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Data Processing, Algorithm and Modelling
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The polynomial least squares operation (PoLeS): A method for reducing noise in NDVI time series data
Pecularities of PoLeS algorithm
The data for the raw and the filtered NDVI values for the 1984 10-day composite data was are shown in
table 1.
Figure 1 shows the various results of filtering using PoLeS method. Like, the BISE, MVC MVI and
TWO, the PoLeS is also sensitive to the length of the sliding period, a.k.a temporal window or moving
window. Two temporal window sizes were tested, where nL = nR =3 and 5. In both window sizes the
general interpolated curve is maintained. However, with greater values of the temporal window (e.g. nL
= nR =5), there could be observed some substantial smoothing, in which case most of the noise have
been removed, albeit it has also smoothed out some of the more important changes inherent in the data.
One particular notable effect of the length of the sliding period may be apparent in figure 1.(f) where the
inherent changing phenology in the two-crop area was emphasized by the PoLeS filtering procedure.
Presuming that the BISE or the TWO method were applied to the same set of data, this valley would not
have been detected nor would it be apparent in the profile.
Applying the PoLeS to land cover types which are assumed to have very minimal or ideal absence of
change in phenology (i.e. tropical, desert areas) had substantially lowered the overall average
comparing the values with the original NDVI data (see table 1) . However, the standard deviation values
of the filtered annual data were not changed significantly.
Table 1. Average NDVI and computed standard deviations of two land cover types (i.e. desert and
tropical) assumed to have minimal changes in seasonal phenology and the NDVI., as shown by their
minimal changes in the data variability before and after applying different temporal window sizes.
Conclusion
The PoLeS provides an alternative method for removing both low and high values from the NDVI profile
data. PoLeS made over extensive periods are effective in reducing influences due to clouds and variable
viewing conditions, but much like the previous profile extraction methods, the length of the temporal or
sliding window affects the smoothness of the entire profile. Longer temporal windows generally smooth
out the curve without affecting the overall standard deviation values of the annual NDVI data. A value
of the temporal window of 5 (nL = nR=5) substantially provides a good fitting of the NDVI profile.
The phenomenon of surface anisotropy due to specific viewing angles and atmospheric conditions can
elicit high NDVI values generally in the forward scattering direction (Gutman, 1991). All previous
methods, like the BISE, MVC, and MVI will always include and retain spurious high values from data
transmission errors and anistropic effects. 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 by preserving the
variance of the data
as shown by the minimal changes in the value standard deviations.
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