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8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 1

GASEOUS POLLUTANTS CHARACTERIZATION OVER

HETEROGENEOUS GROUND FROM AIRBORNE HYPERSPECTRAL

MEASUREMENTS AT HIGH SPATIAL RESOLUTION:

CASE OF INDUSTRIAL SITES.

Ramzi IDOUGHI1, Pierre-Yves FOUCHER2, Laurent POUTIER3 and Xavier BRIOTTET4

1. ONERA (the French Aerospace Lab), Toulouse, France; ramzi.idoughi@onera.fr

2. ONERA (the French Aerospace Lab), Toulouse, France; pierre-yves.foucher@onera.fr

3. ONERA (the French Aerospace Lab), Toulouse, France; laurent.poutier@onera.fr

4. ONERA (the French Aerospace Lab), Toulouse, France; xavier.briottet@onera.fr

ABSTRACT

Anthropogenic sources, especially industrial, emit into the atmosphere gases and aerosols, which

play an important role in atmospheric exchanges. However industrial emissions are poorly

estimated as it needs a sensor with high spatial and spectral resolution. The new hyperspectral

airborne image sensors in the thermal infrared range open the way to new developments in plume

remote sensing.

The thermal domain (LWIR) spectrometry has been widely used to detect and estimate gaseous

pollutants. Indeed, the majority of gas plume have their signature in the thermal domain. However,

the impact of plume’s temperature and the heterogeneity of ground properties make the gas

characterization more difficult.

Existing methods have several limitations: (i) the heterogeneous environment impact on their

performances; (ii) spatial and vertical extent of the plume is not taken into account.

In this work, a new method for characterizing gas plumes is presented to overcome such

limitations. This method is based on an accurate non linear formalism of cloud gas radiative

impact. It includes: (i) a ground classification of the scene, in order to take into account the soil's

heterogeneity and its spectral behavior ; (ii) and an optimal estimation formalism taking into

account constraints on the spatial and vertical plume structure.

Keywords : Hyperspectral, thermal infra-red, plume, gas, detection, characterization.

INTRODUCTION

The air pollution is a very important issue for industrialized societies, both in terms of health – air

quality (respiratory diseases, allergies...) and climate change. Hence establishing sufficiently

detailed air quality assessments is important in order to study the impact of air pollution on our

environment. Anthropogenic sources, especially industrial, are involved with an important

contribution to air pollution. However, these emissions remain poorly estimated at a high spatial

resolution. This is explained by several reasons: the large diversity of species emitted by industrial

sites, the concentration variability as the rates of plants, and the weather. Moreover, the

characterization of pollutants depends on a good knowledge of atmospheric profiles (temperature,

pressure, humidity…) and dispersive properties of pollution plumes.

Recent technological advances in terms of spatial and spectral resolutions of thermal infrared

airborne hyperspectral sensors, open a way of improving gaseous effluents characterization, since

the majority of gas have their signature in the thermal domain.

8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 2

The main objective of plume’s characterization is the retrieval of gaseous concentration and

temperature distribution of the plume in order to estimate the mass flows through the plume or to

validate Chemical Transport Model.

INDUSTRIAL PLUME RADIANCE MODEL

Plume retrieval requires an accurate radiative model of the scene. To model the radiance in

entrance of an airborne sensor, some assumptions must be taken into consideration: 1) for each

pixel, the ground is assumed to be homogeneous, flat and lambertian (reflect the light in all

directions with the same intensity). Thus, the effects of directionality in the reflected radiation and

the effects of the environment will be neglected. 2) The plume is modeled as a flat layer, which is

horizontally homogeneous. 3) As we work in the infrared thermal domain (LWIR), the solar

radiation is neglected. In addition, scattering phenomena will be neglected in our case as we only

take into account gas species.

Under these assumptions, the components of the radiation flux in entrance of an airborne sensor

are presented in Fig. 1.

Fig. 1 : Radiative balance in the infrared thermal domain in the absence (left) and presence (right) of

a gaseous plume.

In clear sky conditions, the at-sensor radiance could be expressed as follows:

(

)

atmsfcsfcsfcdatm TBLLL

τ

ε

ε

)()1(

0

+

−

+

=( 1 )

where : Latm is the up-welling atmospheric radiance, Ld is the down-welling radiance, B is black-

body law, εsfc and Tsfc are respectively the ground emissivity and temperature, and

τ

atm is the

atmospheric transmission between the ground and the sensor.

The presence of a gas plume modeled by a layer of thickness Hp from the ground level, introduces

some modifications to the above radiative transfer equation. The new at-sensor radiance can then

be expressed as follows:

(

)

(

)

atmpppsfcsfcsfcpppdatmp TBTBTBLLL

τ

ε

τ

ε

ε

ε

τ

)()).(1))(((

+

+

−

+

+

= ( 2 )

Where: εp,

τ

p and Tp are the emissivity, transmission and temperature of the plume layer.

The plume is assumed thin enough so that the upwelling terms Latm and

τ

atm remain unchanged.

For the gaseous plume characterization, we usually work with the differential radiance: ΔL = Lp –

L0. That we can express the general mono-layer plume differential signal (Griffin et al. (1)):

8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 3

(

)

(

)

(

)

[

]

dpppsfcsfcsfcppatm LTBTBTBL ⋅+

−

⋅

⋅

−

+

−⋅

−

⋅=Δ )1()(1)()(1

τ

τ

ε

ε

τ

τ

( 3 )

When the reflected down-welling radiance is neglected, the differential radiance can be simplified

as follows:

(

)

[

]

)()(1 sfcsfcppatm TBTBL

ε

τ

τ

−

⋅

−

⋅

=Δ ( 4 )

On the basis of the Beer’s law, and under the assumption that the plume layer is optically thin, we

can express the transmission due to the gas g as a function of the columnar amount qg of this gas,

and its spectral absorption coefficient kg, as:

gggg kq

ε

τ

−

=

−

≅11 ( 5 )

In the multi-gas case, this formalism (Young et al. (2), 2002) for the differential radiance

expression becomes:

g

nbgas

ggatmp CkLLL ∑

=

⋅=−=Δ

1

0

τ

( 6 )

which introduces the thermal contrast for each gas:

∫

∫−

=

λλ

λλε

dk

dkTBTB

qC

g

gsfcsfcp

gg )(

)())()(( ( 7 )

DOWN-WELLING RADIANCE IMPACT

Down-welling radiance computation

The down-welling radiance refers to the hemispherical flux reaching the ground. Using spherical

coordinates, this term could be expressed as:

() () ()

ϕθθθθ

π

π

π

ddLLdsincos

12

0

2

0

∫∫

⋅= ( 8 )

By neglecting the solar radiance, we can assume an azimutal symmetry for the downwelling

radiance, which leads to the simplified the formula ( 8 ) :

() () ()

θθθθ

π

dLLdsincos2 2

0

∫

⋅= ( 9 )

Cutting the domain of the integral into N regular intervals Δθ (5° in this study), and using the

trapezoidal rule yields the following expression for the down-welling radiance:

()( )

[]

() ( )

[

]

∑

−

=

Δ⋅+−Δ⋅Δ⋅++Δ⋅⋅= 1

0

22 )1(coscos)1(2 N

i

diiiLiLL

θθθθ

( 10 )

Inversion methods that take into account down-welling radiance to retrieve the concentration, make

the assumption that the plume is a horizontally unbounded layer. This assumption, imposed by

most of radiative transfer calculations, introduces an error on the inverted concentration. In this

section, we assess the related error.

Down-welling radiance has been estimated for different cases of horizontally bounded plume. We

considered that each plume has an angular extension of 2.θp, with θp varying from 0° (no plume) to

8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 4

90° (horizontally unbounded plume). Here, the plume is seen with a base altitude of Hp. For each

plume, the sum in the formula ( 10 ) is then cut into two contributions :

The plume contribution : for θ ≤ θp we take L(θ) = Lp(θ)

The clear sky contribution : for θ > θp we take L(θ) = L0(θ)

Then we compare the difference in terms of down-welling radiance between each bounded plume

with an angular extension of 2.θp and the unbounded plume.

b

a

Fig. 2 : (a) the spectral maximum relative difference between bounded plume and unbounded plume

in function of the semi-angular extension of the bounded plume. (b) Comparison of the down-welling

radiance (spectral resolution: 1cm-1) for a bounded plume of SO2 (θp = 45°) and the unbounded

plume.

Fig. 2-(a) shows that the less the plume is extended the more the error on the down-welling

radiance is important. With a typical plume of 150m of horizontal expansion and present up to an

altitude of 150 m, θp = 45°, the error introduced by the assumption of unbounded plume exceeds

50 %, as we can notice it on the Fig. 2-(b).

Impact of Down-welling radiance on retrieval

Several inversion methods, especially when using a linear approach, neglect down-welling

radiance assuming the ground behaves as a low reflectance gray-body. Nevertheless, in an

industrial site, this assumption is no longer valid, given the nature of the present materials (steel,

copper, aluminum, asphalt, etc.).

In order to estimate the error introduced by this assumption, we first have simulated an industrial

plume of SO2 (Fig. 3): concentration and temperature distributions follow a Gaussian model

simulation, with a maximum concentration (integrated column) of 1200 ppm.m and a maximum

temperature difference of 100 K.

8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 5

Fig. 3 : The Gaussian concentration distribution of the simulated plume of SO2.

This plume extends to an altitude of 460 m, above a ground supposed to be a gray-body with an

emissivity of 0.9 and a temperature of 282.85 K (winter time case). A Gaussian white noise was

added to emissivity (σ = 0.005) and temperature (σ = 2 K). The area covers 100m x 100m and is

sampled with a 1m spatial resolution. Atmospheric conditions (temperature/pressure/humidity

profiles) are those of a mid-latitude winter. Winter time has been used, as it corresponds to very

low boundary layer and higher plume concentration . To simulate the scene we use a model

designed to improve the computation time to generate the hyperspectral image of the scene and

based on MODTRAN 4 RTM. Thereby, we compute the at-sensor radiance image.

We use two different approaches based on the linear inversion formalism (Young et al., 2002), in

order to evaluate the impact of down-welling radiance.

The first approach does not take into account the down-welling radiance in the calculation of the

thermal contrast which is directly related to the inverted integrated concentration column of present

gas. The second approach introduces the down-welling in the expression of thermal contrast by

first order linearization.

The Fig. 4 represents a comparison of SO2 retrieved for each case. When down-welling radiance is

neglected (a) , noise due to background reflection impact completely hides SO2 signal. When

down-welling radiance is inserted in the model (b) , we can easily notice the SO2 plume shape

even if some residual pixels show a huge instability in the retrieval process. Introducing down-

welling radiance is thus necessary to get an accurate retrieved concentration.

8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 6

Fig. 4 : Inverted integrated concentration column obtained by the two approaches. (a) inversion

without the use of down-welling radiance. (b) inversion using down-welling radiance.

Fig. 5 shows that the mean difference between the inverted concentrations and the true one, along

the central line of the plume, could exceed 50% when down-welling radiance is not used in the

thermal contrast computation. While, taking into account this term reduces the error to less then

15%.

a

b

50%

15%

Fig. 5 : Inversion error in ppm.m along the central line of the plume, using the down-welling radiance

(black curve) and without the use of down-welling radiance (red curve). Percentage error on the right

axis.

8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 7

SPATIAL HETEROGENEITY IMPACT

Impact of ground heterogeneity

Using a linear formalism for the plume concentration retrieval we observe on Fig.4 some

concentration peaks at different pixels whereas down-welling radiance is taken into account and

ground properties are known. Fig. 6 is an illustration of this instability on the retrieved

concentration, along the central line of the plume.

Fig. 6 : Illustration of the instability of retrieved concentration along the central line of a SO2 plume

(the same plume in Fig. 3). This instability is due to the heterogeneity of the ground parameters.

In fact, this instability is caused by the heterogeneity of the ground properties (cf. (3), (4) and (5)).

For pixel where ground brightness temperature is very close to plume temperature, the thermal

contrast is very weak due to the term

∫

∫−

λλ

λλε

dk

dkTBTB

g

gsfcsfcp

)(

)())()(( . It leads to huge values (and some time negatives) of retrieved

concentration. In this case retrieval is managed by model noise amplified by the inverse of thermal

contrast.

In order to overcome the inverted concentration instability, it appears necessary to introduce

spatial constraints on concentration retrieval scheme.

Radiative impact of the vertical profile of the plume

The plume radiance model presented above and commonly used, assumes that the plume is a

homogenous layer in terms of concentration and temperature. This hypothesis is verified for pixels

far from gas emission source.

Nonetheless, for pixels close to emission source, concentration and temperature vertical profiles

show a peak near the altitude of the source. In this case, the homogeneous layer hypothesis is no

more realistic.

In the Fig. 7 we quantify the error induced by modeling the plume as an homogenous layer. We

compare the at-sensor radiance obtained by a radiative transfer model considering the plume as a

homogenous single-layer, and a radiative transfer model with a multi-layer approach for the plume.

8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 8

This comparison was done for two pixels : 7(a) a pixel with a constant vertical profile of

concentration and additional temperature 7(b) a pixel near the emission source, temperature and

concentration vertical profiles show a narrow Gaussian distribution.

ab

Fig. 7 : Comparison, in terms of differential brightness temperature, of the mono-layer homogenous

plume approach with a multi-layers plume radiative transfer model. For (a) an homogenous pixel :

constant concentration of SO2 (10 ppmv between 0m and 460 m) and (b) a pixel with a narrow

Gaussian distribution for the vertical profile of concentration of SO2.

According to Fig. 7, the radiance obtained by the mono-layer raditaive transfer model for a

homogenous pixel shows a good agreement with the radiance given by the multi-layers radiative

transfer. However, the difference between the two models is very important for pixels with a

gaussian vertical concentration distribution . For the pixel in Fig. 7-(b), the difference exceeds 10 K

on the differential brightness temperature.

Fig. 8 shows the evolution of the mean relative difference between the mono-layer and multi-layer

models along the central line of the plume (Fig. 3). Near the source of gas emission the error is

about 60 %. Away from the source the error decreases, but remains important: 10 % for a pixel

located 100 m away from the source.

Fig. 8 : Evolution of the mean relative difference between the two radiative transfer models (mono-

layer and multi-layers) in function of the distance from the gas emission’s source.

This comparison demonstrates that is important for the retrieval of the plume’s concentration to

take into account the vertical profile of the plume.

8th EARSeL SIG Imaging Spectroscopy Workshop, 8-10 April, Nantes, France 9

PROSPECTS : A NON-LINEAR OPTIMAL ESTIMATOR FOR CONCENTRATION RETRIEVAL

In order to improve the concentration retrieval, we have shown the need to take into account all

radiance contributors, including the down-welling radiance. In addition, the modeling of the plume

must integrate its vertical extension by using a multi-layers radiative transfer model. This leads to

developing new kinds of methods in order to introduce spatial constraints on the retrieval scheme.

In this way, we are currently developing a new method of plume inversion. This latter is based on a

non linear optimal estimation including a tunable regularization matrix. The goal is to minimize,

using a Levenberg – Marquardt Iterative regression, the following cost function:

)()())(())(( 1

2

a

it

a

i

im

ti

iXXRXXXFMXFM −−+−Σ−= −

χ

( 11 )

With :

M: Measure vector including spatial and spectral data

X: target vector including parameters for concentration, temperature and ground properties

F: Non linear function from the radiative transfer model

Y = F(X): Simulated vector

Σm-1: noise-whitening matrix

Xa: A priori target vector

R: Regularization matrix

The Regularization matrix (R) supports both spatial constraints on the concentration / temperature

of the plume from a chemical transport model and a Bayesian regularization for the ground

parameters (emissivity and temperature).

This method follows a global approach, since all pixels are inverted at the same time.

Nevertheless, for the initial guess, a pixel-to-pixel inversion method is used. On the basis of this

initial retrieval, a priori plume is built by using a chemical transport model and by estimating a

polynomial or Gaussian structure for the plume vertical and spatial distribution, both in terms of

concentration and temperature.

REFERENCES

1 Griffin M.K, J.P Kerekes, K.E Farrar & H.K. Burke, 2001. Characterization of Gaseous Effluents from

Modeling of LWIR Hyperspectral Measurements. In : Proc. of SPIE, Algorithms for Multispectral,

Hyperspectral, and Ultraspectral Imagery VII, 4381.

2 Young S.J, 2002. Detection and Quantification of Gases in Industrial-Stack Plumes Using Thermal-

Infrared Hyperspectral Imaging. the Aerospace Corporation, El Segundo, ATR-2002(8407)-1

3 Sheen D.M, N.B Gallagher, S.W Sharpe, K.K Anderson & J.F Schultz, 2003. Impact of background and

atmospheric variability on infrared hyperspectral chemical detection sensitivity. In : Proc. of SPIE,

Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX, 5093.

4 Walsh S, L Chilton, M Tardiff & C Metoyer, 2008. Effect of the temperature-emissivity contrast on the

chemical signal for gas plume detection using thermal image data. Sensors. 8 : 6471-6483.

5 Funk C.C, J Theiler, D.A Roberts & C.C Borel, 2001. Clustering to improve matched filter detection of

weak gas plumes in hyperspectral thermal imagery. In IEEE Transactions on geoscience and remote

sensing, VOL. 39, NO. 7.