The Moving Trajectory Fitting Based on Three-Dimensional Digital Model of Barchan Dunes in Taklimakan Desert

Barchan dunes are generally formed in areas with unidirectional or opposite winds, and are named for their planar shape resembling a crescent [1-4]. They are widely distributed in deserts all over the world, thus making their formation, development and evolution frequent study subjects for researchers of aeolian sand landforms and blown sand physics [5-8]. As mobile entities, Barchan dunes often indicate the material transportation direction on earth’s surface with the direction of its own movement [3,9]. Further, a dune’s moving velocity can also be used to estimate the quantity of sand sediment. The metrics of Barchan dunes have become important reference indices in wind and sand fi xation engineering [10-12]. Although signifi cant progress has been made in the research of dune development modes and conditions, morphological evolution, the surface air fl ow and eroded sedimentation, wind-sand fl ow structure and sediment transport rate, sedimentary structure and moving laws of sand dunes and morphological evolution [13-15], there is still no consensus on the processes of morphological evolution, moving speed, moving direction and the infl uential factors of Barchan dunes.


Introduction
Barchan dunes are generally formed in areas with unidirectional or opposite winds, and are named for their planar shape resembling a crescent [1][2][3][4]. They are widely distributed in deserts all over the world, thus making their formation, development and evolution frequent study subjects for researchers of aeolian sand landforms and blown sand physics [5][6][7][8]. As mobile entities, Barchan dunes often indicate the material transportation direction on earth's surface with the direction of its own movement [3,9]. Further, a dune's moving velocity can also be used to estimate the quantity of sand sediment. The metrics of Barchan dunes have become important reference indices in wind and sand fi xation engineering [10][11][12]. Although signifi cant progress has been made in the research of dune development modes and conditions, morphological evolution, the surface air fl ow and eroded sedimentation, wind-sand fl ow structure and sediment transport rate, sedimentary structure and moving laws of sand dunes and morphological evolution [13][14][15], there is still no consensus on the processes of morphological evolution, moving speed, moving direction and the infl uential factors of Barchan dunes.
The existing literature on the moving distance and direction of sand dunes assumes that the moving trajectory is a straight line, but the actual moving trajectory of sand dunes has not been researched or analyzed enough [6,[16][17][18]. With Citation: Lia  Here, the evolution of Barchan dunes was monitored in the hinterlands of the Taklimakan Desert. We used a Huace X90 GNSS receiver in its RTK working mode to obtain 3D coordinates of the dune surface with a high temporal resolution at millimeter precision. Using geological mapping software CASS It can also lay a foundation for the improvement of a formula for moving speed, which is important because many fi elds of research consider the moving speed and direction of mobile sand dunes. Taklimakan desert has a typical temperate continental arid climate, with annual precipitation in the hinterland less than 50 mm and annual evaporation over 3000 mm. The site may be windy for up to seven months each year, with a dominant north-easterly wind and a maximum wind speed of 30 ms -1 [19][20][21]. In the area, tall composite longitudinal dunes and inter-dune lower lands are distributed at intervals. The longitudinal dune direction is N56°E-N50°E with a height of 60-80m, and the main dune stretches abnormally with an asymmetrical transect [22][23][24]. The NW slope is a sand falling slope with a gradient of about 32° and an altitude of 3060 m. It is comprised of overlaying secondary sand falling slopes [25]. The SE slope is gentle, with Barchan dunes overlaid on the upper part. The lower part is mainly comprised of secondary longitudinal dunes or sparse Barchan dune arrays, with a direction consistent with that of the longitudinal dunes [26,27]. The Barchan dunes or dune chains stand at 13m in the 12 km wide stretch of low land between the sand ridges. They have a windward slope gradient of about 11°, a sand falling slope gradient of about 32°, a trend direction of about S70°W and typical morphological development [28,29].

Study area and data acquisition
The survey area is located in the inter-dune area along the petroleum highway of the Taklimakan Desert. The spatial scale of Barchan dunes is relatively small, with two wings pointing downwind from the main NE wind, and the cross sections having an asymmetrical slope [14,30,31]. The mean values of the main morphological parameters of 36 Barchan dunes in the survey area were 15.289 m, 1.238 m, 7°23″ and 27°31″ for average width, height, windward slope angle and leeward slope angle, respectively. The width tends to be about 10 times the height and the dune shape is typical. Data acquisition: In the second half of April 2015, the middle of October 2015, the fi rst half of March 2016 and the mid-to-late period of October 2016, four monitoring sessions were carried out in the evolution monitoring zone. The 3D coordinate measurements were acquired with the Huace X90 GNSS receiver, which consists of a base station, a mobile station, a data chain and control software ( Figure 2). The base station sends the differential correction data through links via a radio station to the mobile station, where data is resolved immediately to acquire high-precision spatial data regarding the position of the mobile station [26,32,33].
The RTK (real-time kinematic) working mode of the X90 GNSS receiver was chosen for the measurement of 3D coordinates. RTK is a real-time dynamic positioning technology based on carrier phase observation values, it can provide realtime 3D coordinates of the station in an appointed coordinate system at millimeter precision. In sum, it offers the advantages of high precision, easy operation and freedom from sighting limitations [34][35][36].
Mobile station coordinates were based on the Beijing 54 Coordinate System. The GNSS receiver was used to measure the surface coordinates of the sand dunes, and the measured coordinates were calculated based on the base station [37][38][39]. To ensure consistency of the starting coordinates of the base station, base station translation was necessary after it migrated or was restarted at unknown spots. In this way, the coordinates of the moving dunes measured during the monitoring period had uniform starting coordinates [29,40,41]. For coordinate measurement, the X90 GNSS receiver was fi rst installed and set up. Then the four boundary points of the monitoring area, A, B, C and D, were determined. Point A was selected as the reference point and point B was selected as the detection point for accuracy of base station translation ( Figure 1). Based on the geometric principle that a plane can be determined with three noncollinear points, the position of the survey area could be accurately identifi ed with the base station starting point, reference point A and detection point B. The surface of the sand dunes was measured in a path along the contour line ( Figure  2). The measuring points were spaced approximately 50 cm apart with the density of measurements increasing as terrain steepened.
Due to the weight of digital fi eld books and the measurement rod, the depth at which the measurement rod penetrated the sand face could hardly be controlled during measurement.
At the same time, the natural surface of the sand dune could also be slightly altered by the measurer's trampling. All of these infl uences led to errors between measured and actual coordinates of each measurement point, and infl uenced the overall accuracy of the measurements. To reduce this measurement error as much as possible, a round rubber pad with a diameter of approximately 5 cm and a thickness of 0.5 cm was fi xed to the lower end of the measurement rod to prevent it from falling into the sand's surface. However, it was impossible to completely prevent measurement error.

Establishment of 3D digital model of barchans dunes:
The 3D coordinate data collected in the fi eld was exported in DAT format, and CASS 9.0 was used to plot the elevation points and draw the boundary lines to create a digital elevation model (DEM). DEM, contour lines with intervals of 0.005 m throughout the entire survey area and contour intervals of 0.001 m for each single sand dune was drawn [42][43][44]. Then, ArcMap 10 was used to project the dune contour using the 28th projection zone in Gauss-Kruger 3° in the Beijing 54 Coordinate System [45][46][47][48]. The 3D digital model of each individual sand dune was established with specifi c steps, as shown in Figure 3.
The establishment of the 3D digital model for the entire survey area was similar to that of the individual sand dune, but it did not require grid clipping [49][50][51][52].
After defi ning the projection, the contour line in the DWG format was exported to SHP format, and a Triangular Irregular Network (TIN) was established. To further simplify the data algorithm and to prepare it for the clipping and smoothing of data, data in TIN format was converted to raster form, which can show details of elevation change and is better formatted for the analysis and processing algorithms and have simple topological relations [53][54][55][56]. The required raster data was extracted by using the existing vector data, and the focus statistics tool was used to smooth data and eliminate "noise" pixels from raster images [57][58][59]. After clipping and smoothing, the data was converted to TIN format and added to ArcScene10 to establish a 3D digital model of both the survey area and the individual dunes ( Figure 4).

Fitting the moving trajectory of Barchan dunes
As a mobile sand dune, a Barchan dune keeps moving under the joint infl uences of many factors, such as wind power. In this paper, taking the typical dune D3 as an example, the fi tting process of the moving trajectory was described based on the simulation and superposition analysis of 3D digital models during different measurement stages. The specifi c fi tted technical route was shown in Figure 5.       Table 1.

Analysis of results of fi tting the moving trajectory and infl uential factors
Analysis of results of fi tting the moving trajectory: Between the fi rst and second monitoring periods, the results of fi tting the movement trajectories of corresponding characteristic points of the eight selected typical sand dunes ( Figure 6   They curved convex to SE or SW with different directions and short lengths, and the corresponding points rotated clockwise with rotation angles ranged from 31° to 37° (Figure 7, Table   1). The movement of the dunes during this period may be understood as a clockwise rotation centered at the front end of the left wing. Therefore, between the second and third monitoring period, the moving speeds of the different points on dunes varied greatly. For example, the moving speed of the right wing end point was much faster than that of the left wing end point, whose trajectory length was also shorter.
Contrary to the rotation direction between the fi rst and second monitoring periods, dunes rotated clockwise in this period.
The appearance of the rotation angle of dunes indicates that the actual movement path of the Barchan dunes between the second and third monitoring periods were curves rather than straight lines.
According to the results of fi tting the moving trajectory of the selected eight typical dunes between the third and fourth monitoring periods (Figure 8,

Analysis of infl uential factors on the moving trajectory
Wind regime is one dynamic factor causing the motion of Barchan dunes. The sand dune here kept rotating clockwise or counterclockwise while moving from NE to SW, which might be the main reason why the sand dune moved along a curve rather than a straight line. The total progress of the dune movement was consistent with the downwind direction of the main local sand-moving winds, which blow ENE, NE and E during all four seasons in the survey area Figure 9) [60,61].
The monitoring took place from May to September (fi rst and second) and from April to September (third and fourth) in subsequent years. The survey area was subjected to sandmoving winds from the ENE, NE and E in the spring and autumn, and from the NNE, N and NNW in the summer. The total annual average sand drift potential of effective sand-moving wind in directions NNW-E was about 189 VU, accounting for over 80%  Figure 10). Therefore, during the two monitoring intervals, the effi ciency of effective sand-moving wind and the wind speeds were at yearly highs. The sedimenttransporting capacity was strong, the wind-sand activity was frequent, and the sand dunes moved forward rapidly from NE to SW. In summer, when the declination between the effective sand-moving wind in directions NNE, N and NNW and the axial direction of the dunes was larger than 30°, the NE side of the sand dune's windward slope became a windward front slope, and the sand strongly eroded. In this situation, the SW side of the Barchan dune became a windward back slope, and it continuously accumulated sand transported from the windward front slope. The erosion and accumulation pattern on the sand dune surface changed the lateral wing of the sand falling slope, and the sand dune rotated counterclockwise. Therefore, during the two periods, the dunes moved forward along the trajectory curve directed from NE to SW and was convex to the NW.
The interval between the second and third monitoring periods lasted from November to February. During this period, the survey area was dominated by winter monsoons. The effective sand-moving wind mainly blew in the ENE, NE and E directions. As a result, the sand-transporting potential from November to February accounted for less than 1% of the whole year ( Figure 10). When the declination between the effective sand-moving wind blowing to the E and ENE and the axial direction of dune was larger than 30°, the SE side of the dune's windward slope became a windward front slope, and the sand was greatly eroded. The NW side of the dune's windward slope became a windward back slope and continuously accumulated sand transported from the windward front slope, so the sand dune rotated clockwise. Therefore, during this monitoring period, the sand dune moved forward slowly along a curve directed from NE to SW that was convex to SE or SW. For the sand dune moving slowly from NE to SW, it may be understood that it rotated clockwise with the front end of the dune's left wing as the center, so the moving speed of the end point of the right wing was much greater than that of the end point of the left wing.

Discussion
Barchan dunes are mobile dunes. Their movement often indicates the material transportation direction on earth's surface [63,64]. Additionally, a dune's moving velocity can be used to estimate the quantity of sand sediment transported. These are important reference indicators of wind prevention and sand fi xation engineering, and they are closely associated with the movement trajectory of all sand dunes [65][66][67][68][69]. So far, there has been little research on fi tting the moving trajectories of Barchan dunes. Many past observational studies have assumed that the dunes move forward along straight lines, of which the length is measured as the moving distance [8,70,71]. However, the actual movement path of sand dunes varies in track length, moving direction and moving speed.
Based on the raw data acquired in the studies of the straight-line moving trajectory of sand dunes, the formula for the moving speed of Barchan dunes shows that the moving speed is inversely proportional to dune height and is proportional to the sand transport amount of wind-sand fl ow [72][73][74][75]. Using mathematical statistics, Yang Gensheng, et al. [76] also obtained a negative linear correlation between the sand dune moving speed and height. His functional expression was y=14.03-0.64h (y-moving speed (m/a), h-dune height (m)). However, if computations are made with the functional correlation obtained in previous studies, the computed values of sand dune moving speed greatly deviate from measured values. This indicates that the existing formulas for dune moving speed still require further improvement. Fitting the Barchan dune moving trajectory accurately may provide a basis for better defi ning and capturing sand dune movement. It may also lay a foundation for further improvement of the formula for computing moving speeds of sand dunes [77,78].
The moving direction of Barchan dunes can indicate the transport direction of surface sand material. Fitting the moving trajectory of sand dunes can provide further confi rmation of the direction in which dunes move. Existing studies show that sand dunes move in a straight line from the starting (front) to ending (rear) points of the sand dune in relation to the downwind direction of synthesis wind, and that the moving direction of different points at different positions is the same along the straight-line moving trajectory. However, the results of this study indicate that the moving trajectory of Barchan dunes is a curve, rather than a straight line, due to its continuous rotation throughout the moving process. Therefore, the moving direction of a point on the dune should be the tangential direction of the point on the trajectory curve and directed in the downwind direction of the synthetic wind. The moving directions of the same point should differ at different positions along the trajectory curve.
Fitting the moving trajectories of Barchan dunes can provide an example for how to fi t the moving trajectories of other mobile sand dunes. It can assist also in gathering more accurate data, such as moving distance and moving speed of mobile sand dunes. Lastly, it lays a foundation for improving the formula for moving speeds of mobile sand dunes and for future studies on other research topics concerning moving speeds and directions of mobile sand dunes.

Conclusion
In the research, an evolution survey area was established for Barchan dunes in the Taklimakan desert hinterland, and the RTK working mode of the Huace X90 GNSS receiver was used to obtain 3D coordinates of the dunes at a high temporal-spatial resolution with millimeter precision. CASS 9.0 and ArcGIS 10.0 were used to establish and superimpose 3D digital models of sand dunes in the survey area. Finally, the three elements of starting point, end point and included angle were used to fi t a moving trajectory curve of corresponding characteristic points on a sand dune with the Auto CAD 2010 software. The results of fi tting showed that the sand dunes in the survey area moved along curves rather than straight lines, and they also displayed evidence of signifi cant seasonal features.
Wind regime is a dynamic factor causing the motion of Barchan dunes. Barchan dunes move along curves rather than straight lines mainly because the dunes continuously rotate either clockwise or counterclockwise while moving forward from NE to SW.
Wind-sand activities were frequent during the intervals between the fi rst and second monitoring periods, as well as between the third and fourth monitoring periods. The effective sand-moving wind was mainly determined by winds in NNW-E directions with strong sand transport capacity, and sand dunes moved forward rapidly from NE to SW. The declination was larger than 30° between the effective sand-moving wind in directions NNE, N and NNW and the axial line of the sand dune, which led to the counterclockwise rotation of the dune. This is the main reason why the moving path of the sand dune was a curve directed from NE to SW and convex to NW, rather than a straight line. During the interval between the second and third monitoring periods, the wind frequency of the effective sanddriving wind in directions ENE, NE and E was small, and the sand transport capacity was weak. The declination between the effective sand-moving wind in directions E and ENE and the axial line of the sand dune was larger than 30°, which led to the clockwise rotation of the dune. This was the main reason why the moving path of the sand dune was a curve directed from NE to SW and convex to either the SE or SW, rather than a straight line. Because the sand dune moved slowly from NE to SW, it could be understood that it rotated clockwise, with the front end point of the left wing as the center, so that the moving speed of the end point of the right wing of the sand dune moved much faster than the end point of the left wing.
Fitting the Barchan dune moving trajectory accurately may provide a basis for better defi ning and capturing sand dune movement. It may also lay a foundation for further improvement of the formula for computing moving speeds of sand dunes, as well as for other future research concerning mobile sand dunes.