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 GeoInformatics
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 highresolution global
slope frequency distribution hinders crossregional 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 slopefrequency 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 scaledependent 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
crossregional 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
Items

Description

Dataset full name

30
m resolution global land slope frequency distribution dataset

Dataset short name

LSF_Globe

Authors

Tang ling,
D47002019, Faculty of Land Resources Engineering, Kunming University of Science
and Technology, 799643248@qq.com
Ma jingwei, AAG37262019, Faculty of Land Resources Engineering, Kunming University of Science
and Technology, 359424547@qq.com
Shao zhiyi, AAG36332019, Faculty of Land Resources Engineering, Kunming University of Science
and Technology, 785383110@qq.com
Peng qiuzhi, AAG36292019, Faculty of Land Resources Engineering, Kunming University
of Science and Technology, pqz20002@163.com

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

Foundation(s)

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,
http://www.geodoi.ac.cn

Address

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 valueadded 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

DOI, DCI, CSCD,
WDS/ISC, GEOSS, China GEOSS

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
nearside 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 ith 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 frequencyslope 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
distribution.

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 (°)

Africa

6.25

5.38

South America

8.25

7.77

Asia

9.63

9.34

Oceania

5.23

5.31

Europe

7.70

6.98

Antarctica

13.53

15.86

North America

9.43

10.74

Earth

8.63

9.28

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 scaledependent 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 crossregion 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.
Acknowledgements
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.
References
[1]
Strahler A N. Quantitative
slope analysis[J]. Geological Society of
America Bulletin, 1956, 67(5): 571596.
[2] Sharpton V L , Head J W . Analysis of regional slope characteristics
on Venus and Earth[J]. Journal of Geophysical
Research: Solid Earth, 1985, 90(B5).
[3]
Aharonson O, Zuber M T, Neumann
G A, et al. Mars: Northern hemisphere slopes and slope distributions[J]. Geophysical Research Letters, 1998,
25(24): 44134416.
[4]
Thomson B J, Head III J W.
Utopia Basin, Mars: Characterization of topography and morphology and assessment
of the origin and evolution of basin internal structure [J]. Journal of Geophysical Research: Planets,
2001, 106(E10): 2320923230.
[5] Yan Y.Z. Research on lunar slope spectrum variations based on
digital elevation models [D]. Nanjing: Nanjing
Normal University, 2015.
[6] Montgomery D R. Slope distributions, threshold hillslopes, and
steadystate topography [J]. American
Journal of science, 2001, 301(45): 432454.
[7]
DiBiase R A, Heimsath A M,
Whipple K X. Hillslope response to tectonic forcing in threshold landscapes [J].
Earth Surface Processes and Landforms,
2012, 37(8): 855865.
[8]
Wolinsky M A, Pratson L F.
Constraints on landscape evolution from slope histograms [J]. Geology, 2005, 33(6): 477480.
[9]
Peng, Q., Tang, L., Chen, J. et
al. Study on the Evolution of Construction Land Slope Spectrum in Shenzhen
during 20002015[J]. Journal of Natural
Resources, 2018, 33(12): 22002212.
[10]
P. O'Neill M, Mark D M. On the
frequency distribution of land slope [J]. Earth
Surface Processes and Landforms, 1987, 12(2): 127136.
[11]
Tang G, Song X, Li F, et al.
Slope spectrum critical area and its spatial variation in the Loess Plateau of
China [J]. Journal of Geographical
Sciences, 2015, 25(12): 14521466.
[12]
Burbank D W, Leland J, Fielding
E, et al. Bedrock incision, rock uplift and threshold hillslopes in the
northwestern Himalaya s[J]. Nature,
1996, 379(6565): 505.
[13]
Iwahashi J, Watanabe S, Furuya
T. Mean slopeangle frequency distribution and size frequency distribution of
landslide masses in Higashikubiki area, Japan [J]. Geomorphology, 2003, 50(4): 349364.
[14]
Zhao S, Cheng W. Transitional
relation exploration for typical loess geomorphologic types based on slope
spectrum characteristics [J]. Earth
Surface Dynamics, 2014, 2(2): 433441.
[15]
Fielding E J, Burbank D W,
Duncan C C. Quantifying Slopes with Digital Elevation Models of the Verdugo
Hills, California: Effects of Resolution [J]. 1996.
[16] Tachikawa T, Hato M, Kaku M, et al. Characteristics of ASTER GDEM
version 2[C]//2011 IEEE international geoscience and remote sensing symposium.
IEEE, 2011: 36573660.
[17] Tang L., Ma J.W., Shao Z.Y., Peng Q.Z., Global Land Slope Frequency
Dataset [DB/OL].Global Change Data Repository, 2020. DOI: 10.3974/geodb.2020.02.02.V1.
[18] GCdataPR Editorial Office. GCdataPR Data Sharing Policy [OL]. DOI:
10.3974/dp.policy.2014.05 (Updated 2017).
[19] NASA; METI. ASTER GDEM v3.0, https://lpdaac.usgs.gov/
[20] Tachikawa, T.; Manabu, K.; Akira, I. ASTER GDEM Version 3 Validation
Report [Z]. NASA, 2015.
[21]
Guzzetti F, Ardizzone F,
Cardinali M, et al. Distribution of landslides in the Upper Tiber River basin,
central Italy[J]. Geomorphology, 2008, 96(12):0122.