Our first goal in this paper is to propose a simplemodel of the adjacency effect, i.e., the reduction ofimage contrast as atmospheric turbulence increases,by using the primary scattering approximation.Then, based on this simple tool for computing adja-cency effects, we conduct an extensive study. Wefirst investigate the effects of the aerosol models andvertical distributions on the model of adjacency ef-fects. Then we study off-nadir views and model theadjacency effects as simply as possible. Finally, wediscuss the influence of environmental effects on theretrieval of data on the abundance of chlorophyll incoastal waters.
The authors are with the Laboratoire Interdisciplinaire des Sci-ences de l’Environnement, ELICO, Centre National de la Recher-che Scientifique, Unite Propre de recherche et EnseignementSuperieur Associee 8051, Universite du Littoral Cote d’Opale, Mai-on de la Recherche, 32 Avenue Foch, B. P. 59 62930 Wimereux,rance. The e-mail address for R. Santer is [email protected]
ittoral.fr.Received 8 March 1999; revised manuscript received 16 July
The photons at the entrance of a satellite sensor havedifferent origins. For observations in the atmo-spheric windows ~spectral regions that can be simplycorrected or ignored from gaseous absorption!, theop-of-the-atmosphere ~TOA! radiance L* can be ex-
pressed as the sum of the atmospheric path radianceLatm ~the radiance observed over a black surface! andf the apparent radiance that corresponds to the sur-ace L*t. To remove the time variation of incident
direct solar irradiance, we refer to reflectance insteadof radiance. If the surface is assumed to be spatiallyhomogeneous, the contribution of the surface to theadjacency effect is expressed, following the formula-tion proposed in the simulation of the satellite signalin the solar spectrum1 ~5S! code, by
rt* 5 T~ms!T~mv!@rty~1 2 rt s!#, (1)
where T is the total transmittance ~the total down-ward irradiance, direct and diffuse, at the surfacelevel for a black surface, normalized by the directsolar irradiance at the top of the atmosphere!, ms ishe cosine of Sun’s angle us ~the subscript v repre-ents the view angle!, and s is the spherical albedo ofhe atmosphere. The denominator of Eq. ~1! ac-ounts for the multiple interactions between the at-osphere and the surface.If the surface is not homogeneous, a dark pixel has,
20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 361
itc
amw
Tfbs
t
3
for example, adjacent bright pixels and, because ofatmospheric scattering, photons reflected by thebright surround may be scattered toward the sensor.Theoretical estimates of the adjacency effect are re-ported, for example, by Tanre et al.2 The effect,which is the result of photons reflected by the envi-ronment ~see Fig. 1!, has at a given point M a reflec-tance rc that generally differs from reflectance rt thatis directly observed from the sensor. The 5S codeexplicitly proposes to formulate the contribution tothe effect of the surface as
where d is the total optical thickness, td is the diffusetransmittance ~the diffuse irradiance at the surfacelevel for a black surface, normalized by the directsolar irradiance at the TOA!, and ^r& is an averagereflectance. In Eq. ~2! the total normalized illumi-nation is T~ms!y~1 2 ^r&s!.
If we consider two adjacent pixels, to first order theatmospheric scattering functions are the same as ^r&.By using the differences in TOA reflectances, we canremove the adjacency effects. Using this technique,Tanre et al.3 proposed a method for following thevariation of the aerosol optical thickness on a con-trasted scene that has good temporal stability. Also,Tanre and Legrand4 compared results of retrieval ofaerosol values over land based on the effects of theaerosols both on contrast reduction in visible imageryand on infrared imagery.
For a nadir view, the location of M is expressed inpolar coordinates ~r, f!, and we express ^r& as
^r& 5 *0
`
r~r!g~r!rdr, (3)
in which
r~r! 5 ~1y2p! *0
2p
r~r, w!dw (4)
Fig. 1. Satellite sensor observes at nadir a pixel O of reflectancert. By atmospheric scattering, a fraction of the incoming signalcan originate from the neighborhood of this pixel. At a given pointM, reflectance re generally differs from the reflectance of the pixelhat is directly observed by the sensor.
62 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000
s the average azimuth value of the surface reflec-ance. If the location of M is given in Cartesianoordinates, then
^r& 5 *2`
`
*2`
`
f ~x, y!r~x, y!dxdy, (5)
where f ~x, y!, which is usually referred to as theatmospheric point-spread function ~psf ! in the liter-ature; see, for example, Vermote et al.5!, correspondsto the fraction of incident photons reflected at M by aLambertian reflector of unit reflectance and thenscattered toward the sensor. The relationship be-tween g and f is simply rg~r! 5 f @r~x, y!#. To evalu-te the psf theoretically, one uses the Monte Carloethod to solve the transfer equation in the back-ard mode. Reinersman and Carder6 conducted a
sensitivity study of adjacency effects over coastal wa-ters based on Monte Carlo computations. They alsodefined an algorithm for atmospheric correction thatincluded adjacency effects and applied it to the Air-borne Visible Infrared Imaging Spectrometer~AVIRIS! imagery. On a more operational basis, forthe Maltiangle Imaging Spectroradiometer ~MISR!on the Earth Observation System ~EOS!, Martonchiket al.7 proposed an algorithm for retrieval of aerosolvalues that is based on blurring effects. An exampleof an atmospheric correction scheme that includesblurring effects was reported by Vermote et al.7 andincludes an illustration of thematic mapper imagery.In the same paper there is also a description of anoperational algorithm for the moderate resolution im-aging spectroradiometer ~MODIS!. Precomputedlook-up tables were used for these algorithms.
Unfortunately, using the Monte Carlo codes istime-consuming and hence does not allow extensivestudies to be conducted. To account for adjacencyeffects in operational atmospheric correction algo-rithms on global scales it is always possible to usecomputed look-up tables. On regional scales, theend-user community will request simpler softwarepackages with which it can input ancillary informa-tion on aerosols derived from in situ measurements orfor a regional climatology. In both cases it is highlydesirable to develop simple modeling.
B. Basic 5S Computations
A simple modeling of the adjacency effect in the 5Scode is proposed for a nadir view and for a scene thatcorresponds to a uniform disk ~radius R! of reflec-tance rt surrounded by a uniform infinite surface ofreflectance rc:
^r& 5 rt F~R! 1 re@1 2 F~R!#. (6)
F~R! is simply the integral of rg~r! between 0 and R.his function is modeled ~or analytically expressed!
rom a best fit of Monte Carlo simulated data foroth Rayleigh and aerosol scattering. Rayleighcattering and aerosol scattering are decoupled.
0
v
aisFfas
atTRTtets
o
Table 1. Atmospheric Conditions To Simulate the Adjacency Effects
ar
at
For molecules, an analytical formulation of F~R! isavailable:
Fm~R! 5 am exp~2am R! 1 bm exp~2bm R!, (7)
where am 5 0.93, bm 5 0.07, am 5 0.08, and bm 5 1.1.For the continental aerosol model, a formulation sim-ilar to Eq. ~7! is proposed, with aa 5 0.375, ba 5.625, aa 5 0.02, and ba 5 1.83.Following Eqs. ~1! and ~2!, the introduction of en-
ironmental effects corresponds to
Dr* 5 td~mv!~^r& 2 r!@T~ms!y~1 2 ^r&s!#. (8)
The maximum contrast between land and water ex-ists in the near infrared at 865 nm. We can assumethat the water reflectance rw is zero. From Satellitepour l’Observation de la Terre ~SPOT! imagery inXS3, we observed an average value of r1 5 0.3 for theland reflectance. The Rayleigh optical thickness is
Fig. 2. Bias at 865 nm ~the environment is neglected! at thecenter of a dark water disk of radius R surrounded by homoge-neous and infinite land of 30% reflectance. Plots are labeled forthe six atmospheric cases of Table 1.
aFor the continental model and three visibilities V, we give, fortwo solar zenith angles, aerosol optical thickness da, sphericallbedo s, total transmittance for a nadir view T~mv!, atmosphericeflectance ra, and total transmittance for the downward path
T~ms!. Cases 1, 2, and 3 correspond to the three visibilities ~50, 23,nd 8 km, respectively! for 30° solar zenith angle; cases 4, 5, and 6he same three visibilities and 60° solar zenith angle.
0.016, and we used the continental model to generatethe aerosol scattering functions: reflectance, totaland diffuse transmittances, and spherical albedo.These values are listed in Table 1. The geometricconditions correspond to a nadir view at two solarangles of 30° and 60°. Three visibilities are used:50, 23, and 8 km.
Figure 2 shows this contribution to the adjacencyeffect, for the above conditions, in the middle of acircular lake relative to the lake’s radius. This effectshould be compared with the atmospheric path radi-ances listed in Table 1. For a lake of R 5 5 km, thesupplementary contribution of the environment tothe atmospheric signal is roughly half of the atmo-spheric signal ~cf. Table 1 and Fig. 2!.
For the nadir view it is easy to modify the 5S codeto introduce spatial inhomogeneities. We just useEqs. ~3! and ~4! in which, simply, rg~r! is the deriv-
tive of F~R!. It is then possible in principle tontroduce the adjacency effects for any type of land-cape. Here we select two schematic situations.irst, for a circular lake of radius R, we compute ^r&
rom the middle of the lake to the shore. Inasmuchs the adjacency effects differ for Rayleigh and aero-ol scattering, we compute ^r&, that is to say, ^rR&
and ^ra&, separately for both of them. Figure 3presents these results for a lake of radius 5 km aswell as for R 5 10 km and R 5 20 km. We maketwo main remarks: First, as Rayleigh scattering ismore isotropic than aerosol scattering, ^rR& isgreater than ^ra&. For a small lake ~R 5 10 km! the
djacency effect is quite uniform near the center ofhe lake and increases sharply close to the shore.able 2 lists values of Dr for circular lakes of radii5 5, 10, 20 km for the atmospheric conditions of
able 1. If we compare the atmospheric reflec-ances listed in the two tables, we see that at thedge of the lake the contribution of the environmento the adjacency effect is greater than the atmo-pheric term.The other schematic situation corresponds to that
f a coastline. Figure 4 also shows ^rR& and ^ra&.This time the interpretation is easier: We retrievethe water ~or the land! reflectance value if we are farenough from the border, and we get just a medium
Table 2. Additional Reflectance ~in percent! Owing to AdjacencyEffects Computed for the Cases of Fig. 2 for Disks of Radii R 5 5, 10,
20 km at the Center of the Disk ~upper value! and at the Edge~lower value!a
aThe six columns correspond to the two solar zenith angles andto the three visibilities.
20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 363
ptRt
sd
364 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000
value on the coastline. Table 3 lists the contributionto the adjacency effect made by the environment com-pared with that of distance to the coast D. Com-
ared with those in Table 2, the adjacency effects onhe coastline are, as expected, similar for a lake with
5 20 km and for the open ocean. We also indicatehe distance D0 for which the contribution of the en-
vironment is less than 1023.
2. Single-Scattering Approximation
A. Formulation for A Nadir View
In the 5S code the adjacency effect depends directlyon the optical thickness through computation ofthe diffuse transmittance td~mv! for the upwardpath. It is expected that the dependence of theradiance on scattering angle will be quite similarfor primary scattering and for multiple scattering.In the 5S code F~R! does not depend on the atmo-spheric turbidity, which means that we can certainlyevaluate F~R! by using the primary scattering ap-proximation. We shall also follow the 5S approx-
Fig. 4. Same as Fig. 3 but versus the distance at sea from astraight coastline. Reflectances given in percent.
aDr is given at various distances D from the coast line for twoolar zenith angles ~30° and 60°! and three visibilities V. D0 is theistance for which Dr becomes less than 0.1%.
Fig. 3. Averaged reflectances ~in percent! for Rayleigh scattering^rR& and for aerosol scattering ^ra& plotted along a radius for cir-cular lakes of ~a! R 5 5 km, ~b! R 5 10 km, and ~c! R 5 20 km.General conditions are those of Fig. 2.
r
ftTwa
Nca
Lsc
imation, which decouples aerosol and Rayleighscattering.
Let us consider ~Fig. 5! an elementary layer of op-tical thickness dt located at an altitude z. A unitadiance is reflected at M and then scattered by dt
with
d2L 5 dtdm@P~m!r~m!y4p#, (9)
where P is the phase function, t is the optical depth ataltitude z, r is the ground reflectance, and m is thecosine of scattering angle u for a nadir view and abeam scattered at altitude z from point M~r!. m issimply given by
m 5 zyÎr2 1 z2. (10)
The total radiance that corresponds to the adja-cency effect will first result from the integration int ~or in z! between the ground surface and the TOAor satellite observations. For airborne observa-ions the integration will stop at the sensor altitude.o compare the primary scattering approximationith the 5S code, we express the contribution to thedjacency effect of the disk of radius R as
L~R! 5 dt *0
2p
*h
1
@P~m!r~m!y4p#dmdw
5 dt *h
1
@P~m!r~m!y2#dm, (11)
where h 5 cos j and that of the whole infinite surfaceas
L~R 3 `! 5 dt *0
1
@P~m!r~m!y2#dm
5 dtH*0
h
@P~m!rey2#dm
1 *h
1
@P~m!rty2#dmJ .(12)
As follows from the 5S formulation, instead of a unitradiance we have to account for the actual irradianceat the surface; then Eq. ~12! becomes
L~R 3 `! 5 @T~ms!msy~1 2 ^r&s!#dtH*0
h
@P~m!rey2#dm
1 *h
1
@P~m!rty2#dmJ , (13)
which can be simplified by ms to yield the reflectance.Now considering Eq. ~2! as given by the 5S formu-
lation and L 5 msr, we can write the adjacency radi-ance contribution:
LeTOA 5 ^r&td~mv!T~ms!msy~1 2 ^r&s!. (14)
According to the reciprocity principle, the radiancefor a nadir view with the Sun at u is equal to aradiance for a view at u with the Sun at zenith.
The primary scattering approximation is written,with m 5 cos u, as
L~m! 5 P~m!dtym4p. (15)
With this approximation we can write the scatteredflux:
f25 *0
2p
*0
1
mL~m!dmdw 5 ~dty2! *0
1
P~m!dm. (16)
The diffuse transmittance is now, as we consider theSun at zenith,
td 5 f2yms 5 f2. (17)
ow that the diffuse transmittance is expressed, wean compare Eq. ~13! with Eq. ~14! and identify F~h!s
F~h! 5 1 2 *0
h
P~m!dmY*0
1
P~m!dm. (18)
Fig. 5. Pixel O viewed at nadir. Let us consider, at an altitudez, an elementary layer of optical thickness dt. The light reflectedby the surface at M, distant from O by r, can be scattered towardthe sensor at scattering angle u. If we consider, as in the 5S code,a disk of radius R, j is the maximum scattering angle.
Fig. 6. Pixel O viewed by the sensor ~uv, wv 5 0 by convention!.et us consider the elementary layer dt at altitude z. We repre-ent a beam reflected by the surface at M. M is located in polaroordinates ~r 5 OzM, w!.
20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 365
c
WId
T
cb
idCread
3
As a first approximation, we can use Eq. ~18! to studythe influence on the adjacency effect of a thin atmo-spheric layer in terms of either altitude ~cirruslouds! or optical thickness ~stratospheric aerosols!.
We now consider a layer of optical thickness d.e consider an optical thickness t for the sublayer dt.
f we neglect the attenuation between the surface andt first, then between dt and the TOA, F~R! can be
simply expressed as
F~R! 5 F*0
d
*h
1
P~m!dmdtGYFd *0
1
P~m!dmG . (19)
o establish the relationship between F~R! and thepsf, again we need to consider the derivative of F~R!or F~h!.
If we assume isotropic scattering, we then have
F~R! 5 1 2 ~1yd! *0
d
hdt. (20)
Return to Eq. ~18! and consider the attenuation; forexample,
t~t, m! 5 t~z, m! 5 exp@2~d 2 t!ym#exp~2t!,
which simply complicates the formulation of F~R!with
F~R! 5
*0
d
exp~2t! *h
1
exp@2~d 2 t!ym#P~m!dmdt
*0
d
exp~2t! *0
1
exp@2~d 2 t!ym#P~m!dmdt
.
(21)
B. Off-Nadir View
The formulation of the problem with an off-nadirview is more complex because we do not have sym-metry in the azimuth. Nevertheless, it is alwayspossible to express the adjacency effects by using theprimary scattering approximation. In Fig. 6, pixel Ois viewed under the condition that uv, wv 5 0 byonvention. Let us consider the elementary contri-ution d3L of a sublayer dt at altitude z, correspond-
ing to an incident beam reflected by the surface at M.M is located here in polar coordinates ~r 5 Oz M, w!,where Oz is distant from O by an amount z tan uv.According to Eq. ~9!, we have
d3L 5 r~m, w!@P~Q!y4pmv#dmdwdt. (22)
The ~m 2 r! correspondence is given by Eq. ~10!, andscattering angle Q is given by
cos Q 5 mvm 1 sin uv sin u cos w. (23)
It is always possible to integrate Eq. ~22! in altitude~in z or in t! for a given point M by using Eqs. ~9! and~23! to establish the link with the psf. For schematicsituations such as our ocean–land system, we shall
66 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000
see below how to express ^r& simply by using a Fourierseries expansion.
C. Introduction of Fresnel Reflection
For sea observation we have to consider Fresnel re-flection. Figure 7~a! illustrates the contributions tothe signal when one is viewing a pixel O that are dueto Fresnel reflection. We first have the sun-glint
Fig. 7. ~a! Sea surface considered as a plane mirror. Curve ones the direct–direct path for Fresnel reflection. For curve two, theirect solar beam is reflected and then scattered toward the sensor.urve three is the fraction of the diffuse downward irradianceeflected toward the sensor. ~b! Pixel O is viewed at nadir. Thelementary layer dt is again at altitude z with the direct solar beams its source reflected by the sea at angle u. The coastline is at aistance R from O, and zmax represents the altitude maximum
reached by the solar reflected beam. ~c! Pixel O is viewed at nadirand again the elementary layer dt is at altitude z with the directsolar beam as its source reflected by the sea at angle u. Thecoastline is at a distance R from O, and zmin represents the altitudeminimum reached by the solar reflected beam.
nl
i
Ema
Fie
tt2
spot, which corresponds to the sea reflection on adirect-to-direct path one. This area is useless forocean color interpretation. Outside the sun-glintspot we first have the solar beam reflected at M,which can be scattered toward the sensor two. Thenwe have the downward-scattered radiance at O,which can be reflected toward the sensor three.Higher-order terms in the coupling between scatter-ing and reflection can be neglected. For the inter-pretation of open ocean imagery, terms two and threeare included in the modeling of the atmospheric pathradiance. For coastal water observations, termthree still exists but term two remains only if point Mbelongs to the sea. In Fig. 7~b! we consider only thereflection of the solar beam that occurs in the princi-pal plane for a land–sea scene and for a water pixel.We assume that an elementary layer dt at an altitudez is lighted by this reflected solar beam; the elemen-tary contribution to the radiance ~we are always us-ing the primary scattering approximation! is
dL 5 r~ms!P~ms!dty4p. (24)
Equation ~24! can be applied to both aerosol and Ray-leigh scattering, which are additive. At a given al-titude z, Eq. ~24! is valid only if the Sun lights thiselementary layer. Pixel O is at a distance R ~as-sumed to be a straight line! from the coast. ws is theazimuth of the solar plane with reference to the coast.
If py2 , ws , 3py2, the entire atmospheric layer islighted. After integration in d, Eq. ~24! becomes,with irradiance p,
L 5 r~ms!dP~ms!y4, (25)
and this equation is included in transfer code compu-tations that deal with oceanic observations. If ws is
ot included in the above range, the atmosphere isighted only at an altitude zmax, where
zmax 5 Rycos ws tan us. (26)
In Eq. ~25! we then have to replace d with dmax, whichs the optical thickness between O and zmax:
Dr 5 r~ms!P~ms!~d 2 dmax!y4ms. (27)
quation ~27! corresponds to a nadir view but re-ains valid for an off-nadir view when the scattering
ngle is simply P–Q.On a qualitative basis the reflection coefficient does
not depend on the wavelength. Then the spectrumdepends only on the scattering properties, and thedependence increases in the blue. For the aerosols,the wavelength dependence of Dr mostly coincideswith the wavelength dependence of the aerosol opti-cal thickness. Compared with that of the aerosols,the spatial range for the Rayleigh scattering is larger,first because the phase function is smoother and sec-ond because the altitude of the molecules is higher.
Figure 7~c! illustrates the coupling of the Fresnelreflection with the atmosphere for a land observation.Of course, for interpretations of land observations theFresnel reflection is not generally accounted for.
Then the supplementary term that is due to theFresnel reflection can be expressed as
Dr 5 r~ms!P~ms!~d 2 dmin!y4ms. (28)
3. Results
A. Sensitivity of the Aerosol Model
First we validate Eq. ~20! for the Rayleigh scattering,comparing it ~Fig. 8! with the 5S formulation. In
ig. 8 we also plot F~R! as derived from Eq. ~21!. Its shown that the transmission terms have a residualffect on F~R!. Equation ~20! is also used in Fig. 9, in
which F~R! is compared for aerosol scattering in the5S expression and in a continental model defined bya Junge size distribution n~r! 5 r2y, with y 5 4, and
Fig. 8. F versus r for a molecular atmosphere according to the 5Scode and with the primary scattering approximation for molecularscale height HR 5 7 km according to Eq. ~20! or ~21!.
Fig. 9. F versus r for the continental aerosol model as proposed inhe 5S code. Comparisons with the primary scattering formula-ion for a Junge size distribution n~r! 5 r24, m 5 1.55, and Ha 5km with Eq. ~20! or ~21!.
20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 367
ee
chbbrAa
AraFi
flctpTmnamptc
r
t
3
a refractive index m 5 1.55. The aerosol’s ~or mol-cules’! vertical distribution is assumed to follow anxponential variation with d~z! 5 d~0!exp~2zyH!,
with a standard vertical scale height Ha 5 2 km forthe aerosols. The aerosol vertical distribution usedfor the 5S computations does not exactly follow anexponential law but corresponds to a more-sophisticated model. Nevertheless, F~R! obtainedby our model is similar to the 5S approximation ofF~R!. These last two comparisons validate the pri-mary scattering approximation used for modeling theadjacency effects.
The influence of the shape of the atmospheric scat-tering phase functions on blurring of surface detail inimages acquired from space has been reported byDiner and Martonchik,8 who used a Monte Carloode. As expected, increased forward scattering en-ances atmospheric blurring near the reflectanceoundaries. The influence of the aerosol model onlurring is shown in Fig. 10 with variations of theefractive index for y 5 4 with m 5 1.33 and m 5 1.44.lso, for m 5 1.55 we varied y: y 5 3.5, 4.5. Ha waslways 2 km. The effect of the aerosol model on F~R!
was quite small.Using the continental model, y 5 4, m 5 1.55, we
then studied the influence on blurring of the aerosolvertical distribution ~Fig. 11!, with Ha 5 1, 2, 4 km.As a matter of fact, we identify the dominant pa-rameter for the adjacency effects. As the verticaldistribution is not accessible from space, this pa-rameter will be the principal source of uncertaintyin an eventual correction of the environmentalproperties. The results in Table 4 list values ofDr* according to Eq. ~8!, and ^r& is computed in
ppendix A. The first three cases in Table 4 cor-espond to different aerosol models; the choice oferosol model has a quite small effect on the results.or cases d and e we have illustrated the strong
nfluence of the aerosol vertical distribution with Ha
68 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000
varying from 1 to 4 km: The higher the aerosol,the stronger the adjacency effects.
B. Reduction of Fresnel Reflection
Table 5 presents the influence of the land mask on theFresnel reflection. The reported results, accordingto Eq. ~27!, correspond to the difference between re-
ectance computed over an open ocean and over aoastal area. The geometric and atmospheric condi-ions are those from Table 1. The principal plane iserpendicular to the coast, and the Sun is over land.hese geometric conditions roughly correspond toorning summer observations of a west coast at mid-orth latitude. When these two geometric effectsre combined, the removal of the Fresnel reflection isaximum. The vertical distribution follows an ex-
onential law with vertical scale heights of 2 km forhe aerosols and 8 km for the molecules. At theoastline ~d 5 0 km!, we simply cancel this direct-to-
diffuse term. At 865 nm we have mainly aerosolscattering. Always for d 5 0 km, for a given atmo-spheric turbidity, DrR does not depend much on thesolar angle: The increase of the viewing air massand of the reflection coefficient with us is counterbal-
Table 4. Contribution at 865 nm of Land to the Oceanic Signal forPoints at Distance d from the Coasta
aThe solar angle is 30° for a visibility of 23 km. For ~a!–~c!, slopen is 4, Ha 5 2 km, and values of the refractive index are, respec-ively, 1.55, 1.44, and 1.33. For ~d! and ~e! we have the case a
aerosol model but with Ha equal to d, 1 km and e, 4 km.
Fig. 10. Influence of the aerosol model on F~R!. The verticaldistribution corresponds to Ha 5 2 km with Junge size distribution
2v and refractive index m.
Fig. 11. Influence on F~R! of the vertical distribution with Ha 51, 2, 4 km for n~r! 5 r2v and m 5 1.55.
sms
stttitTbssot
Table 5. Reduction of the Fresnel Reflection ~in percent! According to Eq. ~28! versus Distance D from the Coast for Three Wavelengths,
to Eq
anced by the decrease of the phase function in theforward direction. Farther from the coast, thesharper decrease for us 5 30° corresponds to the di-rect effect of the geometry on zmax. In the blue, wefirst increase the aerosol contribution but then addmostly Rayleigh scattering. The spatial range ofthis effect is quite high, mainly for larger solar anglesfor which the Fresnel reflection is high. We alsoreport ~Table 6! the influence of the aerosol verticalcale height. When the aerosols are lower, the landask is less effective, but again the aerosol vertical
cale height is a dominant parameter.Although the adjacency effect that results from
ea–land contrast has been reported numerous times,he reduction caused by the presence of the land ofhe Fresnel reflection in the coupling term betweenhe atmosphere and the surface has generally beengnored, even if the effect is much greater than that ofhe radiometric noise of the measuring instrument.he partial removal of the Fresnel reflection causedy the land reduces the adjacency effects for sea ob-ervations, as reported in Table 5. Of course, asoon as the Sun is parallel to the coast or over thecean, there is full Fresnel reflection. We conductedhese computations for a mirror reflection. A more-
aThe Sun is over the land, and computations correspond to a vi
sophisticated study, involving a wave slope distribu-tion model, is not required, as we are outside thesun-glint spot. As the coupling term between reflec-tion and scattering does not depend much on windspeed, we did not take it into account. We did notinclude in this study land observations or the addi-tional contribution to the adjacency effect made bypartial Fresnel reflection, but a quite simple similarstudy can be conducted with Eq. ~28!.
C. Influence of the Viewing Angle
We used the ocean–land case to study the influence ofthe viewing angle, and Appendix A gives an analyt-ical formulation of ^r& for this particular case. Thegeometric conditions are illustrated in Fig. 12. Fig-ure 13 displays ^rR& versus the distance to the coast,always with a sea–land reflectance contrast of 0–0.3.For two symmetric values of uv we have a symmetryfrom the point r 5 0, ^r& 5 0.15. For w 5 90, the viewplane is parallel to the coast: For uv 5 0°, 30°, 60°the phase function has a small influence on the mod-el: rR decreases when uv increases, which leads to agreater influence of the environment. Figure 14 isidentical to Fig. 13, except that we replaced the Ray-leigh phase function by 1 to generate isotropic condi-
ty of 23 km and three aerosol scale heights, 1, 2, and 4 km.
and
!
0°
.12
.59
.23
.40
.78
.33
.33
.43
.67
cases
and
!
0°
.20
.64
.25
.40
.78
.33
.51
.86
.37
sibili
20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 369
s
cssl
0
3
tions. The two plots are similar, and the isotropicapproximation can be used for the Rayleigh case.
To simplify even more, we replaced the molecularatmosphere with a simple isotropic layer concen-trated at an altitude zc. Figure 15 shows that theF~R! function is well retrieved for zc 5 4 km. It thenseems possible to replace the actual molecular atmo-sphere with a simple isotropic layer at 4-km height.We reduced Eq. ~A4! of Appendix A to
^r& 5 *0
1
r~0!~m!dm, (29)
imply because p~0!~mv, m! 5 1 and p~sÞ0! 5 0.The dependence on geometric conditions is simply
given by Eq. ~10! through the position of Oz. Com-putations that use Eq. ~A4! of Appendix A dependonly on the location of Oz to compute r~m!. In prin-iple, it is a nadir view computation. Figure 16hows ^rR& computed for our sea–land system. Thechematic representation of a unique isotropic layerocated at Zc leads to results similar to those shown in
Fig. 13.Figure 17 presents ^ra& for the continental aerosol
Fig. 12. Viewing angles for off-nadir observations.
Fig. 13. ^rR& for the ocean–land system at 865 nm versus distancer at the coast. Solid curve, the nadir view. The scan plane isperpendicular to the coast, with uv 5 30°, 60°. The mean value of.15 is reached over the sea if the satellite is over land.
70 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000
model and Ha 5 2 km. The geometric conditions arethose of Fig. 13 for Rayleigh scattering. As the aero-sols are lower in altitude than the molecules, theeffect on the model of the viewing angle is less im-portant than for Rayleigh scattering. But a simplemodel of the aerosol adjacency effects based on equiv-alence with a unique isotropic layer is not relevantbecause of the strong anisotropy of the aerosol phasefunction.
Figure 18 shows Dr over ocean for us 5 30° and avisibility of 23 km for our ocean–land system at 865nm. The choice of viewing angle is crucial, with astrong contribution to the model made by the landportion when uv increases.
4. Consequences for Satellite Data Interpretation
Because the atmospheric contribution to the TOAsignal is quite high for observations over water sur-faces and because the contrast between land and sea
Fig. 14. Same as Fig. 13 but for isotropic scattering.
Fig. 15. For nadir observations, F~R! is computed for a molecularatmosphere and for an isotropic layer located at z 5 4 km.
T22gad
2
is generally important, the adjacency effect may in-troduce large biases in the interpretation of oceancolor data in coastal waters. To illustrate this point,we follow a quite traditional scheme to interpretspace measurements over the open ocean. First,aerosol remote sensing is performed in the red andnear-infrared bands, for which water reflectances arenegligible. Second, we use this aerosol model tomake the atmospheric correction in the visible bands.Third, we use a blueygreen-ratio technique to deter-mine the chlorophyll content of the water.
A. Aerosol Remote Sensing
Aerosol remote sensing is based on the darkness ofthe water in the red ~670 nm! and the infrared ~865nm!. Under this assumption, the retrieval of aerosolvalues is based, first, on an aerosol model identifica-tion from the spectral dependence of the aerosol path
Fig. 16. Same as Fig. 13 but for a unique isotropic layer locatedat z 5 4 km.
Fig. 17. Same as Fig. 13 but for the continental aerosol with Ha 5km.
reflectance ra and, second, on the restitution of thesignal at 865 nm looping on the aerosol optical thick-ness da. Generally, Shettle–Fenn9 models are used.Here we have selected a power law n~r! 5 r2v for thesize distribution and a refractive index of m 5 1.44without absorption. We used only this model, as asimple model10 of the signal for atmospheric correc-tions over land has been developed. Even if thischoice is quite arbitrary, in what follows, we are con-cerned more with biases that are due to adjacencyeffects rather than with absolute values, whichmakes this choice not so critical. In practice, wecomputed the TOA reflectance, always using the con-ditions of Table 1 and adding the adjacency effectscomputed with the 5S model.
To emphasize the adjacency effects, we ignored thepossible reduction of the adjacency effects caused byoccultation of the Fresnel reflection. The contrastbetween land and ocean always corresponds to 0.3–0at 865 nm and to 0.08–0.01 at 670 nm. The inver-sion of the TOA signal at 670 and 865 nm is quitestraightforward. First we loop on the slope n of thepower law with an angstrom coefficient a in the21.5–0 range. A second loop on da allows us to re-trieve the signal in the two bands. The selectedaerosol model provides consistency between the the-oretical value of a 5 2n 1 3 and a, which correspondsto the spectral variation of the two retrievals at 670and 865 nm. Figure 19 shows a for the invertedaerosol model versus distance to the coastline d.
he simulations were performed for n 5 4 and at d 50 km; we correctly retrieved the expected value a 51. As the contrast between land and ocean is
reater at 865 than at 670 nm, the adjacency effectsre greater at 865 nm, which leads us to overestimatea more substantially at 865 than at 670 nm, as
shown in Fig. 20. As a result, spectral dependencedecreases when we get closer to the coast. The val-ues of da retrieved at 865 nm are plotted in Fig. 20,
Fig. 18. Additional reflectance owing to the adjacency effect at865 nm for the conditions of Fig. 13.
20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 371
4
c
focwvoaav
atat
fldotacewBc
twa1Tet
~
3
and they directly illustrate the increasing adjacencyeffect when we get closer to land.
As we saw in Subsection 3.A, the vertical distribu-tion of aerosols is a key property for the adjacencyeffect. According to Table 4, at aerosol scale heightsof 2–4 km, to retrieve the same level of additionalsignal caused by the adjacency effect we go from dis-tances to the coastline of 2 to 4 km ~Dr 5 0.38! and of
to 8 km ~Dr 5 0.19!, respectively.It is beyond the scope of this paper to propose a
orrection scheme to remove the adjacency effect
Fig. 19. Comparison of retrieval of angstrom coefficient values for30 cases contaminated by ~With! or not contaminated by ~Without!he Rayleigh adjacency effect. Thirty cases were defined forhich there were three visibilities, 50, 23, and 8 km; two solarngles, 30° and 60°; and give distances from the coastline, 1, 2, 5,0, and 20 km. The first six cases in the order described inable 1, correspond to a distance from the coast of 1 km. Thenach set of six points corresponds to an increasing distance fromhe coast.
Fig. 20. Comparison of retrieval of optical thickness values at 865nm for the 30 cases of contamination ~With! or no contaminationWithout! by the Rayleigh adjacency effect.
72 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000
rom the model for retrieval of aerosol values. Basedn the spatial homogeneity of the aerosol, at least wean say that when the angstrom coefficient is stable,e can derive the aerosol model and that the spatialariation of a from the coast may provide informationn the aerosol’s vertical distribution. Then we canpply a correction for the adjacency effects, but suchcorrection is time-consuming, mainly for off-nadir
iews, for which a simple formulation of F~R! is notavailable.
B. Retrieval of Values of the Chlorophyll Content
We consider case 1 waters with in-water reflectance,as given by Morel.11 This marine reflectance wasconverted into a water-leaving reflectance that wasassumed to be isotropic. In a forward mode we com-puted the TOA signal under the conditions of Table 1,to retrieve the values of chlorophyll content in therange of 0–15 mg per liter of water, and we addeddjacency effects as computed versus d, the distanceo the coast. In the backward mode, we used theerosol model obtained in Subsection 4.A. The re-rieved a defined the slope of the power law and da at
440 and 550 nm. We could then derive rw at 440 and550 nm after atmospheric corrections. The blueygreen-ratio technique was then applied to yield thechlorophyll content, as illustrated in Fig. 21 for ob-servations at 10 km from the coast. The solid curveshows the blue–green ratio in terms of abundance ofchlorophyll ~Chla!. The points correspond to the in-
uence of adjacency effects. The adjacency effectso not strongly influence the retrieval of the aerosolptical thickness values at 865 nm but mostly affecthe spectral dependence. According to Fig. 20, event 10 km, a variation of 0.1 in the Ångstrom coeffi-ient implies an error of approximately 10% in thestimate of the aerosol’s reflectance in the blue, tohich we need to add the Rayleigh contribution.ecause the water-leaving reflectance strongly de-reases in the blue when the amount of chlorophyll
Fig. 21. Blueygreen ratio versus chlorophyll content, reference,and contaminated ratio ~two solar angles and three visibilities! fora distance to the shore d of 10 km.
a
increases, the error in the aerosol correction morestrongly affects the blueygreen ratio for high chloro-phyll content. Moreover, the blueygreen ratio is nothighly sensitive to high concentrations of chlorophyll.
In Fig. 22 we show the results of the retrieval ofchlorophyll values: We observed poor performanceat 10 km. Even at a distance of 20 km from the coastthe measurement of chlorophyll content is not com-pletely satisfactory when the atmospheric turbidity ishigh and there is a high chlorophyll concentration, towhich the sensitivity of the blueygreen ratio algo-rithm is poor.
C. Correction of the Rayleigh Scattering
As explained above, the influence of Rayleigh scat-tering on the adjacency effect has been well modeled.
So we can easily account for the adjacency effects thatare due to the molecules and subtract them from theTOA radiance. From a practical point of view, we donot include contribution to the adjacency effects bymolecules in the computation of the signal. Themethodology explained in Subsection 4.B is applied.According to Figs. 19 and 20, the improvements in themodel for retrieval of aerosol values are weak simplybecause the major effect of the environment occurs atl 5 865 nm, for which the contrast between land andsea is large. But at this wavelength the Rayleighcontribution to the adjacency effect is quite negligi-ble. Conversely, the effects of the Rayleigh correc-tion are large for values, retrieval of chlorophyll asshown in Fig. 23. In the blue-green band the Ray-leigh contribution is high, and correcting for the ad-jacency effects that are due to Rayleigh scattering isexpected to result in substantial improvement. It issubstantial at 20 km but, even at 10 km, the influenceof the aerosols remains substantial enough to cancelthe benefit of a Rayleigh correction.
5. Conclusions and Recommendations
We have used the 5S code to compute the adjacencyeffects that appear to be beyond the radiometric sen-sitivity of the measuring instrument. Quite simplemodifications of the 5S formulation allowed us tostudy the typical situation of coastal zone observa-tions. To conduct extensive studies of the adjacencyeffects we used the primary scattering approximationafter a first validation by comparison of it with the 5Scode. Also, we took into account the reduction byland of the Fresnel reflection. A sensitivity study ofthe aerosol model showed that the abundance of aero-sols is the key parameter: If the aerosol verticaldistribution departs from standard values, which canbe the case for high stratospheric aerosol contamina-tions, large inaccuracies appear in a possible correc-tion of the adjacency effects. The aerosol type is asecondary parameter.
Off-nadir observations were studied: When thesatellite is over land and viewing the ocean, a signif-icant number of photons, reflected by the land, arescattered forward toward the sensor. The correctionof the Rayleigh scattering is simplified because wecan simply replace the molecular atmosphere with a
Fig. 24. Observed pixel O viewed at ~uv, wv!. For the sublayer atltitude z the scattering element is in t. Oz is the orthogonal
projection of t. If O is at a distance d from the coast, Oz is at dz.The integration in azimuth is done on a circle of center Oz and ofradius rz.
Fig. 22. Retrieval of chlorophyll values for three distances to theshore d. The six points of each chlorophyll content correspond tothe two solar angles for each of the three visibilities.
Fig. 23. Retrieval of chlorophyll values for three distances to theshore d, not contaminated by the Rayleigh adjacency effect. Thesix points of each chlorophyll content correspond to the two solarangles for each of the three visibilities.
20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 373
2
i
O
I
3
thin isotropic atmospheric layer located at a suitablealtitude. Attempts to perform aerosol correctionpresented more challenges and further studies will berequired for accurate correction.
For a coastal zone, the adjacency effects impart asignificant bias to the model for retrieval of aerosolvalues because of the high contrast between land andocean in the near infrared. First, the aerosol’s opti-cal thickness is overestimated when a classic algo-rithm is used because of the increase of theatmospheric signal. Then the wavelength depen-dence is modified, leading to a bad extrapolation ofthe aerosol’s optical thickness in the blue-green re-gion where the ocean color algorithm applies. Thevariation of the aerosol’s optical thickness betweenthe near infrared and the red on a transect from thecoast can be a good indicator of contamination byadjacency effects of the aerosol product over land andan indicator of this effect on satellite imagery. Theinfluence of the adjacency effect on the retrieval ofvalues of chlorophyll concentration depends stronglyon the aerosol near the coast, and because this effectis strongly affected by the molecular scattering thespatial range is noticeable.
What do we recommend to include the adjacencyeffect in the ocean color algorithm? First, the cor-rection for aerosols seems to be numerically difficultchiefly for off-nadir views. Second, the introductionof aerosols needs to be made with knowledge of theirvertical distribution, which is the crucial parameter.Under these circumstances it seems difficult to rec-ommend an operational basis on which to introduce acorrection for aerosols. Simply, the product of theaerosols will give the depth into the coastal area towhich this contamination extends.
Modeling of the adjacency effects that are due tomolecular scattering can be more accurately andmore simply performed. A correction will then im-prove the retrieval of the value of chlorophyll content,extending the results at least toward the coastline.
Appendix A: Fourier Series Expansion of the SurfaceReflectance for a Land–Ocean System
For the ocean–land case with a straight coastline, firstwe integrate Eq. ~21! into w after expanding phasefunction p and reflectance r into a Fourier series:
P~mv, m, w! 5 (s50
S
~2 2 d0,s!P~s!~mv, m!cos~sw!, (A1)
r~m, w! 5 (r50
R
~2 2 d0,r!r~r!~m!cos~rw!. (A2)
The result of the integral in the azimuth implies thatr 5 s, and then we have
d2L 5 ~dty2mv!dm (s50
S
~2 2 d0,s!r~s!~m!P~s!~mv, m!. (A3)
74 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000
Then we integrate d L in dt and in dm. The normal-zation by the upward irradiance gives ^r& as
^r& 5
F(s50
S
~2 2 d0,s! *0
d
*0
1
r~s!~m!P~s!~mv, m!dmdtGF*
0
d
*0
1
P~0!~mv, m!dmdtG .
(A4)
observed pixel O is viewed under ~uv, wv!. For thesublayer at altitude z, the scattering element is in t.
z is the orthogonal projection of t. If O is at a dis-tance d from the coast, Oz is at dz 5 d 2 z tan uv cos wv.
The integration in the azimuth is done on a circle ofcenter Oz and of radius rz. By definition of a Fourierseries term, we have
r~s!~m! 5 ~1y2p! *0
2p
r~m, w!cos~sw!dw. (A5)
f Oz is in the sea, dz , 0. If, moreover, rz , dz, thefull circle is on the sea, with r~0! 5 rw and r~s! 5 0 ifs Þ 0.
If rz . dz, azimuth w1 gives the intersection of thecircle of radius rz as cos w1 5 dzyrz. We then have
r~0! 5 @rlw1 1 ~p 2 w1!rw#yp,
r~s! 5 ~rw 2 rl!sin~sw1!yps.
If Oz is on land, we need only to replace r1 with rw andvice versa.
This study was supported by the European SpaceAgency within the framework of the Medium Reso-lution Imaging Spectrometer ~MERIS! ground seg-ment development.
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