Yale University
Center for Earth Observation

Classifying Vegetation in the Semi-Arid Near East Using Fourier Series Techniques

Conventional clustering classification schemes (unsupervised classification) are often used to group multitemporal satellite imagery into distinct vegetative classes with similar temporal signatures. These techniques strive to minimize variability in each class by using euclidean distance to measure the separation between pixels. This tends to put a heavy emphasis on the annual mean while ignoring the sequential order of images (e.g. March follows February).
Here we investigate a scheme that emphasizes the cyclic properties of a temporal vegetation signature. The fourier coefficients for a given time series will retain information on the "shape" of that series in a set of independent physically meaningful values.
The central question of this work is does this fourier representation provide any advantages to studying vegetation patterns?

Start with the NASA (GSFC) AVHRR Pathfinder data set.
- Normalized Difference Vegetation Index (NDVI) images (NDVI ranges from -1 to +1 and has a positive correlation with biomass)
- Maximum Value Composites (to reduce cloud cover)
- 8 kilometer spatial resolution
- One image per month from 1982 - 1993
Average 1982 - 1993 to produce a 12 month "average year"
- Helps reduce noise and effects of interannual variability
Compute the first six fourier coefficients for each pixel
Threshold certain coefficients to classify the average year
Compare this result with a traditional unsupervised classification, focusing on "double peaked" (two vegetation maxima per year) classes
Use Landsat TM imagery (30 meter spatial resolution) to relate the regional scale AVHRR classification to local agricultural practices

The classification based on thresholding fourier coefficients is presented in figure 1. Compare this with the result of the (k-means) unsupervised classification of the averaged NDVI data in figure 2. Take special note of the "double peaked" classes (highlighted in purple and green).
The annual NDVI cycles of pixels 3a,b,c,and d are plotted in figure 3 to illustrate some differences between the techniques. The fourier technique classifies pixels 3a and 3d in the same double peak class (#3) while the unsupervised method places them in two different classes (#10 and #15). This is a good example of the importance of the annual mean in the unsupervised technique. Furthermore, the fourier scheme does not classify either pixel 3b or 3c as double peaked, while the unsupervised technique places 3b in same class as 3a (#15) and 3c in the same class as 3d (#10).

Identifying areas of double vegetation maxima on a regional scale has value for certain resource calculations (water budget analysis etc..), but to understand the physical processes behind the double crop signal we need to relate the coarse resolution NDVI signal to finer resolution imagery.
In figure 4 we "zoom in" to a small test site near Netanya, Israel using Landsat TM imagery taken on four different dates to focus on an area of approximately six of the coarser AVHRR pixels (outlined in white). For the four TM scenes, we have computed the average NDVI within each of the six large AVHRR pixels. These values are plotted as points in figure 5 (connected by dashed lines to make them easier to see) along with the annual cycle for each of the AVHRR pixels. The offset in absolute value is due to calibrations we have not performed, but notice the similarities in the trends for each AVHRR / TM pair.
In this case, as in many other areas in the region, the "double" cropping signal is not a result of the same field producing two crops per year, but rather a system where half the fields produce spring crops and the other half produce summer crops.

The emphasis of shape over mean value allows the rules-based fourier series classification to better identify areas with two crops per year. This seems to work well in this region in part because the magnitude of NDVI signals for double peaked pixels varies widely across the scene.
Regional scale AVHRR imagery, which is composed of large heterogeneous pixels, can be explained on a fine scale with high resolution images at lower temporal frequency. Perhaps this will allow end member "unmixing" of these coarse pixels in the future.