Journal of Global Change Data & Discovery2020.4(1):33-39


Citation:Tang, L., Ma, J. W., Shao, Z. Y., et al.Global Land Slope Frequency Distribution 30 m Grid Dataset[J]. Journal of Global Change Data & Discovery,2020.4(1):33-39 .DOI: 10.3974/geodp.2020.01.05 .

DOI: 10

Global Land Slope Frequency Distribution 30 m
Grid Dataset

Tang, L.1  Ma, J. W.1  Shao, Z. Y.1  Peng, Q. Z.1,2*

1. Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming, China;

2. Surveying and Mapping Geo-Informatics Technology Research Center on Plateau Mountains of Yunnan Higher Education, Kunming, China



Abstract: Slope frequency distribution can quantitatively measure slope, which is an important factor in landform characterization. The absence of high-resolution global slope frequency distribution hinders cross-regional comparative analysis. Obtaining 30 m digital elevation models (DEMs) covering a large land area—ASTER GDEM v3.0—permits quantitative slope analysis of Earth’s surface at an unprecedented scale and resolution. We used the ArcGIS Slope and Int routine to obtain the integer slope data in 90 intervals and then calculated the slope frequency distribution for 3 statistic units: 1° (latitude) ×1° (longitude) grids, the 7 continents, and the globe. These areas are different in scale, climate, and tectonic history, but their slope distributions are consistently unimodal. The peak in each distribution appears before 5°. 50% of the total ground surface has a slope less than 5.5°, the land surface slope of Oceania is the most gentle (μ = 5.23°) with the most concentrated distribution (σ = 5.31°), and the ice sheet surface slope of Antarctica is the steepest (μ = 13.53°) with the most dispersed distribution (σ = 15.86°). The data include the land slope frequency distributions for 3 statistic units, 1° (latitude) ×1° (longitude) grid with 22205 data records in total, 7 continents, and the Earth in .xlsx format and the land slope frequency spatial distribution for the 1°x1° grids in .shp format. The dataset is consisted of 631 data files, with a size of 232 MB (compressed to 54.5 MB in one file).

Keywords: Globe; Land; Slope frequency distribution; ASTER GDEM grid

1 Introduction

Slope frequency distribution is the proportion of the total surface falling within certain slope classes, into which the total angular range of slope is subdivided [1]. Slope frequency distribution is a powerful tool for describing topography and has been successfully employed for analysis of planetary landforms [2][3][4][5], geologic hazards [6][7], and regional landscapes and geomorphology [8][9]. Slope frequency distribution can provide regional landform characteristics (e.g. the dominant slope angle) but is not easily comparable across regions. Hence, early studies focused on identification of transformations of slope data to normalized slope distributions[1,10]. Subsequent studies attempted to relate slope frequency distributions to landscape patterns[12–14]; however, regional slope analysis can only provide a reference for a single region because regional slope-frequency distributions show vastly different characteristics. Thus, it is necessary to establish a global benchmark for slope frequency distributions so that different studies can be compared.

Slope is a scale-dependent parameter that changes with digital elevation model (DEM) resolution. As such slope is not comparable between DEMs with different resolutions [15]. The first global land slope frequency distribution appeared in 1985 with a spatial resolution of 1° [2] and has been used to compare the global topographic characteristics of Venus and Earth. Subsequently, the prevalent resolution of global DEM data, which is easy to obtain, has been refined to 1” (about 30 m); however, no study has calculated a global slope distribution using 30 m DEM data. In this contribution, the ASTER GDEM v3.0 DEM which nearly covers Earth’s entire land surface at 30 m resolution [16], was used to calculate slope angle and generate a global land slope histogram, which can provide a reference for cross-regional slope analysis.

2 Metadata of Dataset

The metadata of global land slope frequency dataset [17] is summarized in Table 1. It includes the dataset full name, short name, authors, spatial resolution, data format, data size, data files, data publisher, and data sharing policy, et al.


Table 1  Summary of the global land slope frequency distribution dataset metadata



Dataset full name

30 m resolution global land slope frequency distribution dataset

Dataset short name



Tang ling, D-4700-2019, Faculty of Land Resources Engineering, Kunming University of Science and Technology,

Ma jingwei, AAG-3726-2019, Faculty of Land Resources Engineering, Kunming University of Science and Technology,

Shao zhiyi, AAG-3633-2019, Faculty of Land Resources Engineering, Kunming University of Science and Technology,

Peng qiuzhi, AAG-3629-2019, Faculty of Land Resources Engineering, Kunming University of Science and Technology,

Geographical region

The land surface from 83° north latitude to 83° south latitude.

Spatial resolution

30 m             Data format  .xlsx .shp          Data size   54.5MB

Data files

1°(latitude)´1°(longitude) grid land slope frequency distribution, 7 continents and global land slope frequency distributions


National Natural Science Foundation of China (41961039)

Computing environment

ArcGIS 10.2 (shared within the departmental research group)

Data publisher

Global Change Research Data Publishing & Repository,


No. 11A, Datun Road, Chaoyang District, Beijing 100101, China

Data sharing policy

Data from the Global Change Research Data Publishing & Repository includes metadata, datasets (data products), and publications (in this case, in the Journal of Global Change Data & Discovery). Data sharing policy includes: (1) Data are openly available and can be free downloaded via the Internet; (2) End users are encouraged to use Data subject to citation; (3) Users, who are by definition also value-added service providers, are welcome to redistribute Data subject to written permission from the GCdataPR Editorial Office and the issuance of a Data redistribution license; and (4) If Data are used to compile new datasets, the ‘ten per cent principal’ should be followed such that Data records utilized should not surpass 10% of the new dataset contents, while sources should be clearly noted in suitable places in the new dataset [18]

Communication and

searchable system


3 Methods

Slope data for slope frequency distribution analysis were computed using the 30 m ASTER GDEM v3.0 (GDEM v3) [19], which provides land surface coverage of Earth from 83°N to 83°S latitude with 22912 tiles. The elevation value of the ocean is 0 m which will influence the frequency value at 0° slope; hence, we use the 1:1,000,000 global base map data as a mask to remove the oceans from the GDEM v3. The global land slope frequency distribution dataset can be divided into three categories: 1° (latitude) × 1° (longitude) grid land slope frequency, 7 continents land slope frequency, and global land slope frequency.

3.1 Data Processing

The acquisition of slope frequency distribution data primarily required two steps: slope calculation and slope frequency calculation. Because the DEM dataset has 22912 scenes in total, the scene by scene calculation takes a long time and is prone to errors; hence, a Python (v2.7.0, Guido van Rossum, 2010) script was compiled to automate the calculate process.



Figure 1  Flowchart of the dataset processing


The projected coordinate system used in this study is the World Vertical Perspective (WVP), which has a vertical near-side perspective. The view height of WVP is 35800 km above the surface, just like viewing from geosynchronous satellite. Because of minimal distortion near the center and maximum distortion near the edge, during projection, we take the center of each 1° × 1° grid as the observation center to ensure the smallest distortion of each tile (i.e. distortion is controlled within the range of one tile). To obtain land slope frequency distributions, we first reprojected the DEM and 1:1,000,000 global base map data from WGS 1984 to WVP, and then used the ArcGIS Slope and Int routine to obtain the integer slope data. Finally we used the 1:1,000,000 global base maps as mask to remove the oceans from the slope dataset and calculated the land ratio for each 1° × 1° grid.

4 Results and Validation

4.1 Data Composition

This global dataset was processed on a PC for about 120 hours, which is equipped with a single core 2.66GHz four core 8 thread CPU, 16GB memory, and 5 independent hard disks for parallel reading and writing. Results of this data include one excel file with 2 sheets and 90 vector files. All shapefiles are provided in the WGS84 geographic coordinate system and showed the 1° × 1° grid land slope frequency spatial distribution in .shp format. An excel file was created with land slope frequency distributions using 3 statistic units: 1° × 1° grid, each continent, and the globe. 707 DEM tiles contain little or no data after the oceans were removed; hence, we excluded these tiles from the dataset. The 1° × 1° grid land slope frequency data contain 22205 records rather than 22912 records, which is the total number of DEM tiles. In this paper the slope angle interval is 1°, hence the slope value range of [0°, 90°) is divided into 90 sections (i.e. each slope frequency data contains 90 frequency values). In the excel file, the median slope value of each class is used to represent the individual slope class, that is, (i+0.5)° is used to represent the i-th slope section, and the range of this section is [i°, (i+1)°), i = 0, 1, 2, … 89.

4.2 Data Products

We chose 8 1° × 1° grids located in various typical relief regions, such as the Tibet Plateau, Kazak hills, Alps, Rockies, Amazon plain, Sahara desert, central plain of Oceania, and Antarctic glaciers, which respectively correspond to the figure numbers N33E086, N47E066, N47E012, N53W118, S03W066, N13E003, S30E141, and S77E014 (Figure 2). The slope frequency distribution of each grid is similar to that of the continent where it is located. The change in frequency-slope trend firstly increases and then decreases, except for the Alps and Antarctic glaciers. Results show that the land slope frequency distribution for different landforms may be similar, and the shape of frequency curve is mostly unimodal with a long tail and right skewness.



Figure 2  Global land slope map, and slope frequency distributions in each continent, the Earth, and typical geomorphic regions, which noted as 1° (latitude) ×1° (longitude) grid.


Figure 3  Box chart of 22205 DEM tiles slope frequency


The land slope distributions of the 22205 1° by 1° grids are summarized in Figure 3, where the 1st percentile was used to replace the minimum value, and the 99th percentile was used to replace the maximum value, to avoid the influence of extreme values. The frequency value corresponding to the 99th percentile of 0.5° is 74.26%. From the box chart (Figure 3) and the land slope frequency distributions of each continent and the entire globe (Figure 2), we found the frequency values are all increasing to the maximum before 5°, and then rapidly decrease with increasing slope after the peak. 50% of the total land surface has a slope less than 5.5° (Figures 2 and 4). The ground in Oceania is the flattest (μ = 5.23°) with the most concentrated distribution (σ = 5.31°). 76% of the Oceanian ground has a slope steeper than 6° (Figure 4, Table 2). The ice sheet in Antarctica has the steepest slope (μ = 13.53°) with the most scattered distribution (σ = 15.86°, Figure 4,). 60% of the Antarctic land surface has a slope less than 7° (Table 2).

4.3 Data Validation

Figure 4  Cumulative frequency distributions of slope in 7 continents and the total Earth land surface.

Slope frequency distribution is a quantitative analytical tool for slope analysis. However slope accuracy depends on the DEM data. The ASTER GDEM v3.0 data were created from the automated processing of the entire ASTER Level 1A archive of scenes acquired between March 1, 2000, and November 30, 2013. The ASTER GDEM Version 3 data products offer substantial improvement over the Version 2 products [19]. Although some relief changes during the data acquisition time span, on a global scale the impact of these local topographic changes can be ignored. Figure 2 shows that Antarctica and Greenland have high ground surface slope. Because ice and snow covered areas have high optical reflectivity, stereo correlation was used to produce the ASTER DEM. Therefore, DEM data in this area have poor quality and so do the slope frequency distribution data. We suggest that the slope frequency distribution data for Antarctica and Greenland in this data set be avoided in subsequent research.

Table 2  Land slope frequency distribution for different statistic units

Statistic unit

Mean Value

μ (°)

Standard deviation

σ (°)

Statistic unit

Mean Value

μ (°)

Standard deviation

σ (°)




South America















North America






5 Discussion and Conclusion


Figure 5  Slope frequency distributions from previous studies (black) and a global land slope distribution (red). 1—Lucore hollow an mature basin [1]; 2—the Northwestern Himalayas [12]; 3—wash number is 4mm/yr throughout the continental United States [8]; 4—wash number is 8mm/yr throughout the continental United States [8]; 5—wash number is 16mm/yr throughout the continental United States [8]; 6—landslide areas in Upper Tiber River basin [21].

Slope studies suggest that slope frequency distributions vary between study areas and are also associated with the size and landforms of study areas [1][8][12][21]. Slope distributions significantly vary (black dash line, Figure 5); hence, we can neither compare across regions, nor compare with statistical models. However if compared with a global land slope frequency distribution (red dash line, Figure 5), we can easily and quantitatively describe ground slope in a global uniform context. For example, the peak slope of curve 6 in Figure 5 is the closest to the global land peak slope, indicating that the terrain slope of the study area is relatively gentle. Similarly, the terrain slope of the study area represented by curve 5 is the most rugged.

Slope is a strong scale-dependent parameter that cannot be compared across different DEM resolutions. To date few studies of global slope frequency distribution have been conducted at high resolution. As a useful parameter in earth sciences, which can provide quantitative characteristics for describing ground surfaces, it is essential for the global slope frequency distribution to match the common 30 m DEM resolution. 30 m is one of the common free DEM resolutions. The slope frequency distribution generated from ASTER GDEM v3.0 can provide a global reference for slope frequency analysis (e.g. landslide, geomorphic). This dataset includes land slope frequency distributions for 3 statistical units: 1° (latitude) ´ 1° (longitude) grids, the 7 continents, and the entire globe, that enrich regional and global benchmarks. We hope this suite of land slope frequency distributions will facilitate future quantitative cross-region slope analysis at the 30 m resolution. Because slope frequency distribution data might vary for different DEMs generated from different data sources, this data set can only be used as reference for studies based on GDEM v3.0 data.

Author Contributions

Qiuzhi Peng designed the dataset processing. Ling Tang and Jingwei Ma designed the algorithms for the dataset. Jingwei Ma and Zhiyi Shao contributed to the data processing and analysis. Ling Tang wrote the paper.


We thank Ling Peng, Jiamei Wu for their help in collecting the data and literature. We are appreciative of Jiacheng Li for his help with the figures.


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Institute of Geographic Sciences and Natural Resources Research,Chinese Academy of Sciences

The Geographical Society of China


Committee on Data for Science and Technology (CODATA) Task Group on Preservation of and Access to Scientific and Technical Data in/for/with Developing Countries (PASTD)

Jomo Kenyatta University of Agriculture and Technology

Digital Linchao GeoMuseum