Investigation of the Relationship between Topographic and Forest Stand Characteristics Using Aerial Laser Scanning and Field Survey Data

Abstract

The article thoroughly investigates the relationships between terrain features and tree measurements derived from aerial laser scanning (ALS) data and field surveys in a 1067-hectare forested area. A digital elevation model (DEM) was generated from ALS data, which was then used to derive additional layers such as slope, aspect, topographic position index (TPI), and landforms. The authors developed a mathematical procedure to determine the radii for the topographic position index. The canopy height model was created, and individual trees were segmented using a novel voxel aggregation method, allowing for the calculation of tree height and crown size. Accuracy assessments were conducted between ALS-derived data and field-collected data. Terrain variability within each forest unit was evaluated using characteristics such as standard deviation, entropy, and frequency. The relationships between tree height and the derived topographic features within forest subcompartments, as well as the correlation between the height yield map for the entire area and the TPI layer, were analysed. The authors found strong correlation between the topographic position index and tree heights in both cases. The presented remote-sensing-based methodology and the results can be effectively used in digital forest site mapping, complemented by field sampling and laboratory soil analyses, and, as final goal, in carbon stock assessment.

1. Introduction

Due to climate change, Hungarian/European forests are undergoing rapid and significant changes, with notable fluctuations in the water balance. Both underground and aboveground carbon storage are affected, as well as the role of forests in mitigating the effects of climate change. The currently used methods for site and carbon stock determination are not yet suitable for tracking these rapid changes. Furthermore, only 12% of the Hungarian forest database contains up-to-date site data based on direct site-specific investigations. Therefore, there is an urgent need for more effective and accurate assessment and monitoring of environmental and ecological conditions. The main motivation for this interest is the potential to lower costs and achieve more precise and efficient assessments of forest characteristics.

To develop the aforementioned modern methodology, the SoilSense project was launched in connection with the Hungarian Climate Change Action Plan. It started in the fall of 2023 with the support of the Hungarian Ministry of Agriculture. The methodology to be developed uses surface models generated from point clouds obtained through aerial laser scanning (ALS), individual tree data, and forest stand and soil characteristics collected in the field. This approach aims to refine forest site mapping and determine carbon stock [1]. This is important because precise site mapping and forest inventory play an important role in European forestry.

The ultimate goal is to create an accurate site map from the above data, determine the aboveground and belowground carbon stocks, and develop a modern, cost-effective, objective, repeatable, and detailed site mapping methodology that combines remote sensing with field sampling, applicable to forests both in Hungary and all over Europe. The developed method can support stakeholders and policy makers in forest management decisions to mitigate the effects of climate change.

The project is expected to last 3 years. Among the project’s milestones, the first focuses on establishing the model area, acquiring remote sensing databases, and developing the soil survey methodology. The second milestone involves field surveys and the processing of remote sensing data. The third milestone pertains to the laboratory processing of soil samples and the production of reference data, while the fourth milestone involves model development and validation.

In this article, we aim to report on the establishment of the research area, the processing of aerial laser scanning data, and the comparison of the obtained data with field data. From the laser scanning, we generated an elevation model and a canopy height model, segmented the point cloud into individual trees, and compared it with the circular plot field survey data.

A digital elevation model (DEM) is typically in a raster (regular grid) format, less frequently a vector (irregular triangular network) format, representing the elevation of the Earth’s surface. It provides fundamental information about the terrain surface [2]. From the digital elevation model, one can derive slope, aspect, hydrological models, topographic index, and many other useful thematic layers [3]. The slope indicates the rate of elevation change based on the adjacent 4 (or 8) pixels, while the aspect shows the direction of the steepest descent, measured in degrees clockwise from north [4].

By analysing these derived models, information can be obtained about the study area, such as flow direction [5] and outflow points from the area [6], as well as the distribution of landforms [7]. One of the most important characteristics of a DEM is its spatial resolution, which indicates the area covered by one pixel on the ground. The spatial resolution significantly affects the results of various terrain model analyses, whether it is slope [8], aspect, or even a hydrological model [9,10,11].

Orography, also known as mountain geography, is a branch of physical geography that deals with geological formations, primary and secondary landforms, the surface characteristics of mountains and hills, and their descriptions [12]. Analysing the topographic position index (TPI) is one possible solution for deriving various orographic features.

The topographic position index (TPI) compares the elevation of individual pixels with the average elevation of surrounding pixels within a specified shape (circle, square). Positive TPI values describe points on the terrain that are higher than their surroundings, while negative values indicate the opposite [13]. The classification also considers the slope associated with the given pixel. If the TPI value is significantly less than zero, it typically represents a valley floor (or an area close to one). If the TPI value is close to zero, it could indicate either a flat area or a moderate, open slope; the slope is used to differentiate between these two possibilities [14].

A key aspect of TPI analysis is selecting the appropriate search radius. For example, with a smaller radius, a valley floor’s slight prominence will be clearly defined, but with a larger radius, it may not appear. Conversely, a narrower watershed located on a ridge might not be identifiable with a larger radius, while a smaller radius would only detect the hill or watershed itself without providing information about its broader context. To address this, TPI analysis should be performed using two different radii. By combining the results from these radii, a total of 10 distinct landform types can be distinguished [14]. In this case, the goal is to determine the two radius values that are suitable for categorising landforms at the scale required for site mapping.

An important aspect of applying aerial laser scanning (LiDAR) in forestry is the selection and interpolation of elevation points beneath the forest canopy. Strip-based elevation point selection and averaging were performed by [15]. Recently, several adaptive triangulated irregular network (TIN) fitting methods have been developed [16,17], which filter LiDAR elevation points and produce a vector surface model. Elevation points can also be filtered from LiDAR point clouds using various methods, such as slope filters [18] or morphological filters (combining minimum and maximum filters) [19,20]. Multi-level curvature analysis is another effective method for point selection [21]. Meng et al. [22] give an overview of LiDAR terrain modelling methods. It is also important to mention the latest clothing simulation algorithms [23,24].

Another critical aspect of processing laser scanned data in forested areas is the generation and segmentation of the canopy height model (CHM) to identify individual trees. Early methods sought local maxima in the canopy height model [25,26]. Popescu et al. [27] introduced a tree-height-dependent variable window size to filter nearby local maxima. Morsdorf et al. [28] conducted pine identification. Chen et al. [29] utilised a canopy maxima model based on smoothing the canopy surface maximum and inverse watershed method. Koch et al. [30] employed an inverse watershed. Hyyppä et al. [31] applied region growing. Later, procedures operating directly on 3D point clouds emerged. Lee et al. [32] developed adaptive k-means clustering for tree segmentation. Ferraz et al. [33] used 3D adaptive mean-shift segmentation in multi-layered Mediterranean forests. Li et al. [34] published a top-down region growing approach. Kaartinen et al. [35] and Jakubowski et al. [36] compared available individual tree detection methods. Strîmbu V. and Strîmbu B. [37] developed graph-based segmentation. Duncanson et al. [38] used multi-layered crown delineation. Yang et al. [39] employed a hierarchical minimum cut approach. Lindberg and Holmgren [40] also reviewed available methods. Hu et al. [41] advanced recognition techniques. Ayrey et al. [42] introduced layer stacking recognition. Wan Mohd Jaafar et al. [43] further improved watershed and segmentation procedures. Wang et al. [44] used a method based on a Gaussian distributed regional growth algorithm and Voronoi range constraints to extract street tree geometries from vehicle-mounted LiDAR point clouds. Czimber [45] developed a voxel aggregation method for detecting the canopies of broadleaf trees.

There are also studies which were looking for a connection between topography and forest stand parameters, especially tree height. McNab [46] found out that the geometric shape of the land surface (terrain shape index) is highly correlated with total height of trees in the southern Appalachians. Tateno and Takeda [47] showed that the maximum tree height is greater on the lower part, and the crown closure increased up the slope in a cool-temperate deciduous broadleaved forest in Japan. Rahman et al. [48] proved that canopy height is greater by 5–10 m in the concave valleys than on the convex slopes and ridges in central Japan. Bałazy et al. [49] also showed that tree growth dynamics are largely dependent on local topographic conditions but found out that the role of TPI is relatively small.

2. Materials and Methods

2.1. Introduction of the Project Area

The project’s study area is the Dudlesz Forest, located on approximately 1067 hectares to the north of Sopron, Hungary (Figure 1). Geographically, it belongs to the Fertőmelléki Hills, a young Miocene sedimentary rock landscape characterised by a gently undulating, low-relief, denudational–erosional hill range. Its climate is moderately cool and moderately dry. The potential vegetation types include hornbeam–oak forests and sessile oak forests, but due to the geological conditions, there are also significant edaphic forest communities present. The region is almost entirely covered by Rendzic Leptosols and Cutanic Luvisols or Cambisols [50].

2.2. Laser Scanning

For the creation of surface models, the point cloud was provided by EnviroSense Ltd. (registered in Debrecen, Hungary), surveyed using LiDAR technology with a Riegl V780 II sensor (manufactured by RIEGL Laser Measurement System GmbH, Horn, Austria) from a small aircraft under leafless conditions, in 2023. The provided point cloud has an average point density of 20 points/m², from which the digital surface model (DSM), the digital elevation model (DEM), and the normalised surface model (nDSM) were derived by subtracting the latter from the former, or, in this case, given that it is a forested area, the canopy height model (CHM).

To create the elevation model, we used the TreeDetect (v.1.24.5.10) software (by TopoLynx Ltd., registered in Kőszeg, Hungary), which is specifically developed for processing aerial laser scanning data of forested areas [45]. The software’s algorithms generate raster surface models and vector single-tree data (stem points and crown polygons). In the first phase of the complex processing, the software filters out scattered low points, selects elevation points using a hierarchical morphological method, and interpolates them to create the digital elevation model (DEM). In the second phase, the software filters out scattered high points, selects canopy height model (CHM) points, and performs CHM interpolation and export. In the third phase, TreeDetect employs a specialised voxel aggregation algorithm to segment individual tree canopies. The key parameters of the processing are the voxel size, the voxel aggregation ranges for stem and crown detection, and single-tree segmentation parameters. This method is comparable to the layer stacking method and is particularly advantageous for broadleaved trees, where the canopy surface shows minimal height variation within the stand. By examining the canopy in depth using voxels, the boundaries between individual tree canopies are clearly delineated.

2.3. Thematic Layers Derived from the DEM

The digital elevation model (DEM) generated from the point cloud and the thematic layers derived from it have a spatial resolution of 1 m/pixel. As this resolution falls into the category of high-resolution, detailed models, it can capture even minor features such as small depressions, pits, cones, and forest roads, which are not relevant in site mapping due to their small size. Therefore, it was necessary to apply a Gaussian filter (r = 10 m, s = 100) to remove these micro-relief features, which was performed using QGIS software (v.3.26.2) (Figure 2). We ran slope and aspect analyses on the smoothed elevation model, also using QGIS. The calculation of the topographic position index (TPI) was performed using an algorithm developed by us.

Naturally, each pixel is associated with a slope and an aspect value. However, for easier interpretation and visualisation, we categorised these continuous values: for slope, we used a 5-degree resolution, while for aspect, we distinguished 8 categories based on the 4 cardinal and 4 intercardinal directions. In both cases, areas with a slope of less than 2 degrees were considered flat.

To determine the appropriate radii for the TPI analysis, we initially ran the algorithm with several radius values. These values were chosen based on the DEM resolution (1 m/pixel): starting with five times the resolution and its multiples (i.e., between 5 and 25 m, in 5 m increments), and then three, four, and five times those values (for example, for a 15 m radius, this included 45, 60, and 75 m), resulting in a total of 14 TPI models.

We calculated the standard deviation using focal statistical analysis with a 25 m radius for these models. The global maxima of the resulting standard deviation rasters were plotted on a graph, and a second-order polynomial trendline was fitted. The TPI value closest to the maximum point of the curve provided the larger radius value, while the smaller radius value was selected based on the point where the tangent line intersects the origin. Using these two selected radius values, we classified the pixels into 10 topographic categories (

Table 1. Landform categories [14].

ID	Landform Names	Small Radius TPI	Large Radius TPI	Slope
1	Canyons, Deeply Incised Streams	TPI ≤ −1	TPI ≤ −1
2	Midslope Drainages, Shallow Valleys	TPI ≤ −1	−1 < TPI < 1
3	Upland Drainages, Headwaters	TPI ≤ −1	TPI ≥ 1
4	U-shaped Valleys	−1 < TPI < 1	TPI ≤ −1
5	Plains	−1 < TPI < 1	−1 < TPI < 1	≤2°
6	Open Slopes	−1 < TPI < 1	−1 < TPI < 1	>2°
7	Upper Slopes, Mesas	−1 < TPI < 1	TPI ≥ 1
8	Local Ridges/Hills in Valleys	TPI ≥ 1	TPI ≤ −1
9	Midslope Ridges, Small Hills in Plains	TPI ≥ 1	−1 < TPI < 1
10	Mountain Tops, High Ridges	TPI ≥ 1	TPI ≥ 1

).

After creating the three rasters and categorising them, we examined the standard deviation of elevation and slope angle at the forest subcompartment level. Additionally, we assessed the extent of areas classified into different categories and derived the following metrics:

• Frequency: The area proportion of the largest category;
• Stability: The difference in area proportions between the largest and the second largest categories;
• Shannon Entropy, calculated as [51]:

$$H\left(S\right)=-1\ast \sum _{i=1}^n{P}_i\ast {\log }_2{P}_i$$

(1)

where P_i is the relative frequency (the area of the given category/the total area of the forest subcompartment). We then examined any potential correlations both within a single thematic layer and between different thematic layers.

We established 272 field points on the site, whose centre points were surveyed using GNSS RTK technology (with FORGEO Puli GNSS receiver and Corrigo RTK correction service, Baja, Hungary) and then marked. We assessed the trees within a 12.61 m radius around each field point (500 m² sample areas). For each tree, we recorded the species, diameter at breast height (DBH) with a caliper, height using a trigonometric height meter (Nikon Forestry Pro, manufactured by Nikon, Tokyo, Japan), and distance from the middle of the sample area with an ultrasonic distance meter (Vertex III, manufactured by Haglöf, Långsele, Sweden). We also documented standing and lying deadwood within the sample points.

We compared the field measurements with the LiDAR-derived layers (DEM and CHM) and examined the relationships between tree heights, the topographic model, and derived themes, particularly the topographic position index (TPI). Firstly, within a forest stand (15B) that traverses a deeper valley, we created a height increment map by using tree heights derived from the CHM and the age ratio of the tree stands recorded in the forest stands. We analysed the resulting map data by TPI groups.

The processing steps described above are illustrated in Figure 3 flowchart.

3. Results and Discussion

DEM

We performed the verification of the digital elevation model at the centres of the field points. We compared the elevation of the 272 point centres with the interpolated elevation model derived from the LiDAR data. The average difference between the two elevation datasets was 1 cm, with a standard deviation of 6 cm, which is considered very good for a forested area, especially given the presence of coniferous stands, including Scots pine and black pine species.

• Derived layers

After the creation and categorisation of the slope and aspect rasters, the determination of the two radius values required for the TPI analysis is illustrated in Figure 4.

It can be seen that the second-degree polynomial curve fitted to the maximum deviation peaks at a radius of 100 m (more precisely, 103.03 m), while the tangent line passing through the origin touches the curve near a radius of 25 m (more precisely, 26.75 m). Rounding was necessary both due to the raster’s rounded metre resolution and to enhance clarity. Additionally, the multiplier between the applied radii was considered as an integer value. Thus, the smaller TPI analysis radius was set to 25 m, and the larger radius to 100 m, with a factor of four between them.

The original digital elevation model and the three derived thematic layers are illustrated in Figure 5.

Figure 5 shows that a large portion of the study area falls into the “Open Slope” category (59.90%), where the predominant aspects are to the northeast and east, with slopes ranging from 2°–10°. Steeper slopes are found along the deep valleys that cut through the area (where the aspect varies significantly) and along the western edge, where the southwestern aspect is most prominent. The valley bottoms are characterised by category 1 (Canyons, Deeply Incised Streams: 0.96%), while the slopes are categorised as 4 (U-shaped Valleys: 13.23%). In addition, significant areas fall into category 7 (Upper Slopes, Mesas: 15.16%) and category 5 (Plains: 9.38%). Category 10 (Mountain Tops, High Ridges: 1.20%) is also notable, representing ridges mainly found along the western edge of the area. The remaining four categories are present only in negligible proportions and are dispersed throughout the area.

Figure 6 illustrates the variation in elevation above sea level, slope angle, and the 25 m radius TPI for each forest subcompartment. This is a method for characterising the variability within each spatial unit using the yet-to-be-categorised statistical rasters.

Among these, we identified a relationship between slope and TPI25, illustrated by the graph in Figure 7.

After categorising the three thematic layers, we examined the relationships between frequency, stability, and entropy, which are illustrated in Figure 8 with respect to topographic categories. A second-order polynomial relationship was established between frequency and entropy. Observing the graph, moving backward along the x-axis (frequency), a sudden jump is noted toward lower entropy values on the y-axis. This jump occurs because, beyond this point, no category is in absolute majority, leading to increased variability (Figure 8a). When weighting frequency by stability, the trendline becomes more linear. However, as it approaches the y-axis, deviations increase significantly, resulting in a lower R² value (Figure 8b).

We were also interested in exploring any potential correlations between the three entropy layers in terms of variability. The entropy of these themes by forest subcompartments is illustrated in Figure 9.

The graphs shown in Figure 10 reveal that neither slope (Figure 10a) nor aspect (Figure 10b) resulted in a convergent trend line when compared with landform types. The R² value is around 0.5 in both cases, and visually, it is evident that there is considerable dispersion in the data, indicating that there is no clear correlation between the variability of the three themes.

b.

Tree height comparison

After a detailed analysis of the topography and derived thematic layers, we compared the tree heights measured at the 272 field survey points with those obtained from LiDAR data. For each survey point, we compared the average tree height measured in the field with the average height of tree segments identified in the LiDAR data within the area of the survey point. Before comparison, we filtered out significant errors, such as cases where field height measurements were not taken in areas undergoing reforestation or in dense juvenile stands, or where only the height of residual trees was measured. After filtering, the difference in average height between individual trees was −0.13 m, with a standard deviation of 1.52 m.

We found a clear correlation between TPI values and tree heights obtained from LiDAR point cloud segmentation in areas where the 25 m radius TPI is negative, indicating the area is identified as a local catchment. These areas are the west–east-oriented valleys in the centre of the sample area, which are approximately 20–40 m wide and 3–8 m deep. The results are well illustrated within a forest subcompartment (Figure 11), where the trees are of the same age, but their heights differ. In the valleys, the average tree height is 22.74 m, while in the flat areas it is 18.81 m. In the figure, valleys marked in a dark color contain taller trees marked in blue. The height difference can be explained partly due to phototropism, competition for light among trees. However, it is more attributable to the excess water collected in the valleys and thicker rooting depth, which the trees growing there can utilise.

We also created a height yield map for the entire forested area, derived from the ratio of the CHM-based individual tree heights and the average age of the trees within each forest subcompartment. The results can be presented both on a map and in a chart. Based on the TPI25 raster, we formed groups (with a step size of 0.25) and calculated the average height increment within these groups. We found a strong correlation between the average values of TPI groups and height yield (r² = 0.88). This analysis clearly shows that lower TPI values are associated with greater height increments (Figure 12).

4. Conclusions

Aerial laser scanning proves to be an excellent tool for mapping the topographic conditions of forest areas, including high-precision mapping of site conditions. Using the methods presented, various thematic layers can be derived from the elevation model, which allows for detailed, digital, objective, and automatable descriptions of forest site conditions. The TPI-based analyses involved deriving the applicable radius using mathematical methods. We examined the variability of topographic and orographic features within forest plots and their relationships between entropy and frequency.

The hierarchical morphological filtering algorithm used to generate the elevation model from the LiDAR data preserves even micro-topographical details. The model captures features such as forest roads and depressions caused by uprooted trees. These micro-elements can be filtered out, after which slope, aspect, TPI, and TPI with different radii can be determined. Such categorisation of terrain helps in creating site maps, selecting soil sampling locations, and even in the economic classification of forest areas.

Field GNSS RTK measurements validated the accuracy of the LiDAR elevation model, and field tree height measurements confirmed the accuracy of the LiDAR canopy height model.

We found significant correlations between the tree heights derived from LiDAR and the topographic position index (TPI) values within forest plots (in contrast to the study referenced as [49], where the findings indicated that the role of TPI was relatively small), as well as between the height increment map and the TPI map. These correlations are evident both in maps and graphs. The variability in tree heights within forest plots can be studied from various perspectives. Differences in tree height reflect the variability in terrain and soil. Already, we observe areas on the tree height and forest subcompartment maps where tree heights deviate from the average within the forest subcompartment. These deviations are likely due to varying soil parameters (such as shallower potential rooting depth, soil disturbance, different soil types, and consequently different water-holding capacities).

We carried out an in-depth site assessment at each of the 272 sampling points, including opening soil profile pits and collecting samples from various heights. The laboratory analysis of these samples is still in progress. Once the laboratory results are available, we plan to examine the relationships between the terrain and derived thematic layers, the single trees, and soil characteristics together.

Finally, it is worth emphasising that the goal of our research is to develop a new methodology for forest site mapping and carbon stock estimation supported by aerial remote sensing. As we continue to experience the rapid shift of site parameters, especially the climate and hydrology, this cost-effective, repeatable, yet precise and objective site mapping method is valued more. All of this can assist professionals and decision makers with their management decisions.