The mutation of spaces observed in the Katangese Copper Belt (KCB) causes significant topographical changes. Some colonial geodetic markers are easily noticeable on many of the hills making up the KCB. These hills are subject to mining which ruins the completeness of the network of triangulations: geometric and trigonometric Katangese. In order to keep control of the latter, the study shows on the one hand the possibility of using SRTM data (Shuttle Radar Topography Mission) in the monitoring of the macro-change of the reliefs, from 442 positions, and on the other hand, an indirect (remote) inventory method of the existing geodetic markers, by restoring the mapping of the said triangulation. Statistical and spatial analyses of paired samples of the 442 individuals allowed the study to observe the negative and positive altimetric variations at the locations of 79 geodetic markers, in an area of approximately two square degrees. In both cases, the research considers that the altimetric variations would exclude the physical existence of certain geodetic markers at their positions, and that we do not find the slightest information relating to their official relocations.

The geodetic markers of a country are a framework of triangulation points of known coordinates which serve as a basis for topographic work. They are of obvious scientific interest such as: computing of new point coordinates, definition of the exact shape of the terrain, economics, production of the base map, and derived maps and plans. They are therefore essential supports for the management of the quantity and quality of geometric or trigonometric triangulation networks.

Recent studies on the impact of human activities on forest ecosystems and mining in the Katanga’s Copper Belt (KCB) reveal significant environmental disturbances, particularly due to deforestation and unregulated mining practices [

Mining has gone through three main stages [

In addition to the regression of forests, of which the disfigurement of landscapes and the degradation of soils are some of the inevitable consequences, the proliferation of mineral extraction sites is also accompanied by abrupt alterations of the relief, in particular the razing of mineralized hills and the creation of cuttings, embankments and new mounds, as can be observed at the Luiswishi sites [

The scarcity of accurate synoptic topographic data in the region, both current and historical, available to the public is prompting the development of new analytical approaches to monitor geomorphological mutation and the completeness of geodetic benchmarks in the KCB. Under these conditions, remote sensing techniques, notably satellite RADAR, become essential for characterizing the past and present state of landforms. Satellite RADAR offers the possibility of characterizing topographic variables and adjacent phenomena such as: Soil erosion [^{1}

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In this study, we aimed to analyze the potential applicability of SRTM data for the monitoring of macroscopic terrain mutations and the indirect inventory of geodetic markers. Since there is a paucity of similar work, our research had drawn on work by [

This study, which covers an area of 42,980 km², representing 8.75% of the Katanga Province, uses Geographic Information Systems (GIS), remote sensing, statistics and spatial analysis to carry out a remote inventory of the geodetic markers installed by the Belgians in the beginning of the 20th century. First, we made a statistical analysis to assess the complementarity of the Comité Spéciale du Katanga (CSK) historical topographic data, SRTM and UAV data for geomorphological characterization. On the other hand, we explore spatial autocorrelation analysis to assess and validate change on a geodetic landmark using these data. Apart from the introduction and conclusion, the second section of this work presents our study area and our material and methods. We then present the obtained results in

The coordinates of 25° and 27° East, and −10° and −12° South, fix the study area at approximately 42,980 km^{2}, between the Haut Katanga and Lualaba provinces. Negligible encroachment into Haut-Lomami and Tanganika provinces is observed. The area extends north-west and south-west beyond the boundaries of the KCB, where mining and related activities are concentrated (see

The Katangese Copper Belt runs from Namibia to the Congolese stalk via Solwezi in Zambia. This curvature, was naturally accompanied by various accidents: faults, thrusting and various breaches that favored the uncovering of older stratiform mineralization and created a second mineralizing occurrence in the major faults. With a geostrategic connotation, the KCB contains, according to Dikumbwa et al. [

According to Lerat [

In the study area, the setting of geodetic markers was based on relative methods and included more than 442 triangulation points, of which at least 64 were of the first order, supplemented by about 226 second-order markers and about 144 third-order markers. The categories of the other 8 geodesic markers have not been identified on the map. The procedures for their placement were well defined. The margins of error for the Katanga network were: ±0”,52 (in X), ±0”,42 (in Y) and ±0”,64 (in Z) for the trigonometric levelling of a 10-kilometer range. The resulting cartographic exploitation of the data is adapted to the fundamental two-parallel Lambert conic projection, which is considered robust for cadastral exploitation. The Gaussian conformal system presents important deformations limiting its use [

Three data sources were used: (1) 4 topographic maps numbered S11/25, S12/25, S11/26 and S12/26 representing the 1st, 2nd and 3rd order triangulation network, based on surveys carried out between 1922 and 1929 by the CSK, (2) 22713 elevation points from a high-precision (1 m) topographic survey carried out with a Phantom 4 RTK UAV on 22/11/2021, in a small portion of 2 km² to the west of our study area indicate in

The Katanga triangulation network is based on 9 bases measured between 1912 and 1951. According to Straeten [

Firstly, the topographic maps were used to extract the 442 points representing the elevation levels of the CSK geodetic markers. In a second step, a raster of 30 m spatial resolution was obtained by interpolating the 442 CSK points. We then reprojected the 22713 points cloud collected from the UAV and the SRTM in UTM zone 35S for further processing. This process admitted errors of around 0.73 m in X and Y for the SRTM and around 0.026 m in X and Y for the point cloud, compared with the CSK maps; admissible for pixel resolutions of 30 m (SRTM) and 1 m (UAV), respectively [

Three paired samples of points were then formed. The first corresponds to the elevations in 1922 and 2000 using the original 442 CSK points in 1922 and the extraction of values from the SRTM of 2000 on the same points location. The second corresponds to the elevations in 1922 and 2021 using the 22713 UAV to extract the values on the CSK raster of 1922 and the original UAV values. Finally, the third corresponds to the elevation in 2000 and 2021, using the 22713 UAV to extract the values on the SRTM and the original UAV values. The last two matched samples represent the area covered by the UAV.

The methodology used for this study is based on the variance analysis, in the spirit of Derrick et al. [

The descriptive evaluation of the data series based on normality tests allowed to measure the altimetric distributions of the CSK and SRTM bounds of orders 1, 2 and 3, via the skewness and Kurtosis coefficients:

With

For this purpose, we will note the symmetry when Skewness

The multiple regression of the CSK, SRTM and UAV datasets aimed to reduce the influence of the divergence of the measurement systems used for the surveys and improve the comparative analysis. This made it possible to correct the errors in the SRTM and UAV elevation measurements from the CSK topographic data set. With the CSK geodetic markers as explanatory variables and the SRTM and UAV elevation observations as dependent variables. The residual values provided by the regression model constituted the theoretical deviations to be subtracted.

We calculated the linear regression coefficients:

The quality control of the multiple regression was based on the fit constant resulting from the solution of the equation coordinated at the origin :

The equal sample sizes allowed the study to analyze the homogeneity of the variances of the CSK and SRTM series. Using the Levene [

With

The F-test is done with degrees of freedom written as:

The preceding statistical parameters led to the formulation of a first mathematical expression for the variation of a controlled elevation z from the point

With

If

Spatial exploratory analysis of CSK and SRTM data has identified the locations of atypical and extreme elevation variations at selected geodetic markers. By identifying their spatial clustering patterns and associations, punctuated by various forms of spatial heterogeneity.

From the spatial autocorrelation of elevation changes on 442 geodetic markers we measured the intensity of the variation of an elevation

Modelling such spatial interactions requires specifying the spatial links between each geodetic marker. All these links were recorded in a square spatial connectivity matrix (

The validation of elevation variations on markers is based on Moran’s bivariate scatterplots (

The integration of this dynamism will be written:

The results of the

The choice of the methodology used in this research is privileged by the contexts: lack of inspections of geodetic markers, data updates, physical inventories and maintenance of the triangulation network, throughout the national territory by the commissioned body.

The altimetry data under study show a majority of asymmetrical patterns spread out to the left (

Kolmogorov-smirnova | Shapiro-wilk | ||||||
---|---|---|---|---|---|---|---|

Altitude | Order | Statistics | DF | Sig. | Statistics | DF | Sig. |

CSK | 1 | 0.07 | 64 | 0.20^{*} |
0.967 | 64 | 0.58 |

2 | 0.122 | 226 | 0 | 0.938 | 226 | 0 | |

3 | 0.197 | 144 | 0 | 0.919 | 144 | 0 | |

SRTM | 1 | 0.061 | 64 | 0.20^{*} |
0.984 | 64 | 0.6 |

2 | 0.081 | 226 | 0 | 0.955 | 226 | 0 | |

3 | 0.196 | 144 | 0 | 0.911 | 144 | 0 |

Unlike all statistical tests, the normality test seeks to accept

The two-way spatial correlations of the two elevation series (

N | Correlation | Sig. | ||
---|---|---|---|---|

Pair 1 | SCK order 1 & SRTM order 1 | 64 | 0.929 | 0.00 |

Pair 2 | SCK order 2 & SRTM order 2 | 226 | 0.968 | 0.00 |

Pair 3 | SCK order 3 & SRTM order | 144 | 0.979 | 0.00 |

SCK altitude | SRTM altitude | |||
---|---|---|---|---|

Tau-B of kendall | SCK altitude | Cor coef. | 1 | 0.841^{**} |

Sig | . | 0 | ||

SRTM altitude | Cor coef. | 0.841^{**} |
1 | |

Sig. | 0 | . | ||

Rho of spearman | SCK altitude | Cor coef. | 1 | 0.957^{**} |

Sig. | . | 0 | ||

SRTM altitude | Cor coef. | 0.957^{**} |
1 | |

Sig. | 0 | . |

One would expect very good relationships between CSK and SRTM individuals in the same groups. Pairs of orders 1 and 3 form the extreme correlation bounds of 0.929 and 0.979, respectively.

The comparative study of individuals from the CSK and SRTM topographic data groups shows differences in the statistical means of the elevations of the markers, respectively: 1 (1483.2063 m for and 1470.5469 m); 2 (1395.7690 and 1382.3894 m) and 3 (1380.1286 and 1372.7917 m) (see

The results of the likelihood analyses (

Levene statistic | Df1 | Df2 | Sig. | ||
---|---|---|---|---|---|

Alt_SCK | Based on average | 6.474 | 2 | 431 | 0.002 |

Based on median | 2.688 | 2 | 431 | 0.069 | |

Based on median with adjusted DF | 2.688 | 2 | 396.318 | 0.069 | |

Based on truncated average | 5.631 | 2 | 431 | 0.004 | |

Alt_SRTM | Based on average | 5,325 | 2 | 431 | 0.005 |

Based on median | 2.392 | 2 | 431 | 0.093 | |

Based on median with adjusted DF | 2.392 | 2 | 399.384 | 0.093 | |

Based on truncated average | 4.604 | 2 | 431 | 0.011 |

The analysis of equal variances (

Altitude | Method | Statistics | DF1 | DF2 | Sig. |
---|---|---|---|---|---|

SCK | Welch | 12.174 | 2 | 193.299 | 0 |

Brown-forsythe | 9.003 | 2 | 343.307 | 0 | |

SRTM | Welch | 11.197 | 2 | 192.098 | 0 |

Brown-forsythe | 8.491 | 2 | 343.293 | 0 |

These analyses allowed the study to take into account errors in the assessment of elevation changes. This is due both to the differences in the techniques used during the collection of CSK and SRTM data and to the different levels of accuracy offered by the instruments used in the determination of elevations by the operators. Depending on the order of the geodetic datum, the tolerance ranges of the variation of an elevation are fixed by the confidence intervals of the difference shown in

Order | Avg | SD | Avg std error | 99.99% CI | T | DF | Sig. (bilateral) | |
---|---|---|---|---|---|---|---|---|

Lower | Higher | |||||||

1 | 12.659 | 50.467 | 6.308 | −13.549 | 38.868 | 2.007 | 63 | 0.049 |

2 | 13.380 | 46.322 | 3.081 | 1.173 | 25.586 | 4.342 | 225 | 0.000 |

3 | 7.337 | 39.833 | 3.319 | −5.951 | 20.625 | 2.210 | 143 | 0.029 |

The analysis integrating more than 22,000 points surveyed in 2021 with a UAV, on a small control area, allows the arbitration of the observed elevation differences between the CSK and SRTM data sets (

Elevation variations at the geodetic marker locations, whatever their order in the geodetic network, are characterized by a positive spatial association. See

The study has retained the best results provided by

The top-top and bottom-bottom quadrants contain all 35 markers showing spatially significant elevation variations, ranging from −120.48 to 250.68 m. Thus, for the smoothed result (

Extreme elevation changes are observed on the order 2 marker locations (see

The ratio of about 0.34 characterizes the result grouping the elevation variations. It confirms the spatially very fragmented topographic variations. It reflects both the randomness of the location of the geodetic markers, and the level of disparity of intra-and extra-order changes in the geodetic network, which sometimes rhymes with the geological exceptionally outcrops of the copper-cobalt deposits; generally located on higher ground, at which places there would be geodetic markers in the KCB. Thus, the exploitation of the deposits at the locations of the geodetic markers would be largely responsible for the abrupt change in relief.

We note from the results of the synthesis mapping (

The large loss is observed in the category of benchmarks of order 2, followed by 3. Almost all geodetic benchmarks with a high probability of absence at their locations are found in the KCB, although the exact quantification of the height variation on a geodetic benchmark will require the field survey. This, given that the results of the statistical analysis on the three data sets (CSK, RSTM and UAV) reveal an offset which could be due to differences in the topographic measurement techniques used and the consideration of local datum.

In Dequincey et al. [

The data and tools exploited in this paper are adapted to the need for analysis and characterization of macro-change in relief and inventory of geodetic landmarks. The performance of SRTM proves to be an appropriate response to this need. The average CSK-SRTM height errors were respectively: 12.6594, 13.3796 and 7.3369 m, depending on orders 1, 2 and 3. These values are very close to the vertical root-mean-square error (RMSE) of ±12.526 m obtained by Ibrahim et al. [

The differences in standard deviations of: 40.411 m (SRTM), 42.332 m (Google Earth) and 43.383 m (ASTER GDEM 2) were recorded by Ibrahim et al. [

Altimetric accuracy errors increase with decreasing geodetic terminal orders. Ganie et al. [

The results highlighted in this study show that the data and the methodology used are suitable for identifying major topographic changes. However, they do not allow the detection of minor variations on the landforms bearing the geodetic markers. This limitation could be due to the low spatial resolution of the SRTM image used in the research and to the divergence of reference zeros (local CSK zero and global SRTM zero). This last argument is confirmed by the small difference between the SRTM (2000) and UAV (2021) data in

The discrepancy between CSK, SRTM and UAV data is thought to be due to the penetrating power of the SRTM C and X bands, disrupted by strong topographic features and dense forest cover. References [

Normally, it is recommended to proceed with direct field inspection and measurements for such a study, related to the control and management of the geodetic network, carried out through the indirect inventory of the geodetic markers that constitute it. But currently, the emergence of geomatic sciences (remote sensing and GIS) having boosted new collection and analysis techniques of geospatial information that facilitate their processing, raises the growing interest in the scientific community. The aim is to test the reliability of data derived from geospatial techniques and also to identify the methods that would be suitable for their exploitation [

This work analyzed the state of the geodetic network in an area of heavy mining and forestry, based on CSK (1919–1952) and SRTM (2000) data, arbitrated by the UAV survey carried out in 2021. We have indirectly inventoried the completeness of the existing geodetic monuments and deduced the evolution of the relief in the N-W part of the KCB. The research finds that in the two square degrees under study, on the 442 markers of the geometric and trigonometric triangulation network, 79 markers are missing in their places. With confidence levels varying between p 0.05 and p 0.001. The majority of this loss coincides with the locations of quarrying and mining activities in the KCB and its surroundings.

With this in mind, the present contribution has set out on the one hand to find a method for testing the reliability of SRTM data by comparing them with the topographic data collected by the CSK in the southern part of the DRC. On the other hand, to find a way to remotely monitor the situation of the geodetic network in the KCB. The study proposes a methodological approach applicable to the indexation of major elevation variations at the locations of geodetic markers. Indeed, it is becoming frequent to observe abrupt topographic changes at the locations where geodetic markers are established. In addition, the state institution in charge of the management of the said geodetic network remains without means to play its role.

The authors would like to thank the editor and the reviewers for their contribution to the improvement and publication of our paper.

The authors received funding from CGS SARL for data collection and CarTeS laboratory for technical support.

The authors confirm contribution to the paper as follows: Project design and data collection were carried out by John Tshibangu W.I. For the work concerning processing, analysis and writing, all the authors participated equally. Catherine Nsiami M. supervised the work.

Updated (SRTM, UAV) and historical (CSK) data are stored on the local CarTeS Laboratory server and can be shared with other researchers on request. The digital processing of data was done on the computer using software: Excel, QGIS, SPSS and GeoDa.

The authors declare that they have no conflicts of interest to report regarding the present study.