Effects of DEM overlapping distance on hydrological analysis

Abstract

Keywords: DEM; hydrological analysis; hori-zontal and vertical positional ac-curacies; geomorphometric para-meters; topographic parameters.

Introduction

The process of collecting land surface elevation data is essentially a sampling process because it is not possible to record all points on the Earth’s surface. There are two sampling approaches as systematic and adaptive. In the systematic approach, elevation points are measured at regular intervals. The final product is a matrix containing elevation values and is often called a Digital Elevation Model (DEM) and is used widely in many studies such as hydrological analysis in Geographic Information Systems (GIS).

There are three main data sources for DEMs: measurement of point coordinates (latitude, longitude, and elevation or x, y, z values) by geodetic methods, contours from printed topographic maps if vector datasets are not available, digitization of features such as streams, lakes, etc., and interpretation of image data obtained from aircraft or satellite platforms [1]. When deriving DEMs from topographic maps, in cases where the volume of data used is much higher than the data processing capacity of the GIS tool, DEMs are derived on a map basis and then merged to obtain the DEM mo-

*Corresponding author. *E-mail address: gokgoz@yildiz.edu.tr Published by Yıldız Technical University, İstanbul, Türkiye This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

saic of the study area. However, when DEMs are derived on a map basis and these DEMs are merged, the problem of edge effects, in other words, elevation errors along the DEM boundaries, occurs. The process of deriving DEMs from topographic maps is essentially an interpolation process since the elevation values of DEM cells are calculated by interpolation from the topography and hydrography data given as input. The effect of the interpolation process increases towards the boundaries. For this reason, it is best to merge the overlapping DEMs, i.e. DEMs with common areas along their boundaries. Common areas can be formed by expanding the original map boundaries by a certain amount [2]. Ozulu and Gökgöz investigated the problem of edge effects that occur in DEMs derived from 1:25,000 scale topographic data on a map basis and suggested that as a solution, DEMs should be derived from topographic data in the map boundaries expanded by 6000 m in each direction and these DEMs should be clipped based on the map boundaries expanded by 3000 m in each direction [3]. Six more analyses were conducted by Ozulu to identify whether the 6000 m and 3000 m overlapping distances were appropriate. The boundaries of two 1:25,000 scale topographic maps were expanded by 1000 m each time to create 12 novel map boundaries; the map boundaries, including the common boundary of the two maps, were converted into a line feature, and then each line feature was expanded by 100 m to have 13 test areas. DEMs were derived at the original boundaries, 3000 m expanded boundaries, and 6000 m expanded boundaries, and the DEMs derived at the 3000 m expanded map boundaries were merged. A point feature was created at the centre of each DEM cell in the test areas, the value of each DEM cell was assigned to the point feature created at the centre of that cell, and thus a series of test points known with their locations and elevations were obtained in each test area. The elevation differences calculated at the test points in each test area were examined and the average elevation error in each test area was calculated. As a result, it was found that producing DEMs by expanding the original map boundaries by 6000 m and merging these DEMs after clipping them based on the original map boundaries expanded by 3000 m a) increased the number of points with elevation difference less than 10 cm, b) decreased the number of points with elevation difference greater than 3 m, c) decreased the number of points with elevation difference greater than 5 m and d) reduced the mean elevation error, thus confirming the suitability of the 6000 m and 3000 m distances [4]. In previous studies conducted in the literature, DEMs were generally derived from remote sensing data, and the width of the common areas (overlapping distance) was determined depending on various factors (purpose of the study, data sources, DEM resolution, shape and size of the

study area, etc.) such as a) number of cells [5], b) distance [6-9] and c) percentage [10-16]. This study aimed to determine the effects of DEM overlapping distance on hydrological analysis. To this end, hydrological analyses were carried out on DEM mosaics obtained with 0, 1000, 2000, 3000, 4000, 5000 and 6000 m overlapping DEMs derived from 1:25,000 scale topographic map data; drainage networks and basin boundaries were derived; horizontal and vertical positional errors of the basins, and various geomorphometric and topographic parameters were calculated.

Study AREA And Data

The study area is the first level sub-basin number 2 of the Western Mediterranean Basin, which is one of the 25 basins located in Turkey (Fig. 1 and 2). The Western Mediterranean Basin is approximately 20,332 km2 in the mid-latitude zone (between latitudes 36.13° and 37.67°) with an east-west extension (between longitudes 27.23° and 30.59°). The study area is 1,131 km2. The elevation (contour and elevation point) and hydrography (intermittent stream, perennial stream, channel, lake, coastline) data from TOPO25 databases that were produced by the General Directorate of Mapping (GDM) were used in this study (Fig. 3). These were vector data in 3D point and line geometry types. The main contour interval was 10 m, and the vertical positional (elevation) accuracy

Derivation Of Digital Elevation Models

Figure 3. Contour, elevation point, intermittent stream, perennial stream, and lake data from TOPO25 database belonging to a small area. was ±3 m at 95% confidence level. The horizontal (planimetric) and vertical (elevation) positional accuracies of the hydrography data were ±4 m and ±3 m, respectively, at 95% confidence level [17-19]. These data originally positioned in the geographic coordinate system were repositioned in the Albers equal-area conic projection by Gökgöz et al. with the idea that length and area information are more important than angle (shape) information for hydrological analyses (Table 1). Also, by using the existing GIS tools and special AutoLISP scripts, various geometric and topological errors were removed, i.e. the data was cleaned, and a merged database with six feature classes was formed [17].

Firstly, from the map-based data in the TOPO25 database, non-overlapping DEMs were derived at the original map boundaries by using the ArcGIS/TopoToRaster tool. In this tool, the interpolation method developed by Hutchinson [20] based on the “discretized thin plate spline technique” is employed. In this method, although the primary input data is the contours, additional elevation and hydrography data are also used to adjust the elevations of DEM points corresponding to drainage lines while removing spurious pits. For this reason, the DEM obtained with this method is called “hydrologically corrected DEM”. Thus, it is possible to derive drainage networks in continuous form. The 17 non-overlapping DEMs obtained in this way were merged by using the ArcGIS/Mosaic tool to obtain a DEM mosaic (DEM0) (Figs. 4 and 5). DEM mosaics of overlapping DEMs were obtained through the following four steps. Step 1: The original map boundaries were expanded by 1000, 2000, 3000, 4000, 5000 and 6000 m (Fig. 6). Step 2: The data in the merged database were clipped based on the 6000 m expanded boundaries, and 6000 m overlapping DEMs were derived from these data. The values of the “Output Extent” parameter of the ArcGIS/TopoToRaster tool were determined to be multiples of 10 meters and did not go outside the DEM boundaries because when these values are determined automatically based on the DEM boundaries, they are not multiples of 10 meters, which causes the formation of residual cells along the DEM boundaries and inconsistencies in terms of alignment between neighbouring DEM cells (Fig. 7).

Table 1. Projection and reference coordinate system parameters Projection

Step 3: 6000 m overlapping DEMs were clipped based on 1000, 2000, 3000, 4000 and 5000 m expanded boundaries, and 1000, 2000, 3000, 4000 and 5000 m overlapping DEMs were obtained. Step 4: 1000, 2000, 3000, 4000, 5000 and 6000 m overlapping DEMs were merged to obtain 1000, 2000, 3000, 4000, 5000, and 6000 m DEM mosaics (DEM1000, DEM2000, DEM3000, DEM4000, DEM5000 and DEM6000) respectively (Figs. 8-13). When merging the overlapping DEMs by using the ArcGIS/Mosaic tool, “Mean” was selected for the “Mosaic Operator” parameter, in other words, the elevation value of each cell in the overlapping area was calculated as the arithmetic average of the elevation values of two cells at the same location in the overlapping DEMs. HYDROLOGICAL ANALYSES: DERIVATION OF

Drainage Lines And Basin Boundaries

Basin boundaries are mainly derived from a DEM over the following steps [21, 22]: • Filling the sinks, • Determining the flow directions, • Calculating the flow accumulation values, and • Deriving the drainage networks and determining the basin boundaries based on the flow accumulation values. The process of deriving drainage lines and basin boundaries was performed with the ArcGIS/ArcHydro tool in accordance with the flow chart in Figure 14. As the stream threshold, 1% of the maximum flow accumulation value, which is also offered to the user by the “Stream Definition”

Figure 7. The alignment mismatch problem between neighbouring DEM cells [17].

tool, was used [23]. All the derived drainage networks are shown in Figure 15 in a superimposed manner. To indicate the geometric differences, the drainage networks in the region depicted by a red rectangle in Figure 15 are shown in Figure 16 at larger scale. The geometric characteristics of the drainage networks are given in Table 2 as well.

As a result, it is seen that the DEM cell elevations change depending on the overlapping distances and for this reason, the geometric characteristics of the derived drainage networks are different. However, no direct or inversely proportional relationship can be established between the overlapping distance and the number of drainage lines and the

Figure 13. DEM mosaic of 6000 m overlapping DEMs (DEM6000). total drainage length: while the overlapping distance increases linearly, the number of drainage lines and the total drainage length neither increase nor decrease linearly. The smallest number of drainage lines is derived from DEM0, DEM3000 and DEM4000; the average number of drainage lines is derived from DEM1000, DEM2000 and DEM5000; the highest number of drainage lines is derived from DEM6000. The shortest drainage network is derived from DEM1000; the drainage network with the closest length to the average is derived from DEM5000; the longest drainage network is derived from DEM6000. The flow chart of deriving the basin boundaries is given in Figure 17. All the derived basin boundaries are shown in Figure 18 in a superimposed manner. To indicate the geometric differences, the basin boundaries in the region depicted by a red rectangle in Figure 18 are shown in Figure 19 at larger scale. The geometric characteristics of the basins are given in Table 3 as well. As a result, since the derived drainage networks are different, the basin boundaries are also different, and this is an expected situation. However, it cannot be argued that there is neither a direct nor an inversely proportional relationship between the overlapping distance and the basin boundary length and area: while the overlapping distance increases linearly, the basin boundary length and area neither increase nor decrease linearly. The shortest basin boundary is derived from DEM6000, the longest basin boundary is derived from DEM0 and DEM4000, and the basin boundary with the closest length to the average is derived from DEM3000. Based on the basin areas, the smallest basin is derived from DEM3000, the largest

Figure 14. Derivation of drainage lines. basin is derived from DEM1000, and the basin with the closest area to the average is derived from DEM5000. There is no relationship between the basin boundary length and the basin area. As the basin boundary length increases, the basin area may decrease and vice versa. This situation is natural and depends on the number and length of convex and concave shapes occurring along the basin boundary. If the number and length of concave shapes increase, the area decreases (Fig. 20).

Table 2. Geometric characteristics of the drainage networks DEM

For example, the boundary length of the basin derived from DEM1000 is smaller than the boundary length of the basin derived from DEM0, but the area of the basin derived from DEM1000 is larger than the area of the basin derived from DEM0, which means that there are more concave shapes along the boundary of the basin derived from DEM0. For this reason, only a relative assessment can be made by comparing the boundary lengths and areas of the basins. To make an absolute assessment, a basin boundary that can be considered as “ground truth” is needed. In this study, the basin drawn in three dimensions on stereo models by an experienced operator working in GDM was accepted as the “ground truth” and was mentioned as basinGDM (Fig. 21). In this context, it is understood that basin6000 is closer to the basinGDM in terms of border length and basin3000 in terms of area (Table 3).

Effects Of DEM Overlapping Distance

The horizontal root mean square errors (RMSE) of the basin boundaries were calculated to determine the effects of DEM overlapping distance on the horizontal positional accuracies of the basins, and the vertical (elevation) RMSEs of the DEMs from which the basin boundaries were derived were calculated to determine the effects of DEM overlapping distance on the vertical positional accuracies of the basins. Also, various geomorphometric and topographic parameters were calculated to determine the geomorphometric and topographic effects of DEM overlapping distances. Horizontal Positional Accuracies of the Basins To determine the effects of DEM overlapping distance on the horizontal positional accuracies of the basins, the horizontal RMSEs of the basin0, basin1000, basin2000, ba-

Figure 19. Geometric differences in basin boundaries. Table 3. Geometric characteristics of basin boundaries Basin

Figure 18. Basin boundaries derived from DEM mosaics. sin3000, basin4000, basin5000 and basin6000 concerning the ground truth basin (basinGDM) were calculated by using the following equation. (1) In this equation, di is the horizontal positional difference between each point (measurement point) of the ground truth basin boundary and the derived basin (basin0, basin1000,

basin2000, basin3000, basin4000, basin5000 and basin6000) boundary; n is the number of measurement (horizontal distance) or measurement points. The horizontal positional differences (di) were measured in the AutoCAD environment by using a script, which was written with AutoLISP, the macro programming language of AutoCAD, and print on an Excel page. The horizontal RMSEs (ml) were calculated in Excel with these measurements. The horizontal RMSEs are given in Table 4. As a result, basin0, basin3000 and basin6000 gave the smallest values (233.56 m) in terms of horizontal positional difference, and basin0 and basin3000 gave the smallest values (16.26 m) in terms of horizontal positional error. In this context, it can be argued that basin0 and basin3000 are the closest basins to the ground truth (basinGDM) in terms of horizontal positional error.

Figure 21. Ground truth for the basin boundary (basinGDM). Vertical Positional Accuracies of the Basins When calculating the horizontal RMSEs of the basins, point features are created at the junctions (vertices) of consecutive line segments of basinGDM boundary (the ground truth) and if more than one point is created at a junction, all but one are deleted. Since the basinGDM boundary is three-dimensional, these points are also three-dimensional. In the calculation of the vertical (elevation) RMSE of a derived basin using the following equation, the elevations of these points are accepted as “ground truth values”, and the values of the cells corresponding to these points in the DEM from which the basin was derived (on which these points are located) are accepted as “measurements”.

Conclusion

To determine the effects of DEM overlapping distance on hydrological analysis, drainage networks and basin boundaries were derived in this study by performing hydrological analyses on DEM mosaics of 0, 1000, 2000, 3000, 4000, 5000, and 6000 m overlapping DEMs derived from 1:25,000 scale topographic map data, and various geomorphometric and topographic parameters were calculated along with horizontal and vertical positional accuracies of the basins. The results could be evaluated as follows. • The derived drainage networks were different.

Table 7. Geomorphometric parameters of the basins Parameters Basin 0

Table 8. Topographic parameters [27] Name/Description Length of the main flow path Shape factor Bifurcation ratio Drainage frequency Harmonic slope

The slope of the part-i of the main flow path divided into Elevation difference along the part-i; ∆u: Length of each part]

eem=Uem⁄Rb (eem: Slope of the main flow path; Rb: Basin relief [m])

Table 9. Topographic parameters of the basins Parameters Basin 0

There was no relationship between the overlapping distance, the number of drainage lines and the total drainage length. There was no relationship between the overlapping distance and the basin boundary length and area. The horizontal positional accuracies of the basins derived from DEM mosaics of non-overlapping and 3000 m overlapping DEMs were higher than the others. Although the vertical positional error of the six basins was the same, the vertical positional error of the basin

derived from the DEM mosaic of 4000 m overlapping DEMs was 0.01 m smaller. For this reason, it could be assumed that the vertical positional accuracies of all basins are almost the same. The drainage density, ruggedness and slope characteristics of all basins were the same, but the topographic parameter values were different, except for the harmonic slope. In conclusion, it can be argued that DEM overlapping

distances have an impact on the geometries of the derived drainage networks and basin boundaries and, in this context, the horizontal positional accuracies of the basins and the geomorphometric and topographic parameters but does not affect the vertical positional accuracies.

Acknowledgments

The present study was supported by the Scientific and Technological Research Council of Türkiye (TUBITAK) under project number 115Y411 and by the General Directorate of Mapping under project number 1912310112.

Authorship Contributions

Concept: Türkay Gökgöz, Design: Türkay Gökgöz, Supervision: Türkay Gökgöz, Data: Burak Balıkcı and Türkay Gökgöz, Analysis: Burak Balıkcı and Türkay Gökgöz, Literature search: Burak Balıkcı and Türkay Gökgöz, Writing: Türkay Gökgöz and Burak Balıkcı, Critical revision: Türkay Gökgöz.

Data Availability Statement

The published publication includes all graphics and data collected or developed during the study or the projects mentioned above.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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