Among the tools used in passive remote sensing of Earth resources in the visible and near-infrared spectral regions are measurements of spectral signature and bidirectional reflectance functions (BDRFs). Determination of surface properties using these observables is complicated by a number of factors, including: (1) mixing of surface components, such as soil and vegetation, (2) multiple reflections of radiation due to complex geometry, such as in crop canopies, and (3) atmospheric effects. In order to bridge the diversity in these different approaches, there is a need for a fundamental physical understanding of the influence of the various effects and a quantiative measure of their relative importance. In particular, we consider scene complexity effects using the example of reflection by vegetative surfaces. The interaction of sunlight with a crop canopy and interpretation of the spectral and angular dependence of the emergent radiation is basically a multidimensional radiative transfer problem. The complex canopy geometry, underlying soil cover, and presence of diffuse as well as collimated illumination will modify the reflectance characteristics of the canopy relative to those of the individual elements

Diner, D. J.

Hessom, C.

Martonchik, J. V.

Sythe, W. D.

English

NASA Technical Reports Server

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Ar.10SPHERIC AND SCZ NE COMPLEXITY EFFECTS ON SURFAC~ BIDI~CTIONAL REFLECrANC!:. 
David J. Diner l (Principal Investigator ) 
John V. Martonchikl 
Willi am D. Smythe l ,2 
Charles He ssom2 
IJet Propulsion Labo ratory, Ca lifornia Institute of Technology 
2Universi~y of California at Los Angeles 
1. Justifica tion and Objectives 
Among the tools us ed in passive remo te sensing of Earth resources in the visi-
ble and near-infra r ed spectral regi ons are measurements of spectral signature and 
bidirectional ref1~ct ance fun c tions ( BDRFs ). Determination of surface pnperties 
using these obse rvables is complicated by a number of factors, including (a) mixing 
of surf ace components, such as soil and vege tat ion, (b) multiple re f lections of 
radiation due to complex geomet ry, such as in crop canopies, and (c) atmoapheri c 
effects . Dif feren ce s in surf ace conditions , spectral coverage, viewing a nd illumi-
nation geometry , and a t mos pher ic condit ions make compa rison of observations obtained 
in the laboratory, i n the field, and from a l rc:raft and spacecraft ext r eme ly diffi-
cult. In order to bridge the di vprsity in these different approaches, there is a 
need for a fund amen tal physical unders t anding of the influence of the various effects 
and a quantit a tive measure of their re l ative i mportance . In pa rticular , we consider 
scene complexi ty effects using t he example of reflection by vegetative surfaces. 
The interaction of sunlight wi th a crop canopy and interpretation of the spectral 
and angular dependence of the emergen t radi ation is basi cally a mu lt idimensiona ... 
r adiative trlns f er problem . In the first st?p of the r adiation his torv , s unlight 
is d~re ctly and diffusely t r ansmi cted downward t hrough the Earth's a t mosphere. The 
downward rad iation field then i nte racts wit h the plant canopy. Each element of the 
canopy (l~aves, stems) reflects (and transmits ) light according tc. its i ntrinsic 
bidi rec tional reflectance ( and transmittance ) properties. The complex canopy geo-
met ry , underly i ng soil cover , a nd presence of di ff use as well as collimated illumi-
natior. wi ll modify the reflecc a nce characteristics of the canopy relative to t hose 
of the individual elements. Finally , upwelling radiation eme r gent from the canopy 
will ~ directl:: and di,ffusely t r~n smittec;l 9)1. ~he atmosphere to sp~ce , . ,a~<,i ,some 
. cont atn.i:niit1:ot'!: of' the' spectr'al' si.g'nat~ re' ~it h rcidi ation re'flected from neighbor1.ng 
surface regi ons wi ll occur due to scat tering associated wit~ t he adjacency effect. 
The i nten t of this research program is to develop some of the tools needed in order 
to a chieve a quantita t ive unders tand ing of such phenomena , using d combination of 
expe rimental and theore tica l me thods . 
2. Technical Approach 
The tool s which are needed in order to study this radiative transfer problem 
include (a) knowled ge or t he bidirectional s cattering properties of ind ividual 
cano py element s, prima r ily leaves , as well as of the canopy as .1 whole, (b) 1 
model descri'Jillg the i n t~raction of radiation with the canopy, and (c ) a radi a tive 
::ransfe r a l gorithm for deGcrl.bing the int eract i on of a nonuniform :-adiation field 
· ... ith the .lt~osphe re. In or de r to obt.:lin realistic leaf ~idirectional reflectance 
functions for incorpo r a ti on in t o canopy and scene models , we are using labora tory 
s pect ro~oniometry to ~tudy :he intrinsic scat t ering proper ties of individua~ leaves . 
These ~easu rements provide a da t a set which obv i ates the need for nonphysical model 
assumptions. such as Lambertian leaf BDRFs. We have been using a goniometer located 
93 
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at the University of California, Los Angeles to obtain spectra of 
individual leaves 
for a variety of illumination anc viewing geometries . The instr
ument operates in 
the spectral range 0.4 to 2.5 :.1m. The illuminating source may 
be placed at an 
inclination of a to 90 0 relative to che surface normal and essentially th
e entire 
range of emission a nd azimuth angles may be measured, including ne
ar-zero, grazing, 
and high phase angles . An important attribute is the ability ob
tain data out of 
the principa l plane of scattering. The leaf BORFs obtained in th
is manner wil l be 
made available t o other researchers for incorporation into cano
py models. With 
regard to atmospheric effe cts, including extinction (absorption and scattering
); 
addition of path radiance; mUltiple reflect ions between atmospher
e and ground; and 
adjacency effects ( whereby radiation refle cted from surface regions not in the 
field of view are s cattered into the line of sight), we have been developing compr
e-
hensive computational tools f or solving multidimer:sional radiativ
e transfer prob-
lems . Our t e chnique incorpora tes a two dimensional spatial Fou
rier transform of 
the radiative transfer equation , and the resulting expressions 
for each Fourier 
component of the radiation field are computed. The full 3-D in
tensity field is 
then re constructed using the inverse Fourier transfona. The math
ematica l descrip-
tion is of general form so as to include considera tion of non-L
ambertia n BDRI<'s . 
Our t echnique has been specifically designed to overcome s ome of t
he approximations 
employed in previous methods and h a s bee n implemente d on a minicomp
uter . The me thod 
is nearly a s general as Monte Carlo but has the advantage of provid
ing determinis t ic 
solutions for the upwelling and downwe lling radi a tions fields at
 many altitudes, 
zenith a~gles, and azimuths from a single computer run. 
3. Research Re sults 
Experimental data ha ve been acquired using the UCLA goniometer 
on c amellia, 
cucL.mber, and ca uliflower le aves. In order to 1I0nitor the effect of
 using cut lea·,es 
versus leaves still attached to t he pla nt, the reflectance of a 
cucumber leaf was 
monitored Eo r several hours f~llowing cl ipping. Reflectivity at 0.98 ~m 
i ncreased 
duri ng t his period, indicating ;.Tater stress .md a decrease in the
 strength of the 
water band . To study spec:::al jependence of l eaf BDRF, we obtained spectra of a 
camel : ia le a f at view angles of 0 and 30 degr ees f or illumination
 at no rmal inci-
dence. The ratio of these spectra in the 0.4 - 0.9 ~m region is displayed
 i n Fig. 
L The incre ased no ise level at the short ·oIavelength end is due 
to low(:r detec tor 
. response. and .decreased . 60uI;"ca .l . .:\.g.h.t .. ley~ l,s .•. This plo t shows that the leaf BDRF 
devi a tes markedly from :"ambertian behaVior in ·a· spectrally depend
ent fashic>n~ The 
great es t departure from Lamber :ian reflect a nce is observed in the
 0. 68 ~m chloro-
phyll absorpt ion fe a ture , possibly as a r esult of a decrease i
n the amount of 
mult:ple scatte ring ~ithin t~e lea f. 
As an example of the suc ':ess .:- f our multid i mensional radiative t r
ansfer algo-
rithm, we c onsider :!-:e a l bedo ste? function problem, in which t
wo semi-infinite 
fi e l ds of differi ng a l bedo are adjacen t to ~ne another. This model is useful in 
tha t it provides ( a) an evalua::ion of :he dif fusion of radiation across the sha
rp 
albedo boundary separating t~e ~ wo r eg i ons , a nd (b) ~he ability to verify that ~
he 
solution asymptotica lly ap pr ?ac~es the corr~ct result for a homoge n
eous surface at 
large dis tances from the boundary . This sur fa c e mo de l lIay be con
sidered to repre-
~e nt 1 coastal ::'oundary, In whi c h 1 : ·Irge expanse of low llbedo 
water borders a 
broa d l a nd a r e a of hi g he r ref l ectivi t y . We compar e result .; ob
taine d using the 
?ou::i~r tran s fo r m method wi t h ~on t e Ca rlo re su l ts for an atmospher
ic model consi s t-
ing of 1 ~lear ~tmosphe r~ wit h a sca.e height of 8 km and an optica l ~ep
th of 0.189 , 
corr l!sponding to Ray:ei~h .;ca tt e r i:lg a t 0.47 ~m. The t -0I0 half-planes
 a re Lambertian 
with a l be dos of 0 .0 anJ 0.6, a nd the 301ar zenith ang le i s 40
0 • This se·t of condi-
94 
t i.ons is referred t o as Modell. Figure 2 shows the results of ,' alculations for 
Model 1 using t he Fou rie r transform techni que, along with selec ted points from the 
Monte Carlo results. The to tal upwelling intensities are shown as the sum of the 
diffuse (multiply scattered ) radiation field and che direct field, which con~ists 
of pt.otons transmitted to space without being scattered. The agreement between 
the two methods appears to be excellent. We also show at large distances from the 
boundary the intensities calculated using the one-dimensional matrix operator 
method for uniform albedos of 0 .0 and 0.6, demonstrating that the Fourier transform 
results approach the expected "alues away froll the boundary. In the "icinity of 
the boundary , the adjacency effect is apparent. Due t o scattering within the atmo-
sphere, the upwelling intensities on either side of boundary are affected by photons 
reflected from the surface on the opposite side of the boundary and then scattered 
into the line of sight. In effect, the atmosphere "blurs" the boundary with a point 
spread function whose width is a few kilometers. The Fourier transform technique 
is useful in that its underlying mathematical formalism demonstrates how the atmo-
sphere filterR high spatial frequency information from the upwelling radiation 
field. This filtering can be described by the computa tion of atmospheric mod~lat!on 
transfer functions (MTFs ). Figure 3 is a comparison of HTFs calculated using our 
technique for a Rayleigh a tmosphere and an aerosol laden (hazy ) atmosphere, each 
of total optical depth 0.3 and 5 km scale height. These HTFs indicate that the 
more highly forward scattering haze phase function results in a greater observabil-
ity of the adjacency effect. 
Another area in which the 3-D radiati"e transfer algorithm is proving useful 
is in the development of a technique f or determining atmospheric transmittance 
from surface images acquired at off-nadir view angles. The basis of the ~eth~d is 
as follows: As shown in Fig. 2, the total upwelling radiance is the sum of a direct 
and diffuse component. Radiation directly transmi tted to space is ?roportional to 
the surface albedo distribution, and a sharp discontinuity in the surface albedo 
gives rise to a similar discontinuity in the di rect field. The diffuse fi eld , on 
t he other hand , whi l e exhibiting a qualitative similarity to large scale veriations 
in surface albedo, exhibits a much s~oother character, owing to :he filtering effects 
of the atmosphere, as discussed above. The direct field, which is also proportional 
to atmospheric transmittance exp(-T/Il), where T is the optical depth and Il is the 
cosine of the view angle, thus has a very different spatial character from the 
diffuse field. If we compu te the spatial Fourier transform of upwell ing radiances 
within an image, the spa tial "smoothness" of the diffuse field means that it will 
,make·a, .negligible ,con.tri.buti6n'at, hi gh spatial frequencies. ThuE, if we ~11m1nate 
iow frequency Fourier components we are left with a measurement that is directly 
proportional to the atmospheric transmiss ion factor exp(-T/Il). By obtaining images 
of the same surface region at several view angles . it should in principle be possible 
to solve for T, provided non-Lambertian surface effects can be mi nimizea. Our cal-
culations suggest that acquisit ion of images in the vicinity of 60 0 off-nadi r should 
be sufficient to accomplish this and recover atmospheric transmit tance with an accu-
racy of 5-:'0%. 
4. Signific3nce of Results and Future Directions 
~any investiga tors have studied the spectral properties of a ~ide variety of 
crop samples. The spectral refl~ctance of the foliage is modified by changes in 
the internal structure of the l eaves ass oci ated with various forms of stress , such 
as water or mineral stress. The specularity of the re flected radiation increases 
at wavelengths where increased absorption occurs, presumab ly due to reduced depth 
of penetra tion of the incident radiation into the leat resulting in fever multiple 
/ 
ref lect-ions be tween layers. Therefore, we expect changes in leaf structure regul t-
ing from stress to affect the angul~r as well as spectrdi reflectQnce properties. 
Thus, it is important to incorporate realistic (non-LambertLan) leaf bidirectional 
reflect ance functions into canopy and scene models . The syectrogoniometric leaf 
measurements will provide such data. 
The Fourier transf orm radiat ive transfer algorithm which we have de'/eloped is 
a useful tool for studying the effect of the atmosphere on high spatial resolution 
imaging of the Earth's surface. As discussed above, the sharpness of the adjacency 
effect in the vicinity of albedo boundaries is dependent upon the vertical distribu-
tion of the atmospheric scatterers. We are using our radi;!tive transfer method to 
perform a systematic study of the variation of atmosph~ric point spread functions 
with aeros ol ve rtica l distribution, phase function , S11l1i'e scattering albedo, and 
optical thickness. The results of such calculations will permit evaluation of the 
possibility of observing atmospheric blur dil:ectly in high resolution images of 
the Earth's surface, with the goal of determining aerosol properties. Conversely, 
these calcuilations will lead to techniques for removing spectral contamination 
associated with the adjacency effect. 
Further work is necessary in order to demonstrate the feasibility of implement-
ing the multiple view dngle optica l depth retrieval techni~ue on a space platform. 
The major uncertainty at present is the manner in which the unknown angular reflec-
tance properties of the surface should be taken into account. For the model SORF we 
used in our simulations, off-nadir imaging near 600 appears appropria:e to compe~sate 
for lack of ~ priori knowledge of the shape of the surface BORF. Whether this range 
is appropriate for natural surfaces can onl, be dete~ned by experimentation in the 
field. A number of portable field spectrometers are available for obtaining BORP 
measurements. The success of this te chnique would be signific~nt because it provides 
a ~eans of monitoring tropospheric opacity, which is important not only for a t~o­
spheric studies but also because it is one of the mos t important parameters govern-
ing the effect of the atmosphere on surface images. An extenaivn of the optical 
depth .etrieval technique is ';0 near infrared ;;pectral regions where water vapor 
absorp tion occurs. I~ its current form, the technique relies on the assumption that 
atmospher i c transmittance variesias exp(-T / U) . In the water vapor bands, any finite 
bandwidth spectral channel will inco rporate many individual lines and this law may 
not be followed. In order ,to study the view angle dependence of t ransmittance in 
such' reg io'ns, ' we' 'are' de'veiopirig a' r'adiati"e ': rans'f'er al~:>r::' :;~m which, permi ts' cal:cu-
lation of broadband radi~nces for channe ls containing ~any absorption lines in the 
presence of aerosol scattering. 
Finally, we plan to investigate the applicability of our 3-D radiative trans-
fer method to scattering in plant canopies . In principle, our algorithm Is appli-
cable to heterogeneous media and has the advantage of providing a true solution 
to the multidimensional radiative transfer equation. In addition, solutions are 
obtained at onany view and illumination angles and azimuths, thus providing the 
full canopy BORF. Variation of the BDRF of the individual :eaves will permit 
study of the effect of changing reflectanc::! ;Jroperties of the individual canopy 
aleme nts on the canopy angular and spectral reflectance ~s a whole. Such calcula-
tions will mesh nicely with the goals of the experimental ?ortion of this investi-
gation. 
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Atmospheric and Science Complexity Effects on Surface Bidirectional Reflectance

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