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Journal of Geographical Sciences >

2022 , Vol. 32 >Issue 11: 2365 - 2378

DOI: https://doi.org/10.1007/s11442-022-2052-z

Research Articles

Morphological differentiation characteristics and classification criteria of lunar surface relief amplitude

  • DENG Jiayin , 1, 2 ,
  • CHENG Weiming , 1, 2, 3, * ,
  • LIU Qiangyi 1, 2 ,
  • JIAO Yimeng 1, 2 ,
  • LIU Jianzhong 2, 3, 4
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  • 1. State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
  • 2. University of Chinese Academy of Sciences, Beijing 100049, China
  • 3. CAS Center for Excellence in Comparative Planetology, Hefei 230052, China
  • 4. Lunar and Planetary Science Research Center, Institute of Geochemistry, CAS, Guiyang 550002, China
*Cheng Weiming, PhD and Professor, E-mail:

Deng Jiayin, PhD Candidate, specialized in digital geomorphologic analysis. E-mail:

Received date: 2022-07-10

  Accepted date: 2022-08-22

  Online published: 2022-11-25

Supported by

Strategic Priority Research Program of the Chinese Academy of Sciences(XDB41000000)

National Natural Science Foundation of China(42130110)

National Natural Science Foundation of China(41571388)

Key Project of National Basic Work of Science and Technology(2015FY210500)

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Abstract

Lunar landforms are the results of geological and geomorphic processes on the lunar surface. It is very important to identify the types of lunar landforms. Geomorphology is the scientific study of the origin and evolution of morphological landforms on planetary surfaces. Elevation and relief amplitude are the most commonly used geomorphic indices in geomorphological classification studies. Previous studies have determined the elevation classification criteria of the lunar surface. In this paper, we focus on the classification criteria of the topographic relief amplitude of the lunar surface. To estimate the optimal window for calculating the relief amplitude of the lunar surface, we use the mean change-point method based on LOLA (Lunar Orbiter Laser Altimeter) Digital Elevation Model (DEM) data and SLDEM2015 DEM data combining observations from LOLA and SELenological and Engineering Explorer Terrain Camera (SELENE TC). The classification criterion of the lunar surface relief amplitude is then determined according to the statistical analysis of basic lunar landforms. Taking the topographic relief amplitudes of 100 m, 200 m, 300 m, 700 m, 1500 m and 2500 m as thresholds, the lunar surface is divided into seven geomorphic types, including minor microrelief plains (< 100 m), minor microrelief platforms [100 m, 200 m), microrelief landforms [200 m, 300 m), small relief landforms [300 m, 700 m), medium relief landforms [700 m, 1500 m), large relief landforms [1500 m, 2500 m) and extremely large relief landforms (≥ 2500 m). The minor microrelief plains are mainly distributed in the maria and the basalt filled floors of craters and basins, while the minor microrelief platforms are mainly in the transition regions between the maria and highlands. The microrelief landforms are mainly located in regions with relatively high topography, such as wrinkle ridges and sinuous rilles in the mare. The small relief landforms are mainly scattered in the central peak and floor fractures of craters. The medium relief landforms are mainly distributed in the transition regions between crater floors and crater walls, between crater walls and crater rims, between basin floors and basin walls, and between basin walls and basin rims. Large and extremely large relief landforms are mainly found along crater walls and basin walls. The classification criteria determination for assessing lunar surface relief amplitude described in this paper can provide important references for the construction of digital lunar surface geomorphology classification schemes.

Key words： lunar geomorphological classification schemes; morphometric features; lunar relief amplitude; characteristics analysis; classification criterion

Cite this article

DENG Jiayin , CHENG Weiming , LIU Qiangyi , JIAO Yimeng , LIU Jianzhong . Morphological differentiation characteristics and classification criteria of lunar surface relief amplitude[J]. Journal of Geographical Sciences, 2022 , 32(11) : 2365 -2378 . DOI: 10.1007/s11442-022-2052-z

1 Introduction

Lunar orbit exploration activities have acquired a large amount of high-resolution remote sensing data that provide the possibility for studying the origin of the moon and the evolutionary history of lunar landforms (Wilhelms et al., 1987; Ouyang, 2004). Lunar landforms are the result of geological and geomorphic processes occurring on the lunar surface and are driven by internal and external forces. The study of lunar landforms can help to understand lunar geological features, magmatic activities, and provide essential and fundamental information for future lunar exploration, including landing site selection (Ouyang, 2005). In addition, the digital study of lunar landform types is one of the basic scientific concerns in lunar geomorphology research, as well as one of the fundamental and key scientific issues in lunar geomorphological mapping (Cheng et al., 2018).
The study of lunar geomorphology is younger than that of research into the Earth’s geomorphology. Wang et al. (2017) proposed an automatic classification method of lunar geomorphology based on the Iterative Self Organizing Data Analysis Technique Algorithm (ISODATA) by using three topographic indices, including elevation, slope, and relief amplitude. This method mainly uses the similarity principle for clustering to achieve automatic segmentation of lunar topography units. However, the classification results of different regions have obvious differences, and there are no unified classification criteria for the entire lunar surface. Cheng et al. (2018) proposed a multilevel classification method of lunar landform types considering morphological and chronological characteristics, thus providing an important reference for the classification of lunar landforms. The classification methods of lunar topography and landforms consider morphological characteristics, mineral composition, and geological ages as the classification indices, but there is a lack of quantitative standards for topographic indicators such as elevation and relief amplitude.
Geomorphology is the science that studies the morphology and genesis of landforms. Elevation and relief amplitude are the most basic geomorphological indicators used to describe landforms. When geomorphologists conduct research on 1:1 million geomorphological maps in China, they mainly adopt classification schemes based on landform elements such as morphology, origin, mineral composition, and age and develop cartographic norms. The terrain of China can be considered akin to the rungs of a ladder. From the three-step characteristics of China, the elevations of landforms can be classified into low elevation, medium elevation, high elevation and extremely high elevation, forming a four-level classification scheme representing the elevations of landforms. In addition, the land of China can be divided into 7 basic types according to the relief amplitude: plains, platforms, hills, small relief landforms, medium relief landforms, large relief landforms and extremely large relief landforms. This classification scheme of morphological types based on the elevation and relief amplitude has become consistent across China (Research, 1987; Li and Li, 1994; Li et al., 2008).
Geomorphometry is a quantitative research method used to describe geomorphological features using numerical values. The main morphological indicators include the altitude, slope, and degree of land damage. There are no complex atmospheric systems, liquid water sources or human activities on the moon, thus, there are no landforms produces by related series of external dynamics, such as deposition, transportation, or erosion. Impact events and magmatic activities play significant roles in shaping lunar landforms, so there is no index of damage to lunar surface in the morphometry of lunar landforms. The altitude index is divided into absolute altitude and relative altitude, that is, elevation and relief amplitude. Liu et al. (2021) proposed four thresholds of -2500 m, -1500 m, 1000 m and 3000 m as the classification criteria in the lunar morphological classification scheme. Thus, the lunar surface can be divided into five geomorphic types: extremely low altitude, low altitude, medium altitude, high altitude and extremely high altitude (Liu et al., 2021). The results of this classification scheme are consistent with the boundaries of the three types of lunar crustal terrane to some extent.
The relief amplitude is another important index used to describe lunar landforms. In this paper, we quantitatively study the classification criteria of the relief amplitude, analyze the lunar digital elevation model (DEM) by means of the mean change-point method, determine the best window for calculating the relief amplitude, and analyze the characteristics of the lunar relief amplitude.

2 Datasets

To date, the most direct way to obtain planetary topography is by using a laser altimeter to regularly send laser pulses from orbit and receive regularly returned pulses (Cavanaugh et al., 2007; David E Smith et al., 2001; 2010). The Lunar Orbiter Laser Altimeter (LOLA) is a multibeam Laser Altimeter aboard the Lunar Reconnaissance Orbiter (LRO) with a wavelength of 1064.4 nm and a frequency of 28 Hz. The digital elevation model (DEM) it produced was created by more than 6.5 billion measurements gathered by the Lunar Orbiter Laser Altimeter. LOLA offers highly accurate global coverage with a vertical precision of ~10 cm and an accuracy of ~1 m (Mazarico et al., 2012; David E. Smith et al., 2010). The resolution of LOLA is approximately 118 meters per pixel. The Kaguya teams combined LOLA and the SELENE TC data to generate higher-resolution DEM data, named SLDEM2015 (Barker et al., 2016). The SLDEM covers latitudes within ±60° with a horizontal resolution of ~59 meters per pixel and a vertical accuracy of ~3 to 4 m. Considering the data resolution and the data size of subsequent data processing, this paper uses the DEM generated by LOLA (Figure 1) to study the classification criteria of lunar relief amplitude. The higher-resolution SLDEM data were used to verify the optimum ranges of the lunar relief amplitude calculated from the LOLA DEM. The data were downloaded from https://planetarymaps.usgs.gov/mosaic/Lunar_LRO_LOLA_Global_LDEM_118m_Mar2014.tif and https://astrogeology.usgs.gov/search/map/Moon/LRO/LOLA/Lunar_LRO_LOLAKaguya_DEMmerge_60N60S_512ppd. Due to data size limitations, the SLDEM data of LQ18 were used to verify the optimal lunar relief amplitude window. LQ18 is located in the transition region between the mare and highland (Figure 1).
Figure 1 Topography map of the lunar surface LOLA DEM data and SLDEM data

3 Methodology

The relief amplitude is the elevation difference within a given region, and this variable changes with the size of the study area, i.e., the calculation window, and has a certain dependence on scale. The primary task for determining the optimal criteria for classifying lunar relief amplitude is to obtain the best window for calculating the relief amplitude to adequately reflect lunar landforms. The neighborhood analysis principle is used to calculate the statistics in the specified neighborhood around the input pixel. Analysis windows mainly include rectangular windows, circular windows, annular windows, and fan-shaped windows. Considering that craters are the most common type of lunar landform, a circular window, rather than a rectangular one, is used herein to determine the best calculation window for the lunar relief amplitude.
The mean change-point method is commonly used in statistics and is likewise commonly used to determine the best relief amplitude window in geomorphic classification studies (Han et al., 2012). The basic principle of mean change-point analysis is that the existence of change points increases the gap between the original sample statistic X and the sample statistic Si after segmentation. In this paper, the mean change-point method is used to determine the optimal window size for studying lunar relief amplitude. First, the average relief amplitude per unit area obtained under differently sized analysis windows is calculated. Next, the sample sequence (RAS) is derived by taking the logarithm of those averages. Then, the sample is divided into two subsamples: RAS1, RAS2, …, RASi and RASi+1, RASi+2, …, RASN. The mean arithmetic values ${{\bar{X}}_{i1}}$ and ${{\bar{X}}_{i2}}$ of each subsample, the variance S of the original sample and the variance statistic Si of two subsamples are calculated. The change point, that is, i, is obtained by maximizing the difference between variances S and Si. i is the optimum window for calculating the relief amplitude. The algorithms are defined as follows:
$RA{{S}_{i}}=\ln (R{{A}_{i}}/(\pi {{i}^{2}}))$
$RAS=\{RA{{S}_{ij}},j=1,2,3\ldots \ldots N\}$
${{\overline{RAS}}_{i}}=\frac{\mathop{\sum }_{j=1}^{j=N}RA{{S}_{ij}}}{N}$
$S=~\underset{j=1}{\overset{j=N}{\mathop \sum }}\,{{(RA{{S}_{ij}}-{{\overline{RAS}}_{ij}})}^{2}}$
${{\overline{RAS}}_{i1}}=\frac{\mathop{\sum }_{j=1}^{j=t}RA{{S}_{it}}}{t}$
${{\overline{RAS}}_{i2}}=\frac{\mathop{\sum }_{j=t+1}^{j=N}RA{{S}_{it}}}{N-t}$
${{S}_{i}}=~\underset{j=1}{\overset{j=t}{\mathop \sum }}\,{{(RA{{S}_{it}}-{{\overline{RAS}}_{i1}})}^{2}}-\underset{j=t+1}{\overset{j=N}{\mathop \sum }}\,{{(RA{{S}_{it}}-{{\overline{RAS}}_{i}}_{2})}^{2}}$
${{S}_{\partial }}=S-{{S}_{i}}$
where i is the value representing the different windows, RAi is the relief amplitude for a given window i, RASi is the logarithm of the average relief amplitude per unit area, RASij is the built sample, ${{\overline{RAS}}_{i}}$ and S are the mean and variance of the sample, respectively, ${{\overline{RAS}}_{i1}}$, ${{\overline{RAS}}_{i2}}$ and Si are the mean and variance of the two subsamples, and ${{S}_{\partial }}$ is the difference between S and Si.
To determine the best window for accurately measuring the lunar relief amplitude, in this paper, we use the mean change-point method twice. Initially, the mean change-point method is used to preanalyze the best window. A circular window with a radius of 5 pixels is taken as the starting window, and the step size is 5. The average relief amplitude within 500 pixels and the corresponding statistics are successively calculated to obtain the corresponding pixel number representing the best window. Then, the mean change-point method is used to accurately analyze and verify the best window. A circular window with a radius of 1 pixel is taken as the starting window and given a step size of 1. This is calculated to be twice the number of pixels of the best window obtained in the preanalysis, and the exact value of pixels corresponding to the best window is thus obtained.

4 Results

4.1 The best lunar relief amplitude window

In this paper, the mean change-point method is used twice to calculate the relief amplitude of the moon. Figure 2 shows the results of the preanalysis and more accurate analysis, both using the LOLA data. The preanalysis results show that the best window is circular and has a diameter of 125 pixels. In the more accurate analysis, the corresponding radius of the ideal window was determined to be 62 pixels. Therefore, in this paper, a circular window with a radius of 62 pixels is used to calculate the relief amplitude of the lunar surface.
Figure 2 The preanalysis results (a) and accurate analysis results (b) of the best window for calculating the relief amplitude of the lunar surface by the mean change-point method based on LOLA data

4.2 Distribution characteristics of the lunar relief amplitude

4.2.1 Overall characteristics of the lunar surface

In this paper, a circular window with 62 pixels as the radius is used to calculate and analyze the relief amplitude of the lunar surface. Figure 3 shows the histogram obtained from the frequency distribution statistics of the lunar relief amplitude. It can be seen from the histo gram that the minimum lunar relief amplitude value is 1 m, while the maximum value is 10,999 m. When the relief amplitude is larger than 6000 m, the frequency of raster pixels is small and gradually approaches zero. Therefore, there are outliers in the relief amplitude raster.
Figure 3 Frequency distribution histogram of the lunar surface relief amplitude
The box plot, developed by Tukey (1977), is a way to visualize data that demonstrates the distribution characteristics and key features of a dataset. Box plots can provide the median, the upper quartile, the lower quartile, the highest value and the lowest value of the complete dataset. The interquartile range (IQR) is the upper quartile minus the lower quartile. The maximum outlier is three times the IQR plus upper quartile. This outlier-processing method does not strictly require data to obey the normal distribution (Miller and Brewer, 2003). Table 1 shows the statistical results of the relief amplitude on the lunar surface. The outer boundary is 5695 m, and the cumulative frequency of values below 5695 m is 99.97%. To increase the accuracy of the statistical relief amplitude results, noise points in the polar regions are eliminated in this paper, and the relief amplitude of 7200 m, corresponding to the cumulative frequency of 99.99%, is considered as the outer boundary to preprocess the lunar relief amplitude results.
Table 1 Quantile statistics of lunar surface relief amplitude
Statistic Minimum Lower quartile Median Upper quartile Inner boundary Outer boundary Mean
Relief amplitude 1 687 1240 1939 3817 5695 1393.6
From the histogram of the frequency distribution of the relief amplitude on the lunar surface, the frequency of pixels decreases with increasing relief amplitude. The relief amplitude is concentrated between 1 and 7200 m (Figure 4). In the following section, the cumulative frequency of the lunar relief amplitude is analyzed. Approximately 10% of the lunar surface has a relief amplitude below 299 m, and approximately 90% of the lunar surface has a relief amplitude below 2688 m (Table 2). The map of relief amplitude for the lunar surface (Figure 4) shows that the areas with high amplitudes are mainly distributed in the walls of the craters and basins, and the areas with low amplitudes are mainly distributed in the mare, and the floor the craters and basins.
Table 2 Percentile of cumulative frequency of lunar surface relief amplitude
Cumulative frequency (%) 10 20 30 40 50 60 70 80 90
Relief amplitude (m) 299 562 803 1022 1240 1481 1767 2140 2688
Figure 4 Distribution characteristics of lunar surface relief amplitude, with mare labelled by grey lines

4.2.2 Characteristics of the lunar relief amplitude within mare and highland

There are obvious differences in the topography, material composition, geological features, and thickness of the lunar crust between the nearside and farside of the moon. The moon consists of two main geographic units, the dark mare regions and bright highland regions (Ouyang, 2005). The maria are volcanic plains composed mainly of basalt. They were formed during the Imbrium period and were not modified by large impact events. The highland regions are dominated by plagioclase in composition, which may be the material of the original lunar crust (Warren, 1985; 2001). Impact craters and basins are the dominant landforms on the lunar surface, with more than 1.3 million craters larger than 1 km in diameter (Robbins, 2019). Impact basins are fewer than craters, but they are larger than craters and represent major episodes of the exogenous lunar resurfacing (Melosh, 1989; Wieczorek and Phillips, 1999). Therefore, craters and basins are studied as separate geomorphic features. In addition, the geomorphic units, except craters and basins, on the highland are defined as the lunar land units. According to morphological and genesis characteristics, the basic geomorphic features of the lunar surface are mainly divided into craters, basins, mare, and land. In this paper, the relief amplitudes of basic lunar geomorphic features are statistically analyzed in reference to the lunar geological map from the completed Chinese 1:2,500,000 global Lunar geological Mapping project (Liu et al., 2016) (Figure 5).
Figure 5 The basic geomorphic landforms of the lunar surface
In this work, craters, basins, mare, and land are taken as statistical units to calculate the relief amplitude. The results show that the lowest relief amplitude in mare regions is 23 m, the maximum relief is 4772 m, and the average is 380.27 m. The relief amplitude of all mare regions is approximately 132 m (Figure 6), and approximately 70% of the mare relief values are between 23 m and 445 m. Lunar maria are mainly distributed at the floor of the basins on the nearside of the moon and was formed by condensation of basaltic magma after upwelling to the lunar surface following large impact events (Hartmann and Wood, 1971). Samples collected during the Apollo missions revealed that lunar volcanism occurred mainly between 3.8 billion and 3 billion years ago, and the Chang’e-5 basalt samples were dated to 1.96 billion years ago, revealing that lunar volcanism continued until approximately 2 billion years ago (Che et al., 2021). Hiesinger et al. (2000) revealed that lunar magmatic activity started approximately 4 billion years ago and stopped approximately 1.2 billion years ago by using the method of crater size-frequency distribution (CSFD) improved by Neukum et al. (2001). Most of the mare basalts were formed in the Late Imbrium Period, approximately 3.8 billion to 3.6 billion years ago. During the Eratossonian and Copernican periods, magmatic activity weakened, basaltic eruptions decreased, and basalts in the Copernican period occurred only in Oceanus Procellarum. During the eruption of mare basalts, wrinkle ridges and rilles were formed. In addition, the impact events occurred continuously, so the relief amplitudes of the wrinkle ridges, rilles and craters in the mare were relatively large.
Figure 6 Frequency distribution histogram of lunar mare and highland
Wrinkle ridges and rilles are the main tectonic landforms distributed in the mare region. Wrinkle ridges are positive linear structures with a lower elevation, while the rilles are linear, meandering structures. The relief amplitudes of the wrinkle ridges and rilles are greater than those of the mare plain. Therefore, it is necessary to consider the characteristics of wrinkle ridges and rilles in maria when constructing the classification criteria of lunar relief amplitude to partially distinguish the mare plain region from wrinkle ridges and rilles. In this paper, the wrinkle ridges and rilles data from the completed Chinese lunar geologic mapping project at the scale of 1:2,500,000 (Liu et al., 2016) was used to construct 50,000 random points; then, relief values were extracted from those points. Figure 7 shows that the relief amplitudes of the wrinkle ridges and rilles are mainly clustered near 242 m and 308 m, respectively. Since 50% of mare relief amplitudes are less than 253 m, a 200-m relief amplitude is used to distinguish the mare and land, while 300 m is used to distinguish the mare plain from the wrinkled ridges and rilles. In addition, the relief amplitude of the mare is clustered around a value of 132 m, so the relief amplitude of 100 m is used to distinguish minor microrelief plains and minor microrelief platforms.
Figure 7 Frequency distribution histogram of lunar wrinkle ridges and lunar sinuous rilles
The relief amplitude of the land is predominately centered around 767 m (Figure 6). The lowest relief amplitude is 1 m, the highest relief amplitude is 5396 m, and the average relief amplitude is 1231.69 m (Table 3). This work analyzes the frequency distribution of the relief amplitude of the land. Approximately 10% of the land has relief amplitudes below 507 m, approximately 30% has relief amplitudes below 802 m, and approximately 60% has relief amplitudes below 1250 m (Table 4). The craters analyzed in this paper are those with diameters greater than 10 km. Due to magmatic activity, the craters in the mare are fewer in number than those in the land region. On the other hand, there are a large number of craters with diameters less than 10 km in the land region. Therefore, there are geomorphological units with large relief amplitudes on the land. According to the above analysis, a 700-m relief amplitude was used to distinguish the small relief landforms from the medium relief landforms, while a relief amplitude of 1500 m was used to distinguish the medium relief landforms from the large relief landforms.
Table 3 Quantile statistics of lunar surface relief amplitude in basic lunar geomorphic landforms
Basic lunar
geomorphic feature		 Relief amplitude (m)
Minimum Lower quartile Median Upper quartile Maximum Mean
Mare 23 159 253 445 4772 380.27
Land 1 735 1082 1583 5396 1231.69
Craters 71 1132 1721 2455 7200 1842.39
Basins 1 794 1197 1716 7200 1330.97
Table 4 Cumulative frequency of lunar surface relief amplitude in basic geomorphic landforms and the relief amplitude corresponding to cumulative frequency
Basic lunar geomorphic feature Relief amplitude (m)
10% 20% 30% 40% 50% 60% 70% 80% 90%
Mare 111 143 173 210 253 308 388 521 795
Land 507 665 802 937 1082 1250 1457 1734 2177
Craters 730 1013 1247 1478 1721 1987 2287 2642 3125
Basins 520 709 975 1034 1197 1378 1589 1866 2307

4.2.3 Characteristics of the lunar relief amplitudes within craters and basins

Impact craters and basins are the dominant landforms on the lunar surface. According to the impact event mechanisms, the formation of craters and basins can be divided into three stages: the contact and compression stage, excavation stage and modification stage. An impact excavates the material in the upper crust and produces a transient cavity, which is then modified by gravitational forces before finally producing a crater with crater floor, crater wall and crater rim. For complex craters, uplift occurs in the transient crater floor, leading to the development of a central uplift characterizing is the central peak landform. For impact basins, the gravitationally unstable central uplift collapses outward to form the peak-ring landform (Baker and Head, 2013). Therefore, the relief amplitude of the crater wall and the central peak landform, the peak ring landform and the multiring landform of the basins are relatively large. The relief amplitudes of the craters and basins are mainly concentrated at 1527 m and 1080 m, respectively (Figure 8). Therefore, a relief amplitude of 1500 m is considered to distinguish between the small relief landforms and medium relief landforms of craters. In approximately 80% of craters and basins, the relief amplitude is less than 2642 m and 1866 m, so the relief amplitude of 2500 m is used to distinguish between the large relief landforms and extremely large relief landforms of craters and basins.
Figure 8 Frequency distribution histogram of impact craters and basin

4.3 Lunar relief amplitude classification schemes

According to the analysis results of the relief amplitude of the basic geomorphic landforms of the lunar surface, the relief amplitudes of maria are small, while those of the wrinkled ridges and rilles in maria are larger than those of the mare plains. Therefore, a relief amplitude of 100 m is taken as the criterion to distinguish the microplain and microrelief platform of the mare. The transition region between the mare and the land, the mare plain region and the wrinkle ridges and rilles are distinguished by relief amplitudes of 200 m and 300 m. A relief amplitude of 700 m is used to distinguish the small relief landforms from the medium relief landforms, and a relief amplitude of 1500 m is used to distinguish the medium relief landforms from the large relief landforms. A relief amplitude of 2500 m is used to distinguish the large relief landforms and extremely large relief landforms of craters and basins. The statistical results in Table 5 show that the area with a relief amplitude less than 700 m accounts for 26% of the lunar surface. In addition, since the most abundant geomorphic landforms on the lunar surface are impact craters and the relief amplitude of these craters is relatively large, the proportion of medium-relief, large-relief and extremely large-relief geomorphic landforms on the moon is relatively large, composing approximately 74% of the lunar surface (Table 5).
Table 5 Statistics of the classification criterion of lunar surface relief amplitude
Lunar relief amplitude classification scheme (m)
<100 [100, 200) [200, 300) [300, 700) [700, 1500) [1500, 2500) ≥2500
Geomorphic type Minor
microrelief
plains		 Minor
microrelief
platforms		 Microrelief landforms Small relief
landforms		 Medium relief
landforms		 Large relief landforms Extremely large relief landforms
Proportion (%) 1.06 4.3 4.71 15.48 35.18 27.38 12.89
With reference to the relief amplitude classification criteria of the geomorphic landforms on Earth and considering the characteristics of lunar landforms, the relief amplitude of the lunar surface is classified according to relief amplitudes of 100 m, 200 m, 300 m, 700 m, 1500 m, and 2500 m. The corresponding landforms are minor microrelief plains, minor microrelief platforms, microrelief landforms, small relief landforms, medium relief landforms, large relief landforms and extremely large relief landforms (Figure 9).
Figure 9 The classification results of the lunar surface relief amplitude

5 Discussion and conclusions

In the verification phase, the mean change-point method was used to verify the best window for determining the lunar relief amplitude using SLDEM data derived from LQ18 in the Mercator projection (Figure 10a). A circular window with a radius of 5 pixels is taken as the starting window, and the step size is 5 pixels. The average relief amplitude within 500 pixels and the corresponding statistics are successively calculated to obtain the corresponding pixel number of the optimal window, which is 124 pixels (54π km2) (Figure 10b).
Figure 10 SLDEM data (a) and the analysis results of the mean change-point method based on SLDEM data (b)
The best window for calculating the relief amplitude based on LOLA data is a circular window with a radius of 62 pixels and an area of approximately 53π km2, which is close to the area (54π km2) of the window calculated based on SLDEM with a resolution of 59 m. Therefore, the best window for determining the relief amplitude calculated in this paper was derived from multi source data and can thus be optimally applied in lunar landform classification schemes. Integrating the classification criteria of this paper with the elevation classification scheme proposed by Liu et al. (2021) can identify the basic types of lunar surface landforms and provide a numerical reference useful for the construction of the lunar landform classification scheme.
In this paper, the mean change-point method was used to determine the best window for calculating the lunar relief amplitude based on LOLA and SLDEM data. Moreover, the relief amplitude of the lunar surface was calculated and analyzed, and classification criteria for lunar relief amplitude were proposed. The conclusions are as follows:
(1) In this paper, the mean change-point method is used to determine that the best window for calculating the lunar relief amplitude is a circular window with a radius of 62 pixels (approximately 53 π km2). The lunar surface is divided into four basic geomorphic landforms, including craters, basins, maria and land.
(2) The thresholds of the relief amplitude are determined to be 100 m, 200 m, 300 m, 700 m, 1500 m and 2500 m. Based on these thresholds, the lunar surface is divided into seven types: minor microrelief plains, minor microrelief platforms, microrelief landforms, small relief landforms, medium relief landforms, large relief landforms and extremely large relief landforms.
(3) The minor microrelief plains are mainly distributed in the maria and on the floors of craters and basins filled with basalts, while the minor microrelief platforms are mainly distributed in the transition regions between maria and highlands. The microrelief landforms are mainly located in regions with relatively high topography compared to maria, such as wrinkled ridges and sinuous rilles in maria. The small relief landforms are mainly scattered in the central peaks and floor fractures of craters. The medium relief landforms are mainly distributed in the transition regions between crater floors and crater walls, between crater walls and crater rims, between basin floors and basin walls, and between basin walls and basin rims. Large and extremely large relief landforms are mainly scattered along crater walls and basin walls.

References

Publishing order | Descend order by publishing year | Descend order by cited within
[1]
Baker D M, Head J W, 2013. New morphometric measurements of craters and basins on Mercury and the Moon from MESSENGER and LRO altimetry and image data: An observational framework for evaluating models of peak-ring basin formation. Planetary and Space Science, 86(15): 91-116.

DOI

[2]
Barker M K, Mazarico E, Neumann G A, 2016. A new lunar digital elevation model from the Lunar Orbiter Laser Altimeter and SELENE Terrain Camera. Icarus, 273(15): 346-355.

DOI

[3]
Cavanaugh J F, Smith J C, Sun X, 2007. The Mercury Laser Altimeter instrument for the MESSENGER mission. Space Science Reviews, 131(1): 451-479.

DOI

[4]
Che X C, Nemchin A, Liu D Y, 2021. Age and composition of young basalts on the Moon, measured from samples returned by Chang’e-5. Science, 374(6569): 887-890.

DOI

[5]
Cheng W M, Liu Q Y, Wang J, 2018. A preliminary study of classification method on lunar topography and landforms. Advances in Earth Science, 33(9): 885-897. (in Chinese)

DOI

[6]
Han H H, Gao T, Yi H, 2012. Extraction of relief amplitude based on change point method: A case study on the Tibetan Plateau. Scientia Geographica Sinica, 32(1): 101-104. (in Chinese)

[7]
Hartmann W K, Wood C A, 1971. Moon: Origin and evolution of multi-ring basins. The Moon, 3(1): 3-78.

DOI

[8]
Hiesinger H, Jaumann R, Neukum G, 2000. Ages of mare basalts on the lunar nearside. Journal of Geophysical Research: Planets, 105(E12): 29239-29275.

DOI

[9]
Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 1987. 1: 1000000 Geomorphological Mapping Specification (trail). Beijing: Science Press. (in Chinese)

[10]
Li B Y, Li J Z, 1994. 1: 4000000 Geomorphological Map of China. Beijing: Science Press. (in Chinese)

[11]
Li B Y, Pan B T, Han J F, 2008. Basic terrestrial geomorphological types in China and their circumscriptions. Quaternary Sciences, 28(4): 535-543. (in Chinese)

[12]
Liu J Z, Guo D J, Chen S B, 2016. Chinese 1: 2.5 M Geologic Mapping of the Global Moon. 47th Lunar and Planetary Science Conference, Texas: The Woodlands, 2039.

[13]
Liu Q Y, Cheng W M, Yan G J, 2021. Distribution characteristics and classification schemes of lunar surface elevation. Acta Geographica Sinica, 76(1): 106-119. (in Chinese)

[14]
Mazarico E, Rowlands D D, Neumann G A, 2012. Orbit determination of the Lunar Reconnaissance Orbiter. Journal of Geodesy, 86(3): 193-207.

DOI

[15]
Melosh H J, 1989. Impact Cratering:A Geologic Process. New York: Oxford University Press, 60-184.

[16]
Miller R L, Brewer J D, 2003. The AZ of Social Research: A Dictionary of Key Social Science Research Concepts. Padstow, Cornwall: SAGE Publications, 106-109.

[17]
Neukum G, Ivanov B A, Hartmann W K, 2001. Cratering Records in the Inner Solar System in Relation to the Lunar Reference System. Dordrecht: Springer Netherlands, 55-86.

[18]
Ouyang Z Y, 2004. Scientific objectives of chinese lunar exploration project and development strategy. Journal Advances in Earth Science, 19(3): 351-358. (in Chinese)

[19]
Ouyang Z Y, 2005. Introduction to Lunar Science. Beijing: China Astronautic Publishing House, 56-65. (in Chinese)

[20]
Robbins S J, 2019. A new global database of lunar impact craters > 1-2 km: 1. Crater locations and sizes, comparisons with published databases, and global analysis. Journal of Geophysical Research: Planets, 124(4): 871-892.

[21]
Smith D E, Zuber M T, Frey H V, 2001. Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars. Journal of Geophysical Research: Planets, 106(E10): 23689-23722.

[22]
Smith D E, Zuber M T, Neumann G A, 2010. Initial observations from the Lunar Orbiter Laser Altimeter (LOLA). Geophysical Research Letters, 37(18): 204.

[23]
Tukey J W, 1977. Exploratory Data Analysis. America and Canada: Addison-Wesley Publishing Company, 39-43.

[24]
Wang J, Cheng W M, Zhou C H, 2017. Automatic mapping of lunar landforms using DEM-derived geomorphometric parameters. Journal of Geographical Sciences, 27(11): 15.

[25]
Warren H P, 1985. The Magma Ocean concept and lunar evolution. Annual Review of Earth & Planetary Sciences, 13(1): 201-240.

[26]
Warren H P, 2001. Early lunar crustal genesis: the ferroan anorthosite Epsilon-Neodymium paradox as a possible result of crustal overturn. 64th Annual Meteoritical Society Meeting, 36(9): A219.

[27]
Wieczorek M A, Phillips R J, 1999. Lunar multiring basins and the cratering process. Icarus, 139(2): 246-259.

DOI

[28]
Wilhelms D E, McCauley J F, Trask N J, 1987. Geologic History of the Moon. Washington DC:U.S. Geological Survey Publication Warehouse, 55-82.

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