INFORMATION SYSTEM TO MONITOR

GLOBAL CHANGE IMPACTS

GLOBAL CHANGE IMPACTS

**Copyright: **Creative Commons Attribution 4.0 International

**Copyright: **Creative Commons Attribution 4.0 International

The periodogram was computed at pixel basis for AVHRR NDVI time series for the period
1982-2016 (840 observations). It contains information at 420 frequencies, which is the half of the total time series
observations. This tool is highly interesting to assess vegetation seasonality enabling the identification of the most
significant components of each NDVI time series.
Periodogram is based on the classical mathematical theory of Fourier series in which the signal is decomposed
into a series of sine and cosine waves at different frequencies called Fourier frequencies (f_i):

The significance of each frequency (f_i) in accounting for the variance of the time series is indicated by
the periodogram amplitude at that particular frequency. Thus, the periodogram plots the amplitude at each
frequency versus frequencies.

The most important periodicities are associated with high amplitudes. Since the NDVI3g product provides 24
observations per year, the most relevant amplitudes for assessing vegetation dynamics are at periods 24, 12
and 8, representing annual, semi-annual and four months terms respectively.

**Copyright: **Creative Commons Attribution 4.0 International

The specific autocorrelation coefficients were generated using the MODIS NDVI time series from 2001 to 2012 obtained from the product MOD09Q1. From the NDVI autocorrelation function using MOD09Q1 product can be derived some relevant autocorrelation coefficients for vegetation dynamics assessment. The identification of these AC values depends on the temporal frequency of satellite images. When using MOD09Q1 MODIS product which consists of 8-day composites, the annual temporal dependency is measured by the AC value at lag 46. Thus, the most important lags to assess the temporal patterns of vegetation are the AC values at lags 1, 23, 46, 92 and 138 which measures the temporal dependency of NDVI at 8 days, 6-months, one, two and three years respectively. Each autocorrelation (AC) coefficient is calculated according to the following equation:

**Copyright: **Creative Commons Attribution 4.0 International

The specific periodogram ordinates were generated using the AVHRR NDVI
time series from 1982 to 2016 obtained from the product NDVI3g product. This product contains 24
observations per year so that the most relevant amplitudes for assessing vegetation dynamics are at
periods 24, 12 and 8, representing annual, semi-annual and four months terms respectively, that is, there
is a seasonal cycle every 24, 12 and 8 AVHRR periods.
The Fisher’s Kappa test (FK) can be used for evaluating the NDVI seasonality significance and for
identifying white noise series. The statistic for this test is computed as the ratio between the maximum
amplitude value and the mean of all amplitudes according as follows:

**Copyright: **Creative Commons Attribution 4.0 International