# LiDAR-Based Morphometry of Dolines in Aggtelek Karst (Hungary) and Slovak Karst (Slovakia)

^{1}

^{2}

^{*}

## Abstract

**:**

^{−2}), moderate (10–30 km

^{−2}), and medium (30–35 km

^{−2}) doline densities. In terms of topography, the slope trend is decisive since the doline density is negligible in areas where the general slope is steeper than 12°. As for the lithology, 75% of the dolines can be linked to Wetterstein Limestone. The statistical distribution of the doline area can be well modeled by the lognormal distribution. To describe the DTM-based volume of dolines, a new parameter (k) is introduced to characterize their 3D shape: it is equal to the product of the area and the depth divided by the volume. This parameter indicates whether the idealized shape of the doline is closer to a cylinder, a bowl (calotte), a cone, or a funnel shape. The results show that most sinkholes in the study area have a transitional shape between a bowl (calotte) and a cone.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Base Data

^{2}; and vertical accuracy of DTM (in ETRS89): 0.09 m. The raster DTM with a horizontal resolution of 1 m from LiDAR is also directly available from the database; thus, we used it in the analyses. As for the Hungarian side, the LiDAR database was created by the Envirosense Hungary Kft. on behalf of the Aggtelek National Park in August 2013. The data were provided to us by the Aggtelek National Park Directorate. The density of points classified as ground is 2 points/m

^{2}. It is relatively low because data collection was carried out during the vegetation period. Therefore, a DTM with a resolution of 2.5 m/px was created from the point cloud [18]. This database does not include the easternmost, relatively small plateaus of the Hungarian part of Aggtelek Karst (i.e., Rudabánya (18) and Szalonna (19) units; hereafter, numbers after local plateau names (Figure 1) are the “ID” numbers used in the figures and in the tables).

#### 2.3. Methodology

- Smoothing of the DTM to remove spurious errors.
- Filling of pits smaller than true dolines (by setting the appropriate Z-limit). (In the case of a too-small Z-limit, there are many false positives, i.e., features outlined by the algorithm that are not true dolines. In the case of a too-large Z-limit, there are many false negatives, i.e., dolines that are not recognized by the algorithm. In [18], it was demonstrated that 1 m is the optimal value for Aggtelek Karst; thus, in the present analysis, the same value was used as the Z-limit.) The result is the “filled DTM”.
- Determination of flow directions based on the filled DTM.
- Identification of the remaining sinks (which are deeper than the above Z-limit): these are the “sink points”.
- Delineation of watersheds belonging to the sink points.
- Filling of depressions up to the level of the lowermost point of their rim. The result is the “zonal-filled DTM”.
- Calculation of the difference between the “zonal-filled DTM” and the “filled DTM”: this is the depth.
- Delineation of areas where the depth is larger than 0: these are the dolines (as raster data).
- Conversion of dolines into a polygon shape file for further analysis.
- Calculation of the morphometric characteristics of sinkholes.

^{2}or depth less than 1 m) and were close to other sinkholes (distance less than 30 m) were filled, and the delineation steps were run again. Since the results obtained after the second round were satisfactory, we finished the delineation procedure after this second round.

^{2}

_{px}is the area of one pixel, and h

_{px}is the depth of the form in a given pixel. After some simple transformations, we obtain

_{mean}) can be easily calculated in a GIS environment (e.g., by the Zonal Statistics as Table tool in ArcMap

^{®}10.8 software), and the volume is calculated by multiplying this value with the area of the doline.

^{−2}, “small” for 10–30 km

^{−2}, “medium” for 30–60 km

^{−2}, “large” for 60–100 km

^{−2}, “very high” for 100–200 km

^{−2}, and “extremely high” for above 200 km

^{−2}. According to the literature, there are many well-karstified areas with a doline density of less than 10 km

^{−2}, including some plateaus of Aggtelek and Slovak Karsts; therefore, we recommend slightly modifying Pahernik’s too-strict designations, and our proposal is to call the 1–10 km

^{−2}category “low” density, the 10–30 km

^{−2}category “moderate” density, and the 60–100 km

^{−2}category “high” density; for the other categories, we would leave the original terms of Pahernik.

## 3. Results

#### 3.1. Features Identified in LiDAR versus TOPO Data

#### 3.2. Doline Spatial Distribution Parameters

^{2}= 0.50) negative correlation between the doline density and the mean slope angle (Figure 9). This means that, trend-wise, on the plateaus that are more horizontal, dolines are found in higher densities.

^{−2}) characterizes Borčianska (8), Jasovská (10), Zádielska (9), Szalonna (19), and Aggtelek (17) karst plateaus. A moderate doline density (10.8–30 km

^{−2}) is typical of most plateaus, while the locally highest values (>28 km

^{−2}), though still only “medium” according to the general classification [32], are found on Plešivská (3), Silická (5), E-Alsó-hegy (14), Jósvafő (20), and Bučina (4) plateaus.

^{2}), which results in an outstanding “doline area ratio”. The difference between the interpretation of the doline density and the doline area ratio is also reflected in Figure 11. In the case of similar-sized dolines, the relationship between the doline density and the doline area ratio would be a simple line with R

^{2}close to 1. However, as Figure 11 demonstrates, the strength of the relationship is strong but not very strong. Points above the regression line mean plateaus where the doline density is higher than expected from the doline area ratio due to the high proportion of relatively small dolines. On the other hand, points below the line mark plateaus, where relatively large dolines significantly increase the doline area ratio, even if the doline density is not so high. The most extreme example is the Páska-bükk (16) plateau due to the aforementioned reason.

#### 3.3. Doline Area Empirical Distributions

^{2}, which corresponds to an equivalent diameter of 84 m. However, since the size distribution of the sinkholes is highly skewed, the median value better expresses the size of the “typical doline”. In the study area, this is 3638 m

^{2}, which corresponds to a diameter of 68 m. As described in the doline area ratio section, the Koniarska (2), Jelšavská (1), Szinpetri (15), Zádielska (9), Szalonna (19), and especially the Aggtelek (17), and Páska-bükk (16) plateaus can be characterized by larger dolines. In contrast, the type areas of smaller sinkholes (in addition to the Bôrčianska(8) and Rudabánya(18) units, which have hardly any sinkholes) are the Alsó-hegy (13, 14) and Bučina (4) plateaus. The doline areas according to the bedrock are presented in Figure 12 for the important (i.e., with a proportion of at least 0.9%) lithological categories. It shows that within the most common Wetterstein Limestone category (n = 3834), smaller sinkholes dominate. The dolines formed on Wetterstein Dolomites (n = 154) are similar in median value but somewhat larger in mean value. The size of the dolines formed on Reifling Limestone (n = 119) and Steinalm Limestone (n = 532) occupies an intermediate position, and finally, the largest areas are typical of the dolines formed on Gutenstein Formations (n = 286 altogether).

^{2}(equivalent diameter ca. 8 m) as a lower limit for the doline area, then the statistical tests support the lognormal distribution even in these cases. This means that only a few small features (n = 17, 20, and 12 for Plešivská (3), Silická (5), and E-Alsó-hegy (14), respectively) obscure the lognormal nature of the distributions for these plateaus.

^{2}. This value is much higher than the threshold used during the doline delimitation procedure; thus, it is not an artifact. Therefore, it is stated that the power-law distribution is not suitable to model doline area distributions in this karst terrain.

#### 3.4. Parameters Characterizing the Vertical Shape

^{2}between the mean denudation thickness and doline density is 0.66, while R

^{2}between the mean denudation thickness and mean doline area is only 0.03, and R

^{2}between the mean denudation thickness and mean doline volume is 0.23. As a result, Bučina (4), E-Alsó-hegy (14), Silická (5), and Plešivská (3) plateaus have high denudation thickness values. In contrast, the northeastern plateaus (Bôrčianska (8), Zádielska (9), Jasovská (10)) show quite low values. It is difficult to interpret the magnitude of the volume in itself, but the value of the mean denudation thickness expressed in meters is already more tangible. It is observed that this value varies between 0.4 and 0.8 m. These low values are interpreted in Section 4.

## 4. Discussion

## 5. Conclusions

^{−2}), moderate (10–30 km

^{−2}), and medium (30–35 km

^{−2}) doline densities. Bučina (4), E-Alsó-hegy (14), and Jósvafő (20) plateaus have the most outstanding values. Sinkholes cover 2–17% of the area of the plateaus. From this point of view, the record holder of the study area is the Silická plateau, which has relatively large and densely packed sinkholes. The location of dolines is strongly determined by the general slope angle, in addition to the geological characteristics. Sinkholes above a general slope of 12° are only rarely found, and 90% of the sinkholes are formed on terrains with a general slope of less than 8°. Among the geological conditions, the distribution of the Wetterstein Limestone is the most decisive for the study area, as 72.9% of the dolines are located on this bedrock. It is also observed that dolines formed on this bedrock are typically smaller in size than in the case of other lithologies.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Map of the study area. Karst plateaus are marked by ID numbers: Jelšavská (1); Koniarska (2); Plešivská (3); Bučina (4); Silická (5); Horný (6); Žl’ab (7); Bôrčianska (8); Zádielska (9); Jasovská (10); Kečovská-Haragistya (11); Nagyoldal (12); W-Alsó-hegy (13); E-Alsó-hegy (14); Szinpetri (15); Páska-bükk (16); Aggtelek (17); Rudabánya (18); Szalonna (19); Jósvafő (20).

**Figure 2.**Various doline delineation principles. The brown dashed lines indicate the elevation levels of the contour lines. For further explanation, see the text.

**Figure 4.**A typical result of the delineation algorithm after the first and second rounds for a model area. The doline outlines based on the topographic map are also presented (TOPO). It is obvious that in the case of the large central doline, the delineation is incorrect after the first round; this is why the second round is necessary.

**Figure 5.**Volume formulae of some idealized 3D shapes. Below the shapes, the names of the shapes when dolines are the subjects are given. The volume of the calotte is simplified here, but if the depth is relatively small with respect to the diameter, then the difference from the precise value is negligible.

**Figure 6.**A comparison of topographic map-based (TOPO) and LiDAR-based parameters. In the case of two plateaus (Rudabánya Mountains (18), Szalonna Karst (19)), no LiDAR data were available. Top: doline density; bottom left: box-whisker plot of doline area logarithms; bottom right: box-whisker plot of doline circularity. The vertical line in the box indicates the median, whereas red + indicates the mean values in the box-whisker plots.

**Figure 7.**Dolines of Silická plateau (5) delineated by the LiDAR-based methodology. Doline colors are according to depth. The numbers 4–6 refer to plateaus as in Figure 1 and Table 1. The map containing the whole Aggtelek Karst and Slovak Karst can be downloaded as a Supplementary File (Figure S1).

**Figure 12.**Box-whisker plots of the doline area categorized by bedrock. A vertical line indicates the median value, and “+” is the mean value.

**Figure 13.**Empirical distributions of the doline area after log transformation for the six plateaus with the most sinkholes (Koniarska, Plešivská, Bučina, Silická, Kečovská–Haragistya, E-Alsó-hegy). Blue lines indicate the fitted normal distribution (after the log transformation).

**Figure 14.**Cumulative frequency distributions of the doline area on a logarithmic scale for the six plateaus with the most sinkholes.

**Figure 15.**A box-whisker plot of the doline depth-to-diameter ratio according to lithological categories. A vertical line indicates the median value, and “+” is the mean value.

**Figure 16.**A box-whisker plot of the doline 3D-shape parameter (k) by plateau. A vertical line indicates the median value, and “+” is the mean value.

**Table 1.**Some doline morphometric indicators of the plateaus of the study area: the number of dolines, doline density, doline area ratio, and the doline–area mean and median, n.d. means no data.

Id | Plateau Name | Number of Dolines | Doline Density (km ^{−2}) | Doline Area Ratio (%) | Doline–Area Mean (m^{2}) | Doline–Area Median (m ^{2}) |
---|---|---|---|---|---|---|

1 | Jelšavská | 38 | 12.6 | 8.5% | 6723 | 3863 |

2 | Koniarska | 213 | 17.3 | 11.0% | 6342 | 4657 |

3 | Plešivská | 946 | 28.4 | 14.4% | 5079 | 3597 |

4 | Bučina | 191 | 35.6 | 15.9% | 4474 | 3608 |

5 | Silická | 1436 | 29.9 | 16.3% | 5460 | 3930 |

6 | Horný | 170 | 12.8 | 6.0% | 4676 | 3540 |

7 | Žl’ab | 0 | 0.0 | 0.0% | n.d. | n.d. |

8 | Bôrčianska | 8 | 2.4 | 0.6% | 2408 | 636 |

9 | Zádielska | 30 | 3.8 | 2.9% | 7733 | 4888 |

10 | Jasovská | 152 | 3.2 | 1.6% | 4931 | 2732 |

11 | Kečovská-Haragistya | 380 | 15.8 | 9.6% | 6065 | 3419 |

12 | Nagyoldal | 148 | 23.3 | 10.8% | 4615 | 3544 |

13 | W-Alsó-hegy | 154 | 15.5 | 6.8% | 4378 | 2849 |

14 | E-Alsó-hegy | 645 | 30.0 | 13.6% | 4550 | 3177 |

15 | Szinpetri | 144 | 10.9 | 7.5% | 6929 | 5274 |

16 | Páska-bükk | 21 | 10.8 | 16.5% | 15,229 | 8469 |

17 | Aggtelek | 182 | 8.8 | 9.9% | 11,237 | 5934 |

18 | Rudabánya | 2 | 1.0 | 0.1% | 1254 | 1254 |

19 | Szalonna | 29 | 5.3 | 4.3% | 8094 | 4932 |

20 | Jósvafő | 66 | 33.0 | 16.0% | 4829 | 3333 |

**Table 2.**The percentile values of the general slope angles measured in doline centers. Slope values refer to the general slope of the terrain calculated from the unsmoothed and mean-filtered SRTM 1” DTM.

General Slope Angle Values for Different Percentiles | |||||||||
---|---|---|---|---|---|---|---|---|---|

General Slope Calculated From | 1% | 5% | 10% | 25% | 50% | 75% | 90% | 95% | 99% |

Unsmoothed SRTM 1″ | 1.0 | 1.6 | 2.1 | 3.1 | 4.5 | 6.4 | 8.2 | 9.7 | 12.8 |

3-cell mean-filtered SRTM 1″ | 0.7 | 1.2 | 1.6 | 2.5 | 3.9 | 5.6 | 7.4 | 8.7 | 11.8 |

5-cell mean-filtered SRTM 1″ | 0.5 | 1.0 | 1.3 | 2.3 | 3.7 | 5.3 | 7.0 | 8.4 | 11.9 |

**Table 3.**Distribution of dolines according to lithology. Lithologies with less than 0.9% of all dolines are not shown.

Lithology | Count | Percent of All Dolines (PAD) | Percent of Plateau Dolines (PPD) | Percent of Plateau Area (PPA) | PPD/PPA |
---|---|---|---|---|---|

Wetterstein Limestone | 3834 | 72.9% | 74.1% | 60.5% | 1.22 |

Steinalm Limestone | 532 | 10.1% | 10.6% | 10.7% | 0.99 |

Wetterstein Dolomite | 154 | 2.9% | 2.9% | 4.4% | 0.67 |

Gutenstein Limestone | 121 | 2.3% | 2.3% | 2.7% | 0.87 |

Reifling Limestone | 119 | 2.3% | 1.8% | 1.8% | 0.99 |

Gutenstein Dolomite | 116 | 2.2% | 2.3% | 2.5% | 0.90 |

Deluvial sediments | 71 | 1.3% | 0.9% | 3.0% | 0.32 |

Waxeneck Limestone | 62 | 1.2% | 1.0% | 1.8% | 0.55 |

Szin Beds | 61 | 1.2% | 0.8% | 2.1% | 0.40 |

Gutenstein undistinguished | 49 | 0.9% | 0.8% | 1.4% | 0.54 |

**Table 4.**The test results of doline area distribution fitting for the study area plateaus. Chi-square and Kolmogorov–Smirnov (K-S) tests were used for the log-transformed data. The null hypothesis is that the log-transformed data fit a normal distribution. If p > 0.05, then the null hypothesis cannot be rejected, n.d. means no data.

Id | Plateau Name | Chi-Square Statistic | Chi-Square p-Value | Kolmogorov–Smirnov D | Kolmogorov–Smirnov p-Value |
---|---|---|---|---|---|

1 | Jelšavská | 12.5263 | 0.4850 | 0.1003 | 0.8394 |

2 | Koniarska | 26.0563 | 0.6723 | 0.0424 | 0.8376 |

3 | Plešivská | 115.8750 | 4.60 × 10^{−6} | 0.0507 | 0.0153 |

4 | Bučina | 24.3770 | 0.6615 | 0.0417 | 0.8936 |

5 | Silická | 137.2580 | 6.40 × 10^{−7} | 0.0449 | 0.0061 |

6 | Horný | 29.7647 | 0.3248 | 0.0978 | 0.0773 |

7 | Žl’ab | n.d. | n.d. | n.d. | n.d. |

8 | Bôrčianska | n.d. | n.d. | n.d. | n.d. |

9 | Zádielska | 13.0000 | 0.3690 | 0.1119 | 0.8468 |

10 | Jasovská | 26.5789 | 0.4317 | 0.0616 | 0.6121 |

11 | Kečovská-Haragistya | 28.2737 | 0.8749 | 0.0361 | 0.7057 |

12 | Nagyoldal | 20.3784 | 0.7267 | 0.0727 | 0.4210 |

13 | W-Alsó-hegy | 26.7792 | 0.4210 | 0.0545 | 0.7497 |

14 | E-Alsó-hegy | 69.0791 | 0.0247 | 0.0419 | 0.2085 |

15 | Szinpetri | 31.0000 | 0.1890 | 0.0776 | 0.3543 |

16 | Páska-bükk | 3.1429 | 0.9779 | 0.1060 | 0.9723 |

17 | Aggtelek | 39.0879 | 0.0795 | 0.0541 | 0.6617 |

18 | Rudabánya | n.d. | n.d. | n.d. | n.d. |

19 | Szalonna | 5.5690 | 0.2337 | 0.0859 | 0.9830 |

20 | Jósvafő | 14.6061 | 0.6238 | 0.0748 | 0.8535 |

**Table 5.**Vertical doline parameters: depth, depth-to-diameter ratio, volume, 3D-shape parameter (k), and mean denudation. (Since LiDAR data were not available for Rudabánya (18) and Szalonna (19) mountains, these parameters were not calculated for these units.) n.d. means no data.

Id | Plateau Name | Doline Depth, Mean (m) | Depth-to-Diameter Ratio | Volume, Mean (m^{3}) | 3D-Shape Parameter (k), Mean | Mean Denudation Thickness (m) |
---|---|---|---|---|---|---|

1 | Jelšavská | 7.6 | 0.0866 | 49,560 | 2.21 | 0.6265 |

2 | Koniarska | 8.3 | 0.0943 | 30,421 | 2.23 | 0.5265 |

3 | Plešivská | 8.8 | 0.1078 | 24,277 | 2.56 | 0.6897 |

4 | Bučina | 9.9 | 0.1285 | 23,161 | 2.34 | 0.8235 |

5 | Silická | 8.7 | 0.1063 | 25,009 | 2.41 | 0.7478 |

6 | Horný | 6.1 | 0.0777 | 14,870 | 2.40 | 0.1896 |

7 | Žl’ab | n.d. | n.d. | n.d. | n.d. | n.d. |

8 | Bôrčianska | 4.0 | 0.0457 | 2864 | 2.54 | 0.0067 |

9 | Zádielska | 4.9 | 0.0503 | 20,344 | 2.59 | 0.0764 |

10 | Jasovská | 4.9 | 0.0622 | 14,158 | 2.76 | 0.0456 |

11 | Kečovská-Haragistya | 6.9 | 0.0877 | 27,436 | 2.12 | 0.4330 |

12 | Nagyoldal | 7.1 | 0.0956 | 21,483 | 2.08 | 0.5010 |

13 | W-Alsó-hegy | 5.9 | 0.0846 | 17,456 | 2.00 | 0.2707 |

14 | E-Alsó-hegy | 10.0 | 0.1384 | 26,113 | 2.25 | 0.7828 |

15 | Szinpetri | 7.4 | 0.0840 | 36,645 | 1.97 | 0.3987 |

16 | Páska-bükk | 12.4 | 0.1052 | 139,720 | 2.05 | 1.5124 |

17 | Aggtelek | 8.4 | 0.0835 | 66,745 | 2.04 | 0.5856 |

18 | Rudabánya | 1.0 | 0.0257 | n.d. | n.d. | n.d. |

19 | Szalonna | 8.5 | 0.0885 | n.d. | n.d. | n.d. |

20 | Jósvafő | 4.2 | 0.0571 | 14,796 | 1.90 | 0.4890 |

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Telbisz, T.; Mari, L.; Székely, B.
LiDAR-Based Morphometry of Dolines in Aggtelek Karst (Hungary) and Slovak Karst (Slovakia). *Remote Sens.* **2024**, *16*, 737.
https://doi.org/10.3390/rs16050737

**AMA Style**

Telbisz T, Mari L, Székely B.
LiDAR-Based Morphometry of Dolines in Aggtelek Karst (Hungary) and Slovak Karst (Slovakia). *Remote Sensing*. 2024; 16(5):737.
https://doi.org/10.3390/rs16050737

**Chicago/Turabian Style**

Telbisz, Tamás, László Mari, and Balázs Székely.
2024. "LiDAR-Based Morphometry of Dolines in Aggtelek Karst (Hungary) and Slovak Karst (Slovakia)" *Remote Sensing* 16, no. 5: 737.
https://doi.org/10.3390/rs16050737