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In: Wagner W„ Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Pan 7B 
A formal selection of a set of frequencies would only be 
suitable, if one could a-priori specify the range of relevant 
periodicities within the time series and adjust the band of 
preserved frequencies according to this knowledge. Otherwise 
information about the time series would randomly discarded. 
If one retains for instance the first few frequencies, one 
preserves a rather rough approximation of the time series, as 
these frequencies correspond to the low frequent parts of the 
signal. Using the largest few frequencies would preserve the 
individual time series much better, but makes them no longer 
comparable, as different parts of the signals would be kept. 
(Mohrchen, 2006) proposes the use of one subset of 
frequencies for all time series, thus achieving, that all series 
have the same dimensionality (In the context of a feature 
space point of view on the time series, frequencies represent 
the components of the feature vector that characterises an 
individual time series.) and keeping them comparable. A 
frequency belongs to the subset, if it is necessary to preserve 
an a-priori defined level of information for any of the time 
series. Where all frequencies of a given time series are sorted 
according to their magnitude. And the information level is 
calculated cumulative, starting with the largest frequency, for 
each time series individually. 
3.5 Analysis of the Irregular Component i t 
After subtraction of the long-term mean, the Cyclical and 
Seasonal Components from the original time series remains 
the Irregular Component. This part represents a time series 
that is stationary in wide-sense, as the variance is not 
independent from time. The annual aggregated variance 
differs between years, especially for pixel at the edges of the 
Inland Delta that are not flooded regularly. Provided that the 
variance is constant over the period of 1 year, the quotient of 
the Irregular Component and the variance results in a time 
series that is nearly stationary. 
4. DISCUSSION OF RESULTS 
The following conclusions for the Cyclical and Seasonal 
Component will be illustrated, using pixel listed in Table 5 
that represent the main ecological categories of the Niger 
Inland Delta. The more an area is located towards the edges of 
the delta, the higher its variability in dynamics with low 
frequencies. 
pixel 
ID 
description 
located ecological category 
13 31 
western edge, close 
to delta mort 
periodically flooded, 
semi-arid 
surrounding 
15 45 
central delta, 
southern part 
flooded 
15 48 
central delta, 
southern part 
flooded 
18 26 
northwestern edge 
episodically flooded 
17 29 
Lake district 
regularly flooded 
20 26 
North of Lake Debo 
regularly flooded, 
semi-arid 
surrounding 
16 49 
central delta, 
southern part 
flooded 
19 43 
central delta, 
southern part 
flooded 
Table 5. Reference pixel for Cyclical and Seasonal 
Component 
The Cyclical Component unfolds dynamics that last for more 
than one year. It describes therefore relations between wet and 
dry years. Clearly visible in Figure 6 is the drop in vegetation 
cover during the dry years 1984 / 85 and the strong recovery 
followed 1986/ 87. The 2 nd half of the 1980 years and the 
beginning 90-ies had vegetation cover below the long-term 
mean, while the mid 90-ies showed a at least for parts of the 
Inland Delta a recovering of vegetation above the long-term 
mean. 
The individual components of the time series provide specific 
information about the character of the underlying vegetation 
dynamics. The long term mean (calculated for the entire 
period of 25 Vi years) varies a lot between pixel that cover 
areas in the central Inland Delta and those that cover the edges 
of the Floodplain next to the semi arid environment. The 
NDVI values variability of a specific time series is 
significantly positive correlated with the long term mean. 
Thus, areas with overall high NDVI values show higher 
variability too. 
Figure 4.: relation between long-term mean and variance of 
the NDVI values 
— 13 31 —15 45 —15 48 —18 26 —17 29 —20 26 —16 49 —19 43 
100 ■ ■ : r 
01.01.82 01.01.88 01.01.94 01.01.00 01.01.06 
Figure 6.: Cyclical Component (lag 24) represent dynamics 
with periodicities greater 12 month 
A discrimination of pixel according to their month of highest 
vegetation density can be done with the Seasonal Component 
(Figure 7). While all pixel show the vegetation drop during 
the late dry season (May / June), the different causes for 
vegetation growth result in specific dates of maximum 
vegetation cover. Areas that are mainly influenced by the semi