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Article

Investigating LiDAR Metrics for Old-Growth Beech- and Spruce-Dominated Forest Identification in Central Europe

by
Devara P. Adiningrat
1,*,
Andrew Skidmore
1,
Michael Schlund
1,
Tiejun Wang
1,
Haidi Abdullah
1 and
Marco Heurich
2,3,4
1
Faculty of Geo-Information Science and Earth Observation, University of Twente, 7522 NH Enschede, The Netherlands
2
Chair of Wildlife Ecology and Wildlife Management, University of Freiburg, 79106 Freiburg, Germany
3
Department of Visitor Management and National Pak Monitoring, Bavarian Forest National Park, 94481 Grafenau, Germany
4
Institute for Forest and Wildlife Management, Inland Norway University of Applied Science, 2480 Koppang, Norway
*
Author to whom correspondence should be addressed.
Remote Sens. 2025, 17(2), 251; https://doi.org/10.3390/rs17020251
Submission received: 12 November 2024 / Revised: 5 January 2025 / Accepted: 8 January 2025 / Published: 12 January 2025
(This article belongs to the Special Issue LiDAR Remote Sensing for Forest Mapping)
Browse Figures
Figure 1
<p>Locations of sample plots in the Bavarian Forest National Park. The image is a true-color composite (band 432) of Sentinel-2A imagery acquired on 1 August 2020.</p> "> Figure 2
<p>The frequency of the average stand age of the old-growth and second-growth plots.</p> "> Figure 3
<p>The ranking and relative importance of the selected LiDAR metrics in old-growth forest classification generated through mean decrease accuracy (MDA) analysis. The top-ranked metrics are the metrics with the highest decreases in the accuracy coefficient. The asterisk (*) indicates the top three metrics used as the input predictors in the classification. Metrics with the □ symbol are standard metrics, and metrics with the ▲ symbol are structural metrics.</p> "> Figure 4
<p>Box plots of the Rumple index (<b>a</b>), vertical complexity index (VCI) (<b>b</b>), and gap fraction (<b>c</b>) between the old- and second-growth stages. All of the values in each selected metric were derived from the canopy height model (CHM) in the sample plot, as all the selected metrics are structural diversity metrics. Each metric can significantly distinguish old-growth from second-growth forests, determined by the Wilcoxon test <span class="html-italic">p</span>-value of &lt; 0.05.</p> "> Figure 5
<p>The SHAP summary plot of three important LiDAR metrics for discriminating old- and second-growth forests. The positive axis indicates a greater probability of a feature value to identify a class. In contrast, the negative axis indicates that the feature value has a weak contribution to identifying a class. For example, in the old-growth class, the Rumple index’s high values were distributed on the positive axis, demonstrating a high probability of old-growth emergence prediction in the classification. On the contrary, the Rumple index’s low values were distributed on the positive axis in the second-growth class, indicating that low values of the Rumple index are good predictors for the second-growth class.</p> ">
Versions Notes

Abstract

:
Old-growth forests are essential for maintaining biodiversity, as they are formed by the complexity of diverse forest structures, such as broad variations in tree height and diameter (DBH) and conditions of living and dead trees, leading to various ecological niches. However, many efforts of old-growth forest mapping from LiDAR have targeted only one specific forest structure (e.g., stand height, basal area, or stand density) by deriving information through a large number of LiDAR metrics. This study introduces a novel approach for identifying old-growth forests by optimizing a set of selected LiDAR standards and structural metrics. These metrics effectively capture the arrangement of multiple forest structures, such as canopy heterogeneity, multilayer canopy profile, and canopy openness. To determine the important LiDAR standard and structural metrics in identifying old-growth forests, multicollinearity analysis using the variance inflation factor (VIF) approach was applied to identify and remove metrics with high collinearity, followed by the random forest algorithm to rank which LiDAR standard and structural metrics are important in old-growth forest classification. The results demonstrate that the LiDAR structural metrics (i.e., advanced LiDAR metrics related to multiple canopy structures) are more important and effective in distinguishing old- and second-growth forests than LiDAR standard metrics (i.e., height- and density-based LiDAR metrics) using the European definition of a 150-year stand age threshold for old-growth forests. These structural metrics were then used as predictors for the final classification of old-growth forests, yielding an overall accuracy of 78%, with a true skill statistic (TSS) of 0.58 for the test dataset. This study demonstrates that using a few structural LiDAR metrics provides more information than a high number of standard LiDAR metrics, particularly for identifying old-growth forests in mixed temperate forests. The findings can aid forest and national park managers in developing a practical and efficient old-growth forest identification and monitoring method using LiDAR.

1. Introduction

Old-growth forests play a critical role in biodiversity conservation and ecosystem service provision, characterized by complex forest structures and diverse ecological niches supporting high species diversity [1,2,3,4,5]. They are also prioritized for protection under the EU Biodiversity Strategy for 2030 [4]. However, old-growth forests are scarce across Europe, often fragmented and vulnerable to human interference, with limited areas under strict protection [6,7]. Moreover, defining and mapping these ecosystems is challenging, with definitions varying based on context, purpose, and management goals [4,8,9].
A common metric for defining old-growth forests in Europe is stand age, particularly using a threshold of over 150 years [10], as stands reaching this age often display attributes associated with old growth, such as complex canopy structures and diverse age classes [11,12,13,14,15]. The forests with a stand age of less than 150 years are considered second-growth forests, where post-disturbance forest stands have not undergone forestry operations since establishment or have been left untouched for at least 80 years [16]. Second-growth forest stands have structural attributes and characteristics that exhibit developments toward the old-growth stage [16,17]. The threshold of 150 years reflects the lifespan of dominant species, like Norway Spruce and European Beech, and aligns with global definitions of old-growth forests [2,9,15,18]. Although the tree diameter at breast height (DBH) is often correlated with age [16,17,19,20,21], direct age estimation across extensive forest areas requires labor-intensive methods, like tree-ring analysis, limiting practicality over large landscapes [1,22,23].
The advent of remote sensing technologies, particularly light detection and ranging (LiDAR), has provided new means to map forest structures comprehensively and consistently over large areas. LiDAR-derived metrics can serve as proxies for structural attributes, potentially identifying features indicative of old-growth stages [24,25]. Standard LiDAR metrics, which describe height and density distributions, have traditionally been used, though these are limited in their capacity to capture complex structural characteristics [23,24,26,27,28]. In contrast, structural metrics derived from combinations of standard metrics offer enhanced descriptions of canopy heterogeneity, layering, and openness—key indicators of old-growth conditions [29,30].
Previous studies on old-growth forest mapping using LiDAR have often focused on single indicators, such as tree height [24,31], basal area [32,33], canopy gaps [31,34], forest volume [31,33], or deadwood abundance [35]. However, these metrics alone do not capture the multi-layered, heterogeneous nature of old-growth forests. Additionally, studies incorporating numerous LiDAR metrics encounter multicollinearity issues, which can complicate model performance and interpretation [36]. In this study, we optimize a set of selected LiDAR metrics to focus on the structural complexity of old-growth forests, thereby providing a more practical and parsimonious approach to identifying these ecosystems. Furthermore, we focused our study on a temperate forest landscape in Central Europe for two reasons. First, the use of LiDAR data to map old-growth forests within the Central European temperate forest ecoregion is still limited [37]. Second, this ecoregion spans 7000 km2 across Central Europe and covers ten countries with different managements and policies regarding old-growth forest protection [4,38]. This makes the old-growth forest ecosystems in this ecoregion generally vulnerable. Our study will contribute to the development of old-growth forest mapping benchmarks using remote sensing data, particularly LiDAR.
In this study, we incorporate LiDAR standard and structural metrics that cover multiple old-growth forest structures and investigate which metrics can accurately distinguish old- from second-growth forests in large areas. To accomplish this, we use LiDAR metrics as the independent variables to model the dependent variable of old- and second-growth forests, where old-growth and second-growth forests are differentiated by stand age based on allometric equations of tree DBH that are modified for European temperate forests. The old-growth forests in this study were identified using the EU-stand age threshold of more than 150 years for beech and spruce in Central European mature mixed temperate forest landscapes.
Here, we investigate both LiDAR standard and structural metrics to distinguish old-growth from the younger stages (i.e., second-growth forests) over large areas. Employing a stand age threshold of over 150 years, we focus on beech- and spruce-dominated stands typical of Central European mixed temperate forests. By applying multicollinearity analysis and the Random Forest algorithm, we identify the most informative metrics for classification. Our study will contribute to the research of old-growth forest area monitoring and mapping, with implications for forest and park managers seeking efficient and scalable monitoring tools.

2. Materials and Methods

2.1. Study Area

The Bavarian Forest National Park is situated in south-eastern Germany (43.055° N, 13.203° E) along the border of the Šumava National Park in the Czech Republic (Figure 1). The National Park is a mixed temperate forest landscape consisting of coniferous and deciduous type forests with characteristics of a montane area and an altitude of 600 to 1453 m in an area of 249 km2 [39]. Two tree species predominate at different elevations, namely Norway Spruce (Picea abies) and European Beech (Fagus sylvatica) [40,41]. The national park was established in the Rachel–Lusen Area in 1970 and extended to the Falkenstein–Rachel Area in 1997 [42]. A series of disturbances, such as windthrow, snow breakage, and bark beetle infestations, have occurred since the 17th century, including human disturbance through forestry activities, especially in the Rachel–Lusen Area [39]. However, there was a considerable reduction in forest management in the 1980s. In the 1990s, forest management was reduced to the so-called management zone. Unlike the Rachel–Lusen Area, forest management still takes place in the Falkenstein–Lusen Area, with the non-intervention zone (natural zone) increasing gradually since its establishment in 1997. Small areas of the Bavarian Forest National Park have been protected to preserve old-growth stands (approximately 250 ha) since the mid-18th century [39]. Based on the history of the Bavarian Forest National Park, mature and old forest stands (from 50 to more than 300 years) dominate the landscape. Today, the park consists of historically protected areas (old-growth forest stands/relics), post-logging second-growth forest stands, as well as natural post-disturbance regrowth stands from the 1970s. We also observed that the average amount of deadwood within areas assigned as old-growth forests is 66 m3 ha−1 higher than in second-growth forests, indicating that the Bavarian Forest National Park landscape comprises large areas of “old-growth” forests.

2.2. Field Sampling and Stand Age Estimation

The field plots were located following the BIOKLIM Project transects [40], with field data measured in 2020 (July–August) and 2021 (July–August) (see Figure 1). The BIOKLIM Project comprises four permanent transects established along the length of the National Park, which follow the altitudinal gradient of the park from 700 to 1400 m [40]. Locating our plots close to the BIOKLIM transects had advantages for our study, as the transects have multidate records (2006 and 2016) of environmental variables, including topographic information, forest structural variables, soil physical–chemical properties, and taxonomical groups [43]. In addition, these transects also have complete datasets of high-accuracy remote sensing imagery, mainly terrestrial and airborne LiDAR, as well as airborne image spectroscopy.
In total, 91 field plots with dimensions of 30 m × 30 m were collected (Figure 1). Following the suggestion from Gerzon et al. [16], we measured the DBH minimum of the ten largest over-story trees, or approximately 30% of the total number of dominant tree species within a plot, using DBH tape. As our study site was located in a typical European mixed temperate forest where a positive linear trend between the diameter growth trajectory and age of spruce and beech was found for centuries, we assumed the estimation of stand age could be measured from the DBH [21]. In this study, only trees with a DBH of more than 20 cm were measured to inventory old- and second-growth forests, following the suggestion from Vandekerkhove et al. [13]. The DBH of the minimum ten largest trees in each of the 91 forest plots was then used to estimate the individual tree age by dividing the DBH by the mean annual increment [44]. Values of 0.297 cm and 0.217 cm from Pretzsch and Dieler [20] were used as the mean annual increment diameter growth for Norway Spruce and European Beech, respectively. The values were calculated based on the relationship between the DBH at the beginning of the growth period and the average annual diameter increment growth of Norway Spruce and European Beech [20]. An approach from Di Filippo et al. [45] was used to estimate the stand age of a plot by averaging the age of all individual trees within the plot.
We acknowledge that trees of the same size may have different ages due to variations in growth rates influenced by various factors, such as site quality, altitude, competition, and disturbance trajectory. Therefore, our approach here in using DBH-based calculations was intended as a proxy to estimate stand age patterns rather than to determine the precise individual tree ages. Such an approach introduces uncertainties in the age-variable stands. To minimize the uncertainties, we interpreted stand age as an approximate measure representing dominant structural characteristics rather than an exact chronology of establishment.
Following Oliver and Larson [10], we used a stand age threshold of more than 150 years to determine old-growth forests and less than 150 years as second-growth forests. As a consequence of following this model, we defined our field plot as a second-growth forest between 30 and 150 years old and above 150 years old as an old-growth forest. This decision was made to balance the sample number for statistical and modeling analyses in our study, as the number of samples less than 30 years old were too scarce. Most plots were clustered around the stand age threshold of 150 years (Figure 2). The calculated confidence interval (CI) of the mean stand age of our samples also showed the pattern of the estimated stand age in all plots. Using the CI 95% and a mean estimated stand age of 157.58 years, the confidence interval showed 10.50 years. This implies that the average stand age in the Bavarian Forest National Park lies between 147.08 and 168.08 years. This indicates that mature and old-growth stands dominate the park landscape.

2.3. Airborne LiDAR Data

This study used an airborne laser scanner (ALS) to acquire the LiDAR data. A helicopter-borne Riegl LMSQ 680i LiDAR sensor (wavelength of 1550 nm and beam divergence of 0.5 mrad) covered the entire Bavarian Forest National Park in a flight campaign in June 2017 under the leaf-on condition [46]. The flight altitude was approximately 550 m with a 60% side overlap, producing an average point cloud density of 30 points/m2, with a maximum density of up to 70 points/m2 within the overlap areas. Eight returns were recorded for each pulse. A geometrical check assessed the ALS positional accuracy by adjusting with a flat building polygon [46]. The LiDAR returns and height (z) were normalized with respect to the ground, where the ground points were interpolated to the position below the non-ground returns [47]. The cloth simulation function [48] was used to classify the ground and non-ground returns/points with a cloth resolution of 1 m, and the Triangle Irregular Network (TIN) method was used to interpolate the ground points. The advantage of this approach is that it minimized the inaccuracies of terrain representation and normalized the ground points to a value of zero [47]. The ground classification and normalization were performed in R software version 4.1.2 (https://www.r-project.org/ (accessed on 1 September 2022)) using the lidR package v4.0.3 [47].

2.4. LiDAR Metrics Derivation

Using LiDAR normalized point clouds, we derived 44 standard metrics (i.e., height-based and density-based LiDAR metrics) and seven structural metrics (i.e., advanced LiDAR metrics generated from the canopy structure) (Table 1). The LiDAR structural metrics were primarily generated from the canopy height model (CHM). We generated the CHM by interpolating the normalized point clouds into a 1 m resolution raster cell using Delaunay triangulation [47]. The description of each generated LiDAR metric is provided in Table 1. All metrics were generated as point cloud statistics within the gridded cell with a spatial resolution of 30 m corresponding to our field plot dimensions of 30 m × 30 m. The metrics were processed in R software version 4.1.2 (https://www.r-project.org/) using the lidR package v4.0.3 [47].

2.5. Multicollinearity Analysis

A feature reduction process to remove high-collinearity metrics may facilitate the identification of the LiDAR unique metric(s) that contribute to old- and second-growth forest classification [49]. Furthermore, feature reduction can improve the performance of machine learning algorithms, such as random forest, and stabilize the classification due to the lower dimensionality of input features [24]. Here, we used the variance inflation factor (VIF) approach to reduce the high collinearity of the LiDAR metrics. Following the strategy from Zuur et al. [49], the metrics with high VIFs were continuously dropped and recalculated until the VIFs of the covariate reached the desired threshold. Although VIF ≤ 10 is considered an acceptable threshold for indicating collinearity, Hair et al. [50] argued that it is too lenient and distorts model estimation and accuracy. Therefore, a more stringent criterion of VIF ≤ 5 was applied here.

2.6. Random Forest Classification

We used the non-parametric random forest algorithm [51] to rank the important LiDAR standard and structural metrics and to classify the old- and second-growth forests. The random forest algorithm has recently become common in remote sensing applications for forestry [23,24,52]. The advantages of random forest in the context of assessing the LiDAR attributes of old-growth forest classification include the following: (1) it is relatively insensitive to overfitting; (2) it estimates the internal unbiased error; (3) it generates an estimation of the ranking of variable importance of the classification; (4) it can handle a vast number of input features without any deletion [52,53]. The variable importance computation and classification were executed in the R environment using the randomForest package v4.7-1.2 [54]. Two parameters of random forest were optimized for the classification, namely the number of trees (ntree) and the number of input features (mtry), using the expand.grid and tuneRF functions in the R package caret v.6.0-94, respectively. For each iteration in the optimization, we set an improvement of 0.01 in the test dataset error and 1.5 in the inflated/deflated value. We found ntree of 1500 and mtry of 3 as the optimum values. The random forest-based mean decrease accuracy (MDA) index was used to calculate the variable importance [53]. The MDA utilizes the permuted out-of-bag (OOB) to determine the ranking of variable importance during the OOB error computation phase, with more important variables having larger MDA values [53]. In addition to using the MDA, we followed the suggestion from Gislason et al. [55] to optimize the model by reperforming the classification using the square root of the total number of predictors after the variable importance ranking. The Shapley additive explanation (SHAP) [56] was used to explain the contribution of each important metric to the result of the random forest-based classification.

2.7. Accuracy Assessment

From the 91 plots that were surveyed, 45 of them were split into a training dataset, and the remaining 36 became the test dataset for assessing the accuracy. Furthermore, we also performed internal validation to confirm the robustness of the performance of the training and test datasets of the random forest model using k-fold cross-validation [57].
We then assessed the overall classification accuracy using the test dataset (i.e., 36 samples). The classification accuracy was assessed through a confusion matrix consisting of sensitivity, specificity, and overall accuracy. The true skill statistic (TSS), which is currently adopted for assessing machine-learning models, was also utilized [58]. The TSS, calculated as the sensitivity + specificity − 1, addresses the limitations of Kappa statistics, as it is defined by sensitivity and specificity while at the same time preserving the advantages of Kappa statistics [58]. In addition to the classification result, we added the Wilcoxon test, which was used to observe the significant difference of the predictors in the final classification of old- and second-growth forests.
Table 1. Descriptions of LiDAR metrics generated for this study. Not all of these metrics were used to classify old-growth. Only metrics with low collinearity (VIF < 5) were selected for the final classification.
Table 1. Descriptions of LiDAR metrics generated for this study. Not all of these metrics were used to classify old-growth. Only metrics with low collinearity (VIF < 5) were selected for the final classification.
MetricsDescriptionCategory Description
Standard Metrics
ZMAXMaximum height Height distribution profile of the LiDAR point clouds.
ZMEANMean height above ground
ZSDStandard deviation of height distribution
ZSKEWSkewness of height distribution
ZKURTKurtosis of height distribution
ZENTROPYEntropy of height distribution
ZQxxth percentile of height distribution (5, 10, 15, 20, ……, 99)
PZABOVE2Returns percentage above 2 mNumber of returns/density of the LiDAR point clouds.
PZABOVEZMEANReturns percentage above mean height
ZPCUMxCumulative percentage of return in the xth layer (1 to 9)
PxthPercentage in x returns
PGROUNDReturns percentage classified as “ground”
Structural Diversity Metrics
Rumple indexRatio between outer canopy surface area and projected ground surfaceThese metrics are related to canopy surface roughness, which describes the structural heterogeneity as an impact of distribution and various sizes of canopy gaps and various tree heights [59,60].
RugosityAn outer canopy roughness measured by the standard deviation of the canopy height model
Deep Gaps FractionFraction of canopy gaps per square meterThese metrics are related to the distributions of canopy gaps and openness estimation [30].
Cover FractionThe inverse of the deep gap fraction
Gaps FractionDistribution of gaps in the canopy volume
Vegetation Area Index (VAI)Sum of leaf-area density within the canopy volumeVAI calculates the area, density, and volume of vegetation, which is derived from the sum of leaf-area density (LAD)—a divided leaf area index (LAI) within the height interval [30,31,61,62].
Vertical Complexity Index (VCI)The distribution evenness of the point cloud within a vertical layerVCI is based on the information theory index used for quantifying species evenness. It can also quantify the evenness of three-dimensional point cloud distribution within a vertical layer [63].

3. Results

3.1. LiDAR Metric Selection and Variable Importance

The VIF results revealed that from all generated LiDAR standard and structural metrics, only 11 metrics (i.e., 7 standard and 4 structural metrics) had a VIF ≤ 5 (Table 2). All 11 selected metrics were then assessed for their importance in the old-growth classification with random forest through the mean decrease accuracy index (MDA). The results of the variable importance ranking of the selected LiDAR metrics using the MDA in discriminating old-growth from second-growth forests are presented in Figure 3. The ranking order indicates the most to the least important LiDAR standard and structural metrics when classifying old-growth forests. The top-ranked metrics were all LiDAR structural metrics, namely the Rumple index, vertical complexity index (VCI), and gap fraction, which showed greater MDA differences compared to the other eight metrics. The other eight metrics had comparable performance, though their MDA indices were considerably lower than those of the three top-ranked metrics. Moreover, the square root of the total 11 input LiDAR metrics is three. These three most important LiDAR metrics were considered unique and capable of discriminating old-growth from second-growth forests and used for further classification optimization.
The MDA analysis also revealed that the surface roughness of the outer canopy (Rumple index) was the most important (first-ranked) LiDAR metric for old-growth classification. Compared to other LiDAR metrics, the MDA value of the Rumple index was substantially higher (Figure 3). The other eight LiDAR metrics below the canopy openness/gap fraction (3rd ranked) were considered unimportant, as their values were low (<2), and the MDA differences with the top three were high. To determine which metrics should be used in the final classification, we assessed different combinations of the metrics within the classification process. The classification commenced using only one metric, with other metrics added. We found that adding metrics beyond the three top metrics did not statistically significantly improve the classification accuracy (p-value > 0.05). Consequently, the top three LiDAR metrics were used as predictors in the final classification.

3.2. Old-Growth Forest Classification

The result of the classification accuracy of 36 test plots is presented in a confusion matrix (Table 3). The classification was executed using the random forest algorithm, and the three most important LiDAR metrics were used as the input predictors (Figure 3). The overall accuracy of the classification was 78%, with a TSS of 0.58. The random forest algorithm indicates a reliable prediction of old- and second-growth classes using LiDAR structural metrics, as shown by the higher user’s accuracy (UA) compared to the producer’s accuracy (PA) for the old-growth class. The algorithm accurately predicted the old-growth forests in the ground with a 22% higher UA difference than the second-growth class. However, there was an overestimation of the second-growth class in PA, which caused a lower accuracy of the old-growth class. Generally, the classification method is strong at minimizing false positives (i.e., second-growth classified as old-growth), as shown by the higher specificity (86%) than sensitivity (73%). Furthermore, we found that the misclassified plots from the classification were plots dominated by the European Beech (broadleaf species).

3.3. Differences in the Top Three Important Metrics Between Old- and Second-Growth Forests

The performance of the top three ranked metrics in discriminating old- and second-growth stages is described in Figure 4. The structural metrics, i.e., the Rumple index, VCI, and gap fraction, were able to differentiate the old-growth and second-growth stages and were significantly different (Wilcoxon test with a p-value < 0.05). Each metric had a similar pattern: the median value of the old-growth stage was significantly higher than that of the second-growth stage.
The contribution of the three most important LiDAR metrics is demonstrated in the SHAP summary plot (Figure 5), with the Rumple Index having the highest contribution in old- and second-growth classifications, followed by the VCI and gap fraction, respectively. This contribution ranking follows the same pattern obtained with the variable importance statistic using MDA analysis. The SHAP summary plot also demonstrates that the Rumple index is an excellent predictor of the emerging old-growth forest compared to the other metrics. This is shown by the distribution of the high values of the Rumple index on the positive axis of the old-growth class in the SHAP summary plot.

4. Discussion

Earlier studies of old-growth forests using LiDAR data have mainly targeted one specific forest structure (e.g., stand height, basal area, stand density). This study, for the first time, offers a new and different approach to old-growth forest identification from LiDAR data and demonstrates that larger and older forest stands can be identified with an overall accuracy of 78% and a true skill statistic (TSS) of 0.58 (Table 3), with only three independent airborne LiDAR structural variables, namely the canopy surface roughness/heterogeneity (Rumple index), canopy layering diversity (vertical complexity index), and canopy openness (gap fraction). A Wilcoxon test confirmed there was a significant difference between the old- and second-growth forests for each forest structural metric (p-value < 0.05) (Figure 4). The overall accuracy achieved in our study is 9% higher than the accuracy from de Assis Barros and Elkin’s study [23], which incorporated only standard airborne LiDAR metrics (i.e., height and point density).
Random forest classification and internal validation demonstrated a reliable performance in classifying old- and second-growth forest classes. However, the classification tended to be conservative by minimizing false positives, i.e., second-growth classes were misclassified as old-growth classes. This conservativeness is represented by the higher specificity than sensitivity (Table 3). The conservative classification leads to potential underestimation in classifying the old-growth class, demonstrated by the more misclassified old-growth class than the misclassified second-growth class. Most misclassified plots were dominated by broadleaf species, i.e., European Beech. The misclassification occurred because of the limitation of the LiDAR sensor in penetrating the dense canopy in the areas dominated by beech. Moreover, the landscape of the Bavarian Forest National Park is dominated by mature forests, where beech areas generally have a uniform and dense canopy, constituting high occlusion from the foliage. This high occlusion makes it difficult for LiDAR to capture the structural diversity (mainly vertical diversity) and understory configuration, which is useful for old-growth identification.
From the 11 selected LiDAR metrics (Table 2), we found 4 standard metrics, i.e., ZQ5, ZPCUM9, P4TH, and PGROUND, related to the understory profile describing the understory configuration. For example, ZQ5 describes the fifth percentile of height distribution or the lowest layer of point clouds’ height distribution. Understory configuration has been suggested as a one of characteristics to define old-growth forests [64]. This characteristic explains the arrangement of the understory species profile on the forest floor, where its development is supported by the sunlight that penetrates the top to below the canopy due to emerging canopy gaps [64]. Our results suggest that relying on standard metrics that generate information from one canopy level is insufficient, especially when considering the multiple forest structure information of the old-growth stage. In contrast to our study, de Assis Barros and Elkin [23] found that LiDAR standard metrics appeared to be the most important. We postulate that this probably occurred because they did not perform collinearity analysis, such as VIF, to remove the LiDAR metrics with high collinearity. Our study demonstrates that numerous LiDAR standard metrics can be removed and substituted with a few structural metrics.
The highest-ranked structural metric identified in our analysis, i.e., the Rumple index, captured the 3D complexity of the canopy surface roughness (horizontal heterogeneity). Old-growth forests have a higher variation in tree height and diameter (DBH) due to the emergence of canopy gaps, self-thinning, and regeneration [9,64]. These characteristics form a complex ecosystem structure dominated by large and old trees, allowing for a diverse tree and crown architecture and a higher community composition of tree and understory species at different developmental stages of a forest [65]. Furthermore, this complex ecosystem structure influences the canopy’s ruggedness and roughness, which is effectively identified by the Rumple index [59]. We also consistently found a high Rumple index value in the old-growth forest, as defined with a threshold of 150 years, confirming the results from Kane et al. [59] and Solano et al. [65]. A key finding is that the Rumple index is the single most important LiDAR variable when identifying old-growth forests, as demonstrated by SHAP and MDA analyses, and, therefore, an important dependent prediction variable when modeling old-growth forests in a classification process.
The vertical complexity index (VCI)—the second most important LiDAR metric—explains the continuous variability in the vertical structure or multilayer complexity configuration from the top to the ground [29,63]. A higher VCI indicates an older forest stage, as shown by the median value of the Wilcoxon test (Figure 4b) and SHAP analysis. Old-growth forests have a complex multilayer canopy due to the diversity of different canopy heights of regrowth trees, established old trees, and senescing trees, as well as a varied understory configuration [64]. The VCI is also related to the level of complexity in canopy heterogeneity (as represented by the Rumple index), where the VCI increases with the level of canopy heterogeneity [59,65].
The third most important LiDAR structural metric in our old-growth classification is the gap fraction (Figure 4c), representing the canopy openness. The gap fraction is a characteristic of old-growth forests where the canopy density decreases along with the stand age development [17,59]. This decrease could be influenced by a series of events of windthrow, fire, pathogens, and dieback trees [1]. The gap fraction explains how disturbances, even on a small scale, play an essential role in stand dynamics, particularly in old-growth forests [65].
Our study demonstrates that LiDAR metrics, mainly LiDAR structural metrics, can distinguish and classify old-growth forests using a stand age threshold of 150 years in European temperate forests. LiDAR also has the advantage of substituting traditional in situ measurements for old-growth forest identification, mainly by using an airborne platform [22,26,31]. The capability of LiDAR metrics to derive 3D forest structure information helps depict the complexity and heterogeneity of different forest stand developments, particularly by using LiDAR structural metrics as proxies [28,65]. As the old-growth stage is the most complex structural development of forests, using LiDAR structural metrics is a logical technique for identifying late-stage development.
Our study has optimized the structural metrics using airborne LiDAR with a high density of point clouds (30–70 points/m2). Future studies assessing the LiDAR structural metric efficacy in the upscaling process and using different platforms, such as spaceborne systems with sampling acquisition concepts, e.g., GEDI, will need to investigate the optimal density of LiDAR point clouds for mapping old-growth forests. Utilizing close-range sensing technology, such as a terrestrial laser scanner (TLS) or low-altitude flight uncrewed airborne LiDAR (UAV-LiDAR) with a higher point cloud density, may also advance old-growth forest identification, especially by penetrating the upper canopy to capture vertical and understory profiles. This would also enable identification at a higher resolution. Using higher-density point clouds may improve identification within dense-canopy forest areas, such as broadleaf, which were demonstrated in our study to have the most misclassified old-growth forests.
We recognize that using a single average thickness increment across the altitudinal range and ecological conditions may be less representative as the growth rates depend on many factors and can vary with those factors [66]. In future work, incorporating site-specific models, empirical data from core samples, or methods like chrono-function indicators from Di Filippo et al. [45] could generate higher accuracy of tree age estimation in old-growth stands. However, due to the cost and limited access to such data during our study, we adopted the average increment approach as a pragmatic compromise while recognizing its limitations in accurately reflecting the spatial variability in growth rates. We also acknowledge that stand age in areas affected by disturbances, such as bark beetle outbreaks, constitutes a composite of various age classes and exhibits structural diversity. In these instances, our methodology primarily reflects the age of the dominant cohort that has regenerated following the disturbance event. This approach may not comprehensively encompass the full spectrum of age-related variability within such stands.
It is important to note that our approach requires temperate forest landscapes dominated by Norway Spruce and European Beech that grow under similar site and climatic conditions as those found in the Bavarian Forest National Park. In other words, similarity in growing conditions, species composition, disturbance rates, and types are mandatorily considered to extrapolate our approach. The definition of old-growth forests can be different among biomes, as the drivers of disturbance and ecosystem structure may vary [66].
Another requirement to use our approach for an upscaled process at larger geographical extents is to preserve the horizontal heterogeneity information of old-growth forests [67,68]. As our study was carried out at a plot level, the challenge was to minimize the loss of underlying heterogeneity information as an impact of aggregation in the upscaling process. The loss of underlying heterogeneity information, such as the diversity of tree height and patches of canopy gap, can cause a reduction in the accuracy performance in old-growth forest identification [67]. Therefore, it is recommended to use neighborhood approaches, such as object-based and moving windows, or integration with spatial-based information, such as textural information, for identification and classification in future upscaling studies [67].
The results of this study can promote the development of a LiDAR-driven approach for the precise identification and ongoing monitoring of old-growth forests by forest and park managers. Our approach of using a few LiDAR metrics facilitates the assessment of potential old-growth forest areas, which will further help forest conservation planning and management become more efficient.

5. Conclusions

Our study confirms that LiDAR metrics could accurately discriminate old-growth forests in a temperate forest landscape in Central Europe. However, using standard LiDAR metrics that comprise only one source/dimension of LiDAR point clouds was insufficient to distinguish old-growth from second-growth forests. We showed that LiDAR structural metrics (representing horizontal heterogeneity, vertical diversity, and canopy openness of forest structure) are more important than standard metrics in classifying old-growth forests, particularly in mixed-type forest landscapes. Using LiDAR structural metrics strengthens the concept that old-growth forests should not be defined solely by a single ecosystem structure but rather by multiple structures that more accurately represent and discriminate old-growth forests. Incorporating functional traits, such as productivity and disturbance derived from optical remote sensing indices, could be explored for future studies to investigate further improvement in classification accuracy. Functional traits could provide insights into how forest structural complexity influences the dynamics of ecosystem function in old-growth forest ecosystems. Another potential approach is to integrate LiDAR with satellite multi/hyperspectral data. These data can complement each other, as satellite multi/hyperspectral data provide extensive area coverage and species composition, and LiDAR data provide detailed information on forest horizontal and vertical structure. Such an integration will lead to more comprehensive old-growth forest identification.

Author Contributions

D.P.A.: Conceptualization, methodology, investigation, data collection, formal analysis, visualization, validation, writing—original draft. A.S.: Funding acquisition, conceptualization, methodology, validation, supervision, resources, project administration, writing—review and editing. M.S.: Conceptualization, methodology, validation, supervision, resources, writing—review and editing. T.W.: Conceptualization, methodology, validation, supervision, resources, writing—review and editing. H.A.: Methodology, validation, writing—review and editing. M.H.: Validation, resources, writing—review and editing. All authors have read and agreed to the published version of the manuscript.

Funding

This research is funded by European Research Council—“BIOSPACE-Monitoring Biodiversity from Space” project; grant 397 agreement ID 834709, H2020-EU.1.1.

Data Availability Statement

Access to the data supporting this study can be obtained by contacting the corresponding author (D.P.A.), as they are not publicly available. This is due to the confidential information contained within the data that could compromise the research participants’ privacy.

Acknowledgments

The authors give gratitude to the “Data Pool Initiative” for allowing the Bavarian Forest National Park data to be used in this research. The authors would also like to thank Mélody Rousseau, Alejandra Torres-Rodriguez, Yiwei Duan, Andjin Siegenthaler, Elnaz Neinavaz, Roshanak Darvishzadeh, Marcelle Lock, Yan Cheng, Xi Zhu, as well as Simon Koenig, Lisa Herold, Jakob Rieser from the Bavarian Forest National Park for their support during the fieldwork campaign and data collection.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Locations of sample plots in the Bavarian Forest National Park. The image is a true-color composite (band 432) of Sentinel-2A imagery acquired on 1 August 2020.
Figure 1. Locations of sample plots in the Bavarian Forest National Park. The image is a true-color composite (band 432) of Sentinel-2A imagery acquired on 1 August 2020.
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Figure 2. The frequency of the average stand age of the old-growth and second-growth plots.
Figure 2. The frequency of the average stand age of the old-growth and second-growth plots.
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Figure 3. The ranking and relative importance of the selected LiDAR metrics in old-growth forest classification generated through mean decrease accuracy (MDA) analysis. The top-ranked metrics are the metrics with the highest decreases in the accuracy coefficient. The asterisk (*) indicates the top three metrics used as the input predictors in the classification. Metrics with the □ symbol are standard metrics, and metrics with the ▲ symbol are structural metrics.
Figure 3. The ranking and relative importance of the selected LiDAR metrics in old-growth forest classification generated through mean decrease accuracy (MDA) analysis. The top-ranked metrics are the metrics with the highest decreases in the accuracy coefficient. The asterisk (*) indicates the top three metrics used as the input predictors in the classification. Metrics with the □ symbol are standard metrics, and metrics with the ▲ symbol are structural metrics.
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Figure 4. Box plots of the Rumple index (a), vertical complexity index (VCI) (b), and gap fraction (c) between the old- and second-growth stages. All of the values in each selected metric were derived from the canopy height model (CHM) in the sample plot, as all the selected metrics are structural diversity metrics. Each metric can significantly distinguish old-growth from second-growth forests, determined by the Wilcoxon test p-value of < 0.05.
Figure 4. Box plots of the Rumple index (a), vertical complexity index (VCI) (b), and gap fraction (c) between the old- and second-growth stages. All of the values in each selected metric were derived from the canopy height model (CHM) in the sample plot, as all the selected metrics are structural diversity metrics. Each metric can significantly distinguish old-growth from second-growth forests, determined by the Wilcoxon test p-value of < 0.05.
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Figure 5. The SHAP summary plot of three important LiDAR metrics for discriminating old- and second-growth forests. The positive axis indicates a greater probability of a feature value to identify a class. In contrast, the negative axis indicates that the feature value has a weak contribution to identifying a class. For example, in the old-growth class, the Rumple index’s high values were distributed on the positive axis, demonstrating a high probability of old-growth emergence prediction in the classification. On the contrary, the Rumple index’s low values were distributed on the positive axis in the second-growth class, indicating that low values of the Rumple index are good predictors for the second-growth class.
Figure 5. The SHAP summary plot of three important LiDAR metrics for discriminating old- and second-growth forests. The positive axis indicates a greater probability of a feature value to identify a class. In contrast, the negative axis indicates that the feature value has a weak contribution to identifying a class. For example, in the old-growth class, the Rumple index’s high values were distributed on the positive axis, demonstrating a high probability of old-growth emergence prediction in the classification. On the contrary, the Rumple index’s low values were distributed on the positive axis in the second-growth class, indicating that low values of the Rumple index are good predictors for the second-growth class.
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Table 2. The VIF results of 11 selected LiDAR metrics. The stringent criteria of VIF < 5 ensure the metrics have low collinearity. Metrics with ** indicate that the metrics are related to the top canopy configurations. Metrics with * indicate that the metrics are related to the understory configurations. The vertical complexity index (***) defines the continuous multilayer configuration from the ground to the top canopy. Metric nos. 1–4 are structural metrics, and metric nos. 5–11 are standard metrics.
Table 2. The VIF results of 11 selected LiDAR metrics. The stringent criteria of VIF < 5 ensure the metrics have low collinearity. Metrics with ** indicate that the metrics are related to the top canopy configurations. Metrics with * indicate that the metrics are related to the understory configurations. The vertical complexity index (***) defines the continuous multilayer configuration from the ground to the top canopy. Metric nos. 1–4 are structural metrics, and metric nos. 5–11 are standard metrics.
LiDAR MetricsVIF
1. Rumple Index **4.67
2. Vegetation Area Index **4.14
3. Gap Fraction **3.24
4. Vertical Complexity Index ***2.78
5. ZQ10 *2.16
6. PGROUND *1.52
7. ZMAX **1.45
8. ZQ5 *1.36
9. P4TH *1.27
10. ZPCUM9 *1.24
11. ZPCUM1 **1.22
Table 3. The old-growth forest classification results in a confusion matrix table consisting of overall accuracy (OA), producer’s accuracy (PA), user’s accuracy (UA) and true skill statistics (TSS).
Table 3. The old-growth forest classification results in a confusion matrix table consisting of overall accuracy (OA), producer’s accuracy (PA), user’s accuracy (UA) and true skill statistics (TSS).
ClassOld GrowthSecond GrowthTotalUA (%)
1621889%
6121867%
Total162036
PA (%)73%86% OA: 78%
0.73
(Sensitivity)		0.86
(Specificity)		 TSS: 0.58
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Adiningrat, D.P.; Skidmore, A.; Schlund, M.; Wang, T.; Abdullah, H.; Heurich, M. Investigating LiDAR Metrics for Old-Growth Beech- and Spruce-Dominated Forest Identification in Central Europe. Remote Sens. 2025, 17, 251. https://doi.org/10.3390/rs17020251

AMA Style

Adiningrat DP, Skidmore A, Schlund M, Wang T, Abdullah H, Heurich M. Investigating LiDAR Metrics for Old-Growth Beech- and Spruce-Dominated Forest Identification in Central Europe. Remote Sensing. 2025; 17(2):251. https://doi.org/10.3390/rs17020251

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Adiningrat, Devara P., Andrew Skidmore, Michael Schlund, Tiejun Wang, Haidi Abdullah, and Marco Heurich. 2025. "Investigating LiDAR Metrics for Old-Growth Beech- and Spruce-Dominated Forest Identification in Central Europe" Remote Sensing 17, no. 2: 251. https://doi.org/10.3390/rs17020251

APA Style

Adiningrat, D. P., Skidmore, A., Schlund, M., Wang, T., Abdullah, H., & Heurich, M. (2025). Investigating LiDAR Metrics for Old-Growth Beech- and Spruce-Dominated Forest Identification in Central Europe. Remote Sensing, 17(2), 251. https://doi.org/10.3390/rs17020251

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