Paleotopographic Controls on Loess Deposition in the Loess Plateau of China

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EARTH SURFACE PROCESSES AND LANDFORMS Earth Surf. Process. Landforms (2015) Copyright © 2015 John Wiley & Sons, Ltd. Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/esp.3883

Paleotopographic controls on loess deposition in the Loess Plateau of China

Li-Yang Xiong,1,2,3,4,5 Guo-An Tang,1,2,3* Josef Strobl4 and A-Xing Zhu5 1 Key laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing, 210023, China 2 State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing, 210023, China 3 Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, 210023, China 4 Department of Geoinformatics – Z_GIS, University of Salzburg, Salzburg 5020, Austria 5 Department of Geography, University of Wisconsin-Madison, Madison, USA

Received 16 August 2015; Revised 1 December 2015; Accepted 2 December 2015

*Correspondence to: G.-A. Tang, Key laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University; Nanjing 210023, China. E-mail: [email protected]

ABSTRACT: The underlying pre-existing paleotopography directly influences the loess deposition process and shapes the morphology of current loess landforms. An understanding of the controlling effects of the underlying paleotopography on loess deposition is critical to revealing the mechanism of loess-landform formation. However, these controlling effects exhibit spatial variation as well as uncertainty, depending on a study’s data sources, methodologies and particular research scope. In this study, the geological history of a study area in the Loess Plateau of China that is subject to severe soil erosion is investigated using detailed geological information and digital elevation models (DEMs), and an underlying paleotopographic model of the area is constructed. Based on the models of modern terrain and paleotopography, we introduce a watershed hierarchy method to investigate the spatial variation of the loess- landform inheritance relationship and reveal the loess deposition process over different scales of drainage. The landform inheritance relationships were characterized using a terrain-relief change index (TRCI) and a bedrock terrain controllability index (BTCI). The results show that the TRCI appears to have an inverse relationship with increasing research scope, indicating that, compared with the paleotopography of the region, modern terrain has lower topographic relief over the entire area, while it has higher topographic relief in the smaller, local areas. The BTCI strengthens with increasing drainage area, which demonstrates a strong controlling effect over the entire study area, but a weak effect in the smaller, local areas because of the effect of paleotopography on modern terrain. The results provide for an understanding of the spatial variation of loess deposition in relation to paleotopography and contribute to the development of a process-based loess-landform evolution model. Copyright © 2015 John Wiley & Sons, Ltd.

KEYWORDS: loess deposition; paleotopography; spatial variation; watershed hierarchy

Introduction on the underlying paleotopography is thus critical to a better understanding of its formation mechanism and landform evolu- In the loess deposition process, dust moves and accumulates tion process. on underlying paleotopography, playing a key role in shaping There has been extensive research on the loess dust transport the surface morphology of loess regions, which exist across and deposition rate, and many methods have been developed the globe (Bradley, 2015). The loess landforms of the Chinese to understand the process of loess dust deposition on underly- Loess Plateau, the vast arid desert areas in Central Asia, and ing paleotopography. The literature includes studies that have the Yellow River system, together form a huge geomorphic unit looked at the origin of loess dust transport using mineralogical that extends over an area of ~500 000 km2, almost completely and geochemical methods (Schaetzl, 2008; Muhs et al., 2013; sitting on underlying paleotopography from the Quaternary pe- Zhang et al., 2013), OSL dating to find the loess deposition rate riod (Liu et al., 2001; Lu et al., 2011). Evolved over 2.6 million (Lai et al., 2007; Chen et al., 2013; Stevens et al., 2013a; Yang years in the East Asian monsoon climate, loess deposits have et al., 2014; Youn et al., 2014) and loess relief reconstruction been differentially deposited and eroded in the windward slope through a pedological analysis (Rodzik et al., 2014). Studies and the leeward slope, and have shaped the well-known spe- of the loess and palaeosol layer have explored the relationship cific loess landscapes (Xiong et al., 2014a, 2014b). This unique between climate change and the loess deposition process, and formation mechanism reflects the loess deposition process, be- are prominent in loess-landform research. These include a cause the specific and diverse loess landforms are the conse- comparison of loess-palaeosol layers in China and Europe quence of its spatial variation. A deeper analysis of the loess (Vasiljević et al., 2014), periodic evidence of loess layers and deposition process and its spatial variation and dependency palaeosol layers in rare loess-deposition areas (Hobbs et al., 2011), L.-Y. XIONG ET AL. vertical variations in the luminescence sensitivity of quartz 2014). However, the effect of the original, underlying pre- grains from the Luochuan loess-palaeosol section (Lü et al., quaternary surface, before the loess deposition evolved, has re- 2014), paleoenvironmental changes that are revealed by the ceived scant attention. The morphology and distribution of the interaction of loess sediment distribution and loess-paleosol paleotopography may have significantly affected spatial variation layers (Pan et al., 2012; Kühn et al., 2013; Lehmkuhl et al., in the loess deposition process. Although there have been studies 2014; Wang et al., 2014), and the influence of climate on the of the spatial variations in loess deposition that are influenced by loess deposition process, using detrital remanent magnetiza- hydrologic and geologic factors (Rokosh et al., 2003), there are tion (Wang and Løvlie, 2010). The severe soil erosion in the still few studies looking at how the underlying paleotopography area has also led to frequent analysis (Stolte et al., 2003; Yang controls the loess deposition and its spatial variation in the Loess et al., 2006; Liu and Liu, 2010; Superson et al., 2014; Geng Plateau. It is still not clear if, during the loess deposition process, et al., 2015) and studies of pedogenic processes (Eger et al., the modern terrain has a lower or higher topographic relief than 2012). the original paleotopography at different scales (Figure 1). Also Previous studies have paid more attention to where the loess unclear is how the original paleotopography controlled the deposits come from, the deposition rate and how relevant the evolution of the modern loess landform. Hence, there is a need loess deposition process is to paleoclimate evolution (Guo to examine the effect of scale on the spatial variation of loess et al., 2002; Pan et al., 2012; Stevens et al., 2013b; Lü et al., deposition in relation to paleotopography.

Figure 1. Terrain relationships at different scales of scope. (a) Modern terrain has higher topographic relief compared with original paleotopography at a microscale. (b) Modern terrain has lower topographic relief compared with original paleotopography at a macroscale. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Figure 2. Study area. Area A is a zone of severe soil erosion in the Loess Plateau, Area B is a small area at the intersection of the Wu-Ding River and the Yellow River. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

With the development of the multiple data source acquisition relationships and to further reveal spatial variation in the loess de- and digital terrain analysis method (Geomorphometry; Evans, position process according to different drainage scales. 2012), it is possible to reconstruct pre-existing underlying paleotopography (Alexander et al., 2008; Campani et al., 2012; Perron and Fagherazzi, 2012; Castillo et al., 2014; Xiong et al., Study Area 2014c; Bergonse and Reis, 2015). A comparative analysis of both dual-layer terrains, including modern terrain and paleotopography, The main study area (Area A) (Figure 2) is a zone of severe soil could help to reveal the landform evolution process. In addition erosion in the upper-middle reach of the Yellow River basin to the pixel-based and rectangular block-based terrain analysis (Upper and Middle Yellow River Bureau, 2012) with a geolog- that uses DEM to describe the spatial variation of landform char- ical history that is relatively tectonically stable, located in the acteristics, a real-landform object or unit-based method could Ordos platform surrounded by mountains and rift valleys (Liu, become a standard method in landform analysis. Just as the 1985; Hu et al., 2012; Pan et al., 2012; Yuan et al., 2012; Xiong watershed has been regarded as the principal hydrologic unit et al., 2014c). The area is between 106.4°–12.7° E and 34.29°– for sediment movement in fluvial geomorphology (DeBarry, 40.11°N, with a total area of approximately 144 190 km2.Mod- 2004), it could also be regarded as an ideal unit for landform ern typical loess landforms, i.e. loess hill, loess ridge and loess ta- analysis. In addition, an analysis of watersheds at multiple bleland, were formed on the platform (Xiong et al., 2014a; Zhu scales could allow us to carry out a landform analysis from a et al., 2014). The main study area, Area A, includes the upper- microscale to macroscale scale, which is important because a middle reach of the Yellow River and its three main secondary multi-scale representation of geospatial data is critical in geo- branches, the Wu-Ding River, the North Luo River and the Jing science research (Quattrochi and Goodchild, 1997). River, from northeast to southwest (Figure 2). We also extract a We consider the paleotopography underlying loess deposits in small test area (Area B) from Area A for a detailed accuracy the Loess Plateau while evaluating the spatial variation and assessment. This area is near the intersection of the Wu-Ding River dependency of the loess deposition process. On the basis of de- and the Yellow River, with an area of approximately 9500 km2. tailed geological information from geologic maps and the high- In addition to the loess sediments, gullies and streams are resolution digital elevation model (DEM), we reconstructed the widely distributed in the area, and act, as they do everywhere, paleotopographic surface, and used RMSE to judge the accuracy as the backbone of the landscape. They not only collect and of different interpolation results. Two indicators, a bedrock terrain transport water, sediment, organic matter, and nutrients from controllability index (BTCI) and a terrain relief change index upland mountain regions to the oceans (Willett et al., 2014), (TRCI), have been proposed to define loess-landform inheritance but they also erode the sediment and expose the bedrock chan- and the relationship between the underlying terrain and the mod- nel to natural processes. The Loess Plateau is covered by loess ern terrain. An uncertainty analysis of DEM cell-size dependency deposits and is dominated by a semi-arid continental monsoon was also conducted to check the stability of the relationships climate, which caused the loess dust from the northwestern de- between these two terrains. Based on the modern terrain and un- sert areas to be deposited in the study area during the Quaternary. derlying paleotopography relationship, we introduced a water- Loess deposits currently cover >80% of the entire area (Figure 3), shed hierarchy method to statistically analyze their surface with the remaining areas represented by different types of

Figure 3. Geology and study area samplings. (a) geology (b) outcrops. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Figure 4. Modern surface and suspect underlying surface interpolated by outcrops.

Copyright © 2015 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2015) L.-Y. XIONG ET AL. bedrock channel outcrops exposed continuously along the in positive terrain (convex). The unique geological and geo- gullies and streams. The outcrops are located in gullies and graphical background of the area allows for an evaluation and streams in negative terrain (concave) surrounded by loess deposits reconstruction of the pre-existing, underlying terrain (Figure 4).

Figure 5. Terrain relationships between modern terrain and underlying terrain. (a) Modern terrain has lower topographic relief than underlying paleotopography, corresponding with the slope of their scatter diagram (a-p) being smaller than 1. (b) Topographic relief of the underlying and modern terrains is the same, corresponding with the slope of their scatter diagram (b-p) being equal to 1. (c) Modern terrain has higher topographic relief than underlying paleotopography, corresponding with the slope of their scatter diagram (c-p) being greater than 1.

Figure 6. Scales of watershed delineation. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Materials and Methods unify the resolution, the SRTM data were resampled using the nearest neighbor method to obtain a DEM with a resolution of Materials 100 m. This SRTM is used to discuss the paleotopographic controls on loess deposition for the entire study area. Geologic Two types of DEM were employed. The first one, used for the maps (Figure 3(a)) with a scale of 1:200 000, created by the small Study Area B, is a 25 m horizontal resolution DEM, digi- Institute of Geology and Geophysics (Chinese Academy of Sci- tized from contours of 1:50 000 topographic maps produced ences), were the data source for bedrock outcropping points by the Shaanxi Bureau of Surveying and Mapping. This DEM detected in the loess area. is used for a detailed accuracy assessment because it has relatively high resolution. The second one, used for the entire Study Area A, was derived from the Free Shuttle Radar Topography Underlying paleotopography modeling and terrain Mission (SRTM), an international project to obtain a DEM at relationship definitions near-global scale from 56°S to 60°N (Nikolakopoulos et al., 2006; Farr et al., 2007). The horizontal resolution of the SRTM The coordinates and elevations of outcropped bedrock strata data in the Loess Plateau is approximately 90 m. In order to located in gullies and streams, and especially those located at

Figure 7. Study workflow. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Figure 8. Underlying terrain using different interpolation methods. (Kriging: Ordinary Kriging with Spherical Semivariogram model, Number of points in a radius = 12. IDW: Power = 2, Number of points in a radius = 12. Spline: Tension Spline, Weight = 0.1, Number of points in a radius = 12.) This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Copyright © 2015 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2015) L.-Y. XIONG ET AL. the boundary of loess deposits and bedrock channels, were col- correspond to Figure 5(b_p), with n equalto1.Inthispaper,the lected from DEMs and geological maps. Google Earth imagery n value is defined as the terrain-relief change index (TRCI). was then applied for georeferencing these outcrops. Finally, a n dataset of 28076 underlying terrain outcrops (Figure 3(b)) was ∑ ðÞ ðÞ xi x yi y obtained and a paleotopographic surface model could be con- ¼ R ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii 1 (2) n n structed using interpolation. We used the Ordinary Kriging ∑ ðÞ 2 ∑ ðÞ 2 xi x y i y method with a Spherical Semivariogram model to interpolate i¼1 i¼1 the surface of the study area after comparing a number of interpolation methods (Franke, 1982; Mitas and Mitasova, 1988; Hengl and Evans, 2009). Ninety percent of the dataset (25268 The correlation (R) between these two terrains could also be outcrops) were used for the interpolation, and the remaining regarded as the controlling effect of the pre-Quaternary underly- 10% (2808 outcrops) were used for accuracy detection. ing terrain on the modern terrain, that is, the bedrock terrain con- Theoretically, there should be three topographic relief rela- trollability index (BTCI). tionships between the pre-existing paleotopography and the modern terrain: the modern terrain has lower topographic relief compared with the paleotopography (a in Figure 5), indicating Watershed hierarchy terrain analysis a deposition process in which the loess dusts were more likely The watershed is a basic geographical unit with independent to have been deposited and accumulated on the concave part landform characteristics. One drainage basin drains into an- of the paleotopography; the modern terrain has higher topo- other in a hierarchical pattern, with smaller sub-drainage basins graphic relief compared with the underlying terrain (c in combining into larger drainage basins (Figure 6). The spatial Figure 5), indicating that the loess dusts were more likely to variations of landform characteristics from microscale to have been deposited and accumulated on the convex part of the paleotopography; and both the terrains have comparable relief (b in Figure 5). These relationships can be expressed quantitatively by plotting the elevation of the modern terrain against the underlying paleotopography. Their relationships can be expressed as a simple linear function.

Y ¼ m þ nX (1)

where X is the elevation of the paleotopography, Y is the elevation of the modern terrain, and m and n are coefficients obtained from the linear equations. These relationships can be revealed by a scatter diagram. If the modern terrain has a higher topographic relief (c in Figure 5), it corresponds to Figure 5(c_p) with slope value n greater than 1, while if it has a lower topographic relief (a in Figure 5), it corresponds to Figure 5(a_p) with slope value n less than 1. Terrains of comparable relief (b in Figure 5) Figure 10. Terrain relationship tendency in the small study area (Area B).

Figure 9. Extracted profiles of different interpolation results from two locations shown in Figure 8. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Table I. Evaluation of different interpolation methods

IDW Kriging Natural Neighbor Spline TIN

Maximum error (m) 69.86 61.97 63.27 70.81 66.74 Minimum error (m) 0 0 0 0 0 Mean error (m) 4.60 3.91 3.91 4.63 3.99 Standard deviation 6.23 5.12 5.02 5.68 5.15 RMSE 7.74 6.44 6.37 7.33 6.51

Copyright © 2015 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2015) PALEOTOPOGRAPHIC CONTROLS ON LOESS DEPOSITION macroscale could also be revealed using a watershed hierarchy across hierarchies of watersheds. We used this method to ana- statistical analysis. lyze the loess deposition process in watersheds between areas A number of methods are available that delineate watershed from 10 km2 to 10 000 km2 in order to reveal loess-landform in- hierarchies and extract drainage networks (Castronova and heritance characteristics. Goodall, 2014). We used the standard method in ArcGIS Spa- The workflow for the study is shown in Figure 7. As shown tial Analyst to delineate watershed hierarchies because it is suf- in the figure, we identify the outcrops of the pre-existing un- ficient for the loess landform of the Loess Plateau (Zhu et al., derlying terrain first, and then construct a dual-layer terrain 2013). We divided the test area into watershed hierarchies with model that contains the modern and underlying terrain. After a minimum threshold of 10 km2 – because this is considered an accuracy assessment of underlying terrain using RMSE (root the minimum watershed landform unit (Zhu et al., 2013) in mean square error) and DEM cell size (Hengl and Evans, the Loess Plateau – and with a maximum threshold of 10 2009), we investigate the loess-landform inheritance and 000 km2. We could then statistically characterize the terrain loess-deposition process by using the aforementioned terrain

Table II. Terrain relationships in two study areas with different watershed thresholds

Study area B(25 m cell size) Study area A(100 m cell size)

Threshold (cells) Watershed area (km2) Watershed number TRCI BTCI Watershed area (km2) Watershed number TRCI BTCI

1000 0.625 5921 2.43 0.36 10 11863 1.71 0.54 2500 1.5625 2297 2.04 0.42 25 4580 1.56 0.55 5000 3.125 1191 1.79 0.47 50 2317 1.5 0.57 10000 6.25 558 1.58 0.53 100 1153 1.38 0.6 25000 15.625 229 1.39 0.60 250 453 1.24 0.63 50000 31.25 105 1.31 0.66 500 234 1.15 0.64 100000 62.5 59 1.24 0.69 1000 117 1.1 0.68 250000 156.25 26 1.12 0.75 2500 39 0.92 0.75 500000 312.5 8 1.04 0.797 5000 16 0.87 0.77 1000000 625 3 1.04 0.81 10000 9 0.91 0.83

Figure 11. Hierarchical structure of watershed division over the entire study area. (a) Watershed area with threshold of 10 000 km2. (b) Watershed area with threshold of 1000 km2. (c) Watershed area with threshold of 100 km2. (d) Watershed area with threshold of 10 km2. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Copyright © 2015 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2015) L.-Y. XIONG ET AL. relationship definitions and watershed hierarchy terrain analy- its relatively low standard deviation and RMSE compared with sis method. those of the other methods.

Results Spatial variation of landform inheritance

Paleotopography The loess-landform inheritance relationship from underlying terrain to modern terrain, or the BTCI and TRCI, was investi- The reconstructed loess-underlying paleotopography, modeled gated according to the terrain relationship definitions and with different interpolation algorithms, is shown in Figure 8(b)–(f). Equation (1), at different scales of drainage, and is shown in Figure 8(a) shows the modern DEM for comparison. The figure Figure 10 and Table II. For the small study Area B, the average shows that when using high-density points for interpolation, the values of BTCI and TRCI are detected from a number of spline-method appears to result in increasing noise with higher watersheds that range from 3 (corresponding to a threshold of RMSE value (Figure 9, Table I), although the method is suitable 1 000 000 cells or 625 km2) to 5921 (corresponding to a thresh- for the underlying terrain structure with sparse origin points old of 1000 cells or 10 km2). Results confirm that with increas- (Xiong et al., 2014c). The accuracy assessment of the remaining ing thresholds, the TRCI gradually decreases, and that there is 10% of data is shown in Table I. The table shows that the accu- an increasing BTCI during the loess-deposition process. Besides racy results for other methods do not appear to be significantly a gradually decreasing trend, the average TRCI values are all different from each other, all showing a maximum error of around greater than 1 but gradually move toward 1, suggesting that 65 m, mean error around 4 m, and a similar standard deviation modern terrain has a higher topographic relief than underlying and RMSE. In light of all of these factors, we selected the results terrain in these relatively small watersheds, a finding that of the Ordinary Kriging method for further loess-deposition anal- appears to contradict results from other studies (Xiong et al., ysis, because of its lowest maximum and mean error, as well as 2014c). The finding from study Area B warranted more detailed

Figure 12. Statistical units of different spatial scales of watershed. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Copyright © 2015 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2015) PALEOTOPOGRAPHIC CONTROLS ON LOESS DEPOSITION research on the TRCI by expanding the research scope to the shows that the BTCI in all watershed hierarchies with a thresh- entire Loess Plateau. old of 10 000 km2 is around 0.83, which shows the profound For the entire study Area A, we used the aforementioned controlling effect at a relatively macro scale that the underlying watershed terrain analysis method to investigate the loess- paleotopography has on the evolution of modern terrain. This landform inheritance relationship. Figure 11 shows several controlling effect appears to decrease significantly, however, watershed hierarchies with different thresholds (Table II). The when the watershed area is smaller (0.54 corresponding to figure shows that, from the entire study area located in the mid- 10 km2 watershed), in which case the strong controlling effect dle reaches of the Yellow River basin, nine second-order tribu- remains only in the southeast; these locations are mainly lo- taries, such as the Wu-Ding River, the North Luo River and the cated in areas with less dense loess cover, near the mountains Jing River, could be classified as having a watershed area (i.e. Ziwu and Huanglong Mountains in the south, and Lvliang threshold of 10 000 km2 (Figure 2), and as many as 11863 wa- Mountain in the east). This demonstrates that the BTCI is tersheds are classified in the entire area with a hierarchical smaller in the thick loess-covered area than it is in areas with level of a 10 km2 watershed area threshold (Figure 12). All wa- less dense loess cover. The phenomenon demonstrates that a tersheds were used to calculate their terrain relationship and profoundly controlling effect existed at the beginning of the landform inheritance using the aforementioned terrain relation- loess-deposition process. ship definitions and Equations (1), (2) and (3).

Terrain-relief change index Bedrock terrain controllability index Figure 15 shows the spatial variation in the terrain-relief change Figure 13 shows the spatial variation of the bedrock terrain index (TRCI) from the underlying terrain to modern terrain in controllability index (BTCI) for different watershed hierarchies. different watershed hierarchies. Figure 16 shows their corre- Figure 14 shows their corresponding frequency distribution. It sponding frequency distribution. The TRCI in all watersheds

Figure 13. Spatial variation of BTCI in watershed hierarchies. (a), (b), (c), (d) correspond with a watershed area of 10 000 km2, 1000 km2, 100 km2, 10 km2. (BTCI closer to 1 means a stronger controlling effect.) This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Figure 14. Frequency of spatial variation in BTCI in watershed hierarchies. on a hierarchical level of 10 000 km2 is smaller than 1, which of the sensitivity of the DEM resolution to the loess deposition indicates that modern terrain has lower topographic relief than process and landform inheritance characteristics is necessary. underlying terrain (Figure 5(a)). However, with the decrease in With the underlying terrain modeled by Kriging (Figure 8(b)), watershed thresholds, the results vary. The TRCI in some water- we resampled both terrains from the original 25 m to 500 m cell sheds is still smaller than 1, while in other watersheds it re- size at an interval of 10 m. Figure 18 shows the loess-deposition verses and becomes greater than 1 (meaning that modern relationship according to Equation (1) with different DEM cell terrain has higher topographic relief), until the drainage area sizes. It shows that the terrain relief change (Figure 10(a)) from reaches 2500 km2 (Table II), when the overall trend of the TRCI the underlying terrain to the modern terrain appears to fluctuate reverses to greater than 1 from smaller than 1(Figure 5(c)). slightly with increasing cell size, until the resolution is greater These highlighted watersheds with TRCI greater than 1 (higher than 350 m, when the result becomes unstable. The result of topographic relief) are mainly located in the northwest part of bedrock terrain controllability (Figure 10(b)) is similar, that is, the study area and in the Dong-zhi loess tableland area. The until the resolution is greater than 400 m, the characteristics northwest area is near the desert where the dust originated, of bedrock terrain controllability appear unstable. These results and is characterized by the process of continual loess dust de- prompted us to conduct an analysis on the loess-deposition position and severe wind erosion. The Dong-zhi tableland area process, with SRTM DEM of 100 m cell size over the entire area is the largest, and a typical, loess-tableland landform area with of severe soil erosion in the Loess Plateau, in order to illustrate gullies that are quite deep. This topographic characteristic in a comprehensively the loess-deposition process variance and its small watershed of modern terrain clearly has higher topo- dependency on bedrock terrain. graphic relief than the original paleotopography.

Controls on loess deposition Discussion Profound controlling effects that shape the morphology of mod- Evaluation of the paleotopography ern topography from the paleotopography could be found over the study’s entire macro-scale Loess Plateau (Liu, 1985; Yuan An interpolation of the underlying terrain is clearly key to re- et al., 2007a; Xiong et al., 2014c). Our results also suggest that vealing paleotopographic controls on loess deposition. The ini- modern topography preserved the primary trend of the tial accuracy results (Table I) suggest that the Kriging method is paleotopography during the loess-deposition process. The pri- suitable for paleotopography reconstruction. However, the in- mary trend of modern topography is still high in the NW and terpolated result could also be influenced by the input low in the SE, which is similar to the paleotopography in the parameters (Bergonse and Reis, 2015), such as the Semivariogram study area, and which corresponds to the BTCI, which is close models and the number of points in a radius. Figure 17 shows the to 1. The modern terrain also has a lower relief than the results for different input parameters for the Kriging evaluation. It paleotopography, according to this macroscale controlling ef- suggests that Circular, Exponential and Spherical models have a fect. The loess dust was more likely to fill the original valleys similar RMSE, which is lower than Gaussian and Linear models. (Saey et al., 2008), completely covering the original low hills, The selection of the Spherical Semivariogram model and of which resulted in a TRCI of greater than 1. the 12 points in the radius could be suitable input parameters However, when downscaling the research domain, that is, for this study. decreasing the area of watersheds, spatial variation and scale A reasonable DEM resolution is a function of both the source effect of paleotopographic controls on loess deposition can data and the interpolation process that is carried out on the be seen in the study area. The BTCI appears to decrease signif- source data (Fisher and Tate, 2006), and is critical to the accu- icantly with the decrease of watershed thresholds, while the racy of a landform-process investigation. Thus, an assessment TRCI appears to have an inverse relationship with increases in

Figure 15. Spatial variation of the TRCI in watershed hierarchies. (a), (b), (c), (d) corresponding with a watershed area of 10 000 km2, 1000 km2, 100 km2,10km2. (TRCI less than 1 means modern terrain has lower topographic relief compared to the underlying terrain, greater than 1 means modern terrain has higher topographic relief compared to underlying terrain.) This figure is available in colour online at wileyonlinelibrary.com/journal/espl research scope. The TRCI result suggests that modern terrain, The BTCI becomes stronger with increasing drainage area, but not paleotopography, reverts to a higher topographic relief showing a strong controlling effect in the overall study area, in the smaller, local areas. The mean-value tendency for the en- while it is weak in local areas from the paleotopography under- tire study area was also investigated and the results are shown lying modern terrain. in Figure 19 and Table II. They show that the mean values of Because the East-Asian monsoon climate and wind-blown BTCI and TRCI are detected from nine watersheds (correspond- loess-deposition process have existed across the study area during to a threshold of 1 000 000 cells or 10 000 km2) to 11863 ing the Quaternary period, studies of genetic linkages between watersheds (corresponding to the threshold of 1000 cells or deserts and loess-covered areas help us to know where the 10 km2). These tendencies appear to match the former results, loess dusts originated (Guo et al., 2002; Pan et al., 2012; demonstrating that with increasing thresholds, the degree of Stevens et al., 2013b; Lü et al., 2014), but not how modern to- TRCI gradually decreases, and there is an increase in BTCI dur- pography was shaped during the loess-deposition process. The ing the loess-deposition process. The TRCI appears to show a morphological differences in the original terrain should be one reversal process depending on the research scope, that is, with of the key factors in controlling the spatial variation of the loess- increasing drainage area, the topographic relief of modern ter- deposition process and in shaping the modern topography. The rain appears at first to be greater than that of paleotopography differentiated uplift process of tectonic divisions and the ero- (e.g. when the drainage area is 10 km2), but the increase in re- sion process at the Yellow River basin are the key factors in lief gradually decreases until the drainage area reaches shaping the morphological differences of the original terrain. 2500 km2, when the topographic relief of modern terrain is less During the Cenozoic period, there were three major tectonic than that of the paleotopography, indicating that the modern divisions in the Loess Plateau: the Ordos stable platform, the terrain has lower topographic relief in the prevailing trend of Longxi region and the Fenwei-Hetao graben (Pan et al., 2011; the entire area, while it has higher topographic relief in the Hu et al., 2012; Yuan et al., 2012). The Ordos platform is se- smaller, local areas compared with the underlying terrain. lected here because it is a key part of the Loess Plateau, with

Figure 16. Frequency of spatial variation in the TRCI in watershed hierarchies. This figure is available in colour online at wileyonlinelibrary.com/ journal/espl

Figure 19. Terrain relationship tendency over the entire study area. Figure 17. Input parameters evaluation for Kriging interpolation. This figure is available in colour online at wileyonlinelibrary.com/journal/espl appeared across the entire platform, which contributes to ex- tremely weak tectonic deformation in this area (Liu, 1985; the most typical loess-deposition process and loess landforms. Kusky and Li, 2003; Yuan et al., 2007b; Li and Li, 2008; Pan The Ordos platform is a large, intracratonic platform (Yuan et al., 2012; Cheng et al., 2014). Although a stable area was se- et al., 2007b). The tectonic activity of this platform has lected here, the other tectonic divisions with differentiated up- remained relatively stable since the Mesozoic period. An inte- lift should be the focus of future research concerned with grated and intermittent uplift process with a rare, slow speed paleotopographic controls on loess deposition.

Figure 18. DEM cell size dependence of the terrain relationship. (a) Terrain relief change dependent on DEM cell size. (b) Bedrock terrain controllability dependent on DEM cell size.

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