical Thickness(real coverage) August 28, 2000
sfit lt 0.009 (for instantaneous t values)
?BC(0.55) simulated by GOCART using assumed
emission
?BC(0.55) simulated by GOCART using retrieved
emission
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inverting model output Desert Dust
August 28, 2000 (108 kg of mass/day) (two weeks
inversion)
Assumed Emission
Retrieved Emission
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Optical Thickness August 28, 2000
sfit lt 0.008 (for instantaneous t values)
?dust(0.55) simulated by GOCART using assumed
emission
?dust(0.55) simulated by GOCART using retrieved
emission
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Model ? Observations
Extra - assumptions in the inversion

• 24 hours constant emissions
• Components
• Mfine(xyzt)
• (BC OC sulfates fine dust fine sea salt)
• Mcoarse(xyzt)
• (coarse dust coarse sea
• salt)

GOCART output
MODISproducts

• MASS M(xyzt)
• 2o?2.5o,20 min
• Components
• BC hydrophilic
• BC hydrophobic
• OC hydrophilic
• OC hydrophobic
• sulfates
• dust (size d.)
• sea salt
• (fine, coarse)

• Aerosol Optical thickness
• ?(xyt)
• 1o?1o,
• global coverage in 2 days
• Components
• ?fine(0.55?m)
• ?????coarse(0.55?m)

?
A priori constraints
Using GOCART emissions as a priori estimates (
assimilation)
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Steepest Descent Methodwith a priori
constraints
for p??, steepest descent method is equivalent
to multi-term LSM (Dubovik 2004, Dubovik and
King, 2000)
A priori estimates correction METHODS Kalman
filter, Rogers optimal estimates, Twomey,
Correction by a priori limitation of
derivatives METHODS Phillips-Tikhonov-Twomey
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MODIS Aerosol Product for 24 hours
MODIS ttotal(0.55) (Total AOD (degraded to 20 x
2.50 )
MODIS tfine(0.55) (Fine Mode AOD (degraded to 20
x 2.50 )
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inverting model output sub-sampled according to
actual MODIS coverage Black Carbon
August 28, 2000 (107 kg of mass/day) (two weeks
inversion)
Assumed Emission
Retrieved Emission
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Optical Thickness August 20-28, 2000
sfit lt 0.009 (for instantaneous t values)
?BC(0.55) simulated by GOCART using assumed
emission
?BC(0.55) simulated by GOCART using retrieved
emission
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inverting model output sub-sampled according to
actual MODIS coverage Fine Mode Aerosol
August 20-28, 2000(107 kg of mass/day) (two weeks
inversion)
Assumed Emission BCOCSulfates
Retrieved Emission Single Fine mode aerosol
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Optical Thickness August 28, 2000 (two weeks
inversion)
sfit lt 0.02 (for instantaneous t values)
sMODIS 0.030.05 ?
?BC(0.55) ?OC(0.55) ?sulfates(0.55) simulated
by GOCART using assumed emission
?BC(0.55) simulated by GOCART using retrieved
emission
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inverting model output sub-sampled according to
actual MODIS coverage Desert DUST
August 28, 2000 (108 kg of mass/day) (two weeks
inversion)
Assumed Emission
Retrieved Emission
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Optical Thickness August 28, 2000
sfit lt 0.006 (for instantaneous t values)
?BC(0.55) simulated by GOCART using assumed
emission
?BC(0.55) simulated by GOCART using retrieved
emission
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Fine Mode Aerosol Black Carbon Organic Carbon
Sulfate
August 20 - 28, 2000
MODIS Observations (opt. thickness)
Retrieved Emission
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9 day average, Optical Thickness retrieval is NOT
CONSTRAINED to the land
sfit lt 0.04 (for instantaneous t values) sMODIS
0.030.05 ?
Optical Thickness (August 20-28, 2000)
MODISAERONET Observations (Fine Mode opt.
Thickness, (degraded to 20 x 2.50 )
Model output using retrieved emission
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Emission Sources COMPARISON
GOCART Emission Sulfates BC OC
Retrieved Emission (total fine aerosol)
Combination of satellite hotspots (TRMM and
ATSR), satellite burned area (MODIS), and a
biogeochemical model (CASA) Guido van der
Werf Jim Collatz
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Coarse Aerosol Desert Dust Sea Salt etc.
August 20 - 28, 2000
GOCART emissions Desert Dust (mass)
Retrieved emissions Coarse Aerosol (mass)
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Optical Thickness
sfit lt 0.05 (for instantaneous t values)
MODIS AOD (Coarse Mode AOD (degraded to 20 x 2.50
)
Model output using retrieved emission
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Fine Mode Aerosol Monthly retrievals
February 2001
May 2001
July 2001
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OC BC 0.5 (MG) Inverted emissions
FRP CMG 0.5 (MW) Fire Radiative Power
Fossil Fuel Emissions OC BC adjusted for
anthropogenic sources
Vermote et al. 2007
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Correlation of FRP and emissions
FRP (Fire Radiative Power)
Vermote et al. 2007
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Estimating the Emission Factor
Vermote et al. 2007
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Perspectives

• retrievals over bright surfaces - sensitivity
  to aerosol type - sensitivity to vertical
  profile

• inverting data from MISR, POLDER,
  APS,CALISPO, etc.

• improved coverage- retrievals over bright
  surfaces - sensitivity to aerosol type-
  sensitivity to vertical profile - sensitivity to
  aerosol source variability

• inverting multi-instrument dataMODIS MISR
  POLDER APS

• Deriving regional emissions from
  geostationary observations
  (METEOSAT)

• higher time resolution - higher spatial
  resolution

INVERSION REFINEMENTS - using a priori
knowledge about emissions - inverting satellite
radiances