The objective of this paper was to determine hyperspectral narrow-wavebands that are best suited for estimating agricultural crop biophysical characteristics. The data for this study comes from ground level reflectivity measurements of cotton, potato, soybeans, corn, and sunflower. Hyperspectral reflectivity was measured in 1.43-nanometer-wide 490-discrete narrow-wavebands (or channels) between 350 and 1050 nanometers. Observed crop characteristics included wet biomass, leaf area index, plant height, and for cotton only, yield.

Four types of hyperspectral predictors were tested and compared with the well known broad-waveband Thematic Mapper NDVI. The hyperspectral predictors were: Optimum multiple narrow-waveband reflectivity (OMNBR), Derivative vegetation indices, Narrow-waveband NDVI involving all possible 2-band combinations of 490 channels, and the soil adjusted vegetation indices. A critical problem with OMNBR models was that of "over fitting" (e.g., the likelihood of using more spectral channels than experimental samples to obtain a perfect R² value). This problem was overcome by comparing the R² values of crop variables with the R² values computed for random data of a large sample size. The combinations of 2 to 4 narrow-wavebands in OMNBR models explained most (64 to 92 percent) of the variability in crop biophysical variables.

The second part of the paper describes a rigorous search procedure to identify the best narrow-waveband NDVI models of crop biophysical variables. Special narrow-waveband lambda (l ₁) versus lambda (l ₂) plots of R² values illustrate the most effective wavelength combinations (l ₁ and l ₂) and waveband widths (D l ₁ and D l ₂) for predicting the biophysical quantities of each crop. The best of these two-waveband indices were further tested to see if soil adjustment or non-linear fitting can improve their predictive accuracy. The best of the narrow-waveband NDVI models explained 64 to 88 percent variability in different crop biophysical variables.

A remarkable cluster of information is located in specific narrow-wavebands in the later portion of red , 0.650 to 0.700 m m, with primary or secondary clusters in early portion of green, 0.500 to 0.550 m m, in one particular section of the near-infrared, 0.900 to 0.940 m m, and in the moisture sensitive near-infrared, centered at 0.975 m m. The study lead to the recommendation of 12 narrow-wavebands along with their waveband-widths, in the visible and NIR portion of the spectrum, as optimal number of wavebands required for extracting agricultural crop biophysical information. The waveband centers and the waveband widths for this "new" sensor are: l ₁ = 0.495 m m (D l ₁ = 0.030 m m), l ₂ = 0.525 m m (D l ₂ = 0.020 m m), l ₃ = 0.550 m m (D l ₃ = 0.020 m m), l ₄ = 0.568 m m (D l ₄ = 0.010 m m), l ₅ = 0.668 m m (D l ₅ = 0.004 m m), l ₆ = 0.682 m m (D l ₆ = 0.004 m m), l ₇ = 0.696 m m (D l ₇ = 0.004 m m), l ₈ = 0.720 m m (D l ₈ = 0.010 m m), l ₉ = 0.845 m m (D l ₉ = 0.070 m m), l ₁₀ = 0.920 m m (D l ₁₀ = 0.020 m m), l ₁₁ = 0.982 m m (D l ₁₁ = 0.030 m m), and l ₁₂ = 1.025 m m (D l ₁₂ = 0.010 m m).

Spectral data from the current generation of Earth orbiting satellites carrying broad-waveband sensors such as Landsat Thematic Mapper (TM), Le Syste¢ me pour l'observation de la terre (SPOT) high resolution visible (HRV), and the Indian Remote Sensing (IRS) Linear Imaging Self-Scanning (LISS) have limitations in providing accurate estimates of biophysical characteristics of agricultural crops (Fassnacht et al., 1997; Thenkabail et al. 1995; Weigand et al. 1991; Weigand and Richardson, 1990), vegetation (Friedl et al., 1994; Moran et al., 1995), and in establishing other quantitative terrestrial ecosystem characteristics (Moran et al., 1994; Running, 1989). This motivated the inclusion of hyperspectral narrow-waveband sensors onboard the new generation of satellites planned for launch by the United States private industry and by various Governments by the year 2000 (e.g., see ASPRS, 1998, Stoney and Hughes, 1998). The upcoming narrow-waveband hyperspectral sensors include High Resolution Imaging Spectrometer (HIRIS) with 192 spectral bands in 0.4-2.5 m m onboard the National Atmospheric and Space Administration (NASA) Earth Observing System (EOS), Moderate resolution imaging spectrometer (MODIS) with 36 channels (with 10 in visible, 6 in short-wave infrared or middle infrared, 5 in thermal infrared, and the rest beyond) onboard EOS AM-1, and Australian Resource Information Environmental Satellite (ARIES), and ORBVIEW-4 (a United States private industry satellite).

Increased accuracy's in estimations of quantitative biophysical characteristics of crops, and vegetation using data from hyperspectral narrow-wavebands, when compared with the data from the broad-wavebands of the present generation of satellites, have been demonstrated in some recent studies. Hyperspectral studies were conducted using data gathered from field spectroradiometers (Carter, 1998; Elvidge and Chen, 1995; Shibayama and Akiyama, 1991; Curran, 1990), Compact Airborne Spectrographic Imager (CASI, see Gong et al. 1995), and the NASA designed Airborne Visible-infrared Imaging spectrometer (AVIRIS, see Elvidge and Mouat, 1989). These studies were conducted for rice yield (Shibayama and Akiyama, 1991), chlorophyll content of slash pine (Curran, 1990), coniferous forest LAI (Gong et al., 1995), pinyon pine canopy LAI (Elvidge and Chen, 1995), and photosynthesis and stomatal conductance in pine canopies (Carter, 1998). The vegetation indices used in these studies were: narrow-waveband versions of the broad-waveband NIR and red based indices and/or derivative indices along the chlorophyll red-edge, and/or multiple linear regression indices. This study will use a more comprehensive approach that will involve 5 agricultural crops, 3 to 4 crop variables for each crop, and four distinct groups of hyperspectral narrow-waveband vegetation indices derived from a 512-waveband field spectroradiometer. Hyperspectral data contain large amounts of redundant information for any given application. This will require determining the optimum number of wavebands, waveband centers, and waveband widths required to maximize information. The effort should lead to identifying wavebands that are most critical to a particular application, and in eliminating the need to gather and transmit data from a huge number of hyperspectral wavebands by designing an sensor with optimum number of wavebands.

In the past three decades, spectrally derived broad-waveband vegetation indices (VIs) have been widely used to quantify crop variables such as wet biomass (WBM), leaf area index (LAI), plant height (PLNTHT), and grain yield (YLD) (see for example, Weigand et al., 1992; Thenkabail et al., 1995). These relationships are mostly regional in nature as a result of variations in climate, soils, cultivars, cultural practices, management variables, and technological inputs. Further the relationships are dependent on sensor characteristics. Recent literature (for example, Blackburn, 1998; Shibayama and Akiyama, 1991; Elvidge and Mouat, 1989) has shown that the narrow-wavebands may be crucial for providing additional information with significant improvements over broad-waveband indices in quantifying biophysical characteristics of agricultural crops. Spectral vegetation indices that have evolved over the years perform one or a combination of tasks in normalizing for solar elimination, correcting for soil background reflectance, reducing atmospheric haze effects, and use data from distinct spectral wavebands. The most common of these indices are based on the absorption of the incident light in the red (red for Thematic Mapper-TM band 3: 0.630 to 0.690 m m) and the contrasting reflectance of the incident light in the near-infrared (NIR for TM band 4: 0.760 to 0.900 m m) by green vegetation leading to computation of Landsat TM broad-waveband normalized difference vegetation index (broad-waveband NDVI) (group 1 index, Table1). This distinct characteristic behavior in two wavebands were used to develop simple yet powerful vegetation indices that have been found very useful in quantitative estimation of crop variables such as biomass, leaf area index, plant height, and grain yield by numerous authors (see for example, Tucker, 1979; Wiegand et al., 1991). However, the NIR and red based indices have pronounced soil background influences at low vegetation cover (Elvidge and Lyon, 1985, Huete et al., 1985). These factors lead to development of soil adjusted vegetation indices (see group 4 indices in Table1; Huete, 1988). Soil adjusted vegetation indices and its numerous modifications (see Qi et al., 1994; Rondeaux, 1996) reduce the effects of soil background but are dependent on a soil line which varies based on soil characteristics such as color, texture, and organic content. Where human activity like cultivation of crops are involved further alteration of soil characteristics results from the application of fertilizer, irrigation, tillage and drainage. Recently Rondeaux et al. (1996) conducted experiments that provided an optimal value for the "Xfactor" in soil adjusted vegetation indices (SAVI) as 0.16 leading to a new index called OSAVI. The transformed soil-adjusted indices (TSAVI's) (see group 2 index in Table1) uses slopes and intercepts of the specific soil line of the study area (Baret et al. 1989) and can normally be expected to perform better than "universally" adjusted SAVI and OSAVI (Lawrence and Ripple, 1998). The literature (e.g., Curran and Williamson, 1986; Richardson et al., 1992, and other mentioned in this section) has shown strong relationships between these spectral vegetation indices and the crop variables. These studies have also indicated that the relationships are site (or region) and time dependent. However, the above discussed indices use average spectral information over broad-waveband widths (e.g., TM band 3 or red:0.63-0.69 m m, and TM band 4 or NIR:0.76-0.90 m m) resulting in loss of critical information available in specific narrow-wavebands with or without adjustments for soil background effects. Also, all the above discussed indices obtain information only from the red and NIR wavebands. This calls for an investigation in use of vegetation indices computed using wavebands other than NIR and red. Thereby, in this paper an exhaustive evaluation of all possible combinations of hyperspectral narrow-waveband normalized difference vegetation indices (narrow-waveband NDVI's; group 3 indices in Table1) were proposed and their relationships with crop biophysical variables evaluated and compared with broad-waveband and other narrow-waveband indices.

All the above indices involve two-wavebands. According to (Lawrence and Ripple 1998; Gong, 1995) the use of two-waveband vegetation indices unnecessarily constrain the regression analysis. They argue that if a study requires knowledge of an ecological variable of interest (e.g., above-ground biomass or LAI) the researchers must ultimately analyze the relationship between the spectral index used and ecological variable, generally through a regression analysis. Piece-wise multiple regression models (Gong, 1995; Shibayama and Akiyama, 1991) performed on discrete narrow-wavebands provide flexibility in choosing the wavebands that provide maximum information at a given period of crop growth. As the conditions vary in the field, different waveband combinations combine to explain variability in crop growth and yield variables which are otherwise difficult to account for (Shibayama and Akiyama, 1991; 1993). Crop variable data is dependant on a complex set of factors such as crop types, cultivar types, plant density, background reflectance (e.g., soils, weeds), atmospheric effects (e.g., clouds, aerosols), management variables (e.g., drainage, tillage), biochemical composition (e.g., leaf water, chlorophyll), canopy architecture, climatic conditions, and irrigation practice. Practically it is quite infeasible or atleast very expensive to account for variability for all these different variables. However, with the availability of narrow-waveband continuous spectra there is a likelihood through multiple regression to minimize variability of crop growth and yield models (and to maximize R² values). Ripple (1994), and Lawrence and Ripple (1998) studies demonstrated multiple linear regressions to explain greater variability than using NDVI based linear or curvilinear relationships with ecological variables. Thereby, in this study optimum multiple narrow-waveband reflectivity (OMNBR's, group 2 indices in Table1) regression models of crop biophysical variables were established and their performance compared with the broad-waveband NDVI's and narrow-waveband NDVI's computed using two-waveband data.

Also of particular interest in assessing the sensitivity of crop and vegetation biophysical variables when hyperspectral data is available will be the chlorophyll red-edge (0.700-0.780 m m) portion of the spectrum. This waveband portion has the greatest change in reflectance per unit change in wavelength of any green leaf spectral feature in visible and NIR wavebands (Elvidge and Chen, 1995). The derivative indices are expected to perform better than broad-waveband indices in estimating biophysical variables such as LAI (Hall et al., 1990, Demetriades-Shah et al., 1990, and Elvidge and Chen, 1995). Higher red-edge amplitude for the plant canopy over bright backgrounds and a lower red-edge amplitudes for canopies underlain by the dark backgrounds result in non-linear mixing (Elvidge and Chen, 1995). These phenomenon lead to the development of derivative green vegetation indices (DGVI's, group 5 indices in Table1).

Crop variables that are most commonly used in relationships with spectral indices are leaf area index (LAI), wet biomass (WBM), grain yield (YLD), and to a lesser extent plant height (PLNTHT). LAI is known to be one of the first plant responses to stress because it is structurally more specific variable of plant community (Bartlett et al., 1988), directly related to exchange of energy, CO_2, and mass from plant canopies (Fassnacht et al., 1997), determines the amount of light intercepted, and known to be sensitive to the leaf cell enlargement to water deficit (Weigand and Richardson, 1990; Shibayama et al. 1993). LAI is used as input in computing evapotranspiration (for example, decrease in LAI is indicative of decrease in evapotranspiration), and is used in crop reflectance modeling (Clevers et al., 1994, Verhoef, 1984). Characterization of vegetation in terms of LAI rather than species composition was considered a critical simplification for comparison of different terrestrial ecosystems world-wide (Running, 1989). However, there is strong correlation across biome types relating LAI to net primary productivity (Running, 1989; Gholz,1982). Biomass (WBM or DBM), and plant height (PLNTHT), are excellent indicators of crop growth, condition, and their yield potential. WBM of crops have shown better relationship with spectral data than LAI (e.g., Thenkabail et al., 1994). Biomass is also an excellent indicator of leaf or crop moisture (Penuelas, 1993). The YLD is generally the most sought after crop information. However yield and plant height are generally far less predictable using spectral data compared to LAI and WBM (see for example, Thenkabail et al., 1995). As a result of the above importance and possibilities, spectral vegetation indices derived using ground-based, airborne, or spaceborne sensors are increasingly used for rapid quantitative characterization of crop biophysical variables such as biomass, leaf area index, plant height, and yield (see for example, Baret et al., 1989; Weigand et al., 1991, Weigand et al., 1992; Richardson et al., 1992; and Thenkabail et al., 1994). Such results are expected to facilitate powerful and more accurate means of quantifying agronomic variables (e.g., crop growth and yield) over large areas, help develop well understood spectro-biophysical functional relationships (e.g., Richardson et al., 1992), and make possible routine collection of basic data of terrestrial vegetation component of the biosphere from global to local scales.

The main goal of this research was to evaluate the performance of various types of hyperspectral vegetation indices in estimating agricultural crop biophysical variables. The spectral reflectivity data used in the study was gathered using a field spectroradiometer designed by the Analytical Spectral Devices^TM (Fieldspec, 1997). The hyperspectral narrow-waveband indices were computed by taking the 490 narrow-wavebands, each of 1.43 nanometer-wide, spread across 0.350 to 1.050 µm portion of the spectrum. Four distinct types of narrow-waveband vegetation index models of crop biophysical variables were involved. These were: piecewise multiple linear regression models involving narrow-waveband reflectivity, narrow-waveband normalized difference vegetation index (NDVI) models involving all possible 2-band combinations, transformed soil adjusted narrow-waveband index models, and the derivative green vegetation index models. The performance of these narrow-waveband models were compared with the Landsat Thematic Mapper broad-waveband NDVI models. The soil adjusted indices were computed for the best narrow-waveband NDVI indices. The derivative indices were computed by integrating near continuous discrete narrow-waveband spectra in 0.626 to 0.780 µm. The spectral and biophysical data were gathered for 5 crops (corn, cotton, potato, soybeans, corn, and sunflower) from the farmer managed, summer irrigated fields in the semi-arid environments of Syria. Agricultural crop biophysical variables modeled for each of these crops were LAI, biomass, plant height, and, for cotton only, yield.

The final goal was to recommend optimal number of hyperspectral wavebands (along with their waveband widths), in the visible and NIR portion of the spectrum (0.350-1.050 m m), required to best estimate agricultural crop biophysical variables.

The study area is around Aleppo, Syria. The central location is 36· 1^'27.5^" northern latitude and 36· 57^'22.5^" eastern longitude (about 35 kilometers Southwest of Aleppo). Measurements were taken in farm fields that surround this area with the points falling within the area encompassed by Upper left: 36· 26¢ 29.5836² northern latitude, 36· 35¢ 24.3816² eastern longitude; Lower right: 34· 57¢ 46.3428² northern latitude, 37· 43¢ 47.3736² eastern longitude.

Aleppo area is characterized by Mediterranean climate-hot and dry summers and cool and wet winters (annual rainfall varies from 300-350 mm). This climate pattern is generally common in 30-40 degree Northern latitude throughout the world. The largest single contiguous area experiencing this climate is in the Mediterranean basin covering parts of West Asia, North Africa, and Southern Europe. Many summer and winter crops in this climate are common with similar growing seasons and management practices. Hence a study conducted in such a representative area (Aleppo) has broader application across much of the other Mediterranean region falling within similar climatic, vegetation, and agricultural patterns. The overall study area had four soil types: very fine clayey chromic calcixerert (in Jindiress), very fine clayey calcixerollic xerochrept (Tel Hadya), clayey calcixerollic xerochrept (Breda), and clayey mixed thermic calcic gypsiorthid (Ghrerife) (Ryan et al., 1997).

In this paper spectral and biophysical data gathered for five summer (July-October) crops were used. During summer, 10-20 percent of the farms in the study area are cultivated by irrigation by either deep under ground wells (recharged by acquifers), or by canal irrigation from the Euphrates river. Otherwise most of cultivation is rainfed during spring (November-April).

Spectral data was obtained using a hand-held Spectroradiometer. Field data collection including hand-held Spectroradiometer measurements were made during 13-22 September, 1997 (summer season). The ground-truth data to correspond with Spectroradiometer data consisted of quantitative and qualitative measurements of crops and soils as described in section 3.2 and 3.3 below.

A 0.350 µm to 1.050 µm (0.3318-1.06395 µm to be precise) range spectroradiometer manufactured by Analytical Spectral Devices^TM (Fieldspec, 1997) was used to gather spectral data of crops and soils. Measuring data over 0.3318 m m through 1.06395 m m in discrete 1.43-nanometers (0.00143 m m) resulted in 512 channels or narrow-wavebands. Due to severe noise in data in the very early and late portions of the spectrum, only the data gathered in 0.350 m m through 1.050 m m was used reducing the number of spectral channels to 490. The waveband centers were rounded off to nearest whole number (e.g., 549.86 nanometers as 550 nanometers or 0.550 m m). Spectroradiometer unit consisted of a main spectrometer, a personal computer, fiber optic cable, a pistol grip, and different field of view (FOV) cones. Inside the spectrometer instrument light is projected from the fiber optics onto a holographic diffraction grating where wavelength components are separated and reflected for independent collection by the detector(s) (FieldSpec, 1997). Each detector converts incident photons into electrons that are stored, or integrated, until the detector is read out. At the read out time, the photoelectric current for each detector is converted to a voltage and is digitized by a 16-bit analog to digital (A/D) converter. This data is directly transferred to the computer main memory which is in turn available for further processing by the controlling software (FieldSpec, 1997). Gathering spectra at any given location involved optimizing the integration time (typically set at 17 milliseconds), providing foreoptic information, recording dark current, collecting white reference reflectance, and then obtaining target reflectance. The target reflectance is the ratio of energy reflected off the target (e.g., crops) to energy incident on the target (measured using a BaSO₄ white reference). Since the dark current varies with time and temperature it was gathered for each integration time (virtually for each new reading).

Reflectance=((target-dark current)/(reference-dark current))*100 percent.

Five major crops were identified for spectral and crop biophysical measurements. The major crops during this summer period were: cotton (Gossypium), potato (Solanum Erianthum), soybeans (Glycine max), corn (Zea mays), and sunflower (Helianthus). Since these farms were on four distinct soil zones, the characteristics of these soils were measured as well. Spectral data from Spectroradiometer and quantitative and qualitative data on crops, and on soils were obtained from 194 ground truth locations spread across the study area. These locations were: cotton (73 sample locations), potato (25), soybeans (27), corn (17), sunflower (9), and top soils (43) (see mean spectral plots of these measurements in Figure1). These were sufficiently large number of samples except for sunflower. Large sample sizes are necessary to adequately characterize the statistical properties of both ground and remotely sensed data even at localized scales (Friedl et al., 1994; Curran and Williamson, 1986). All crops except sunflower had 2 growth stages. The mean spectral plots of these growth stages are shown in Figure2a through 2d. The distinctive growth phases were (Figure2a through 2d): early vegetative (potato, soybeans), late vegetative (soybeans, corn), critical (cotton, soybeans, corn), and yielding/maturing (cotton).Illustrations of some of the typical growth stages are shown in Figure3a through 3f.

At each ground truth site, reflectance measurements were consistently taken with a nadir looking view, from a height of 1.2 meters for cotton, potato, and soybeans, using a 18 degree FOV. This resulted in viewing an area of 1134 cm². For corn, and sunflower the height was about 1.5 meters. Sample locations were chosen randomly by driving around the study area and stopping for measurements at various locations. At each farm an area of 1 m² that was considered representative portion of the farm (by eye observation of the growing conditions) was chosen for all measurements. At each site two to four sets of reflectance measurements, covering the entire 0.350-1.050 µm wavelength in 512 channels (each with 1.4 nm-wide narrow-wavebands) offered by the Spectroradiometer, were taken for one representative plant. The same plant sample above the ground was taken for laboratory analysis. Above ground plant height (mm), number of plants in 1 m² area, and number of rows were recorded. Observations were made on the crop growth stage, and crop condition. Where, farmers were available, planting dates were recorded that were used in conjunction with crop growth stages. A digital photograph was taken at each site to further supplement above quantitative and qualitative observations. Digital photographs provided valuable additional information on each site such as , for example, in identifying cotton fields that are nearing harvest versus those that are in critical/flowering stages (e.g., Figure3a and 3b). They also help in identifying gross mistakes, if any, in plant density calculations, and crop condition rating. Global Positioning System (GPS) location were noted in geographic co-ordinates (latitude/longitude in degree, minutes, seconds) and in universal transverse mercator (UTM in meters).

In the laboratory, plant samples were analyzed for leaf area (m²), wet weight (kilograms), and in case of cotton for yields (kg lint/ha). Leaf area was obtained by running the leaves over a LI-COR 3100 leaf area meter. The leaf area obtained from one representative plant is multiplied by the number of plants in one m² area to obtain leaf area index (m²/ m²). Plants were cut and weighed on a simple weighing machine. This weight was multiplied by number of plants in one m² to obtain biomass (kg/ m²). Leaf area index (LAI) and wet biomass (WBM), and plant height (PLNTHT) measurement were made for all crops-cotton, potato, soybeans, corn, and sunflower. Yield (YLD) was also obtained for cotton. For this cotton bolls were counted and converted to kilograms lint per hectare (kg lint/ha) using 600 bolls per one kg lint. Yields were not gathered for other crops.

Forty-three spectral measurements of soils were taken using the Spectroradiometer at the top soil. The soil types in the study area were (see Ryan 1997): very fine clayey Calcixerollic Xerochrept and Chromic Calcixerert (in Tel Hadya region), very fine clayey Chromic Calcixerert (Jindiress), and clayey Calcixerollic Xerochrept (Breda) and clayey mixed thermic calcic gypsiorthid (Ghrerife). The mean reflectance values obtained for these soils were plotted for: (a) Landsat TM broad-wavebands (red: 0.678-0.683 m m and near infrared NIR: 0.907-0.912 m m); and (b) various narrow-wavebands (see narrow-waveband widths for l ₁ and l ₂ for various indices in Table3). These are fitted using the equation of type: NIR=a * red + b. The slopes (a) and intercepts (b) obtained from the soil lines (see Table5) will be required for several soil adjusted vegetation indices (e.g., narrow-waveband TSAVI's).

Five types of spectral vegetation indices (Table1) were computed using the hyperspectral spectroradiometer data.. These index types were:

Computation procedure for each of these groups are discussed below.

The narrower-bands of TM and MSS improved relationships over broader bands from sensors such as AVHRR only slightly (Elvidge and Chen, 1995). In this paper, a preliminary sensitivity analysis had established that the vegetation indices computed for a wide range of currently existing satellite sensors such as Landsat MSS, Landsat TM, SPOT HRV, and IRS-1C were highly correlated (R² value=0.95 or higher) and hence computing vegetation index for any one of these sensors will suffice. Thereby, the only broad-waveband index computed and reported throughout this paper was broad-waveband NDVI (group 1 indices in Table1). For this the discrete 1.43-nm-wide narrow-waveband data obtained using the spectroradiometer were aggregated over the spectral wavebands 0.76 to 0.90 µm (for TM band 4) and 0.63 to 0.69 µm (for TM band 3) to obtain broad-waveband NDVI for each data point. Tassel cap green vegetation index (GVI) that involved first 4 TM bands has also been reported (GVI defined in the footnote of Table2). The GVI was computed by pooling all data points of crops and soils of the first 4 bands of Landsat TM derived from spectroradiometer data and computing the 4 dimensional coefficients of GVI through principal component analysis (Wheeler and Misra, 1976) using SAS algorithms (SAS, 1997a).

The optimum multiple narrow-waveband reflectivity, OMNBR (group 2 indices in Table1), were related to crop biophysical variables through multiple linear regression analysis. Dependent variable (B_i) in the model are crop variables and independent variables are reflectance's (R_j) in the 490 discrete-narrow-wavebands. The model equation is:

Of several statistical methods available to run piecewise linear regression models, the stepwise MAXR procedure is considered the best (SAS, 1997a) and hence used in this study. The MAXR method begins by finding the one variable model producing the highest coefficient of determination (R²) value (SAS, 1997a). Then another variable, the one that yields the greatest increase in R² value, is added. Once the two-variable model is obtained, each of the variables in the model are compared to each variable not in the model. For each comparison, MAXR determines if removing one variable and replacing it with the other variable increases R². After comparing all possible switches, the one that produces the largest increase in R² is made. Comparisons begin again, and the process continues until MAXR finds that no switch could increase R². The two-variable model thus achieved is considered the BEST two-variable model. Another variable is then added to the model, and the comparing-and-switching process is repeated to find the best three-variable model, and so forth (SAS 1997a, and 1997b) until the best n-variable model is determined.

Availability of hyperspectral data in 490 (N) discrete narrow-wavebands facilitates computation of N x N= 240,100 narrow-waveband NDVI's for any one crop variable. In comparison the 7 Landsat TM bands have just 49 (7 x 7) possible indices. However, it will suffice to calculate narrow-waveband NDVI's only below the diagonal of the 490 by 490 matrix as values above the diagonal are the transpose of values below the diagonal. All computations were performed by writing appropriate algorithms in SAS (1997a and 1997b). the NDVI for narrow-wavebands i and j will be:

Various crop biophysical variables were then related to all possible combinations of narrow-waveband NDVI indices and their R² values determined (e.g., Figure7 and Figure8-discussed in detail in section 5.4).

 4.4 Narrow-waveband soil adjusted vegetation indices

The narrow-waveband transformed soil adjusted vegetation indices (TSAVI) uses site specific soil line and are known to explain more variability in the vegetation cover than the other soil-adjusted indices (Lawrence and Ripple, 1998). The narrow-waveband TSAVI requires slope (or gain) and intercept (or offset) values of a soil line. The narrow-waveband TSAVI were computed for the best narrow-waveband NDVI indices. There are 4 specific soils in the study area for which the soil lines were plotted and the slopes and intercepts of the soil line determined (Table5) using the soil spectra of these soils and based on the definition of the best narrow-waveband-NDVI indices for each crop variable. The soil spectra were integrated for the best indices taking their waveband widths (D l ₁ and D l ₂- see Table3), plotted, and their slopes (a) and intercepts (b) were determined. Since the waveband widths (D l ₁ and D l ₂ ) change for each index (Table3) separate a and b values need to be computed for each index (Table5).

The availability of near continuous discrete narrow-waveband spectra facilitates computation of derivative indices. The derivative indices measure amplitude of the chlorophyll red-edge and are best measured using continuous narrow-waveband spectra from 0.626-0.795 µm (Elvidge and Chen, 1995). In this study several first and second order derivative spectral vegetation indices were initially explored by integrating discrete narrow-waveband spectra along the chlorophyll red-edge (0.700-0.780 m m), it's other regions of influence (0.626 to 0.780 m m), and regions of rapid change in slope per unit change in wavelength (e.g., 0.676 to 0.760 m m, 0.490 to 0.560 m m, 0.560 to 0.590 m m, 0.630 to 0.760 m m, and 0.525 to 0.575 m m- see changes in slopes of the first order derivative spectra of different crops in Figure4).

The first-order derivative green vegetation indices (DGVI1) derived by integrating spectra over 0.626-0.795 µm was consistently performing better than the other derivative indices when related to crop biophysical variables. Thereby, DGVI1 is the only derivative index reported throughout this paper.

Linear or non-linear models were fitted based on the plot trends and best fit R² values. When non linearity existed , exponential or power or quadratic models were attempted. These equation forms were: 1. Exponential vegetation indices crop variable=a*e^b*VI ; 2. Linear vegetation indices crop variable=a+b*VI; 3. Quadratic vegetation indices crop variable= a*VI²+b*VI+c; 4. Power vegetation indices crop variable=a*VI^b; where a=slope and b=intercept of soil line (obtained by plotting red versus NIR bands), VI= vegetation index . Crop variables are WBM:wet biomass (kg/m²), LAI:leaf area index (m²/m²), PLNTHT:plant height (mm), and YLD:yield (kg/lint/ha). An overwhelming proportion of the best spectro-biophysical relationships were either non-linear exponential or linear. On rare occasions, quadratic or power models provided only marginal increase in R² values, but these increases were generally insignificant. Hence only linear or non-linear exponential relationships were reported throughout the paper.

Spectroradiometer data was analyzed using combination of softwares PORTSPEC^TM and VNIR^TM supplied by the manufacturer of the instrument (Analytical Spectral Devices^TM), and Statistical Analysis System (SAS) version 6.12 (SAS, 1997a and SAS, 1997b). All relationships between spectrally derived vegetation indices and crop growth and yield variables were developed using SAS. Tests of significant differences between two groups of data were done using the least significant means procedure. Statistical discrimination procedures allow assessment and comparison of datasets for applications. The essential notion is that the distribution of sample data may be used to attach confidence levels to spectrally separable classes (Wallace and Campbell, 1989).

The relationships between the 4 biophysical variables of 5 crops with various types of hyperspectral indices and with broad-waveband indices are presented and discussed below. Except at few places the results of sunflower were not considered due to low sample size (9 samples).

As a first step, reflectivity in the 512 individual narrow-wavebands were correlated with crop biophysical variables wet biomass, WBM (Figure5a), and leaf area index, LAI (Figure5b), of all the 5 crops. The results showed (Figure5a and 5b) maximum negative correlation coefficients (r) in the red waveband portion were mostly centered around 0.680 µm. This is a region of maximal chlorophyll absorption in green vegetation. The maximum negative r values for relationships between reflectivity and WBM were (Figure5a) at 0.682 µm for cotton (r = -0.75), potato (-0.47), soybeans (-0.72), and corn (-0.41). For sunflower it was centered at 0.625 µm (r=-0.58). There was similar trends with LAI (Figure5b). Around 0.700 µm amount of energy reflected off green vegetation begins to increase (with absorption decreasing). Wavelength portion 0.700 to 0.740 µm (early part of the red-edge which goes from 0.700 to 0.780 µm), has rapid and highest change in reflectance per unit change in wavelength in all of the visible and NIR portion of the spectrum reaching peak around 0.780 µm (see Figure1). As a result r values change dramatically from negative maxima around 0.682 µm to positive maxima or near-maxima around 0.740 µm for WBM (Figure5a) and LAI (Figure5b) for all crops. In 0.740 to 0.875 µm portion of the spectrum r values for WBM and LAI remain near flat but provide the near highest positive values. Beyond 0.875 µm r values increase or decrease at specific wavelength portions. For example, maximum r values for cotton crop reflectance with: (a) WBM was 0.55 at 0.910 µm (Figure5a), and (b) LAI was 0.51 also at 0.910 µm (Figure5b). Maximum positive r values between reflectivity and WBM were (Figure5a) 0.55 at 0.910 for cotton, 0.51 at 0.910 for potato, 0.83 at 0.825 for soybeans, 0.32 at 0.940 for corn, and 0.53 at 0.868 for sunflower. Similarly, maximum positive r values between reflectivity and LAI were (Figure5b) 0.51 at 0.910 for cotton, 0.59 at 1.025 for potato, 0.65 at 0.854 for soybeans, 0.17 at 0.768 for corn, and 0.46 at 0.882 for sunflower. Reflectance in 0.780-0.920 µm increased significantly for cotton (Figure2a) crop and to a much lesser extent corn (Figure2d). For cotton in critical growth stage the reflectance increased from 44 percent at 0.740 µm to 54 percent at 0.920 and the corresponding increase for cotton in yielding growth stage was from 48 percent to 59 percent-both substantial increases (Figure2a) contributing to r peaks around 0.920 µm (Figure5a and 5b). The 0.940-1.040 m m is the moisture sensitive "trough" portion of the spectrum with "dip" in "trough" minima increasing with increase in biomass and crop moisture (Penuelas 1993). The trough minima was around 0.980 µm for most crops (see Figure2a through 2d). Around this waveband all crops have r minima (Figure5a and 5b).

In contrast to NIR shoulder (0.780 to 0.900 µm), in which spectral reflectance changes only marginally for all crops except cotton, and to a lesser extent corn, the visible portion of the spectrum (0.400-0.700 µm) is highly sensitive in different discrete portions in blue (0.400-0.500 µm), green (0.500-0.600 µm), and red (0.600-0.700 µm) as evident in Figure2a through 2d. This characteristic resulted in rapidly changing correlation coefficient (r) between crop biophysical variables (WBM, LAI) and spectral reflectivity for a given crop in discrete narrow-wavebands of 0.400-0.700 µm compared to the relatively uniform r values in 0.780-0.900 µm (Figure5a and 5b).

Using the MAXR procedure described in section 4.2, the best 1-variable, the best 2-variable, and the best 4-variable optimum multiple narrow-waveband reflectivity (OMNBR) models were determined for estimating wet biomass, leaf area index, and plant height of 4 crops (cotton, Potato, soybeans, and corn) as well as yield of cotton crop (Table2). In 10 out of 13 biophysical variables, the first 4 narrow-waveband variables explained 76 percent or above variability (Table2). This is nearly the same percentage of variability explained when the ratio (M/N) of the number of independent variables (M) to that of total number of samples (N) for that variable is between 0.15 and 0.20 in different crop variables (see Figure6). As M approaches N the R² value approaches 1. Beyond M/N of 0.15 to 0.20 (see Figure6) there was only an incremental small increases (often, statistically insignificant) with addition of a variable. This feature has been illustrated in Figure6 for the relationships between narrow-wavebands and LAI of 4 crops by comparing them with idealized random (RAND in Figure6) plot which shows the nature of the curve when the sample sizes are large (350 in this case). For each crop the R² values were statistically significant for the 1-variable models, increasing dramatically with the addition of a second variable (Figure6 and Table2). A quality factor (R² of a crop/R² of RAND) demonstrates this. For example, R² of cotton/R² of RAND for the first five values of cotton crop were 3.38, 2.50, 1.93, 1.89, and 1.81. The first 2-variables explain most of the variability. However, as we can observe in Figure6 and Table2 there is significant further increase in R² value with addition of third and most often the fourth independent variables. Four-variable models explained 64 to 92 percent variability in crop biophysical variables, a significantly higher percentage relative to 53 to 81 percent by 2 variable models, and 18 to 69 percent by 1 variable models (Table2). Beyond this the increases with addition of each variable is very small and often statistically insignificant. So any increase beyond M/N=0.15 to 0.20 is an mathematical artifact rather than having real physical meaning such as in 2-band indices involving high absorption properties of red and high reflection properties of NIR for green vegetation. This has also been pointed out by Blackburn (1998) who mentions that there is a likelihood of the multiple narrow-waveband models being "over-fit" and hence the relationships need to be validated using independent datasets.

The first 2 bands, typically, constitute a red and a NIR or a red and a green or a red-edge and a NIR waveband combinations (see wavebands of 2-variable models in Table2). In 4-variable models the wavebands that occur most clustered in late red (0.651 to 0.700 m m), moisture sensitive NIR (0.951 to 1.000 m m), early green (0.501 to 0.550 m m), and late NIR (0.900 to 0.940 m m). This results highlight the fact that the optimal information on crops is not necessarily concentrated in the red and NIR wavebands. An interesting result in Table2 is the frequent appearance of narrow-wavebands from the visible portion (0.40 to 0.70 m m) apart from the later portion of the NIR (0.901-0.950 m m), and the moisture sensitive NIR (0.940-1.040 m m). The visible spectrum is very sensitive to loss of chlorophyll, browning, ripening, and senescing (Idso et al., 1980), carotenoid (Blackburn, 1998; Tucker, 1977) and soil background effects. When more than one senescing date data are involved, senescing rates in the visible spectrum can be used to better predict grain yield (Idso et al., 1980). This was obvious from the Narrow-waveband combination R² value as much as 0.77 for cotton crop yield (Table2) relative to R² value of only 0.64 when two band red and NIR indices (COT-YLD-Index 1) are used (Table4a and Table4b).

The relationships between the narrow-waveband vegetation indices (narrow-waveband NDVI) and crop biophysical variables (wet biomass-WBM, leaf area index-LAI, plant height-PLNTHT, yield-YLD) were established and their coefficient of determination (R²) determined. A contour plot of the R² values between wavelength l ₁ (0.350 to 1.050 m m) and wavelength l ₂ (0.350 to 1.050 m m) are plotted for (Figure7 and Figure8): (a) WBM of cotton (values below the diagonal in Figure7), (b) WBM of soybeans (values above the diagonal in Figure7), (c ) LAI of corn (values below the diagonal in Figure8), and (d) LAI of potato (values above the diagonal in Figure8). In both Figure7 and Figure8, only R² values above 0.4 are plotted for clarity. Similar plots (not illustrated) were done for all biophysical variables of each crop. These plots show the waveband combinations that provide the best indices (see various "bulls-eye" formations in Figure7 and Figure8 for relationships with crop biophysical variables.

Based on the above discussed results, waveband centers (l ₁ and l ₂) and waveband widths (D l ₁ and D l ₂) that combine to form the best seven indices (ranked based on R² values) are determined for WBM and LAI of cotton, potato, soybeans, corn, and for the pooled data of all crops (Table3). For example, the best index for cotton WBM (referred to as: COT-WBM-Index 1) has waveband centers and widths as (Table3): l ₁=0.682 m m (D l ₁=0.028 m m), and l ₂=0.918 m m (D l ₂=0.020 m m). Waveband centers and widths for this index (COT-WBM-Index 1), Table3, were extracted from the contour plot range of 0.70 to 0.75 (showing highest R² value) in the lower diagonal portion of the Figure7. The second best index (COT-WBM-Index 2) is then selected from the contour plot region with R² value range of 0.65 to 0.70. Similar procedure is adopted for determining l ₁, l ₂ , D l _1, and D l ₂ for other indices of crop variables of all the other crops and for the pooled data of all crops (Table3). These results show a remarkable cluster of information in narrow-wavebands centered at the later portion of red-band, 0.650 to 0.700 m m, a particular portion of NIR, 0.900 to 0.940 m m, and early portion of the green-band, 0.500 to 0.550 m m (see specific narrow-waveband centers and their widths in Table3 and the clusters in Figure16).

The Figure7 and Figure8 depict R² values for linear relationships between crop biophysical variables and hyperspectral indices. However, most relationships between crop biophysical variables and spectral indices were non-linear. It was noticed in this study that an overwhelming proportion of the best non-linear models were exponential. Hence throughout this paper linear or exponential models were fitted for the data based on the trends noticed. The waveband centers (l ₁ and l ₂) and waveband widths (D l ₁ and D l ₂) determined for the best 7 linear models (Table3) were used for computing non-linear exponential models. The R² values for the 7 best linear and non-linear hyperspectral narrow-waveband vegetation index models were computed and listed for each biophysical variable (Table4a and Table4b). Except in 3 cases, non-linear models performed substantially better than the linear models (see R² values of linear and non-linear models in Table4a and Table4b). However, in 3 cases (corn wet biomass, corn LAI, and cotton yield) linear models performed better than the non-linear models.

The best hyperspectral models for WBM explained 79 percent variability for cotton (COT-WBM-Index 1), 76 percent variability for potato (POT-WBM-Index 1) , 84 percent variability for soybeans (SOY-WBM-Index 1), 71 percent variability for corn (COR-WBM-Index 1), and 59 percent variability for all crops (ALL CROPS-WBM-Index 1) (Table4a and Table4b). The best LAI models explained 66 percent variability for cotton (COT-LAI-Index 1), 88 percent variability for potato (POT-LAI-Index 1), 80 percent variability for soybeans (SOY-LAI-Index 1), 86 percent variability for corn (COR-LAI-Index 1), and 65 percent variability for all crops (ALL CROPS-LAI-Index 1). Based on this study, it is reasonable to infer that most of the relationships between WBM and LAI with vegetation indices are non-linear (found true for cotton, soybeans, and potato in this study). This has been found true for most other crops as well (see Weigand et al., 1992, Thenkabail et al., 1995, Lawrence and Ripple, 1998). However, corn WBM and LAI provided linear relationships with spectral vegetation indices unlike non-linear relationships of the same variables of cotton, potato, and soybeans (Table3). A likely reason for the differences in these relationship trends is due to significantly higher WBM for corn when compared with cotton, soybeans, and potato (see Table6). All corn fields were either in late vegetative or critical growth phases (Figure2d) resulting in a narrow dynamic rage of their indices (see Figure11a and 11b).

The narrow-waveband transformed soil adjusted vegetation index (TSAVI) models of crop biophysical variables were calculated for each of the best narrow-waveband NDVI models (see Table4a and Table4b) using the slopes and intercepts of the soil lines of the 4 prominent soils (Table5). Except in case of potato WBM, and to a much lesser extent soybean LAI the increase in the soil adjusted models over the other narrow-waveband NDVI models were insignificant. Potato and soybeans were the two crops with highest soil background influences. Both of these crops had two very distinct growth stages (see Figure2b and 2c). Of the 25 potato fields 17 were in early vegetative and 8 in middle or late vegetative (Figure2b). The 17 fields had about 15-20 percent canopy cover. Even the late vegetative fields had only about 35 percent canopy cover. Below 25-35 percent canopy cover, soil background reflectance is the principal contributor to overall spectral response (Tueller 1987). Of the 27 soybeans fields 13 were in early vegetative growth phases with about 40 percent canopy cover with the rest having about 90 percent canopy cover (Figure2c). These conditions resulted in potato WBM showing highest increase in R² value (5 percent) for the narrow-waveband TSAVI models over the best narrow-waveband NDVI models. This was followed by a marginal increase in R² value (2 percent) of soybean LAI over narrow-waveband NDVI models. However, in general narrow-waveband TSAVI models showed only a marginal or no increase in R² values over the best narrow-waveband NDVI models.

Determining the precise soil line is crucial to the success of soil adjusted vegetation indices. Sufficiently large R² values (0.95 and above) of each soil line (Table5) is required to ensure this. It is desirable to have R² values of 0.99 or above for each soil line. This will ensure more precise estimates of slopes and intercepts of soil line leading better accounting of soil variability that lead to better estimates of crop biophysical variables. However, the soil line is a function of so many variables (e.g., texture, color, organic content) and hence practically difficult to obtain a perfect soil line. Further, even for same soil types, the micro conditions vary even within a field (e.g., moisture-rainfall, irrigation, tillage, drainage, slopes) resulting in the absence of a perfect soil line. Naturally with these problems, a complete accounting of soil background reflectance was not possible. Also, normalization of the soil background influences to a constant ratio or a perfect one-dimensional soil line only removed bare soil spectral influences and not the greater soil brightness influences (Huete et al., 1985).

Generally, soil background effects can be reduced using indices such as TSAVI (Elvidge and Chen, 1995) especially for agricultural crops or homogeneous plant canopies (Rondeaux, 1996). The soil adjusted vegetation indices are more significant when agricultural crops on widely varying soils are studied (see, for example, Lawrence and Ripple, 1998). The four soil types (Table5) in this study area did not have big differences- all having fine or very fine clayey Calcixerollic Xerochrept and Chromic Calcixerert soils Thereby, the slopes of these soils (Table2) for indices involving two similar wavebands were close to one another. For example, the NIR and red based indices (COT-WBM-Index 1, COT-LAI-Index 1, All crops-WBM-Index 1) have very similar slopes and intercepts (Table5). Similarly the green and red waveband based indices (e.g., POT-WBM-Index 1, and all crops-LAI-index 1) had similar slopes and intercepts. However, in areas of considerable soil variations these slopes and intercepts are expected to change for similar waveband combinations. Thereby, the soil adjusted vegetation indices are expected to be of greater value when several distinct soil types are involved.

For cotton yield, the soil adjusted index (COT-YLD-Index 1-SA) explained 9 percent less variability compared to the corresponding narrow-waveband index (COT-YLD-index 1). This can be attributed to mix of spectral signature from the cotton Lint (see Figure3b), cotton leaves that are changing color from green to light green or yellowish-green, exposed cotton stems (as a result of falling leaves) and some soil background. Fifty of the 73 fields were in the yielding/near harvest growth stage. For these fields cotton yield were estimated. These fields had about 75 percent canopy cover (due to exposed areas as a result of falling leaves). The presence of cotton Lint and the drier maturing cotton of the yielding/maturing growth phases resulted in higher reflectance throughout visible waveband but lower reflectance in the NIR portion relative to cotton in critical growth phases (See Figure2a). The narrow-waveband TSAVI models use slopes and intercepts of the soil line to correct for soil background influences only. However, when other factors (e.g., Lint, stem, different shades of leaves) become prominent, the soil adjustment can reduce the accuracy of the prediction.

The first-order derivative green vegetation index, DGVI1, explained 35 to 86 percent variability in different crop variables (see last column in Table2). In 4 cases (cotton plant height, cotton yield, soybean wet biomass, soybean plant height, and corn plant height) DGVI1 performed better than the broad-waveband indices. For soybean WBM the DGVI1 explained more variability than the best narrow-waveband NDVI model (see Figure11c and 11d). Cotton yield was better estimated using DGVI1 (R²=0.67) compared to narrow-waveband NDVI (R²=0.54) or 4-variable optimum multiple reflectivity models (R²=0.64) (Table2). Soybeans had a mixture of highly vegetated vigorous fields (14 of the 27) with about 90 percent canopy cover. The other 13 fields had about 40 percent canopy cover. Cotton YLD fields had a mix of canopy and other conditions-drying or falling leaves, exposed soils and plant stem as a result of falling leaves, cotton lints. The red-edge sensitivity is high in the presence of such contrasting changes in canopy and background effects. Earlier Elvidge and Chen (1995) demonstrated the utility of the derivative indices for the complex grassland canopies that included the green and dry biomasses with various background effects. Thus, DGVI1 exhibited robustness to complex biophysical conditions (e.g., dry and wet biomass intermingled with significant soil background effects).

However, derivative indices performed significantly poorer than the other narrow-waveband, as well as, most broad-waveband indices (Table4a and Table4b, Table2). These results agree with the findings of Carter (1997), and Guyot et al. (1992). Carter (1997) demonstrated that the narrow-waveband NDVI explained 17-29 percent more variability of net CO₂ assimilation in pine canopies relative to broad-waveband indices. Guyot et al. (1992) showed that when compared to broad-waveband vegetation indices the red-edge position is relatively insensitive to variation in leaf inclination angle, soil reflectance, and atmospheric effects. In contrast, however, Elvidge and Chen (1995) concluded that there is little benefit in having high spectral resolution data if vegetation indices are to be formed using narrow-waveband versions of broad-waveband indices such as the broad-waveband NDVI. Shibayama and Akiyama (1991) indicated similar possibilities for crops. It is likely that the first-order (DGVI1) and the second-order (DGVI2) derivative indices may be more sensitive to changes in sparsely vegetated and complex (mixture of green and brown) grassland canopies rather than for plant canopies (Curran, 1990; Carter, 1997; and Elvidge and Chen, 1995). For example, the maximum green canopy cover in Elvidge and Chen study was Just 17.8 percent whereas in this study this percentage is the bare minimum canopy cover. Relatively poor performance of the derivative indices are attributed to these indices capturing information over rather large spectral range of the chlorophyll red-edge (0.626-0.795 m m), chlorophyll fluorescence (Lichtenhaler, 1989), and secondary pigments (Curran et al., 1991).

For potato LAI, the best index (POT-LAI-Index 1) had waveband centers at 0.620 m m and 0.590 m m providing an R² value of 0.86 (Figure8, and Figure11b). When an index is formulated using such two close waveband centers (close to diagonal in Figure8) it is indicative of the rapidly changing slope of the wavebands per unit change in wavelength. These areas are ideal for computing Hyperspectral derivative indices.

The best narrow-waveband NDVI models explained an additional 3 to 16 percent variability relative to Landsat TM broad-wavebands NDVI models (Table4a and Table4b). These increases were generally higher for LAI models. For LAI, the increase using narrow-waveband indices over TM NDVI indices were 5 percent for cotton, 10 percent for potato, 8 percent for soybeans, and 16 percent for corn (Table4a and Table4b). The corresponding increases for the WBM models were 3 percent for cotton, 9 percent for potato, 5 percent for soybeans, and 12 percent for corn. The 4-variable optimum multiple reflectivity, OMNBR, models explained 3 to 40 percent additional variability relative to broad-waveband NDVI models (Table2). Each one of the 13 crop OMNBR models performed significantly better than broad-waveband NDVI models. Also, in 8 out of 13 models, the 4-variable OMNBR models explained 4-38 percent additional variability relative to narrow-waveband NDVI models (Table2). However, there were four cases in which narrow-waveband NDVI models performed better than the 4-variable OMNBR models by explaining 3-8 percent additional variability.

Saturation of the sensor is a limitation on a proportional increase in sensitivity of vegetation indices to incremental increases in physiological and other changes. The NIR and red based indices often have serious problems of saturation. This can be seen in the broad-waveband models of potato wet biomass, WBM, (Figure10a) and to still greater extent in soybean LAI (Figure10c). For potato (Figure10a), initially when WBM is less than 0.7 m²/m² there is an incremental increase in NDVI showing a clear linear trend in relationship. Beyond this (WBM greater than 0.7 m²/m² ) the trend of the plot becomes non-linear. For soybeans (Figure10c), initially when LAI is less than 1.0 m²/m² there is an incremental increase in NDVI showing a clear linear trend in relationship. Beyond this (LAI greater than 1.0 m²/m² ) the trend of the plot becomes non-linear reaching a plateau around LAI of 3.0 m²/m^2. In such cases, hyperspectral data offers opportunity to scout for waveband combinations that: (a) offer the best 2-band based NDVI type of relationships (see Figure7 and Figure8 that are often different from the widely used NIR and red based indices; or (b) perform multiple linear regressions (Table2) that help overcome or reduce limitations of saturation in spectral data by incorporating additional information from unique wavebands from different portions of the spectrum. For example, improved relationships using 2 visible wavebands (Figure10b and Figure10d) compared to commonly used NIR and red based wavebands (Figure10a and Figure10c) is clear. The narrow-waveband centers at 0.550 m m (green band peak) and 0.682 m m (red band absorption maxima) in Figure10b explained 14 percent greater variability relative to the broad-waveband NIR and red based index (Figure10a). Similarly, two visible wavebands, 0.625 m m (beginning of the red band) and 0.688 (near the end of the red band), were found the best for determining soybean LAI (Figure10d). Also, when spectral responses from multiple wavebands such as the 4-variable OMNBR models are involved greater percentage of variability is generally explained (Table2). Sellers (1987) had indicated that at higher growth stages NIR and red based indices saturate. This is more pronounced for crops like soybeans which have direct nitrogen fixation. Soybeans in critical growth stages had the significantly higher NDVI (e.g., broad-waveband NDVI of 0.84 or narrow-waveband NDVI of 0.88) compared to growth stages of any other crop (Table6). This is because, soybean LAI increases dramatically from 0.49 m²/m² to 3.17 m²/m² from early to critical growth stage and has equally rapid increase in spectral vegetation indices with broad-waveband NDVI raising from 0.49 to 0.84 and a visible waveband based index, VBNDVI2, from -0.033 to 0.46 (Table6). Nitrogen requirements of the soybeans were largely met by the symbiotic fixation process whereby modulated legumes are able to utilize atmospheric nitrogen. In contrast, nitrogen requirements of the other crops studied here (corn. Potato, sunflower, cotton) are met by direct nitrogen fixation (fertilizer application)(Norman, 1978). The sensitivity of vegetation to nitrogen is also a likely reason for the very high vegetation indices of soybeans-especially when it is in critical growth stages with near 100 percent canopy cover (Table6).

The data points of NIR and red based narrow-waveband models (e,g., Figure9b, Figure9d, and Figure12b and 12c) cluster closer (have less variability) and have larger dynamic range of values relative to the NIR and red based broad-waveband models (e,g., Figure9a, Figure9c, and Figure12a). For example, the broad-waveband NDVI values range from 0.22 to 0.88 (Figure9a) compared to the corresponding narrow-waveband soil adjusted model having and increased dynamic range of 0.10 to 0.89 (Figure9b). Similar trends are seen in cotton LAI (Figure9c and 8d). More dramatic illustration of this can be seen in Figure12. The dynamic rage of NDVI changes from 0.25 to 0.76 for TM broad-waveband index (Figure12a) relative to 0.22 to 0.81 for hyperspectral narrow-waveband index (Figure12b) and 0.13 to 0.81 for the soil adjusted version of the hyperspectral narrow-waveband index (Figure12c). The indices in 12b and 12c involve moisture sensitive NIR waveband centered at 0.982 m m. The formation of the "trough" and it's magnitude in the 0.940 to 1.040 m m portion (Figure2a through 2d) of the spectrum are related to the growth characteristics (WBM, LAI) and moisture in plant. The "dip" maxima is around 0.968 to 0.980 m m with mean around 0.975 m m (Figure1). The more pronounced magnitudes in the "dip" are seen in plants that are in higher growth stages or having higher WBM and LAI levels (Figure2a through 2d and Table6. The NIR and red based indices often show lack of sensitivity at higher growth stages leading to saturation or plateauing (e.g., Figure10c), and scattering (e.g., Figure10a and Figure12a) effects. This effect can be reduced by using indices other than the NIR and red based indices such as the: green/red index (Figure10b), red/red index (Figure10d), and red/moisture NIR index (Figure12b). The availability of data from distinct growth stages within each crop (Figure2a through Figure2d) resulted in a range of spectral and biophysical values that stretched along a large dynamic range (Figure9 through Figure12).

Piecewise multiple linear regressions help overcome the problems of saturation through the use of spectral responses from multiple wavebands. High percentage of variability in crop variables were explained, for example, using distinct waveband responses (Table2). In the best 1-variable, 2-variable, and 4-variable models different distinct wavebands or waveband combinations were involved (Table2). The model equations provided by different distinct waveband responses are used to predict crop variables (Figure13a through Figure13d). The 4 different crop variables predicted using 4-variable models (4 narrow-wavebands) were correlated with actual values (measured in the field) crop variables (Figure13a through 13d). The high degree of these predicted versus actual relationships demonstrate the value of using multiple-waveband responses.

The crop growth stages and crop types are critical in understanding the sensitivity of wavebands from different portion of the spectrum. In order to illustrate this (Table6) two Thematic Mapper indices (broad-waveband NDVI and broad-waveband GVI), and four hyperspectral indices (a green and a blue band based index- narrow-waveband NDVI1; a green and a red band based index- narrow-waveband NDVI2; a first-order derivative green vegetation index- DGVI1; and a red and NIR based index- narrow-waveband NDVI3;) were used. Statistical tests of significance's were performed on mean vegetation indices of the distinctive growth stages (Table6).

The mean broad-waveband NDVI for corn (0.67) and cotton (0.66) were about the same (Table6). Similar insensitivity was detected even when the 4 TM bands were used in broad-waveband GVI which provided values of 42.45 for corn and 44.06 for cotton. In comparison, narrow-waveband NDVI1 involving two visible wavebands provided significant statistical differences (at 95 percent confidence level) for corn (0.41) and cotton (0.29). Similarly, results were obtained using narrow-waveband NDVI2 involving two other visible wavebands which had mean values of 0.18 for corn and 0.11 for cotton. Further, the magnitude of differences in one or the other narrow-waveband indices were often higher than broad-waveband NDVI indices. For example, broad-waveband NDVI indices provided significant difference between soybeans (0.67) and potato (0.73) (Table6). This difference increased when narrow-waveband NDVI2 (0.22 for soybeans and 0.33 for sunflower. Overall, the narrow-waveband NDVI2 provided significant difference between 9 combinations of crop types (corn-cotton, corn potato, corn-sunflower, cotton-potato, cotton-soybeans, cotton-sunflower, potato-soybeans, potato-sunflower, and soybeans-sunflower),. In comparison, narrow-waveband NDVI1 provided significant difference for only 5 combinations, and narrow-waveband NDVI3 with 6 combinations (Table6). Compared to this the broad-waveband indices provided significant difference between only 3 or 4 combinations of crops. Similar trends can be observed for the growth stages. For example, the broad-waveband NDVI indices were about the same for corn in critical (0.67) and corn in late vegetative (0.67) (Table6). Compared to this narrow-waveband indices in Table6 show dramatically improved sensitivities. These results imply that through use of indices derived from various narrow-wavebands it is possible to maximize crop information. Often information is captured at specific narrow waveband better than the other portions depending on phonological and physiogtraphic variability.

Sensitivity of indices can be enhanced by grouping the data into appropriate distinct categories based on crop growth stages. For example, cotton fields that are mature and are nearing harvest (50 samples) with reduced nitrogen levels of leaves were separated from those fields in critical/flowering growth stages (23 samples) which have higher nitrogen levels. Once the boll load builds up, the nitrogen levels of leaves decrease because of the boll demand (Basset et al., 1970). The cotton yield were estimated for all fields (best model R²=0.51-results not presented). Taking only the fields that are nearing harvest (50 samples), the yield estimates increased considerably with the new model involving COT-YLD-Index 1 explaining 64 percent of the variability (Table4a and Table4b) with root mean square error (RMSE) of 198 kg/ha compared to earlier 51 percent variability explained when the entire dataset was used with RMSE of 222 kg/ha.

Further, a single equation can be fit for all 5 crops to model leaf area index, LAI, (Figure14) and wet biomass, WBM, (Figure15). For LAI, the narrow-waveband model providing the highest R² value involved 2 visible narrow-wavebands (Figure14a) followed by a model that involved a NIR and red narrow-waveband (Figure14b). For WBM, the narrow-waveband model providing the highest R² value involved a NIR and red narrow-wavebands (Figure15a). A model that involved 2 visible wavebands provided the third highest R² value (Figure15b). These relationships further highlight the utility of using different waveband responses in establishing crop characteristics.

The results obtained using narrow-waveband NDVI models (e.g., Table3, Table4a and Table4b, Figure7 and Figure8, Figure16) and optimum multiple narrow-waveband reflectivity, OMNBR, models (e.g., Table2, Figure16) were used for determining the optimal hyperspectral wavebands and their waveband widths that are most suitable in estimation of crop biophysical variables. The narrow-wavebands (l ₁ and l ₂) that appear in 2-band NDVI type of models ranked 1, 2, and 3 (see index 1, 2, and 3 in Table3), and the narrow-wavebands that occur in 1-variable, 2-variable, and 4-variable OMNBR models (Table2) of different crops were evaluated (Figure16). The percentage of these narrow-wavebands clustering or appearing in every 50-nanometer width of waveband, in the visible and NIR portion of the spectrum (0.350 to 1.100 m m), were established (Figure16). In both model types, an overwhelming proportion of crop information was in narrow-wavebands clusters in later portion of red, 0.650 to 0.700 m m, a particular portion of NIR, 0.900 to 0.950 m m, and a early portion of green, 0.500 to 0.550 m m. These were followed by, early half of NIR shoulder, 0.800 to 0.850 m m, red-edge, 0.701 to 0.750 m m, and the moisture sensitive NIR, 0.951 to 1.000 m m (Figure16). Specific narrow-wavebands and their waveband widths within these clusters, that provide optimal crop information, were identified and recommended to be included in future generation of sensors. For example, A remarkable 36.4 percent of all the wavebands that occur in the first-, second-, and the third-best models of narrow-waveband NDVI type models were clustered in 0.651 to 0.700 m m region of the spectrum (Figure16, Table3). In the same spectral region, the best three OMNBR models had between 19.2 to 38.5 percent of all the wavebands (Figure16, Table2).

The waveband widths (D l ₁, D l ₂) were determined from the l ₁, versus l ₂ plots as the one's illustrated in Figure7 and Figure8 and listed in Table3. The D l ₁ and D l ₂ of the best three models (Index 1, Index 2, and Index 3 in Table3) were used to determine the frequency of occurrence of various waveband widths as follows:

1. Very narrow-wavebands (1 to 15 nanometers)-----------------19 (number of occurrences)-------------- 29 (percent)

2. Narrow-wavebands (16 to 30 nanometers)-------------------- 32--------------------------------------- 48

3. Intermediary wavebands (31 to 45 nanometers)----------------05----------------------------------------08

4. Broad-wavebands (greater than 45 nanometer)----------------10----------------------------------------15

It is clear from these results that an overwhelming proportion of the wavebands have narrow (0.016 to 0.030 m m) or very narrow waveband (0.001 to 0.015 m m) widths. Even when the waveband widths are intermediary or broad, the narrower portion of the waveband widths are required for several indices to obtain the best models. This is illustrated, for example, by taking 3 models each having red waveband centers at 0.682 m m but having different bandwidths. These models are (Table3):POT-WBM-Index 1 (D l ₂=0.004 m m for l ₂= 0.682 m m), ALL-LAI-Index 1 (D l ₂=0.010 m m for l ₂= 0.682 m m), and for COT-WBM-Index 1 (as D l ₂=0.028 m m for l ₂= 0.682 m m). All models provide best results only if the waveband widths are taken commonly as D l ₂=0.004 m m. If larger waveband widths (e.g., D l ₂=0.028 m m) are used in models POT-WBM-Index 1 (instead of D l ₂=0.004 m m), or ALL-LAI-Index 1 (instead of D l ₂=0.010 m m) the R² values reduce, often substantially. In contrast if smaller waveband widths (e.g., D l ₂=0.004 m m) are used in models COT-WBM-Index 1 (instead of D l ₂=0.028 m m), or ALL-LAI-Index 1 (instead of D l ₂=0.010 m m) the R² values increase or atleast remain as high as they were with broader bandwidths. This demonstrates the greater value in using narrower-wavebands.

The above discussed results and discussions helped identify the hyperspectral wavebands that occur frequently (Table3 and Table2). This resulted in identifying 12 wavebands and their waveband widths (Table7) that provide optimal crop biophysical information. The information cluster in different waveband portions are shown in Figure16. The specific wavebands (Table7) are discussed in the following paragraphs (see Figure16).

The red absorption maxima occurs around 0.682 m m . This is the single most frequently occurring waveband across crops and their variables in both type of models (2-band, and multiple linear). The three other most frequently occurring red narrow-wavebands in different crop biophysical models were:0.678 m m (red band absorption pre-maxima), 0.696 m m (red band absorption late maxima), and 0.668 m m (red band absorption early maxima). Since 0.678 m m is very close to 0.682 m m, both can provide equally good results. Thereby, only the most frequently occurring of these wavebands, 0.682 m m (l ₆-waveband number 6 as is Table7) , is recommended along with other two red wavebands 0.668 m m (l ₅) and 0.696 m m (l ₇). Since the absorption in the red vary significantly from one farm field to another due to changes in factors such as biomass, LAI, soil background, cultivar types, and nitrogen in plants there is no definitive narrow-waveband where red absorption is most sensitive. Indeed red absorption vary significantly depending on a host of these variables (Elvidge and Chen, 1995; Carter, 1997; Blackburn, 1998). As a result it is justified to recommend three narrow-wavebands in red spectrum. Depending on a complex set of biophysical and physiological conditions one or the other narrow-waveband performs better. The results of this research (section 5.1 through 5.8) also demonstrated (e.g., see for example Figure9 through Figure12) that the narrow-wavebands such as the one's discussed in this section dramatically improve relationships compared to similar relationships obtained using broader wavebands such as 0.668 to 0.696 m m or 0.630 to 0.690 m m (later is TM band 3). The waveband widths (D l ₁ or D l ₂) for the red narrow-wavebands typically range between 0.004 to 0.028 m m (Table3). The best suggested band widths for any red narrow-waveband is 0.004 m m (see a related discussion in previous paragraph). Elvidge and Chen (1995) used 4-nm-wide band at 0.674 m m for red and 0.780 m m for the NIR to compute the narrow-waveband NDVI for pine canopies. In contrast, Carter (1997) found 0.701+ 0.002 m m for Red and 0.820+ 0.002 m m for NIR as the best wavebands for computing narrow-waveband NDVI also for pine canopies but of different varieties. More recently. for grassland canopies Blackburn (1998) found best correlation with plant pigments when narrow-wavebands in 0.635 to 0.680 m m for red and another narrow-waveband centered at 0.800 m m for NIR are used in indices.

The wavebands that most frequently appeared in the NIR portion of the spectrum, in the 2-band and multi band models, were: 0.910 m m (NIR shoulder reflectance pre-peak), 0.918 m m or 0.925 m m (NIR shoulder reflectance peak), and 0.940 m m (NIR shoulder post-peak) (Table3 and Table2). The "NIR shoulder" (near similar reflectance across a range of wavelength) goes from 0.780 to 0.900 m m (see Figure1). In this wavelength range (0.780 to 0.900 m m), change in reflectance with change in wavelength was relatively insignificant for potato (Figure2b), soybeans (Figure2c), and sunflower (Figure1)-hence called the NIR shoulder. However, the change was highly significant for cotton (Figure2a) and to a much lesser extent for corn (Figure2d). Further, all crops had peak NIR reflectance in the 0.900 to 0.940 m m region. These factors contributed to frequent occurrence of narrow-wavebands from the 0.900 to 0.940 m m region of the NIR spectrum in two-band models (Table3) and multi band models ( Table2) resulting in a second most significant cluster of information in this portion of the spectrum (Figure16). Most existing satellite sensors have broad-wavebands along the NIR shoulder. The performance of indices involving wavebands in the range of 0.910 m m to 0.940 m m was about the same. Hence, a single waveband centered at the very peak (0.920 m m- l ₁₀) will suffice. Band widths for these wavebands typically varied between 0.010 m m to 0.060 m m. A band width of 0.010 m m is recommended. The NIR shoulder is represented by a broad-waveband centered at 0.845 m m (l ₉).

Narrow-wavebands in the green portion of the spectrum in combination with a red or other visible wavebands often model crop biophysical variables better than the widely used NIR and red based models (e.g., compare Figure10b and 10d with Figures 10a and 10c). The most frequently occurring narrow-wavebands were (See Table3 and Table2) 0.550 m m (green band maxima), 0.525 m m (positive change in slope per unit change in wavelength is maximum around this waveband across crops-see Figure4a through Figure4e), 0.568 m m (negative change in slope per unit change in wavelength is maximum around this waveband-see Figure4a through Figure4e), and 0.540 m m (green band pre-maxima). Since 0.540 m m and 0.550 m m are close to one another and have near-similar information-only one of these wavebands (green waveband maxima at 0.550 m m- l ₃) was retained along with 0.525 m m (l ₂), and 0.568 m m (l ₄). The band widths were then decided based on widths of wavebands in the best three indices of Table3. This led to a band widths of 0.020 for 0.550 m m, 0.020 for 0.525 m m, and 0.010 m m for 0.568 m m.

The narrow-wavebands within the NIR moisture sensitive portion, 0.940 to 1.040 m m, figure prominently in several hyperspectral biophysical models (see Table2 and Table3). For example, in 11 of the 13 best 4-variable multiple variable, OMNBR, models there was atleast one waveband in the 0.940 to 1.040 m m (Table2). This is a remarkable result highlighting the intrinsic value of wavebands in this portion of the spectrum to provide very distinct information. The most frequently occurring moisture sensitive wavebands were centered at 0.982 m m (moisture NIR "dip" maxima of the moisture sensitive band), 0.968 m m (moisture NIR "dip" pre-maxima of the moisture sensitive band), and 1.020 m m (moisture NIR post-maxima of the moisture sensitive band). A waveband centered at 0.975 m m- l ₁₁(to represent both 0.982 m m and 0.968 m m) with a waveband width of 0.030 m m, and 1.020 m m with of 0.010 m m are recommended.

Along the red-edge (0.700 to 0.780 m m) the most frequently occurring wavebands were centered between 0.718 m m to 0.725 m m. The positive maxima in change in reflectance per unit change in wavelength along the red-edge occurs around 0.717 m m to 0.727 m m (see Figure4a through Figure4e). So a single waveband centered at 0.720 m m (l ₈) with an waveband width of 0.010 m m should suffice. Wavebands in the blue waveband portion of the spectrum were not very prominent. One waveband centered at 0.495 m m (l ₁ -later portion of the blue band) can be considered as more significant than the other blue bands (Table3). The waveband widths can be taken as 0.030 m m based on the results in Table3. l ₁₂ =1.025 m m represents the steep and sudden rise after the moisture sensitive "trough" of the NIR waveband to complete the 12 wavebands.

The above 12 narrow-wavebands provide optimal crop information. Most of these wavebands are not in any of the current generation of the sensor highlighting the usefulness of this research findings.

The outcome of this research lead to recommendation of a optimum number of hyperspectral wavebands, along with their optimal waveband widths, (Table7) required to best estimate agricultural crop biophysical characteristics. Data for this research was gathered from 5 crops (cotton, potato, soybeans, corn, and sunflower) each consisting of three biophysical variables (leaf area index-LAI, wet biomass-WBM, plant height-PLNTHT) and, for cotton only, yield (YLD). The hyperspectral data was obtained using a field spectroradiometer having 490 spectral channels, each of 1.43-nanometer-wide, and spread across the visible and NIR (0.350 to 1.050 m m) portion of the spectrum. The 4 types of hyperspectral vegetation indices used for estimating crop biophysical variables were: 1. multiple waveband reflectivity involving 490 channels, 2. narrow-waveband normalized difference vegetation indices (NDVI) involving all possible 2-band combinations of 490 wavebands, 3. narrow-waveband soil-adjusted indices, and 4. the derivative indices using near-continuous spectra along the chlorophyll red-edge (0.700 to 0.780 m m). The performance of the narrow-waveband indices were compared with broad-waveband indices.

The optimum multiple narrow-waveband reflectivity (OMNBR) models involving 2 to 4 independent variables, and the narrow-waveband NDVI models involving 2-bands performed the best amongst the different types of narrow-waveband and broad-waveband indices evaluated. A rigorous procedure adopted here to compute narrow-waveband NDVI models showed that the best 2-band combinations (see l ₁ and l ₂ of best 3 indices in Table3) often involve: (a) a red and a NIR or (b) a red and a green or (c) a red and a moisture sensitive portion of NIR, or (d) a red-edge and a NIR wavebands. These results demonstrates that the widely use red and NIR waveband combinations are not necessarily the best for 2-band NDVI indices for estimating crop variables. This is mainly as a result of the variability due to host of factors such as growth stage, growth condition, soil background, management variables and cultivar differences. Different wavebands or waveband combinations provide the best information depending on the host of variables mentioned. Even when a red and a NIR wavebands are involved they, often, appear in unique portions of the spectrum that are not part of any existing satellite sensor. For example, the best index (index 1) for cotton wet biomass had waveband centers at 0.682 m m for red and 0.918 m m for NIR with very narrow or narrow waveband widths (Table7 and Table3). The unique spectral responses from the narrow-wavebands in different portions of the spectrum in the OMNBR models helped in further improving the relationships relative to all other model types. The four-variable OMNBR models explained 3 to 40 percent additional variability relative to broad-waveband NDVI models compared to 3 to 16 percent additional variability explained by narrow-waveband NDVI models. In 8 out of 13 models evaluated, the 4-variable OMNBR models explained 4-38 percent additional variability relative to narrow-waveband NDVI models. The most frequently appearing narrow-wavebands in the 4-variable OMNBR models were (Table2): red (e.g., 682 m m), moisture sensitive NIR (e.g., 0.982 m m), green (e.g., 0.525 m m), and later portion of NIR (0.920 m m). However, OMNBR models do not offer the simplicity of the narrow-waveband 2-band models. Also, a significant proportion of the 2-band narrow-waveband NDVI models perform nearly as well as 4-variable OMNBR models. For example, The best OMNBR models for wet biomass (WBM) explained 79 percent variability for cotton, 80 percent variability for potato, 81 percent variability for soybeans, and 78 percent variability for corn. In comparison the best narrow-waveband NDVI models for WBM explained 79 percent variability for cotton, 76 percent variability for potato, 84 percent variability for soybeans, and 71 percent variability for corn. Similarly, the best OMNBR models for leaf area index (LAI) explained 70 percent variability for cotton, 80 percent variability for potato, 76 percent variability for soybeans, and 78 percent variability for corn. The best narrow-waveband NDVI models for LAI explained 66 percent variability for cotton, 88 percent variability for potato, 80 percent variability for soybeans, and 86 percent variability for corn. In OMNBR models, most of the variability in different crop variables were explained using the first 2 to 4 narrow-wavebands with addition of further wavebands adding only small (often, statistically insignificant) incremental increases in R² values. Also, it was established that when the ratio (M/N) of the number of independent variables (M) to that of total number of samples (N) exceeds anywhere between 0.15 to 0.20 "over-fitting" of OMNBR models will be a serious problem.

The NIR and red based NDVI indices are most widely used in remote sensing. This study recommends that the best hyperspectral narrow-waveband NIR and red based indices can be computed by taking: (a) very-narrow waveband centered at 0.682 m m (D l = 0.004 m m) for red, and (b) narrow-waveband centered at 0.920 m m (D l = 0.020 m m) for NIR. Two additional red wavebands (0.668 m m with D l = 0.004 m m, and 0.696 m m with D l = 0.004 m m) and one additional NIR waveband (0.845 m m with D l = 0.070 m m) have also been suggested.

The narrow-waveband transformed soil-adjusted vegetation index (TSAVI) models did not provide significant improvement in relationships compared to narrow-waveband NDVI models except in one case of potato WBM. Further studies are required where crop data from soils with distinct differences are investigated. The first-order derivative green vegetation index (DGVI1) models were highly correlated with crop biophysical variables by explaining 35 to 86 percent in their variability. However, overall the best derivative indices performed significantly poorer than an overwhelming proportion of the narrow-waveband NDVI, OMNBR, and even when compared with most of broad-waveband NDVI models. Derivative indices may be more suited for grassland canopies or crops with complex physiological conditions (e.g., dry and wet biomass intermix such as in later plant growth stages, significant soil background, significant presence of flower or other changes in canopy color).

The optimum number of wavebands and waveband widths (Table7) required to best model agricultural crop characteristics were established. The 12 narrow-wavebands (Table7) constitute a "new" sensor that is expected to provide optimal crop information. A remarkable cluster of information (Figure16) is located in specific narrow-wavebands within the later portion of red , 0.650 to 0.700 m m, with primary or secondary datasets in early portion of green, 0.500 to 0.550 m m, in one particular section of the near-infrared, 0.900 to 0.940 m m, and in the moisture sensitive near-infrared, centered at 0.975 m m. These waveband regions are followed by red-edge portion centered around 0.720 m m, and NIR shoulder centered around 0.845 m m. An overwhelming proportion of these channels had waveband widths that were classified as: (a) very narrow (0.001 m m to 0.015 m m wide); or (b) narrow (0.016 m m to 0.030 m m wide).

The 12 optimum number of wavebands (Table7) that have been recommended provide data from unique waveband centers that help optimize crop (and possibly all other vegetation) information. Many of these wavebands are not part of any of the present generation of sensors. The l ₁₀ (0.920 m m) is a new uniquely centered waveband that provides peak of NIR reflectance for most crops, l ₁₁ (0.975 m m) is "dip" maxima in the 0.940 to 1.040 m m portion of the spectrum and is in the crop moisture and biomass sensitive portion of the NIR waveband, l ₆ (0.682 m m) is the peak chlorophyll absorption (least reflectance) portion of the spectrum for most crops and growing conditions with very narrow-waveband width, and l ₃ (0.550 m m) is the "new" green narrow-waveband highlighting the reflectance peak in the visible waveband portion. The wavebands l ₂ (0.525 m m) is the point of greatest positive change in slope per unit change in wavelength in visible spectrum, and l ₄ (0.568 m m) is the greatest negative change in slope per unit change in wavelength in visible spectrum. Similarly, l ₈ (0.720 m m) represents the point of greatest positive change in slope per unit change in wavelength in red-edge portion of the spectrum. The other two red narrow-wavebands-l ₅ (0.668 m m), and l ₇ (0.696 m m), are of importance depending on crop type, growth stage, and growing conditions including cultural practices wherein there is a likelihood of absorption maxima shifting to these wavebands from the most common waveband (0.682 m m). The l ₁ = 0.495 m m is the most significant blue band and l ₁₂ =1.025 m m represents the steep and sudden rise after the moisture sensitive "trough" of the NIR waveband. The NIR shoulder is represented by a broad-waveband centered at 0.845 m m (l ₉) to complete the 12 wavebands.

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The authors would like to thank Prof. Dr Adel El-Beltagy, Director General, Dr John H. Dodds, Assistant Director General (Research) of the International Center for Agricultural Research in the Dry Areas (ICARDA) for permission and encouragement in carrying out this project. We are grateful for field work support and/or active participation of Mr. Afif Dakermanji, Dr. Mustafa Pala, Dr. Ahmed Osman, Dr. John Ryan, Mr. A.F. Tarsha, Dr. J. Diekmann, Dr. Mohan Saxena, Dr. Euan Thomson, Mr. Pierre Hayak, Mr. Zuhair Arous, Mr. Haitham Halimeh, Mr. Hisham Salalieh, Mr. Samir Masri, and Mr. Mohammed Salem of ICARDA. Thanks also for the useful discussions provided by our colleagues Dr. Frank Hole, Dr. Nicholos Kouchoukos, Mr. Paul Gluhosky, Mr. Art Gleason (currently with NOAA), Ms. Jane Foster, Mr. Jeff Albert, Dr. Xhui Hui , and Ms. Carrie Howard at the Center for Earth Observation (CEO), Yale University. The funding for the project comes from the National Aeronautics and Space Administration (NASA) Earth Science Enterprise (formerly, Mission to Planet Earth) grant number NAG5-3853.

Table1. Hyperspectral narrow-waveband and broad-waveband vegetation indices used in this study.

Table2. The best R² values and narrow-wavebands for 1-variable, 2-variable, and 4-variable hyperspectral narrow-waveband multiple linear vegetation index (OMNBR) models for different crop variables and their comparison with broad-waveband NDVI and narrow-waveband NDVI models^AA,BB.

Table3. Waveband-centers (l ₁ and l ₂) and waveband widths (D l ₁ and D l ₂) for the best 7 linear narrow-waveband NDVI models for different crop variables^AA.

Table4a and Table4b. The R² values for the 7 best linear, and non-linear hyperspectral narrow-waveband NDVI models and their comparison with narrow-waveband transformed soil adjusted vegetation indices (TSAVI) models, and broad-waveband NDVI models.

Table5. Slopes and intercepts of the soil line for the narrow-waveband TSAVI computed for the narrow-waveband NDVI-Index 1 models in Table3 and 4^AA.

Table6. Mean crop growth stage and crop type discrimination: biophysical variables and spectral indices^AA,BB.

Table7. Recommended optimal visible and NIR hyperspectral narrow-wavebands for agricultural crop and vegetation studies.

Figure1. Mean spectral plots of the five crops and the soils. The sample sizes were: cotton (73), potato (27), soybeans (26), corn (17), sunflower (9), and soils (43).

Figure2. Spectral reflectance characteristics of different crops at distinct growth phases. Sample sizes are shown inside the legend brackets of each crop.

Figure3. Illustrations of typical growth stages of 3 crops. Figure3a. cotton in yielding/harvest growth stage; Figure3b. cotton in flowering/critical growth stage; Figure3c. soybeans in early growth stage; Figure3d. soybeans in late vegetative/early flowering or critical growth stage; Figure3e. potato in early growth phases; and Figure3f. potato in late growth stages.

Figure4. First-order derivative spectral plots of the 5 crops. See the peaks of the first-order derivative spectra at about 0.525 m m (positive change in slope with unit change in wavelength is maximum around this in the visible spectrum), 0.568 m m (m (negative change in slope with unit change in wavelength is maximum around this in visible spectrum), and 0.718 m m m (positive change in slope with unit change in wavelength is maximum around this in Red-edge).

Figure5. Correlation coefficients (r) between spectral reflectivity in the 512 discrete channels and biophysical variables of the 5 crops for: (a) wet biomass (WBM), and (b) leaf area index (LAI).

Figure6. Plot of the ratio M/N (where, M is number of samples in total number of sample N) versus R² value.

Figure7. Contour plot showing R² values obtained from the relationships between wet biomass (WBM) and narrow-waveband NDVI values calculated for 490 narrow-wavebands spread across l ₁ (0.350 to 1.050 m m) and l ₂ (0.350 to 1.050 m m). R² values below the diagonal are for cotton WBM and R² values above the diagonal are for soybean WBM. Only the R² values above 0.4 are plotted for clarity. The different areas of "bulls-eye" are the regions with high R² values which were ranked and from which waveband centers (l ₁ and l ₂) and waveband widths (D l ₁ and D l ₂) were calculated for the 7 best indices of each crop variable as in Table3.

Figure8. Contour plot showing R² values obtained from the relationships between leaf area index (LAI) and narrow-waveband NDVI values calculated for 490 narrow-wavebands spread across l ₁ (0.350 to 1.050 m m) and l ₂ (0.350 to 1.050 m m). R² values below the diagonal are for corn LAI and R² values above the diagonal are for potato LAI. Only the R² values above 0.4 are plotted for clarity. The different areas of "bulls-eye" are the regions with high R² values which were ranked and from which waveband centers (l ₁ and l ₂) and waveband widths (D l ₁ and D l ₂) were calculated for the 7 best indices of each crop variable as in Table3.

Figure9. Comparison between the broad-waveband and the narrow-waveband soil adjusted indices for cotton WBM (a and b), and cotton LAI (c and d). NIR and red based indices of broad-wavebands and narrow-wavebands.

Figure10. Comparison between the broad-waveband and the narrow-waveband soil adjusted indices for potato WBM (a and b), and soybeans LAI (c and d). NIR and red based indices of broad-wavebands (a and c) versus visible waveband based indices of narrow-wavebands (b and d).

Figure11. Performance of visible waveband based narrow-waveband index (b) versus broad-waveband NIR and red based index (a) for corn crop. The sensitivity of the chlorophyll red-edge to soybean WBM is illustrated through a derivative index (c) and a red-edge and NIR based index (d).

Figure12. The contribution of the moisture sensitive NIR waveband (centered at 982 nanometers) in assessing potato LAI in a narrow-waveband index (b), soil adjusted version of this index (c) were compared with the broad-waveband index (a) and predicted LAI from 4-variable narrow-band index computed using multiple linear models (d).

Figure13. Crop variables predicted using 4-variable narrow waveband piecewise multiple linear models were plotted against their actual values for cotton YLD (a), soybean PLNTHT (b), cotton LAI (c), and corn WBM (d).

Figure14. The best two indices (in terms of R² values) for LAI of all crops. Index 1 involved 2 visible narrow-wavebands (a), and Index 2 involved NIR and red narrow-wavebands (b).

Figure15. The first- and the third-best indices (in terms of R² values) for WBM of all crops. Index 1 involved NIR and red narrow-wavebands (a), and Index 3 involved 2 visible narrow-wavebands (b).

Figure16. Percentage of occurrences of hyperspectral narrow-wavebands in the best 3 NDVI models and in best 3 narrow-waveband 4-variable multiple linear models.