Remote sensing of aerosol plumes: a semianalytical model

Remote sensing of aerosol plumes: asemianalytical model

Alexandre Alakian,1,* Rodolphe Marion,1 and Xavier Briottet2

1Commissariat à l’Energie Atomique, BP 12, 91680 Bruyères-le-Châtel, France2Office National d’Etudes et de Recherches Aérospatiales, 2 rue Edouard Belin, 31055 Toulouse, France

*Corresponding author: [email protected]

Received 6 August 2007; revised 18 December 2007; accepted 13 February 2008;posted 22 February 2008 (Doc. ID 86104); published 4 April 2008

A semianalytical model, named APOM (aerosol plume optical model) and predicting the radiative effectsof aerosol plumes in the spectral range ½0:4;2:5 μm�, is presented in the case of nadir viewing. It is devotedto the analysis of plumes arising from single strong emission events (high optical depths) such as fires orindustrial discharges. The scene is represented by a standard atmosphere (molecules and natural aero-sols) on which a plume layer is added at the bottom. The estimated at-sensor reflectance depends on theatmosphere without plume, the solar zenith angle, the plume optical properties (optical depth, single-scattering albedo, and asymmetry parameter), the ground reflectance, and the wavelength. Its mathe-matical expression as well as its numerical coefficients are derived from MODTRAN4 radiative transfersimulations. The DISORT option is used with 16 fluxes to provide a sufficiently accurate calculation ofmultiple scattering effects that are important for dense smokes. Model accuracy is assessed by using a setof simulations performed in the case of biomass burning and industrial plumes. APOM proves to be ac-curate and robust for solar zenith angles between 0° and 60° whatever the sensor altitude, the standardatmosphere, for plume phase functions defined from urban and rural models, and for plume locationsthat extend from the ground to a height below 3km. The modeling errors in the at-sensor reflectanceare on average below 0.002. They can reach values of 0.01 but correspond to low relative errors then(below 3% on average). This model can be used for forward modeling (quick simulations of multi/hyper-spectral images and help in sensor design) as well as for the retrieval of the plume optical properties fromremotely sensed images. © 2008 Optical Society of America

OCIS codes: 280.1100, 290.1090.

1. Introduction

Understanding the effect of aerosols on climate andon human health is a field of research that still re-quires new developments [1]. Aerosols are liquidand solid particles suspended in the atmosphere thatoriginate from natural or man-made sources of emis-sion. They can reflect and absorb solar radiation (theaerosol direct effect) and modify cloud properties(the aerosol indirect effect) [2]. These phenomenaare very variable depending on sources of emission,which makes difficult the assessment of the aerosoleffect on the radiative budget [2]. Aerosol particles

can originate from various sources. For example,carbonaceous substances are generally emitted bybiomass burning and industrial incomplete combus-tions, sea-salt particles by the ocean, and ashes andsulfuric acid particles by volcanic eruptions. Wind-blown mineral particles gather desert dust, sulfate,and nitrate aerosols resulting from gas to particlesconversion [1]. These particles generally remain inthe boundary layer (typically between 0 and 2km)or can be raised to higher altitudes during theirtransport [1]. For example, smoke from large firescan be emitted from near the ground to 7 − 8kmabove the ground, depending on the fire intensity.

Aerosol particles are characterized by their shape,their size, their chemical composition, and theiramount. These properties determine their radiative

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characteristics. Assuming sphericity and homogene-ity of particles as well as their complex refractionindex and their size distribution, Mie theory [3] al-lows one to compute the optical properties of aero-sols. Whereas molecules have localized spectralfeatures that allow their assessment, aerosols exhi-bit slow spectral variations and then they have aradiative effect in a wide range of wavelengths.Remote sensing methods are well suited for aero-

sol characterization. They generally make use of afew wavelengths [4,5] and multiangle [6,7] and polar-ization information [8]. Active remote sensing canalso be used (lidars [9]). In order to better understandthe global effect of aerosols, it is necessary to char-acterize the local sources of emission [10]. In thisstudy, we focus on smoke plumes that result fromsingle local high emission events, like biomassburning plumes and industrial plumes, observedby sensors with high spatial resolution (e.g., tensof meters). Studies on pollution and climate are usingmodels on particles circulation htat are valid at a glo-bal scale [10]. These models require local data as re-ferences. This paper aims at characterizing the localsources of aerosols and then contributes to providingsuch data. Moreover, it would help in understandingthe spatial distribution of natural and anthropogenicaerosols.The paper is devoted to the mathematical parame-

trization (semianalytical model) of the spectralsignal (at-sensor reflectance) above plumes in thespectral range ½0:4; 2:5 μm�. Multiple scattering playsa great role in the case of dense plumes. It can beaccurately computed by using algorithms like DIS-ORT [11] (discrete ordinates radiative transfer),but unfortunately this operation is very time con-suming and cannot be applied for satellite opera-tional algorithms. Disposing of a semianalyticalmodel that would take into account multiple scatter-ing would then be a fruitful advance in the purposeof forward modeling but also in the purpose of solv-ing the inverse problem. Indeed, usual techniquesmainly rely on a lookup table scheme involving com-plex numerical procedures and a huge amount ofdata. The size of the database can be in principlebe reduced using the polynomial approach [12] orneural networks techniques [13]. The main short-coming of these methods is, however, inflexibility.For instance, the change of the position, width, ornumber of spectral channels forces us to constructa new database or neural network training. This doesnot allow us to use algorithms developed for a givenspectrometer or radiometer to interpret data ob-tained from different instruments on board multiplesatellite platforms using the same database con-structed. Similar problems arise also in our particu-lar case if one needs to feed the algorithm with newor updated aerosol microphysical information. Ourgoal is then to develop a simple, explicitly invertable,semianalytical formula for remote sensing of aerosolplumes from the MODTRAN4 [14] numerical for-ward model (not explicitly invertable). Note that

such an approach has already been conducted for lit-toral [15], vegetation [16], and cloud [17] studies.

The outline of this paper is the following. In a firststep, the plume signal is modeled as a function of theoptical properties of aerosols (optical depth, single-scattering albedo, asymmetry parameter), the view-ing conditions (solar zenith angle, sensor is at nadir)and the ground reflectance. It yields a semianalyticalmodel named APOM (aerosol plume optical model).The obtained formula allows one to explicitly com-pute the at-sensor signal from the parameters men-tioned above. In a second step, the accuracy and therobustness of the model are assessed by using opticalproperties computed from a data set of biomass burn-ing and industrial particles. The possible extendeduses of the model in forward and inverse purposesare detailed and discussed at the end.

2. Description of the Aerosol Plume Optical Model

In this section, we first present the theoretical de-scription of APOM. Afterward, the algorithm anddata used to derive its numerical coefficients arepresented.

A. Analytical Formulation

Considering a plane-parallel atmosphere, the at-sensor radiance is the result of photons coming fromthe landscape and the atmosphere. The at-sensorreflectance ρsensor is defined here as

ρsensor ¼ πLsensor

μsEs; ð1Þ

where Lsensor is the at-sensor radiance, μs is the co-sine of the solar zenith angle θs, and Es is the extra-terrestrial solar irradiance. Considering reflectancerather than radiance allows us to overcome varia-tions of Sun irradiance and Sun geometry. This nota-tion is used whatever the altitude of the sensor,which can be either airborne or satelliteborne. As-suming a homogeneous Lambertian surface with areflectance ρ, ρsensor can be expressed as [18]

ρsensor ¼ ρatm þ Tatmρ1 − Satmρ ; ð2Þ

where ρatm is the upwelling atmospheric reflectance,and the second term is the additional contributiondue to the surface. Wavelength dependency of eachterm has been omitted for clarity. According to Refs.[19,20], the total transmittance Tatm of the atmo-sphere along the Sun–ground–sensor path may beinterpreted as the product of the transmittance(direct plus diffuse) in the solar direction for uniformillumination of the atmosphere from above by thetransmittance (direct plus diffuse) in the sensor di-rection for uniform illumination of the atmospherefrom below. Satm is the atmospheric spherical albedofor uniform illumination of the atmosphere frombelow. The distinction between illumination fromabove and below is crucial in our case because

1852 APPLIED OPTICS / Vol. 47, No. 11 / 10 April 2008

the atmosphere is vertically inhomogeneous (seeRef. [21] for a detailed discussion on this subject).Note that in this study, all numerical computationsof the atmospheric terms ρatm, Tatm, and Satm havebeen made using MODTRAN4, so this distinctionis fully accounted for.Now, let us consider a homogeneous absorbing

aerosol plume added in a layer just above the ground.The atmospheric terms ρatm, Tatm, and Satm are thenmodified by the presence of the plume. The goal ofAPOM is to derive amathematical formula that mod-els the variation of these terms in the presence of theplume. For this, APOM assumes that each atmo-spheric term can be expressed as the combinationof two terms: a first one that is the corresponding at-mospheric term for the same scene without plumeand a second one due to the plume (see Fig. 1). APOMproposes to model ρatm, Tatm, and Satm for a nadirviewing sensor as functions of the plume opticalproperties (fully characterized by the optical depthτ, the single-scattering albedo ω0 , and the asymme-try parameter g), and the solar zenith angle. At agiven wavelength, ρatm, Tatm, and Satm are modeledwith the following expressions:

ρatmðτ;ω0; g; μsÞ ¼ ρatm0 ðμsÞ þ ρatmplumeðτ;ω0; g; μsÞ; ð3Þ

Tatmðτ;ω0; g; μsÞ ¼ Tatm0 ðμsÞTatm

plumeðτ;ω0; g; μsÞ; ð4Þ

Satmðτ;ω0; gÞ ¼ Satm0 þ Satm

plumeðτ;ω0; gÞ; ð5Þ

where ρatm0 , Tatm0 , and Satm

0 are, respectively, the up-welling atmospheric reflectance, the total transmit-tance (direct plus diffuse), and the atmosphericspherical albedo in the case of a given atmospherewithout plume. This atmosphere without plume

takes into account gaseous and natural aerosol pro-files from ground to sensor and will be referredas standard in the following. By natural aerosols,we point out the aerosols that are present in thescene without plume, i.e., the background aerosols.ρatmplume, T

atmplume, and Satm

plume are the corresponding atmo-spheric terms that are due to the plume. They in-clude the effect of the plume itself, the couplingbetween plume particles and atmospheric gases,and, especially for ρatmplume, the transmission loss be-tween the top of the plume and the sensor. The cou-pling between plume particles and natural aerosolsis neglected (this assumption will be discussed inSubsection 3.D). The plume terms are expressed by

ρatmplumeðτ;ω0; g; μsÞ

¼ α0ðω0; gÞ241 − exp

0@XNτ

k¼1

αkðω0; g; μsÞτk1A35; ð6Þ

Tatmplumeðτ;ω0; g; μsÞ ¼ exp

0@XNτ

k¼1

γkðω0; g; μsÞτk1A; ð7Þ

Satmplumeðτ;ω0; gÞ

¼ β0ðω0; gÞ241 − exp

0@XNτ

k¼1

βkðω0; gÞτk1A35;

ð8Þ

where Nτ is the degree of the polynomial in τ, α0 andβ0 are functions of ω0 and g, ∀ k ∈ f1; :::;Nτg, αkand γk are functions of ω0, g, and μs, and βk are

Fig. 1. APOMprinciple.When adding the plume, changes in photons paths are taken into account by the equations of ρatm, Tatm, andSatm.At-sensor atmospheric terms (ρatm, Tatm, Satm) are modeled as combinations of standard atmospheric terms (ρatm, Tatm

0 , Satm0 ) and plume

atmospheric terms (ρatmplume,Tatmplume,S

atmplume). Standard terms are computed by considering the scene without plume and by taking into account

gaseous and natural aerosol profiles from ground to sensor. Plume terms are computed from APOM coefficients.


functions of ω0 and g. The dependency on wavelengthcannot be easily modeled (see below), which is whyeach wavelength is considered separately.We will now describe how these expressions have

been established. Let us consider a given solar zenithangle θs. When there is no plume (i.e., τ ¼ 0), ρatmequals the standard upwelling atmospheric reflec-tance ρatm0 . When τ increases, ρatm varies. As theplume is assumed to be lying at the bottom of the at-mosphere and to have a limited vertical extension(typically a few hundreds meters, i.e., far lower thanthe total atmospheric column), we consider that add-ing aerosols can only have an increasing effect onρatm. Computations show that the error in ρatm begot-ten by this assumption is below 0.001 in the spectralrange ½0:4; 2:5 μm�. Then ρatm − ρatm0 must be modeledwith a positive function. The solution should tend to-

ward 0 when τ tends toward 0 whatever the values ofω0 and g. Another condition is that the solutionshould converge toward a limit value for the highvalues of τ. Indeed, when the plume is very dense,the photons cannot pass through a wall of aerosols,and then adding more particles would not changeanything. The dependency on τ of ρatm − ρatm0 is re-presented in Fig. 2 for various couples ðω0; gÞ. Theshape of the dependency can pretty well be fittedwith a law in the form αð1 − eβτÞ, α > 0, β < 0. Thisform checks the limit conditions defined before. Gen-eralizing the τ-dependency as a polynomial in τ (witha constant part equaling zero) in the exponentialallows a better fit of ρatm and then its expressionbecomes the one given by Eqs. (3) and (6).

As the functions α0ðω0; gÞ and αkðω0; g; μsÞ have asmooth dependency on ω0 and g (see Fig. 3 for α0),

Fig. 2. Evolution of ρatm − ρatm0 as a function of τ (ω0 and g being fixed). (a) g ¼ 0:45, ω0 ∈ f0:45;0:60; 0:69; 0:77;0:84; 0:90; 0:95;0:98g (thehigher ω0, the upper the curve), (b) ω0 ¼ 0:84, g ∈ f0:01;0:10; 0:20; 0:30;0:45; 0:60; 0:75;0:90g (the higher g, the lower the curve). In thesesimulations, nadir viewing sensor altitude is 20km, standard atmosphere is 1976 U.S. Standard with no natural aerosol, solar zenithangle θs is 15°, and aerosol plume phase function type is urban (as defined in MODTRAN4). Dependency on τ can be roughly modeledwith a law in the form αð1 − eβτÞ, α < 0, β < 0.

Fig. 3. Surface α0ðω0; gÞ. The smooth behavior along ω0 and g allows a fit using a polynomial approach.


they can be modeled by performing a polynomialapproach (for a given μs):

∀ k ∈ f0;…;Nτg; αkðω0; gÞ ¼X

0≤i≤Nω0≤j≤Ng

ηijkωi0g

j; ð9Þ

where ηijk are the surface fitting parameters, and Nωand Ng are, respectively, the degrees of the polyno-mials in ω0 and g. We can notice that if ω0 equals0 (i.e., no scattering), then ρatm should be the samewhatever the value of g: as no photons are scattered,the direction of scattering does not matter. Thenevery ηijk should equal 0 for i ¼ 0; j ≥ 1;∀ k.Along the Sun–ground path, the photons that cross

a horizontal plume (optical depth τ) with a zenithangle θs travel along an effective optical depthτμ−1s . Along the ground–sensor path, the effective op-tical depth is τ because the sensor is at nadir. Then,the dependency on the solar zenith angle θs can beincluded by replacing ηijk by ðbijk þ cijkμ−ks Þ. bijk char-acterizes the ground–sensor path, whereas cijk char-acterizes the Sun–ground path. Then, ρatmplume can bewritten as follows:

ρatmplumeðτ;ω0; g; μsÞ ¼X

ði;jÞ∈I×J

aijωi0g

j

×

241 − exp

0@ X

ði;j;kÞ∈I×J×K

ðbijk þ cijkμ−ks Þτkωi0g

j

1A35; ð10Þ

where I ¼ f0;…;Nωg, J ¼ f0;…;Ngg, K ¼ f1;…;Nτg, and aij ¼ bijk ¼ cijk ¼ 0 for i ¼ 0; j ≥ 1;∀ k.These considerations have been made for one

wavelength. Modifying the wavelength does notchange the shape of ρatmplume, but the fitting parametersaij, bijk, and cijk are different. This is due to a cou-pling [22] between the aerosol plume and the gasesfrom the standard atmosphere. This coupling isdue to Rayleigh scattering (important for the shorterwavelengths) and to the numerous gaseous ab-sorption lines along the spectrum. Then, the fittingparameters are calculated for each wavelength sepa-rately. Unfortunately, it seems that it is not possibleto model each parameter as a simple function ofwavelength. Note that if only τ, ω0, g, and μs inter-vene in the expression of ρatmplume, the coefficients aij,bijk, and cijk take into account the coupling betweenthe plume and atmospheric gases (changing the stan-dard atmosphere, and then the coupling leads to lowmodeling errors; see Subsection 3.E).Similarly, the same study has been conducted for

Satmplume and Tatm

plume. The behavior of Satmplume can be mod-

eled exactly in the same way as ρatmplume. However, wecan note two differences. The first one is that Satm

plumedoes not depend on solar zenith angle because bydefinition it is computed from an integration overall angles. The second difference is that Satm

plume cantake negative values for low values of ω0. Indeed,

adding dark absorbing particles in the atmospheredecreases its scattering effects and then decreasesSatm. We obtain

Satmplumeðτ;ω0; gÞ

¼X

ði;jÞ∈I×J

dijωi0g

j

241 − exp

0@ X

ði;j;kÞ∈I×J×K

f ijkτkωi0g

j

1A35;

ð11Þwhere dij ¼ f ijk ¼ 0 for i ¼ 0; j ≥ 1;∀ k.

For Tatmplume, we have the following expression:

Tatmplumeðτ;ω0; g; μsÞ

¼ exp

0@ X

ði;j;kÞ∈I×J×K

ðuijk þ vijkμ−ks Þτkωi0g

j

1A; ð12Þ

where uijk ¼ vijk ¼ 0 for i ¼ 0; j ≥ 1;∀ k.

B. Estimation of the Model Coefficients

We have described the general formulation of theatmospheric terms in the presence of a plume. Wenow present the algorithm and data used to establishthe model.

The radiative transfer code used to simulate ρsensoris MODTRAN4. The DISORT option is used with16 fluxes to accurately account for multiple scatter-ing effects. The establishment of the model requiresus to fix some parameters, which are the sensor al-titude, the atmosphere without plume that is re-ferred as the standard atmosphere, the type of theaerosol plume phase function, and the plume loca-tion. They will be referred to in the following asthe fixed parameters. The atmosphere is definedby the 1976 U.S. Standard profile, without naturalaerosols (the effect of their addition to the scene isassessed in Subsection 3.D), with an added plume lo-cated between the ground and an altitude of half akilometer. The remote sensor is located at an altitudeof twenty kilometers, looking at the nadir direction.

The aerosol phase function of the plume is a keyparameter that quantifies the probability of the scat-tering directions. In the case of dense plumes, forwhich multiple scattering is quite important, themean behavior of this function may be sufficient todescribe its whole effect, and then the asymmetryparameter g is used for this purpose. However, anasymmetry parameter must be connected to an asso-ciated phase function that then needs to be chosen.Indeed, g only characterizes the average behavior ofthe phase function. Two phase functions that havethe same average are not necessarily equal. As theaerosol phase function depends on the type of parti-cle and as the model presented is general (in τ, ω0,and g), the phase function corresponding to urbanparticles as described in MODTRAN4 has beenchosen. Urban particles composition (by number)is 20% of soot, 56% of water-soluble substance,and 24% of dustlike aerosols [23]. This choice is


motivated by the fact that biomass burning particlesand industrial particles are very often carbonaceous[24–26] and then must have a similar behavior tourban particles. The urban phase function is com-puted from Mie theory, and then is preferred tothe analytical phase function of Henyey–Greenstein[27], which is generally less accurate. The effect ofthis choice will be discussed in Subsection 3.E.The simulations of ρatm, Satm, Tatm, and ρsensor by

MODTRAN4 are, respectively, referred to asρatmMODTRAN , Satm

MODTRAN , TatmMODTRAN , and ρsensorMODTRAN .

APOM simulations are referred to as ρatmAPOM,SatmAPOM , Tatm

APOM, and ρsensorAPOM .The method used for the determination of the

model coefficients is the same for ρatmAPOM, SatmAPOM,

and TatmAPOM;then it is only described for ρatmAPOM. For

a given wavelength λ0, the simulations with the fullsets for τ, ω0, g, and θs are considered. The estimatesaijðλ0Þ, bijkðλ0Þ, and cijkðλ0Þ of the fitting parametersaijðλ0Þ, bijkðλ0Þ, and cijkðλ0Þ are computed simulta-neously by

haijðλ0Þ; bijkðλ0Þ; cijkðλ0Þi ¼ Arg minaij;bijk;cijk

Δρðaij; bijk; cijkÞ;

ð13Þ

where

Δρðaij; bijk; cijkÞ ¼X

τ0∈Iτω00∈Iω

g0∈Igθ0s∈Iθ

ðρatmMODTRANðτ0;ω00; g

0; μ0sÞ

− f ρðaij; bijk; cijk; τ0;ω00; g

0; μ0sÞÞ2;ð14Þ

and where f ρðaij; bijk; cijk; τ;ω0; g; μsÞ is defined by theexpression of ρatmAPOMðτ;ω0; g; μsÞ given in Eqs. (3) and(10), and Iτ, Iω, Ig, and Iθ are, respectively, the varia-tion ranges of τ, ω0, g, and θs.We use a generalized reduced gradient method [28]

to solve Eq. (13). The values of aij, bijk, and cijk havebeen constrained between −8 and 8 in order to accel-erate the algorithm convergence and to reduce thenumber of local minima of Δρ. Their initial valuesare computed randomly between −0:8 and 0.1 (thenumerical values have been obtained by trial anderror). As the functionΔρmay have many local mini-ma, the algorithm is run several times with differentrandom initial inputs. The optimal coefficients arechosen as the ones that minimize Δρ. This processis conducted for every wavelength. Finally, we obtainthe optimal expressions of aijðλÞ, bijkðλÞ, and cijkðλÞ inthe least mean squares sense.Nτ, Nω, and Ng must be chosen carefully. Too low

values will lead to a poor modeling, whereas too highvalues can lead to overfitting phenomena and in-crease considerably the computing time requiredfor solving Eq. (13). We found that choosing Nτ ¼ 3,Nω ¼ 4, and Ng ¼ 3 was a good trade-off between

model accuracy and computation time (see Section 3for details on modeling errors).

For each wavelength, 119 non-null coefficients areneeded to model ρatm, 68 non-null coefficients forSatm, and 102 non-null coefficients for Tatm. Thenρsensor is modeled with 289 coefficients at each wave-length. APOM coefficients can be obtained from theauthor upon request.

The presented model has been computed with aspectral resolution of 15 cm−1. Such a resolution issufficient for a future use with hyperspectral sensorsthat have resolutions of about 10nm in the spectralrange ½0:4; 2:5 μm�. If one is required to use the modelfor a particular sensor, coefficients that are adaptedto its spectral bands are required. Then, for a givensensor, all the computations performed so far withMODTRAN4 have to be convolved with the normal-ized spectral response. The method described beforeis then applied to determine the model coefficients.In the example of the hyperspectral sensor AVIRIS(Airborne Visible/InfraRed Imaging Spectrometer[29], 224 bands), the plume signal measured by thissensor can be modeled with 64,736 coefficients(224bands × 289 coefficients). Note that once thedatabase of simulations has been computed at15 cm−1, the model coefficients corresponding to agiven sensor are determined fast and can be usedfor all images from this sensor.

The APOM coefficients computed over all thewavelengths of interest allow us to generate quasi-instantaneously ρsensor within ½0:4; 2:5 μm�, whateverthe plume optical properties τ, ω0, and g, and what-ever the solar zenith angle θs (note that a full MOD-TRAN4 run with DISORT 16 fluxes is very timeconsuming; see the conclusion section at the endfor a discussion).

The set of simulations has been conducted byvarying the optical properties of the plume, thewavelength, and the solar zenith angle. These para-meters will be referred to in the following as thevarying parameters (by opposition to the fixed para-meters described before). The optical depth τ cantake values in the set Iτ ¼ f0:0; 0:1; 0:2; 0:4; 0:6;0:8; 1:0; 1:3; 1:6; 2:0; 2:4; 2:8; 3:2g. The single-scatter-ing albedo ω0 takes its values in the set Iω ¼f0:00; 0:45; 0:60; 0:69; 0:77; 0:84; 0:90; 0:95; 0:98g. Va-lues of the asymmetry parameter g belongto Ig ¼ f0:01; 0:10; 0:20; 0:30; 0:45; 0:60; 0:75; 0:90g.Ranges are defined from available data on plumes(see Subsection. 3.B for details). g can theoreticallytake negative values, but the simulations of opticalproperties as done in Subsection 3.B show that itnever happens in the considered cases. These setshave been established by studying the effect of eachparameter: simulations show that this effect in-creases faster and faster as ω0 increases and τ andg decrease, which explains the variable steps usedfor each set. For wavelength, as said above, all thecomputations are made on MODTRAN4 wave-length grid 15 cm−1 in the range ½0:4; 2:5 μm�.The solar zenith angles θs are chosen in the set


Iθ ¼ f15°; 30°; 45°; 60°g. Note that the model only de-pends on τ, ω0, and g;then the model is fully general(for aerosol plumes with g > 0).

3. Accuracy and Robustness of Aerosol PlumeOptical Model

A. Principles of Aerosol Plume Optical ModelPerformances Evaluation

APOM performances are now estimated by consider-ing MODTRAN4 as a benchmark. Its accuracy is as-sessed by varying the plume optical properties τ, ω0,and g as well as the solar zenith angle θs and wave-length (i.e., the varying parameters). Afterward, nat-ural aerosols are added to the atmosphere, and theireffects on modeling errors are evaluated. Finally, therobustness of the model is assessed by varying thesensor altitude, the standard atmospheric model,the plume phase function, and the plume location(i.e., the fixed parameters). The validation strategyis detailed below.In a first step, a large set of spectral optical proper-

ties is computed with Mie theory in the spectralrange ½0:4; 2:5 μm� from a wide range of microphysi-cal properties that can be observed in biomass burn-ing and industrial plumes (see Subsection 3.B andTable 1). These optical properties are used to assessthe modeling errors.In a second step, the atmospheric terms ρatm, Tatm,

Satm, and ρsensor associated with these optical proper-ties are computed by using MODTRAN4 and APOMand by considering the original fixed parametersused to establish the model (nadir viewing sensor al-titude of 20km, U.S. 1976 standard atmosphere, andurban plume phase function), and no natural aerosol.As the model has been established for solar zenithangles belonging to the set f15°; 30°; 45°; 60°g, its ac-curacy needs to be estimated for a wider range of an-gles. Then the set f0°; 10°; 20°; 30°; 40°; 50°; 60°; 70°gis considered for the assessment. MODTRAN4 andmodel simulations are compared in Subsection 3.Cin terms of values (full spectrum) and absolute spec-tral errors that are defined for each wavelength asΔρatm ¼ jρatmMODTRAN − ρatmAPOMj, ΔTatm ¼ jTatm

MODTRAN−

TatmAPOM j, ΔSatm ¼ jSatm

MODTRAN − SatmAPOMj, and Δρsensor ¼

jρsensorMODTRAN − ρsensorAPOMj (wavelength dependency isomitted for clarity).In a third step, the effect of adding natural aerosols

in the atmosphere is estimated. For this particularcase, assessment is performed by setting θs to 20°and by using a set of 16 types of plume particlesrandomly selected from Table 1 that correspond to

various spectral behaviors and by varying the parti-cles concentration (i.e., the amplitude of opticaldepth). The same error analysis between MOD-TRAN4 and model simulations is led by consideringeach condition separately (see Subsection 3.D).

In a fourth step, the sensor altitude, the standardatmospheric model, the aerosol phase functiontypes, and the plume location are varied to assessthe model robustness. The sets of optical propertiesdefined from Table 1 are used, and θs is varied in theset f10°; 30°; 50°g.

In a fifth step, the respective effect of modelingerrors in ρatm, Tatm, and Satm on ρsensor is assessed(see Subsection 3.F). Furthermore, the effect of un-certainties on ground reflectance is also discussed.

The flowchart in Fig. 4 illustrates the main lines ofthe validation strategy. For every simulation, a grayground reflectance is considered. A mean value of 0.3is used so the joint effects of the atmospheric termson the sensor signal can be observed.

B. Microphysical Properties of Aerosol Plumes

Biomass burning and industrial particles are consid-ered to validate the model. Note that other types ofparticles (e.g., volcanic particles) could also havebeen considered because the model is general in τ,ω0, and g. The aerosol optical properties are definedfrom their microphysical properties which are theconcentration, the refractive index (composition),and the size distribution. They will be detailed below.

Biomass burning particles are described with acoated sphere where a black carbon (BC) core is sur-rounded by a nonabsorbing organic shell (OC) [30].This is the BC content of the aerosol particles thatdetermines their absorbing behavior. Then the lowerthe BC, the higher ω0 and the higher the scattering.The relative amount of BC usually ranges from 2% to30% [24]. The wavelength-dependent refractive in-dex of particles has to be assumed. For BC, the valuesfrom Fenn et al. [31] for soot are used. For wave-lengths above 2:0 μm, the values of Sutherland andKhanna [32] are taken for OC. For other wave-lengths, very limited information about the refrac-tive index of OC exists. Then by inspiration fromthe work of Trentmann et al. [30], the index of am-monium sulfate was chosen for wavelengths in therange ½0:4; 2:0 μm� because it has the same spectralbehavior. The refractive index of the internal mixtureis computed using the Maxwell–Garnett mixing rule[33], assuming the same density for BC and OC, asperformed in Ref. [30]. As the humidification factoris generally low for biomass burning particles [34],

Table 1. Aerosol Microphysical Properties Used to Model Optical Properties ofBiomass Burning Particles and Industrial Particles

Microphysical Property Biomass Burning Particles Industrial Particles

Composition 2%BC 10%BC 30%BC 40% BC ASSize distribution modal radius rm ðμmÞ 0:05 0:10 0:15 0:05 0:15Size distribution standard deviation σm 1:35 1:65 1:90 1:60 1:90τ550 0:4 0:8 1:3 2:4 0:4 0:8 1:3


the effect of humidity on the optical properties isneglected in this study.The size distribution of biomass burning aerosols

is modeled as a monomodal lognormal law. Indeed,even if several modes exist, one has generally muchmore radiative effect than others [24]. The range ofmodal radii and standard deviations varies betweenfresh smoke and aged smoke. Collection of datashows modal radii between 0:05 μm for fresh smokeand 0:15 μm for aged smoke, with a medium value of0:10 μm and standard deviations between 1.35 and1.90, with a medium value of 1.65 [24].Plume particles concentrations are highly variable

[34] in space and in time. In our study, they havebeen defined from the optical depth at λ ¼ 550nm,which is referred to as τ550. From available measure-ments [34], τ550 typically varies from 0.4 to 2.4, whichis representative of observations and applies to thickplumes.A few pieces of information have been gathered

so far concerning industrial particles. The analy-sis of the measurements performed during theESCOMPTE (Expérience sur Site pour Contraindreles Modèles de Pollution atmosphérique et de Trans-port d’Emissions) campaign [26] shows that in-dustrial particles are generally composed of carbo-naceous particles as we can find in biomass burningparticles but also ammonium sulfate particles, notedAS. The composition, the size distribution, and theconcentrations used to characterize industrial parti-cles are also summarized in Table 1.

Figure 5 presents the optical properties computedfrom Mie theory for two types of particles: the firstone corresponds to a biomass burning plume, the sec-ond one to an industrial plume. These two examplesshow that each optical property may have very vari-able spectral behaviors. The large database of opticalproperties that have been computed from Table 1may allow us to cover most of the encountered beha-viors. By considering every wavelength, this data-base gathers optical depths varying between 0 and3.5, single-scattering albedos varying between 0.03and 1, and asymmetry parameters varying between0.04 and 0.88. Note that every triplet of optical prop-erties [τðλÞ, ω0ðλÞ, gðλÞ] in which τðλÞ could exceed 3.5has been excluded from the database.

C. Model Accuracy

As an illustration, Fig. 6 compares ρsensor as com-puted by MODTRAN4 and by the model. The opticalproperties that are used are those represented inFig. 5 and correspond to biomass burning and indus-trial plumes. The highest absolute error [about 0.005at λ ¼ 0:8 μm; see Fig. 6(b)] corresponds to a relativeerror of 2%. APOM fits accurately MODTRAN4 si-mulation at every wavelength in both cases that cor-respond to very different spectral optical properties.

As the simulations corresponding to biomass burn-ing and industrial plumes present the same charac-teristics in terms of values and absolute errors,they will be represented in the same figures with-out distinguishing them. Indeed, the r2 correlation

Fig. 4. Flowchart describing assessment method of APOM performances. For accuracy assessment, τ, ω0, g, and θs are varying. Forrobustness assessment, the same parameters are varying as well as standard atmosphere, sensor altitude, plume location, and typeof aerosol plume phase function.


coefficients between MODTRAN4 and APOM areabout the same in both cases for ρatm, Tatm, Satm,and ρsensor (r2 ≥ 0:999 for each case).Figure 7 presents ρatm, Tatm, Satm, and ρsensor (for

ρ ¼ 0:3) values as calculated by MODTRAN4 andby APOM over ½0:4; 2:5 μm� for θs varying between0° and 60°. Figure 8 shows the corresponding spec-tral errors Δρatm, ΔTatm, ΔSatm, and Δρsensor. Eachatmospheric term is analyzed separately. Δρatm doesnot exceed 0.012 (mean error below 0.002), as seen inFig. 8(a). Note that the highest absolute errors corre-spond to low relative errors below 3% (for example,Δρatm ¼ 0:012 corresponds to ρatm ¼ 0:40). ΔTatm

remains below 0.008 over ½0:4; 2:5 μm� (mean erroraround 0.002). The highest errors in Tatm mainly cor-respond to relative errors around 2% (r2 > 0:999).Satm is accurately modeled in the full spectrum(average error below 0.002, r2 ¼ 0:999) but canreach values of 0.02 inside strong gaseous absorptionbands (and 0.01 outside them) as seen in Figs. 7(c)

and 8(c). Fortunately, such errors have little effect onρsensor (more details are given in Subsection 3.F).Errors in ρatm, Tatm, and Satm may compensate. Fig-ures 8(a) and 8(d) show that the spectral behaviorof Δρsensor is about the same as Δρatm, which isquite accurate. This behavior is explained in Sub-section 3.F.

The results of the sensitivity study on ρatm, Tatm,Satm, and ρsensor by considering each solar zenith an-gle separately over the spectral fields ½0:4; 0:5 μm�,½0:5; 0:8 μm�, and ½0:8; 2:5 μm� outside strong gaseousabsorption bands are gathered in Table 2. The stan-dard deviations associated with the mean errorsapproximately equal them. For angles between 0°and 60°, the mean modeling errors are very lowand remain below 0.002 in ½0:4; 2:5 μm�. The modelhas been established for angles varying between15° and 60°, and then the extrapolation between0° and 15° remains accurate. On the contrary, foran angle of 70°, extrapolation is far less accurate

Fig. 5. Aerosol optical properties for (a) biomass burning plume (BC content of 10%, rm ¼ 0:15 μm, σm ¼ 1:65 and τ550 ¼ 0:8) and (b) in-dustrial plume (AS particles, rm ¼ 0:05 μm, σm ¼ 1:60, and τ550 ¼ 0:8).

Fig. 6. Comparison between MODTRAN4 and APOM simulations at θs ¼ 30° for ρsensor in case of (a) biomass burning plume and (b) in-dustrial plume (associated optical properties are represented in Fig. 5). For clarity, the represented spectral errors are multiplied by 10. Inboth cases, modeling errors are on average below 0.002. They reach a maximum of about 0.005 in (b), which corresponds to a relative errorof 2%.


(modeling errors are between three and six timeshigher than for other angles) but still acceptable(mean errors in ρsensor remain below 0.01).On the whole, for solar zenith angles between 0°

and 60°, the model reproduces accurately the simu-lations performed with MODTRAN4 using the DIS-ORT 16 fluxes option: modeling errors are in generallower than 0.002. Moreover, high absolute errors cor-respond to low relative errors (below 3% in general).

D. Impact Evaluation of Natural Aerosols

The presence of natural aerosols in the scene has notbeen considered during the computation of APOMcoefficients. APOM assumes that their effect canbe fully included in the computation of ρatm0 , Tatm

0 ,and Satm

0 for a scene without plume. The coupling be-tween natural aerosols and plume aerosols is thenassumed to be negligible. This hypothesis is assessednow.Natural aerosols located above and below the

plume have little interaction with it (computationsshow that they do not affect APOM performances),but it is not the case for the ones located insidethe plume. Indeed, natural and plume aerosols aremixed externally, which modifies the global plumeoptical properties. As this phenomenon is not taken

into account in the model, its effect needs to beestimated.

For a given type of plume particle and a given typeof natural aerosol, the analysis is performed as fol-lows. On one hand, the optical properties of theexternal mixture between plume aerosols and natur-al aerosols are computed. MODTRAN4 uses theseoptical properties as inputs to simulate ρatm, Tatm,Satm, and ρsensor. On the other hand, APOM simula-tions are performed by using as inputs the plume op-tical properties (which do not take into account thenatural aerosols) as well as ρatm0 , Tatm

0 , and Satm0 com-

puted with MODTRAN4 for a scene without a plumeand containing a layer of natural aerosols located be-tween the ground and an altitude of half a kilometer(i.e., the plume location). MODTRAN4 and APOM si-mulations are then compared in terms of absolutespectral errors.

Three types of natural aerosols defined in MOD-TRAN4 are considered in this study: rural, maritime,and urban. MODTRAN4 atmospheric profiles showthat the natural aerosol column located inside theplume (0–500m) represents generally less than25% of the natural aerosol column over all the atmo-sphere. Then, by considering visibilities between10km and 20km at 550nm over all the atmosphere

Fig. 7. Comparison of (a) ρatm, (b) Tatm, (c) Satm, and (d) ρsensor (for ρ ¼ 0:3) values as computed by MODTRAN4 and by APOM for biomassburning and industrial plumes and for θs between 0° and 60°. Computations performed outside and inside strong gaseous absorption bandsare respectively represented in dark gray and light gray. Correlation coefficient is higher than 0.999 for every case.


(i.e., τnatural550 varying between 0.2 and 0.4), the naturalaerosol column inside the plume τnatural550 � varies be-tween 0.05 and 0.10. Both values have been usedfor the assessment.Simulations show that absolute errors have the

same level whatever the plume optical depth. Foreach natural aerosol type, Table 3 gathers the abso-lute spectral errors over the set of simulations dedi-cated to this study by making a distinction between

values of τnatural550 � (see Subsection 3.A for details). Asthe number of simulations performed is not as highas for the study of the other parameters, a direct com-parison cannot be reasonably done. However, itclearly appears that errors in ρatm, Tatm, and ρsensorare almost as low for rural and maritime naturalaerosols as the errors obtained in Table 2. Errorsare higher when urban natural aerosols are con-sidered, especially for τnatural550 � ¼ 0:1. This can be

Fig. 8. Spectral errors between MODTRAN4 and APOM for (a) ρatm, (b) Tatm, (c) Satm, and (d) ρsensor (for ρ ¼ 0:3) for biomass burning andindustrial plumes and for θs between 0° and 60°. Mean values are represented by black dots.

Table 2. Mean Errors in ρatm, Tatm, Satm and ρsensor for Different Solar Zenith Angles and OverThree Spectral Intervalsa and Outside Strong Gaseous Absorption Bandsb

103Δρatm 103ΔTatm 103ΔSatm 103Δρsensor

Bands Λ1 Λ2 Λ3 Λ1 Λ2 Λ3 Λ1 Λ2 Λ3 Λ1 Λ2 Λ3

0° 1.5 0.9 0.7 2.2 2.2 2.0 1.0 0.8 1.7 1.5 1.3 1.110° 1.9 1.1 0.7 2.0 2.1 2.0 1.0 0.8 1.7 1.7 1.2 1.020° 1.3 0.9 0.7 1.6 1.9 2.0 1.0 0.8 1.7 1.3 1.0 1.030° 0.8 0.9 0.8 1.7 1.7 1.9 1.0 0.8 1.7 1.0 0.9 0.940° 1.3 1.3 1.0 2.4 1.7 1.9 1.0 0.8 1.7 1.3 1.2 1.050° 1.4 1.4 1.2 2.7 1.8 1.7 1.0 0.8 1.7 1.3 1.3 1.260° 1.0 1.3 1.3 1.5 1.6 1.7 1.0 0.8 1.7 1.0 1.5 1.50°–60° 1.3 1.1 0.9 2.0 1.9 1.9 1.0 0.8 1.7 1.3 1.2 1.1

70° 8.8 6.8 2.7 14 7.8 3.8 1.0 0.8 1.7 7.4 6.9 3.5

aΛ1 ¼ ½0:4; 0:5 μm�, Λ2 ¼ ½0:5; 0:8 μm�, Λ3 ¼ ½0:8;2:5 μm�.b0°60° gives the mean errors over all angles between 0° and 60°. The standarddeviations associated with the mean errors approximately equal them.


explained by the fact that such absorbing parti-cles have low values of ω0 (below 0.65 at everywavelength) and then reduce the global ω0 in thecase of nonabsorbing plumes (AS): a value of ω0 thatchanges from 1 to 0.97 may have a significant effecton the atmospheric terms. In the worst case (ASplume particles with τ550 ¼ 1:3, urban natural aero-sols with τnatural550 � ¼ 0:1), Δρsensor (for ρ ¼ 0:3) canreach values of 0.03 for wavelengths close to0:4 μm, which corresponds to a relative error of about8%. Errors in Satm can reach values as high as 0.03but have little effect in ρsensor, as it will be shown inSubsection 3.FIt is possible to remove the modeling errors due to

natural aerosols by doing as follows. As APOM is amodel that depends only on optical properties, itcan directly take into account the presence of naturalaerosols inside the plume. Indeed, it is just needed tocompute the optical properties of the external mix-ture between plume and natural aerosols and to in-troduce them into APOM rather than the plumeoptical properties alone. A rigorous applicationwould require then to compute ρatm0 , Tatm

0 , and Satm0

by considering only the natural aerosols locatedabove the top of the plume (otherwise, the contribu-tion of the natural aerosols inside the plume wouldbe taken into account twice).

E. Model Robustness

APOM should be used in a general purpose. Then, itis necessary to assess its robustness by changing itsfixed parameters, which are the sensor altitude, thestandard atmospheric model in the scene, the type ofthe aerosol phase function, and the plume location.Each parameter is studied separately. The sensor

altitude takes values of 2km, 5km, 10km, 20km(APOM), and 99km. The standard atmospheric mod-el and the aerosol phase function types are beingvaried with models defined in MODTRAN4. Thestandard atmospheric model is chosen as tropical,midlatitude summer (Mid-L sum), midlatitude win-ter (Mid-L win), subarctic summer (Sub-A sum), sub-arctic winter (Sub-A win), and 1976 U.S. standard.The plume location is defined by the altitudes ofits bottom and top (zmin − zmax) which are 0–0:5km(APOM), 0–1km, 0–2km, 0–3km, 0–4km, 0–6km,0:5–1km, 2–3km, 3–5km, and 6–8km.

As explained in Subsection 2.B, the asymmetryparameter g is connected to a plume phase functionwhich is typical of urban particles as defined inMODTRAN4. To assess the effect of this choice, si-mulations are performed by connecting g to otherplume phase function types defined in MODTRAN4,which are the rural type and the maritime type. Therural type is defined with particles composed of 70%of water-soluble substance and 30% of dustlike aero-sols. The maritime type is defined by a mixing of seasalts and water [23].

The model requires standard atmospheric termsthat characterize the scene without plume. Then,ρatm0 , Tatm

0 , and Satm0 are computed for each configura-

tion corresponding to different sensor altitudes anddifferent standard atmospheric models. Afterward,they are introduced as inputs in the model.

The results of the sensitivity study at MODTRAN4resolution have been gathered in Table 4. It appearsthat the model is not sensitive to the sensor altitude.Indeed, the modeling errors for a sensor altitude of20km are about the same as for other altitudes.The same conclusion can be made by comparingthe errors from the U.S. Standard atmosphere tothe other standard atmospheres outside strong gas-eous absorption bands. However, inside the strongabsorption bands the modeling errors are increasedby a factor between 1.5 and 3, as seen in Fig. 9. Thedifferent standard atmospheres do not present thesame concentrations of gases, which is why the devia-tion with the U.S. Standard atmosphere is mostly lo-cated in the absorption bands. However, Δρatm andΔTatm do not exceed 0.020 (on average below0.004). High values ofΔSatm around 0.04 do not havemuch effect on ρsensor (see Subsection 3.F). Then themodel can be used over the whole spectrum, what-ever the type of the standard atmosphere.

Concerning the type of the plume phase function,rural and maritime types provide the same level oferrors for Tatm and Satm as the urban type (bench-mark). For ρatm and ρsensor, the rural type leads toquite accurate results (mean error below 0.005),whereas the maritime type is less accurate (meanerror around 0.01) but is still acceptable. As the aero-sol plume types are close to the urban or the ruralones (rural type is actually the urban type without

Table 3. Mean Errors in ρatm, Tatm, Satm, and ρsensor over Three Spectral Intervalsa outside Strong GaseousAbsorption Bands for Different Natural Aerosolsb


Aerosol Bands Λ1 Λ2 Λ3 Λ1 Λ2 Λ3 Λ1 Λ2 Λ3 Λ1 Λ2 Λ3

Maritime τnatural550� ¼ 0:05 2.2 0.9 0.5 1.7 2.1 1.7 5.8 7.9 2.7 2.3 0.7 0.4τnatural550� ¼ 0:10 2.6 1.3 0.4 1.3 1.4 1.6 10 14 4.6 3.1 1.1 0.4

Rural τnatural550� ¼ 0:05 2.6 0.9 0.5 1.7 2.0 1.7 6.0 7.6 1.9 2.8 0.8 0.5τnatural550� ¼ 0:10 3.2 1.2 0.5 1.9 1.5 1.5 11 14 3.2 4.0 1.1 0.4

Urban τnatural550� ¼ 0:05 4.8 1.7 0.6 3.9 2.3 1.9 7.0 6.3 2.0 5.4 2.1 0.5τnatural550� ¼ 0:10 7.4 2.4 0.6 6.0 3.0 1.7 13 12 3.8 9.1 3.8 0.6

aΛ1 ¼ ½0:4; 0:5 μm�, Λ2 ¼ ½0:5;0:8 μm�, Λ3 ¼ ½0:8;2:5 μm�.bτnatural550� is the optical depth of natural aerosols inside the plume (0–0:5km). Thetotal optical depth of natural aerosols over all the atmosphere is given by τnatural550 ¼ 4τnatural550�


carbonaceous matter [23]), the model is well adaptedto our applications.We consider now the effect of the plume location

(see Table 4). When the plume dilates at the altitudes0–1km, 0–2km, and 0–3km, the modeling errors re-main quite low: the mean error is below 0.007 forρatm, Satm, and ρsensor outside strong gaseous bandsand below 0.004 for Tatm. In the worst cases, Δρatmand Δρsensor can reach values of 0.02 but they corre-spond to relative errors below 5%. For greater plumevertical extensions (0–4km, 0–6km), errors becomeunacceptable (Δρsensor exceeds 0.01 on average forshort wavelengths and can reach values above 0.03).When the plume bottom does not lie on the ground,

the modeling errors are higher for the shorter wave-lengths. Actually, the Rayleigh scattering due to theatmospheric layer below the plume may be maskedby the plume, especially for high optical depths. AsAPOM does not take into account this phenomenon,it tends to overestimate ρatm. Modeling errors remainlow for 0:5–1km but are quite high for 2–3km,3–5km, and 6–8km (Δρsensor exceeds 0.02 on averagefor short wavelengths). For plume locations that can-not be accurately modeled, the analytical formula-tion of APOM may be valid, but the numericalcoefficients should be then recalculated.It has been proved that APOM could be used in

the presence of natural aerosols, whatever the sensoraltitude, the standard atmosphere and for plumesthat extend from the ground (or close to the ground)

to a height below 3km. Then, for a particular scenecontaining a plume, an APOM user should computeρatm0 , Tatm

0 , and Satm0 in the exact conditions of the

scene without a plume, and afterward introducethem and the desired optical properties as inputsin the model to obtain quasi-instantaneously ρatm,Tatm, Satm, and ρsensor.F. Error Budget

Modeling errors in ρatm, Tatm, and Satm do not havethe same effect on ρsensor. Then we propose to assesstheir respective effects by differentiating Eq. (2):

dρsensor ¼ dρatm þ ðρUÞdTatm þ ðTatmρ2U2ÞdSatm

þ ðTatmU2Þdρ; ð15Þ

where U ¼ ð1 − SatmρÞ−1. Considering the previousground reflectance of 0.3 and the mean value 0.15over all simulations for Satm, Eq. (15) becomes

dρsensor ¼ dρatm þ 0:3dTatm þ 0:1TatmdSatm

þ 1:1Tatmdρ: ð16Þ

By considering the mean values of Δρatm, ΔTatm andΔSatm outside strong gaseous absorption bands (seeTable 2) and Eq. (16), it clearly appears that ρatm hasthe dominating effect and Satm has a second-ordereffect (0 ≤ Tatm ≤ 0:8 in plumes). However, inside

Table 4. Mean Errors in ρatm, Tatm, Satm, and ρsensor over Three Spectral Intervalsa outside Strong Gaseous Absorption Bands for Different SensorAltitudes, Standard Atmospheric Models (No Natural Aerosol), Plume Phase Functions, and Plume Locationb.


Fixed Parameters Bands Λ1 Λ2 Λ3 Λ1 Λ2 Λ3 Λ1 Λ2 Λ3 Λ1 Λ2 Λ3

Sensor Altitude 2km 1.8 1.4 1.2 5.2 2.9 1.9 0.9 0.9 1.7 2.1 1.6 1.45km 1.5 1.3 1.2 3.1 2.3 1.8 0.9 0.9 1.7 1.6 1.5 1.410km 1.4 1.3 1.2 2.3 2.0 1.8 0.9 0.9 1.7 1.2 1.3 1.399km 1.5 1.4 1.2 2.4 1.9 1.7 0.9 0.9 1.7 1.6 1.5 1.320 km 1.5 1.3 1.2 2.4 1.9 1.7 0.9 0.9 1.7 1.4 1.3 1.3

Standard Atmospheric Model Tropical 1.6 2.1 1.8 2.3 2.1 2.3 1.0 1.1 1.7 1.5 2.1 2.1Mid-L sum 1.6 1.9 1.6 2.3 2.0 2.0 1.0 1.0 1.6 1.5 1.9 1.7Mid-L win 1.6 1.6 1.3 2.4 1.9 1.9 1.0 0.9 1.8 1.6 1.5 1.4Sub-A sum 1.6 1.7 1.4 2.4 1.9 1.8 0.9 1.0 1.7 1.5 1.7 1.5Sub-A win 1.6 1.6 1.4 2.4 2.0 2.3 0.9 1.0 1.9 1.6 1.5 1.7U.S. 1976 1.5 1.3 1.2 2.4 1.9 1.7 0.9 0.9 1.7 1.4 1.3 1.3

Plume Phase Function Maritime 9.4 8.5 2.7 2.4 1.9 1.7 0.9 0.9 1.7 9.4 8.6 2.7Rural 3.9 4.8 1.6 2.4 1.9 1.7 0.9 0.9 1.7 3.6 4.8 1.8Urban 1.5 1.3 1.2 2.4 1.9 1.7 0.9 0.9 1.7 1.4 1.3 1.3

Plume Location 0–0:5 km 1.5 1.3 1.2 2.4 1.9 1.7 0.9 0.9 1.7 1.4 1.3 1.30–1km 2.0 1.4 1.2 2.5 1.9 1.7 1.2 0.9 1.7 2.1 1.3 1.30–2km 5.0 1.7 1.2 2.6 2.3 2.2 2.9 1.3 1.8 4.8 1.5 1.40–3km 6.7 2.5 1.6 3.7 3.4 2.2 4.7 1.7 2.0 5.9 2.0 1.60–4km 12 3.6 1.6 6.2 7.5 4.3 5.8 1.9 2.2 10 2.2 1.60–6km 17 4.2 2.1 7.3 8.1 4.8 6.4 2.1 2.4 15 3.0 1.80:5–1km 3.8 1.3 1.3 2.4 2.0 2.1 5.3 1.5 1.7 3.7 1.3 1.32–3km 22 11 5.8 5.0 4.7 2.3 22 5.9 4.1 19 12 8.33–5km 36 14 6.7 5.4 4.9 2.3 32 8.1 4.1 34 14 6.36–8km 51 17 6.6 7.3 5.6 2.3 51 13 4.7 47 17 6.3

aΛ1 ¼ ½0:4; 0:5 μm�, Λ2 ¼ ½0:5;0:8 μm�, Λ3 ¼ ½0:8; 2:5 μm�.bThe standard deviations associated with the mean errors approximatelyequal them.


strong gaseous absorption bands, ΔSatm can reachhigh values as 0.04 [see Fig. 9(c)]. Fortunately, suchcases correspond to low transmittances (Tatm ≤ 0:3),and then the effect on Δρsensor is insignificant (be-low 0.001).Adding the absolute values of the weighted errors

from each atmospheric term do not illustrate the glo-bal error on ρsensor. Indeed, comparisons betweenFigs. 8(a) and 8(d) show that the spectral errors inρatm and ρsensor have about the same distributions(for all values and on average). It clearly means thaterrors in ρatm, Tatm, and Satm compensate; otherwise,Δρsensor would have at least on average higher valuesthan Δρatm.A parenthesis is made about the knowledge on the

ground reflectance ρ. In the purpose of retrieving theaerosol optical properties over a nondark ground (forexample, by using lookup tables), the ground reflec-tance under the plume is assumed with a given un-certainty Δρ. Equation (15) allows us to assess theeffect of this uncertainty on ρsensor. By assuming amean value of 0.15 for Satm, the begotten uncertaintyon ρsensor is 0:88Δρ for a low τ around 0.3 (Tatm ¼ 0:8),of 0:44Δρ for a high τ around 1.0 (Tatm ¼ 0:4), and of0:11Δρ for a very high τ around 2 (Tatm ¼ 0:1). Δρcan reach values higher than 0.1, which yields hugeerrors up to 0.09 in ρsensor (for low optical depths).

Then, to minimize the ground effect, one should firstretrieve the optical properties from the plume partsfor which the ground located below is known quiteaccurately (e.g. dark surfaces) or from the denserparts of the plume that correspond to mostly maskedgrounds. The retrieved optical properties could thenbe used to invert by extrapolation the other parts ofthe plume.

The assumption of a Lambertian ground reflec-tance used by APOM is now discussed. As nadirviewing is considered, the bidirectional characterof the surface does not intervene much (exceptfor a Sun close to nadir). Moreover, the ground effectdecreases as the plume optical depth increases[and then the atmospheric transmittance decreases,see Eq. (16))]. However, further work is required toassess accurately this point.

G. Using Aerosol Plume Optical Model for Inversion

In this section, investigations are done to character-ize the optical properties of plumes from hyperspec-tral images with APOM. At first, APOM requiresthe plume spectral optical properties as inputs. Asaerosols exhibit slow spectral variations (see Fig. 5),Alakian et al. [35] showed that it is possible to modelaccurately the spectral dependency of the plume

Fig. 9. Study of standard atmospheric model (see Fig. 8 for details). Errors are amplified inside strong gaseous absorption bands incomparison to 1976 U.S. standard model. This is due to different gases concentrations from one standard model to another.


optical properties in the spectral range ½0:4; 1:1 μm�,for which the plume effect is maximum, as

τðλÞ ¼ a0 þ a1 ln λþ a2ln2λ;ω0ðλÞ ¼ b0 þ b1 ln λþ b2ln2λ; gðλÞ ¼ c0 þ c1λ;

where a0, a1, a2, b0, b1, b2, c0, and c1 are eight mod-eling coefficients. These equations generalize theAngström law τ ¼ βλ−α [36] and the work from Kingand Byrne [37].Outside gaseous absorption bands, the model

APOM and the modeling of the spectral optical prop-erties enable us to characterize the spectral at-sensorreflectance ρsensorðλÞ from the plume coefficients a0,a1, a2, b0, b1, b2, c0, and c1 (unknown), the cosineof the solar zenith angle μs (known), the sensor spec-tral bands λ (known), the ground reflectance ρðλÞ (un-known) and the standard atmospheric terms ρatm0 ðλÞ,Tatm

0 ðλÞ, Satm0 ðλÞ (unknown).

The standard atmospheric terms can be estimatedfrom pixels that are not contaminated by the plume.The ground reflectance, if unknown, can be esti-mated using the shortwave infrared bands [38].Then, the eight unknown aerosol parameters needto be retrieved. By using hyperspectral sensors thatprovide tens or hundreds of bands, this can be doneby minimizing the least squares between observedand modeled ρsensor. The main advantage of suchan inverse method is that it does not assume anya priori knowledge on the type of particles (on thecontrary to lookup tables). Then, it could be usedto invert plumes for which emitted particles are com-pletely unknown (e.g., industrial plumes). The devel-opment of this method is still ongoing.

4. Conclusion and Discussion

The semianalytical forward model APOM for the ra-diative effects of aerosol plumes in the spectral range½0:4; 2:5 μm� has been presented in the case of nadirviewing. It is devoted to the analysis of plumes aris-ing from single strong emission events (high opticaldepths) such as fires or industrial discharges. Thescene is represented by an atmospheric layer (mole-cules and natural aerosols) located above the plumelayer. The at-sensor reflectance is completely definedby the atmospheric upwelling reflectance, the totalatmospheric transmittance, the atmospheric spheri-cal albedo, and the ground reflectance. Each atmo-spheric term is modeled as a function of the solarzenith angle, the aerosol optical depth, the single-scattering albedo, the asymmetry parameter, andthe wavelength. The mathematical formula as wellas the numerical coefficients are derived from MOD-TRAN4 radiative transfer simulations. The DISORToption is used with 16 fluxes to provide a sufficientlyaccurate calculation of multiple scattering effects,which are important for dense smokes.A large set of simulations is performed in the case

of biomass burning and industrial plumes in order to

validate the model. APOM proves to be accurate forsolar zenith angles between 0° and 60°. Themodelingerrors in ρsensor are on average below 0.002. The high-est errors can reach values of 0.01 that correspond tolow relative errors (below 3%). The addition of natur-al aerosols in the atmosphere does not affect APOMaccuracy except for some particular cases (nonab-sorbing plume particles and absorbing natural parti-cles) that can be processed by directly considering theoptical properties of the external mixture betweenplume aerosols and natural aerosols (rather thenconsidering them separately). APOM preserves itsaccuracy whatever the sensor altitude, the standardatmospheric model and for plumes whose bottom zminis close to the ground (≤0:5km) and top zmax is below3km. For other plume locations, the analytical for-mulation of APOM could still be used, but the asso-ciated numerical coefficients should be recalculated.APOM also proves to be accurate for particles forwhich the phase function is defined from the urbanand the rural types in MODTRAN4. An airborne ex-periment using a hyperspectral sensor is planned tovalidate APOM on real data.

The model is modular and may be improved by in-cluding the sensor direction (zenith and azimuth an-gles) as a parameter. It would be performed in thesame manner as for the solar zenith angle by repla-cing in Eq. (10) bijk by bijk cos−1 (viewing zenithangle). Further work is required to achieve this ex-tension (maybe a dependency on azimuth should alsobe added). Then, APOM could be used for multiangleimaging sensors.

This model may be used in forward modeling andretrieval of optical properties of aerosols. In forwardmodeling, it allows quick simulations of hyperspec-tral (and multispectral) images of plumes. To givean idea about the gain in time, the simulation ofone pixel with MODTRAN4 at AVIRIS spectral reso-lution with given optical properties requires aboutone hour with current computers (e.g., AMD Opteron2:40GHz). Once model coefficients have been com-puted, APOM allows quasi-instantaneous simula-tions. This model can also help in designing asensor (choice of the wavelengths and viewing an-gles) to optimally estimate the aerosol properties.It also allows to assess the sensitivity of the sensorsignal to the optical properties.

For retrieval, the generation of huge lookup tablesis now possible very quickly with a high accuracy(DISORT 16 fluxes accuracy). It is also possible to de-velopmore accurate methods of retrieval by adaptingthe existing methods in signal processing that useanalytical models (gradient descents). If the stan-dard atmospheric conditions are known or can be es-timated (for example, outside the plume), theretrieval process to characterize the plume opticalproperties only depends on the plume itself. A meth-od that models the plume optical properties witha few coefficients and combine them with APOM iscurrently in development.


References1. Y. J. Kaufman, D. Tanré, H. R. Gordon, T. Nakajima, J.

Lenoble, R. Frouin, H. Grassl, B. M. Herman, M. D. King,and P. M. Teillet, “Passive remote sensing of troposphericaerosol and atmospheric correction for the aerosol effect,”J. Geophys. Res. 102, 14581–14599 (1997).

2. Y. J. Kaufman, D. Tanré, and O. Boucher, “A satellite view ofaerosols in the climate system,” Nature 419, 215–223 (2002).

3. G. Mie, “Beiträge zur Optik trüberMedien, speziell kolloidalerMetallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).

4. Y. J. Kaufman and C. Sendra, “Algorithm for automatic atmo-spheric corrections to visible and near-ir satellite imagery,”Int. J. Remote Sens. 9, 1357–1381 (1988).

5. Y. J. Kaufman, A. Wald, L. Remer, B. Gao, R. Li, and L. Flynn,“The modis 2:1-μm channel-correlation with visible reflec-tance for use in remote sensing of aerosol,” IEEE Trans.Geosci. Remote Sens. 35, 1286–1297 (1997).

6. J. Martonchik, D. Diner, R. Kahn, T. Ackerman, M. Verstraete,B. Pinty, and H. Gordon, “Techniques for the retrieval of aero-sol properties over land and ocean using multiangle imagery,”IEEE Trans. Geosci. Remote Sens. 36, 1212–1227 (1998).

7. J. Veefkind, G. de Leeuw, P. Stammes, and R. Koeljemeier,“Regional distribution of aerosol over land derived fromASTR-2 and GOME,” Remote Sens. Environ. 74, 377–386(2000).

8. M. Leroy, J. L. Deuzé, F. M. Bréon, O. Hautecoeur, M. Herman,J. C. Buriez, D. Tanré, S. Bouffiès, P. Chazette, and J. L. Rou-jean, “Retrieval of atmospheric properties and surface bidirec-tional reflectances over land from POLDER/ADEOS,”J. Geophys. Res. 102, 17023–17037 (1997).

9. D. Winker, M. Vaughan, and W. Hunt, “The CALIPSOmissionand initial results from CALIOP,” Proc. SPIE 6409, 1–8(2006).

10. H. Akimoto, “Global air quality and pollution,” Science 302,1716–1719 (2003).

11. K. Stamnes, S.-C. Tsay, W. Wiscombe, and K. Jayaweera,“Numerically stable algorithm for discrete-ordinate-methodradiative transfer in multiple scattering and emitting layeredmedia,” Appl. Opt. 27, 2502–2509 (1988).

12. J. Fischer and H. Grassl, “Detection of cloud-top height fromreflected radiances within the oxygen A band. Part 1. Theore-tical studies,” J. Appl. Meteorol. 30, 1245–1259 (1991).

13. F. Fischer, L. Schuller, and R. Preusker, “Cloud top pressure,”MERIS Algorithm Theoretical Basis Doc. ATBD 2.3 (FreeUniversity of Berlin, (2000).

14. F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd,E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P.Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, andS. A. Clough, “The MODTRAN 2/3 Report and LOWTRAN7 MODEL,” Technical report, prepared by Ontar Corporationfor PL/GPOS (1996).

15. Z. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S.Patch, “Hyperspectral remote sensing for shallow waters. I.A semianalytical model,” Appl. Opt. 37, 6329–6338 (1998).

16. S. Jacquemoud, F. Baret, B. Andrieu, F. M. Danson, and K.Jaggard, “Extraction of vegetation biophysical parametersby inversion of the prospectþ sail models on sugar beet cano-py reflectance data. Application to TM and AVIRIS sensors,”Remote Sens. Environ. 52, 163–172 (1995).

17. A. A. Kokhanovsky and V. V. Rozanov, “The physical parame-trization of the top-of-atmosphere reflection function for acloudy atmosphere–underlying surface system: the oxygenA-band case study,” J. Quant. Spectrosc. Radiat. Transfer85, 35–55 (2004).

18. S. Chandrasekhar, Radiative Transfer (Dover, 1960).19. G. E. Thomas and K. Stamnes, Radiative Transfer in the At-

mosphere and Ocean (Cambridge University Press, 1999).

20. N. F. Larsen and K. Stamnes, “Use of shadows to retrievewater vapor in hazy atmospheres,” Appl. Opt. 44, 6986–6994(2005).

21. K. Stamnes, “Reflection and transmission by a vertically inho-mogeneous planetary atmosphere,” Planet. Space Sci. 30,727–732 (1982).

22. V. V. Rozanov and A. A. Kokhanovsky, “On the molecular-aerosol scattering coupling in remote sensing of aerosol fromspace,” IEEE Trans. Geosci. Remote Sens. 43, 1536–1541(2005).

23. E. P. Shettle and R. W. Fenn, Models for the Aerosols of theLower Atmosphere and the Effects of Humidity Variationson Their Optical Properties (Air Force Geophysics Laboratory,1979).

24. J. S. Reid, R. Koppmann, T. F. Eck, and D. P. Eleuterio, “A re-view of biomass burning emissions. Part II: intensive physicalproperties of biomass burning particles,” Atmos. Chem. Phys.Discuss. 4, 5135–5200 (2004).

25. O. Dubovik, B. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman,M. D. King, D. Tanré, and I. Slutsker, “Variability of Absorp-tion and optical properties of key aerosol types observed inworldwide locations,” J. Atmos. Sci. 59, 590–608 (2002).

26. M. Mallet, J. C. Roger, S. Despiau, O. Dubovik, and J. P.Putaud, “Microphysical and optical properties of aerosol par-ticles in urban zone during ESCOMPTE,” Atmos. Res. 69,73–97 (2003).

27. I. G. Henyey and J. L. Greenstein, “Diffuse radiation in thegalaxy,” Astrophys. J. 93, 70–83 (1941).

28. L. S. Lasdon, A. D. Waren, A. Jain, andM. Ratner, “Design andtesting of a generalized reduced gradient code for nonlinearprogramming,” ACM Trans. Math. Softw. 4, 34–50 (1978).

29. R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M.Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J.Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spec-troscopy and the airborne visible/infrared imaging spectro-meter (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).

30. J. Trentmann, M. O. Andreae, H.-F. Graf, P. V. Hobbs, R. D.Ottmar, and T. Trautmann, “Simulation of a biomass burningplume: comparison of model results with observations,” J. Geo-phys. Res. 107 (2002).

31. R. W. Fenn, S. A. Clough, W. O. Gallery, R. E. Good, F. X.Kneizys, J. D. Mill, L. S. Rothmann, E. P. Shettle, and F. E.Volz, Handbook of Geophysics and the Space Environment,Optical and Infrared Properties of the Atmosphere (A. S. Jursa,1985).

32. R. A. Sutherland and R. K. Khanna, “Optical properties oforganic-based aerosols produced by burning vegetation,”Aerosol Sci. Technol. 14, 331–342 (1991).

33. C. F. Bohren and D. R. Huffman, Absorption and Scattering ofLight by Small Particles (Wiley, 1983).

34. J. S. Reid, T. F. Eck, S. A. Christopher, R. Koppmann, O.Dubovik, D. P. Eleuterio, B. N. Holben, E. A. Reid, andJ. Zhang, “A review of biomass burning emissions. Part iii.Intensive optical properties of biomass burning particles,”Atmos. Chem. Phys. Discuss. 4, 5201–5260 (2004).

35. A. Alakian, R. Marion, and X. Briottet, “Hyperspectral remotesensing of biomass burning aerosol plumes: sensitivity to op-tical properties modeling,” Proc. SPIE 6362, 63620D (2006).

36. A. Angström, “On the atmospheric transmission of Sun radia-tion and on dust in the air,” Geogr. Ann. 12, 130–159 (1929).

37. M. D. King and D. M. Byrne, “A method for inferring totalozone content from spectral variation of total optical depth ob-tained with a solar radiometer,” J. Amos. Sci. 33, 2242–2251(1976).

38. S. Bojinski, D. Schläpfer, M. E. Schaepman, and J. Keller,“Aerosol mapping over rugged heterogeneous terrain with im-aging spectrometer data,” Proc. SPIE 4816, 108–1199 (2002).


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Remote sensing of aerosol plumes: a semianalytical model