The objective of this research is to develop a 3-dimensional radiative transfer model for predicting the bidirectional reflectance distribution function (BRDF) for heterogeneous vegetation canopies. The model (named BIGAR) considers the angular distribution of leaves, leaf area index, the location and size of individual subcanopies such as widely spaced rows or trees, spectral and directional properties of leaves, multiple scattering, solar position and sky condition, and characteristics of the soil. The model relates canopy biophysical attributes to down-looking radiation measurements for nadir and off-nadir viewing angles. Therefore, inversion of this model, which is difficult but practical should provide surface biophysical pattern; a fundamental goal of remote sensing. Such a model also will help to evaluate atmospheric limitations to satellite remote sensing by providing a good surface boundary condition for many different kinds of canopies. Furthermore, this model can relate estimates of nadir reflectance, which is approximated by most satellites, to hemispherical reflectance, which is necessary in the energy budget of vegetated surfaces

Norman, J. M.

English

NASA Technical Reports Server

~' 
/ 
/ 
, I 
/' 
';/" . I. 
.'" ,/ I. i/.:/:I 
, I , 
/ '..-.-f-' ' 
/~ . 
I 
. /1" -- :, ", 
/! 
I 
I 
1 
, . 
, I I ,. 
.' 
i 
1-.: : / 
l. ./ 
'I , ). 
;. 
; 
; / 
, . ! I I , , I .- ! I 
" / 
.. ~ . ( 
N8 
-
BIDIRECTIONAL REFLECTANCE I'DDEUNG OF NON-Ha-IOGENEOUS PLANl' CANOPIES 
John M. Norman 
University of ~=braska 
Lincoln , NE 68583 
Objective 
i , 
37 
The objective of this research is to develop a 3-dimensional radiative 
tran~ fer model for predicting the bidirectional reflectance distribution 
function (BRDF) for heterogeneous vegetation canopies. The model (named 
ElGAr,) considers the angular distribu~ion of leaves, leaf area index, the 
location and size of individual subcanopies such as ~~dely spaced rows or 
trees, spectral and directional properties of leaves, multiple scattering, 
solar position and sky condition, and characteristics of the soil. The modeJ 
relates canopy biophysical attributes to d~-looking radiation measurements 
for nadir and off-nadir viewing angles . Therefore inversion of this model, 
Which i8 difficult but practical, should provide surface bio?hysical 
properti~s from radiation meas~rements for nearly any kino of vegetation 
pattern; a fundamental goal of r~te sensing. Su:h a model a!so will help to 
evaluate atmospheric limita tions to satellite remote sensir.g by proviJing a 
good surface bounda ry condition for many different kinds of canopies. Further 
this model can relate estimates of nadir reflectance, which is approximated b) 
nv:'st satellites, to hemispherif'?' !'ef1e,~:::-:r:c, -..-:-::d: £~ ::::::::: E:iT~' in the 
energy budget of vegetated surfaces. 
Techn ica l A~proact 
The approach to this research requ ires development of the mathematica l 
equations and computer coding of the heterogeneous-canopy model, better 
characterization of leaf anQ soil properties which are a ~eriou5 li~itat ion at 
'tl;e' 'p~I::'s ent 't~,' a'nd fi.'nally 'compari'son of modei predictions with field 
~asurement9 that are obtained from other im·estigato:-s. The Bidirectional 
General Array Model (BlGAR) is based on the concept that heterogeneous 
c~nopies can be described by a combina tion of many subcanopies, ~lich contai~ 
all the foliage, and these aubcanopy enve10pes can be characterized by 
ellipsoids of various sizes and shapes. Tne foliage within an ellipsoid may 
be randomly positioned or non-randoaly positioned. Estimates of multiple 
scattering are obta ined by transforming each point of interest in a particular 
ellipsoidal canopy to an equivalent one-dimensiona l canopy and solving the 
radiative transfer equations for this simple caSE. The B~F for individual 
leaves has been measured so that appropriate leaf properties can be used in 
the model. The BRDF for several soils has been measured and modeled with a 
simple block-modeling approach to provide a reasonable lower boundary 
co(,d i.tion for the canopy model. Ficlci measurements ot co::n and soybean ca:10IJY 
BRDFs are compared with model pred ictions. 
46 
.. I 
" 
y 
.' / , 
https://ntrs.nasa.gov/search.jsp?R=19860004327 2020-03-20T16:36:46+00:00Z
/ 
'# , (" \ 
\ ~ 'I. '. 
. ~: 
.' :' 
~. 
~ --. -
-: 
---------------------- ---------------------------------------------------~--.---
Research Results 
The results of this study are three fold: 1) A simple soil BRDF model 
tested with measurements, 2) laboratory measurements of leaf BRDFs for live 
corn and soybean plantA gr~ in the greenhouse and th~ field. and 3) the 
development and validation of B 3-dimensional canopy BRDF model of 
heterogeneous vegetation that combines soil, leaf, and canopy-architectural 
information. 
The 8imple 80il BRDF model approximates a soil aggregate by a single 
rectangular block placed on a fixed lot area with a fixed orientation relative 
to the sun azimuth. The relative reflectance factor in any view direction is 
computed fsam projections of block faces and the shadow of the block on the 
horizontal. Fig. 1 contains a comparison of model results with measurements 
in the solar waveband over a rough surface that was recently plowed from sod 
with furrows approximately 15 em deep. The RMS difference between the 
surfaces is 2.2% in reflectance. The simple-black-model predictions fit 
measurements from smooth (0.5-1 em gr~el ) and medium rough (2 to 5 em clods 
from multiple tillages) even better with 1% RMS differences in r.eflectance. 
Leaf BRJF L~esurements were m3de at 3 Hource incidence angles (20, 45, 
70) and about 50 view angles for intact co:~ and soybean leaves attached to 
their respective plants. The distribution visible and near-infrared, 
reflectance and transmittance factors is shown in Fig. 2 for a 45 degree 
suun.:e .i.!)ci~c"'-t: oHl!.le. The leaf hemispherical reflecr:ance, omich 1.S 
essential to all models of vegetation radiation exchange, was calculated from 
the integral of the BRDF (Table 1). Clearly nonnal incidence valves which 
currently are being use~ in other models may not be appropriate since mean 
leaf-sun angles for most canopies are be~en 45 and 60 degrees and not near 
normal incidence. 
. . .. ' . . .. .. . . 
The 3-dimensional bidirectional reflectance general array model (BlGAR) 
predictions h~ve been comQared to measurements on corn and soybeans that ~ere 
obtained from the LJboratory for Applications to Remote Sensing (LARS), 
Purdue, Unlversity, West Lafayette, Indiana as part of the AGRISTARS program. 
An example of how ellips.:>ids are used to represent a young corn canopy is 
shown in Fig 3 and a compar ison of measured and modeled results i s in Fig. 4. 
In general the model predictions agree very well with measurements considering 
that soil BRDF measurements cannot be made for the same site as the vegetation 
BRDF measurements. 
A simple 3-term emp irical equation has been derived to fit measured and 
modeled, soil and canopy BRDFs over a wide range of waveleng~hs. The RMS 
reflectance di ffe rence between the 3-term empirical equation and modeled or 
measured distributions (including view zenith angles from 0 to 60 de~"~e~) i~ 
about 0.2% in the visible and 2X in the near infrared for soybeans and several 
soils; a remarkably good fit. 
47 
! 
I .. 
. . , 
, .. 
\ 
Significance of ReFults 
Significant research results from this study impact on vegetation remote 
sensing in three ways : 1) relation of soil BRDF to roughness and sun angle, 2) 
interactions between soil BRDF and canopy reflectance properties that lead t o 
confounding the discrimination of sparse vegetation using angle-of-view 
observa tions, and 3) interpreta tion of leaf BRDF measurements to provide more 
suitable leaf spectral properties for model s of vegeta tion radiative transfer. 
The very simple block model , which has beem verified wi th field 
measurements, relates the soi l BRDF to roughness. Unfortunat~ iy the roughness 
is a relative roughness and thus not the t;a;:ne kind of " roubhness" used by soil 
physicists, Thus 8 disked field and a gravel lot can have similar relative 
roughne~ses (ratio of ; ize to spacing) and BRDFs but r epresent very different 
roughne~ses to the soil physicist. 
The RRDF of sparse vegetation is not as d ifferent from soil as is 
desirable for discrimination based on vi ew angle observations. However the 
structure of sparse canopies may be distinguishable from each other or soil 
backgrounds with zeni th view angels of 600 • Unfortunately this is not 
possible from satellites. In addition we now understand how a BRDF is 
differe.nt fOl· a E'Jil below a canopy than a soi l in the open even though th~ir 
physica l characteristics ar e i dent ical. Tn~ 3-term eID?irical equation fits 
soil and vegetation BRDFs 50 well t hat it may greatly simplify extraction of 
canopy properties hom off-nad ir obsi!rvationF for natural surfaces so that use 
oi s,-,!:;. ':ai." lUoy Gc.':':"1le practicel. Perhaps it may even reduce the tlu::-.~er 01 
off-nadir angles needed for obtainin& canopy properties frorr. satellite 
observations. 
During thi s Rtudy we have measured lea f BRDFs for corn and soybean; a 
rather f ormidahle task tha t few have attempted . From this work \o.>e ha'-'e 
lj!a!T\eq ~ha t .Illo<;\e 1.5 . bp!l~d -an. nOITlll!- l -.i.nc. idel1<;e. inte.g:~ t ing sphere leaf spec tr a 1 
properties, and to date nearly al l leaf spectra l property data is for normal 
i ncidence, are uping underestimates of leaf reflectance and overestimates of 
transoittance. Using the more appropriate leaf spectral properties may change 
canopy reflectance by 5 to 15% of the reflectance value. The improved 
estimates of leaf spe.: tral properties will also improve estimates of canopy 
wcter use and photosynthesis. In fact the reduced water use of an isogenic 
line of dcn~e pubescence (dense hairs) soybeans could only be explained by the 
leaf BRDF and not normal incidence integrating sphere measurements. 
Future Work 
Future research should emphasize the inve rs ion of 3-dimensional 
vege tation-soil bidirectional reflectance factor models and deve lop simpler 
inver s ion algorithms from exercising these complex models, Bo t h M'~.1I1 ar (vielJ 
direction) and wavelength information should be combined in the inversio~ 
process to extract t he maxUnum amount of infonnation; perhaps inverting the 
di stribution of normalized-difference with view angle may hold promise . The 
l ogical extens ion of this 3-D mode l is to include mor e compl ex canopoy 
architecture such as conifer t r ees , and also extend the wavelengLh band to the 
thermal. 
4tl 
\ . 
Table 1. Hemispherical reflectance and transmittance of corn and soybean 
calculated by integrating the r esults of leaf BRDF measurem~n t s. 
Incidence Visible IUR 
Crop Angle Refl (%) Trans (;.;) Refl (X) Tr ans (%) 
Corn 0 7.7 3.9 
20 9. 1 4.2 34.6 39.3 
45 9.3 3.4 33.0 :;:' .4 
70 14.2 3 . 9 45.2 45.0 
Soybean o 8.3 4 . 9 
20 9.3 4 . 3 41.7 30. 9 
45 9.6 3.7 44.9 33.2 
70 15 . 3 3 . 1 51.6 32.0 
' • • • ••• • , ' • ••• f • 
I 
!' 
. . 
r 
- -! . , ~ 
.' 
. . ' . ' .. . 
' J. 
/ I 
./ 
.' . 
(a) 
(b) 
Fif· 1. Soil BRDF predict ed from sir.plc moce~ (H cO.~. L=u.eS 
We O.1 , -0.67) and cea s ured for a rough pJ o~ d 50il 
\dt l. 15 cm furro\.' s and clods for a sol a r :o:cnith an!;le 
of (0) 63 0 one (b) 28 0 • The R."IS diff e r enc e Let\.' ce n 
measured B~ : ~ode 1Ld for <a) is 2 . 21 Bcd for (b) is 1.1% 
i n reflect an ce units. Ha xmum zenith vic\.' ar:gle is 600 
(oute r r~ ). center i6 n~ dir and Eun a zimuth 1s 0°. 
!>o 
--, 
,I( 
(a) (b) 
NIP SUN Z Ef'J=45 v' I~, IPLE ~,UN :?C~=-t:, 
50 YBERI'~ L::~;:-# I I SO Y B ~ M t-.J LEA F' # I 1 16~ 
\ 
\ , 
" " , 
.... 
] e0 
...... 
.. .... 
o 
REFLECTANCE TRANSMI TTA NCE REFLECTRN ':== TPA~6MI T TAr-JCE 
ec) Cd) 
Fig. 2. Leaf BRDF and bidirectiona l trensmi ttance distribution function 
at a source inc1d ~nce anble of 45 0 and az~ugh of 00 for (8) cern 
at ncar infr a red wavelengths, (b) corn at visible wavelengths, 
(c) soybean at near infrared wavelengthe. and (d) 60ybean at 
visible wavelengths. 51 
• 
J, 
I 
" 
~ 
, 
---
_., 
. ~ 
,;. ".~ 
I - •• _ 
O utline of ellip5e 
projGcted on horixontal 
from direct i~n of un 
' . . ... 
maxhr.um Idth 
I I 
\i- O.18m~ 
I 
I 
• I 
I 
I 
I 
I 
I 
I 
· I I 
· 
Fig. 3. Ske tch of a corn canopy ~ith LAl- 0 . 4 including the 
ellipsoids used t o approximate the canopy envelope . 
52 
- - ---_._-- - - - - -
0.21 rn 
I 1 
.----~~.:-.-. 9 
, 
I ,. 
I 
I 
I 
, 
" 
/' 
... ' .... 
-- ~ / 
I 
/ 
/ 
r 
.. ) 
'/" ) 
" , 
. ' , 
. . 
30 
w 
I 
.:;. 
E 
r-
'--' W 
-.J 
~ 
W 
U: 
./ 
'" 
CF\IGi~'~ ,'l.~ : : :. ~:~ : I:; 
OF POOR QUALITY 
(a) 
(b) 
/ 
./ 
". 
/ 
Fib' 4. Compariso~ of mea s urements and model predictiJns for a 
corn canopy of LAI '"' (j.l. having north-south rows. ( a ) 
sola r azimu th - 70 , solar zenith" 18 0 , (b) sola r aziII:u th" 
2760 , solar zenith" 4 7°. South is 0° . ~!ax1.wum .... ie:w 
zenith anble is 600 ( outer riI:J) and nadir vi e .. ' is at 
the center. 
53 
,I 
</ 
i 
, I 
1 
J 
i 
, 


Bidirectional Reflectance Modeling of Non-homogeneous Plant Canopies

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server