In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
arid rainfall and not flooded, have their maximum vegetation 
during end of August or early September. Contrary to this, 
flooded areas show maximum vegetation during October / 
November and these extrema show significantly higher values 
see pixel 19 43 as an example for this ecological category. 
rn13 31 O 15 45 -▼-15 48 -A-18 26 >-17 29 ->-20 26 -0-16 49 -*-19 43 
260 
Figure 7.: Seasonal Figure derived with phase mean 
algorithm 
all frequencies —13 31 —19 43 —20 26 
cycles per year 
non-significant frequencies removed, 80% of power 
— 13 31 —19 43 —20 26 
0123456789 10 11 
cycles per year 
Figure 8.: power spectra for low-pass filtered time series; 
top - a) all 294 frequencies, bottom - b) only 
frequencies that preserve min. 80% of total power 
for each of the time series 
The Analysis of seasonal features in the frequency domain can 
be reduced to the question, which frequencies shall be 
considered as significant for the seasonal figure. As explained 
in Section 3.3 of this paper, it is mandatory to retain the same 
set of frequencies throughout all time series to ensure the 
comparability between different series. The effect of reducing 
the no. of frequencies is shown in Figure 8b, where the lower 
graph shows a reduced spectrum to 80% level of power. This 
preserved information level is achieved with only 25% of the 
original 294 frequencies. Even a nearly complete preservation 
of the information of the time series (99% level of power) 
yields to a reduction in frequencies to approx. 75% of the 
original frequencies (223 out of the 294). 
After normalisation with the annual variance, the irregular 
component should form a stationary time series. If so, no 
specific feature should be detectable within the series. This is 
true for some time series but as can be seen in Figure 9 it is 
not for all the case. While the series from pixel 19 43 can 
treated as stationary for most of the time, the series from pixel 
13 31 shows significant extrema. This gives evidence that the 
seasonal figure is imperfectly modelled with the approaches 
suggested in this paper (and therefore seasonal features fall 
partially by mistake into the irregular component) end / or the 
vegetation dynamics contain significantly non-periodic 
elements. Therefore a non-stationary time series for an 
irregular component points out a not periodically growth of 
vegetation due to an episodically flooded area. 
Figure 9.: examples for the Irregular Component, the one for 
pixel 13 31 shows strong extrema 
5. SUMMARY AND CONCLUSIONS 
Long-term dynamics are clearly detectable within the NDVI 
GIMMS time series. These features can be extracted by 
filtering the time series with an appropriate FIR. Modelling 
the seasonal dynamics is somewhat more ambiguous. The 
phase mean algorithm treats all values of a certain acquisition 
date as source for a mean value that is representative for the 
period of the entire time series. Every difference between a 
value of the time series and the corresponding modelled phase 
mean is treated as part of the Irregular Component. If the 
seasonal figure is modelled from the power spectra of the 
Fourier Transform, the shape of the figure depends on the no. 
of frequencies that is used. The Irregular Component of the 
time series contains information about non-periodic dynamics 
of the vegetation cover. These are significantly present in the 
time series as the extent of flooding varies widely between the 
years. 
REFERENCES 
Breman H. and DeRidder, N., 1991. Manuel sur les 
pâturages des pays sahéliens. Karthala, Paris.