This paper is recommended by Zhao Ming

Lunar Topographic Model CLTM-s01 from Chang’E-1 Laser Altimeter

PING JinSong ①*, HUANG Qian①②*, YAN JianGuo①⑤, CAO JianFeng③, TANG GeShi③ & SHU Rong④

①Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China ② Graduate University of Chinese Academy of Sciences, Beijing 100049, China

③Beijing Aerospace Control Center, Beijing 100094, China ④Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China ⑤State Key Laboratory of Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan,

430070, China * E-mail：pjs@shao.ac.cn； huangqian@shao.ac.cn

Abstract: More than 3 million range measurements from the Chang’E-1 Laser Altimeter have been used to produce a global topographic model of the Moon with improved accuracy. Our topographic model, a 360th degree and order spherical harmonic expansion of the lunar radii, is designated as Chang’E-1 Lunar Topography Model s01 (CLTM-s01). This topographic field, referenced to a mean radius of 1738km, has an absolute vertical accuracy of approximately 31m and a spatial resolution of 0.25o (~7.5km). This new lunar topographic model has greatly improved previous models in spatial coverage, accuracy and spatial resolution, and also shows the polar regions with the altimeter results for the first time. From CLTM-s01, the mean, equatorial, and polar radii of the Moon are 1,737,103m, 1,737,646m, and 1,735,843m respectively. In the lunar-fixed coordinate system, this model shows a COM/COF offset to be (-1.777, -0.730, 0.237) km along the x, y, and z directions, respectively. All the basic lunar shape parameters derived from CLTM-s01 are in agreement with the results of Clementine GLTM2, but CLTM-s01 offers with higher accuracy and reliability due to its better global samplings. Keywords: Chang’E-1, Laser Altimeter (LAM), Lunar Topographic Model

1 Introduction

Topography is one of the principal measurements required to quantitatively describe a planetary body[1,2]. When combined topographic data and gravitational data with some reasonable geologic assumptions and by using some downward continuation analyzing methods, it is possible to obtain inverted important geophysical parameters such as crustal thickness, elastic thickness, and crustal and mantle density[3]. Those parameters enable the determination of the global crust and upper mantle, which can help us to better understand the lunar internal structure and its thermal history [1].

The topography of the Moon has been measured by several means, including the use of laser altimetry, stereo-photogrammetry, radar interferometry, and radar sounding. Because of the Moon’s synchronous rotation, most early lunar topography studies were restricted either to the nearside or along the equatorial ground tracks of the Apollo command. Both the accuracy and resolution of those regional models were tremendously poor[4]. The first reliable near-global topographic model of the Moon was GLTM2, which was obtained by the Clementine LIDAR mission in 1994[1,2]. It was a 72nd spherical harmonic model, using 72,548 effective laser measurements, with an absolute vertical accuracy of approximately 100m and a spatial resolution of 2.5o. However it was not a complete global lunar topographic model because of its lack of poleward ± 25o altimetry measurements. The

RISE/SELENE team of Japan treated the Clementine 0.25o gridded data production with a multiple-step least-square fitting method, and obtained a 180th spherical harmonic model NLT180A[5].

In order to get a global lunar topographic model, researchers have been using various methods, such as from Earth-based radar interferometry data and Clementine stereoimages measurements [6,7], to obtain the elevations over lunar polar regions. The U. S. Geological Survey (2002) topographic model[8] is totally based on the achievements of Clementine, which has combined 72,548 altimetry measurements and 1,724,872 polar regions points derived from the stereo-photogrammetrys. ULCN2005 (The Unified Lunar Control Network 2005)[9,10] is the latest global control network of the Moon, which has made use of 43,866 historical photo-grammetry measurements from Earth-based, Apollo, Marine 10, Galileo and Clementine missions, yielding a total of 272,937 effective lunar control points. However, all of the topographic models were limited to the non-global laser altimetry observations. Comparisons between LIDAR and Earth-based radar interferometry measurements over the Tycho crater showed that the laser ranges had systematic position errors of ~3km [11]. Therefore, a lunar topographic model with high accuracy and resolution completely based on the laser altimetry data is quite necessary.

The year of 2007 represented the beginning of a new era of lunar exploration. Not only were the Chinese Chang’E-1 and Japanese SELENE (Kaguya) missions successfully launched in this year, but these are closely followed by the Indian Chandrayaan-1 mission in October 2008 and the American Lunar Reconnaissance Orbiter (LRO) later in spring 2009. Chang’E-1 is the first lunar exploration mission of China, aiming to obtain 3D images of the lunar surface, analyze the content of useful elements and types of materials, and explore the characteristics of lunar soil and the space environment between the earth and the Moon. The Chang’E-1 satellite was successfully launched on October 24, 2007 from Xichang Satellite Launch Center, and was placed into a 2-hour circular lunar polar orbit on November 7th. One of the payloads of Chang’E-1, the Laser Altimeter (LAM), is used to measure the distance between the orbiter and the lunar surface, and we can obtain a lunar topographic model with these ranging measurements. This paper will introduce the LAM system, its present status, the LAM data processing, and its first results of the lunar topographic model CLTM-s01.

2 Chang’E-1 LAM Data Processing

In lunar Laser Altimetry Mission (LAM), the laser altimeter transmits a beam of high-power narrow laser pulse to the lunar surface, and receives its returned signals by an optical telescope. By measuring the out and home time delay of the laser beam, we can calculate the distance between the satellite and the lunar surface. Those ranging data sets not only can provide stereo-photogrammetry with necessary calibration parameters, but also can be used to obtain the elevations of the nadirs when combining with corresponding orbital and attitude data. Fig.1 shows the principle of using the ranging, orbit and attitude data to determine the elevations. Here ur is a laser altimeter measuring vector at a certain

measuring time, which is determined by the altimetry ranging and its corresponding attitude; SRr

is

the selenocentric position vector of the satellite, which is given by precise orbits; R is the mean radius of the Moon (In order to calculate the elevations, people usually choose a sphere with radius of

1738km as a basic for converting the range measurements to elevations). Combining with ur SRr

,

one can obtain the selenocentric position vector of the light spot (see formula (1)); after converting to

GRr

, one can get the elevation of the light spot (see formula (2)): h

G SR R u= +r r r

(1)

Gh R R= −r

(2)

Fig. 1 Schematic diagram of Laser Altimeter elevation calculation

2.1 The LAM System

The Chang’E-1 LAM system consisted of two subsystems, namely the Altimeter Optical Head and the Altimeter Circuit Box. The Altimeter Optical Head comprised a laser transmitting system and an optical receiving system. The laser transmitter contained a Q-switched Diode-pumped Nd:YAG source that produced lasing every second at a wavelength of 1064nm. The laser had a pulse-width of less than 7ns, with pulse energy of 150mJ and a laser divergence of less than 0.5mrad, which formed a surface spot size of 120m when the satellite altitude was about 200km. The optical receiver included a Cassegrain telescope, which had a telescope diameter of 140mm and a focal length of 538mm. The size of the Optical Head was 356mm* 290mm* 174.5mm and its weight was 9.9kg. The Altimeter Circuit Box was a control unit used to do the ranging measurement and to supply the laser power. It had a size of 260mm* 200mm* 190mm and a weight of 5.8kg. Therefore the total weight of the Laser Altimeter System was 15.7kg. Specifications of the LAM are given in Table 1. Here, the along-track shot spacing was about 1.4km when assuming a 100% laser ranging probability, and the across-track shot spacing was determined by two adjacent orbits.

Table 1 Chang’E-1 LAM Instrument Characteristics

Characteristics Values Effective distance range (200±25)km

ur

hSRr

GRr

R

Moon Center

Footprint <Φ200m Wavelength 1064nm

Energy 150mJ Width of Laser Pulse 5~7ns

Repeat rate 1Hz Receiver telescope diameter 140mm

Telescope focal length 538mm Distance resolution 1m

Distance error 5m Data rate 384bps Weight 15.7Kg Power 35W Life 1 Year

Along-track shot spacing ~1.4km Across-track shot spacing Based on orbital spacing,

the spacing is 30.3km in once global coverage.

The LAM was installed parallel to the Z axis of the orbiter, with an installation pointing/aligning

error of about 2′. The boresight of LAM was parallel to the CCD detecting system with a measuring accuracy of ±1′. Both laser transmitter and receiver telescope were installed on the side of the spacecraft facing to the lunar surface. The LAM can work well when the orbit slope was less than 15o. The ranging accuracy played the key role in lunar topographic measurements. The ranging resolution of the LAM was about 1m after ground tests, and the ranging accuracy was in-flight estimated to be less than ±5m in aircraft tests.

Health check of LAM was carried out during the in-orbit test phase from Nov. 5th to Nov. 20th without laser firing. The first laser ranging experiment was carried out successfully on Nov. 27th. The LAM can obtain detecting data on both ascending and descending arcs, so only half month of observations in about 155 orbits can cover the whole lunar surface once. Until Jan. 22nd 2008, more than 5 million range data from orbits 0243-0878 were received and recorded normally. Since the large voltage instrument breaks and the orbit controls many times, about 171 passes of altimetry data were lost. However, those measurements can basically cover the whole lunar about four times, with along-track and across-track resolution of ~1.4km and ~7km, respectively. Those ranging data can be used to make high resolution global lunar topographic maps.

2.2 Orbit Determination and Attitude Control

In order to determine a global topographic data set from the LAM ranging data, it was necessary to compute the precise spacecraft orbits and the attitudes which were subtracted from the range profiles to yield relative surface elevations. The precise orbit of Chang’E-1 was determined mainly by the close-loop two-way Unified S-band (USB) Doppler and Ranging data, and assisted by VLBI delay and delay rate data collected by four VLBI stations [12]. In the operation periods of LAM, the orbits of Chang'E-1 were precisely characterized in radial accuracy of 30m (3σ ), and along track accuracy of 50~100m (1σ ). The radial errors of the orbits are the main error of calculating elevations. Comparing

with 100km altitude orbiters, such as the Japanese SENELE-1, Chang’E-1 with a 200km altitude high orbit would fly more stably because of less gravitational anomalous effects. This stable orbit would be most helpful with onboard precise laser altimetry measurements.

Chang’E-1 is a three-axis stabilized satellite using a set of star sensors to measure the attitude. In the orbital coordinate system, the values and variations of all the three Euler angles are quite small. By analyzing the measured attitude data, the stability of each angle is better than 0.008o/s (3σ ), and the vertical error caused by attitude control is less than 1m (3σ ).

Table 2 lists the sources of radial errors in calculating the elevations. In addition to errors caused by the instrument, orbit and attitude, the radial error, caused by spot size has also been considered to be less than 5m, when the laser altimeter is in a critical tilt state of about 15o.

Table 2 Sources of Radial Error of Calculating elevations

Error Source Approximate

Magnitude (m)

Comment

Laser Altimeter instrument < 5 3σ

Orbit Repeatability (radial) < 30 3σ

Spacecraft pointing/attitude < 1 3σ

Spot Size < 5 3σ

Total < 31

2.3 LAM Data Processing

This article processes all the recorded ranging data from orbit 0243 to orbit 0878 of Chang’E-1 normal mission. During the first forward flying phase, the orbit maintenance is quite frequent and some orbital arcs have no ground-tracking, forcing us to reject about 7 orbits ranging data without orbital tracking information. The returned laser pulse is substantially influenced by the characteristics of the laser spot, and if the first returned ranging is out of the hardware-based range thresholds, the data management system then will record a fake value which is far bigger than the orbital altitude to show that it is out of the detecting dynamic range of the instrument. The first step of LAM ranging data processing is to delete those fake ranges. Generally, more than 7000 ranging points can be obtained in a single orbit, and the fake data deleting ratio is about 30%. The next step is to perform the systemic calibrations on the ranges according to the instrument technical parameters.

The topography profiles are last generated by combining the ranging measurements with the precise orbit and attitude data according to Figure 1. The topography profiles are coincident with the actual lunar topographic features very well. It shows multiple complicated craters in the southern hemisphere and wide smooth maria in the northern part. Figure 2(a) represents the topographic profile of orbit 0249. The Map from left to right, corresponds to the actual lunar topography from south to north, showing multiple morphological structures of the lunar surface. However, there still exist some jumped pseudo-elevations which are not consistent with the actual topographic changes of the Moon and should be removed. As the continuity of the profile is quite good, we just used a simple method to

reject the inconsistent points in a single orbit. Each orbit has singled out and removed about 10 to 20 pseudo-point elevations, at a rate of much less than 1%, basically retaining the original elevation information. Figure 2(b) depicts the topographic profile of orbit 0249, with the pseudo-elevations efficiently removed, showing that the elevation data sequence looks visually more reasonable and clear.

5.4432 5.4432 5.4432 5.4432 5.4432 5.4432 5.4432 5.4432 5.4432 5.4432

x 104

-1

-0.5

0

0.5

1x 10

4

Elev

atio

ns(m

)

Orbit 0249(before filtering)

5.4432 5.4432 5.4432 5.4432 5.4432 5.4432 5.4432 5.4432 5.4432 5.4432

x 104

-6000

-4000

-2000

0

2000

4000

6000

8000

Elev

atio

ns(m

)

MJD(UTC)

Orbit 0249(After filtering)

(a)

(b)

Fig.2 The topographic profile of orbit 0249 by LAM

(a) before removing pseudo-elevations; (b) after removing pseudo-elevations

In all the 455-track ranging data, about 5 million laser points have been processed, resulting in about 3.21 million effective elevations which compose the Chang’E-1 lunar elevation series. The famous MOSCOVIENSE (149oE, 28oN) has been proved to be an impact crater with typical mascon characteristics and positive circular free-air gravitational anomaly [13]. Fig.3 shows four sequential elevation passes through the Moscoviense crater. The longitude is from 152oE to 149oE, corresponding to orbits from 0253 to 0256. Fig.3 clearly demonstrated that the LAM can detect not only the general profile but also the precise topographic features, such as the impact crater’s detailed outer ring and its central peak.

Comparisons between the Chang’E-1 LAM and Clementine LIDAR measured data show that over large maria regions (such as IMBRIUM and SERENITATIS), the elevation differences are small (~200m), but over some undulating and Clementine uncovered areas, the differences are quite big. This is because the vertical accuracy of Clementine is about 100m and its altimetry coverage is quite sparse.

Fig.3 Topographic profiles of Moscoviense crater (149oE, 28oN) by LAM. Outer ring and central peak are clearly displayed. Horizontal axis is lunar latitude(One degree corresponds to 30.3km). The Height is referenced to a sphere with a radius of 1738km and the origin as the center of mass. (a) ~ (d) is along

the longitude of 152oE, 151oE, 150oE and 149oE, respectively

3 Lunar Topographic Model CLTM-s01

Combining two months effective laser measurements (from Nov. 27th 2007 to Jan. 22nd 2008) with precise orbits and attitudes data, we obtain the lunar global elevations series with more than 3.21 million effective elevations. As those data sets represent discrete irregular points, they are not quite user-friendly. Generally, people prefer to use regular grid and spherical harmonics to represent the lunar topography [1, 2, 14].

3.1 Spherical Harmonic Model

Based on the actual elevation spacing (along-track about 1.4km and across-track about 7km), all the

elevations are assembled into a 0.25o×0.25o average grid. A global model of topography can be expanded in spherical harmonic with the form:

H

1 0

( , ) (sin )( cos sin )N l

lm lm lml m

H P C m S mλ ϕ ϕ λ= =

⎡ ⎤= +⎢ ⎥⎣ ⎦∑∑ λ (3)

where the symbols ϕ and λ are the selenocentric latitude and longitude of the surface; lmP are

the normalized associated Legendre functions of degree l and order m; lmC and lmS are the

normalized spherical harmonic coefficients[15] with units in meters; and is the maximum degree

representing the resolution of the topography field. Here

N

lmC and lmS coefficients provide

information on the distribution of global topography. We have performed a 360 degree and order spherical harmonic expansion of topography, designated as the Chang’E-1 Lunar Topographic Model (CLTM-s01). This model, shown in Fig. 4 with the nearside on the right and farside on the left, has a resolution of 7.5km and a vertical accuracy of 31m. The elevations are all referenced to a sphere with a radius of 1738km.

This model gives the lunar polar maps made by laser altimeter data for the first time. It is easy to distinguish all kinds of characteristics on the map. There are widely smooth mare regions with low elevations on the nearside, and on the farside the relief is more complicated with numerous various size impact craters. We can clearly recognize not only all the plateaus, maria regions, but also the detailed features, such as the sinus and lacus. The dark blue region on the far side is the well-known South Pole-Aitken basin, which has been identified as the largest and deepest impact basin in the solar system[2]. The deepest point is in the South Pole-Aitken basin at (211.375oE, 61.375oS) with a maximum depth of 9.23km. The highest topography of 9.84km above the reference sphere appears also on the far side in the highlands north of the Korolev Basin at (201.375oE, 5.375oN).

By the LAM data, it is possible for us to make improved estimates of the fundamental parameters of the Moon’s shape, which are mainly derived from the long-wavelength field[1, 16]. The mean radius of the Moon given by CLTM-s01 is 1,737013m, which is a little less than 1,737,103m of GLTM2. By performing a rotating ellipsoid fit to the gridded data, we have estimated the mean equatorial, polar radii and flattening to be 1,737,646m, 1,735,843m and 1/963.7526, respectively, which are all smaller than the parameters given by GLTM2. As the CLTM-s01 has more complete coverage, especially aound the polar regions, the radii calculated by CLTM-s01 seems to be more reliable.

It has long been known that the Moon’s geometric center was displaced from its center of mass[15], and the first-order harmonic coefficients represent the position of the center of mass. Our analysis shows the COM/COF offset to be (-1.74，-0.75，0.27) km in the x, y, and z directions, respectively. As a result of CLTM-s01, we know this displacement deviates from the Earth-Moon line, and on the farside of the Moon the COM/COF offset is displaced approximately 22o toward the western limb. Table 3 lists the lunar basic shape parameters of CLTM-s01 and GLTM2.

Another fundamental characteristic of the lunar shape is that the topographic signatures of the nearside and farside are very different[1]. As shown in Fig.5, the lunar surface is most abundant with -6km to 4km elevations. The shape of the farside is broader than the nearside, where the highest and deepest regions are both on the farside. The sharpness of the nearside is a result of the maira, which can be defined as an equipotential surface[1]. Those big differences between the two sides have reflected apparent dichotomy of the Moon.

Table 3 Basic parameters comparison between CLTM-s01 and CLTM2

Parameters CLTM-s01 GLTM2

Mean radius/m 1,737,013 1,737,103

Mean equatorial radius/m 1,737,646 1,738,139

Mean polar radius/m 1,735,843 1,735,972

Flattening 1/f 1/963.7526 1/802.0946

COF/COM difference(km) (-1.777, -0.730, 0.237) (-1.74，-0.75，0.27)

Fig.5 Histogram of heights of all lunar topography (square black dot line), nearside topography

(diamond black dot line), and the farside (up-triangle grey dot line)

3.2 Comparison with other Lunar Topography Models

The Chang’E-1 laser altimeter-based lunar global topography model CLTM-s01 is an improvement upon earlier models not only in data coverage and range measuring accuracy, but also in spatial resolution. The measuring accuracy has been improved from 100m of Clementine LIDAR to 31m of Chang’E-1 LAM, while the spatial resolution has been enhanced from about 20km along-track and 60km across-track to ~1.4km and ~7.5km, respectively. Fig.6 compares the locations of laser topographic measurements from Chang’E-1 LAM and Clementine LIDAR. The white swaths show areas of sparse or no data coverage. The Clementine LIDAR has only 72,548 valid laser points, or less than 2% of Chang’E-1 LAM. Clementine LIDAR had no observation in the polar regions, and its

resolution is relatively poor with lots of blank areas on the farside. Two-month coverage of LAM is better than LIDAR, and from the results of LAM we can more clearly distinguish all the lunar features.

Fig.4 Topography of the Moon from the Chang’E-1 laser altimetry data. The elevations are referenced to a sphere with the mean radius of 1738km. (top) left is the north hemisphere, latitude from 55oN to 90oN, right is the south hemisphere, latitude from 55oS to 90oS, all with Stereographic Equal-Angle

projection. (bottom) is the Cylindrical equidistant projection, with a center meridian of 180oE, latitude from 60oS to 60oE

Fig.6 Locations of laser topographic measurements from Chang’E-1 LAM (a) and Clementine LIDAR (b), all with a Mollweide projection and a center meridian of 270oE, and with the nearside on the right

and farside on the left. The interval of longitude and latitude are all at 30degree.

Fig.7 shows the elevation differences between CLTM-s01 and ULCN2005. CLTM-s01 is entirely based on laser altimetry results, with a resolution of ~7km and vertical accuracy of ~31m. ULCN2005 combines all the historical stereo-photos, with an interpolated resolution of ~6.8km, and laser measurements and stereo-photos accuracies of ~100m and ~500m, respectively. Over the large maria regions on the nearside, such as the PROCELLARUM, IMBRIUM and SERENITATIS, the differences are very small at the 200m level, but over some undulating places these differences are quite big. This is because the ULCN2005, using the stereo-photos to interpolate the elevations, will somehow introduce certain extraneous errors. Fig.8 shows the poleward ±65o topography of CLTM-s01, ULCN2005 and GLTM2. There is no data coverage over ±75o of GLTM2((c), (c’)), and the interpolated and extrapolated elevations are quite poor. Though ULCN2005 ((b), (b’)) has used the stereo-photos to derive the poleward elevations, the resolution is still very limited when compared with CLTM-s01 ((a), (a’)). In general, CLTM-s01 is the clearest topographic map, in which one can distinguish a variety of small and middle-scale structures of the Moon. Comparing the spherical harmonic coefficients spectral power of different models reveals the response of different models to different lunar feature-scales. Fig.9 shows the amplitude spectrum comparison between CLTM-s01, MoonUSGS359, ULCN359 and GLTM2C. The MoonUSGS359 and ULCN359 are based on USGS2002 and ULCN2005, respectively, which have been expanded to 359th order and degree (Wieczorek, http://www.ipgp.jussieu.fr/~wieczor/SH/SH.html). GLTM2C is another spherical harmonic model expanded to 90th order and degree. Fig.9 shows that the power spectrum of CLTM-s01 is obviously higher than the other three previous models at longer wavelength, owing mostly to more complete altimetry sampling of the lunar surface, particularly over the lunar farside. As the CLTM-s01 and GLTM2C are based only on laser altimetry data, their energy spectra are close to each other in low degrees. The departure of GLTM2C after degree 70 is mainly due to its lack of data in polar regions. The MoonUSGS359 and ULCN359 depart from CLTM-s01 on order 25, because that using stereo-photos to derive the elevations may cause a great deal of topographic information distortion. On the whole, compared with previous models, the CLTM-s01 lunar topographic model is a great improvement, with more complete sampling, higher elevation accuracy, better resolution, showing the topographic maps of the polar regions for the first time. It has provided a good global model of the lunar topography, which would help human beings gain a deeper understanding of the Moon. No single mission will observe the complete Moon in one or two years. Besides Chang’E-1, the Japanese lunar explorer KAGUYA (SELENE) has been circling the Moon for more than 1 yr, and its laser altimeter mission LALT has obtained quite beautiful results of the lunar topography[17]. The Indian lunar mission Chandrayaan-1 was successfully launched on October 22nd 2008. On November 16th its lunar laser ranging instrument (LLRI) was successfully switched on and it can take up to 10 measurements per second. This will be closely followed by the American Lunar Reconnaissance Orbiter (LRO) in spring 2009, and its LOLA laser altimeter onboard could detect the lunar surface 30 points per second with 10cm range accuracy. We believe that all these lunar missions would make significant improvements in lunar topography.

Fig. 7 Elevations Differences between CLTM-s01 and ULCN2005. The projection is the same of Fig. 4,

but with a central meridian of 270oE

Fig.8 ±65o poleward topography of CLTM-s01, ULCN2005 and GLTM2. (a), (b), (c) is north pole, (a’), (b’), (c’) is the south pole. From left to right is CLTM-s01((a), (a’)),ULCN2005((b), (b’)) and

GLTM2((c), (c’)), respectively. All is with Stereographic Equal-Angle projection.

Fig.9 Lunar topographic amplitude spectrum based on CLTM-s01, MoonUSGS359, ULCN359 and

GLTM2C.

4 Summary

More than 3 million topographic measurements collected in two months by the Chang’E-1 laser altimeter (LAM) have been used to produce an accurate global lunar topographic model CLTM-s01. This model has greatly improved the previous ones, especially over the polar regions, with accuracy and resolution better than 31m and 7.5km respectively. This paper presents the laser altimeter data and its topography results in detail, from which the fundamental parameters of the lunar shape are obtained. All the parameters are in good agreement with the results of Clementine, but with higher accuracy. As the estimated orbit is the main error source of the topography model, our next important task is to improve the orbit information as much as possible by analyzing all the available satellite observation data. Meanwhile, how to effectively remove pseudo-elevations, thoroughly assess the lunar topographic model, and make use of the topography in conducting geophysics research, are the basic work in lunar geodesy to follow. Acknowledgments. This project has been co-supported by Chang’E-1 monitoring and control systems, scientific applications system and the satellite systems. The data analysis is also supported by the

knowledge innovation project the “Hundred Excellent Project” of Chinese Academy of Sciences. Authors like to thank Dr. M. A. Wieczorek and G. A. Neumann for the constructive opinions on processing the lunar laser altimetry data. References： 1 Smith D E , Zuber M T, Neumann G A, et al. Topography of the Moon from the Clementine Lidar, J. Geophys. Res, 1997,102, 1591–1611 2 Zuber M T, Smith, D E, Lemoine F G, et al. The Shape and Internal Structure of the Moon from the Clementine Mission, Science, 1994, 266, 1839–1843. 3 Wieczorek M A, The Gravity and Topography of the Terrestrial Planets, Treatise on Geophysics, 2007, 10, 165-206 4 Wieczorek M A, Jolliff B L, Khan A, et al, The Constitution and Structure of the Lunar Interior, Reviews in Mineralogy & Geochemistry,2006, Vol.60, pp. 221-364 5 Ping J S, Heki K, Matsumoto K, et al. A Degree 180 Spherical Harmonic Model for the Lunar Topography, Advances in Space Research, 2003, Volume 31(11), Pages 2377-2382 6 Margot J -L, Campbell D B, Jurgens R F, et al. Topography of the Lunar Poles from Radar Interferometry: A survey of Cold Trap Locations, Science, 1999, 284, 1658–1660 7 Cook A C, Watters T R, Robinson M S, et al. Lunar polar topography derived from Clementine stereoimages. J Geophys Res, 2000, 105: 12,023-12,033 8 Cook A C, Spudis P D, Robinson M S, et al. Lunar Topography and Basins Mapped Using A Clementine Stereo Digital Elevation Model, Lunar and Planetary Science XXXIII (2002) 9 Archinal B A, Rosiek M R, Kirk R L, et al. The Unified Lunar Control Network 2005, U. S. Geological Survey Open-File Report 2006-1367, 2006, Version 1.0 10 Archinal B A, Rosiek M R, Kirk R L, et al. Report on the Final Completion of the Unified Lunar Control Network 2005 and Lunar Topographic Model, U. S. Geological Survey Open-File Report, 2007 11 Margot J –L, Campbell D B, Jurgens R F, et al. Topography of Tycho Crater, J. Geophys. Res., 1999, 104, 11,875-811,882 12 Huang Y，Orbit Determination of the First Chinese Lunar Exploration Spacecraft CE-1，Doctorial Thesis， 2006，Graduate University of Chinese Academy of Sciences(Shanghai Astronomical Observatory) 13 Konopliv A S, Asmar S W, and Yuan D N, Recent Gravity Models as a Result of the Lunar Prospector mission, Icarus, 2001, 150, 1–18 14 Li Z L，Zhu Q，Digital Elevation Model (second edition), Wuhan，2007，Wuhan University Press 15 Kaula W M, Theory of Satellite Geodesy, New York, 2000, Dover Publicationa 16 Sagitov M U, Bodri B, Nazarenko V S, et al, Lunar Gravimetry, Academic Press, London, 1986, Academic Press

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