ÓPTICA PURA Y APLICADA – Vol. 37, núm. 3 - 2004
Inversion of global distribution of aerosol sources using
MODIS and AERONET data
Oleg Dubovik
(1,2), Tatyana Lapyonok
(1,3), Yoram J. Kaufman
(4), Mian Chin
(4), Paul
Ginoux
(5), Lorraine Remer
(4), Brent N. Holben
(1)1.
Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, MD
2.
GEST Center, University of Maryland, Baltimore County, Baltimore, MD
3.
Science Systems and Applications, Inc., Lanham, Maryland
4.
Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, MD
5.
Geophysical Fluid Dynamics Laboratory, NOAA, Princeton, NJ
REFERENCES
[1] Chin, M., P. Ginoux, S. Kinne, O. Torres, B. N. Holben, B. N. Duncan, R.V. Martin, J. A. Logan, A. Higurashi, T. Nakajima, Tropospheric aerosol optical thickness from the GOCART model and comparisons with satellite and Sun photometer measurements, J. Atmos. Sci., 59 (3): 461-483 2002
[2] Chin, M., R. B. Rood, S. J. Lin, J. F. Muller, A. M. Thompson, Atmospheric sulfur cycle simulated in the global model GOCART: Model description and global properties, J. Geophys. Res., 105 (D20): 24671-24687 OCT 27 2000
[3] Collins, W. D., P. J. Rasch, B. E. Eaton, B. V. Khattatov, J. F. Lamarque, C. S. Zender, Simulating aerosols using a chemical transport model with assimilation of satellite aerosol retrievals: Methodology for INDOEX, J. Geophys. Res., 106 (D7): 7313-7336 APR 16 2001
ABSTRACT:
The paper describes a method to retrieve global sources of tropospheric aerosol
from satellite observations by inverse modeling of aerosol transport. The method
uses an adjoint operation to the aerosol transport of GOCART model that allows
performing inversion with original space (2 x 2.5 degrees) and time (20-60 min)
resolution of GOCART model. A version of retrieval algorithm has been
developed, tested and applied to the retrieval of location and strength of fine
mode aerosol emission from a combination of MODIS and AERONET
observations.
Key words:
[4] Collins, W. D., P. J. Rasch, B. E. Eaton, D. W. Fillmore, J. T. Kiehl, C. T. Beck, C. S. Zender, Simulation of aerosol distributions and radiative forcing for INDOEX: Regional climate impacts, J. Geophys. Res., 107 (D19): Art. No. 8028 SEP-OCT 2002
[5] Dubovik, O., M.D. King, A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements, J. Geophys. Res., 105 (D16), 20673-20696, 2000
[6] Dubovik, O., B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, Variability of absorption and optical properties of key aerosol types observed in worldwide locations, J. Atmos. Sci., 59, 590-608, 2002.
[7] Dubovik, O., “Optimization of Numerical Inversion in Photopolarimetric Remote Sensing”, in Photopolarimetry in Remote Sensing (G. Videen, Y. Yatskiv and M. Mishchenko, Eds.), Kluwer Academic Publishers, Dordrecht, Netherlands, 65-106, 2004a.
[8] Dubovik, O., et al., Retrieving aerosol global sources from satellite and AERONET observations by inverse modeling, J. Geophys. Res., to be submitted, 2004b.
[9] Brasseur, G. P., J. J. Orlando, G. S. Tyndall, Atmospheric Chemistry and Global Change, Oxford University Press; 1st edition, 654p, 1999
[10] Elbern, H., H. Schmidt, A. Ebel, Variational data assimilation for tropospheric chemistry modeling, J. Geophys. Res., 102, 15967-15985, 1997
[11] Enting, I. G., C. M. Trudinger, R. J. Francey, A synthesis inversion of the concentration and δ13C of
atmospheric CO2, Tellus, Ser. B, 47 (1-2): 35-52,1995
[12] Ginoux, P., M. Chin, I. Tegen, J. Prospero, B. N. Holben, O. Dubovik, and S. J. Lin, Sources and distributions of dust aerosols simulated with the GOCART model, J. Geophys. Res., 106, pp. 20,255 – 20,274, 2001
[13] Holben, B.N., et al., AERONET – A federated instrument network and data archive for aerosol characterization, Remote Sens. Environ., 66, 1-16, 1998
[14] Kasibhatla, P. S., M. Heimann, P. Rayner, N. Mahowald, R. G. Prinn, D. E. Hartley, Inverse Methods in Global Biogeochemical Cycles, American Geophysical Union, 324 pp, 2000
[15] Kaufman, Y. J., Tanré D., Boucher O., A satellite view of aerosols in the climate system, NATURE, 419 (6903), 215-223, 2002
[16] King, M. D., Y. J. Kaufman, D. Tanré, and T. Nakajima, Remote sensing of tropospheric aerosols from space: Past, present, and future. Bull. Amer. Meteor. Soc., 80, 2229-2259, 1999
[17] Kinne, S., et al., Monthly averages of aerosol properties: A global comparison among models, satellite data and AERONET ground data, J. Geophys. Res., 108, 4634, 10.1029/2001JD001253, 2003
[18] Menut, L., R. Vautard, M. Beekmann, C. Honoré, Sensitivity of photochemical pollution using the adjoint of a simplified chemistry-transport model, J. Geophys. Res., 105 (D12): 15379-15402, 2000
[19] O’Neill, N., O. Dubovik and T. F. Eck, A modified Angstrom coefficient for charac-terization sub-micron aerosols, Appl. Opt. , 40, 2368-2375, 2001
[20] Patra, P. K., S. Maksyutov, Y. Sasano, H. Nakajima, G. Inoue, T. Nakazawa, An evaluation of CO2 observations with Solar Occultation FTS for Inclined-Orbit Satellite sensor for surface source inversion, J. Geophys. Res., 108 (D24): Art. No. 4759, 2003
[22] Remer, L.A., Y.J. Kaufman, D. Tanré, S. Mattoo, D.A. Chu, J.V. Martins, R-R. Li1, C. Ichoku, R. C. Levy, R.G. Kleidman, T. F. Eck, E. Vermote, B. N. Holben, The MODIS Aerosol Algorithm, Products and Validation J. Geophys. Res., in press, 2004
[23] Sato, M., J. Hansen, D. Koch, A. Lacis, R. Ruedy, O. Dubovik, B. Holben, M. Chin, T. Novakov, Global [24] atmospheric black carbon inferred from AERONET, Proc. Nat. Acad. Sci., 100, (11), 6319-6324, 2003.
[25] Tanré, D., M. Herman and Y.J. Kaufman, Information on aerosol size distribution contained in [26] solar reflected spectral radiances. J. Geophys. Res., 101, 19043-19060, 1996
[27] Tanré, D., Y.J. Kaufman, M. Herman and S. Mattoo, Remote sensing of aerosol properties over [28] oceans using the MODIS/EOS spectral radiances. J. Geophys. Res., 102, 16971-16988, 1997
[29] Vukicevic, T., M. Steyskal and M. Hecht, Properties of advection algorithms in the context of variational data assimilation, Month. Weather Rev., 129 (5): 1221-1231, 2001.
1. Introduction
Knowledge of the global distribution of tropospheric aerosols is important for studying the effects of aerosols on global climate. Satellite remote sensing is the most promising approach to collect the information about global distributions of aerosol (King et al., 1999; Kaufman et al., 2002). However, in spite of the recent advancements in space technology, the satellite-collected data do not provide yet the required accuracy and details on time and space scale of the aerosol properties variability. Tropospheric aerosol may have strong local variations and any single satellite needs at least several days of observations to provide global images with appropriate resolution. Also, satellite characterization of aerosol is limited to daytime clear-sky conditions. Comprehensive global simulations of atmospheric aerosols with adequate time and space resolution can be obtained using chemical transport models that rely on known meteorological fields and account for aerosol advection by winds and removal processes. However, the accuracy of global aerosol models is limited by uncertainties in estimates of the aerosol emission sources, knowledge of atmospheric processes and utilized meteorological fields. As a result, even the most recent models are mainly expected to capture the global features of aerosol transport, while the quantitative estimates of average regional properties of aerosol may disagree between different models by the magnitudes exceeding the uncertainty of remote sensing aerosol observations (e.g. see Kinne et al., 2003, Sato et al., 2003). One of the promising ways of improving knowledge of global aerosol distributions is constraining and adjusting chemical transport models by available observations. Such approach has been effectively used for refining fidelity of the trace gas chemical modeling (e.g. Kasibhatla et al., 2000, Elbern et al., 1997, Para et al. 2003) and shown to be efficient for improving chemical model predictions of regional aerosol distribution (Collins
et al., 2000, 2001). Our paper is aimed to explore a possibility to use satellite observations to derive independently the global distribution and strength of aerosol emission sources. The knowledge of aerosol emission sources is recognized as a major factor limiting the accuracy of global aerosol modeling. The paper describes and tests a method for retrieving global sources of tropospheric aerosols from satellite observations by inversion of GOCART model.
2. Methodology of inverse modeling
The spatial and temporal behavior of atmospheric constituents is simulated in chemical models by solving continuity equation (Brasseur et al., 1999):
∂m
∂t = −v∇m+
∂m
∂t
diff
+ ∂m
∂t
conv
+S−R, (1)
where v is the transport velocity vector, m is mass,
diff denotes turbulent diffusivity, conv denotes convection, S and R denote source and loss terms respectively. The characteristics m, v, S and R in Eq.(1) are explicit functions of time t and spatial coordinates x = (x,y,z)
.
Continuity equation does not yield general analytical solution and usually solved numerically where differential equation is replaced by discrete analogue and solution is derived at given times and discrete locations. The different component processes in numerical equivalent of Eq.(1) are isolated and treated sequentially for each time step ∆t :m
(
x,t+ ∆t)
=T( )
x,t(
m( )
x,t +s( )
x,t)
∆t, (2)T
( )
x,t =TnTn−1...T3T2T1 , (3)where Ti (i=1,…,n) are operators of isolated transport processes such as advection, diffusion, convection, wet scavenging, etc. Thus, the calculation of mass at any given time moment can be reduced to numerical time integration of known transport and source functions:
m
( )
x,t = T( )
x,t(
m( )
x,t +s( )
x,t)
t0
t
∫
dt. (4)If the transport operator is linear, Eq.(4) can be equivalently written via matrix equation:
M=T m
(
0+S)
, (5)where m0 is a vector of mass values in all locations at time t0; M and S are correspondingly the vectors
of mass and emission values in all locations at all considered times t0, t1,…, tk-1 , tk ; T is matrix of the
coefficients defining the transport of mass to each location x and time step tk from all locations x and previous time stepsti<k. Thus, the source vector can
be retrieved by solving matrix equation if the mass measurements M* = M + ∆M are available. For the
normally distributed errors ∆M, the optimum solution (with the smallest errors) is given by Least Square Method (LSM):
ˆ
S =
(
TTC−m1T)
−1TTC−m1M* (6)Here, for simplicity, m0 is neglected, Cm denotes
covariance matrix of the measurements, TT
indicates transposed matrix. If the problem is ill-posed and Eq.(5) does not have unique solution some a priori constraints can be applied. For example, statistical information about sources can be utilized for obtaining the optimum constrained solution:
ˆ
S =
(
TTCm−1T+C−s1)
−1(
TTC−m1M*+C−s1S*)
, (7)where S*= S + ∆S is a vector of a priori estimates of the sources and ∆S is vector of normally distributed errors with covariance matrix CS.
Equations (6-7) are designed to minimize the quadratic form formulated using noise assumptions (see details e.g. in Dubovik, 2004). Namely, Eq.(7) minimizes:
2Ψ(S)=2
(
Ψm+ ΨS)
= ∆MTCm
−1∆M+ ∆STC
s
−1∆S,
(8)
where ∆M=M(S)−M* and ∆S=S−S*. LSM
solution by Eq.(6) minimizes only the measurement term 2Ψm in Eq.(8). The methods analogous to Eq.(7) are used for retrieving sources of CO2 from surface based and satellite observations (e.g. see Enting et al. 1995, Patra et al. 2003). However, direct implementation of Eqs.(6-7) for retrieval of aerosol emission sources is not feasible due to very large dimensions of matrix T and vectors S and M. For example, CO2 emission sources can be assumed monthly or yearly constant for large geographic areas (e.g., Patra et al. 2003 used 22 and 53 global regions). The time and spatial variability of tropospheric aerosol and its emission is much higher. For aerosol, GOCART model (see below) has 2ox2.5o horizontal resolution (144 longitudes,
91 latitudes) and 30 vertical layers with possibility to have variable source in the each model domain. Correspondingly, inversion of a few weeks of observations by Eqs.(6-7) requires one to deal with the vector S having dimensions NS far exceeding
200,000, even under conservative assumptions of near-surface daily independent sources. Performing direct operations of Eqs.(6-7) with vectors and matrices of such high dimensionality is problematic. The strategy of developing algorithm in such situation is attempting to perform inversion in the same style as it is done in forward modeling. As shown by Eq.(5) transport modeling can be formulated as matrix operator. However, in practice, the transport models are implemented by numerical time integration (Eq.(4)) via sequential computing chemical transport during each time step ∆t (Eq.(2)) with separate treatment of isolated processes (Eq.(3)). Similar approach can be employed in inverse modeling by means of developing of so-called “adjoint” transport operators (e.g. Elbern et al. 1997, Menut et al. 2000). Indeed, any inversion can be implemented by iterations without explicit use of matrix inversion. For example, the solution equivalent to the one of Eq.(6) can be obtained by the steepest descent method iterations:
ˆ
S p+1=S ˆ p−tp∆S ˆ p, (9)
∆S ˆ p= ∇Ψ
m(Sp)=TTC−m1∆Mp , (10)
written as follows (detailed derivations are given in Dubovik et al. 2004b):
∆s ˆ p
( )
x,t = T∗( )
x,t(
∆s ˆ p( )
x,t +∆m( )
x,t)
tt0
∫
(−dt),(11a)
T*
( )
x,t =T1*T2*T3*...Tn*−1Tn* (11b)where ∆s ˆ p
( )
x,t and ∆m( )
x,t denote the elements of ∆S ˆ p and Cm−1∆Mp respectively. Equation (11) is allied to Eq.(4) with the difference that it uses∆m
( )
x,t in place of s( )
x,t and ∆s ˆ p( )
x,t in place of m( )
x,t and performs the backward time integration of adjoint operator T*(x, t) . If T(x, t) functionally equivalent to the matrix operator T, then adjoint operator T*(x, t) is an equivalent to the transposed matrix TT. Therefore, the main idea ofdeveloping adjoint operator T* from T can be sensed from considering matrix transposition. For example, since the integration of transport operator (e.g. see Eq.(3)) can be approximated by multiplication of matrices, the following matrix identity is helpful:
T3T2 T1
(
)
T =T1
( )
TT2
( )
TT3
( )
T. (12)This reversing of the order of operations by transposition results in reversing of the order of integration in Eq.(11), i.e. in backward time integration Eq.(11a) and in overturned sequence of applying component processes within each time step Eq.(11b). Also, transposition of matrix Ti
changes rows and columns, therefore if T is non-square, input of (Ti)T should have dimension of Ti
output and output of (Ti)T should have dimension of
Ti input. Thus, adjoint model (executing Eq.(11)) can be developed on the basis of the original model (executing Eq.(4)) by reversing order of operations and switching inputs and outputs of routines (e.g. Elbern et al. 1997, Menut et al. 2000).
Implementing inversion via adjoint modeling has a potential drawback, because it is based on iterative retrieval strategy. In general, the iterations of Eqs.(9-10) converge to the exact solution at very large number of iterations (p→∞). Even the faster iterations by the method of conjugated gradients may require up NS iterations (Press et al., 1992).
Nevertheless, due to local character of transport processes, a rather limited number of simple iterations appear to be effective for inverse modeling of high dimensionality. For instance, the iterations by Eq.(9-10) converge from arbitrary initial guess to the solution, if the following sequence leads to zero matrix (Dubovik, 2004a):
I−tpTTCm−1T
(
)
p=1
∞
∏
⇒0, (13)where I is unity matrix. It is clear, that fast convergence in Eq.(13) can be achieved at the only condition if TTT is predominantly diagonal (C
m is
often diagonal and does not cause problems). Fortunately, in transport modeling, the diagonal elements of TTT dominate because local aerosol
emission can quickly influence only nearest vicinity.
Above equations describe an approach to invert linear transport model (Eq.(5)) provided the global measurements of aerosol mass M* are available. In practice, the transport model may be non-linear and the global data of aerosol fields are available only in form of satellite optical measurements:
f = f(m(x,t);λ;θ;...), (14) where f(…) is generally non-linear function depending on aerosol m(x,t), instrument specifications λ, observation geometry Θ, etc. Therefore, in practice, the following non-linear equation should be solved instead of Eq.(4):
F*=F M
(
(S))
+ ∆F, (15)where F and ∆F - vectors of global optical data and their uncertainties. Since, the steepest descent method can be applied to both linear and non-linear problems, Eqs.(9-11) can be expanded for solving Eq(15). For example, for a general case when both optical measurements F* and a prioriS* estimates are available, solution can be written as:
ˆ
S p+1=S ˆ p−tp∆S ˆ p, (16)
∆S ˆ p= ∇ΨS(Sp)+ ∇Ψf(Sp) = =C−s1∆Sp+TpTKpTC−f1∆Fp
(17)
∆s ˆ p
( )
x,t =(
s ˆ p( )
x,t −s*( )
x,t)
/σs2( )
x,t ++ Tp*
( )
x,t Fp*
( )
x,t(
∆s ˆ p( )
x,t + ∆f( )
x,t)
tt0
∫
(−dt). (18)The a priori term in Eq.(18) is written for the case non-correlated s*(x,t), i.e. Cs is diagonal with the elements σs2
( )
x,t ; ∆f(x,t) represent ∆Fp=F(Sp)- F*. Tp*(x,t) and Fp*(x,t) are adjoint operators to mass transport T(s(x,t)) and optical model F(m(x,t)), index p indicates that these adjoint operators are equivalents of transposed Jacobi matrices TpT andcalculated in vicinity of the vector Sp. The
development of Fp*(x,t) is quite transparent because optical properties f(m(x,t), …) usually related only with local aerosol and therefore
Fp*(x,t) can be explicitly replaced by transposed Jacobi matrix KpT. Thus, Eqs.(16-18) can be used
for sources S retrieval, as long as development of adjoint operator Tp*(x,t) is feasible with employed chemical model.
2. GOCART model
The Georgia Tech/Goddard Global Ozone Chemistry Aerosol Radiation and Transport (GOCART) model (Chin et al., 2000, 2002; Ginoux et al., 2001) has been used in the study. The model uses the assimilated meteorological data from the Goddard Earth Observing System Data Assimilation System (GEOS DAS) and provides four-dimensional distribution of aerosol mass at several atmospheric layers (20-30) with horizontal resolution of 20 latitude by 2.50 longitude. The
model calculates aerosol composition and size distribution, optical thickness and radiative forcing. There are seven modules representing atmospheric processes: emission, chemistry, advection, cloud convection, diffusion (boundary layer turbulent mixing), dry deposition, and wet deposition. The model solves continuity Eq.(1) using operator splitting technique (Eqs.(2-3)). The model time is 20 min for advection, convection and diffusion and 60 min for other processes.
2. MODIS and AERONET observations
The MODerate resolution Imaging Spectroradiometer (MODIS) aboard both NASA's Terra and Aqua satellites provides near global daily observations of the earth in a wide spectral range (0.41 to 15.0 µm). These measurements are used to derive spectral aerosol optical thickness and aerosol size parameters over both land and ocean (Remer et al., 2004). The main available aerosol products include aerosol optical thickness (at three visible wavelengths over land and seven wavelengths over ocean), effective radius of the aerosol and fraction of optical thickness attributed to the fine mode. The present study uses MODIS optical thickness product composed to 10 by 10 spatial resolution.
The expected accuracy of MODIS optical thickness ∆τ = ± 0.03 ± 0.05 τ over ocean (Tanré et al. 1997) and ∆τ = ± 0.05 ± 0.15 τ over land (Remer et al, 2004).
AErosol RObotic NETwork (AERONET) of ground-based sun/sky radiometers (Holben, et al. 1998) provides accurate (within ~0.01) measurements of spectral aerosol optical thickness at more than 150 worldwide locations. AERONET also provides detailed optical properties of total
atmospheric column ambient aerosol (Dubovik and King, 2002; Dubovik, et al. 2002).
2. Algorithm, its testing and application
The particular interest of this study was exploring a possibility of using inverse modeling for characterizing of emission of absorbing tropospheric aerosols dominated by black carbon. However, as concluded from sensitivity studies (Tanré et al. 1996), information content of MODIS data insufficient for deriving such detailed information as aerosol absorption and refractive index, while it allows separating contributions of fine and coarse modes into total optical thickness. On the other hand, it is known that absorbing aerosols with high concentration of black carbon, such as, biomass burning and urban pollution are dominated by fine mode particles (Dubovik, et al. 2002). Therefore, the present developments are focused on characterizing fine mode aerosols and applied to the MODIS observations during periods with significant biomass burning activity. Specifically, two last weeks of August 2000 are analyzed. The global distribution of the optical thickness of fine aerosol particles at 0.55 µm has been set as an input for inverse modeling. The spectral dependence of the total aerosol optical thickness τtotal(λ) has been used for extracting fine
mode contribution τfine(0.55) from τtotal(0.55)
measured by MODIS. The following formulation (O’Neill et al., 2001) has been used:
τfine≈τtotal (αtotal - αcoarse)/( αfine - αcoarse), (19)
where αtotal, αfine, and αcoarse denote Angstrom
parameters of total, fine mode and coarse mode aerosol optical thickness. The value of αtotal has
been calculated from spectral dependence of MODIS optical thickness. The values αfine, and
αcoarse where simulated using African Savanna
biomass burning model (Dubovik et al. 2002). Thus, MODIS product of τtotal(λ) that given
globally at 10 by 10 was converted to τ
fine(0.55) and
then rescaled to GOCART horizontal resolution 20
by 2.50. MODIS data are complemented by the
available AERONET observations of the fine mode optical thickness. The values of τfine(0.55) were
interpolated from the daily averages of τfine(0.44)
and τfine(0.67) derived by AERONET (Dubovik et
al. 2002). If both the MODIS and AERONET measurements were available for the same grid (20
by 2.50), then only AERONET values of τ
fine(0.55)
were taken.
developed by redesigning GOCART modules for each atmospheric process. Namely, adjoint operator of advection has been performed by original advection algorithm of GOCART to the signed-reverse wind fields (Vukicevic et al. 2001). The adjoints of local aerosol mechanisms were developed by direct matrix operations. Specifically, cloud convection, diffusion, dry deposition, and wet deposition affect only vertical aerosol motion. In the model, for a single time step, these local processes work independently with each horizontally resolved vertical domain. Such processes can be easily modeled via explicit use of matrices of small dimension and the corresponding adjoint operators can be obtained by direct transposition of those matrices.
The employed inversion algorithm (Eqs.(16-18)) treats the strength of aerosol emission at each global location as an unknown, therefore, original emission module of GOCART has not been used. In principle, GOCART emission could be included in the a priori term of Eqs.(17-18), however we have explored the potential of unsupervised retrieval (no constraints by a priori sources) to distribute the global aerosol emission based only on satellite observations and transport. Hence, no information about sources (i.e. a priori term) has been used in the algorithm. Also, since MODIS observations do not provide constraints necessary for differentiating aerosol type, the developed algorithm does not assume any discriminate the aerosol type in retrieved emission. Only total “fine mode” aerosol is considered in the retrieval. Chemical transformations (used in GOCART model) of aerosol are neglected in the retrieval. The optical thickness was modeled from GOCART mass of aerosol in total atmospheric column, by deriving the aerosol volume (using density 1 g/cm3)
and assuming that it has the same optical properties as fine mode of smoke during Zambian Savana burning (Dubovik et al. 2002). The appearance of aerosol sources is allowed at 10 lower aerosol layers (i.e. approximately below 2 km). The sources are assumed constant during 24 hours.
The global “measurements” of τfine(0.55) where
simulated from the assumed sources and then these measurements were inverted by developed retrieval algorithm. The tests were accommodated to the same period as the one chosen for inverting actual observation, i.e. the meteorology of 2 last weeks of August 2000 was used in the preformed tests. The “real” sources where assumed equal to the total emission of black and organic carbon as it is set in GOCART model for the same two weeks.
Figure 1 – Illustration to inversion tests: upper panel - aerosol sources (107 kg of mass emitted by one grid box
per hour) assumed as “real” for August 28, 2000; lower panel shows aerosol emission retrieved after 40 iterations for same day (in total 9 days data were inverted).
Figure 2 – Illustration to inversion tests: upper panel - “August 28, 2000 measurements” of τfine(0.55)
simulated using “real” aerosol emission; lower panel -
τfine(0.55) simulated using retrieved emission
σabs= 1
Ni τi
*−τ
i(ˆ S )
(
)
2i
∑
, (20)σrel=100
Nk
τk*−τ
k(ˆ S ) τk*
2
i
∑
, (τk*≥0.05), (21)where absolute standard deviation σabs is simulated
using all locations and times and relative standard deviation σrel simulated using only points where τfine(0.55) is not smaller than 0.05. The value σabs
was introduced for characterizing accuracy of fitting observations of aerosol events with high loading. For test shown on Fig. 1 σabs ≈0.005and
σrel ≈9 % after 40 iterations, i.e. accuracy of fitting is below the expected measurements accuracy. The number of other various tests (not shown) where performed. For example, for the test when optical thickness was simulated using original GOCART model was slightly higher: σabs ≈ 0.01 and σrel ≈ 20%. Thus, the algorithm allows rather accurate fitting of observations with adequate strength and distribution of aerosol sources. It is important to note that “initial guess” used for source retrieval inversion was set as “no aerosol emission”, i.e. zero sources.
The tested algorithm was applied to the actual measurements of τfine(0.55) obtained by MODIS
and AERONET during the period of 20 to 28 August, 2000. Figure 3 shows the retrieved emission averaged over 9 days of the considered period.
Figure 3 – Averaged (August 20-28, 2000) aerosol sources (107 kg of mass emitted by one grid box per
hour) retrieved from MODIS and AERONET data: upper panel – retrieval with emission constrained to land only; lower panel - retrieval with emission not constrained to
land
Figure 4 compares average MODIS and AERONET observations of τfine(0.55) with the values fitted by
retrieval algorithm. The fitting accuracy of global observations was σabs ≈ 0.04 and σrel ≈ 48% after 40 iterations. Thus, as follows from Fig.4 and the values of σabs, and σrel, the τfine(0.55) simulated
from retrieved sources reproduces most of spatial and temporal tendencies in MODIS and AERONET observations.
Figure 4 – Illustration of fitting MODIS and AERONET data in the inversion: upper panel – averaged (August 20-28, 2000) measurements of τfine(0.55), lower panel –
averaged (August 20-28, 2000) measurements of
τfine(0.55) simulated using retrieved emission
Figure 5 shows the GOCART emission of fine mode aerosols (sulfates, black and organic carbon) averaged analogously to Fig. 3. Hence, comparison of Figs. 3 and 5 suggests that the placement of the major retrieved sources agrees with assumptions of GOCART emission in most locations with a few differences. For example, retrieval does not have intensive emission source assumed by GOCART over northern Canada. This can be explained by the lack of MODIS observations over this region (Fig. 4).
mass emitted by one grid per hour) assumed in GOCART model.
Figure 6 – Monthly (August, 2000) carbon emission (g /m2) obtained from combining satellite hotspots and
burned area with a biogeochemical model (Van der Werf et al., 2003).
Contrary, the retrieval shows well-pronounced sources in the south of the North America and over Indonesian Islands. GOCART does not have significant emission in those locations. Comparisons of these results with carbon emission (Fig.6) obtained from a combination of satellite data and biogeochemical modes (Van der Werf et al., 2003) suggest that there was carbon emission in those locations during August 2000.
Conclusions
Both numerical test and the results of actual data inversion show that developed method allows appropriate retrieval of the location and the strength of the global aerosol emission. Specifically, the global placement of the fine mode aerosol sources retrieved from observations was coherent with available independent knowledge. That was particularly encouraging since the developed inverse method did not use any a priori information about sources and it was initialized under “no aerosol emission” assumption. Also, the method allowed reproducing of two weeks instantaneous global observations of MODIS and AERONET
with the standard deviation in fitting of aerosol optical thickness of ~ 0.04. The optical thickness during high aerosol events of loading was reproduced with the standard deviation of ~ 48%. Such agreement between global modeling and observation seems to be quite encouraging given that the principle coherency between models and observations are limited by a number of reasons and factors. Specifically, spatial variability of aerosol can be much higher than the model resolution. The remote sensing measurements have limited accuracy. The models have uncertainties other than emission assumptions. For example, there are uncertainties in meteorological data (wind fields, 3 dimensional cloud distribution, etc.). Formalization of atmospheric processes has limited accuracy due to employed physical assumptions, numerical instabilities, etc. As a result, the models prediction can significantly differ from observations even for monthly and yearly averaged regional aerosol properties (Kinne at al., 2003, Sato et al. 2003).
Thus, the developed method can be a useful tool for improving global aerosol sources in chemical models. Nevertheless, this paper described only the first phase of the efforts and further analysis is necessary for understanding full potential of the method. Specifically, the following developments are planned: application of the method to longer record of observations, adding coarse mode aerosols into inverse modeling, including assimilation mode to the method for exploring a priori constraints about aerosol emission.
