1. Introduction

2. Materials and Methods

2.2. Image and map procedures

This work was performed in GIS (Geographical Information Systems) environment, using ArcGIS software, version 10.8.1 (ESRI). The statistical analysis was done with SPSS software (IBM). After extensive data acquisition, a pre-analysis was made and data treatment was performed in order to process the desired information through spatial and statistical analysis by producing several maps and a comprehensive and solid database, explained in further detail as follows:

2.2.1. Land cover and topography

Using Soil Cover maps (COS – “Carta de Ocupação do Solo”), obtained from the Portuguese National Geographic Information System (SNIG) database, a pre-analysis was done to verify whether changes in the soil use occurred within the study area, during the study’s time interval (2004-2010-2015). The COS maps closest to the study’s moments (years) were acquired, in this case, 2007, 2010 and 2015. In this study, only the areas corresponding to “Cork oak forests” and “Cork oak agro-silvopastoral systems” will be subject to analysis.

The Digital Terrain Model (DTM) for Portugal, with a 25-meter resolution, obtained from the Portuguese Directorate General for the Territory (DGT), was used to characterize the study area’s hypsometry, slope and aspect:

• Hypsometry: altitude’s graphic representation of points over a reference plane;
• Slope: obtained from the DTM using the ArcGIS tool Slope. Afterwards, a reclassification was done, according to the cork and holm oak mortality inventories (Ribeiro et al., 2008; Ribeiro et al., 2016), as shown in the following Table 1:

• Aspect: obtained from the DTM, using the ArcGIS Aspect tool. They are in degrees, divided in four quadrants (Table 2), noting that the null aspect corresponds to a perfectly flat area:

2.2.2. Edapho-Climatic aptitude

Following the Regional Plan for Forest Management (PROF) for Alentejo and Lisboa and Vale do Tejo regions [35], the cork oak’s aptitude was calculated by assessing the relationship between the species edaphic and climatic attributes.

Based on the Portuguese Soil Classification, each soil unit was classified according to its the limitations on forest development [14]. Therefore, cork oak edaphic aptitude is determined according to the following table (Table 3):

Climatic aptitude was calculated based on the relationship between three indexes [36], in this case, spanning 10 year intervals and calculated from data collected from the nearby meteorological station, each one ending in one of the study’s moments, i.e., 1994-2004, 2000-2010 and 2005-2015 (Table 4):

• Thermicity index (It) – it considers the winter’s cold intensity, using the following equation:

It = (T + m + M)*10,

(1)

• , where: T – mean annual temperature (ºC); m – mean of the coldest month minimum temperatures (ºC); M – mean of the coldest month maximum temperatures (ºC).;
• Ombrothermic index (Io): relates the mean annual precipitation (Pp) with the mean annual temperature (Tp):

Io = Pp/Tp,

(2)

• Continentality index (Ic): corresponds to the temperature’s mean annual amplitude:

Ic = Tmax – Tmin,

(3)

• ,where Tmax is the hottest month mean temperature and Tmin is the coldest month mean temperature.

The final determination is based on the law of minimums between the edaphic and climatic aptitudes, resulting in the bioclimatic aptitude of this species for the study site.

2.2.3. Solar radiation

Considering that the increase in solar radiation directly reaching soil level could be a factor to the tree’s decline [37,38], this variable was added to the analysis. The solar radiation map in matricial format was confined to the study area, and converted to vectorial format – polygons (without any reclassification). This map corresponds to the average of the Global Horizontal Irradiation daily total values from 1994 to 2018.

2.2.4. Dead trees and crown cover

The methods used for the identification of dead trees in the three studied moments followed the procedures and criteria applied for the “National Cork Oak Mortality Inventory based on the digital aerial photography of 2004/2006” [9,13].

Provided by the Portuguese Geographic Institute, orthophotomaps (50 cm resolution) covering the region were processed according to Surový et al. methodology, with ArcGIS software, resulting in a false colour image by combining RGB (specific permutation) and IV bands in which the contrast between vigorous and dead/decrepit trees is evident [39]. Dead tree identification was performed with visual detection and manual selection followed by the living cork oak trees’ discrimination from the background (RGB colour space transformation) using the B-square index. Though its accuracy matches those of other indexes its overestimation error is lowest [39]. From the histogram’s grey levels threshold, segmentation was calculated and all pixels under this threshold were marked as black and above as white. Such procedures produced diachronic maps figuring on one hand dead trees, resulting in a polygon (vectorial format) for each dead tree and using its centroid to attribute the tree’s coordinates, and on another tree crown cover, later classified (taking into account an evenly distribution of the polygons among classes) as: less than 20%; between 20 and 29%; 30 and 34%; 35 and 40%; and greater than 40%. The cork oak’s identification was performed using its crown spectral signature.

2.2.5. Mortality index

The mortality index (IM) for the three studied moments, relating the number of dead trees, the crown cover and the area is given by:

$$\mathrm{IM}=\frac{\mathrm{N}º \mathrm{dead} \mathrm{trees} \mathrm{per} \mathrm{hectare}}{\mathrm{Crown} \mathrm{cover} (\%)},$$

(4)

This index values are divided in 6 classes, described as follows (Table 5):

Table 5. Mortality index classes

Table 5. Mortality index classes

Mortality index class	$\mathbf{Interval} \left({10}^{-3}\right)$
1	0 – 3
2	3 – 6
3	6 – 12
4	12 – 24
5	24 – 48
6	> 48

3. Results

Table 6. Number of dead trees during the studied period

4. Statistical analysis

4.1. Diachronic study

The results presented in table 8 showed that the significant variables associated with cork oak mortality are the climatic aptitude, area, crown cover and period (Table 8).

Table 8. Fixed coefficients, the dead/ha being the dependent variable

Table 8. Fixed coefficients, the dead/ha being the dependent variable

Source	F	df1	df2	Sig.
Corrected model	151	21	6359	< 0.001
Soil cover	2.642	2	6359	0.071
Solar radiation	ª	0
Climatic aptitude	31.613	1	6359	< 0.001
Area	2930	1	6359	< 0.001
Period	46	2	6359	< 0.001
Crown cover	3.466	4	6359	0.008
Solar radiation * Crown cover	3.657	5	6359	0.003

Probability distribution: Gamma; Function Link: Log. ª Did not compute due to the absence of degrees of freedom.

The area is highly significant due to the bias caused by the polygon dimensions up to 1 hectare, as revealed by the graphical analysis. This variable inclusion corrects this, due to the fact that the dependent variable is the dead trees per hectare. Besides this, not only is the crown cover a significant variable, but so is its interaction with the solar radiation.

Mortality index values were lower with the climatic aptitude above the reference for the cork oak than the regular one. However, in general, there was an increase in the mortality index over time (Figure 3).

The solar radiation, while not showing significance throughout the entire area, had an interaction with the stand’s crown cover, thus a separate analysis for each crown cover class was warranted.

5. Cadastre

6. Discussion

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