Deriving light interception and biomass from spectral reflectance ratio

REMOTE SENS. ENVIRON. 43:87-95 (1993)

Deriving Light Interception and Biomass from Spectral Reflectance Ratio S. Christensen Department of Weed Control, Research Centre for Plant Protection, Flakkebjerg~ Slagelse, Denmark

J. Goudriaan Department of Theoretical Production Ecology, Agricultural University, Wageningen, The Netherlands

L i g h t interception and reflection in different cultivars of spring barley (Hordeum vulgare) were measured in a field experiment and used to verify a theoretical relation between the fraction of intercepted photosynthetically active radiation (fp~) and the relative vegetation index (RVI). The RVI was calculated as the ratio between infrared (790810 nm) and red (640-660 nm) reflectance. The cultivars form a different canopy structure. However, a regression analysis did not show any cultivar effect on the relation between R VI and fPA,. The predicted fpA, from frequently measured RVI was used to calculate the product of daily fp,~ and incoming PAR (cumulative PAR interception) in all spring barley cultivars grown in monoculture and in mixture with oil seed rape (Brassica napus). A regression analysis showed that the relation between cumulative intercepted PAR and total above ground biomass was the same in all monocultures and mixtures. The ratio a of incremental dry matter and intercepted PAR was normally 2.4 g MJ-1, but it declined below this value when temperatures fell below 12 ° C.

Address correspondence to Svend Christensen, Dept. of Weed Control, Research Centre for Plant Protection, Flakkebjerg, DK4200 Slagelse, Denmark. Received 23 April 1991; revised 14 July 1992. 0034-4257 / 93 / $5.00 ©Elsevier Science Publishing Co. Inc., 1993 655 Avenue of the Americas, New York, NY 10010

INTRODUCTION

Crop growth is normally investigated by repeated and destructive assessments of dry matter, but this is a tedious and time-consuming method. However, during the past several years, estimation of biomass from spectral reflectance measurements has shown promising results. Bunnik (1981) demonstrated that reflection of red, green, and near-infrared radiation contains considerable information about crop biomass owing to the contrast between soil and vegetation. Various combinations of the reflection coefficients in the nearinfrared region (750-1350 nm, P0 and in the red region (600-700 nm, pr) have been considered (Tucker, 1979; Ahlrichs and Bauer, 1983). Among these, the normalized difference vegetation index NDVI = (p~ - Pr) / (P, + Pr)

(1)

and the ratio vegetation index RVI = p, / Pr

(2)

have become the most popular ones (Wiegand et al., 1990). For the purpose of prediction ofbiomass from spectral reflection indices, two main approaches have been followed. One approach attempts to use a correlation between RVI or NDVI and biomass (Tucker, 1979; Ahlrichs and Bauer, 1983; Petersen, 1989). However, since the reflection

87

88

Christensen and Goudriaan

coefficients are primarily determined by green foliage and not by amount of dry matter, this correlation is not a stable one. During the growth of a crop, accumulated dry matter increases relatively more than current green foliage does. This consideration leads to a second approach which is based on the well-known relation between the amount of dry matter (Wo~,) and accumulated intercepted photosynthetically active radiation (400-700 nm) (AL,~) (Monteith, 1977; Gallagher and Biscoe, 1978; Russell et al., 1989). Experimental results (Gallagher and Biscoe, 1978; Legg et al., 1979; Kumar and Monteith, 1981; Steven et al., 1983; Green et al., 1985; Kasim and Dennet, 1986; Wiegand et al., 1989; 1991) have shown that WD, is a time-integrated product of the fraction of intercepted PAR (f~) and the daily incident radiation of PAR above the canopy (S0,p,,), WD. =

3'afeARZ0,pAadt,

THEORY

The ratio between transmitted PAR under a canopy (Ss,pAR)and incoming PAR (S0.p,~) declines approximately exponentially with the leaf area index L,

Ss,,,R / S0,p,R= exp( - K~,RL),

(4)

Kumar and Monteith (1981), Steven et al. (1983), Asrar et al. (1984), Gallo et al. (1985), and Wiegand et al. (1989; 1991) showed that f~,, was correlated to RVI and NDVI and introduced empirical models describing the relationship between f~,, and these indices. Kumar and Monteith (1981), Asrar et al. (1984), and Choudhury (1987) demonstrated that the relationship between fp,, and NDVI or RVI must be nonlinear. Further, Asrar et al. (1984) showed that NDVI is less sensitive to solar zenith angles than RVI. In contrast, a preliminary regression analysis of our own results did not show any significant difference between the two indices, and we therefore used RVI because of simplicity. The objectives of this article are to analyze the correlation between RVI andre** measured in different monocultures of spring barley cultivars. Further, the article considers calculation of dry matter formation on basis of the Eqs. (3) and (4)

(5)

where Kp~ is the extinction coefficient for PAR radiation and L is the leaf area index. The fraction of PAR intercepted is then ft,, = 1 - exp( - K~**L).

(6)

Similarly, the fraction of red radiation intecepted is

fr = 1 -- exp( - KrL)

(3)

where a = the conversion factor for intercepted PAR into dry matter. Russell et al. (1989) summarized values of a for different species and environmental conditions, showing considerable variation. If a is constant over the growing season, it can be moved outside the integration sign

WD, = a.Ifi^~So,~^~ dt.

and discusses the value of a for the different eultivars during the vegetative growth period.

(7)

describes the relative interception of red radiation (Kr = the extinction coefficient in the red waveband). The coefficients Kr and K~,~ are not exactly the same, but it is reasonable to assume that The ratio p of radiation reflected from the canopy to the incoming radiation is influenced by the reflectance from both canopy and soil. The spectral reflectance to red (p~) and near infrared (pi) radiation from a crop with horizontal leaves is given by

p,.=p,.,®+(rl,./p,.,=) exp(-2KrL), pro. + fir exp( - 2K,-L)

(8)

where P r , oo - - P r , 8

rt"=pr,,- 1/Pr,..'

(9)

and similarly

Pi

p,,o. + (rl~/p,,®) exp( - 2K.,L), Pi,~ + rli exp( - 2K~L)

(10)

pi,® - p,,s

(11)

where r/i =

P~,s _ 1 / pioo

(Goudriaan, 1977). The parameters Pr.® and p~® are the red and near infrared reflectance at high LAI (LAI > 8). The p~,, and p~,, are the red and near infrared reflectance from the bare soil (LAI = 0). The parameters Kr and Ki are the ex-

Deriving Light Interception and Biomass 89

tinction coefficients of red and infrared radiation. The RVI is then a function of LAI:

Table 1. The Parameter Values [Eqs. (6)-(13)] of the Experiment Estimated from a Bare Soil and a Dense Green Sward

RVI = [p'= + (t/,/p,,®) exp( - 2/Q.L)] IPr,= + (llr/ Pr,**) exp( - 2KcL)] "1- ~r e x p ( -- 2 K r L ) ]

Near Infrared (12)

x [[11+r/, exp( - 2K,L)} ' Although not immediately obvious, this expression collapses to RVI=p,,,/pr,, for LAI at zero (L=0). For PAR (and practically also in the red waveband), the value of K is about 0.7, but it may still vary a little with solar height and leaf angle distribution. Notwithstanding this variation, K values for different wavebands are affected in a similar way, and so their ratios for a given vegetated surface are quite stable. Assuming that K, = 0.5 * Kr (Rodskjer, 1972) and using that exp ( - KrL) = 1 -f~A~ the RVI can be expressed infix: RVI = [p''®+ (tl,/p,,®)(1 ~Or,¢~+ (~r/ pr,~)(1

--fP~a)] --fpss) 2]

ll + r/r(1 --fpAa)2)

x/1 +,7,(1 -fP )l"

(13)

This relation between fPA~ and RVI is nonlinear, and its curvature depends on the parameter values. The reflection and extinction coefficients vary significantly among cultivars and species that differ in canopy structure, pigment density, nitrogen content, and structure of the leaves. The coefficients also depend on direction of the incoming radiation. Water content of the soil surface affects the parameter values of P~,s and Pr.~ (Huete et al., 1985). Wiegand et al. (1990) reported that the particular wave bands within the red and near infrared wavelength intervals used in instrumentation may influence the measured values of the reflection coefficients. The parameter values for pi,=, P~,=, Pi,~, and p~,~ will determine the correlation between f~A, and RVI, However, the influence of a change in extinction coefficient is restricted to the small variation in the ratio Kr/K,, so that different extinction coefficients still result in very similar relations between f ~ . and RVI. Thus, for prediction of fi^, from RVI, the influences of soil type and instrumentation have to be eliminated by reference measurements of soil reflectance and canopy reflectance at very high LAI (Table 1).

Red

Ratio

Extinction coefficient /~ ffi0.35 /G ffi0.70 /~ / K,-ffi0.5 Reflectance at infinite LAI p~ffi0.400 prffi0.040 p~/prffilO.O Reflectance from bare soil Pt, ffi0.28 p,., ffi0.20 pt, / Pr~ffi1.4

EXPERIMENT Methods and Materials A field experiment was carried out in 1990 on a sandy loam at the Department of W e e d Control, Flakkebjerg (latitude 55°), Denmark. The experimental design was a f~tctorial design with 12 cultivars of spring barley grown in monoculture and in mixture with 200 plants per square meter of oil seed rape. The plan was a completely randomized block design and four blocks. The plots were 2.5 m x 7.5 m in size. Rows were oriented northsouth and spaced 0.12 m apart. The cultivars (Table 2) represented the variation in commercial spring barley cultivars in Denmark. The fertilizer (100 N kg/ha, 19 P kg/ha, and 48 K kg/ha) and the oil seed rape were broadcast before the cultivars were seeded. All cultivars and oil seed rape emerged between 20 and 22 April. The 5 May densities of cultivars were = 3 5 0 plants/m 2. The total above-ground dry matter of cultivars and oil seed rape was measured five times (Table 3) during the vegetative growth by sampling 0.25 m 2 at random in each of the 96 plots (5 times * 12 cultivars * 2

Table 2.

UPOV (1981) Variety Description of the Spring Barley Cultivars ~

Cultivar Growth Habit Straw Length Time of Heading Grit Ida Lenka Formula Jenny Tikko Alis Digger Sewa Alexis Regatta Harry

Semiprostrate Semierect Intermediate Semiprostrate Intermediate Semierect Semiprostrate Semiprostrate Intermediate Semiprostrate Semierect Intermediate

Medium Very long Medium Very short Very long Long Very short Short Medium Medium Long Very long

Medium Early Early Medium Early Early Late Medium Early Medium Late Medium

a The characteristics were assessed at Department of Variety Testing, Tystofte, Denmark.

90

Christensen and Goudriaan

Table 3.

S u m m a r y o f M e a s u r e m e n t s in t h e E x p e r i m e n t "

Days after Emergence 3 5 7 10 13 19 26 33 37 41 48 54 60 69 76

Stage

f~..

Seedling growth Tillering

Stem elongation

+

Booting

+

Heading

+

Milk ripe

+

R VI

Wo.

+ + + + + + + + + + + + + +

a The fp.~ was only m e a s u r e d in the barley. The RVI and the total above-ground dry matter (Wo.) were measured in both barley and barley-rape plots.

levels of oil seed rape infestation * 4 blocks = 480 samples). Photosynthetically active radiation (PAR) 400700 nm at the surface of the soil (S,,,,~) and above the canopy (S0~-A,) were recorded simultaneously with two line quantum sensors (LI-COR LI 191SB) connected to a datalogger (LI-COR LI 1000). The measurements were made in each plot of the monoculture about 14.00 h (solar noon = 13.00 h). In order to minimize disturbance of the canopy structure, the line quantum sensor was inserted in the canopy along the rows of the crop. The PAR measurements were replicated during the growth, but only three measurements were made on the same day as the spectral reflectance measurements (Table 3). The fraction of intercepted PAR,f~,~ was calculated as fF*R= 1 -- S~,~.~/S0,~.~

(14)

where Ss,.../So .... is the ratio of transmitted to incident PAR. The spectral incoming and reflected near infrared and red radiation were measured with twoband sensors (SKYE SKR 110). The sensors consist of two pair of silicon photodiodes and two specific interference filters that transmit the wavelength intervals 640-660 nm (red) and 790810 nm (infrared). The analog output from the transducers was amplified and converted by an internal A / D converter in a portable computer (Toshiba T3100e / 40).

One sensor was cosine-corrected (hemispherical) and was used to measure the incoming nearinfrared (S,,~) and red (S*,r) radiation. The other sensor had a restricted field-of-view (FOV) of 25 ° and was used simultaneously for measurements of reflected near-infrared (St,i) and red (St,r) radiation from the canopy. The sensors were mounted on an arm of a portable gallows at a height of 2.56 m. The 25 ° FOV device gave a circular 1.0 m ~ sample. The data from both sensors were acquired and stored interactively by plot n u m b e r using an existing software program and an acquisition system. The RVI value was instantaneously presented on the screen device. Spectral measurements were taken at four random sites in each plot. At each site, measurements were replicated five times in order to minimize the influence of leaf fluttering. Following Russell et al. (1989) and Petersen (1989), spectral measurements were acquired between 11.00 h and 15.00 h (solar noon 13.00 h) without considering the variation in cloud cover or soil wetness. To sample 96 plots, 1 h was needed. The reflection coefficients S,,~/S,,, and St.r~ S,,r were used to calculate the spectral reflectance ratio, RVI = P-t/ = St.i/ S~.i Pr S?,r/ Sl,r"

(15)

The RVI of each plot was measured 14 times (Table 3) during the period from emergence until the milk stage of the grain ( = 3 weeks after heading). Statistics

The influence of cultivars and blocks on the correlation between RVI and f~,~ was analyzed in the regression models as d u m m y variables (Weisberg, 1985). The regression model, that linearized the relation between RVI and fF,~, ln(RVI) = ,6o + ~1 * f,,,~ + fl2(A) + fi3(A) *f~,, + P4(C) + error,

(16)

where A = cultivar = 1, 2 . . . . . 12, C = block = 1, 2, 3, 4, was used to test the homogeneity of the slopes for different cultivars.

Deriving Light Interception and Biomass 91

Next, a regression model was used to examine the influence of cultivars, oil seed rape infestation, and blocks on the correlation between dry matter (WD~,) and accumulated intercepted PAR (AIp^,): WDM --~#0 4" ~1 *

RESULTS

AIp..+ flz(A) + ]~z(B)+ ~ 4 ( ~

+ #5(a),AIp.. + P6(B) * AI...

Relation between RVI and f,^. (17)

+ flV(Q * AIpA. + e r r o r ,

where A = cultivar = 1, 2 . . . . . 12, B = oil seed rape infestation = 1, 2, C = block = 1, 2, 3, 4. The statistical analyses were performed using the Figure i. A) The relation between calculated (solid curve) [Eq. (13)] and measured spectral reflectance ratio RVI and fraction of intercepted f,^R. The symbols are the mean values of the measurements in spring barley cultivars without oil and seed rape infestation. B) The regression model [Eq. (16)] fitted to the measured RVI. 12 Days after emergence z~ 19 o 37 o 48

~

General Linear Models of the SAS statistical package (SAS, 1985).

6

~

A

Using the parameter values from Table 1 in Eq. (13) the theoretical relation between f,^~ from RVI is described by the curve in Figure 1A. The interception of the vertical axis is the RVI for LAI = 0 estimated from measurements in a plot of bare soil. The upper asymptote is the RVI for highfp,, estimated from measurements in a dense sward. The measuredfp^~ and RVI in spring barley cultivars with different growth habit agreed well with the theoretical curve (Fig. 1A), indicating that the K,/K~ ratio was the same in all cultivars and that the leaf orientation did not affect the relation. A nonlinear regression of RVI on fp^, using Eq. (13) was impossible, because of missing low and high values offpA.. Nevertheless, the resuits in Figure 1A demonstrate that the theoretical curve gave a good description of the data. An exponential model also described the data sufficiently (Fig. 1B). A regression analysis of the linearized model [Eq. (16)] showed that the cultivars did not contribute significantly to the sum of squares (Table 4). In terms of Eq. (13), this result indicates that the Kr/K~ ratio did not vary much among cultivars.

AIp.~ Estimation Using Eq. (13) and linear interpolation between the clays where RVI was measured (Table 3), daily values of fp,. were obtained. The daily ft.. was calculated for all monocultures and mixtures assuming that the parameter values in Table 1 were

fPAR

12 Days after emergence z~ 19 <> 37 O 48

0

°6

.'4

.'6 fPAR

Table 4. Partial F-Test of the Influence of Cultivars and Blocks on the Relationship between In(RVI) and fp,~ [Eq. (16)]" Source

d.f.

SS

F-Value

fPAR Cultivar fp^~*cultivar Block Residual R2= 0.960

1 11 11 3 108

25.2905 0.1523 0.0992 0.0445 1.1268

2423.96* 1.33 0.86 1.42

a , Significance at a = 0.05.

92 Christensenand Goudriaan

1000.

DM = 1.939 (0.012)

Day=76

x AIpAR, R2=0.98

800 Day=54 •

*

60O o

Day=4

400

Day=33 j ~

o,%

,b

o 'o

Figure 2. The correlation between total

AIPAR(MJ/rn2)

above-ground biomass and accumulated intercepted PAR (AI~) per square meter measured in spring barley cultivars in both barley monoculture (0) and in barley rape mixture (+). Only mean values of four blocks are presented. The five groups of data distinguish the five dates (Table 3), at which both RVI and biomass were measured. The regression line is forced through the origin. Standard errors of the regression coefficient are given in parentheses.

~-

o ¢,~,o ~. g +

200

Day=19

I

I

1

I

100

200

300

400

also valid for oil seed rape. The daily intercepted PAR of each plot was calculated as D,,, =f,^R * So,,,,,

ground dry matter (WD,) and AI~,~. The results of sequential sampling of total dry matter (WoM)(Table 3) and AIp,~ estimated from RVI measurements is shown in Figure 2. The relation was almost linear. In the beginning of the period, WD, and AIp,~ were significant higher in plots with oil seed rape infestation, but after 76 days WD, of the barley monoculture and barley-rape mixture were the same. At this time, oil seed rape was 10-40% of WD., depending on the competitive ability of the cultivars. The slope of the line in Figure 2 is the mean conversion coefficient a throughout the vegetative period. A regression analysis (Table 5) showed that the discrete variables cultivar, oil seed, and block hardly contribute to the sum of squares, that is, the mean slope of the regression line was

(18)

where So,~,~was the daily incoming PAR estimated as So * 0.48. The So was the daily incoming shortwave radiation (300-2800 nm) obtained at the local meteorological weather station. The accumulated intercepted PAR was then 76

AL,~ = EDp,R

(19)

0

during the investigation period. Biomass Estimation

The next step in derivation of biomass from RVI was to analyze the relation between total above-

Table 5. Partial F-Test [Eq. (17)] of the Influence of Cultivars, Oil Seed Rape Infestations (Weed), and Blocks on the Relation between Total Above-Ground Biomass and Accumulated Intercepted PAR (AI~^~) for Different Harvest Dates Separately"

19

Source AIp,~ Cultivar Weed Block AI**~* cultivar AIp^,* weed AIrA,* block Residual R2

d.f. 1 11 1 3 11 1 3 94

38.85*** 1.64 0.52 2.01 1.58 0.57 1.10 0.83

Days after Emergence 33 41 54 F-Values 13.68"** 1.37 0.22 5.15" 1.25 0.32 4.71" 0.83

17.05"** 0.93 3.28 0.09 0.82 3.58 0.08 0.78

Significance at * a =0.05, ** a=0.01, and *** a=0.001.

76

8.39** 1.46 0.19 3.54* 1.45 0.29 3.11"

9.74** 1.46 2.92 0.85 1.45 2.32 0.92

0.81

0.75

Deriving Light Intercept~a and B~gmass 93

Table 6. The Regression CoetBcients (Standard Errors of Estimates in Brackets) of the Linear Correlation between Total Above-Ground Biomass (WDM)and Accumulated Intercepted PAR (AIp^R)for Different Harvest Dates Separately"

30 0 i .,.a

20

Day

Intercept

Slope (a)

R~

19 33 41 54 76

-1.53 (3.43) -46.8* (18.8) -36.0 (29.4) - 12.6" (57.1) -9.94 (111.)

1.58"** (0.13) 1.87"** (0.18) 1.73"** (0.18) 2.40*** (0.22) 2.09*** (0.29)

0.63 0.60 0.51 0.56 0.36

10

° The unit of the slope is g/MJ. Significance at *a = 0.05 and ***a = 0.O01, respectively.

20

r.o

the same for all cultivars in both monoculture and mixture and in all blocks. The systematic deviation from the line in Figure 2 at the beginning of the growth indicated that a changed during the growth. The regression coefficients (Table 6) showed an increase of a from day= 19 until day=54 and a decrease from day=54 until day= 76. The maximum a of 2.4 g MJ -1 was obtained at day = 54, which was the time of anthesis. The deviation from the line in Figure 2 probably reflects the environmental effect on a, such as light saturation or a temperature effect. An examination of the daily mean temperature obtained at the local meteorological station showed two periods with temperatures lower than 12°C (Fig. 3). Adjusting the fp,. value at low temperature by a reduction factor R: 76

AR,,R = ~,,R * O,.,

(19')

0

o

I

I

16

o

12 o e.~

E

8 4

0

0

I

I

I

20

40

60

80

Days after emeruence

Figure 3. The daily mean temperature and incoming radiation So measured at the local meteorological station during the investigation period in 1990.

improved the fit of data (Fig. 4). The value of R was a linear function of daily temperature (T) between 6°C and 12°C a = ( r - 6) / 6.

(9.0)

Below 6°C, R was 0, and, above 12°C, no adjustment was needed. The results of this approach

1000 DM = 2.209 (0.011) x ARpAR, R2=0.99 800

°Day=IS d ~ /

600

D

400

D a y = 4 ~

0F 0

e

°~

I 100

, E00

a

y

=

*

TM

-+300

AR PAR(MJ/m2)

, 400

Figure 4. The relation between total aboveground biomass and accumulated intercepted PAR modified at low temperature (AR,An). The symbols are explained in Figure 2. The regression line is forced througi: origin. Standard errors of the regression coefficient are given in parentheses.

94

Christensen and Goudriaan

verify that a was modified at low temperature. Results in Bartlett et al. (1990) also indicate that t e m p e r a t u r e modified a. In general, water deficit, nutrients, and diseases may r e d u c e a or f~A~, or both. G r e e n et al. (1985) and Kasim and D e n n e t (1986) showed that a was identical in two cultivars of Vicia faba, but was modified by water shortage and light saturation of the leaves. In the experiment described in this article, growth was r e d u c e d due to a short period with water stress after second assessment of biomass. At that period, some of the cultivars w e r e also influenced by diseases before an efficient control was achieved. Altogether, this may explain the slight deviation from the regression line in Figure 4. The m e a n value of a in the investigated period is quite similar to values reported from other experiments, for example, summarized in Russell et al. (1989) and Charles-Edwards et al. (1986). However, Russell et al. (1989) claimed that the values w e r e incomparable because of methodical disparities in m e a s u r e d biomass, f~^R, solar radiation So or S0,p,~.

C O N C L U D I N G REMARKS The advantage of the p r e s e n t e d m e t h o d lies in the prospects of obtaining fast and accurate information about the light interception of the crop. Further, frequently m e a s u r e m e n t s can be used to estimate the biomass and next the growth parameters of the crop. Wiegand et al. (1989; 1991) related the yield of different crops to cumulative NDVI and AI~^R, which is useful in forecasting. In principle, daily m e a s u r e m e n t s of RVI are desirable. However, it appears to be a cumbersome strategy, and investigations of adequate sampiing technique have to be initiated with the objective of minimizing the n u m b e r of measurements without introducing systematic errors caused by interpolation b e t w e e n the days w h e r e RVI is assessed.

The authors acknowledge J. Kristensen and J. Rasmussen, Department of Weed Control, Flakkebjerg, Denmark for developing the data acquisition system and helpful comments on the manuscript. The research was supported by the Danish Veterinary and Agricultural Council and the Danish Scientific Academy.

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