The polynomial least squares operation (PoLeS): A method for reducing noise in NDVI time series data
Jose Edgardo L. Aban
Center for Environmental Remote Sensing (CEReS)
Chiba University
1-33 Yayoi, Inage, Chiba-ken, Japan
Tel: +81-43-290-3965
Fax: +81-43-290-3857
E-mail: aban@ceres.cr.chiba-u.ac.jp
Japan
Ryutaro Tateishi
Center for Environmental Remote Sensing (CEReS)
Chiba University
1-33 Yayoi, Inage, Chiba-ken, Japan
Tel: +81-43-290-3965
Fax: +81-43-290-3857
E-mail: aban@ceres.cr.chiba-u.ac.jp
Japan
Renchin Tsolmon
Center for Environmental Remote Sensing (CEReS)
Chiba University
1-33 Yayoi, Inage, Chiba-ken, Japan
Tel: +81-43-290-3965
Fax: +81-43-290-3857
E-mail: aban@ceres.cr.chiba-u.ac.jp
Japan
Abstract
The Polynomial Least Squares Operation (PoLeS) is proposed as an alternative novel technique used
to reduce noise in the Normalized Difference Vegetation Index (NDVI) time-series from the Advanced
Very High Resolution Radiometer (AVHRR) data. The PoLeS method preserves more valuable
elements of the NDVI profile and considers both cloud contamination that depress the NDVI profile, and
anistropic sources of high value noise which tend to have the opposite effect. Previous profile
extraction algorithms only tend to discard low frequency NDVI values. Whereas, other previous
algorithms introduce a bias due to the assumption that a lower values of NDVI are considered only as
noise while retaining higher values, the PoLeS does not suffer from such a bias. Furthermore, the
PoLeS preserves the inherent variability in the NDVI data.
Introduction
The Normalize Difference Vegetation Index (NDVI) remains to be the most common measure of
physiological and biochemical plant processes. The spectral response of vegetation as measured by the
NDVI can be defined as the difference between near infrared and the red reflectance divided by the sum
of the two. NDVI values are closely linked to plant cover under many conditions. A generalized NDVI
profile for vegetation cover is characterized by an increasing trend (rising) as plant cover increases
(growth) reaches a peak, or a plateau and falls off as the plant undergoes change in leaf coloration and
senescence, and eventually towards death. In areas where the vegetation canopy changes very little with
time, e.g., deserts and tropical rainforests, the NDVI profiles usually do not show marked increases or
decreases in value. Thus the NDVI can provide a means for describing the vegetation phenology.
Furthermore, the relationship on NDVI on cover, and thus the profile, may be affected if the vegetation
is stressed in a way which affects the canopy. Also, the relationship between NDVI and plant cover is
known to vary between vegetation types and so different biomes can have different NDVI profiles. Also,
the NDVI profiles for a given vegetation type can vary from area to area and year to year depending on
the existing weather.
Since 1982, the National Oceanic and Atmospheric Administration’s (NOAA) Advanced Very High
Resolution Radiometers (AVHRR) provide daily Earth observations. From these data, NDVI profiles have
been built and complied through the years. Such multi-annual profiles data have been used to monitor
primary production (Prince and Tucker 1986), to study the dynamics of major biomes (Malingreau,1986),
for land cover classification (Townsend et al. 1991), and for estimation of crop yield (Bartholome’, 1991).
Changes in the NDVI derived from AVHRR data are usually indicative if changes in the surface
conditions, most predominantly changes in vegetation. However, there are other extrinsic factors that
cause changes in the overall NDVI profile, among which are cloud contamination, atmospheric variability
and bi-directional effects (Gutman 1991); these changes are usually considered as undesirable noise in
vegetation studies. A widely used method to reduce this noise is the Maximum Value Composite (MVC)
technique proposed by Holben (1986) and those of Prince and Justice (1991).
The MVC retains the highest NDVI value for a given location over a pre-defined compositing period, the
assumption being that all contamination depress NDVI values. The technique works best with a long
compositing period, around 2 to 4 weeks. But too long a period will distort the profile and may
completely mask short term changes in vegetation condition. Short compositing periods are more
generally used for example, the standard NOAA Product, the Global Vegetation Index (GVI), is created
on a weekly basis (NOAA, 1990) though this still retains a lot of noise.
A widely used technique is that of the Best Index Slope Extraction or the BISE (Viovy et al, 1992). From
the first date of the time series, the BISE algorithm searches forward and considers the succeeding
point if it is of higher value than the preceding point. Where the NDVI value from one day to the next
decreases, this decrease is only accepted if there is no point in a pre-defined period of time (called a
sliding period) with a value greater than 20 percent of the difference between the first low value and the
previous high value. If such a high value is encountered it is selected and the low point is ignored.
A similar technique called the Temporal Window Operation (TWO) was developed by Park et al (1998).
The TWO proceeds by looking at the trajectory of each pixel and finding the low NDVI value and
replacing this by a linearly interpolated value. The algorithm starts at the beginning of the NDVI curve
(start point) and checks whether the NDVI for the current period is equal to or greater than the previous
NDVI value within the window. If it is higher, current value is assigned as the start point of next window.
If there is no higher value within the window, the next biggest value is chosen as the next start point,
with the lower values being replaced by linearly interpolated values from the current start point to the
next.
The Maximum Value Interpolated (MVI) is an enhancement of the MVC (Taddei, 1997). The MVI method
consists of recording not only the NDVI maximum value within a period (e.g., a month) , but also the
day when the value was recorded. Through simple linear interpolation between these points it is
possible to detect, fo r each time period, a representative NDVI value.
Here we present another method for extracting NDVI profiles from ten-day composite data, called the
Polynomial Least Squares Operation (PoLeS). The seasonal characteristics of vegetation are generally
predictable , depending on ecoclimatic zonation (Prentice, 1990). The PoLeS method accounts for the
phenomenon that plant growth and development is often asymmetric, i.e. there exists periods of growth
and senescence which are not equal, and that in addition to somewhat gradual changes such as drought
induced stress, sudden changes can occur in the vegetation canopy, such as fire, deforestation or crop
harvest. As a performance test, the PoLeS is compared with three other smoothing techniques as well
as that of the BISE and the TWO techniques.
