Linear mixture modeling for quantifying vegetation cover using time series NDVI data
Linear Mixture Modeling
Linear mixture modeling assumes that each image pixel contains information about the proportion and the
spectral response of each component within the ground resolution unit, and the response of each pixel is
taken as linear combination of the responses of all components in the mixed target. Actually, this
assumption should be true only for original channels. However, recent studies have demonstrated that a
linear combination of NDVI values implies only very minor inaccuracies (Kerdiles and Grondona, 1995). In
this study, the linear mixture model can be formulated as
Where i tNDVI is the time series monthly composite NDVI value for a pixel in period band i , ij pNDVI is the
pure monthly composite NDVI value of component j in period band i , j f is the proportion of component
j in the pixel, and i e is the error term for period band i
Subject to the constraints
Since the sum of the proportions for any resolution element must be one and the proportion values must be
nonnegative. The Constrained Least Squares method is applied to estimate the proportion of each
component in a pixel by minimizing the sum of squares of the errors.
Local Area Study
Test Area
The test area , 90 x 60 km, with geographical coordinates from 42 0 15þN to 42 0 45þN and 122 0 0þE to
122 0 45þ E, is located in a typical agricultural area of Liaoning province in the northeast region of China. The
main cover types are forests, pastures and crops. The most common crops are corn and paddy, as well as
soybean, wheat, etc. Dominant forests consist of pine and poplar. The main crop season is from April to
October. The information collected by ground truth survey is useful for t he classification of multi-temporal
Landsat TM, NOAA AVHRR and SPOT VEGETATION monthly composite NDVI data and the application
of linear mixture modeling.
Image Data and Preprocessing
Two Landsat TM images are used as the basis for endmember collection in linear mixture modeling, and in
validation of the fraction images. The multitemporal Landsat TM images collected on 19 May 1994 and 8
September 1994 are selected mainly because they are the cloud- free s cenes in the crop season. A scene
of 2700 x 1800 pixels is cut from each Landsat TM image and georeferenced using nearest neighbor
resampling algorithm, with resampling size of 25m pixel yielding RMS error of less than 1 pixel. All
channels of TM data are used except the thermal channel 6.
The NOAA AVHRR 1km 10-day composite NDVI data spanning April 1992 through March 1993 is based
on the Interrupted Goode Homolosine map projection. In order to march different purposes, it is
transformed to latitude/longitude projection (Plate Carree Projection) with 30-seconds resolution. The
SPOT VEGETATION 1km 10 -day composite NDVI data spanning from January to December 2000 is
already in latitude/longitude projection with 1/112-degree pixel size. It is also transformed to 30-seconds
resolution. Then, these dataset are recomposed to monthly composite NDVI dataset based on maximum
value compositing method, in which the NDVI is examined pixel by pixel during the compositing process to
determine the maximum value. The retention of the highest NDVI value reduces the number of
cloud- contaminated pixels and selects the pixels nearest to nadir (Holben, 1986). The monthly composite
NDVI data of the test area , image of size 90 lines by 60 samples, are cut from these two datasets. In this
study, all 12 months time series monthly composite NDVI data are used in order to include full phenological
information of the whole year.
Approach
Multi-temporal Landsat TM data is classified by maximum likelihood method to generate a reference land
cover map. Eight land cover classes are deemed sufficient to cover almost all the variability of the test area
(Forest, Corn, Paddy, Grassland, bare land, Urban, Water and Seasonal water). The overall classification
accuracy is estimated to exceed 85 percent (Zhu and Tateishi, 2000). Also, three land cover types, namely
forest, grassland and farmland, account for 97.1 percent of the total test area. Time series NOAA AVHRR
monthly composite NDVI data is also classified using minimum distance method in order to provide a
comparison with the fraction images obtained from linear mixture modeling.
For application of linear mixture modeling, the classified image of Landsat TM data is filtered using a 5 x 5
majority filter in order to reclassify isolated pixels belonging to one land cover type to the same land cover
type as the majority of their neighbors in the image. Then, the filtered image is degraded to the spatial
resolution of 1km data to make it easy for endmember collection. Assuming three components within a
pixel, the CLS method is applied to the NOAA AVHRR and SPOT VEGETATION monthly composite NDVI
data, respectively. The extracted fraction images are scaled to integer values from 0 to 200.
