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Leaf area estimates from measurements of photosynthetically active radiation in wheat canopies
Agricultural and Forest Meteorology, 32 (1984) 13--22 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
13
L E A F A R E A E S T I M A T E S F R O M M E A S U R E M E N T S OF PHOTOSYNTHETICALLY ACTIVE RADIATION IN WHEAT CANOPIES*
M. FUCHS**, G. ASRAR and E.T. KANEMASU
Evapotranspiration Laboratory, Kansas State University, Manhattan, KS 66506 (U.S.A.) L.E. HIPPS
Utah State University, Logan, UT (U.S.A.) (Received June 6, 1983; revision accepted December 19, 1983)
ABSTRACT Fuchs, M., Asrar, G., Kanemasu, E.T. and Hipps, L.E., 1984. Leaf area estimates from measurements of photosynthetically active radiation in wheat canopies. Agric. For. Meteorol., 32: 13--22. Transmission of photosynthetically active radiation (PAR) measured with quantum sensors in three wheat cultivars during periods of clear sky were used to indirectly determine the leaf area index (LAI). The exponential description of direct and diffuse radiation penetration, which depends on leaf inclination, was correlated to the transmission measurements at various solar zenith angles. The highest correlations were found for fixed leaf inclinations of 60 and 75 °, and for the spherical leaf angle distribution. Angular shape coefficients corresponding to these leaf inclinations were then used to solve the exponential equation for LAI taking incoming PAR to be direct. This was shown to be an acceptable approximation when the proportion of direct radiation in the incoming PAR was higher than 0.85. Predictions of LAI were found to be within 0.7 units for a range of LAI from 1.5 to 5.0. A statistical analysis of the results indicated that the most suitable leaf inclination was a combination of 60 and 75 ° fixed angles, and spherical distribution.
INTRODUCTION Some crop growth models require information on factors influencing the size a n d p r o d u c t i o n r a t e o f t h e p h o t o s y n t h e t i c a p p a r a t u s . F o r a g i v e n c r o p , this i n f o r m a t i o n c a n b e d e r i v e d f r o m t h e l e a f a r e a i n d e x a n d t h e i n c l i n a t i o n a n g l e d i s t r i b u t i o n o f t h e leaves ( R o s s , 1 9 8 1 ) , w h i c h d e t e r m i n e t h e l i g h t d i s t r i b u t i o n w i t h i n t h e p l a n t c a n o p y a n d its a b s o r p t i o n b y t h e f o l i a g e . F o r this a p p r o a c h , the spatial d i s t r i b u t i o n of foliage e l e m e n t s n e e d s to be k n o w n . I n d e n s e l y p l a n t e d c r o p s , like w h e a t , w i t h o u t a v i s i b l e r o w s t r u c t u r e , it c a n
* Contribution No. 83-237-J from EvapotranspirationLaboratory, Agronomy Department, Kansas State University, Manhattan, KS 66506, U.S.A. ** On sabbatical leave from the Division of Agricultural Meteorology, Agric. Res. Org., Volcani Center, Bet Dagan, Israel.
0168-1923/84/$03.00
© 1984 Elsevier Science Publishers B.V.
14 be assumed that the horizontal distribution of foliage elements is uniform. For most plants the orientation of leaves is nearly random, and the effects of preferential azimuthal distribution have been shown to be small (Lemeur, 1973). Accordingly, the penetration of unscattered light rays, r, can be given (Monsi and Saeki, 1953) as r = exp (--KL)
(1)
where L is the leaf area index cumulated from the top of the canopy to the level at which light penetration is considered, and K is an angular shape coefficient. The angular shape coefficient, K, for uniform canopies of spherical leaf angle distribution is a single valued function of the zenith angle of the incident ray, 7, and is given by K = 0.5/cos77
(2)
For a fixed leaf inclination its value is K = cos 0
for
(zr/2 -- 0) ~> 77
K = c o s 0 [ 1 + (2/~)(tan co--co)]
for
(7r/2--0) ~ ~
(3)
where co -- arccos [cot 0 cot ~?]
(4)
and co/Tr is the fraction of the leaves with their backside in the direction of the light rays, and 0 is the leaf inclination measured from the horizontal plane. Equation 1 does n o t account for the light that is scattered by the elements of the foliage, and, therefore, does not provide an adequate description of the radiative transfer through a canopy. However, in the photosynthetically active region of the spectrum ( 4 0 0 - 7 0 0 n m ) , penetration and transmission are almost identical, due to the high absorption coefficient of the leaves. Therefore, transmission measurements of photosynthetically active radiation (PAR) can be used to verify the validity of penetration predictions by eq. 1 (Anderson, 1970). An important consequence of this validation is that it permits the use of these transmission data for an indirect eva]uation of the leaf inclination angle and the leaf area index.
MATERIALS AND METHODS A field experiment was conducted during the 1980--1981 growing season at the Evapotranspiration Research site near Manhattan, Kansas (39°09'N, 96°37'W, 3 0 5 m above M.S.L.). Photosynthetically active radiation (PAR) was measured above and below the canopy of two cultivars of winter wheat (Triticum aestivum L., 'Centurk' and 'Newton') planted at three seeding densities of 22.4, 44.8 and 67.2 k g h a -1 , referred to as low, medium and high density, respectively.
15 Four quantum sensors (LiCor model LI-190SB) wired in parallel were placed facing upward beneath the canopy to record the PAR reaching the soil surface. One sensor was m o u n t e d above the canopy to measure the incoming PAR. The sensors were connected to a data acquisition system (Hewlett-Packard 9820A) and their o u t p u t was recorded by a teletypewriter during daylight hours. Three 0.5-m sections of rows were harvested from the radiation measurement sites for leaf area determination by an optical planimeter (LiCor model LI-3100). Data presented in this report are from two cloudless days, early in the season (28 March and 30 March 1981) and a cloudless day later in the season (24 April 1981) when leaf area index values were about maximum. A second set of data collected on a spring wheat cultivar ( T r i t i c u m a e s t i v u m , L., 'Fieldwin') during two cloudless days (10 July and 26 July 1982) in Logan, Utah (41°45'N, 111°50'W, 1490 m above M.S.L.), also was used to test the relation between L and PAR. The sun zenith angles corresponding to each set of measured PAR values were c o m p u t e d from the time and date of acquisition of the data, based upon the equations used in Nautical Almanac (Walraven, 1978). Since the radiation measurements included direct sunlight and diffuse sky light, the ratio of direct to total p h o t o s y n t h e t i c radiation, q, was estimated based on the equations of atmospheric transmissivity compiled by List (1971) q = 2am~(1 + a m )
(5)
where m = (P/P0) sec 7, and a = exp (-- T), with m being the optical airmass number, a the atmospheric transmission coefficient and T the average scattering coefficient of the atmosphere for the PAR waveband. The ratio of atmospheric pressure at the observation site P, and the sea level P0, were used to correct for the effect of altitude on the atmospheric transmission coefficient. The scattering coefficient was empirically derived from T = - - l n [ 2 R t / ( R o cos ~1) -- 1] (P/Po) cos 7/
(6)
where Rt is the p h o t o s y n t h e t i c p h o t o n flux density above the canopy and R0 is the corresponding extraterrestrial p h o t o n flux density at normal incidence, c o m p u t e d from the solar spectrum data (Robinson, 1966). Diffuse sky radiation penetration, d, was c o m p u t e d as 2n
~r/2 I
d
(11~)
j-
j- fr sin 7? cos r~d~dq~
0
0
(7)
where ¢ is the azimuth angle between 0 and 27r, r is the penetration of a ray given by eq. 1, and f is the relative hemispherical radiance distribution of the clear sky (Robinson, 1966). The measured transmission, Tin, was taken as Tm = Rb/R t
(8)
16 where Rb is the average PAR measured beneath the wheat canopy. Since scattering of PAR by the canopy is assumed to be negligible, Tm is equivalent to the total penetration. For the same reason the theoretical value of total penetration, Tp, is given by Tp
= qr + ( 1 - - q ) d
(9)
Values of Tp were c o m p u t e d based on the measured leaf area index values for fixed leaf inclinations of 15, 30, 45, 60 and 75 ° and for spherical leaf angle distribution. Solar zenith angles were those corresponding to the time of the PAR measurements.
RESULTS AND DISCUSSION The ratios of the direct to total components (q) of photosynthetically active radiation (PAR) were c o m p u t e d from eqs. 5 and 6. Figure 1 depicts the predicted changes in q as a function of the sun zenith angle. Measurements of the direct and diffuse components of PAR were not available to independently verify the computations. However, the average PAR scattering coefficient of the atmosphere c o m p u t e d from eq. 6 was 0.110. This is close to the value of 0.127 derived by integrating the monochromatic Rayleigh scattering, weighted by the extraterrestrial p h o t o n flux distribution function over the frequency band corresponding to the PAR. Therefore, the q values c o m p u t e d from eq. 5 for clear sky conditions can be considered reliable. The estimated q values also follow a trend similar to the data for global radiation given by Paltridge and Platt (1976). The value of Tp in eq. 9 depends upon the ratio of direct to total p h o t o n flux density, q, the angular shape coefficient, K, and the leaf area index, L. However, only q and K are dependent on the zenith angle. Since the determination of q was standardized, the correlation between the distributions of Tm and Tp as a function of solar zenith angle for any given value of L depends upon the choice of K. Table I presents the correlation coefficients between the measured Tm and Tp values c o m p u t e d for K at fixed leaf inclinations of 15, 30, 45, 60 and 75 ° , and the spherical leaf angle distribution. Low frequency of PAR measurements and incomplete spatial sampling resulted in generally low correlation coefficients (Table I). They decrease systematically with increasing L. As gaps in the canopy become less frequent with increasing leaf area index, the measurements of PAR penetration require denser spatial sampling. Thus, larger sampling errors will occur at higher leaf area indices. Higher correlations are consistently f o u n d at fixed leaf inclinations steeper than 45 ° and with the spherical leaf angle distribution. Differences betweell 60 and 75 °, and spherical distribution are tenuous. Therefore, any of these leaf angle distributions can adequately characterize the wheat canopies.
17
0
0
0
o 0 [ ~.. 0
oo
O'3
c~c~ c~
c~ c~c~
c~ c~c~
c~ c~c~
c~ c~c~
c; c~c~
•,~ cO
L'~ 0.1
LQ cO oO
¢0 cO L~I
c~
c~
0
c~c;
d~d
ddd
0
cS c;c~
dNd
o 0
LQ ¢~1 CO
0
0
01 ~'xl cO
03 LO
O~ ¢xl O0 0
0 0 0
0 0
,-~ CO
0
0 0
0
CO LQ
0
O 0
oo 0
O 0
0
O 0
e~ ¢xl LQ ~.D
0 O0 O0 [~-
0
0
0
0
0
oo 0
0 0 0
0 0 0
¢ 0 C'~ O0 0 0 0
0 0 0
~COCO 0 0 0
~"xl Ol O0
0 0 0
0 0 0
0'~ oO 03
0
0
0
o3 0
0 0 0
~'~1 ¢ x 1 0 3 O 0
L~O00
r.r-I <
~0
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18
1.0 ,.~°s..o.oOo...
,.
•
"°'o,.
Q8
z
b 0.6
I-
04
Qc
0.2
U A N H A T T A N , KS MARCH 30, 1981
0.0 30
40
50 60 70 Z E N I T H ANGLE
80
Fig. 1. Relation b e t w e e n the sun zenith angle and fraction o f direct incident PAR.
The leaf area index can be computed from the PAR penetration data at known zenith angles with a proper choice of the angular shape coefficient from L = --(ln
r)/K
(10)
where In r is the arithmetic mean of the natural logarithm of the penetration, and K is the mean of the corresponding angular shape coefficients. Since the Tm values include both the direct and diffuse components, it is necessary to determine under what condition penetration of direct PAR (i.e., r) can be approximated by the total penetration, Tp. Figure 2 shows the relation between r and Tp vs. q for a fixed leaf inclination of 60 ° and L equal to 1.4 on 30 March 1981. The data indicate that for q ~ 0.85, direct and total penetration are essentially identical. Under this condition measured Tm values can be used to approximate r in eq. 10. This condition excludes data iO
08
MANHATTAN, KS MARCH 30, 1983
o o u.
o o
06
o e = 60 ° L A I = 14 o TOTAL DIRECT
02
0 I
0.2
03
04
05
PENETRATdON
Fig. 2. Direct and total P A R p e n e t r a t i o n as related to the fraction o f direct incident PAR for a wheat canopy.
19 TABLE II Linear regression parameters and correlation coefficients (R) for comparison between predicted and measured leaf area index (LAI) Leaf angle (o)
Intercept
Slope
R
SD a
Spher. 45 60 75
0.42 0.43 0.46 0.33
0.96 0.91 1.04 1.13
0.89 0.87 0.89 0.93
0.59 0.64 0.66 0.56
a Standard deviation on predicted LAI. c o l l e c t e d at large z e n i t h angles. F o r example, on clear days like 30 March 1981 (Fig. 1) t h e limiting z e n i t h angle is 70 ° . All o f t h e Tm values c o r r e s p o n d i n g to q ~ 0.85 f o r each d a y were used to estimate L f r o m eq. 10. T h e results were c o m p a r e d with the m e a s u r e m e n t s using linear regressions and c o r r e l a t i o n c o e f f i c i e n t s {Table II). All f o u r t e s t e d leaf angle distributions have statistically similar o f f s e t values. T h e slopes are close to o n e b u t are nevertheless significantly d i f f e r e n t ( P ~ 0.025). T h e highest c o r r e l a t i o n c o e f f i c i e n t and smallest s t a n d a r d deviation are o b t a i n e d with the 75 ° leaf inclination. H o w e v e r , the steep slope o f the line corresp o n d i n g to this leaf inclination causes increasingly larger o v e r e s t i m a t e s at high L values, as illustrated in the scatter diagram in Fig. 3. T h e scatter diagrams for the spherical and 60 ° leaf angles have slopes close to u n i t y (Figs. 4 and 5) and show a m o r e c o n s i s t e n t p r e d i c t i o n over the range o f t e s t e d L values. T h e L values f o r the t w o w i n t e r w h e a t cultivars are overe s t i m a t e d , b u t t h o s e f o r the spring w h e a t are u n d e r e s t i m a t e d . T h e reason for this disparity is n o t k n o w n . These results indicate t h a t the e s t i m a t e d L values have a s t a n d a r d d e v i a t i o n t h a t does n o t e x c e e d 0.7 units. T h e m e a s u r e d Tm values used in the c o m p u t a t i o n s o f L c o v e r a wide range o f solar z e n i t h angles f r o m 20 to 65 ° . Since t h e a c c u r a c y o f t h e measurem e n t s d e p e n d s on t h e m a g n i t u d e o f the i n c i d e n t flux, and t h e i r representativeness is a f u n c t i o n o f the spatial gap d i s t r i b u t i o n , Tm values f o r s o m e solar z e n i t h angles m a y be m o r e suitable t h a n o t h e r s in p r e d i c t i n g L. T h e e f f e c t o f solar z e n i t h angles was investigated b y stratifying t h e d a t a into f o u r z e n i t h angle classes o f 20--30, 30--40, 4 0 - - 5 0 and ~ 50 °. It should be n o t e d t h a t the n u m b e r o f d a t a p o i n t s used t o c o m p u t e t h e m e a n L f r o m eq. 10 f o r each class differs, since m o r e d a t a with q ~ 0.85 are f o u n d at smaller z e n i t h angles. L e a f area i n d e x values c o m p u t e d f o r each z e n i t h angle class and for leaf inclinations o f 45, 60 and 75 °, and the spherical d i s t r i b u t i o n were linearly regressed against the m e a s u r e m e n t s . T h e regressions were c o m p a r e d in a f o r w a r d stepwise statistical analysis. T h e solar z e n i t h angle appears t o have very little e f f e c t o n t h e p r e d i c t i o n o f L, b u t m o d i f i e s slightly the c h o i c e o f the m o s t a p p r o p r i a t e leaf angle d i s t r i b u t i o n {Table III).
20
e = 60 = • MANHATTAN, KS 1981 LOGAN,UT 1982
8.0
.:
c~ z -
5.0
"~
40
~ 30
N 2.O
I0
I0
2.0
&O
MEASURED
Comparison
Fig.
3.
leaf
inclination
of
4.0
LEAF
510
AREA
between
6.0
INDEX
computed
a n d m e a s u r e d values o f l e a f area i n d e x f o r a f i x e d
60 ° .
e = 75 ° 60
z
• MANHATTAN, KS 1981 • L O G A N , UT 1982
•
_~30i
-
2.0
I0
/
i
j/
/
J iO
•
~
50
,, 4 °
• |
i
=
=
20
30
40
MEASURED
LEAF
AREA
i
J
50
6.0
INDEX
F i g . 4 . Comparison between measured and computed values of leaf area index for a fixed leaf inclination of 7 5 ° .
The 75 ° leaf inclination provides the best statistical fit for the zenith angle class of 2 0 - - 3 0 ° and zenith angles ~ 50 °. However, when the forward stepwise analysis included the L values corresponding to the 60 ° leaf inclination, the error term of the linear regression decreased significantly for these two zenith angle classes. The 60 ° leaf inclination was the only one suitable for predicting L from the measured PAR values corresponding to 4 0 - - 5 0 ° zenith angles. The best correlation between measured and predicted L values for the 3 0 - - 4 0 ° zenith angles is given by the spherical leaf angle distribution (Table III). These results indicate that n o n e o f the fixed leaf inclinations consistently provide the best estimate of the angular shape coefficient for all of the solar
21 SPHERICAL 6.0
,x,
• MANHATTAN, KS 198[ I LOGAN, UT 1982
5.0
• •
l
/
/\"
~ 40 ~ 30
8
82.0
.
.y /
,
./
I0
0
"
3.0
MEASURED LEAF
4,0
AREA
5.0
6.0
INDEX
Fig. 5. Comparisonbetween measuredand computed valuesof leaf areaindex for spherical leaf angle distribution. TABLE III Correlation coefficients (R) for the linear models of measured vs. predicted LAI for different classes of leaf and solar zenith angles (the results are based on stepwise regression analysis of the combined data sets for the two experiment sites) Zenith angle (o)
Leaf angle (o)
R
> 50
75 75 + 60 75 + 60 + spher. 60 spher. spher. + 45 spher. + 45 + 60 75 75 + 60
0.92 0.95 0.97 0.85
40--50 30--40 20--30
0.92 0.93 0.92 0.93
zenith angle classes. This is also the case with the spherical leaf angle distrib u t i o n . No u n i q u e c o m b i n a t i o n o f leaf and z e n i t h angles yields t h e best p r e d i c t e d L values c o n s i s t e n t l y t h r o u g h o u t the day. However, for the large (7 > 50°) a n d the small (7 = 2 0 - - 3 0 ° ) z e n i t h angles, t h e c o m b i n e d 75 and 60 ° leaf inclination was f o u n d to be t h e m o s t suitable. F o r o t h e r z e n i t h angles, either spherical or 60 ° leaf angle d i s t r i b u t i o n s resulted in b e t t e r p r e d i c t i o n s o f leaf area index.
SUMMARY AND CONCLUSIONS M e a s u r e m e n t s o f p h o t o s y n t h e t i c a l l y active r a d i a t i o n ( P A R ) for clear days were used t o evaluate i n d i r e c t l y the leaf area index (L) and leaf angle
22 d i s t r i b u t i o n o f w h e a t . Since t h e p r o c e d u r e is based o n t h e p e n e t r a t i o n o f d i r e c t r a d i a t i o n t h r o u g h t h e gaps in t h e foliage, a s i m p l e a t m o s p h e r i c transmissivity m o d e l was used t o s e p a r a t e t h e d i r e c t a n d diffuse c o m p o n e n t s o f i n c o m i n g P A R . A c c o r d i n g l y , w h e n t h e f r a c t i o n o f d i r e c t to t o t a l P A R was larger t h a n 0.85, t o t a l a n d direct p e n e t r a t i o n w e r e p r a c t i c a l l y identical. A statistical c o m p a r i s o n o f t h e m e a s u r e d P A R t r a n s m i s s i o n w i t h the penet r a t i o n o f sun a n d s k y light derived f o r the selected a n g u l a r s h a p e coe f f i c i e n t o f t h e foliage s h o w e d t h a t t h e spherical leaf angle d i s t r i b u t i o n a d e q u a t e l y d e s c r i b e d t h e w h e a t c a n o p y , b u t f i x e d leaf inclinations o f 60 and 75 ° also w e r e s a t i s f a c t o r y . T h e p r e d i c t e d L values w e r e s c a t t e r e d a l o n g a z o n e a b o u t 1.5 units wide. T h e m o s t c o n s i s t e n t e s t i m a t e s w e r e o b t a i n e d w i t h t h e spherical leaf angle d i s t r i b u t i o n a n d t h e 60 ° f i x e d leaf inclination. T h e s t r a t i f i c a t i o n o f t h e P A R p e n e t r a t i o n m e a s u r e m e n t s a c c o r d i n g to solar zenith angles, a n d o f t h e angular s h a p e f a c t o r a c c o r d i n g t o leaf inclination, p r o v i d e s f u r t h e r i n f o r m a t i o n o n t h e w h e a t foliage a n g u l a r d i s t r i b u t i o n , s h o w i n g t h a t t h e d o m i n a n t leaf i n c l i n a t i o n is 75 °, w i t h a large 60 ° leaf angle c o m p o n e n t . T h e spherical angular d i s t r i b u t i o n a c c o u n t s f o r t h e r e m a i n d e r o f t h e leaf angles.
REFERENCES Anderson, M.C., 1970. Interpreting the fraction of solar radiation available in forest. Agric. Meteorol., 7:19--28. Lemeur, R., 1973. A method for simulating the direct solar radiation regime in sunflower, Jerusalem artichoke, corn and soybean canopies using actual stand structure data. Agric. Meteorol., 12:229--247. List, R.J., 1971. Smithsonian Meteorological Tables. 6th edn., Smithsonian Institute Press, Washington, DC, 527 pp. Monsi, M., and T. Saeki, 1953. Ueber dem Lichtfaktor in den Pflanzengesellschaften und seine Bedeutung fuer die Stoffproduktion. Jpn. J. Bot., 14:22--52. Paltridge, G.W. and C.M.R. Platt., 1976. Radiative Processes in Meteorology and Climatology. Elsevier, New York, pp. 114--121. Robinson, N., 1966., Solar Radiation. Elsevier, Amsterdam, 347 pp. Ross, J., 1981. The Radiation Regime and Architecture of Plant Stands. W. Junk, The Hague, 391 pp. Walraven, R. 1978. Calculating the position of the sun. Sol. Energy, 20:393--397.
13
L E A F A R E A E S T I M A T E S F R O M M E A S U R E M E N T S OF PHOTOSYNTHETICALLY ACTIVE RADIATION IN WHEAT CANOPIES*
M. FUCHS**, G. ASRAR and E.T. KANEMASU
Evapotranspiration Laboratory, Kansas State University, Manhattan, KS 66506 (U.S.A.) L.E. HIPPS
Utah State University, Logan, UT (U.S.A.) (Received June 6, 1983; revision accepted December 19, 1983)
ABSTRACT Fuchs, M., Asrar, G., Kanemasu, E.T. and Hipps, L.E., 1984. Leaf area estimates from measurements of photosynthetically active radiation in wheat canopies. Agric. For. Meteorol., 32: 13--22. Transmission of photosynthetically active radiation (PAR) measured with quantum sensors in three wheat cultivars during periods of clear sky were used to indirectly determine the leaf area index (LAI). The exponential description of direct and diffuse radiation penetration, which depends on leaf inclination, was correlated to the transmission measurements at various solar zenith angles. The highest correlations were found for fixed leaf inclinations of 60 and 75 °, and for the spherical leaf angle distribution. Angular shape coefficients corresponding to these leaf inclinations were then used to solve the exponential equation for LAI taking incoming PAR to be direct. This was shown to be an acceptable approximation when the proportion of direct radiation in the incoming PAR was higher than 0.85. Predictions of LAI were found to be within 0.7 units for a range of LAI from 1.5 to 5.0. A statistical analysis of the results indicated that the most suitable leaf inclination was a combination of 60 and 75 ° fixed angles, and spherical distribution.
INTRODUCTION Some crop growth models require information on factors influencing the size a n d p r o d u c t i o n r a t e o f t h e p h o t o s y n t h e t i c a p p a r a t u s . F o r a g i v e n c r o p , this i n f o r m a t i o n c a n b e d e r i v e d f r o m t h e l e a f a r e a i n d e x a n d t h e i n c l i n a t i o n a n g l e d i s t r i b u t i o n o f t h e leaves ( R o s s , 1 9 8 1 ) , w h i c h d e t e r m i n e t h e l i g h t d i s t r i b u t i o n w i t h i n t h e p l a n t c a n o p y a n d its a b s o r p t i o n b y t h e f o l i a g e . F o r this a p p r o a c h , the spatial d i s t r i b u t i o n of foliage e l e m e n t s n e e d s to be k n o w n . I n d e n s e l y p l a n t e d c r o p s , like w h e a t , w i t h o u t a v i s i b l e r o w s t r u c t u r e , it c a n
* Contribution No. 83-237-J from EvapotranspirationLaboratory, Agronomy Department, Kansas State University, Manhattan, KS 66506, U.S.A. ** On sabbatical leave from the Division of Agricultural Meteorology, Agric. Res. Org., Volcani Center, Bet Dagan, Israel.
0168-1923/84/$03.00
© 1984 Elsevier Science Publishers B.V.
14 be assumed that the horizontal distribution of foliage elements is uniform. For most plants the orientation of leaves is nearly random, and the effects of preferential azimuthal distribution have been shown to be small (Lemeur, 1973). Accordingly, the penetration of unscattered light rays, r, can be given (Monsi and Saeki, 1953) as r = exp (--KL)
(1)
where L is the leaf area index cumulated from the top of the canopy to the level at which light penetration is considered, and K is an angular shape coefficient. The angular shape coefficient, K, for uniform canopies of spherical leaf angle distribution is a single valued function of the zenith angle of the incident ray, 7, and is given by K = 0.5/cos77
(2)
For a fixed leaf inclination its value is K = cos 0
for
(zr/2 -- 0) ~> 77
K = c o s 0 [ 1 + (2/~)(tan co--co)]
for
(7r/2--0) ~ ~
(3)
where co -- arccos [cot 0 cot ~?]
(4)
and co/Tr is the fraction of the leaves with their backside in the direction of the light rays, and 0 is the leaf inclination measured from the horizontal plane. Equation 1 does n o t account for the light that is scattered by the elements of the foliage, and, therefore, does not provide an adequate description of the radiative transfer through a canopy. However, in the photosynthetically active region of the spectrum ( 4 0 0 - 7 0 0 n m ) , penetration and transmission are almost identical, due to the high absorption coefficient of the leaves. Therefore, transmission measurements of photosynthetically active radiation (PAR) can be used to verify the validity of penetration predictions by eq. 1 (Anderson, 1970). An important consequence of this validation is that it permits the use of these transmission data for an indirect eva]uation of the leaf inclination angle and the leaf area index.
MATERIALS AND METHODS A field experiment was conducted during the 1980--1981 growing season at the Evapotranspiration Research site near Manhattan, Kansas (39°09'N, 96°37'W, 3 0 5 m above M.S.L.). Photosynthetically active radiation (PAR) was measured above and below the canopy of two cultivars of winter wheat (Triticum aestivum L., 'Centurk' and 'Newton') planted at three seeding densities of 22.4, 44.8 and 67.2 k g h a -1 , referred to as low, medium and high density, respectively.
15 Four quantum sensors (LiCor model LI-190SB) wired in parallel were placed facing upward beneath the canopy to record the PAR reaching the soil surface. One sensor was m o u n t e d above the canopy to measure the incoming PAR. The sensors were connected to a data acquisition system (Hewlett-Packard 9820A) and their o u t p u t was recorded by a teletypewriter during daylight hours. Three 0.5-m sections of rows were harvested from the radiation measurement sites for leaf area determination by an optical planimeter (LiCor model LI-3100). Data presented in this report are from two cloudless days, early in the season (28 March and 30 March 1981) and a cloudless day later in the season (24 April 1981) when leaf area index values were about maximum. A second set of data collected on a spring wheat cultivar ( T r i t i c u m a e s t i v u m , L., 'Fieldwin') during two cloudless days (10 July and 26 July 1982) in Logan, Utah (41°45'N, 111°50'W, 1490 m above M.S.L.), also was used to test the relation between L and PAR. The sun zenith angles corresponding to each set of measured PAR values were c o m p u t e d from the time and date of acquisition of the data, based upon the equations used in Nautical Almanac (Walraven, 1978). Since the radiation measurements included direct sunlight and diffuse sky light, the ratio of direct to total p h o t o s y n t h e t i c radiation, q, was estimated based on the equations of atmospheric transmissivity compiled by List (1971) q = 2am~(1 + a m )
(5)
where m = (P/P0) sec 7, and a = exp (-- T), with m being the optical airmass number, a the atmospheric transmission coefficient and T the average scattering coefficient of the atmosphere for the PAR waveband. The ratio of atmospheric pressure at the observation site P, and the sea level P0, were used to correct for the effect of altitude on the atmospheric transmission coefficient. The scattering coefficient was empirically derived from T = - - l n [ 2 R t / ( R o cos ~1) -- 1] (P/Po) cos 7/
(6)
where Rt is the p h o t o s y n t h e t i c p h o t o n flux density above the canopy and R0 is the corresponding extraterrestrial p h o t o n flux density at normal incidence, c o m p u t e d from the solar spectrum data (Robinson, 1966). Diffuse sky radiation penetration, d, was c o m p u t e d as 2n
~r/2 I
d
(11~)
j-
j- fr sin 7? cos r~d~dq~
0
0
(7)
where ¢ is the azimuth angle between 0 and 27r, r is the penetration of a ray given by eq. 1, and f is the relative hemispherical radiance distribution of the clear sky (Robinson, 1966). The measured transmission, Tin, was taken as Tm = Rb/R t
(8)
16 where Rb is the average PAR measured beneath the wheat canopy. Since scattering of PAR by the canopy is assumed to be negligible, Tm is equivalent to the total penetration. For the same reason the theoretical value of total penetration, Tp, is given by Tp
= qr + ( 1 - - q ) d
(9)
Values of Tp were c o m p u t e d based on the measured leaf area index values for fixed leaf inclinations of 15, 30, 45, 60 and 75 ° and for spherical leaf angle distribution. Solar zenith angles were those corresponding to the time of the PAR measurements.
RESULTS AND DISCUSSION The ratios of the direct to total components (q) of photosynthetically active radiation (PAR) were c o m p u t e d from eqs. 5 and 6. Figure 1 depicts the predicted changes in q as a function of the sun zenith angle. Measurements of the direct and diffuse components of PAR were not available to independently verify the computations. However, the average PAR scattering coefficient of the atmosphere c o m p u t e d from eq. 6 was 0.110. This is close to the value of 0.127 derived by integrating the monochromatic Rayleigh scattering, weighted by the extraterrestrial p h o t o n flux distribution function over the frequency band corresponding to the PAR. Therefore, the q values c o m p u t e d from eq. 5 for clear sky conditions can be considered reliable. The estimated q values also follow a trend similar to the data for global radiation given by Paltridge and Platt (1976). The value of Tp in eq. 9 depends upon the ratio of direct to total p h o t o n flux density, q, the angular shape coefficient, K, and the leaf area index, L. However, only q and K are dependent on the zenith angle. Since the determination of q was standardized, the correlation between the distributions of Tm and Tp as a function of solar zenith angle for any given value of L depends upon the choice of K. Table I presents the correlation coefficients between the measured Tm and Tp values c o m p u t e d for K at fixed leaf inclinations of 15, 30, 45, 60 and 75 ° , and the spherical leaf angle distribution. Low frequency of PAR measurements and incomplete spatial sampling resulted in generally low correlation coefficients (Table I). They decrease systematically with increasing L. As gaps in the canopy become less frequent with increasing leaf area index, the measurements of PAR penetration require denser spatial sampling. Thus, larger sampling errors will occur at higher leaf area indices. Higher correlations are consistently f o u n d at fixed leaf inclinations steeper than 45 ° and with the spherical leaf angle distribution. Differences betweell 60 and 75 °, and spherical distribution are tenuous. Therefore, any of these leaf angle distributions can adequately characterize the wheat canopies.
17
0
0
0
o 0 [ ~.. 0
oo
O'3
c~c~ c~
c~ c~c~
c~ c~c~
c~ c~c~
c~ c~c~
c; c~c~
•,~ cO
L'~ 0.1
LQ cO oO
¢0 cO L~I
c~
c~
0
c~c;
d~d
ddd
0
cS c;c~
dNd
o 0
LQ ¢~1 CO
0
0
01 ~'xl cO
03 LO
O~ ¢xl O0 0
0 0 0
0 0
,-~ CO
0
0 0
0
CO LQ
0
O 0
oo 0
O 0
0
O 0
e~ ¢xl LQ ~.D
0 O0 O0 [~-
0
0
0
0
0
oo 0
0 0 0
0 0 0
¢ 0 C'~ O0 0 0 0
0 0 0
~COCO 0 0 0
~"xl Ol O0
0 0 0
0 0 0
0'~ oO 03
0
0
0
o3 0
0 0 0
~'~1 ¢ x 1 0 3 O 0
L~O00
r.r-I <
~0
~0
0
0
0~
18
1.0 ,.~°s..o.oOo...
,.
•
"°'o,.
Q8
z
b 0.6
I-
04
Qc
0.2
U A N H A T T A N , KS MARCH 30, 1981
0.0 30
40
50 60 70 Z E N I T H ANGLE
80
Fig. 1. Relation b e t w e e n the sun zenith angle and fraction o f direct incident PAR.
The leaf area index can be computed from the PAR penetration data at known zenith angles with a proper choice of the angular shape coefficient from L = --(ln
r)/K
(10)
where In r is the arithmetic mean of the natural logarithm of the penetration, and K is the mean of the corresponding angular shape coefficients. Since the Tm values include both the direct and diffuse components, it is necessary to determine under what condition penetration of direct PAR (i.e., r) can be approximated by the total penetration, Tp. Figure 2 shows the relation between r and Tp vs. q for a fixed leaf inclination of 60 ° and L equal to 1.4 on 30 March 1981. The data indicate that for q ~ 0.85, direct and total penetration are essentially identical. Under this condition measured Tm values can be used to approximate r in eq. 10. This condition excludes data iO
08
MANHATTAN, KS MARCH 30, 1983
o o u.
o o
06
o e = 60 ° L A I = 14 o TOTAL DIRECT
02
0 I
0.2
03
04
05
PENETRATdON
Fig. 2. Direct and total P A R p e n e t r a t i o n as related to the fraction o f direct incident PAR for a wheat canopy.
19 TABLE II Linear regression parameters and correlation coefficients (R) for comparison between predicted and measured leaf area index (LAI) Leaf angle (o)
Intercept
Slope
R
SD a
Spher. 45 60 75
0.42 0.43 0.46 0.33
0.96 0.91 1.04 1.13
0.89 0.87 0.89 0.93
0.59 0.64 0.66 0.56
a Standard deviation on predicted LAI. c o l l e c t e d at large z e n i t h angles. F o r example, on clear days like 30 March 1981 (Fig. 1) t h e limiting z e n i t h angle is 70 ° . All o f t h e Tm values c o r r e s p o n d i n g to q ~ 0.85 f o r each d a y were used to estimate L f r o m eq. 10. T h e results were c o m p a r e d with the m e a s u r e m e n t s using linear regressions and c o r r e l a t i o n c o e f f i c i e n t s {Table II). All f o u r t e s t e d leaf angle distributions have statistically similar o f f s e t values. T h e slopes are close to o n e b u t are nevertheless significantly d i f f e r e n t ( P ~ 0.025). T h e highest c o r r e l a t i o n c o e f f i c i e n t and smallest s t a n d a r d deviation are o b t a i n e d with the 75 ° leaf inclination. H o w e v e r , the steep slope o f the line corresp o n d i n g to this leaf inclination causes increasingly larger o v e r e s t i m a t e s at high L values, as illustrated in the scatter diagram in Fig. 3. T h e scatter diagrams for the spherical and 60 ° leaf angles have slopes close to u n i t y (Figs. 4 and 5) and show a m o r e c o n s i s t e n t p r e d i c t i o n over the range o f t e s t e d L values. T h e L values f o r the t w o w i n t e r w h e a t cultivars are overe s t i m a t e d , b u t t h o s e f o r the spring w h e a t are u n d e r e s t i m a t e d . T h e reason for this disparity is n o t k n o w n . These results indicate t h a t the e s t i m a t e d L values have a s t a n d a r d d e v i a t i o n t h a t does n o t e x c e e d 0.7 units. T h e m e a s u r e d Tm values used in the c o m p u t a t i o n s o f L c o v e r a wide range o f solar z e n i t h angles f r o m 20 to 65 ° . Since t h e a c c u r a c y o f t h e measurem e n t s d e p e n d s on t h e m a g n i t u d e o f the i n c i d e n t flux, and t h e i r representativeness is a f u n c t i o n o f the spatial gap d i s t r i b u t i o n , Tm values f o r s o m e solar z e n i t h angles m a y be m o r e suitable t h a n o t h e r s in p r e d i c t i n g L. T h e e f f e c t o f solar z e n i t h angles was investigated b y stratifying t h e d a t a into f o u r z e n i t h angle classes o f 20--30, 30--40, 4 0 - - 5 0 and ~ 50 °. It should be n o t e d t h a t the n u m b e r o f d a t a p o i n t s used t o c o m p u t e t h e m e a n L f r o m eq. 10 f o r each class differs, since m o r e d a t a with q ~ 0.85 are f o u n d at smaller z e n i t h angles. L e a f area i n d e x values c o m p u t e d f o r each z e n i t h angle class and for leaf inclinations o f 45, 60 and 75 °, and the spherical d i s t r i b u t i o n were linearly regressed against the m e a s u r e m e n t s . T h e regressions were c o m p a r e d in a f o r w a r d stepwise statistical analysis. T h e solar z e n i t h angle appears t o have very little e f f e c t o n t h e p r e d i c t i o n o f L, b u t m o d i f i e s slightly the c h o i c e o f the m o s t a p p r o p r i a t e leaf angle d i s t r i b u t i o n {Table III).
20
e = 60 = • MANHATTAN, KS 1981 LOGAN,UT 1982
8.0
.:
c~ z -
5.0
"~
40
~ 30
N 2.O
I0
I0
2.0
&O
MEASURED
Comparison
Fig.
3.
leaf
inclination
of
4.0
LEAF
510
AREA
between
6.0
INDEX
computed
a n d m e a s u r e d values o f l e a f area i n d e x f o r a f i x e d
60 ° .
e = 75 ° 60
z
• MANHATTAN, KS 1981 • L O G A N , UT 1982
•
_~30i
-
2.0
I0
/
i
j/
/
J iO
•
~
50
,, 4 °
• |
i
=
=
20
30
40
MEASURED
LEAF
AREA
i
J
50
6.0
INDEX
F i g . 4 . Comparison between measured and computed values of leaf area index for a fixed leaf inclination of 7 5 ° .
The 75 ° leaf inclination provides the best statistical fit for the zenith angle class of 2 0 - - 3 0 ° and zenith angles ~ 50 °. However, when the forward stepwise analysis included the L values corresponding to the 60 ° leaf inclination, the error term of the linear regression decreased significantly for these two zenith angle classes. The 60 ° leaf inclination was the only one suitable for predicting L from the measured PAR values corresponding to 4 0 - - 5 0 ° zenith angles. The best correlation between measured and predicted L values for the 3 0 - - 4 0 ° zenith angles is given by the spherical leaf angle distribution (Table III). These results indicate that n o n e o f the fixed leaf inclinations consistently provide the best estimate of the angular shape coefficient for all of the solar
21 SPHERICAL 6.0
,x,
• MANHATTAN, KS 198[ I LOGAN, UT 1982
5.0
• •
l
/
/\"
~ 40 ~ 30
8
82.0
.
.y /
,
./
I0
0
"
3.0
MEASURED LEAF
4,0
AREA
5.0
6.0
INDEX
Fig. 5. Comparisonbetween measuredand computed valuesof leaf areaindex for spherical leaf angle distribution. TABLE III Correlation coefficients (R) for the linear models of measured vs. predicted LAI for different classes of leaf and solar zenith angles (the results are based on stepwise regression analysis of the combined data sets for the two experiment sites) Zenith angle (o)
Leaf angle (o)
R
> 50
75 75 + 60 75 + 60 + spher. 60 spher. spher. + 45 spher. + 45 + 60 75 75 + 60
0.92 0.95 0.97 0.85
40--50 30--40 20--30
0.92 0.93 0.92 0.93
zenith angle classes. This is also the case with the spherical leaf angle distrib u t i o n . No u n i q u e c o m b i n a t i o n o f leaf and z e n i t h angles yields t h e best p r e d i c t e d L values c o n s i s t e n t l y t h r o u g h o u t the day. However, for the large (7 > 50°) a n d the small (7 = 2 0 - - 3 0 ° ) z e n i t h angles, t h e c o m b i n e d 75 and 60 ° leaf inclination was f o u n d to be t h e m o s t suitable. F o r o t h e r z e n i t h angles, either spherical or 60 ° leaf angle d i s t r i b u t i o n s resulted in b e t t e r p r e d i c t i o n s o f leaf area index.
SUMMARY AND CONCLUSIONS M e a s u r e m e n t s o f p h o t o s y n t h e t i c a l l y active r a d i a t i o n ( P A R ) for clear days were used t o evaluate i n d i r e c t l y the leaf area index (L) and leaf angle
22 d i s t r i b u t i o n o f w h e a t . Since t h e p r o c e d u r e is based o n t h e p e n e t r a t i o n o f d i r e c t r a d i a t i o n t h r o u g h t h e gaps in t h e foliage, a s i m p l e a t m o s p h e r i c transmissivity m o d e l was used t o s e p a r a t e t h e d i r e c t a n d diffuse c o m p o n e n t s o f i n c o m i n g P A R . A c c o r d i n g l y , w h e n t h e f r a c t i o n o f d i r e c t to t o t a l P A R was larger t h a n 0.85, t o t a l a n d direct p e n e t r a t i o n w e r e p r a c t i c a l l y identical. A statistical c o m p a r i s o n o f t h e m e a s u r e d P A R t r a n s m i s s i o n w i t h the penet r a t i o n o f sun a n d s k y light derived f o r the selected a n g u l a r s h a p e coe f f i c i e n t o f t h e foliage s h o w e d t h a t t h e spherical leaf angle d i s t r i b u t i o n a d e q u a t e l y d e s c r i b e d t h e w h e a t c a n o p y , b u t f i x e d leaf inclinations o f 60 and 75 ° also w e r e s a t i s f a c t o r y . T h e p r e d i c t e d L values w e r e s c a t t e r e d a l o n g a z o n e a b o u t 1.5 units wide. T h e m o s t c o n s i s t e n t e s t i m a t e s w e r e o b t a i n e d w i t h t h e spherical leaf angle d i s t r i b u t i o n a n d t h e 60 ° f i x e d leaf inclination. T h e s t r a t i f i c a t i o n o f t h e P A R p e n e t r a t i o n m e a s u r e m e n t s a c c o r d i n g to solar zenith angles, a n d o f t h e angular s h a p e f a c t o r a c c o r d i n g t o leaf inclination, p r o v i d e s f u r t h e r i n f o r m a t i o n o n t h e w h e a t foliage a n g u l a r d i s t r i b u t i o n , s h o w i n g t h a t t h e d o m i n a n t leaf i n c l i n a t i o n is 75 °, w i t h a large 60 ° leaf angle c o m p o n e n t . T h e spherical angular d i s t r i b u t i o n a c c o u n t s f o r t h e r e m a i n d e r o f t h e leaf angles.
REFERENCES Anderson, M.C., 1970. Interpreting the fraction of solar radiation available in forest. Agric. Meteorol., 7:19--28. Lemeur, R., 1973. A method for simulating the direct solar radiation regime in sunflower, Jerusalem artichoke, corn and soybean canopies using actual stand structure data. Agric. Meteorol., 12:229--247. List, R.J., 1971. Smithsonian Meteorological Tables. 6th edn., Smithsonian Institute Press, Washington, DC, 527 pp. Monsi, M., and T. Saeki, 1953. Ueber dem Lichtfaktor in den Pflanzengesellschaften und seine Bedeutung fuer die Stoffproduktion. Jpn. J. Bot., 14:22--52. Paltridge, G.W. and C.M.R. Platt., 1976. Radiative Processes in Meteorology and Climatology. Elsevier, New York, pp. 114--121. Robinson, N., 1966., Solar Radiation. Elsevier, Amsterdam, 347 pp. Ross, J., 1981. The Radiation Regime and Architecture of Plant Stands. W. Junk, The Hague, 391 pp. Walraven, R. 1978. Calculating the position of the sun. Sol. Energy, 20:393--397.