**1. Introduction**

Forests represent perhaps the most complex terrestrial ecosystem, given their ecosystem role, as well as habitat and socioeconomic development. The increasing pressure exerted by the global economy and climate change leads to the degradation and shrinking of global forest areas [1–4]. The reduction of the forest area and its degradation have negative repercussions on the environment, in general, but especially on the quality of the air, the soil, and the security of the water resources [5–12]. Thus, a series of programs and researches were initiated aimed at evaluating, monitoring, and reporting the physical and biological states of the forest (Convention on Long-Range Transboundary Air Pollution (CLRTAP) [13];

UN Collaborative Programme on Reducing Emissions from Deforestation and Forest Degradation (REDD) [14]; International Long Term Ecological Research Network (ILTER) [15]; NASA's Carbon Monitoring System (CMS) [16]; Climate Change Initiative (CCI) [17]).

The reduction of forest areas as well as the process of fragmentation of the forest is a ubiquitous problem worldwide. Haddad et al. estimated that half of the planet's forests are less than 500 m from an inhabited area and most of the forested areas have an area of less than 10 hectares [18].

The satellite images offer an unprecedented perspective on the spatial evolution of the cover surfaces with forest vegetation, allowing the mapping of the compactness of the surfaces as well as their degree of fragmentation over time [19–22].

Forest fragmentation assessments have been completed for many countries, such as Canada, China, the Democratic Republic of Congo, India, the UK, or the USA [23–26]. Many of the researchers who developed these studies point out that fragmentation of forest areas has negative effects on the natural ecosystems by increasing the isolation, creating artificial margins, and reducing the basic areas of habitats.

In Romania, forests are under pressure due to climate changes (extreme temperatures, low rainfall, strong winds, and even tornadoes) and natural disturbances (insect outbreaks), but mainly due to anthropogenic causes (various forms of property, poor pest control, illegal logging, large demands on wood for export, etc.). Although Romania's forest area is estimated at about 29% of the country's total area, well below the EU average level of 40%, logging is still at a high rate [27].

A continuous, accurate, and reliable monitoring of the territorial evolution of forests as well as their state of sanogenesis is required both locally, in Romania, and regionally, Europe or worldwide. Such monitoring systems can be based on the information provided by the satellite monitoring networks correlated with on-site measurements and with accurate methods of quantification [28–32].

Establishing methods of continuous observation and accurate determination of long-term environmental changes is necessary to ensure the sustainability of the forest ecosystem and the efficiency of the planned ecological restoration [33].

The method proposed in this study wants to perform a fractal analysis regarding the deforestation of forests at the level of Romania.

### **2. Methodology**

In order to start the analyses for GIS and fractal methods used, we downloaded layer (a raster image in tiff format) corresponding to the granule with the top-left corner at 50°N, 20E (in which Romania is situated), containing the forest loss (loss year) data, for the 2001–2018 [34].

The images prepared for the fractal analyses followed a step-by-step algorithm, consisted on the extraction by mask procedure. The input feature mask was the vector limit of each relief unit of Romania, in our case 11 vector limits (the Carpathians, the Subcarpathians, the West Hills, the Danube Delta, Transylvania Depression, Dobrogea Plateau, Mehedinți Plateau, Getic Plateau, Moldova Plateau, Romania Plain, and West Plain). For each of the 11 input limits, 21 images in tiff format were exported providing pixels with useful informations. The first image exported contains the geographical limit for the relief unit, the other 18 images contain the yearly forest loss, from 2001 to 2018, and another image contains the cumulated forest loss for the entire period (2001–2018) and the last image the

**127**

*Use of Fractal Analysis in the Evaluation of Deforested Areas in Romania*

tree-cover information. We have to mention that for the best results, all the images exported were in black-and-white tones (the pixels corresponding to limits, to the forest loss, and to the tree cover were in white, while the background was in black color). Other important aspects were the scale and the image position: in order to avoid the information errors that might have appeared during the export processes, for each input feature mask (relief unit), the same scale and the same

The exported images provided useful informations that were extracted by using

The applicability of fractal geometry is limited not only to static phenomena but also to the study of dynamic phenomena, in evolution, such as the phenomena of

A versatile possibility to determine the deforestation patterns but also their impact on forest compaction is the fractal fragmentation index (FFI). FFI is a recent indicator and describes fractal fragmentation and can also be interpreted as an index of compaction of the analyzed surfaces, being a dimensionless

\_ log*N*(ε) log \_1 ε

where *FFI* is the fragmentation fractal index, *DA* is the fractal dimension of the summed areas, and *DP* is the fractal dimension of the summed perimeters; ε represents the size of the box; log*N*(ε) represents the number of contiguous and non-overlapping boxes needed to cover the object area; and log *N*′( ε) represents the number of contiguous and non-overlapping boxes needed to cover only the object's

When the value of the indicator has *FFI* = 0, it means that the analyzed fractal objects (in our case the deforested areas or forests) are very small, of the order of 1–4 pixels, so that their outline cannot be extracted, *DA*D = *DP* =0. When the FFI value tends to be 1, the occupied areas are large and compact. *FFI* = 1, when analyzing a Euclidean object, 100% compact, without any discontinuity (*DP =* 1 and *DA =* 2). When the areas occupied by the fractal are smaller, more dispersed, and more fragmented, the value of the FFI approaches more than 0. The FFI was calculated using IQM-plugin-FFI, available online at https://sourceforge.net/projects/iqmplugin-ffi/,

The analysis of the evolution of the analyzed parameter is carried out through a series of steps. In advance, IQM 3.50 software is downloaded from https://sourceforge.net/projects/iqm/files/latest/download; then, IQM-plugin-FFI is downloaded from the address https://sourceforge.net/projects/iqm-plugin-ffi/files/latest/download. The downloaded plug-in is inserted in the plug-in folder of the IQM program,

) − limε→0 (

\_ log *N*′( ε) log \_1 ε

) (1)

some specific softwares for the fractal and nonfractal analyses. We mentioned that, depending on the surfaces of the relief units, the images were exported to different scales and analyzed later fractal objects. Thus, for the Carpathians, the exported images kept the scale 1:1,750,000; for Subcarpathians, 1:1,300,000; the Transylvanian Depression, 1:1000,000; Moldova Plateau, 1:1,500,000; Dobrogea Plateau, 1:800,000; Getic Plateau, 1:650,000; Mehedinți Plateau, 1:200,000; the West Hills, 1:1,500,000; Romania Plain, 1:1,350,000; West Plain, 1:1,500,000; and the Danube Delta, 1:600,000. Even if the exported images were analyzed at different scales, the pixel sizes being the same for each exported image, there were no

*DOI: http://dx.doi.org/10.5772/intechopen.91621*

unmoved image position were kept.

indicator [36].

perimeter.

distortions or errors in their subsequent processing.

growth in biology or of development of urban populations [35].

The FFI is calculated using the equation (Eq. (1)):

*FFI* = *DA* <sup>−</sup>*DP* = limε→0 (

for open source software IQM 3.5 [37].

and a series of steps are taken.

#### *Use of Fractal Analysis in the Evaluation of Deforested Areas in Romania DOI: http://dx.doi.org/10.5772/intechopen.91621*

*Advances in Forest Management under Global Change*

Change Initiative (CCI) [17]).

of habitats.

**2. Methodology**

year) data, for the 2001–2018 [34].

have an area of less than 10 hectares [18].

UN Collaborative Programme on Reducing Emissions from Deforestation and Forest Degradation (REDD) [14]; International Long Term Ecological Research Network (ILTER) [15]; NASA's Carbon Monitoring System (CMS) [16]; Climate

of the surfaces as well as their degree of fragmentation over time [19–22].

well below the EU average level of 40%, logging is still at a high rate [27].

measurements and with accurate methods of quantification [28–32].

the deforestation of forests at the level of Romania.

The reduction of forest areas as well as the process of fragmentation of the forest is a ubiquitous problem worldwide. Haddad et al. estimated that half of the planet's forests are less than 500 m from an inhabited area and most of the forested areas

The satellite images offer an unprecedented perspective on the spatial evolution of the cover surfaces with forest vegetation, allowing the mapping of the compactness

Forest fragmentation assessments have been completed for many countries, such as Canada, China, the Democratic Republic of Congo, India, the UK, or the USA [23–26]. Many of the researchers who developed these studies point out that fragmentation of forest areas has negative effects on the natural ecosystems by increasing the isolation, creating artificial margins, and reducing the basic areas

In Romania, forests are under pressure due to climate changes (extreme temperatures, low rainfall, strong winds, and even tornadoes) and natural disturbances (insect outbreaks), but mainly due to anthropogenic causes (various forms of property, poor pest control, illegal logging, large demands on wood for export, etc.). Although Romania's forest area is estimated at about 29% of the country's total area,

A continuous, accurate, and reliable monitoring of the territorial evolution of forests as well as their state of sanogenesis is required both locally, in Romania, and regionally, Europe or worldwide. Such monitoring systems can be based on the information provided by the satellite monitoring networks correlated with on-site

Establishing methods of continuous observation and accurate determination of long-term environmental changes is necessary to ensure the sustainability of the forest ecosystem and the efficiency of the planned ecological restoration [33].

The method proposed in this study wants to perform a fractal analysis regarding

In order to start the analyses for GIS and fractal methods used, we downloaded layer (a raster image in tiff format) corresponding to the granule with the top-left corner at 50°N, 20E (in which Romania is situated), containing the forest loss (loss

The images prepared for the fractal analyses followed a step-by-step algorithm,

consisted on the extraction by mask procedure. The input feature mask was the vector limit of each relief unit of Romania, in our case 11 vector limits (the Carpathians, the Subcarpathians, the West Hills, the Danube Delta, Transylvania Depression, Dobrogea Plateau, Mehedinți Plateau, Getic Plateau, Moldova Plateau, Romania Plain, and West Plain). For each of the 11 input limits, 21 images in tiff format were exported providing pixels with useful informations. The first image exported contains the geographical limit for the relief unit, the other 18 images contain the yearly forest loss, from 2001 to 2018, and another image contains the cumulated forest loss for the entire period (2001–2018) and the last image the

**126**

tree-cover information. We have to mention that for the best results, all the images exported were in black-and-white tones (the pixels corresponding to limits, to the forest loss, and to the tree cover were in white, while the background was in black color). Other important aspects were the scale and the image position: in order to avoid the information errors that might have appeared during the export processes, for each input feature mask (relief unit), the same scale and the same unmoved image position were kept.

The exported images provided useful informations that were extracted by using some specific softwares for the fractal and nonfractal analyses. We mentioned that, depending on the surfaces of the relief units, the images were exported to different scales and analyzed later fractal objects. Thus, for the Carpathians, the exported images kept the scale 1:1,750,000; for Subcarpathians, 1:1,300,000; the Transylvanian Depression, 1:1000,000; Moldova Plateau, 1:1,500,000; Dobrogea Plateau, 1:800,000; Getic Plateau, 1:650,000; Mehedinți Plateau, 1:200,000; the West Hills, 1:1,500,000; Romania Plain, 1:1,350,000; West Plain, 1:1,500,000; and the Danube Delta, 1:600,000. Even if the exported images were analyzed at different scales, the pixel sizes being the same for each exported image, there were no distortions or errors in their subsequent processing.

The applicability of fractal geometry is limited not only to static phenomena but also to the study of dynamic phenomena, in evolution, such as the phenomena of growth in biology or of development of urban populations [35].

A versatile possibility to determine the deforestation patterns but also their impact on forest compaction is the fractal fragmentation index (FFI). FFI is a recent indicator and describes fractal fragmentation and can also be interpreted as an index of compaction of the analyzed surfaces, being a dimensionless indicator [36].

The FFI is calculated using the equation (Eq. (1)):

In maex or compaCHO or the anatyzze surfaces, being a dimensionless factor [36].

The FFI is calculated using the equation (Eq. (1)):

$$FFI = D\_A - D\_P = \lim\_{\varepsilon \to 0} \left( \frac{\log N(\varepsilon)}{\log \frac{1}{\varepsilon}} \right) - \lim\_{\varepsilon \to 0} \left( \frac{\log N'(\varepsilon)}{\log \frac{1}{\varepsilon}} \right) \tag{1}$$

where *FFI* is the fragmentation fractal index, *DA* is the fractal dimension of the summed areas, and *DP* is the fractal dimension of the summed perimeters; ε represents the size of the box; log*N*(ε) represents the number of contiguous and non-overlapping boxes needed to cover the object area; and log *N*′( ε) represents the number of contiguous and non-overlapping boxes needed to cover only the object's perimeter.

When the value of the indicator has *FFI* = 0, it means that the analyzed fractal objects (in our case the deforested areas or forests) are very small, of the order of 1–4 pixels, so that their outline cannot be extracted, *DA*D = *DP* =0. When the FFI value tends to be 1, the occupied areas are large and compact. *FFI* = 1, when analyzing a Euclidean object, 100% compact, without any discontinuity (*DP =* 1 and *DA =* 2). When the areas occupied by the fractal are smaller, more dispersed, and more fragmented, the value of the FFI approaches more than 0. The FFI was calculated using IQM-plugin-FFI, available online at https://sourceforge.net/projects/iqmplugin-ffi/, for open source software IQM 3.5 [37].

The analysis of the evolution of the analyzed parameter is carried out through a series of steps. In advance, IQM 3.50 software is downloaded from https://sourceforge.net/projects/iqm/files/latest/download; then, IQM-plugin-FFI is downloaded from the address https://sourceforge.net/projects/iqm-plugin-ffi/files/latest/download. The downloaded plug-in is inserted in the plug-in folder of the IQM program, and a series of steps are taken.

Step 1: Import the images into the information quality metric (IQM - An Extensible and Portable Open Source Application for Image and Signal Analysis in Java) [File—Open Image(s)] (**Figure 1**).

#### **Figure 1.** *Importing images to analyze.*

Step 2: Convert RGB images into 8 bits [Process—Convert Image–extract G] (**Figure 2**).

**Figure 2.** *Convert RGB images to 8 bits.*

Step 3: Open the FFI plug-in [Plug-in—Image—FFI v2.0].

Method P-Dimension (Pyramid Dimension) is selected (because it is much faster than box counting and the results are similar), and the number of boxes is 9; then press Preview and the fractal analysis is done (**Figure 3**).

**129**

**3. Study area**

*Obtaining the results of the FFI index.*

**Figure 4.**

(**Figure 4**).

*Using the FFI plug-in.*

**Figure 3.**

*Use of Fractal Analysis in the Evaluation of Deforested Areas in Romania*

Step 4: This gives the FFI value on the last column of the displayed table

Romania is a state located in the Southeast of Central Europe, on the lower Danube, north of the Balkan Peninsula, and on the northwestern shore of the Black Sea. The population, at the level of 2019, is estimated at 19.4 million citizens. On its territory are the southern and central parts of the Carpathian Mountains and the lower Danube basin. It borders Bulgaria to the south, Serbia to the southwest, Hungary to the northwest, Ukraine to the northeast, the Republic of Moldova to the

east, and the Black Sea to the southeast (**Figure 5**).

*DOI: http://dx.doi.org/10.5772/intechopen.91621*

*Use of Fractal Analysis in the Evaluation of Deforested Areas in Romania DOI: http://dx.doi.org/10.5772/intechopen.91621*

**Figure 3.** *Using the FFI plug-in.*

*Advances in Forest Management under Global Change*

Java) [File—Open Image(s)] (**Figure 1**).

Step 1: Import the images into the information quality metric (IQM - An Extensible and Portable Open Source Application for Image and Signal Analysis in

Step 2: Convert RGB images into 8 bits [Process—Convert Image–extract G]

Step 3: Open the FFI plug-in [Plug-in—Image—FFI v2.0].

then press Preview and the fractal analysis is done (**Figure 3**).

Method P-Dimension (Pyramid Dimension) is selected (because it is much faster than box counting and the results are similar), and the number of boxes is 9;

**128**

**Figure 2.**

*Convert RGB images to 8 bits.*

(**Figure 2**).

*Importing images to analyze.*

**Figure 1.**

Step 4: This gives the FFI value on the last column of the displayed table (**Figure 4**).


**Figure 4.** *Obtaining the results of the FFI index.*
