# Identification of Old-Growth Mediterranean Forests Using Airborne Laser Scanning and Geostatistical Analysis

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Study Area

^{−1}(range 400–1900 mm) and the average temperature is 11.7 °C. Pines are the main coniferous trees in the area, with Aleppo pine (Pinus halepensis Mill.), Maritime pine (P. pinaster Ait.) and black pine (P. nigra subsp. salzmannii) distributed in slopes and valleys according to edaphic and climatic conditions. Common hardwood species are Quercus ilex L. and Q. faginea Lam., which grow at lower altitudes and are often mixed with maples (Acer spp.), aspens (Populus spp.), rowans (Sorbus spp.), and ashes (Fraxinus angustifolia). Black pine is the most abundant species in the Natural Park, covering 60,000 ha between 1000 and 2000 m [53]. This species can reach 40 m in height and 1.2 m in diameter and is well adapted to poor and shallow soils, steep slopes, and upper and rocky areas, where other more demanding species cannot survive [54]. We selected the Navahondona forest (15,588.73 ha) in the Natural Park as a pilot area and focused on the management units of the forest in which P. nigra is the dominant tree species (>80%, 4487 ha).

#### 2.2. Forest Inventory Data

^{2}(15 m radius) systematically distributed in a grid of 200 m sides resulting in a density of 1 plot per 4 ha. There was no pre-field screening to check if the plots were in forested areas. The inventory included the diameter at breast height (DBH) and total height (HT) of every tree.

#### 2.3. Calculation of Old-Growth Indices

^{−1}) of large trees; (3) mean tree DBH; and (4) density (trees ha

^{−1}) of all trees. These four structural variables can be used to compute an OGI, according to Equation (1) [8]:

_{i}is the observed value for the ith structural variable; x

_{i}

_{young}is the mean value of the ith structural variable for young stands; and x

_{i}

_{old}is the mean value of the ith structural variable for old stands. When the value of any structural variable in a plot is less than that calculated for young stands, the value for young stands applies. Likewise, when the value of the variable exceeds that of the old stands, the value corresponding to an old stand is assigned. Hence, the OGI ranges from 0, when all structural variables correspond to the values of young stands, to 100, when all structural variables correspond to the values of old stands.

_{j}is the basal area of tree j in the plot. Second, for the definition of large trees, we used the thresholds of 50 cm [59], 70 cm [37], and 100 cm DBH [55], and calculated the density of trees (in trees ha

^{−1}and basal area (m

^{2}ha

^{−1}) with DBH > 50, 70, and 100 cm in each plot. As a result, 15 OGIs were calculated, combining different definitions of the aforementioned structural variables (Table 1). Each of the structural variables was compared between old and young forests using analysis of variance.

#### 2.4. Geostatistical Modeling

_{i}is the error term assuming that e

_{i}~ N(0, σ

^{2}+ σ

_{1}

^{2}) and Cov[e

_{i}, e

_{j}] = σ

^{2}[f(d

_{ij})], with f(d

_{ij}) a function of the distance between the locations s

_{i}and s

_{j}. We chose the spherical distance function f(d

_{ij}) = [1 − 1.5(d

_{ij}/ρ) + 0.5(d

_{ij}/ρ)

^{3}] if d

_{ij}< ρ, and f(d

_{ij}) = 0 otherwise. Parameters σ

_{1}

^{2}, σ

^{2}+ σ

_{1}

^{2}, and ρ correspond to the nugget, sill, and range of the geostatistical model, respectively.

#### 2.5. ALS Data Analysis

^{2}, and vertical root mean square error (RMSE) < 0.20 m. The summary statistics of ALS return density within the plots (pulses m

^{−2}) were: mean = 0.4, minimum = 0.13, maximum= 2.25, and standard deviation = 0.23.

_{1}, X

_{2}, … X

_{n}are metrics derived from the ALS dataset (Table 2); ß

_{0}, ß

_{1}, … ß

_{n}are the parameters to be estimated; and ε is an additive error term.

^{2}adj) statistics. Heteroscedasticity was checked with the Breusch–Pagan test. Finally, RMSE and root mean square error of prediction (RMSEP) were compared to verify that the selected model was not overfitted.

## 3. Results

#### 3.1. Selection of Structural Parameters and OGI

^{−1}) was significantly larger in the young stands, which also were dominated by smaller diameter trees (<60 cm), unlike the larger trees observed in older stands (Figure S1). Although clear differences have been observed among successional stages, high variability was observed in most of the variables (particularly N and N50 in young forests; see Table 3). Values of basal area and density of trees > 70 and >100 cm were null in early successional stages (young forests).

^{−1}), but differ in the structural parameter included to account for DBH variability: standard deviation of tree DBH in OGI 1, GC in OGI 4, and none in OGI 7 (Table 1). The values of OGI 1 and OGI 7 are highly correlated (Pearson r = 0.96) and have a similar frequency distribution (Figure 5), while the distribution of OGI 4 is skewed to higher values and less strongly correlated with OGI 1 and OGI 7 (r = 0.88 and 0.79, respectively). In this case, the GC (included in OGI 4) is not an adequate old-growth attribute because the mean value in the inventory plots (0.418) is very close to the mean value for old stands (0.449; Table 3) and, thus, this parameter will not properly distinguish young and old stands. This is because, in order to calculate the old-growth index, the value of the structural variable (in this case, GC) that is included in the index (see Equation (1)) cannot exceed the characteristic value for old stands (in that case, the characteristic value for old stands applies). In our case, this happens in 38.4% of the inventory plots, which is a very high value. In this high percentage of plots, the value that enters in the OGI is the same (the characteristic for old-growth stands), so the discriminatory power of using GC as a structural stand characteristic for evaluating old growth is very low.

#### 3.2. Geostatistical Model

#### 3.3. ALS Model

_{95}is the 95th percentile; h

_{L2}is the second-order moment; and CRR is the canopy relief ratio (describing the degree to which canopy surfaces are in the upper (CRR > 0.5) or lower (CRR < 0.5) portions of the height range) [73]. Figure 6 is a scatterplot of the predicted versus measured OGI 1 values. For this regression model, the RMSE was 14.84 (337 degrees of freedom) and the RMSEP was 14.54. Further information about the model can be seen in Table 5.

## 4. Discussion

#### 4.1. Stand Structure Differences between Young and Old-Growth Forests

#### 4.2. OGIs to Distinguish Old Growth from Young Forests

#### 4.3. Geostatistics and ALS to Estimate OGIs

_{95}, h

_{L2}, CRR, and ARAM.TFR, from which h

_{95}and h

_{L2}contained the most information about the response. The presence of h

_{95}in the model confirms the strong relationship of height with stand age, this being one of the percentiles most useful in modeling stand height using an area-based approach [87]. On the other hand, numerous studies have utilized L-moments for characterizing dasymetric variables with ALS data, e.g., [88,89,90]. In particular, h

_{L2}(i.e., measurement of dispersion similar to standard deviation, with less weight given to outliers [91]) as a predictor variable is in accordance with the results obtained in the characterization of OGFs (such forests showed greater diameter standard deviation). In addition, the OGI selected in this study includes the standard deviation of the diameter.

^{−2}) [42,62]. Notably, [92] recommended a minimum of 1 pulse m

^{−2}(>4 pulses m

^{−2}for dense forests on complex terrain) to produce an operational ALS-based enhanced forest inventory. The results could also be explained by ground plot georeferencing errors, but in the present study, large-size ground plots were used (706 m

^{2}); in relation to this, [93] point out that regression analysis using larger plots (>314 m

^{2}) appeared more robust to the ill effects of GPS error and therefore, this source of error can be considered less important than the low density of ALS data. The temporal cover provided by PNOA flights has been set at 6 years and new flights will provide a higher density of returns (2 returns m

^{−2}), which will influence the precision of the relationships between ALS metrics and OGIs; hence, it can be expected that future models estimating OGIs from ALS data will obtain better results. Moreover, future PNOA flights will also allow monitoring of the forests over time.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Study site location (red area) in Cazorla, Segura and Las Villas Natural Park (pink area) in Andalusia, Spain (

**a**) left; (

**b**,

**c**) Physiognomy of old-growth stands in the study area.

**Figure 2.**Scatterplot of mean diameter at breast height (DBH) and total density (trees ha

^{−1}) (

**a**) and total basal area (m

^{2}ha

^{−1}) (

**b**) at the inventory plots. The curved line shows the tendency (penalized B-spline).

**Figure 3.**Boxplots of the 15 types of old-growth index (OGI) calculated in the study area. The structural variables that are included in each index are described in Table 1.

**Figure 4.**Scatterplots (dot plots) and frequency distributions (histograms) of OGIs 1, 4, and 7. The range of the x-axis in the histogram plots is 0–100 and the amplitude of each histogram bar is 7 units. OGI 1 includes the standard deviation of DBH and OGI 4 includes the Gini coefficient, but OGI 7 does not include any tree DBH dispersion parameter. OGI: old-growth index; DBH: diameter at breast height.

**Figure 6.**Measured old-growth index (OGI) values versus OGI values predicted by the geostatistical model at the inventory plots (

**a**) and measured old-growth index (OGI) values versus OGI values from the validation dataset of the ALS model (

**b**). The straight line shows a 1:1 relationship, while the curved line shows the tendency (penalized B-spline).

**Table 1.**Structural variables selected to calculate the old-growth index (OGI) in the study area. Structural parameters were weighted to obtain an OGI with 0–100 range. All varieties include the mean DBH of the plot as the structural variable. OGI: old-growth index; STDDBH: standard deviation of tree DBH; GC: Gini coefficient. Density values are in trees ha

^{−1}and basal area is in m

^{2}ha

^{−1}.

Structural Parameters | ||
---|---|---|

OGI Type | DBH Variability | Density of Large Trees |

1 | STDDBH | Density of trees > 50 cm DBH |

2 | STDDBH | Density of trees > 70 cm DBH |

3 | STDDBH | Density of trees > 100 cm DBH |

4 | GC | Density of trees > 50 cm DBH |

5 | GC | Density of trees > 70 cm DBH |

6 | GC | Density of trees > 100 cm DBH |

7 | - | Density of trees > 50 cm DBH |

8 | - | Density of trees > 70 cm DBH |

9 | - | Density of trees > 100 cm DBH |

10 | STDDBH | Basal area of trees > 50 cm DBH |

11 | STDDBH | Basal area of trees > 70 cm DBH |

12 | STDDBH | Basal area of trees > 100 cm DBH |

13 | - | Basal area of trees > 50 cm DBH |

14 | - | Basal area of trees > 70 cm DBH |

15 | - | Basal area of trees > 100 cm DBH |

ALS Metrics | Description |
---|---|

h_{mean,} h_{mode} | mean, mode |

h_{min,} h_{max} | minimum, maximum |

h_{SD,} h_{CV} | standard deviation, coefficient of variation |

h_{Skw} | skewness |

h_{kurt} | kurtosis |

h_{ID,} | interquartile range, |

h_{AAD} | average absolute deviation |

h_{MADmedian} | median of the absolute deviations from the overall median |

h_{MADmode} | median of the absolute deviations from the overall mode |

h_{L1}, h_{L2}, h_{L3}, h_{L4} | L-moments |

h_{Lskw} | L-moments of skewness |

h_{Lkur} | L-moments of kurtosis |

h_{01}, h_{05}, h_{10}, h_{20}, h_{25}, …, h_{90}, h_{95}, h_{99} | Percentiles |

CRR | canopy relief ratio: mean height-min height/max height-min height |

CC | canopy cover: percentage of first returns above 4.5 m/total returns |

PARA3 | percentage of all returns above 3 m/total all returns |

ARA3.TFR | ratio between all returns above 3 m and total of first returns |

PFRAM | percentage of first returns above mean/total all returns |

PARAM | percentage of all returns above mean/total all returns |

PARAMO | percentage of all returns above mode/total all returns |

PFRAMO | percentage of first returns above mode/total all returns |

ARAM.TFR | ratio between all returns above mean and total of first returns |

ARAMO.TFR | ratio between all returns above mode and total of first returns |

**Table 3.**Comparison of values (average and standard deviation in parenthesis) of structural variables for old and young stands. Different letters within each row represent significant differences (p value < 0.05).

Structural Variables | Old Forests (n = 21) | Young Forests (n = 18) | F (p > F) |
---|---|---|---|

Mean tree diameter (mDBH, cm) | 70.48 (15.0) a | 17.58 (2.01) b | 219.55 (<0.0001) |

Diameter standard deviation (STDDBH) | 30.89 (17.2) a | 4.28 (2.23) b | 42.45 (<0.0001) |

Basal area (G, m^{2} ha^{−1}) | 36.08 (15.2) a | 5.74 (5.75) b | 47.88 (<0.0001) |

Basal area of trees > 50 cm DBH (BA50, m^{2} ha^{−1}) | 34.69 (15.2) a | 1.67 (0.71) b | 91.92 (<0.0001) |

Basal area of trees > 70 cm DBH (BA70, m^{2} ha^{−1}) | 31.35 (12.0) a | 0 (0) b | 86.98 (<0.0001) |

Basal area of trees > 100 cm DBH (BA100, m^{2} ha^{−1}) | 27.26 (10.5) a | 0 (0) b | 12.35 (0.0012) |

Density (N, trees ha^{−1}) | 83.15 (41.9) b | 285.30 (277.7) a | 10.88 (0.0022) |

Density of trees > 50 cm DBH (N50, trees ha^{−1}) | 58.94 (29.9) a | 0.78 (3.33) b | 67.00 (<0.0001) |

Density of trees > 70 cm DBH (N70, trees ha^{−1}) | 42.10 (19.6) a | 0 (0) b | 82.30 (<0.0001) |

Density of trees > 100 cm DBH (N100, trees ha^{−1}) | 11.57 (13.3) a | 0 (0) b | 13.59 (0.0007) |

Gini coefficient (GC) | 0.45 (0.21) a | 0.26 (0.11) b | 11.67 (0.006) |

**Table 4.**Geostatistical model selection process. −2LL: −2 Log Likelihood. AIC: Akaike information criterion (the smaller the better). The selected model is model 5.

Model | Description | −2LL | AIC |
---|---|---|---|

1 | With nugget, covariates, and different spatial covariance in areas North and South | 6545.5 | 6575.5 |

2 | = Model 1 but same spatial covariance in areas North and South | 6549.4 | 6575.4 |

3 | = Model 2 but without nugget | 6751.6 | 6775.6 |

4 | With covariates but no spatial covariance | 6563.5 | 6585.5 |

5 | = Model 2 but without covariates | 6560.4 | 6568.4 |

**Table 5.**Parameter estimates and goodness-of-fit statistics of the model selected for estimating the OGI 1 from ALS data. ARAM.TFR: ratio between all returns above mean and total of first returns; H95: 95th percentile; H

_{L2}: second-order moment; CRR: canopy relief ratio.

Parameter | Estimate | Standard Error | t-Value | p >|t| |
---|---|---|---|---|

Intercept | −30.14945 | 5.25588 | −5.736 | <0.0001 |

ARAM.TFR | −0.25675 | 0.08158 | −3.147 | 0.0018 |

h_{95} | 1.90980 | 0.38434 | 4.969 | <0.0001 |

h_{L2} | 8.86526 | 2.12298 | 4.176 | <0.0001 |

CRR | 32.37033 | 10.86575 | 2.979 | 0.0031 |

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**MDPI and ACS Style**

Hevia, A.; Calzado, A.; Alejano, R.; Vázquez-Piqué, J.
Identification of Old-Growth Mediterranean Forests Using Airborne Laser Scanning and Geostatistical Analysis. *Remote Sens.* **2022**, *14*, 4040.
https://doi.org/10.3390/rs14164040

**AMA Style**

Hevia A, Calzado A, Alejano R, Vázquez-Piqué J.
Identification of Old-Growth Mediterranean Forests Using Airborne Laser Scanning and Geostatistical Analysis. *Remote Sensing*. 2022; 14(16):4040.
https://doi.org/10.3390/rs14164040

**Chicago/Turabian Style**

Hevia, Andrea, Anabel Calzado, Reyes Alejano, and Javier Vázquez-Piqué.
2022. "Identification of Old-Growth Mediterranean Forests Using Airborne Laser Scanning and Geostatistical Analysis" *Remote Sensing* 14, no. 16: 4040.
https://doi.org/10.3390/rs14164040