**4. Methodology**

The methodology adopted to develop this research encompasses various steps as described in the flowchart shown in Figure 2.

**Figure 2.** Flowchart of the procedures followed in this study (TM—Thematic Mapper, OLI—Operational Land Imager).

## *4.1. Image Co-Registration*

Image co-registration has been conducted for Landsat *TM* and *OLI* data for eliminating the errors that may occur in the satellite data, due to image rotation, skew and scale. In this case, we proceeded to correct the images, since the study constituted of multitemporal dynamics, in which the images were compared and required to be perfectly coincident in space. Image co-registration is the adjustment of the coordinate system (pixel/lines) of one image to be equivalent to the other image of the same region [9,12]. In this work, we applied pixel resampling method using the nearest neighbor interpolation obtaining the GLS image from the National Institute of Space Research (INPE—*Instituto Nacional de Pesquisas Espaciais*) for choosing the control points. The image co-registration was conducted using SPRING software, in which the first phase was characterized by modifying the extension of the Landsat scenes (path/row: 221/79) for all the years studied with an average of 15 control points, accepting an error of less than one pixel, with a maximum value of 0.55.

#### *4.2. Principal Component Analysis*

After the co-registration of images, Principal Component Analysis (PCA) has been conducted with the objective of detecting the land use/land cover (LULC) changes that occurred within the 10 km buffer area surrounding the RCSP. This analysis will allow us to conclude, first, concerning the impact of the construction of the power plant and, second, whether the environmental compensation regarding the Park area was indeed incentivized and implemented properly. Another fact worth mentioning is the inclusion of the buffer zone to analyze is there were any changes in the area surrounding the park for this study to provide subsidy and aid in the future proposal of outlining the buffer zone, given that, until now, it is not present in the managemen<sup>t</sup> plan or posterior projects. The study of the multitemporal dynamics in 1990, 2004, and 2016 were aided by the Principal Component Analysis to compare the changes before and after the formation of the Campos Novos Hydroelectric Power Plant.

The PCA is a digital image processing technique that uses statistical parameters is considered as efficient in detecting changes in the landscape. In general, the calculation of the principal components of a set of data is conducted by obtaining the eigenvalues and eigenvectors using the correlation matrix or the variance-covariance matrix between the variables of the set [13]. PCA reduces the dimensionality of satellite data that leads to improved data visualization and manageability of data analysis [14,15] and is recognized as one of the best methods for mapping and monitoring interannual and interdecadal vegetation anomalies [16]. The application of PCA, however, depends on the objective of the researcher who can analyze each component according to the work schedule. According to Duarte et al. [17], to identify LULC changes, comparing the differences in the information contained in two or more satellite images is necessary. This identification (of LULC changes) is possible by the application of PCA, which also has the function of determining the extension of the correlation of the image bands and removes them, reducing the dimension of the data and excluding the redundant information that is of no interest (to the user).

Vegetation mapping using automatic methods, such as band rations or vegetation indices are relatively straight forward. However, these methods are not always suitable for differentiating exactly where the changes occurred, but good for what types of changes occurred (native and reforested areas in this case) and PCA has the advantage of mitigating this limitation to some extent by reducing the data dimensionality [14]. Furthermore, the actual nature of changes occurred has been identified by a field visit in this study. It has been observed in a previous study that the overall accuracy and kappa coefficient in vegetation mapping increase when PCA has used along with the main bands of satellite data [18].

The first Principal Component is comprised of the information that is common to all original bands (PC1), the second (PC2) contains the most significant spectral feature of the set. The higher the order of the PCs are, the less significant the spectral features will be. The last principal component has only the information that remained from the set or the noise. We analyzed the correlations of the bands related to the red wavelength (TM3) of the Landsat 5 (1990 and 2004) along with near-infrared (TM4) of the year 2004, generating a new set of images denominated principal components, in a total of three PCs. The use of only three bands is justified by presenting the number of iterations and scenes distinct from when processed by the PCA, resulting in the information of change detection during the period, as confirmed by Lopes [19]. Furthermore, it has been affirmed that the inclusion of the first three PCs corresponds to more than 99.5% of the total variance of satellite data [20].

The same procedure was conducted with the same band combination for comparing the period between 2004 and 2016 after the construction of the RCSP in 2004. The false-color composite image used is comprised of the 2nd (G) and 3rd (R) principal component and the band related to the shortwave infrared (B5) of the original image referent to the most recent year. After applying the PCA, we proceeded to the supervised classification per region based on the Bhattacharyya distance (B). The Bhattacharyya distance can be used as a class separability measure for feature selection [21]. For two normally distributed classes, the Bhattacharyya distance (b) between two classes is defined as:

$$b = \frac{1}{8} (\mu\_2 - \mu\_1)^{\mathrm{T}} \left[ \frac{\sum\_1 + \sum\_2}{2} \right]^{-1} (\mu\_2 - \mu\_1) + \frac{1}{2} \ln \frac{\left| (\sum\_1 + \sum\_2) / 2 \right|}{\left| \sum\_1 \right|\_{1/2} \left| \sum\_1 \right|^{1/2}},\tag{1}$$

where, μi and Σi are the mean vector and covariance matrix of class i, respectively. This algorithm is inbuilt in the SPRING software for image processing.

## *4.3. Supervised Classification*

To proceed with the supervised classification, it is necessary that the user has previous knowledge of the study area. This classification requires the field observation of specific locations shown in the image, from which one can obtain ground-truth data [9,22]. The supervised classification is based on the statistical functions that analyze and compare the characteristics of the spectral reflectance of the pixels associated with a standard class defined by the user. Generally, we calculate the average values, and standard deviations of the defined classes and these values serve as criteria to group the pixels that fulfill the limits close to a specific class [8]. According to Novo [23], the classification process can be distinguished regarding the unit to be grouped. In this work, we used the region-growth algorithm from which we extract homogeneous regions according to the limits tested and established and from the group of contiguous pixels grouped.

The limit of similarity and area used were equal for all images (30). Despite the images being di fferent and from di fferent years, these limits were the most adequate for the identification of LULC. It is worth mentioning that the similarity limit demonstrates the smallest di fference accepted between the average value of two pixels (or a set of pixels) and is considered the maximum distance between the spectral centers of two regions. The area limit represents the minimum size of the segmen<sup>t</sup> the user wishes to analyze.

In the supervised classification stage, we identified the areas with changes and no changes occurred comparing data acquired between 1990 and 2004, 2004 and 2016, and from 1997 to 2016. Using the false-color composite images from principal components, we observed the areas in which change occurred and those that remained with the same characteristics over the years using the multitemporal Landsat data. We determined the existence of cultivation and reforestation areas with the economic survey and fieldwork studies. However, when analyzing the images, we verified the presence of exposed soil in some regions, with well-formed texture and form. Based on the experience of the user knowledge of the area, allied to the analysis of images from di fferent dates, we perceived that most regions were undergoing an exchange in monocrops or a shallow cutting of exotic species for replanting.

Furthermore, when analyzed the areas in which change occurred or not, we observed an intense increase of the bed of Rio Canoas, due to the creation of the Campos Novos Hydroelectric Power Plant managed by ENERCAN. The power plant is in operation since 2006 and provided approximately 1 4 of the total energy consumption for the state of Santa Catarina. Therefore, we conducted a supervised classification of the areas in which change occurred on the riverbed before and after the creation of the power plant using a historical raifall data series encompassing 30 years in the Campos Novos station and the monthly total rainfall data for 2016 and 2004 to remove the influence of rainfall on the increase of the riverbed and analyze these di fferences.
