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.