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Evaluating the impact of DEM interpolation algorithms on relief index for soil resource management

  • Maan Habib ORCID logo EMAIL logo , Bashar Bashir , Abdullah Alsalman and Hussein Bachir
Published/Copyright: August 12, 2024
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Open Geosciences
From the journal Open Geosciences Volume 16 Issue 1

Abstract

Soil resource management is fundamentally integral to environmental sustainability and agricultural productivity. The digital elevation model (DEM) is the fundamental data for analyzing landform surfaces, which introduces an opportunity to obtain a broad spectrum of terrain factors to simplify interpreting the patterns and processes in the geoscience field. The accuracy and resolution of DEM are crucial for their effective use, and many algorithms have been developed to interpolate digital elevation data from a set of known points. Although primary topographic variables derived from grid datasets are important, secondary variables, such as the relief index (RFI), play a more critical role in understanding the complicated relationship between soil properties and landform attributes. The RFI is attained from a DEM by calculating the elevation range within a given neighborhood surrounding a central cell. It is an essential predictor of soil natural resource management that measures the degree of differentiation surface relief. In addition, it is beneficial for perceiving the landscape and its management. This study presents a comprehensive zonal analysis comparing the RFI values derived from multiple interpolation-based DEMs. It investigates deterministic and geostatistical interpolators, such as inverse distance weighted and natural neighbor across distinct zones with diverse topographical characteristics. The findings indicated a high correlation between the RFI and the reliability of the DEM, and the natural neighbor technique provided superior performance against others. The results revealed that the choice of spatial interpolation technique significantly affects the accuracy and reliability of RFI models.

Keywords: DEM; spatial interpolation; relief index; IDW; natural neighbor; soil

1 Introduction

Landscape topography is vital in controlling processes in the Earth’s near-surface layer [1,2]. It is one of the soil formation components that are applied for mapping spatial heterogeneity variability of soil physical attributes [3,4] as it affects climatic and meteorological parameters [5] and gravity-driven overland and intrasoil lateral flows [6]. However, quantifying topographic information obtained from several sources is broadly utilized in soil science [7]. Today’s trendy wave of geospatial technologies has enormously impacted the diversity of data acquisition techniques, processing, and representation approaches. The digital elevation model (DEM) is a three-dimensional approximation of the Earth’s surface [8,9]. It is considered the primary data source for GIS-based spatial analysis to manage various geomorphological and natural resource problems [10]. In reality, various attributes characterize DEM surface, including resolution, accuracy, and others, which are decisive components for extracting vital terrain variables [11,12,13] required in many scientific disciplines [14,15]. The quality of the DEM relies on grid spacing, data collection methods, interpolation algorithms, and morphological terrain features [16,17,18,19]. Therefore, the errors associated with the DEMs are also propagated to DEM-derived factors [20,21].

Spatial interpolation, a fundamental technique in geospatial analyses, is pivotal in transforming discrete spatial data into continuous surfaces. It is vital in various fields, from climate studies to environmental sciences, as they comprehensively understand spatial variability. The spatial interpolation technique is applied to expect the value of features at specific locations relying on a set of sampled data [22,23]. This process is based on Tobler’s first law of geography: “Everything is related to everything else, but near things are more related than distant things.” [24]. Various spatial interpolation algorithms have been constructed, involving deterministic methods such as inverse distance weighting (IDW) and natural neighbor and statistical approaches similar to ordinary kriging. Cressie [25] reported the difference between these models for building raster surfaces over a region. Several comparative analyses of the interpolation methods have been performed [26,27,28,29].

Understanding spatial variability becomes paramount in soil sciences, especially when analyzing the relief index (RFI) as a measure often utilized to indicate terrain variations and their influence on soil characteristics. The RFI is one of the critical topographic parameters extracted from the DEM grid used in the geoscience domain [30]. Therefore, the accuracy and reliability of the RFI can significantly impact decisions made in soil resource management, from conservation strategies to agricultural planning. The deviations in obtained values from the interpolated surface are owed to the complicated relationship between the estimation model and acquired variables [31]. Hence, the comparative appropriateness of interpolation models should be performed to evaluate them based on the different terrain characteristics [32].

Despite the crucial role of spatial interpolation in shaping the RFI, limited research has explored how various interpolation choices affect its modeling. Such gaps in literature might lead to less-than-ideal soil management decisions, given that distinct interpolation methods can introduce variations in the resulting RFI. This study aims to bridge this knowledge gap by investigating the most effective spatial interpolation methods for characterizing RFI surfaces. In addition, the spatial tools utilizing ArcGIS Model Builder are designed to automate and improve the repeatability of geoprocessing tools. The DEM is established using a synthetic dataset collected from a scanned topographic map with a broad spectrum of landforms to simulate Earth’s topographic features as the basis for RFI analysis.

2 Materials and methods

Spatial variability within a region is an essential factor in environmental complexity. The DEM is a quantitative visualization of the terrain surface and geospatial data, which plays a central role in scientific studies. Its structure form for storing, displaying, and analyzing spatial data differs from the traditional paper-based. DEM-derived metrics quantify spatial heterogeneity to perceive the geographic context and landscape characteristics [33]. The RFI is an essential metric for assessing topographic complexity and landscape morphology, which plays a critical role in soil resource management and earth surface processes [34,45]. Accurate RFI modeling highly depends on the DEM quality used in the analysis [30]. Various interpolation techniques can be employed to generate DEMs from sparse elevation data, which can significantly impact the accuracy and resolution of the resultant DEMs [11,17].

In contrast, soil management is a delicate balance, reliant on accurate data and robust modeling. The decisions made here have long-lasting ecological and economic impacts. With the RFI serving as a foundational tool in many of these decisions, understanding the influence of spatial interpolation on its modeling is critical. The limited literature in this domain suggests gaps in the current methodologies, potentially leading to suboptimal soil management practices. This study demonstrates the importance of selecting appropriate interpolation methods and using high-quality elevation data for generating DEMs and calculating RFI values. This section concentrates on the definition of the investigated area, test data set, interpolation algorithms, and validation methods.

2.1 Research methodology

Geomorphometry is the discipline of a quantitative investigation of the Earth’s terrain to identify diverse multiscale geoscientific issues [35,36]. It is mainly devoted to extracting topographic variables from DEM and separating the land surface into spatial features to recognize the patterns and processes in geoscience fields [37,38]. In practice, the RFI as a terrain parameter plays a vital role in hydrological and geomorphological processes to quantify the relief variability [34]. In order to assess the performance of diverse interpolation models concerning their suitability to represent RFI maps, visual and statistical approaches were chosen for testing. Figure 1 represents a schematic description of the workflow process framework applied in this research for evaluating DEM quality and RFI.

Figure 1 Graphical illustration of the general research methodology.
Figure 1

Graphical illustration of the general research methodology.

2.2 Test dataset

The study focuses on the Irbid region in Jordan, characterized by a diverse range of topographical features, including hills, valleys, and flat terrains. This area was chosen to comprehensively understand the interplay between elevation, topography, and soil resources. The primary data source for the research is elevation points obtained from NextGIS company. The data set encompasses an area of approximately 150 km². Elevation values within the dataset range from −347 to 1,140 m above mean sea level, with a vertical accuracy of ±0.5 m and a point density of 20 points per hectare (pts/ha; Figure 2).

Figure 2 Location of the study area.
Figure 2

Location of the study area.

2.3 Interpolation-based DEMs

Spatial interpolation is a cornerstone of geospatial analysis. At its most basic level, it involves predicting values for unsampled locations based on known values from sampled locations. Due to the large number of applications, various methods have been developed, each catering to specific types of datasets and research questions. This section explores the spatial interpolation techniques employed in this study, indicating their mathematical foundations and the rationale behind their selection. The IDW, natural neighbor (NN), and ANUDEM are chosen for their advantages in DEM interpolation. IDW is valued for its simplicity and effectiveness in handling non-uniformly distributed sampling points, which helps create smooth surfaces crucial for accurate terrain analysis. NN is particularly adept at dealing with irregular data sets, as it can interpolate without requiring a predefined mesh and effectively maintains local terrain variations, which are vital for precise RFI calculations. Although not extensively discussed initially, ANUDEM offers significant potential by producing hydrologically correct DEMs, potentially increasing the accuracy of RFI measurements in hydrologically sensitive areas. These methods were selected based on their ability to manage the different topographic characteristics and various data distribution scenarios in soil resource management.

2.3.1 IDW

IDW is one of the most popular and accessible methods in the domain of spatial interpolation. Rooted in a straightforward principle, IDW operates on the assumption that the influence or importance of a known data point diminishes as one moves farther from it. This means that nearby observations usually affect the interpolated value more than those located further away (Figure 3). The foundational concept behind IDW is encapsulated in its name: the weight (or influence) given to each observation is inversely proportional to the distance from the location of interest. In practical terms, when estimating a value for an unsampled point, the known data points closer to that location will carry more weight in determining its value than the distant ones. Mathematically, the interpolated value z(u) at location u is given by [10,39]:

(1) z u = ∑ i = 1 n z i w i ∑ i = 1 n w i , w i = 1 d i k ,

where z u is the estimated value at the unsampled position u; n is the number of measured points used for the interpolation; z i is the known value at the ith location; w i is the weight; d i is the distance between the unsampled location u and the ith location known data point; k is a positive constant, often referred to as the power parameter, which determines the rate of decay in weight with increasing distance. The choice of the power parameter k is crucial. A larger value of k will result in a sharper decrease in weight with increasing distance, making the interpolation heavily reliant on the closest observations. In contrast, a smaller k will spread the influence over a larger area, sometimes risking the introduction of more general, less localized estimates.

Figure 3 IDW Interpolation approach.
Figure 3

IDW Interpolation approach.

2.3.2 Natural neighbor

Natural neighbor interpolation is a technique utilized to estimate values at unknown points based on the values of known points in a dataset. It is beneficial when the data points are irregularly spaced. The technique relies on Voronoi diagrams (Figure 4), which partition a space into regions around each data point such that each point in a given region is closer to its NN data point than any other [40,41]. The Voronoi polygon area corresponding to nearby data points provides the basis to determine the weight in NN, which is employed to estimate the value at the NN’s query point, as indicated in equation (2).

(2) z P = ∑ i = 1 n z i w i ∑ i = 1 n w i , w i = A i p ,

where w i is the weight of each Voronoi polygon; A ip is the area of intersection between the Voronoi polygons of the points i (red color) and natural neighbor of query point p (green color); z i is the height of Vornoi points i.

Figure 4 Natural neighbor interpolation method.
Figure 4

Natural neighbor interpolation method.

2.3.3 ANUDEM (topo to raster)

ANUDEM is a spatial interpolation technique developed by Michael Hutchinson. It is commonly applied to generate continuous surface models from point data, contour lines, and other types of elevation information [42]. ANUDEM is the algorithm behind the “Topo to Raster” tool in ArcGIS and other GIS software. It aims to produce hydrologically correct DEMs by enforcing drainage network consistency. ANUDEM employs an iterative finite difference interpolation technique that considers the elevation of the known points and the natural drainage structure. The algorithm minimizes the elevation differences between adjacent cells while adhering to the imposed drainage constraints. The algorithm iteratively refines an elevation grid ∇z(x, y) by minimizing an objective function F, which generally has equation (3). In addition, ANUDEM also includes a mechanism to enforce drainage consistency by identifying and enforcing sinks, streams, and other hydrological features (Figure 4). These features are coded into the algorithm as additional constraints, modifying the objective function F (Figure 5).

(3) F = ∑ i = 1 n w i ( z ( x i , y i ) − z i ) 2 + λ ∑ j = 1 n ∇ z ( x j , y j ) ,

where w i is the weight assigned to each known point; z(x i , y i ) is the gradient term that enforces smoothness in the surface; λ is a smoothing parameter that balances the trade-off between fitting the data and producing a smooth surface.

Figure 5 Flowchart of ANUDEM interpolation model.
Figure 5

Flowchart of ANUDEM interpolation model.

2.4 RFI

The RFI is a quantitative measure used in geomorphology and GIS to characterize the topographic heterogeneity or the variability in elevation of a landscape. It provides insight into the roughness or smoothness of a given area, which can be important for understanding various ecological and geological processes. In addition, RFI is an essential tool in soil resource management, providing crucial data that influences various decisions, from erosion control to crop management. Integrating RFI data with other geospatial information creates a comprehension understanding of the landscape, leading to informed and sustainable soil management practices. The following indicates the importance of RFI in soil resource management [3,43,44,45,46]: (1) soil formation and characteristics are influenced by the relief of an area, affecting the type and rate of soil development. For instance, steeper terrains can have thinner soils due to increased erosion, while flat areas might possess deeper soils. Understanding the relief can assist in predicting soil types and depths; (2) erosion risk assessment is crucial in areas with high relief indices, as they often have an increased risk of soil erosion, particularly if they lack vegetative cover. Management strategies such as contour plowing, terracing, or afforestation can be implemented to minimize erosion by identifying these areas; (3) landslide vulnerability assessment using the RFI helps determine areas at risk of landslides. Regions with high relief can be more susceptible to slope failures, especially when factors such as rainfall intensity, soil saturation, and land-use changes come into play. Planners and geologists can identify potential landslide hotspots by understanding and quantifying a region’s relief. Hence, they can take preventative measures such as slope stabilization, setting up proper drainage systems, and implementing land-use regulations to reduce the risk of landslides; (4) water drainage and retention are heavily influenced by relief, determining how water traverses and permeates the landscape. Areas with high relief can experience swift runoff, reducing water availability for crops. In contrast, regions with low relief can be susceptible to waterlogging. Understanding the relief can shape the development of drainage systems and provide insights into irrigation practices; (5) land use planning is informed by the RFI, which assists in determining the optimal use of land based on its topography. Steep terrains, for instance, can be better suited for forestry or pasture rather than cultivation; (6) fertility management is crucial as soil fertility can vary with terrain. Upland soils can be less fertile due to leaching and erosion, while valleys or lower terrains can accumulate organic matter and nutrients, making them more fertile. Understanding relief can help in designing location-specific fertilization programs; (7) microclimate prediction is influenced by terrain, affecting local climatic conditions and subsequent soil processes. Areas with high relief can experience cooler temperatures and increased moisture because of orographic effects. These conditions can further impact soil microbial activity, organic matter decomposition, and various other soil properties; (8) infrastructure development involves the construction of soil conservation structures such as check dams, contour bunds, or terraces. The knowledge about the relief is crucial in this context. Such structures are designed based on the slope and relief to maximize their efficiency in conserving soil and water; (9) in precision agriculture, modern farming methods depend on in-depth knowledge of the land to fine-tune inputs and enhance yields. Integrating the RFI with other data layers, such as soil type, moisture content, and vegetation, can develop detailed management zones tailored for precision agriculture applications.

Accordingly, the RFI is critical in erosion modeling, specifically in computing the length-slope (LS) factor within the Universal Soil Loss Equation (USLE). The LS factor quantifies the effect of topography on erosion rates by including slope length and steepness, which are significantly influenced by the relief characteristics of the terrain. Studies demonstrated that the RFI effectively captures variations in elevation that directly impact runoff behavior and soil erosion potential [47]. For instance, a higher RFI, indicating greater elevation differences within a specific area, often correlates with increased surface runoff and potential erosion risk [48]. This correlation is crucial for accurately predicting erosion in various topographical settings and implementing appropriate soil conservation measures. Zhang et al. [49] applied the RFI in USLE models to improve the spatial accuracy of erosion predictions. These studies confirm that including detailed relief data can enhance the predictive power of erosion models, facilitating more precise soil management strategies.

Modern geospatial methods offer innovative approaches to depict and measure the Earth’s surface using grid-based DEMs and introduce algorithms to derive geomorphometric characteristics [50]. Neighborhood tools are frequently used in DEM analysis processes, calculating specific statistics for a central cell within a predefined moving window centered on a critical point [51,52]. This research utilizes a 3 × 3 window to minimize the impact of cell dimensions on model outcomes [53], moving across the DEM surface to define terrain data (Figure 6). There are several methods for determining RFI using a DEM, depending on the specific goals of the analysis. Some measures can be more suited to large-scale landscape analyses, while others can be more appropriate for localized studies. In addition, the resolution of DEM used can influence the results, as can the size of the moving window applied in specific methods, as listed in Table 1. This study proposes the root mean square of elevation difference between a central pixel and its surrounding pixels within a defined neighborhood in a DEM to determine RFI, as shown in equation (4) and Figure 7.

(4) RFI = ∑ k = 1 n ( z o − z k ) 2 / n ,

(5) ∑ k = 1 n ( z o − z k ) 2 = ( e − a ) 2 + ( e − b ) 2 + … + ( e − i ) 2 ,

where z o is the central pixel elevation in a roving window; z is the elevation of each of the surrounding pixels; n is the number of surrounding pixels.

Figure 6 Neighborhood operations of a 3 × 3 input cell grid.
Figure 6

Neighborhood operations of a 3 × 3 input cell grid.

Table 1

Benchmarking the addressed models against original DEM and RFI values

Zones DEM RFI
ANUDEM IDW NN ANUDEM IDW NN
Minimum
Slight 1.00 1.00 1.00 0.59 0.48 1.00
Medium 0.04 −5.53 0.98 0.95 0.68 1.00
High 0.88 1.03 0.98 0.37 1.10 1.00
Very high 0.95 0.98 1.00 0.73 0.39 1.00
Maximum
Slight 2.12 0.98 1.07 0.77 1.31 1.00
Medium 1.06 1.03 0.97 0.88 0.99 1.00
High 1.02 1.00 0.99 0.81 1.02 1.00
Very high 0.99 0.99 1.00 0.77 1.09 1.00
Average
Slight 1.00 1.00 1.00 0.82 0.86 1.00
Medium 1.00 1.00 1.00 0.83 0.89 1.00
High 1.00 1.00 1.00 0.85 0.84 1.00
Very high 1.00 1.00 1.00 0.86 0.89 1.00
Standard deviation
Slight 1.00 1.00 1.00 0.77 1.04 1.00
Medium 1.00 1.00 1.00 0.74 1.14 1.00
High 1.00 1.00 1.00 0.87 0.98 1.00
Very high 1.00 1.00 1.00 0.88 1.15 1.00
Figure 7 Numerical application for computing RFI.
Figure 7

Numerical application for computing RFI.

2.5 Quality analysis

Applying zonal analysis to evaluate the performance of the RFI derived from DEM surfaces provides a detailed and localized approach for assessing topographical variations. This technique segments a geographical landscape into distinct zones using specific criteria, such as elevation ranges, slope categories, or aspect orientations [54,55,56]. When applied to the RFI, this tool enables an in-depth exploration of the topographical changes within each zone, ensuring a precise evaluation rather than a generalized overview. In this study, the slope surface is classified for RFI zonal analysis, with each zone assigned a unique RFI value. This offers insights into the topographical variability inherent to each specific region. Within these zones, statistical measures can be systematically computed, providing an understanding of the terrain’s complexity and potential anomalies. The zonal approach is especially crucial when comparing the derived RFI values with actual ground surface or field data. Discrepancies between the two can be swiftly identified, determining potential errors in the DEM or the used interpolation techniques.

An inter-zone comparison becomes possible with zonal analysis, allowing for detecting patterns or inconsistencies in the DEM surface. For instance, recognizing a gentle slope zone indicating a significantly higher RFI than an adjacent zone with a steeper slope can highlight underlying issues or anomalies in the data representation. In addition, visual representation tools can improve the zonal analysis by providing clear illustrations of the RFI’s accuracy and reliability across various zones. This visualization aids in quickly identifying areas with high variability or potential errors and facilitates more informed decision-making processes in diverse fields.

A widely adopted approach for validating the RFI quality involves comparing a selected sample of relief differences obtained from the predicted surface with reference values gathered from field measurements, as illustrated in Figure 8. Evaluating the effectiveness of various interpolation algorithms presents challenges, primarily when relying on a limited dataset because it becomes difficult to identify the nature of measurement errors. Consequently, the comparative analysis of interpolation techniques encompasses an additional procedure predominantly sensitive to RFI precision. Typically, the statistical metrics compare the differences between each referenced and extracted value of RFI to determine the power of their relationship. This difference is demonstrated in equation (6), which represents the standard deviation (StDev) of residuals [57]. The StDev value represents a metric for assessing the consistency between the training dataset and the statistical model. A larger StDev suggests a more pronounced discrepancy between these datasets. Conversely, the Q–Q (quantile–quantile) plot, a widely used graphical tool, examines whether the predicted residuals conform to a standard distribution, as Chirico et al. [58] described.

(6) StDev = 1 N − 1 ∑ i = 1 N ( RFI r e f i − RFI mean i ) 2 ,

where RFIref and RFImean are reference and predicted values of RFI, respectively.

Figure 8 Schematic diagram of results quality analysis.
Figure 8

Schematic diagram of results quality analysis.

3 Results and discussion

Figure 9 represents the original and predicted surfaces generated by ANUDEM, IDW, and NN interpolation techniques in a mountainous area. With a visual inspection of the three DEMs in Figure 9 and the original one, it can be observed that IDW and ANUDEM models reveal some differences. At the same time, NN is the best method that fits the elevation data. On the other hand, there is a need for further analysis to investigate the differences in these models.

Figure 9 DEM surfaces generated by the addressed interpolation methods: (a) Original surface; (b) ANUDEM; (c) IDW; (d) NN.
Figure 9

DEM surfaces generated by the addressed interpolation methods: (a) Original surface; (b) ANUDEM; (c) IDW; (d) NN.

The comparative analysis of DEM surfaces (Figure 10) indicates a similarity in the primary trend between the original case and the investigated models (ANUDEM, IDW, and NN). The equality plots confirm that these models successfully replicate the general characteristics of the original DEM. The congruence of these models with the original DEM suggests that these interpolation techniques perform reliably in replicating basic terrain features. On the other hand, contrary to the DEM results, the RFI surfaces (Figure 11) exhibit considerable variation across the interpolation techniques compared to the original case. This divergence necessitates a deeper investigation to uncover underlying patterns and implications for soil resource management. The distinct responses of the RFI to different interpolation methods highlight the sensitivity of secondary terrain variables to the choice of interpolation technique. Figure 12 provides a statistical distribution comparison for both DEM and RFI surfaces. The DEM outcomes are relatively consistent across the different techniques, whereas the RFI exhibits significant variations. The ANUDEM model shows a distribution for the first and third quartiles (Q1 and Q3) between the original case, which has the highest Q1 and Q3, and the IDW, which has the lowest. The close resemblance in results between the IDW and NN models for both DEM and RFI surfaces requires further exploration to understand their similarities and differences.

Figure 10 Comparison of the DEM surfaces from the interpolation techniques against the original case.
Figure 10

Comparison of the DEM surfaces from the interpolation techniques against the original case.

Figure 11 Comparison of the RFI surfaces from the interpolation techniques against the original case.
Figure 11

Comparison of the RFI surfaces from the interpolation techniques against the original case.

Figure 12 Overall statistical distribution for the DEM and RFI surfaces using the investigated techniques.
Figure 12

Overall statistical distribution for the DEM and RFI surfaces using the investigated techniques.

A zonal analysis was conducted to investigate and extract the hidden patterns within the results. This zonal analysis offers a more detailed examination of how various DEM interpolation techniques evaluate the RFI across different terrain zones. Based on normalized DEM values from the original data set, these zones were categorized as slight, medium, high, and very high. This categorization was based on a normalization process applied to the DEM values from the original dataset. The normalization involved scaling the elevation values to fall within a standardized range, facilitating a clear distinction of the terrain into these four categories. Each zone represented a specific quartile of elevation values, encompassing the full spectrum of terrain variation within the study area. This approach ensured that the analysis covered a range of topographical features, from low- to high-elevation regions.

Figure 13 indicates that in the slight zone, the minimum elevation values reported for the original, ANUDEM, IDW, and NN models are −328, −327.94, −327.68, and −327.41, respectively. The proximity of these values to each other indicates a consistent performance across all models in capturing low-relief areas. However, the maximum elevation values reveal a different pattern, with the original model at 35 and the NN model peaking at 78.09, suggesting a variation in capturing the upper elevation range in low-relief areas. The average and StDev values, marginally different across the models, reflect a general consistency in representing this terrain category. The minimum and maximum elevation values in the medium zone exhibit a wider range across models, indicating a variation in capturing moderate relief features. The IDW model mainly shows a deviation with the lowest minimum (−7.70) and a high maximum (423.81) compared to the original model. This variation suggests that the IDW model can interpret medium relief areas with greater contrast than the original dataset, potentially impacting the interpretation of soil resources in these areas. The differences in elevation values become more pronounced among the models for high and very high relief areas. In the high zone, the maximum elevations range from 764 (original) to 783.13 (IDW), indicating a tendency for the IDW and NN models to slightly overestimate the highest elevations. The very high zone shows a similar trend, with the original model presenting the highest maximum elevation (1,129) and the ANUDEM model showing a lower maximum (1111.10). These variations can be crucial for understanding soil properties in steep terrain, where slight elevation changes can significantly affect soil formation and erosion processes.

Figure 13 Zonal analysis for the DEM surface of the investigated techniques.
Figure 13

Zonal analysis for the DEM surface of the investigated techniques.

Figure 14 illustrates the analysis of the RFI surfaces across the four terrain zones. In the slight zone, the minimum TRI values are relatively similar across all models, ranging from 0.099 to 0.353, indicating a uniform representation of low relief variability in all models. However, the maximum TRI values vary more significantly, with the original model at 4.77 and the ANUDEM and NN models showing a lower maximum (3.68 and 4.83, respectively). This discrepancy demonstrates that in areas of slight relief, the ANUDEM and NN models can underrepresent relief variations compared to the original dataset, impacting soil erosion risk assessment in these areas. For the medium relief zone, the TRI values again show noticeable differences. The original model’s average TRI value is higher (2.47) than ANUDEM and NN (2.05 and 1.83, respectively). This difference indicates that the original model can interpret medium relief areas as having more significant relief variations, which can be critical for understanding soil moisture retention and runoff patterns in these areas. In high and very high relief zones, the variations in TRI values become even more pronounced. For example, the original model’s average TRI in the very high zone is 2.08, while the ANUDEM and NN models report lower averages (1.78 and 1.57, respectively). This exhibits that the ANUDEM and NN models can underestimate the relief variability in steep terrain. Such underestimation can influence the understanding of soil formation processes and potential erosion risks in these areas, where relief plays a significant role in soil dynamics.

Figure 14 Zonal analysis for the RFI surface of the investigated techniques.
Figure 14

Zonal analysis for the RFI surface of the investigated techniques.

Table 1 compares the three investigated DEM interpolation methods across the slight, medium, high, and very high terrain zones. The study’s results bring to light the significant impact of DEM interpolation techniques on the accuracy of the RFI. Although most interpolation methods consistently capture primary topographic features, the RFI exhibits sensitivity to the choice of these methods. This finding is significant for soil resource management, where the RFI is a crucial indicator. The NN interpolation technique stands out for its superior performance in maintaining the accuracy and reliability of the RFI. This indicates that the NN method can be the most suitable choice for applications requiring precise measurement of secondary terrain variables, such as the RFI. The study’s zonal analysis highlights significant variations in RFI values across different terrain zones. All the DEM interpolation models (original, ANUDEM, IDW, and NN) exhibit a relatively consistent terrain representation in slight and medium relief areas. However, the differences become more pronounced in high and very high relief zones. In these areas, the choice of interpolation model can lead to variations in the representation of terrain features, affecting the accuracy of the RFI. These variations underscore the complex relationship between topography and soil characteristics, particularly in areas with diverse relief. For effective soil resource management, understanding these variations is crucial, as the accuracy of RFI data directly influences the assessment of soil quality, erosion potential, and land suitability for various uses.

Accordingly, the interpolation method plays a crucial role in the accuracy of DEMs, as different terrains and spatial structures can significantly influence the outcome of the interpolation process [32,59]. The NN interpolation method shows considerable robustness in maintaining high accuracy in RI calculations across diverse topographical zones. This is aligned with the findings of Habib [60], who observed that geostatistical methods such as NN tend to preserve topographical continuity and thus provide a more accurate depiction of relief characteristics. In contrast, the IDW method, while effective in specific contexts, showed a tendency to exaggerate elevation extremes, which can lead to discrepancies in RI values, particularly in zones with complex terrain structures. Salekin et al. [59] and Chen and Liu [61] support this observation, highlighting the sensitivity of IDW to spatial data distribution, which often results in variability when the data points are unevenly distributed. In addition, the ANUDEM method, known for its smoothing effects, tends to underrepresent smaller-scale topographical variations [62]. This can potentially lead to underestimations of the RI, particularly in areas where micro-relief features play a significant role in soil and environmental processes. However, the sensitivity of the RFI to different DEM interpolation techniques has considerable implications for soil resource management. The study reveals that the choice of interpolation technique can significantly influence the understanding of soil distribution, type, and erosion risk, particularly in regions with high relief variability. Accurate representation of terrain relief, as reflected in the RFI, is vital for assessing soil quality and determining appropriate land management strategies. Finally, this research demonstrates that while primary topographic features are generally well-captured by various DEM interpolation methods, the accurate calculation of secondary terrain variables, such as the RFI, is highly sensitive to these methods. This underscores the necessity for careful selection of interpolation techniques in terrain analysis, particularly for soil resource management and environmental planning. Future research should aim to evaluate the impact of these variations in RFI on practical soil management strategies and explore methods to optimize interpolation techniques for more accurate terrain analysis.

4 Conclusion

This study explores the critical role of DEM interpolation techniques in determining RFI as an essential factor in soil resource management. The comprehensive analysis underscores the differential impact of various interpolation methods, ANUDEM, IDW, and NN, on depicting topographical features and their subsequent influence on RFI calculations. In comparing these interpolation techniques against the original DEM, it was observed that while primary topographic features are generally well-replicated, the RFI is sensitive to the chosen interpolation method. Among the evaluated techniques, the NN interpolation method demonstrated superior efficacy in maintaining the accuracy and reliability of the RFI, establishing itself as a preferred choice for applications necessitating precise measurements of secondary terrain variables. The zonal analysis, which categorized terrain into slight, medium, high, and very high relief zones, further highlighted the complex interplay between topography and soil characteristics. It was indicated that all examined interpolation models exhibit consistent terrain representation in slight and medium relief areas. However, in high and very high relief zones, the selection of interpolation models led to significant variations in terrain representation, affecting the RFI’s accuracy. The sensitivity of the RFI to different DEM interpolation techniques has profound implications for soil resource management. The study reveals that the choice of interpolation technique significantly influences the understanding of soil distribution, type, and erosion risk, particularly in regions with substantial relief variability. An accurate representation of terrain relief, as reflected in the RFI, is vital for assessing soil quality and formulating appropriate land management strategies. Finally, while primary terrain features are generally accurately captured by various DEM interpolation methods, the precise calculation of secondary terrain variables, such as the RFI, is highly contingent on these methods. This finding emphasizes the importance of carefully selecting interpolation techniques in terrain analysis, especially for soil resource management and environmental planning. Future research should focus on evaluating the impact of these variations in RFI on practical soil management strategies and investigating methods to refine interpolation techniques for more accurate terrain analysis. The insights gained from this study significantly contribute to enhancing the understanding and management of soil resources, advancing environmental sustainability and agricultural productivity.

  1. Funding information: This research was supported by the Researchers Supporting Project number (RSP2024R296), King Saud University, Riyadh, Saudi Arabia.

  2. Author contributions: The authors confirm their contribution to the paper as follows: study conception and design: MH, BB, AA, and HB; analysis and interpretation of results: MH, BB, AA, and HB; draft manuscript preparation: MH and BB; manuscript review & editing: AA and HB. All authors reviewed the results and approved the final version of the manuscript.

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

  4. Data availability statement: Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

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Received: 2023-12-29
Revised: 2024-05-10
Accepted: 2024-06-24
Published Online: 2024-08-12

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  139. Special Issue: Natural Resources and Environmental Risks: Towards a Sustainable Future - Part I
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  141. Exploring environmental awareness, knowledge, and safety: A comparative study among students in Montenegro and North Macedonia
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  143. Application of remote sensing in monitoring land degradation: A case study of Stanari municipality (Bosnia and Herzegovina)
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  145. Assessing risk-prone areas in the Kratovska Reka catchment (North Macedonia) by integrating advanced geospatial analytics and flash flood potential index
  146. Analysis of the intensity of erosive processes and state of vegetation cover in the zone of influence of the Kolubara Mining Basin
  147. GIS-based spatial modeling of landslide susceptibility using BWM-LSI: A case study – city of Smederevo (Serbia)
  148. Geospatial modeling of wildfire susceptibility on a national scale in Montenegro: A comparative evaluation of F-AHP and FR methodologies
  149. Geosite assessment as the first step for the development of canyoning activities in North Montenegro
  150. Urban geoheritage and degradation risk assessment of the Sokograd fortress (Sokobanja, Eastern Serbia)
  151. Multi-hazard modeling of erosion and landslide susceptibility at the national scale in the example of North Macedonia
  152. Understanding seismic hazard resilience in Montenegro: A qualitative analysis of community preparedness and response capabilities
  153. Forest soil CO2 emission in Quercus robur level II monitoring site
  154. Characterization of glomalin proteins in soil: A potential indicator of erosion intensity
  155. Power of Terroir: Case study of Grašac at the Fruška Gora wine region (North Serbia)
  156. Special Issue: Geospatial and Environmental Dynamics - Part I
  157. Qualitative insights into cultural heritage protection in Serbia: Addressing legal and institutional gaps for disaster risk resilience
https://doi.org/10.1515/geo-2022-0667
Keywords for this article
DEM; spatial interpolation; relief index; IDW; natural neighbor; soil
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