**4. Discussions**

The efficiency of the whole proposed methodology was assessed and discussed on selected aspects and the comparison with existing methods was basically empirical. At first, depending on their goals, previous MSDI-based studies analyzed only the standard deviation of the red and near infrared wavelengths, while those integrating vegetation indices were limited to three of them [40, 43, 52]. Because the goal of proposing aMSDI in this study was to assess consecutives dry season anomalies and discriminate them from empirical statuses of the forest-savanna specificities, we integrated nine spectral indices, selected on the basis of targeted phenological or physiological weaknesses, and whose computations basically integrate several wavelengths. Interestingly, although only one CVA magnitude was chosen per index, all individual models showed the expected visual convergence of similarity or dissimilarity trends.

Moreover, previous applications stated that the common calculation of MSDI on raw spectral index, gives outputs with a minimum value of zero and a maximum value determined by those of the pixels evaluated [43]. Consequently, outputs value cannot be directly compared. Here, by applying the averaging process to binarized CVA, **[0,1]**, this study alternatively addressed these issues for a multidate analysis. With same or divergent visual patterns, all outputs were scaled inside the identical interval, **[0–0.083]**, although showing convergent or divergent spatial patterns. The significance of the spatial and non-spatial autoregression models, has helped to confirm the inner variability of each aMSDI although identical scales of values and apparent same trends between others, as well as convergences/divergences of trends with the reference aMSDI (MSAVI2). Consequently, the output spotting anomalies was proof of complementary among individual contributions and spatial agreements.

Besides, common attempts of mapping distribution, typology, and delineation of forest and savanna, have always been supported by fieldwork, based on climate parameters, as well as including paleo-ecological evidences and detailed floristic survey to be efficient [8]. The methodology presented in this paper has predicted three different axes of vegetation, resulting from the PCA processing and thresholding (**Table 5**). For each of the six study periods, the first ax in the south part is composed by a dense and potentially healthier vegetation, highly correlated with the referential data MSAVI2. Whereas the other two axes, more and more sparse towards north, are divergent with the first one and somehow each with another (**Figure 10a**&**b**). Nevertheless, their individual trends foresee some overlapping, in the center and in the northern areas. A sampling of each ax along the transect of 1544 pixels, showed how interweaved and complexes are the boundaries among forest-savanna species (**Figure 10b**).

To answer the interrogations behind these ambiguities, a simple multicollinearity test was run, showing how independent one ax is from another. When the correlation between two independent variables is considerably high, it is a problem in the


**Table 5.**

*Vegetation axes, proposed groups and PCA thresholds used to binarize.*

#### **Figure 10.**

*a. the three main axes of vegetation's spatial distribution. b. Pixels' value along the transect of the vegetation's axes.*

modeling process. The VIF (variance inflation factor) and tolerance were used for diagnosis. VIF is the reciprocal of tolerance, knowing that, tolerance is **<sup>1</sup>** *<sup>R</sup>***<sup>2</sup>**. We used the lowest known VIF, *<* **3**, while expecting the highest tolerance, so to measure independence. Therefore, while the occurrence percentiles of value **1** on each ax highlights interweaving in between **[62.5–78.3]** for axes 1 and 2, and **[69.5–99.97]** for all, low VIF (**1***:***33**≤ *VIF* ≤ **1***:***35**) and high tolerance (**0***:***74**≤ *Tol* ≤**0***:***89**) confirm the total separability, i.e., less collinearity among axes (**Table 6**).

Although from this study, we cannot properly use the qualifier of "bistable" forest or savanna, because it highly depends upon climate and paleo-ecological parameters, it is important to notice how ambiguous is the distribution and blurry are the boundaries. Thoroughly, on any ML output, three zooms distributed on three different latitudes helped to notice different types of transitions (**Figure 11**). Between the lower latitudes 50 30'-6<sup>0</sup> 30'North, the transition is from the first (moist broadleaf forest) to


**Table 6.** *Multicollinearity test results.*

*Dynamics, Anomalies and Boundaries of the Forest-Savanna Transition: A Novel Remote… DOI: http://dx.doi.org/10.5772/intechopen.105074*

#### **Figure 11.**

*Zooms on the transitions, a sign of anisotropic distribution with latitudes. Yellow square = lower latitudes (5<sup>0</sup> 30'- 60 30'N) transition; red square = middle latitudes (6<sup>0</sup> 30'-7<sup>0</sup> 30'N) transition; blue = upper latitudes (7<sup>0</sup> 30'- 80 30'N) transition.*

#### **Figure 12.**

*Anomalies versus LULC classes. (A) SVM classification map. (B) Two extreme classes of anomalies at* 3 3 *pixel moving window size. (C) & (D) subset of comparison among classes of LULC and anomalies. (E) Stacking results with the following details: Black, yellow, purple, and ginger pink circles = extremely severe anomaly spots extended to part of the entire vegetation, in the grassland/savanna –savanna/shrubland transition area; orange circle = low or inexistent anomaly spot in the savanna/shrubland transition, characterized as drier and more exposed vegetation to degradation; cyan circle = low or inexistent anomaly on bare soil.*

third ax of vegetation (shrubland savanna), although the second ax (grassland savanna) would have been "expected." Between the middle latitudes 6<sup>0</sup> 30'- 70 30'North, the transition mixes in the below area, the "-'unexpected" third ax (shrubland savanna) with the 'expected' first ax (moist broadleaf forest) of vegetation, before the wide expansion of the 'expected'second ax (grassland savanna). At this point, the only "expected" transition was inside the upper latitudes 70 30'- 80 30'North, where the second ax (grassland savanna) gradually gave way to third ax (shrubland savanna) of vegetation. These elements of analysis support the qualifier of "bistable" area, while still questioning the anisotropic distribution with latitudes, and encouraging the finest scale of analysis, i.e., spatial and spectral resolution.

Finally, the display of anomalies with the LULC classes disambiguated the confusion of savanna and degraded forest. The observation was made by overlaying the highest and the lowest values of anomalies in the most concentrate area, on the SVM output. On three spots covered by grassland, shrubland and bare soil, the modeled extremely severe anomalies concern just a part of each class. Whereas, on two spots of lower to no-anomalies, savanna as well as bare soils are partially concerned (**Figure 12**).
