Canonical correlation relationships among spectral and phytometric variables for twenty winter wheat fields

REMOTE SENS. ENVIRON. 43:1-10 (1993)

Canonical Correlation Relationships among Spectral and Phytometric Variables for Twenty Winter Wheat Fields R. M. Korobov and V. Ya. Railyan Institute of Genetics, Academy of Sciences of Moldova, Kishinev, Moldova, CIS

T o assess the adequacy of remote and conventional agricultural surveys, aircraft spectrometry of 20 commercial winter wheat fields was obtained in southern Moldova, CIS, and related to plant measurements using canonical correlation. Measurements were made over the 420-1200 nm range at intervals of 10 nm. A total of 510-575 reflectance spectra were obtained for each of the five phenophases studied and the extrema of the averaged curves of bidirectional reflectance factor (bA) were determined. The blue and red minima, as well as the relative maximum in the visible region, were positionally highly stable during the season (about 480 nm, 550 nm, and 670 nm, respectively). In the NIR region the b~ curve rose smoothly between 750 nm and 1070 nm, and its steepness was probably determined by soil background reflectance. The values of b4~o, b.5.~o,b~,0, and b,s~0 were the spectral variables chosen, and they were related, through canonical correlation analysis, to phytometric variables (dry aboveground phytomass, plant height, plant density, and percent plant cover) obtained from the corresponding ground-based agronomic measurements. There was a close relation between spectral and phyto-

Address correspondence to R. M. Korobov, Institute of Genetics, Academy of Sciences of Moldova, Lesnaya str. 20, 277018 Kishinev, Moldova, CIS. Received 15 August 1991; revised 15 February 1992. 0034-4257 / 93 / $5.00 ©Elsevier Science Publishing Co. lnc., 1993 655 Avenue of the Americas, New York, NY 10010

metric variables' when the canopy was green (the first canonical correlation coejficient was 0.974 in the booting stage), but the closeness decreased with crop maturation. Canonical variables for spectral reflectance explained, at most, about 75% of the variance in phytometric variables while the first canonical variable for phytometric features accounted for 90% of the spectral variance. The NIR and red reflectances contributed most to canonical variables and had the highest correlations with the plant measurements. Among the phytometric variables, percent plant cover and dry aboveground phytomass related more closely to spectral reflectance than did plant height and plant density. On the whole, the results obtained confirm the high information potential of aircraft spectrometry for estimating winter-wheat crop conditions.

INTRODUCTION

In recent decades, a number of techniques have been proposed for quantitative and qualitative evaluation of plant covers of various agrosystems based on their spectral reflectances (Bauer, 1985; Kleschenko, 1986; Kondratyev et al., 1990; Rachkulik and Sitnikova, 1981). Studies on the adequacy of remote and conventional agricultural surveys are continuing, because new cultivars and agricultural practices and improved remote sens-

2 Korobov and Railyan

ing devices and carriers are constantly being developed and introduced. Correlation and regression analyses have been the most commonly used statistical procedure applied (Aase and Siddoway, 1981; Dusek et al., 1985; Korobov et al., 1991; Rudorf and Batista, 1990; Tucker et al., 1981). Canonical correlation (Cooley and Lohnes, 1971) is particularly useful because it allows sets of spectral and plant measurements to be regarded as dependent variables and their relationships to be estimated. Thus, it is a powerful tool for comparing and interpreting the information contained in surveys obtained by various means. The objective of this article is to summarize the results of applying canonical correlation in relating spectral and phytometric parameters for winter wheat fields. MATERIALS A N D METHODS

The data from aircraft spectrometric surveys of commercial fields of winter wheat (Triticum aestivum) conducted in southern Moldova in the 1986 growing season using an airborne spectroradiometer served as initial material in this study. The instrument (Dobrozrakov et al., 1983) has a diffraction monochromator as the main components of its design and measures simultaneously the spectral distribution of incident and of reflected solar radiation over the range 420-1200 nm at 10 nm wavelength intervals. The recording time of one spectrum is 1.5 s. The bidirectional reflectance factor (bx) was computed as the ratio of scene spectral radiance to the corresponding parameter of an ideal (Lambertian) reflector. Acquisition was conducted from an aircraft at an altitude of 100 m and flight speed of 160 k m / h under clear sky conditions and a solar elevation angle of 40-60 ° . At this altitude, the radiometer sampled an area about 30 m in width and 6070 m in length during one spectrum. Commercial fields served as the units of data acquision. Fields are plots of agricultural land with relatively homogeneous soil planted to a monoculture and managed uniformly. For this study fields were no less than 50 ha (125 acres). The spectral reflectance of 20 fields planted to three varieties of winter wheat (Odesskaya 51, Obri and Lan) was measured periodically during the growing season. The sampled fields differed in yield potential from excellent to very bad. This

range in crop conditions was necessary to provide a range in variation in parameters studied and to improve representativeness of the resultant conclusions. Considering the fact that the study was conducted in ordinary commercial fields, no special modeling of their conditions by varying agronomic practices was done. The fields were chosen from a large array kindly provided for the purpose by various farms. The distance between fields varied from 1-2 km to 25-30 kin. As a rule, acquisition was conducted just prior to a phenophase (growth stage) onset in the majority of plants, on the day of the onset and on the following day. In one overpass, 10-20 spectra were recorded along the diagonal transect over each field. For subsequent analysis, the spectra acquired for each phenophase, that is, within 2-3 consecutive days, were averaged. A total of 510-575 spectra were recorded for each phenophase. Agronomic sampling and ground phytometric measurements were carried out at booting, heading, and milky ripeness. The measurements were performed within 1 day of the corresponding radiometric measurements on plant samples from various subsites in each field. The number of plant samples per field varied from 12 to 24, depending on the crop growth stage and condition. Sample sites were randomly selected along the field diagonals at intervals of 50-60 m, resulting in statistically independent samples (Kleschenko, 1986). Each sample was 0.25 m 2 in area (0.50 m x 0.50 m frame). The crop phytometric features to be measured were the above-ground dry phytomass (DM), plant height (PH), plant density (PD), and percent plant cover (PC). The above-ground phytomass was obtained as dry weight of green above-ground plant parts per unit area of soil surface (g / m2). The measurement procedure consisted in cutting the aerial parts of all plants in the registration plot and oven drying them at 70-80°C until constant weight was reached with subsequent recalculation on a per square meter basis. Canopy height was determined on 10 plants in each plot as an average distance (in cm) from the soil surface to the canopy top. Plant density here is the number of plant stems per square meter. It was determined by counting the number of plant stems in 0.5 m segments of two adjacent rows in a frame and multiplying by the number of rows per meter.

Spectral-PhytometricRelationships of Wheat 3

.

40

Percent plant cover was determined by visual estimation from aboard the air-craft by two to three observers simultaneously which resulted in a more objective estimation. Canonical correlation was run on personal computer system using the SAS CANCORR procedure (SAS Institute, 1988).

30

4//

RESULTS AND DISCUSSION In general, the resulting reflectance spectra of winter wheat fields (Fig. 1) agree well with current understanding of optical properties of the "normal" or "average" green leaf (Bunnik, 1978; Vygodskaya and Gorshkova, 1987). Most plots clearly showed visible and near-infrared (NIR) regions, reflectance extrema (maxima and minima), and spectrum amplitude dependent on crop growth stage. To complete the picture, Figure 1 also shows the reflectance curves during flowering and wax-ripeness stages when corresponding phytometric measurements were not taken. The blue minimum of reflectance in the visible region of the spectrum is located within the 470-490 nm range, and the red, within the 660670 nm (at flowering it is somewhat stretched, occupying the region of 640-680 nm). In mature crops, this minimum disappears following complete chlorophyll degradation. The relative green maximum of reflectance resulting from incomplete overlapping of individual absorption bands is the most clear-cut and positionally stable (550 nm) peak in the visible region. It disappeared upon complete yellowing of the crop at the waxripeness stage. These extrema are constantly changing in value during the season: Visible reflectance is rather synchronously declining from the booting till flowering and, then, with the onset of canopy senescence, begins to increase, with the reflectance factor at 670 nm in the milky stage exceeding that at booting. The reflectance spectrum of wax-ripe wheat is practically a monotonically increasing function. Analyzing reflectance in the NIR region, it should be first noted that the term "NIR-plateau" frequently used to describe vegetation reflectance spectrum between 750 nm and 1200 nm (Bauer, 1985; Vygodskaya and Gorshkova, 1987) is, in this case, somewhat arbitrary, since, upon reaching the long-wavelength border of the red edge (Hor-

'S 820 C

.2

20

Q)

10

~l~6

1 1 1 l ] l l l l l l l l l l l l l l l L I I t l [ q l l l l l l l J l t l l

600

800 wavelength, nm

1000

1200

Figure 1. Reflectance spectra of winter wheat fields at

different growth stages acquired with airborn speetroradiometer: 1-5) booting, heading, flowering, milky, and wax ripeness stages, respectively; 6) spectral reflectance of bare soil (black fallow, ordinary and carbonate chernosemz). In the inset: visible region of the spectrum at fivefold magnification.

ler et al., 1983), the reflectance keeps increasing smoothly up to a maximum value observed at about 1070 nm. This increase is interrupted by water absorption bands forming a deep double minimum within the 940-960 nm range. The observed slope, which is unusual for the NIR reflectance of single leaves, was probably due to the effect of soil, whose spectral reflectance curve averaged over survey time is also shown in Figure 1. The soil reflectance resulting from gaps in the canopy as well as from light transmission by the canopy itself (Roberts et al., 1990) seems to be superimposed on the vegetation reflectance to produce the slope of the curve. This is indicated by the fact that the slope remains practically unchanged despite seasonal fluctuations in the absolute value of the NIR reflectance and the proportion of bare soil falling within the field of

4 Korobov and Railyan

Table 1. Means (~) and Standard Deviations (s) of the Crop Parameters ghenophase Booting Parameter

~

Heading s

£

Milky Ripeness s

Yc

s

Spectral (%) b4so

1.91

0.80

1.83

0.48

2.01

0.47

b55o

4.19

1.09

3.50

0.64

3.65

0.48

b67o

2.34

1.07

2.24

0.88

2.93

0.64

bsso

31.62

7.19

28.80

5.53

18.30

3.56

Phytometric Dry phytomass

( g / m z)

Plant height (em) P l a n t d e n s i t y ( n o . / m 2) Percent

cover (%)

927.2

442.5

1012,5

407.0

1521.9

57.1

9.7

70.0

14,3

78.8

15.7

1863.5

591.4

1317.7

528.1

783.3

208.3

71.1

26.7

69.9

23.7

71.1

23.2

view of the instrument. Characteristically, a similar slope is also observed in the visible region at the wax-ripeness stage when light absorption terminates following complete pigment degradation. Given the fact that our coordinates for the bx extrema agree well with the locations of the spectrum regions most informative in green vegetation studies (Bunnik, 1978), subsequent canonical analyses use the values of b× at wavelengths X=480 nm, 550 nm, 670 nm, and 860 nm [or, more precisely, in the narrow (10 nm) spectral intervals in which the extrema occur] as the spectral variables representing blue, green, red, and NIR bands, respectively. Swain and Davis (1978) showed that an adequate representation of a multidimensional spectral space of vegetated scenes is usually provided by a certain optimum set of Table 2.

Correlations

among

the

Original

b4~0

1.000

bs~ll

b,5,5o

Heading

b67o 0.968

- 0.639

1.000

0.876

- 0.453

1.000

- 0.775

bs,~o

DM

Milky Ripeness

b4~o

bsso

b67o

bs6o

b4~o

b5.5o

1.000

0.919 1,000

0,931

- 0.771

1,000

0.478

0.726

0.936

- 0.752

1.000

0.498

0.291

1.000

- 0.890

1.000

- 0.646

1.000

DM

PN

1.000

0.677 1.000

1.000

0.814 1.000

Ptt PD PC

b~so

bs6o

0.941

bfiT0

spectral data ("intrinsic dimensionality'), and that the use of more than four bands does not, as a rule, translate into a higher information level of the survey. Mean values ofbx for the selected wavelengths as well as phytometric parameters of winter wheat fields are listed in Table 1. As expected from the nature of "light-plant organ" interactions (Allen and Richardson, 1968; Knipling, 1970), there is a positive correlation between phytometric variables of crops and their reflectance values in the NIR region; the corresponding correlation in the visible region is negative (Table 2). However, it is impossible to provide a unique assessment of the degree of this correlation since it depends on a number of factors such as region of the spectrum, type of phytometric feature, and plant growth stage. The correlation

Variables

Booting b4so

PD

569.4

b~7o

1.000

b~so - 0.290

l.O00

PC

DM

PH

PD

PC

DM

PH

PD

PC

0.819

0.943

1.000

0.798

0.826

0.823

1.000

0.792

0.916

0.836

0.432

0.737

1.000

0.504

0.802

1.000

0.819

0.797

1.000

0.699 1.000

1,000

0.761 1.000

DM

PN

PD

PC

DM

PH

PD

PC

DM

PII

PD

PC

- 0.729

- 0.505

- 0.,567

- 0.734

- 0.713

- 0.742

- 0.593

- 0.310

- 0.461

- 0.179

- 0.416

- (I.497

t)zz~

- 0.572

- 0.294

- 0.450

- 0.568

- 0.756

- 0.675

- 0.647

- 0.784

- 0.034

- O. 13(}

- 0.082

- 0.250

t;~7o

- 0.828

- 0.578

- 0.684

- 0.857

- 0.825

- 0.780

- 0.676

- 0.896

- (}.602

- 0.366

- 0.634

- 0.672

b~o

0.930

0.717

0.830

0.946

0.835

0.744

0.678

0.935

0.666

0.615

0.791

0.594

Spectral-Phytometric Relationships of Wheat 5

and linear combination coefficients as the canonical coefficients or canonical weights. The subsequent analysis consists in generating ( q - 1) additional pairs of linear combinations (where q is the number of variables in the smaller set) selected in such a way as to maximize the correlation between them at this step, with each estimated canonical variable showing correlation with no other variable except its counterpart in the opposite set. Geometrically, this is essentially a transformation of a multidimensional space of original variables into a q-space of canonical variables. The first canonical correlation (Table 3) is higher than any between-set correlation, indicating a very strong relationship between the two sets of original variables, describing, on the one hand, the spectral image of the field and, on the other, its condition expressed by traditional phytometric features. Besides, it is statistically significant. The hypothesis that the first canonical correlation and all of the smaller correlations within the population are equal to zero tested using an F-approximation (SAS Institute, 1988) is rejected under Pr > F being less than 0.001, 0.01, and 0.05 at booting, heading, and milky ripeness, respectively. As with simple pairwise correlation, the first canonical correlation becomes weaker with the crop development: Its contribution to the total information contained in the overall canonical correlation reduces from a very high value (96.2%) in the early season to 77.2% in the milky-ripeness stage. The data in Table 3 are well illustrated by the

coefficients (r) are largest for NIR reflectance, somewhat less for the red, and considerably less for the blue and green reflectances. Among the phytometric variables, percent plant cover and above-ground dry phytomass are, on the whole, better correlated with spectral refectance while plant height and plant density are less well correlated to it. A maximum correlation between the NIR reflectance and phytometric variables occurs during the booting stage with subsequent decrease, for the majority of phytometric variables, by the end of the growing season. In the visible region maximum r is, on the whole, shifted into the heading stage. Certain pairs of correlates show some deviation from the general trend, thereby complicating the situation. The observed high within-set correlation between variables (a feature not to be ignored in multivariate analysis) also makes the canonical procedure attractive. Before considering the canonical correlation, let us briefly recall its meaning (Cooley and Lohnes, 1971). In general, it is a technique for analyzing the relation between two sets of variables. Simple and multiple correlations, when one or both sets contain a single variable each, can be regarded as specific cases of canonical correlation. The procedure reduces to finding a linear combination within each set that maximizes the correlation between the two sets. Combinations obtained in the first step of the procedure are referred to as the first canonical variables, the correlation between them as the first canonical correlation, Table 3.

C a n o n i c a l C o r r e l a t i o n Analysis

Canonical Correlation

Standard Error

0.974 0.592 0.359 0.242

0.012 0.158 0.211 0.288

0.958 0.519 0.235 0.116

0.021 0.183 0.236 0.247

0.878 0.621 0.495 0.210

0.055 0.149 0.183 0.232

Eigenvalue

Proportion

Pr > F

0.962 0.028 0.007 0.003

0.000 0.552 0.649 0.385

0.962 0.032 0.005 0.001

0.009 0.883 0.937 0.692

0.772 0.143 0.074 0.011

0.031 0.342 0.395 0.452

Booting 18.749 0.539 0.148 0.062

Heading 11.142 0.369 0.059 0.014

Milky Ripeness 3.378 0.627 0.325 0.046

6 Korobovand Railyan

0")

booting

k_

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1o

o El._ 0

2 °-3

I

I

I

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._c Ck

I heading

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milky ripeness

>

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Canonical varioble for- reflectance First canonical variables for reflectance spectra versus first canonical variables for phytometric parameters of wheat fields. F i g u r e 2.

plot of the relationship of variance-standardized first canonical variables for spectral and for phytometric parameters (Fig. 2). This relationship is linear with a narrow scatter of points during the

first two phenophases, especially for excellent and good fields (the top right portion of the plot), and with a broader scatter and an obvious intercept by the end of the growing season. The remaining canonical correlations are not worthy of consideration due to their large P-values and insignificant contribution to the total information. This conclusion is supported by canonical redundancy analysis examining how well the original variables can be predicted from the canonical ones. Indeed, if we consider the proportion of variance of the crop spectral features, explained by the canonical variables (Table 4), we shall see, that for green canopy the first canonical variable explains 94-97% of the overall nonstandardized (raw) variance. In other words, almost the entire body of information is clustered along a single space vector, with the remaining three pairs of canonical variables contributing virtually nothing. It is as late as in the milky-ripeness stage, with the onset of intensive leaf yellowing, that these correlations explain about 30% of the variance. The space structure of phytometric variables appears to be of higher dimensionality, but even in this case the first canonical variable accounts for as much as 80 % of the overall variance at booting. Therefore, we shall largely deal with the first canonical correlation. It is extremely important, in terms of remote sensing, that canonical correlation for spectral variables accounts for about three-fourths of the variance in phytometric variables during the most informative growth stages, indicating that potentially it is a good predictor of traditional crop features. The first canonical correlation for phytometric variables at their maximum values explains, in its turn, nearly 90% of the raw variance in spectral variables. The contribution of each original variable to the overall correlation can be inferred from their canonical weights or coefficients in linear combinations representing canonical variables. The information on the absolute size of contribution is provided by nonstandardized coefficients and that on the relative contribution, which is more important for interpreting the results, by the standardized ones (zero means and unity variances of original variables; unity variance of canonical variables). The data in Table 5 clearly indicate that throughout the recording period the largest con-

Spectral-Phytometric Relationships of Wheat 7

Table 4. The Proportion of Variance" of the Winter Wheat Field Parameters explained by Their Own and the Opposite Canonical Variables Spectral Variable

Phytometric

Variable

The Variance Explained by Canonical Variables Own

Opposite

Own

Canonical Variable

o~

o~

~

~

1 2 3 4

0.940 0.015 0.004 0.041

0.659 0.024 0.027 0.289

0.892 0.005 0.001 0.002

0.626 0.008 0.004 0.017

1 2 3 4

0.973 0.002 0.024 0.002

0.815 0.048 0.107 0.030

0.892 0.001 0.001 0.000

0.748 0.013 0.006 0.000

1 2 3 4

0.705 0.283 0.001 0.011

0.532 0.362 0.020 0.087

0.544 0.109 0.000 0.000

0.410 0.139 0.005 0.004

a

Opposite ~

o~

0.793 0.063 0.094 0.050

0.757 0.003 0.009 0.007

0.753 0.022 0.012 0.003

0.735 0.069 0.12l 0.076

0.580 0.006 0.012 0.002

0.674 0.018 0.007 0.001

0.602 0.141 0.185 0.072

0.505 0.028 0.014 0.009

0.464 0.054 0.045 0.003

Booting 0.798 0.008 0.072 0.122

Heading 0.632 0.024 0.210 0.134

Milky Ripeness

" o, = row, o, =

0.655 0.073 0.059 0.213

standardized variance.

tribution to the first canonical variable of spectral reflectance is made by the NIR and red regions, especially in the case of green canopy. In the booting stage, their weights exceed that of the blue region 2- and 2.5-fold, respectively, with the green region effect almost completely lacking. At heading, the weight of the green reflectance is comparable to that of the red region; their net effect is, however, nearly 2.5-fold lower than in the NIR region. At milky ripeness, the red and NIR reflectance weights are again 2- and 2.5 times, respectively, as high as that of the blue

region. As far as phytoparameters are concerned, percent plant cover and above ground dry phytomass are the variables that have the highest weights in the first two phenophases. At milky ripeness, it is plant density that exhibits the highest weight. At the same time, it should be noted that signs of canonical coefficients and of correlations between canonical and original variables do not always coincide. At booting, for example, coefficients for b480 and bs~o are positive whereas the correlation is negative. At heading, canonical co-

Table 5. The Canonical Coefficients and Correlation between the Original Variables and the First Canonical Variables (Structure Coefficients) Booting

Original Variable b4s0 bss0 b670 bs60 Dry phytomass

Plant height Plant density Percent cover

Canonical Coefficients StanRaw dardized

Heading Structure Coefficients

Own

Opposite

0.359 0.048 -0.639 0.084

0.299 0.054 -0.718 0.640

-0.753 -0.583 -0.877 0.980

-0.734 -0.568 -0.854 0.955

0.000 0.003 0.000 0.027

0.197 0.026 0.090 0.710

0.965 0.725 0.850 0.996

0.941 0.706 0.828 0.970

Canonical Coefficients StanRaw dardized

Milky Ripeness Structure Coefficients

Own

Opposite

Canonical Coefficients StanRaw dardized

Structure Coefficients Own

Opposite

0.095 -0.202 -0.195 0.131

0.047 -0.134 -0.180 0.766

-0.833 -0.834 -0.943 0.990

-0.793 -0.799 -0.903 0.948

-0.395 -0.162 -0.624 0.145

-0.193 -0.078 -0.412 0.546

-0.688 -0.217 -0.944 0.845

-0.604 -0.191 -0.829 0.742

0.001 -0.013 -0.0003 0.036

0.459 -0.181 -0.164 0.866

0.893 0.798 0.730 0.985

0.856 0.765 0.699 0.944

-0.001 -0.051 0.007 0.037

-0.546 -0.795 1.362 0.870

0.800 0.582 0.873 0.816

0.703 0.511 0.767 0.717

8 Korobov and Railyan

Table 6. Coefficients of D e t e r m i n a t i o n (R 2) b e t w e e n t h e Original Variables a n d t h e Canonical Variables defining t h e O p p o s i t e Set of F e a t u r e s Booting Original Variables

1

2

Heading 3

4

1

Canonical Variable 2 3

Milky Ripeness 4

1

2

3

4

n 2

b4s0 b~50 b670 b86o

0.539 0.323 0.730 0.913

0,540 0.343 0.738 0.918

0.541 0.356 0.738 0.918

0.566 0.385 0.750 0.919

0.637 0,639 0.816 0.900

0.680 - 0.640 0.823 0.900

0.684 0.653 0.828 0.901

0.685 0.654 0,828 0.901

0.365 0.036 0.687 0.551

0.453 0.363 0.723 0,659

0.454 0.382 0.723 0.659

0,467 0.383 0,724 0.660

Dry phytomass Plant height Plant density Percent cover

0.885 0.499 0.686 0.941

0.891 0.580 0,686 0.942

0.896 0.611 0.698 0.943

0,896 0.611 0.709 0.943

0.732 0.585 0.489 0.891

0.736 0.642 0.497 0.895

0.746 0.646 0.510 0.895

0,746 0.648 0.512 0.896

0.494 0.261 0.588 0.514

0,516 0,381 0,664 0,514

0.532 0.465 0.665 0.594

0.543 0.465 0.667 0.549

efficients for plant height and plant density are negative, the correlations being positive. Original variables like these are generally viewed as suppressor variables, that is, as variables whose contributions partially "suppress" contributions of other variables highly correlated with them (SAS Institute, 1988). Given a high within-set correlation among bx values in various bands of the visible region as well as between individual phytometric variables, the observed suppression effect is not unexpected. The multicolinearity of the original matrices results in the contribution of some variables being partially suppressed by the opposing contribution from others when considering their effects simultaneously. Therefore, the canonical coefficients of these suppressor variables can be lower when the whole set of original variables is considered than when they are considered independently. As an illustration, consider the first canonical variable for spectral reflectance. It assumes a more familir form, that of the weighted difference between the NIR and visible reflectances, only as late as at milky ripeness when cross correlation between spectral variables becomes weaker. The large negative contribution of the red reflectance at booting is partially suppressed by the positive contribution of the blue and green reflectances highly correlated with it at this stage. The suppression effect is a serious limitation in assessing the actual significance of the parameters in question from their canonical coefficients; therefore, the coefficients of correlation between original and canonical variables or so-called coefficients of structure, mentioned earlier, seem to provide more objective criteria for the above

assessment. Furthermore, coefficients of structure provide correlations both with their "own" canonical variables and with the opposite ones. This is of particular interest for the present study. The NIR and red reflectances are the variables showing the highest correlation with the first canonical variable. The coefficients of correlation are 0.980 at booting, 0.990 at heading, and 0.845 at milky ripeness for NIR, and -0.877, -0.943, and -0.944 for red, respectively. The coefficients of structure for the blue and green reflectances are somewhat lower in absolute value. However, they are greater than the weights of these reflectances as determined by the canonical coefficients. The NIR and red reflectances also exhibit higher correlations with the first canonical variable for phytometric features, thus numerically illustrating an a priori known thesis that plant canopy variations are more pronounced in these regions. By incorporating in the statistical model not only the first but also the subsequent variables, multiple correlation between the original variables and the opposite canonical variables can be obtained. Squares of this correlation (coefficients of determination, R2) at the number of canonical variables ranging from 1 to 4 are listed in Table 6 and can be regarded as a proportion of the overall variation in one original variable set explained by the other set. Consider, first, R2 in terms of the "direct objective" of remote sensing, that is, identifying factors underlying the formation of the spectral image of the object. As is seen from Table 6, the proportion of overall variation in spectral reflectance, explained

Spectral-Phytometric Relationships of Wheat 9

by the crop physiological and agronomic condition, reaches its maximum value for the NIR reflectance at booting (91.9%), gradually decreasing to 66.0% at milky ripeness. In the red region, the maximum is reached at heading (82.8%), being 7"2-75% at the other growth stages. The blue and green reflectances also have maximum values of R2 (68.5 % and 65.4 %, respectively) at heading. Consider now the canonical structure of phytometric variables. The correlation between percent plant cover and the first canonical variable is 0.996 at booting, 0.985 at heading, and 0.816 at milky ripeness; for dry above-ground phytomass, it is 0.965, 0.893, and 0.800, respectively (Table 5). A moderately high correlation is also characteristic of the other two variables. However, it is the relationship between phytometric features and canonical variables for reflectance spectrum that is more important. In this case the degree of relationship is just as high (Table 6). Thus, about 94.3% of the overall variance in percent cover and 89.6% of that in dry aboveground phytomass can be explained by spectral variables at the most informative growth stages. Spectral reflectance is a considerably worse indicator of variation in plant height and plant density.

SUMMARY AND CONCLUSIONS

1. Aircraft spectrometry of winter wheat crops in narrow spectral bands confirms the high degree of relationship between spectral and phytometric variables of green winter wheat canopies. Maximum canonical correlation between the two types of variables (0.974) occurs at booting, gradually declining with crop maturation. 2. The information contained in canonical variables for the spectral reflectance of the green winter wheat canopy explains nearly 3 / 4 of the crop phytometric variance; the first canonical variable accounts for as much as 90% of the spectral variance. 3. The NIR and red reflectances show the greatest contributions to canonical variables as well as the highest correlations with phytometric features of winter wheat in commercial fields. Among the phytometric variables, percent plant cover and dry above-ground phytomass are more readily

identifiable from spectral reflectance data than are plant height and plant density. A logical completion of the above interpretation would be to perform a multiple regression analysis and to derive equations relating each variable to the opposite set of variables. However, we are at this point interested not so much in finding specific mathematical expressions relating spectral variables to phytometric ones as in estimating the total potential information contained in one set compared with that in the other set of variables. Canonical correlation provides a fairly successful solution to the problem. The authors are deeply grateful to Dr. O. A. Voinov for organizing and supervising the field surveys pertaining to this study. We also wish to thank Mr. G. K. Lakhman for his invaluable assistance in preparing the English version of the manuscript.

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