INT. J. REMOTE SENSING, 1994, VOL. 15, NO. 10, 2065 -2086

An atmospheric correction method for the automatic retrieval ofsurface reflectances from TM images

M. A. GILABERTt, C. CONESE and F. MASELLI

I.A.T.A.-C.N.R. (Istituto di Analisi ambientale e Telerilevamento applicatiall'Agricoltura), P. le delle Cascine 18, 50144-Firenze, Italy

(Received 29 July 1992; in final form 7 October 1993)

Abstract. Most of the atmospheric correction methods proposed in the litera-ture are not easily applicable in real cases. The most sophisticated modelsfrequently require inputs which are not commonly available, whilst traditionalsimple dark object subtraction techniques do not generally give real reflectancevalues. In the present work an atmospheric correction method applicable toLandsat-TM data is described, which requires only inputs that are commonlyavailable and the presence in the imaged scenes of some dark surfaces in TMbands 1 (blue) and 3 (red). The method consists of an inversion algorithm basedon a simplified radiative transfer model in which the characteristics of atmos-pheric aerosols are estimated by the use of the path radiance in two TM bandsrather than a priori assumed. On the basis of this information, which is crucial fordetermining the atmospheric properties, the retrieval of real reflectances fromTM images is possible. The method can be applied to all TM scenes in whichsome dark points can be realistically supposed to be present, which is particularlyadvantageous in retrospective studies. Several TM scenes taken from differentlandscapes and in different seasons were corrected using the model. The reflec-tance values found were tested against ground measurements and compared withdata from the literature. The results show a substantial improvement in theaccuracy of the reflectance estimates with respect to estimates without atmos-pheric correction. Given some care in the identification of dark values, therelative error in actual reflectance retrieval is always rather low (=10-20 percent); this error can be considered acceptable for most practical applications.

I. IntroductionIn recent years the use of remotely-sensed data has found increasing applications

in a wide range of environmental sciences and monitoring techniques. In particular,the advent of third generation satellites such as the Landsat-5 with the highresolution sensor Thematic Mapper (TM) aboard, has led to notable improvementsin operationally monitoring vegetation, soils, rocks, water bodies and urban areas.

In all these applications, a major assumption is that the reflectance responses ofthe observed objects are indicative of their intrinsic physical and chemical properties.Unfortunately, atmospheric gases and aerosols scatter and absorb electromagneticradiation and can, therefore, modulate the radiation reflected from the target byattenuating it, changing its spectral distribution, and introducing some skylight intothe sensor field-of-view (Kaufman 1989). The image observed by the sensor is thus

1- Current address: Departament de Termodinámica, Facultat de Física, Universitat deValéncia, 46100-Burjassot, Valéncia, Spain.

2066 M. A. Gilabert et al.

extremely variable, depending not only on the sensed surfaces, but also on theatmospheric characteristics.

For this reason, numerous investigations have dealt with mathematical andstatistical procedures for the atmospheric correction of satellite scenes. Most of themore sophisticated methods make use of radiative transfer models which require insitu field data of specific targets in the imaged scene or simultaneous measurementsof atmospheric parameters (Tanré et al. 1986, Kneizys et al. 1988). A cleardisadvantage of these methods is that they rely on information other than the digitalimage data and they are therefore not usable when this is not available, as is the casein most retrospective studies.

To overcome these shortcomings, other methods have been proposed, usuallybased on simple dark object subtraction procedures. These methods are straightfor-ward and easily applicable, but they are merely scattering or haze removaltechniques, and can not yield real reflectance data. The improved dark objectsubtraction method developed by Chavez (1988), though more reliable and efficient,is no exception.

An alternative approach is that of hybrid theoretical and practica] procedures,which derive the optical characteristics of the atmosphere at the time of the satellitepassage from some features of the images themselves (Ahern et al. 1977, Kaufmanand Sendra 1988). In general, a major weakness of these methods lies in thedefinition of the aerosol optical properties, which are extremely variable in space andtime (Fraser and Kaufman 1985). As a result, some assumptions about thisparameter often have to be made, and these are subjective and not always easilyapplicable (Hill and Sturm 1991).

The present work proposes an operational methodology for retrieving realreflectance values from TM images which relies only on information that is generallyavailable in actual cases but which also defines the atmospheric characteristics moreobjectively. In practice, the method consists of an inversion technique based on asimplifed radiative transfer model in the atmosphere. A horizontally homogeneousatmosphere has been assumed, so that transmittance and path radiance are constantover the scene and their values can be determined for each image. On the basis of thepresence of dark points in the imaged scenes and using a combination of two TMbands (TM-1, blue, and TM-3, red) the actual aerosol model is estimated throughthe wavelength dependence of the aerosol path radiance. In this way, approximateknowledge of the atmosphere composition and structure is possible, and the retrievalof actual reflectances from the sensed images can be carried out with good levels ofprecision.

In the current paper, after a brief introduction on the physical bases ofatmospheric radiative transfer, the procedure developed is fully described. It is thenapplied to several TM scenes taken from different landscapes and in differentseasons. Various kinds of test are performed in order to evaluate the real possibilitiesand accuracy of the technique; the results of these tests are quite satisfactory innearly all the situations examined.

2. Atmospheric correction modelAssuming the Earth's surface Lambertian in nature, the reflectance of a given

surface, R s(),), as measured from satellite, can be approximated by the equation (1):

Rs(/1)=(knLs(Á))1(Eg(.1) cos 0,) (1)

TOP OFATMOSPHERE

ATMOSPHER E

EARTH SURFACE

Atmospheric correction of TM images 2067

where

Rs(),) is the reflectance of the surface at wavelength (dimensionless);Ls(.1) is the radiance of the surface (Wm ,um sr -1);Eg()) is the global solar irradiance on the horizontal surface (Wm 2 — 1);

00 is the solar zenith angle; andk accounts for the change in the Sun-Earth distance taking into account theeccentricity of the Earth's orbit and the Julian day (Singh and Cracknell 1986,Zibordi and Voss 1989).

Figure 1 shows a diagram with the different contributions to the signal recordedby the sensor. From this figure it can be seen that neglecting the atmospheric effectcorresponds to approximating the radiance of a given surface by the remotely-sensedradiance, Lo, and the solar radiation incident on this surface by the extraterrestrialsolar irradiance, Eo. In this way, only the apparent or planetary reflectance (Epema1992), Rs , can be obtained:

R's(.1)=(knLo(.1))1(Eo(A) cos 00 ) (2)

where E 0 can easily be found (Price 1987), and Lo) can be estimated from the digitalvalues, DC, of the image, by:

L0(1)=a0(2)+ al(.1.)19C(.1.) (3)

a0 and a, being the calibration constants of the sensor (Price 1987).

TARGET ADJACENT TARGET

(1:1 s (%)

Figure 1. Diagram of the electromagnetic interactions which affect solar radiation in theatmosphere. Solid lines refer to the radiation components considered in the model, E0being the extraterrestrial solar irradiance, E„ the direct solar radiation incident on thesurface, Ed the diffuse solar radiation incident on the surface (sky light), Lp the pathradiance and L, the radiance coming from the target surface of reflectance R,. Dashedlines refer to radiation components which have been neglected in the model: a refers tothe effect due to an adjacent target with reflectance R,, and m refers to the multiplescattering in the atmosphere. 00 and 0 refer, respectively, to solar zenith angle and viewzenith angle. In the model O was taken as zero.

2068 M. A. Gilabert et al.

When the evaluation of actual surface reflectance is necessary the aboyeapproximations are not sufficient and the effect of the atmosphere on Ls and Eg mustbe estimated as precisely as possible. As a matter of fact, the atmospheric effectsbefore and after the reflection at the surface refer to the same physical principies,and the two terms Ls and Eg could be described as an unity. In our model, however,the former term is estimated first and independently of the latter, and the presen-tation will follow the logical flow of the model working more than the flow ofradiation from the illumination source to the sensor.

2.1. Determination of the radiance of the surface, Ls(2)For a uniform Lambertian surface, the radiance recorded by a satellite sensor,

1,0 (),), can be approximated by summing two componente: (i) the contribution fromthe scattering of the direct Sun beam by the atmospheric constituents, L p(;t,), which iscalled the path radiance, and (ii) the contribution from the radiation which isdiffusely reflected by the Earth's surface, 4(4 Mathematically,

L0(.1)=Lp(/1)+4(Á)TT(.1)/(1 — sR s(Á)) (4)

where TT(.1) is the beam transmittance of the atmosphere in the upward direction. Inthis expression, s refers to the fraction of the upward radiation backscattered by theatmosphere to the surface. For small optical thicknesses and/or rather dark surfaces,sR,(.1) 1, so this term can be eliminated from equation (4), which means neglectingthe multiple reflections between the surface and the atmosphere. With this assump-tion, the radiance reaching the top of the atmosphere in the direction O to the zenithcan be written as,

Lo(2)= Lp(),)+ Ls())71(5t) (5)

For the atmospheric contribution, Lp(T), if the aerosol optical thickness isrelatively small the separability of the Rayleigh and aerosol atmospheres can beassumed (Gordon 1978):

Lp().)= L,.(),)+ La()) (6)

where r refers to Rayleigh contribution, and a to aerosol (Mie) contribution.The radiance of the surface of interest will be, according to (5):

Ls(;0= (L0(.1)— Lp(.1))ITT (.1)

(7)

It can be observed that we need to determine Lp(.1) and TI().) to know Ls, sinceL0(.1) can be obtained from the digital images.

Our model assumes that the path radiance, Lp(il), can be determined from thedark pixels of the image, since it has been shown that the remote sensing of a darksurface (very low reflectance) will be affected mainly by atmospheric backscatteringof the direct sunlight to the sensor (Kaufman 1989); then, if LS O,

L;',(.1) (8)

where (*) indicates that we are working with dark values. That is, the path radiancecan be estimated directly from the image by determining the radiance measured bythe sensor over dark areas. These dark areas should be black 0 per centreflectance) but because of the atmospheric scattering, the corresponding pixelspresent a nonzero DC value, which represents the DC* that must be used to

Atmospheric correction of TM images 2069

determine the path radiance by means of our model. With this assumption, only thefirst-order scattering can be removed (Chavez 1988).

Operationally, the selection of the appropriate DC* can be done by using the DCfrequency histogram of a digital image (Chavez 1988). On the histograms for thedifferent spectral bands, in particular for bands in the visible spectrum, there isusually a very sharp increase in the number of pixels at some nonzero DC or grey-level. This DC value is assumed to be the DC* in that particular band. The method isbased on the fact that there is generally a high probability that at least a few pixelswithin an image will be black (Chavez 1988). These dark surfaces can correspond toareas shadowed by clouds or topographic effects (low reflectance in all the bands),but also to water bodies (low reflectance in red and near-infrared wavelengths), toareas with dense vegetation such as coniferous forests (very low reflectance in blueand red regions of the spectrum) or to mixtures of some of these factors (Kaufmanand Sendra 1988). As, a priori, it is not possible to know which area the dark pixelsbelong to, only the TM-1 (blue) and TM-3 (red) bands have been used, since theTM-2 band corresponds to the green region of the spectrum, where vegetationpresents a relative maximum and it is not always possible to find a realistic value forthe DC*. As will be seen, these two TM bands are sufficient to estimate the maincharacteristics of atmospheric aerosols (kind and quantity), which is the crucialinformation for our methodology.

The assumption of zero reflectance of the dark points found has a probabilisticbasis and can involve a certain approximation. The identification of suitable darkvalues, however, is crucial to the whole methodology. This is the only subjective stepin the procedure, and it must be carried out with extreme care to avoid errors in thecomputation of surface reflectances. In effect, as for other, similar methods, there isno way to evaluate precisely the errors that can be made in the identification of thedigital counts in TM bands 1 and 3 which correspond to dark, non-reflectivesurfaces. In this sense, only the variations in the surface reflectances computeddepending on the different selection of dark values can be determined, which will bemade in the experimental section.

Once computed Lp(TM-1) and Lp(TM-3) from the dark points, it is possible toevaluate the aerosol contribution to the path radiance, La(),), from (6). In fact, theRayleigh contribution, is practically constant in the atmosphere and onlydependent on the solar and view zenith angles. It can be obtained for TM-1 andTM-3 bands from (Saunders 1990):

L,.={E0(1) cos 00P,./47r(cos 00 + cos 0)}

x {1 — exp [— T,.(.1)((l/cos 0 0) + (l/cos 0))]}

x tozt()L)toz1(.1)

(9)

where

E0 (2) is the extraterrestrial solar irradiance at wavelength 2.;00 and 0 are the solar zenith angle and the view zenith angle, respectively. In ourcase (sensor TM): 0 0° and cos 0 1;Pr is the Rayleigh phase function. The classical phase function has been applied(Schanda 1986):

P,.= (3/4)(1 + cos 2 12) (10)

2070 M. A. Gilabert et al.

where Q is the scattering angle. For 9 0°, 180 — 00.T r is the molecular optical thickness, which can be written as a function of the

wavelength, íl (Kaufman 1989), and the height, h 0, of the surface abo ye sea level(Zibordi and Maracci, 1988):

Tr(A, h0)=Hr(h0 {0 . 00859A -4(1+ O-0113.1 -2 + 0 . 00013). -4)} (11)

where A refers to the central wavelength (in pm) of each spectral band, and Hr(h 0) is

Hr(ho)=exp (— 0 . 1188h0 —0 . 00116h¿) (12)

with h0 expressed in km.

tozTW and taz ,1,(.1) are, respectively, the transmittances for the ozone in theupward and downward directions. They can be calculated from (Sturm 1981):

taz T (íl)=. exp (— Toz(/1)) (for cos 0= 1)

(13)

t„,I,(.1)= exp (— Toz(.1)/cos 00) (14)

The optical thickness for the ozone has been obtained applying an interpolationmethod to the values reported by Sturm (1981), which are wavelength dependentand also change according to the period of the year (summer and winter).

With La(TM-1) and La(TM-3) it is possible to obtain some information aboutthe kind of the atmosphere which is producing the scattering that affects the satelliteimage. This is an important step of the methodology. The identification of theaerosol scattering phase function and single scattering albedo is in fact a majorsource of uncertainty in all similar inversion models. If suitable measurementscontemporaneous with the satellite acquisitions are not available, some hypothesismust be made based on ancillary information or previous knowledge (Hill andSturm 1991). In our method the process is rendered more automatic and objective bya linear interpolation based on the wavelength dependence of the aerosol pathradiance. In this way the aerosol spectral properties which are interesting for theinversion technique can be inferred instead of being merely assumed.

The optical thickness of aerosols, assuming a radious power law distribution ofparticles, can be given by the Ángstrom formula (Iqbal 1983):

Ta(A)= (22' (15)

where a and b are, respectively, related to the concentration and size distribution ofparticles. If a linear dependence between aerosol path radiance and aerosol opticalthickness is assumed (Arauvachapun 1986 a),

La(A)=f{ta(M = CT „()) (16)

it is possible to express La(A) as

La(),) F2. -6(17)

where F ca and (5Taking into account the central wavelength for the interval TM-1 — TM-3 and

the aerosol radiances (La(TM-1) and La(TM-3)) determined previously, it is possibleto find F and (5 for each satellite image and, therefore, to determine I, a(2) for all thespectral bands. Given that in this model thc exponent term, ¿), is seen as an indicatorof the aerosol size distribution, some information can be inferred from it about thekind of aerosol present in the atmosphere. Taking a wavelength dependence of

Atmospheric correction of TM images 2071

ó =0 . 80 for a very hazy Mie atmosphere, and of b =4-08 for the ideal Rayleighatmosphere (Iqbal 1983, Chahine 1983), the percentage of molecular atmosphere(PER), can be defined as

PER = (,1 -(5 2,-o-8)/(/1-4.os _ /1-0.8) (18)

where refers to the average wavelength of the spectral interval between TM-1 andTM-3.

With the PER value a new phase function for aerosols can be defined as

P'a = PER x P r + (1—PER) x Pa (19)

where

Pr is the Rayleigh phase function (equation 10);Pa is the aerosol phase function. In this case, the Two-Term Henyey-Greenstein

(TTHG) phase function has been applied (Aranuvachapun 1983, Liou 1980):

Pa = a(1 — gi)/( 1 + —2g 1 cos 00)312

+ (1 — oc)(1 — 95)1( 1 + 91— 2g 2 cos 00)3/2

(20)

where a, g1 and g2 are the asymmetry factors, which strongly depend on the aerosolsize distribution. This analytical function has been demonstrated to be in closeagreement with the Mie theory. It can be assumed constant in the visible and near-infrared bands for a given type of aerosol (Aranuvachapun 1986 b). Because of alack of information on aerosol type, the values

a =0 . 978 g1=0.884

g2= —0.749

have been used for a hazy atmosphere composed by continental aerosols (Aranuva-

chapun 1983), and the values •

a=0.935

91=0 . 795 g2 = —0.568

for a hazy atmosphere with maritime aerosols (Aranuvachapun 1986 b). Figure 2shows the phase-function values obtained versus the scattering angle. From theprevious discussion it can be understood that the actual phase function used in theinversion procedure lies between those corresponding to continental or maritimeaerosols and that corresponding to a molecular atmosphere, as is reported infigure 2.

With the new phase function for aerosols, the aerosol optical thickness for eachspectral band can be determined, since the aerosol path radiance is known for all theTM bands. This can be obtained from the expression which gives the aerosolcontribution to the path radiance for a nadir view angle (0 = 0°):

La(.1)= { E0 (.1) cos 00 w0/ a/4n(cos 00 + 1)}

x {1 — exp [ — t a(),)(( /cos 0 0) + 1)]} tal(),)tal(.1) (21)

where:

ta is the atmospheric transmittance for aerosol-scattered radiation, given by

ta l'(.1)= exp { — toz(2)— Ti.(),)} (22)

ta l(2)= exp { — (r oz(.1)/cos 00 )— (Tr(A)/cos 00 )} (23)

11 1 1 I 1 1 1 1 1 1 1

— Molecular

ContinentalMaritime

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. 1 1 1

2072 M. A. Gilabert et al.

for the upward and downward directions, respectively.wo is the aerosol single scattering albedo, obtained from

wo = PER x 1 . 00 + (1— PER) x 0 . 90 (24)

the values 1 . 00 and 0 . 90 being the aerosol single scattering albedos which respect-ively correspond to an ideal Rayleigh atmosphere with non-absorbing aerosols andto a hazy atmosphere with a higher proportion of absorbing aerosols in a typicalagricultural environment (Iqbal 1983). If the scene corresponds to an urban areawith a high proportion of carbon, a lower value for the second aerosol singlescattering albedo will be used instead of 0 . 90 (Iqbal 1983).

All the parameters in (21) are known, except ta(i1). Therefore, the aerosol opticalthickness can be obtained by inverting this formula. For this process, since theargument of the exponential function is generally much less than 1, it can bedeveloped as a Taylor series:

exp { —Ta(;t)[(1/cos 61 0 )+ 1]} ti 1 — {-cci(;t)[(1/cos 0 0) + 1]} (25)

With this approximation, the derivation of t a(y1) from (21) is less problematic from amathematical viewpoint, because exponential functions usually present some draw-backs in inversion procedures and in the aforementioned expression there arevarious sources of uncertainty. Therefore, in our approximation the aerosol opticalthickness is given by

a().) = [4n La()-)ii[Pa w o] (26)

0 30 60 90 120 150 180

Scattering angle (°)

Figure 2. Phase-function values employed in the model versus the scattering angle for threedifferent kinds of atmosphere: a molecular atmosphere, a hazy atmosphere composedof continental aerosols and a hazy atmosphere composed of maritime aerosols.

100

10

oooo

a) 1ca

o.cy)

0 . 1

cciocr)

0.01

1E-3

Atmospheric correction of TM images 2073

Finally, the atmospheric beam transmittances can be obtained from:

TT(A)=exp { — Toz().)—T,.(.1)— t a(.1)} (27)

T1(.1)=exp {(--c,z(Á)— Z t ( ))/ cos 00 } (28)

2.2. Determination of the global solar irradiance, Eg(.1)The global solar irradiance, is the sum of direct (beam) irradiance and

diffuse irradiance:

Eg(11)= Eb(.1)+ Ed().) (29)

where g refers to global, b to direct (beam), and d to diffuse irradiances.The expression for direct irradiance is

Eb(A)= Eo(),) cos 90 T,[(2) (30)

with 71(A) referring to the beam transmittance in the downward direction asobtained in the previous section.

On the other hand, if the diffuse irradiance due to multiple reflections betweenthe ground and the atmosphere is neglected, we can write, according to Iqbal (1983):

E d().) = E dr(),) + E da(11)

(31)

where Edr().) refers to the diffuse irradiance due to Rayleigh scattering, and Eda(11) tothe diffuse irradiance due to aerosol scattering. According to Iqbal (1983),

Ed(),)= (1/2)E, cos 9 0 [1— tr 1(.1)]ta l(A)t„1 )

+ F,(00)E0 cos 00 [1 — ta ,j,(44.1(.1)toz 1(.1)w0(32)

where the spectral transmittances in the downward direction as due to the molecularscattering, aerosol scattering and ozone absorption effects are, respectively,

tr1(2.)=exp { --cr())/cos 0 0 } (33)

t a l(.1) = exp { — Ta(2.)/cos 00 } (34)

toz 1(.1)=exp { — T oz(.1)/cos 0 0 } (35)

Equation (31) takes into account the isotropic nature of the Rayleigh scatteringby means of the factor (1/2), and the non-isotropic nature of the aerosol scatteringby means of the factor F,(00). This last factor represents the forward scatterance,that is, the energy scattered in the forward direction with respect to the total energyscattered. For F, values we shall make use of the values given by Iqbal (1983) whichare for discrete solar zenith angles. Therefore, for angles for which F, values are notavailable, a linear interpolation method will be used for calculating this parameter.

Globally, by the model described, given a certain TM scene containing somedark pixels, all the parameters required in equation (1) can be obtained for eachpixel, so that the relevant Rs(.1) values can be computed.

3. Testing of the modelThe procedure described was implemented into the existing I.A.T.A.-C.N.R.

software package. The package consists of FORTRAN-77 programs for generaldata processing and of GENSTAT 5 procedures for statistical analyses. All the

2074 M. A. Gilabert et al.

Table 1. Information concerning the TM images analysed in the study. DC*(1;3) refers tothe dark values, in TM bands 1 and 3, which have been employed in the atmosphericcorrection algorithm.

Imaget Date Latitude Height (m) Aerosol DC*(1;3)

CS1 22 August 45°55' 1000 C 51;11CS2 26 May 43°40' 200 C 52;11CS3 14 August 43°40' 200 C 51;11CS4 30 April 43°40' 300 C 48;10CS5 20 August 43°40' 300 C 42;08CS6 26 May 43°40' 300 C 56;12CS7 14 August 43°40' 300 C 57;14CW8 20 February 43°40' 300 C 35;07MS1 16 July 43°20' O M 57;12MS2 12 May 40°41' O M 63;11MW3 18 March 43°00' O M 52;13MW4 8 November 43°20' O M 33;07

tIn the labels, C and M refer to the geographical location (continental and maritime),and S and W to the season (summer and winter).

In this column C refers to continental aerosols and M to maritime ones.

programs and procedures were designed and performed in the computer centre ofthe Institute, running on a Digital VAX 11/750 and on a Micro VAX 3900.

Several TM scenes were used to evaluate the performance of the proposedmethodology. In table 1 a full list of these scenes is reported, together with theparameters required to run the model and the digital counts of the dark pixels inbands TM-1 and TM-3. As described previously, these values were found out by astandard method utilizing the original digital count frequency histograms (see alsoChavez 1988); the histograms were always derived from 1024 pixel by 1024 pixelscenes, so as to work with sufficiently representative samples, but not with too largea size as to invalidate the horizontally homogeneous atmosphere assumption. In allthe cases examined the presence of some dark pixels in TM-1 and TM-3 bands couldbe realistically assumed.

The aerosol optical thicknesses found by the described inversion method for eachTM band of the examined scenes are reported in table 2. Figure 3 shows thecorresponding beam atmospheric transmittances, rt(),), for 0 = 0°, divided into twocategories (continental and maritime) depending on their geographic location and onthe consequent kind of phase function used. About these curves some preliminary,qualitative considerations can be made.

First, all the values of optical thickness found are in ranges which are generallyconsidered acceptable and quite common for the relevant wavelengths in clear skyconditions (for example, 0 . 04-0 . 21 at 480 nm). As a consequence, all the atmospherictransmittances lie in the range 0 . 68-0 . 82 for band 1, with increasing values at longerwavelengths; these values can be considered quite realistic when dealing withcommonly used TM images. Different wavelength dependences have been found,which indicates different size distributions and, consequently, spectral properties ofthe aerosols as estimated from the model.

In many cases, the transmittance values are quite consistent with external,qualitative information about the sensed scenes as derived from independent

Atmospheric correction of TM images 2075

sources. For example, the scene taken in Northern Italy (scene CS1) was alreadyknown to correspond to a rather haze contaminated acquisition (Conese and Maselli1991), with the steep wavelength dependence which accords well with the kind ofatmosphere expected in a temperate mountainous zone during the summer period.Another example, of a maritime aerosol case, is given by the first scene of the Tuscancoast (scene MW3), in which the atmosphere was known to be so hazy at the time ofthe satellite overpass as to complicate even the visual interpretation of the images(Maselli et al. 1988).

In order to evaluate the effects of the choice of slightly different dark values onthe model outputs, simulations using digital counts in bands TM-1 and TM-3 ± 1 thevalues previously determined were performed for all the scenes (table 3). It must behighlighted that those reported are the maximum transmittance errors derived fromall the possible dark value combinations (3 by 3) and averaged over the six TMreflective bands. From some computations it has been found that these transmit-tance errors can generate relative reflectance errors of about twice the size, for solarangle O, = 30°, and of about four times when the Sun zenith angle is 70°.

As can be seen, the transmittance relative errors are all smaller than 15 per cent,which corresponds to generally acceptable uncertainty levels in the determination ofthe reflectance in the specific acquisitions. The effects of different dark digital countsare clearly more evident in winter, because of the reduced dynamic ranges of therelevant acquisitions.

The actual quantitative testing of the algorithm was carried out in three differentways: by direct comparisons with reflectance data collected in situ, through theevalution of the reflectances of an invariant surface at different times, and, finally, byfinding out the reflectances of some known cover types and comparing them withvalues reported in the literature.

3.1. Test 1: Comparisons with ground measured reflectancesA measurement campaign was carried out in a sea zone near the Tuscan coast

contemporaneously with a TM acquisition, on 16 July 1989 (image MS1). Duringthis campaign the radiances emerging from the sea in the first four TM bands weremeasured within half an hour of the satellite passage by means of an Exotech 101

Table 2. Aerosol optical thickness found by the described inversion method for all the scenesand for each TM band.

Image TM-1 TM-2 TM-3 TM-4 TM-5 TM7

CS1 0.165 0.124 0.095 0.063 0.019 0.011CS2 0.065 0.057 0.050 0.041 0.023 0.018CS3 0.110 0.091 0077 0.058 0.026 0019CS4 0.077 0.066 0.057 0.045 0.023 0.017CS5 0.036 0.031 0.027 0.022 0.012 0.009CS6 0.093 0.076 0.063 0.046 0.019 0.013CS7 0.180 0157 0.139 0.114 0.064 0.050CW8 0085 0053 0034 0.017 0.002 0.001MS1 0057 0045 0037 0.027 0.010 0007MS2 0.091 0.053 0.032 0.014 0.001 0.001MW3 0.205 0.168 0.140 0.104 0044 0031MW4 0.092 0058 0038 0.019 0003 0001

1.00

0.95 —

0.90 —

0.85 —

0.80

0.75

0.70 —

0.65 — á

0.60

--------- -

1.)U

1.00

0.95

0.90

0.85E

c.CDct

0.80

0.75

0.70

0.65

0.60

(a)

2076 M. A. Gilabert et al.

400 820 1240 1660 2080 2500

Wavelength (nm)

—9— CS1 —+— CS2 --*- CS3 • -°- CS4

--x- CS5 —e-- CS6 --° CS7 ---- CW8

400

820

1240

1660

2080

2500

Wavelength (nm)

—x— m sl MW4 MW3 MS2

(b)

Figure 3. Beam atmospheric transmittances (TT(.1)) for O at- O° corresponding to the TMimages analysed in the study and divided into two categories according to the kind ofaerosols. (a) Continental. (b) Maritime.

radiometer equipped with suitable filters. Six sampling cites were chosen, corres-ponding to points with high differences in white sediment concentration due to theadjacent discharge of an artificial channel (Maselli et al. 1990). As a consequence ofthese differences, wide variations existed in the relevant radiance measurements,especially in TM bands 1 and 2, which are also the most strongly influenced by theatmospheric effect. Clearly, this high spatial variability also caused a certain level ofimprecision in the correspondence between ground measured and satellite data,which is however unavoidable in this kind of comparison. The radiance values werethen converted into reflectances through the standard method described in Pinteret al. (1987).

The ground measured reflectance values were compared to the satellite reflec-tance values as derived from the model, trained as reported in table 1. Apparent

Atmospheric correction of TM images 2077

Table 3. Relative errors (%) in the transmittance and reflectance values obtained with themodel as a consequence of a uncertainty of +1 DC in the dark-value inputs.

Image ERRORT(%) ERRORR(%)

CS1 5.9 15CS2 5.6 13CS3 6.8 16CS4 7.6 18CS5 14 34CS6 3.7 8.4CS7 8.0 19CW8 12 40MS1 1.7 3.9MS2 1.4 3.2MW3 6.2 17MW4 8.6 34

reflectances were also computed, as defined in equation (2), so as to give an idea ofnon corrected data. Figure 4 graphically reports all these comparisons for bandsTM-1, TM-2 and TM-3, which only showed sufficient dynamic ranges due to theextremely high absorption of water in the infrared bands.

There is a considerable degree of agreement between estimated and groundmeasured reflectances. As can be observed from figure 4, the correspondencebetween measured and estimated scores is very good for band TM-2, but a notablesimilarity is also present in the trends of bands TM-1 and TM-3. Apparentreflectances, even if closer to the ground measurements in some cases (for example,the low values in band 1), show a marked reduction in the relevant ranges whichmakes the estimates only valid in limited intervals. This accords well with theoreticalconsiderations and with the findings of other investigations (Kaufman and Fraser1984, Fraser and Kaufman 1985, Kim and Elman 1990); globally, the atmosphereacts so as to increase the low reflectance estimates (due to the path radiance) and todecrease the estimates from highly reflective surfaces (because of atmosphericabsorption and scattering).

The linear regression equations clearly confirm this quantitative evaluations, ascan be seen from table 4. For all the bands, the expressions corresponding to the fitbetween the model and the real reflectance values are much better than thoseobtained with apparent reflectances. In bands TM-1 and TM-2, the intercept as wellas the slope are more similar to those which would correspond to the ideal case(diagonal: y=x). Even in TM-3 band, where the slope obtained for the apparentreflectance fit is 1, the model adjustment is better because the intercept is one orderof magnitude inferior, and so, closer to zero (ideal case).

3.2. Test 2: Evaluation of invariant surface reflectancesAssuming that the model of reflectance retrieval works correctly, a logical

consequence of its application to multi-temporal scenes taken over the same zone isthat invariant surfaces should maintain their spectral signatures approximatelyconstant, independently of the atmospheric condition. On the other hand, therelevant apparent reflectances should change in relation with the latter parameter.

030.0

0.0 0.1 0.2

0.3

0.2

0.1

0.00 0 0.1 0.2 0.3

Measured reflectanceR » (MODEL) + la' (APPARENT) - Ideal case

0.3

o

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CD

coa)

E 0.1

cnL1J

Measured reflectanceR • (MODEL) + (APPARENT) -Ideal case

2078

M. A. Gilabert et al.

0.15

C.) 0.10

co

Ua)

a)

0.05

coEcip

LL1

0.000.00 0.05 0.10

0.16

Measured reflectance* R. (MODEL) + (APPARENT) -Ideal case

Figure 4. Model-estimated and apparent reflectances versus in situ measured reflectancescorresponding to different sea sites for the TM image of 16 July 1989, in the spectralbands TM-1, TM-2 and TM-3.

Thus, invariant cover types can be used to test the performances of the techniquedeveloped. Unfortunately, the identification of such surfaces is not simple, as thespectral invariance of most non-vegetated surfaces is only apparent. Our choice fellon a wide, concrete barrage recently built in a Tuscan area east of Florence forwhich two acquisitions were available (scenes CS4 and CS5). The spectral invarianceof this barrage can be assumed with high reliability, especially for the first four TMbands, which are mainly influenced by the atmosphere but less affected than themiddle infrared channels by possible, slight differences in moisture content.

In figure 5 the model-estimated and apparent reflectances of the pixels corres-ponding to the barrage in the two acquisitions are reported for TM bands 1-4. Ascan be seen, the model-estimated reflectances are quite similar for the two scenes inall the four bands, with dynamic ranges which are considerably wider than those ofthe apparent reflectances. This tallies fairly well with the preceding considerations, asthe effect of the atmosphere is expected to lower high reflectance values due toabsorption.

Atmospheric correction of TM images 2079

Table 4. Top: Linear regression equations corresponding to the relationships between theestimated reflectances (by model or by the apparent reflectance expression) and theground measured reflectances, for the July campaign. Bottom: Deviation of interceptand slope values respect to those corresponding to an ideal case (y=x).

Model reflectance Apparent reflectance

TM-1

TM-2

y= —0 . 019+0 . 80xr=0. 98

y= —0 . 001+0 . 93xr= 0 . 97

y=0.055 +0.57xr= 0.98

y= 0-041+0.73xr= 0.97

TM-3 y= 0 . 007r= 0 . 92

+ 1 . 16x y= 0.037+1.00xr= 0.92

Deviations (intercept) (slope) (intercept) (slope)

TM-1 0.019 0.20 0.055 0.43

TM-2 0.001 0.07 0.041 0.27

TM-3 0007 0.16 0.037 0.00

This effect is greatest in bands TM-2 and TM-3, which show relatively highreflectance values, whilst it decreases in band TM-1, where the reflectance of thebarrage is lower and the path radiance seems to compensate the influence ofabsorption, and, to a lesser degree, in band TM-4, where the latter is almostnegligible (figure 3). Furthermore, the differences in apparent reflectances betweenthe two acquisitions are also in accordance with the transmittance values found bythe model; in fact, a clear atmosphere (scene CS5) absorbs and scatters less than ahazy one (scene CS4), so that the reducing effect of the former is less marked in thisrange of reflectance.

35

30

25

CG>

20

152

3 4TM band

Figure 5. Estimated reflectance (R*) and apparent reflectance (R') of a pseudo-invariantsurface (a barrage) in two different acquisitions (scenes CS4 and CS5) for TM bands 1-4.

5

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TM band

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2080 M. A. Gilabert et al.

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P.) 15c

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Figure 6. Spectral signature of coniferous forest in May (scene CS2) and August (sceneCS3), as determined using the apparent reflectance (R') and the reflectance atmospheri-cally corrected by the model (R*).

3.3. Test 3: Spectral signatures of known cover typesA wide range of information was available in the Institute from previous works

on the cover surfaces corresponding to severa] TM acqusitions. The model-estimatedand apparent reflectances of these cover types were found in order to compare thevalues obtained with those reported in the literature. Clearly, this is only an indirecttest, but it can give an idea of the general utility of the methodology proposed.

Only a few of the most interesting examples available have been reported here.The first determination of model-estimated and apparent reflectances was made onconiferous and deciduous woods imaged in May (scene CS2) and in August (sceneCS3), (Maselli et al. 1991). As is seen in figures 6 and 7, the apparent spectralsignatures show the usual reduction in dynamic ranges with respect to model-estimated reflectances. The differences in spectral signatures are particularly markedin band TM-1, due to the extremely low reflectance of these cover types and to theeffect of path radiance.

R. -R'

35

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20C.)a>

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5

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O

Atmospheric correction of TM images 2081

2

3 4

5

7TM band

2

3 4

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7

TM band

Figure 7. Spectral signature of deciduous forest in May (scene CS2) and August (scene CS3),as determined using the apparent reflectance (R') and the reflectance atmosphericallycorrected by the model (R*).

As absolute values, the model-estimated reflectances of coniferous forest in thevisible bands are in optimum accordance with the values reported in the literature(about 0 . 02 in the blue, 0 . 04 in the green and 0 . 03 in the red (see Kaufman andSendra 1988)), whilst the apparent reflectance curves are much higher in these bandsand do not show the typical relative maximum in the green region of the spectrum.The constancy of the model-estimated values in the two acquisitions is alsoconsistent with previous findings, given the weak fluctuations in ecophysiologicalconditions which are typical of coniferous species. Deciduous wood also showsreflectance values which agree with the referentes (Kaufman and Sendra 1988), andin this case it is also possible to note the slightly higher vegetation activity in spring.

Other reflectance estimates were made of two typical agricultural cover types,wheat and maize, from two scenes taken in April (CS4) and in August (CS5) (DeFilippis et al. 1991). As figures 8 and 9 show, also in these cases the model-estimatedreflectances tally more closely with the values in the literature than the apparentreflectances (Badhwar 1984, Hlavka et al. 1980). As concerns wheat, the most

45

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2082 M. A. Gilabert et al.

2 3 4 5 7

TM band

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40

35

30

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20

15

10

5

2

3 4 5

7

TM band

Figure 8. Spectral signature of wheat in April (scene CS4) and A ugust (scene CS5), asdetermined using the apparent reflectance (R') and the estimated reflectance (R*).

interesting feature from the first scene is the notable difference between apparent andmodel-estimated reflectances in bands TM-3 and TM-4, respectively positive andnegative in sign (figure 8). These differences would lead to quite different computa-tions of vegetation indices from the two parameters. A similar behaviour is alsoapparent, with lower intensity, for maize in the second scene, while the other twocases (wheat in late summer and maize in early spring) are not particularlyinteresting because they represent only almost completely bare soil.

In general, as the atmosphere affects the red and the near-infrared regions of thespectrum in a different manner, vegetation indices such as the normalized differencevegetation index (NDVI) appear to be very sensitive to the correction procedure,presenting a wider range when model-estimated reflectances are used. As a conse-quence, the contrast in NDVI of the scenes is enlarged, which may lead to anincrease in information content for scene classification. This was found experimen-tally in all the cases examined. As an example, the NDVI computed for the sceneCS1, where different forest cover types are present, gives a much higher between

Atmospheric correction of TM images 2083

40

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30

(-) 25

a> 20

15

10

5

1 2

3 4 5 7

TM band

40

35

30

a..) 25

t.', 20

r t.) 15

10

5

2 3 4

5

7

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Figure 9. Spectral signature of maize in April (scene CS4) and August (scene CS5), asdetermined using the apparent reflectance (R') and the estimated reflectance (R*).

class/within class ratio value when using the model reflectances than when employ-ing apparent reflectances. This clearly indicates an increase in the relevant informa-tion content, which allows the identification of spectral classes which were notseparable in the NDVI derived from the apparent reflectance images. Thus, while thespectral classes corresponding to Norway spruce and hophorbean showed, beforethe atmospheric correction, the same NDVI value (0 . 56), after correcting the imagesthese classes presented NDVI values of 0 . 75 and 0 . 69 respectively. A similarbehaviour can also be observed from the scene CS4 for non-vegetated areas: beforecorrection, maize in early season (almost bare soil) and the artificial barrage showedpractically the same NDVI value (0 . 03 and 0 . 04 respectively). After correction thecorresponding values are 0 . 11 and 0.02.

This trend is also evident from a measurement of image information content,such as entropy (Davis and Dozier 1990, Conese and Maselli 1993). The NDVIcomputed from the corrected images is generally more informative than thatcalculated from apparent reflectance images; from a first evaluation, an increase ofabout 10 per cent in information content has been found in some case studies.

2084 M. A. Gilabert et al.

4. ConclusionsThe method for the atmospheric correction of TM scenes developed in the

current work has two basic, distinguishing features. First, it requires only par-ameters which are commonly easily obtainable and information which is generallycontained in most TM scenes. Second, it allows not only a simple correction of theatmospheric scattering, but also the retrieval of the real reflectances of the sensedsurfaces.

Relying on a probabilistic identification of dark points, the methodology isapplicable to all cases in which the presence of some non-reflective surfaces can berealistically assumed. In practice, this assumption can hold for all the scenes takenover zones where shadows, dense vegetation, clear water bodies or some other darksurfaces are known to be present.

As has been demonstrated by various kinds of test, the actual performance of themethod is generally good, with relative error levels in the determination of surfacereflectances which are usually in a range ( < 20 per cent) which is consideredacceptable for most applications (Gonima 1993, Moran et al. 1992, Richter 1990,1991). A major source of uncertainty is related to the correct selection of dark-objectdigital counts, which, however, may be problematic only in areas without darksurfaces. A certain degree of subjectivity remains in the identification of the darkvalues in TM bands 1 and 3, but this is unavoidable considering the statistical,operational nature of the method. The second main source of error is represented bythe use of aerosol phase functions not found experimentally. However, the estima-tion of the aerosol optical characteristics made by the use of two differentwavelengths tends to alleviate this intrinsic drawback and to render the whole modelmore objective and easily applicable than those previously reported in the literature.The other assumptions concerning the atmospheric characteristics are the samereported in most radiative transfer models and can be expected to cause largemisfunctioning only in extreme illumination conditions.

The advantages offered by the method are notable, especially from an oper-ational viewpoint. The use of real reflectance values allows more reliable researchabout the surface properties, particularly in multitemporal studies, and gives thepossibility of comparing information taken from different studies. Furthermore, theprocedure proposed also permits the recovering of reflectances from old TMimagery in retrospective studies. Eventually, the creation of data bases containingthe reflectance values of the most widespread cover types may also be possible, withevident improvements in the potential of unsupervised investigations.

Even if the procedure has been demonstrated to be capable of retrieving realreflectances fairly accurately, there is ample room for improvement. In the radiativetransfer model, the effects of multiple reflections between the atmosphere and theEarth's surface could be included, and different, more straightforward definitions ofthe aerosol phase function are possible. Also, the adjacency effect could beconsidered when computing reflectances for pixels in highly variable zones and otherpossible extensions could account for the topographic effect in highly ruggedterrains. Research in these directions is presently being conducted by the authors.

AcknowledgmentsThe present work was partially supported by an ASI (Agenzia Spaziale Italiana)

grant. It was carried out during M. A. Gilabert's visit to the IATA-CNR which wasfinanced by a postdoctoral fellowship from the CEAM (Consellería de Cultura,

Atmospheric correction of TM images 2085

Educació i Ciéncia de la Generalitat Valenciana (Spain); DOGV 15 February 1991).The authors want to thank Professor E. Pranzini and Dr G. Profeti for theiressential contribution to the measurement campaign in the Tuscan sea. Specialthanks are also due to the anonymous referee whose suggestions greatly improvedthe quality of the paper.

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