Change Vector Analysis on Long Time Series NDVI data
  1. Introduction


    2. Change vector analysis is an effective approach for detecting and characterizing land-cover change. It processes and analyses change in all multi-spectral/multi-temporal data layers. When change vector analysis is applied to multi-temporal data, it compares the differences in the time-trajectory of a biophysical indicator for successive time periods. When the time trajectory of these indicators over a particular pixel departs from that expected for that pixel, a process of land-cover change can be detected (Lambin, et. al., 1994). We can take NDVI – a biophysical indicator as an example to describe the concept of change vector analysis. The seasonal dynamics of NDVI can be represented, for each pixel, by a point in a multidimensional space, with the number of dimensions of this space corresponding to the number of observations n. Each year, these observation comprise the axes of an n-dimensional space. The NDVI values of any pixel at each observation ith during a year is defined as a vector. Any change in the accumulated value and/or in the seasonal dynamic of NDVI between two years will result in a displacement of the pixel’s point in the n-dimensional space. The change of the pixel’s point between two years can be characterized by a change vector with a measureable direction and magnitude. The magnitude of change vector measures the intensity of the change in land cover. It can be computed as the Euclidean distance between two points in the n-dimensional space: i.e.,

    Where NDVI1 and NDVI2 are the year 1 and year 2 pixel value of NDVI and i is the observation period during the year.

  2. Modified Change Vector Analysis


    3. There are three main processes of interannual land-cover change acting in the Senegal. First, the timing of vegetation activity varies from one year to another as a result of variations in rainfall distribution. These changes are nonpermanent and are driven by the interannual climatic variability. Second, changes in vegetation types occur as a result of human activity or longer-term climatic changes. These changes are not well documented for the region and probably occur at a slow rate. Third, biomass burning is an important process of land-cover change and ecological degradation that affects the area. Currently, we are focusing on the second process. Senegal is characterized by a large interannual variability in climatic conditions, leading to large interannual variations in vegetation productivity. It might therefore be difficult to distinguish the trends of land-cover changes caused by human disturbances or by long-term changes in climatic conditions from noise created by aperiodic and recurring rainfall shortages. The multitemporal change vector method can be adapted to allow this less-signifiant interannual variability of vegetation condition to be taken into account. If long-term data on the spectral behavior of every pixel have been collected and archived, the current position of one pixel in the multidimensional space can be compared with the set of positions of that pixel during the previous years of observation. If there is a large number of these past records, the Mahalanobis distance can be used in place of the Euclidean distance. In the formulation of the Mahalanobis distance, the distance between a point, defined by the vector Pi, and the mean of a set of other points is modulated with the covariance matrix, which confers a degree of directional sensitivity to the measure:

    Where m and å are the mean vector and covariance matrix of the archived data. Therefore, the magnitude of a change in a certain direction is weighted by the probability that the natural interannual variability of the climate leads to a change in that direction, this probability being inferred from the covariance matrix of past observations.

    For conveniently describing the nature of the land cover change process, we plotted the seasonal curves of NDVI (1990) of different land-cover types in Senegal.

    The multitemporal vectors for these land-cover types is shown as follow:

     The desertification can be represented using change vector as shown:

      In our study, the winter term includes Jan., Feb., March, and April. The summer term includes June, July, Aug., and Sept.. The dimension in change vector analysis we employed is 8. To stabilize the variance, the moving average technique was introduced to this study. Current year's value can be replaced by taking the average of previous k years' and current year's values. The computing formula is:

    Where NDVIt' and NDVIt are forecasted and actual values separately.

  3. Results and Analysis
In our study, we selected k=4. The modified change vector analysis was employed for the time series from 1986 to 1997. The magnitude maps through 1986 to 1997 of change vector analysis were obtained. According to the frequency distribution of each magnitude map, the maps were classified to 4 classes: unchanged (magnitude<1.0), a little change (1<magnitude<3), medium change (3<magnitude<10) and big change (magnitude>10). Because magnitude of change vector is a distance that is always a positive value, we can not get the directional information of change. It means the single magnitude can not give me any significant information for the land cover performance in the long time series. For avoiding the disadvantage, the direction of change vector was calculated. Since it is complex to calculate the direction in 8 dimensions space, we can simplex the calculation in two dimension space. One dimension is mean value of winter term, the other is mean value of summer term. From the picture of seasonal curves of NDVI, we found that the winter’s NDVIs of different land-cover types are close. It means that the summer’s NDVI plays main role in magnitude of change vector. So we further take change direction of mean value of summer’s NDVI of each year as the direction of change vector and obtained positive and negative direction map separately for each year (from 1986 to 1997). The project’s main objective is to investigate the trends of land-cover performance in the long time series. Current results can only show us the change and direction of each year comparing with the whole time series. Therefore, a method of moving window over six years was designed in this study. This method was described as follows:
  1. the magnitude and direction maps of each successive 6 years in the long time series from 1986 to 1997 were taken to process.
  2. For magnitude maps, if one pixel has same change class in four out of six years, the pixel will be assigned to this class, or else zero. The result will show us which pixel keep change and how big the change is during the six years.
  3. for direction maps, the maps of six years are added together. If the value of one pixel in the result map is larger than 4, the pixel will be assigned to 1, or else 0. The pixel with value 1 is thought as keeping change in the same direction.
  4. the overlay is operated on the two maps from step 2 and step 3. The change direction and change magnitude of pixels that keep change in the six years will be displayed in the final map.
  5. repeat step 1 to step 4. The maps (shown below) for 86-91, 87-92, 88-93, 89-94, 90-95, 91-96, and 92-97 were obtained. Apart from these maps, the map (shown blow) for 86-97 was also generated. The procedure is the same as above, but the processing duration is whole time series and the threshold is 10 not 4.

 * the yellow and green represent negative and positive direction separately, the dark to bright of color indicates small to big of change magnitude.

These maps presented directional trends during each 6 successive years. The west part and central area in Senegal mainly had positive and negative change direction separately before 1990. After 1990, the situation has changed. The change including positive and negative mainly happened in the west part. The landcover type of the two areas is crop. Human being puts a lot of impacts on this area. As to southeast of Senegal, this area 's landcover is woodland/forest. It presented negative change before 1989 and had positive change after 1989.

Some pixels of directional change also showed in component 2, component 3 and correlation coefficients maps. In PCA analysis, three sites have been examined. But Only one site (red rectangle) appeared in the CVA maps. This site is a known degradated area Touba located in the central part of Senegal. It presented gradually change and shrunk in the following 5 years of 1986 and disappeared after 1991. It means that this area's NDVI didn't change or change a little after 1991. The correlation coefficient of integrated NDVI and precipitation is 0.19. It indicated that NDVI didn't change with rainfall through the time series from 1982 to 1997. This site in component 2 presented local anomaly comparing to the negative value around it. The reason why the other two sites didn't show in the component 2 and correlation coefficients map is that they both didn't change or changed a little in the long time series of 82 to 97.

From the 86-97 CVA map, we found some pixels encircled by white polygon showed negative directional change from 82 to 97. The same pixels showed local anomalies in the component 2 and correlation coefficients map.

Some pixels in CVA map also presented in the component 3. In PCA analysis, we have examined the loadings and NDVI time series curve. They showed that NDVI is gradually decreasing after 1992. This result (the pixels encircled by white rectangle) also showed in the 91-96, 92-97 CVA maps.