Using Multispectral Imagery and Linear Spectral Unmixing Techniques for Estimating Crop Yield Variability

USING MULTISPECTRAL IMAGERY AND LINEAR SPECTRAL UNMIXING TECHNIQUES FOR ESTIMATING CROP YIELD VARIABILITY

C. Yang, J. H. Everitt, J. M. Bradford

ABSTRACT. Vegetation indices derived from multispectral imagery are commonly used to extract crop growth and yield information. Spectral unmixing techniques provide an alternative approach to quantifying crop canopy abundance within each image pixel and have the potential for mapping crop yield variability. The objective of this study was to apply linear spectral unmixing techniques to airborne multispectral imagery for estimating grain sorghum yield variability. Five time-sequential airborne multispectral images and yield monitor data collected from a grain sorghum field were used for this study. Both unconstrained and constrained linear spectral unmixing models were applied to the images to generate crop plant and soil abundances for each image and for all 26 multi-image combinations of the five images. Yield was related to unconstrained and constrained plant and soil abundances as well as to the normalized difference vegetation index (NDVI) and the green NDVI (GNDVI). Results showed that unconstrained plant abundance had better correlations with yield than NDVI for all five images, but GNDVI had better correlations with yield for the first three images. Unconstrained plant abundance derived from the fourth image provided the best overall correlation with yield (r = 0.88). Moreover, multi-image combinations generally improved the correlations with yield over single images, and the best three-image combination resulted in the highest overall correlation (r = 0.90) between yield and unconstrained plant abundance. These results indicate that linear spectral unmixing techniques can be a useful tool for quantifying crop canopy abundance and mapping crop yield. Keywords. Abundance, Endmember, Linear spectral unmixing, Multispectral imagery, Vegetation index, Yield monitor, Yield variability.

emote sensing data, including ground reflectance derived from the visible to NIR portion of the spectrum are spectra, satellite imagery, and airborne imagery, often used to quantify crop variables such as leaf area index, have long been used to extract crop growth and biomass, and yield (Tucker et al., 1980; Wiegand et al., 1991; yield information. Although these data can be di- Thenkabail et al., 1995; Yang and Anderson, 1999; Plant et Rrectly related to crop biophysical parameters, vegetation al., 2000; Yang et al., 2001). Yang et al. (2000) and Yang and indices derived from various wavebands in the data are more Everitt (2002) used two band ratios (NIR/Red and NIR/ effective and therefore are more widely used. Many of these Green), NDVI, and the green NDVI [GNDVI = (NIR − indices are formed from combinations of red and near- Green)/(NIR + Green)] derived from airborne color-infrared infrared (NIR) wavebands. Indices based on these two bands (CIR) imagery to generate yield maps for delineating within- exploit the fact that living green vegetation absorbs radiation field spatial variability as compared with yield monitor data. in the red band, due to the presence of chlorophyll and other Although vegetation indices are by far the most popular absorbing pigments in leaves, and strongly reflects radiation techniques for extracting quantitative biophysical informa- in the NIR band, because of the internal structure of the leaf tion, many, if not most, indices only use two spectral bands that is responsible for the high reflection. Two of the earliest in the data. This may be sufficient if the data contain only a and most widely used vegetation indices are the simple ratio few bands. However, if a large number of bands are available, (NIR/Red) (Jordan, 1969) and the normalized difference veg- as in some multispectral and hyperspectral data, other tech- etation index [NDVI = (NIR − Red)/(NIR + Red)] (Rouse et niques that can use all the bands in the data may have the po- al., 1973). These indices along with other vegetation indices tential to offer better results. Linear spectral unmixing is one such technique (Adams et al., 1986). Spectral mixing occurs when materials with different spectral properties are repre- Submitted for review in November 2005 as manuscript number IET sented by a single image pixel. Multispectral and hyperspec- 6192; approved for publication by the Information & Electrical Technolo- tral imagery can be viewed as a collection of band images, gies Division of ASABE in December 2006. Presented at the 2005 ASAE and each image pixel contains a spectrum of reflectance val- Annual Meeting as Paper No. 051018. ues for all the wavebands in the imagery. These spectra may Mention of trade names or commercial products in this article is solely be considered as the signatures of ground materials such as for the purpose of providing specific information and does not imply rec- ommendation or endorsement by the USDA. crop plants or soil, provided that the material occupies the The authors are Chenghai Yang, ASABE Member Engineer, Agricul- whole pixel. Spectra of mixtures can be analyzed with linear tural Engineer, James H. Everitt, Range Scientist, and Joe M. Bradford, spectral unmixing, which models each spectrum as a linear Supervisory Soil Scientist, USDA-ARS Kika de la Garza Subtropical Agri- combination of a finite number of pure spectra of the materi- cultural Research Center, Weslaco, Texas. Corresponding author: Cheng- hai Yang, USDA-ARS Kika de la Garza Subtropical Agricultural Research als located in the pixel area, weighted by their fractional Center, 2413 E. Highway 83, Weslaco, TX 78596; phone: 956-969-4824; abundances (Adams et al., 1986; Smith et al., 1990). The fax: 956-969-4893; e-mail: cyang@ weslaco.ars.usda.gov. unique ground materials are referred to as endmembers, and

Transactions of the ASABE Vol. 50(2): 667−674 2007 American Society of Agricultural and Biological Engineers ISSN 0001−2351 667 their spectra are referred to as endmember spectra. A simple (2) relate grain yield to plant and soil abundances as well as linear spectral unmixing model has the following form: to NDVI and GNDVI. m = + ε = yi ∑ aij x j i , i 1, 2, ..., n (1) = j 1 METHODS where IMAGERY AND YIELD DATA PREPROCESSING yi = measured reflectance in band i for a pixel Airborne digital CIR images and yield monitor data col- aij = known or measured reflectance in band i for lected from a 21 ha grain sorghum field in south Texas in 1998 endmember j were used for this study. The geographic coordinates near the ° ′ ″ ° ′ ″ xj = unknown fractional abundance for endmember j center of the field were 26 29 27 and 98 00 03 W. Grain ei = residual between measured and modeled reflectance sorghum (Asgrow 570) was planted to the field on 15 Febru- for band i ary and was harvested on 22 June. The CIR imagery was ac- m = number of endmembers quired on five different dates during the growing season using n = number of spectral bands. a three-camera digital imaging system described by Escobar This model is referred to as the unconstrained linear spec- et al. (1997). The system consisted of three Kodak MegaPlus tral unmixing model. For constrained linear spectral unmix- charge-coupled device (CCD) digital cameras and a comput- ing, the following additional condition should be satisfied: er equipped with three image-grabbing boards. The cameras were filtered for spectral observations in the visible green m = (555-565 nm), red (625-635 nm), and NIR (845- 857 nm) ∑ x j 1 (2) j=1 bands. The image-grabbing boards had the capability to cap- ture 8-bit image frames with 1024 × 1024 pixels. CIR imag- That is, the fractional abundances for all the endmembers es were obtained at an altitude of approximately 1680 m should sum to unity. Nevertheless, both unconstrained and (5500 ft) between 12:00 and 15:00 h local time under sunny constrained unmixing can result in negative abundance val- conditions on five dates: 15 and 22 April, 18 and 29 May, and ues and values greater than 1 for any endmember. Assuming 16 June 1998. A Cessna 206 aircraft was used to acquire the that the endmembers are not linearly dependent, the mixing imagery. The imagery had a ground pixel size of approxi- fractions can be determined from the data. For a given num- mately 1 m. ber of spectral bands n, an exact solution can be found for The three band images in each composite CIR image were each pixel for the unconstrained model if m = n and for the first registered to correct the misalignments among them. constrained model if m = n + 1. However, if m < n for uncon- The registered CIR images were then rectified to the Univer- strained unmixing or if m < n + 1 for constrained unmixing, sal Transverse Mercator (UTM), World Geodetic Survey then a least squares fitting procedure can be applied to obtain 1984 (WGS-84), Zone 14, coordinate system based on the best fit. ground control points located with a submeter-accuracy GPS The fractional abundances determined by linear spectral Pathfinder Pro XRS system (Trimble Navigation Limited, unmixing may be preferred to band ratios and NDVI for Sunnyvale, Cal.). All rectified images were resampled to a tracking spectrally defined materials (i.e., endmembers) spatial resolution of 1 m using the nearest-neighbor resam- since it uses all the bands in the data (Bateson and Curtiss, pling method. Total RMS (root mean square) errors for all 1996). When linear spectral unmixing is applied to an image, rectified images were less than 2 m. For radiometric calibra- it produces a suite of abundance images, one for each end- tion, reflectance spectra were taken from three sites (an as- member in the model. Like a NDVI image, each abundance phalt road, a concrete parking lot, and a roof) within the image shows the spatial distribution of the spectrally defined image. These sites had stable reflectance response over the material. season and represented a wide range of reflectance values. Different varieties of linear spectral unmixing have been The reflectance spectra for the three sites were measured us- used with multispectral and hyperspectral imagery for map- ing a FieldSpec HandHeld spectroradiometer (Analytical ping the abundance and distributions of geological materials Spectral Devices, Inc., Boulder, Colo.) sensitive in the 350 to and vegetation types in many different applications (Adams 1050 nm portion of the spectrum with a nominal spectral res- et al., 1986, 1995; Roberts, et al., 1998; Lobell and Asner, olution of 1.4 nm. Each rectified multispectral image was 2004). However, there has been no report on the use of this converted to reflectance based on the calibration equations technique for estimating crop yield variations. As many veg- for the three bands determined between the measured reflec- etation indices such as NDVI are an indirect measure of plant tance and the digital count values extracted from the image vigor and abundance, the fractional abundance of crop plants at the three sites. The procedures for image registration, recti- determined from linear spectral unmixing is a more direct fication, and calibration were performed using ERDAS measure of plant abundance and provides a more intuitive IMAGINE (Leica Geosystems Geospatial Imaging, LLC, link between image data and ground observations. For exam- Norcross, Ga.). The images were then used in ENVI (Re- ple, field observers can readily understand the significance of search Systems, Inc., Boulder, Colo.) for linear spectral un- a pixel having 80% green vegetation and 20% soil, but they mixing analysis. have more difficulty interpreting the equivalent band reflec- Yield data were collected using an AgLeader Yield Moni- tance values and vegetation index values. tor 2000 system (Ag Leader Technology, Ames, Iowa) inte- The objectives of this study were to: (1) apply linear spec- grated with a submeter AgGPS 132 receiver (Trimble tral unmixing techniques to airborne CIR imagery for esti- Navigation Limited, Sunnyvale, Cal.). Instantaneous yield, mating grain sorghum plant and soil abundances, and moisture, and GPS data were simultaneously recorded at 1 s intervals. The combine equipped with the yield monitoring

668 TRANSACTIONS OF THE ASABE system had an effective cutting width of 8.69 m (nine 38 in. Since the number of endmembers (m = 2) was smaller than rows). The yield monitor was calibrated to ensure data accu- the number of bands in each original CIR image (n = 3) or in racy before grain was harvested in late June. The yield and each combined image (n = 6, 9, 12, or 15), the least squares GPS data were viewed and evaluated using SMS Basic soft- fitting procedure was used to determine the fractional abun- ware (Ag Leader Technology, Ames, Iowa). Points falling on dance images for both unconstrained and constrained unmix- the top of a harvested path or points with extreme high or low ing models. values along each path were first examined and then removed In order to examine how variations in endmember spectra if they were determined to be erroneous. The filtered yield affect the results, 27 different plant spectra were generated by data were exported in ASCII format for further filtering and varying the spectrum values for each of the three bands at processing using self-developed programs. An optimum time three different levels. The digital spectrum values for each lag of 12 s, as determined using the method of Yang et al. band were set to be 0.8, 1.0, or 1.2 times the original plant (2002), was used to align yield data with position data. Yield spectrum values. Both unconstrained and constrained spec- data were adjusted to 14% moisture content. tral unmixing procedures were performed on the 29 May image for each of the 27 plant spectra. LINEAR SPECTRAL UNMIXING ANALYSIS The first important step in linear spectral unmixing analy- GIS AND STATISTICAL ANALYSIS sis is to determine the endmembers and their spectra. Many The CIR images and fractional abundance images were studies of spectral unmixing have used uncalibrated spectra converted into grids in ArcInfo (ESRI, Inc., Redlands, Cal.). derived from training areas of images as endmember spectra The preprocessed yield data were imported into ArcInfo as a (Adams et al., 1995). When relatively pure, image endmem- point coverage. Since the combine’s effective cutting width bers can be used to model mixed pixels within an image. Be- was 8.69 m and the cell size of the image data was 1 m, these cause of different plant growth stages and temporally variant images were aggregated by a factor of 9 to increase the cell soil surface and moisture conditions during a growing season, size to 9 m. The digital value for each output cell for each the reflectance spectra of crop plants and soil background band image and each fractional abundance image was the change from time to time. Therefore, endmember spectra de- mean of the 81 input cells that the 9 × 9 m output cell encom- rived from an image should be used only for that particular passed. The yield value for each output cell was the mean of image, no matter whether the image is radiometrically cali- the yield points falling within the 9 × 9 m output cell. On the brated or not. It is not feasible to use image endmember spec- average, each output cell contained seven yield points. tra derived from one image taken on a particular date for In order to see how the aggregation of abundance values images taken on other dates. In this study, grain sorghum from 1 m cell size to 9 m cell size was compared with the plants and bare soil were selected as two meaningful end- abundance values derived directly from images with 9 m cell members. To obtain pure spectra for sorghum plants, 20 pix- size, the five images were aggregated from 1 m cell size to els that had a bright red color (corresponding to healthy plants 9 m cell size. Then both unconstrained and constrained linear on a CIR image) were first identified from the 15 April image, spectral unmixing models were applied to the images with and the same pixels were then viewed on the other four imag- 9 m cell size. es to make sure the training pixels on all five images repre- Vegetation indices NDVI and GNDVI were derived from sented some of the most healthy sorghum plants. Similarly, the three spectral bands of each CIR image for comparison 20 pixels that contained pure bare soil were identified from with spectra unmixing results. Correlation matrices were cal- the first image and verified on the other four images. culated among grain sorghum yield, the two vegetation The endmember spectra for plants and soil for each image indices, and all the plant and soil abundance images. Linear were obtained by averaging the spectra of the respective regression was performed to determine the best-fitting equa- training pixels from that image. Although the same training tions and their coefficients of determination (r2) for relating pixel locations were used to extract endmember spectra from yield to each vegetation index and to each fractional abun- all the images in this study, different training pixels could dance index. Statistical analysis was performed using SAS have been used for different images as long as reliable pixels software (SAS Institute Inc., Cary, N.C.). were identified from each image. Alternatively, computer- ized methods such as the pixel purity index and the n- dimensional visualizer in ENVI can be used to identify purest RESULTS AND DISCUSSION pixels for the endmembers. However, these automatic meth- Table 1 summarizes the simple statistics of plant and soil ods are not always reliable. For example, weed plants can be abundances derived from the five time-sequential airborne mixed with crop plants, and atypical soil surface areas with CIR images for the grain sorghum field based on both the un- too dark or too bright colors can be misidentified as typical constrained and constrained unmixing models. The statistics soil. Since there were only two endmembers in this particular for the sum of plant and soil abundances are also presented. application, simple manual identification of pure pixels of Ideally, fractional abundance values should be within the 0-1 each endmember was reliable and efficient. range, but in practice abundances may assume negative val- Originally, there were five CIR images, and each had three ues and values greater than 1. This is because spectral unmix- bands. By stacking two to five of the CIR images, 26 new im- ing results can be affected by the purity of the endmembers ages with 6 to 15 bands were generated. Both unconstrained and the completeness of endmembers. Moreover, the lineari- and constrained linear spectral models were applied to: (1) ty assumption of linear spectral unmixing is at best an the five individual CIR images, (2) the ten combinations of approximation of the generally non-linear mixing of surface any two CIR images, (3) the ten combinations of any three materials. Therefore, the simple statistics of the abundance CIR images, (4) the five combinations of any four CIR imag- values can be used to determine how well the linear es, and (5) the combined image from the five CIR images.

Vol. 50(2): 667−674 669 Table 1. Simple statistics of endmember abundances derived from air- abundance values greater than 1 (17.9%), while the 29 May borne color-infrared images obtained from a 21 ha grain image resulted in the largest percentage of soil abundance sorghum field in south Texas on five different dates in 1998. [b] values less than 0 (16.6%). For the constrained model, the Endmember Abundance 18 May image had the largest percentage of plant abundance UPA CPA values greater than 1 (20.0%) and the largest percentage of [a] Statistic UPA USA +USA CPA CSA +CSA soil abundance values less than 0 (20.0%). 15 April Mean unconstrained plant abundance was the lowest <0 0.0% 1.5% 0.0% 1.0% 1.2% 0.0% (0.56) on 15 April, increased to 0.63 on 22 April, reached its Min. −0.02 −0.10 0.69 −0.22 −0.29 1.00 maximum (0.86) on 18 May, and then decreased to 0.80 on Mean 0.56 0.33 0.89 0.46 0.54 1.00 29 May and 0.73 on 16 June. This general trend agreed with STD 0.19 0.17 0.07 0.23 0.23 0.00 the plant growth pattern of grain sorghum. The 15 April Max. 1.19 0.92 1.11 1.29 1.22 1.00 image was taken when plants were at the boot stage (plant >1 0.9% 0.0% 7.5% 1.2% 1.0% 0.0% head extended into the flag leaf sheath) and canopy cover was 22 April over 50%, and the 22 April image was taken one week later <0 0.0% 12.3% 0.0% 0.1% 5.0% 0.0% while the plants were predominately in the same stage. By Min. −0.04 −0.21 0.56 −0.06 −0.36 1.00 18 May, the plants were at the bloom stage and most of the Mean 0.63 0.25 0.88 0.62 0.38 1.00 plants were fully expanded and reached their maximum can- STD 0.26 0.22 0.10 0.27 0.27 0.00 opy cover and vigor. When the 29 May image was taken, the Max. 1.34 0.94 1.18 1.36 1.06 1.00 plants were at the soft-dough and hard-dough stages and still >1 5.2% 0.0% 11.7% 5.0% 0.1% 0.0% provided maximum canopy cover, but some of the leaves 18 May started showing dull green coloration and necrotic lesion. Al- <0 0.0% 14.8% 0.0% 0.2% 20.0% 0.0% though the amount of plant materials did not decrease, the Min. 0.04 −0.07 0.77 −0.05 −0.27 1.00 plant abundance values decreased. This is because only two Mean 0.86 0.11 0.97 0.83 0.17 1.00 endmembers (plants and soil) were used in the model and the STD 0.18 0.14 0.05 0.22 0.22 0.00 Max. 1.17 0.89 1.12 1.27 1.05 1.00 spectral deviation from the spectrum for healthy plants would >1 17.9% 0.0% 26.9% 20.0% 0.2% 0.0% lower the plant abundance estimate. The 16 June image was taken shortly before harvest, when the plants were approach- 29 May ing physiological maturity and the leaves were senescing. <0 0.0% 16.6% 0.0% 0.2% 14.6% 0.0% Again, although there was little change in the amount of plant Min. 0.10 −0.12 0.75 −0.08 −0.20 1.00 Mean 0.80 0.16 0.96 0.76 0.24 1.00 materials, the spectral characteristics of the plants changed STD 0.21 0.19 0.07 0.25 0.25 0.00 significantly, resulting in lower plant abundance estimates. Max. 1.12 0.86 1.15 1.20 1.08 1.00 As expected, mean unconstrained soil abundance had the >1 7.6% 0.0% 30.0% 14.6% 0.2% 0.0% opposite trend, with the highest value (0.33) for the 15 April 16 June image and the lowest value (0.11) for the 18 May image. The <0 0.0% 10.8% 0.0% 0.4% 5.8% 0.0% mean sums of unconstrained plant and soil abundances were Min. 0.10 −0.12 0.81 −0.05 −0.19 1.00 0.89, 0.88, 0.97, 0.96, and 0.96 for the five time-sequential Mean 0.73 0.23 0.96 0.69 0.31 1.00 images from 15 April to 16 June, respectively. Although the STD 0.24 0.22 0.04 0.26 0.26 0.00 unconstrained model did not force the endmember abun- Max. 1.16 0.92 1.09 1.19 1.05 1.00 dances to sum to 1, these sum abundance values were close >1 7.2% 0.0% 16.5% 5.8% 0.4% 0.0% to 1, especially for the three later dates, indicating that the un- [a] <0 = samples with abundance values less than 0 as a percentage of the constrained two-endmember linear unmixing model was ap- total number of samples (total number of samples = 2497), and >1 = propriate for characterizing plant and soil abundances in the samples with abundance values greater than 1 as a percentage of the total images. The difference between 1 and the sum abundance number of samples. value was partly due to endmembers unaccounted for [b] UPA = unconstrained plant abundance, USA = unconstrained soil abundance, CPA = constrained plant abundance, and CSA = constrained (i.e., shading) in the model. For example, the unconstrained soil abundance. model explained only 88% of the materials for the 22 April image. In addition to shade, the wet soil background in a unmixing models work for a particular image. Table 1 also small portion of the field, which was being irrigated at the presents the percentage of samples that had negative values time of imaging, was not accounted for in the unconstrained and the percentage of samples that had values greater than 1. model. For the constrained model, the sum abundance was 1 Overall, the majority of the abundance values for the two because the constrained model forced the endmember abun- endmembers fell in the 0-1 range for the five time-sequential dances to sum to 1. Therefore, endmember abundances may images based on the unconstrained and constrained models. have been under- or overestimated if some significant end- The 15 April image had the best results for the unconstrained members were not included in the model. In fact, mean model, with only 0.9% of the plant abundance values greater constrained plant abundance values were 0.46, 0.62, 0.83, than 1 and 1.5% of the soil abundance values less than 0. This 0.76, and 0.69 for the five time-sequential images from image also had the best results for the constrained model, 15 April to 16 June, respectively. These constrained plant with 1.2% of the plant abundance values greater than 1 and abundance values had a similar trend as the unconstrained 1.2% of the constrained soil abundance values less than 0. values, but were consistently lower than the respective un- The other four images had larger percentages of abundance constrained abundance values. On the other hand, the values falling outside the 0-1 range. For the unconstrained constrained soil abundance values were consistently higher model, the 18 May image had the largest percentage of plant than the respective unconstrained abundance values. There- fore, unconstrained linear unmixing may be more appropri−

670 TRANSACTIONS OF THE ASABE Table 2. Correlation coefficients (r) between yield monitor data and Table 4. Correlation coefficients (r) between yield monitor data and spectral variables (two vegetation indices and four endmember abun- endmember abundances derived from different combinations of dances) derived from airborne color-infrared images obtained from a five time-sequential airborne color-infrared images obtained 21 ha grain sorghum field in south Texas on five different dates in 1998. from a 21 ha grain sorghum field in south Texas in 1998. The spectral variables were based on the vegetation indices and abun- Endmember Abundance[b] dance images aggregated from 1 m cell size to 9 m cell size. Image Combination[a] UPA USA CPA CSA Date[b] Spectral 1-2 0.786* −0.711* 0.779* −0.779* Variable[a] 15 April 22 April 18 May 29 May 16 June 1-3 0.833* −0.781* 0.827* −0.827* NDVI 0.709* 0.747* 0.775* 0.849* 0.837* 1-4 0.888* −0.846* 0.837* −0.837* GNDVI 0.757* 0.799* 0.843* 0.858* 0.844* 1-5 0.875* −0.850* 0.851* −0.851* UPA 0.732* 0.788* 0.816* 0.877* 0.853* 2-3 0.837* −0.725* 0.850* −0.850* USA −0.680* −0.715* −0.820* −0.840* −0.825* 2-4 0.887* −0.810* 0.872* −0.872* CPA 0.696* 0.789* 0.797* 0.823* 0.858* 2-5 0.881* −0.817* 0.881* −0.881* CSA −0.696* −0.789* −0.797* −0.823* −0.858* 3-4 0.842* −0.798* 0.837* −0.837* [a] NDVI = (NIR − Red) / (NIR + Red), GNDVI = (NIR − Green) / (NIR + 3-5 0.844* −0.831* 0.839* −0.839* Green). UPA = unconstrained plant abundance, USA = unconstrained 4-5 0.881* −0.859* 0.855* −0.855* soil abundance, CPA = constrained plant abundance, and CSA = 1-2-3 0.847* −0.742* 0.852* −0.852* constrained soil abundance. [b] * = significant at the 0.0001 level. Number of samples = 2497. 1-2-4 0.876* −0.803* 0.854* −0.854* 1-2-5 0.866* −0.806* 0.856* −0.856* 1-3-4 0.860* −0.804* 0.851* −0.851* Table 3. Correlation coefficients (r) between yield monitor data and spectral variables (two vegetation indices and four endmember abun- 1-3-5 0.862* −0.830* 0.855* −0.855* dances) derived from airborne color-infrared images obtained from a 1-4-5 0.898* −0.872* 0.865* −0.865* 21 ha grain sorghum field in south Texas on five different 2-3-4 0.865* −0.772* 0.868* −0.868* dates in 1998. The spectral variables were based on the vegetation 2-3-5 0.865* −0.794* 0.871* −0.871* indices and abundance images with 9 m cell size. 2-4-5 0.902* −0.849* 0.887* −0.887* [b] Spectral Date 3-4-5 0.860* −0.828* 0.854* −0.854* Variable[a] 15 April 22 April 18 May 29 May 16 June 1-2-3-4 0.871* −0.781* 0.868* −0.868* NDVI 0.715* 0.752* 0.771* 0.852* 0.838* 1-2-3-5 0.871* −0.797* 0.871* −0.871* GNDVI 0.762* 0.803* 0.845* 0.860* 0.845* 1-2-4-5 0.897* −0.843* 0.876* −0.876* UPA 0.740* 0.793* 0.816* 0.880* 0.854* 1-3-4-5 0.874* −0.835* 0.864* −0.864* USA −0.685* −0.719* −0.821* −0.842* −0.826* 2-3-4-5 0.879* −0.814* 0.878* −0.878* CPA 0.704* 0.793* 0.797* 0.827* 0.860* 1-2-3-4-5 0.884* −0.816* 0.878* −0.878* CSA −0.704* −0.793* −0.797* −0.827* −0.860* [a] 1 = 15 April, 2 = 22 April, 3 = 18 May, 4 = 29 May, and 5 = 16 June. [b] [a] NDVI = (NIR − Red) / (NIR + Red), GNDVI = (NIR − Green) / (NIR + * = significant at the 0.0001 level. Number of samples = 2497. Green), UPA = unconstrained plant abundance, USA = unconstrained UPA = unconstrained plant abundance, USA = unconstrained soil soil abundance, CPA = constrained plant abundance, and CSA = abundance, CPA = constrained plant abundance, and CSA = constrained constrained soil abundance. soil abundance. [b] * = significant at the 0.0001 level. Number of samples = 2497. plant abundance for the 29 May image also provided the best ate than constrained linear unmixing for this particular ap- overall correlation with yield (0.88) among all the images. plication. Moreover, unconstrained plant abundance had better correla- Tables 2 and 3 summarize the correlation coefficients of tions with yield than NDVI for all five images. It also gave grain yield with two vegetation indices and four plant and soil better correlations than unconstrained soil abundance for all abundances for the five time-sequential airborne CIR images the images except for the 18 May image. Both constrained of the grain sorghum field based on aggregated abundance plant and soil abundances had identical absolute correlations values from the abundance images with 1 m cell size and non- with yield. However, constrained abundances had lower cor- aggregated abundance values with 9 m cell size, respectively. relations with yield than unconstrained plant abundances for A comparison of the two tables shows that the r-values based three of the five images. on the aggregated abundance values are essentially the same Table 4 presents the correlation coefficients between yield as those based on the non-aggregated abundance values. monitor data and endmember abundances derived from dif- Moreover, the mean and standard deviation for the plant and ferent combinations of the five time-sequential images. Sim- soil abundances based on the non-aggregated abundance val- ilar to the results for the individual images, unconstrained ues with 9 m cell size (not shown) were exactly the same (to plant abundance was generally better related with yield than the 1/100) as those shown in table 1. Therefore, aggregating unconstrained soil abundance or constrained abundances. abundance values from 1 m cell size to 9 m cell size was a fea- The correlation coefficients for the best two-, three-, four-, sible approach in the correlation analysis. and five-image combinations were 0.89, 0.90, 0.90, and 0.88, Grain yield was positively related to the two vegetation respectively. These r-values were slightly higher than or sim- indices and the unconstrained and constrained plant abun- ilar to the best r-value (0.88) for the 29 May image. Moreover, dances, and negatively related to the unconstrained and the four- and five-image combinations did not have better constrained soil abundances. GNDVI provided the best cor- r-values than the three-image combination. A possible ex- relations with yield for the first three images, while uncon- planation for this may be that variations in the additional im- strained plant abundance had the best correlation for the ages were already contained in the best three-image 29 May image and constrained plant or soil abundance had combination and some of these additional variations might the best correlation for the 16 June image. The unconstrained not be due to the variation in yield. Nevertheless, the unmix−

Vol. 50(2): 667−674 671 Table 5. Correlation coefficients (r) between yield monitor data and Table 6. Linear regression results for relating grain sorghum yield to endmember abundances based on 27 different plant spectra and one plant abundance derived from the best single image and the best two-, soil spectrum. The endmember abundances were derived from three-, four-, and five-image combinations of five time-sequential air- an airborne color-infrared image obtained from a 21 ha borne color-infrared images obtained from a 21 ha grain sorghum field grain sorghum field in south Texas on 29 May 1998. in south Texas in 1998. For comparison, linear regression Endmember Abundance[b] results for relating grain yield to NDVI and GNDVI Plant for the best-single image are also presented. Spectrum[a] UPA USA CPA CSA Image Model SE[c] 0.8-0.8-0.8 0.877* −0.840* 0.878* −0.878* Combination[a] Regression Equation[b] r2 (kg/ha) 0.8-0.8-1.0 0.876* −0.846* 0.877* −0.877* 4 Yield = −1787 + 8226*UPA 0.769 941 0.8-0.8-1.2 0.875* −0.848* 0.875* −0.875* 1−4 Yield = −1867 + 9427*UPA 0.788 902 0.8-1.0-0.8 0.878* −0.851* 0.879* −0.879* 2−4−5 Yield = −1451 + 8405*UPA 0.813 848 0.8-1.0-1.0 0.876* −0.856* 0.876* −0.876* 1−2−4−5 Yield = −1422 + 8848*UPA 0.804 867 0.8-1.0-1.2 0.875* −0.859* 0.872* −0.872* 1−2−3−4−5 Yield = −2315 + 9188*UPA 0.781 917 0.8-1.2-0.8 0.878* −0.858* 0.878* −0.878* 4 Yield = −12229 + 24691*NDVI 0.721 1034 0.8-1.2-1.0 0.877* −0.864* 0.873* −0.873* 4 Yield = −16122 + 31100*GNDVI 0.737 1005 0.8-1.2-1.2 0.876* −0.866* 0.866* −0.866* [a] 1 = 15 April, 2 = 22 April, 3 = 18 May, 4 = 29 May, and 5 = 16 June. 1.0-0.8-0.8 0.877* −0.821* 0.836* −0.836* [b] The best fitting linear model relating yield to plant abundance was 1.0-0.8-1.0 0.877* −0.829* 0.829* −0.829* significant at the 0.0001 level. Number of samples = 2497. 1.0-0.8-1.2 0.876* −0.834* 0.822* −0.822* UPA = unconstrained plant abundance, NDVI = (NIR − Red) / (NIR + 1.0-1.0-0.8 0.878* −0.832* 0.830* −0.830* Red), and GNDVI = (NIR − Green) / (NIR + Green). [c] 1.0-1.0-1.0 0.877* −0.840* 0.823* −0.823* SE = standard error. 1.0-1.0-1.2 0.876* −0.845* 0.815* −0.815* 1.0-1.2-0.8 0.878* −0.841* 0.823* −0.823* Compared with the reference r-value (0.877) for the origi- 1.0-1.2-1.0 0.877* −0.849* 0.811* −0.811* nal spectrum, the change in correlation coefficients was very 1.0-1.2-1.2 0.877* −0.854* 0.807* −0.807* small, indicating that small to moderate variations in end- 1.2-0.8-0.8 0.877* −0.804* 0.807* −0.807* member spectra had very little effect on the correlation with 1.2-0.8-1.0 0.877* −0.813* 0.801* −0.801* yield for unconstrained plant abundance. For unconstrained 1.2-0.8-1.2 0.876* −0.820* 0.795* −0.795* soil abundance, the r-values ranged from −0.804 for the 1.2-1.0-0.8 0.878* −0.815* 0.801* −0.801* 1.2-0.8-0.8 plant spectrum to −0.866 for the 0.8-1.2-1.2 plant 1.2-1.0-1.0 0.877* −0.824* 0.796* −0.796* spectrum. The deviations from the reference r-value (−0.840) 1.2-1.0-1.2 0.877* −0.831* 0.790* −0.790* were slightly larger, but still relatively small. For constrained 1.2-1.2-0.8 0.878* −0.825* 0.796* −0.796* plant or soil abundance, the r-values ranged from 0.783 for 1.2-1.2-1.0 0.878* −0.834* 0.790* −0.790* the 1.2-1.2-1.2 plant spectrum to 0.878 for the 0.8-0.8-0.8 1.2-1.2-1.2 0.877* −0.840* 0.783* −0.783* plant spectrum, with a larger deviation from the reference [a] 0.8-1.0-1.2 represents a plant spectrum generated by multiplying the r-value (0.823) than for unconstrained plant or soil abun- NIR, red, and green digital values in the original endmember spectrum dance. Therefore, the unconstrained model did not appear to for sorghum plants by 0.8, 1.0, and 1.2, respectively, while the soil be as sensitive to the variation in endmember spectra as the spectrum remained the same. 1.0-1.0-1.0 represents the original plant spectrum. constrained model, and unconstrained abundance values [b] * = significant at the 0.0001 level. Number of samples = 2497. seemed to provide better and stable correlations with yield UPA = unconstrained plant abundance, USA = unconstrained soil than constrained abundance values. abundance, CPA = constrained plant abundance, and CSA = constrained Table 6 summarizes the linear regression results for relat- soil abundance. ing grain sorghum yield to unconstrained plant abundance derived from the best single image and the best two-, three-, ing techniques allowed more bands to be used and produced four-, and five-image combinations of the five time- better correlations than any of the single images or any of the sequential airborne CIR images. For comparison, the linear vegetation indices. regression results for relating grain yield to NDVI and to The purity of the endmembers derived from the images GNDVI are also presented in table 6. The r2 values were 0.77, had a direct effect on the results of linear spectral unmixing. 0.79, 0.81, 0.80, and 0.78 for the best single image (29 May), Inaccurate endmember spectra could cause inaccurate plant two-image (15 April and 29 May), three-image (22 April, and soil abundance estimation, thus affecting the correlations 29 May, and 16 June), four-image (15 and 22 April, 29 May, between yield and abundances. In order to demonstrate the and 16 June), and five-image combinations, respectively. effect of the variation in endmember spectra on the correla- The best two-image combination explained 2% more of the tions with yield, table 5 summarizes the correlation coeffi- yield variability than the best single image, while the best cients between yield and plant and soil abundances based on three-image combination explained 2% more variability than the 27 different plant spectra and the original soil spectrum the best two-image combination. And the four- and five- for the 29 May image. The plant spectrum 1.0-1.0-1.0 is the image combinations explained even less variability in yield original spectrum extracted from the image, and the r-values than the three-image combination. Compared with uncon- for the spectrum can be used as a reference for comparison. strained plant abundance, NDVI and GNDVI explained 72% When the spectral values of each of the three bands in the and 74% of the variability in yield, respectively, based on the original plant spectrum varied from 80% to 120% of the orig- best overall relations with yield from the 29 May image. inal values, the correlation coefficients between yield and un- Figure 1 shows scatter plots and regression lines between constrained plant abundance varied from 0.875 for the grain sorghum yield and plant abundance derived from the 0.8-0.8-1.2 plant spectrum to 0.878 for many of the plant best single image and the best two- and three-image com- spectra. binations as well as the scatter plot and regression results

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Figure 1. Scatter plots and regression lines between grain sorghum yield and plant abundance derived from the best (a) single image (29 May), (b) two- image combination (15 April and 29 May), and (c) three-image combination (22 April, 29 May, and 16 June) of five time-sequential airborne color- infrared images, as compared with the regression results between yield and (d) the best GNDVI (29 May) for a 21 ha grain sorghum field in south Texas in 1998.

between yield and GNDVI. It can be seen from the plots that ages, while GNDVI had better correlations with yield than plant fractional abundance derived from the best two- and plant abundance for some of the images. Nevertheless, un- three-image combinations provided better estimation than constrained plant abundance provided the best overall cor- GNDVI for higher yield values. relation with yield. Moreover, unconstrained plant abundance derived from the best two- and three-image combinations provided better correlations with yield than any CONCLUSIONS single image or any of the two vegetation indices. These results indicate that linear spectral unmixing tech- This study demonstrated the use of linear spectral unmix- niques can be a useful tool for quantifying crop canopy abun- ing techniques for determining grain sorghum plant and soil dance and mapping crop yield. Since spectral unmixing abundances from airborne multispectral imagery for crop allows all the bands in an image or in a multi-image combina- yield estimation. The unconstrained and constrained two- tion to be used, it has the potential to provide better results endmember linear spectral unmixing models presented in than vegetation indices in some applications. Therefore, this article proved to be appropriate for determining plant and spectral unmixing techniques can be used in conjunction with soil abundances. Both unconstrained and constrained abun- vegetation indices for extracting crop growth and yield infor- dances were significantly related to yield. Compared with mation. This study was one of the first, if not the first, to use NDVI and GNDVI, unconstrained plant abundance had bet- linear spectral unmixing techniques for crop yield estima- ter correlations with yield than NDVI for each of the five im- tion. Although the results were promising, further research is

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