The topographic controls on the decadal-scale erosion rates in Qilian Shan Mountains, N.W. China

Earth and Planetary Science Letters 292 (2010) 148–157

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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l

The topographic controls on the decadal-scale erosion rates in Qilian Shan Mountains, N.W. China Bao-tian Pan, Hao-peng Geng ⁎, Xiao-fei Hu, Ran-hao Sun, Chao Wang Key Laboratory of Western China's Environmental Systems, Ministry of Education, Lanzhou University, Lanzhou 730000, PR China Room 313, Key Laboratory of Western China's Environmental Systems (MOE), Lanzhou University, No. 222 South of Tianshui Road, Lanzhou, Gansu 730000, PR China

a r t i c l e

i n f o

Article history: Received 23 July 2009 Received in revised form 16 January 2010 Accepted 19 January 2010 Available online 11 February 2010 Editor: T.M. Harrison Keywords: Qilian Shan Mountains erosion mean local relief topography climate

a b s t r a c t The relationships between climate, topography, and erosion are significant in understanding landscape evolution. In order to study this relationship in a tectonically active landscape, the details of 11 drainage basins were collected from Qilian Shan Mountains. Decadal-scale erosion rates, including the mechanical load and solute load contributions, are estimated in natural conditions. The calculated erosion rates show that the average erosion rate of Qilian Shan Mountains is about 0.08 mm/yr, while the variation of annual erosion rates within each basin is significant. The changes of topography and climate, which potentially control erosion rates, are also employed in this paper for correlating analyses. Correlation analyses indicate that erosion rates are more closely correlated with topographic variables, such as mean local relief and mean slope, than all of the climatic variables; and mean local relief and decadal-scale erosion rates show a linear relationship in these tectonically active mountains. However, some topographic variables like basin area and elongation ratio exert limited influence on erosion rates; while others, such as basin elevation, basin relief and basin roughness, show poor correlation. The results indicate that topographic control, like aspects of the local terrain steepness, plays the most important role in spatial distribution of decadal-scale erosion rates throughout Qilian Shan Mountains. Under topographic control, some climatic variables, like discharge and runoff, however, could account for the significant variation of annual erosion rates in individual basin. When comparing erosion rates on different timescales, we found that the decadal-scale erosion rates are lower than the long-term river incision rates, as well as the exhumation rates during early and middle Miocene. The change to more arid climatic condition since the middle Miocene combining with tectonic uplift should attribute to the inconsistent erosion rates over different timescales in Qilian Shan Mountains. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Previous studies have presented a theoretic coupling and feedback between tectonics, climate, and erosion in long-term landscape evolution (Molnar and England, 1990; Brozovic et al., 1997; Willett, 1999; Beaumont et al., 2001; Zhang et al., 2001; Montgomery and Brandon, 2002; Molnar, 2003). In this coupling and feedback system, the critical issues are the competing role of tectonic and climatic influence on erosion rates, whereas agreements have never been reached (Burbank et al., 2003; Dadson et al., 2003; Reiners et al., 2003; Wobus et al., 2003). Tectonics and climate could control the type and intensity of erosional processes individually and collectively, and

⁎ Corresponding author. E-mail addresses: [email protected] (B. Pan), [email protected] (H. Geng). 0012-821X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2010.01.030

thereby could modify topography and eventually landscape evolution, so current topography can be viewed as interactive results between tectonics, climate and erosion (Brozovic et al., 1997; Willett, 1999; Montgomery et al., 2001; Molnar, 2003). In a short timescale, a lot of previous works by many researchers have focused on the role of topographic control on erosion processes. Some evidence, from large rivers to small mountainous rivers, indicated that the erosion rate was highly related to topographic variables, which are emphasized in terms of basin area (Milliman and Syvitski, 1992), average slope of drainage basin (Harrison, 2000; Aalto et al., 2006), average basin elevation (Pinet and Souriau, 1988), basin relief (Schumm, 1963), local curvature of the landscape (Roering et al., 1999), local relief (Ruxton and McDougall, 1967), basin relief ratio (Summerfield and Hulton, 1994) and mean local relief (Ahnert, 1970), respectively. Since most of these variables are associated with the steepness of terrain (i.e. slope and relief), it has been suggested that greater relief and steeper slope could lead to faster erosion (Schumm, 1963; Ahnert, 1970; Pazzaglia and Brandon, 1996). Nevertheless, it is not widely accepted whether erosion rate simply depends on topographic control. Some evidence indicates that

B. Pan et al. / Earth and Planetary Science Letters 292 (2010) 148–157

certain climatic variables, including precipitation, discharge or runoff, play the most important role in short-term erosion rate (Summerfield and Hulton, 1994), even in a tectonically active mountain range with abrupt slope and high relief (Galy and France-Lanord, 2001; Gabet et al., 2008). After 5 yrs of monitoring discharge and suspended sediment concentrations during the monsoon season in the High Himalayas, Gabet et al. (2008) reported average erosion rates increased along with the enhanced discharge and precipitation across the entire study area. Similarly, Galy and France-Lanord (2001) suggested the intensity of the monsoon acted as the first-order control on the high erosion rates in the Himalayas. Erosion rates on different timescales, derived from modern sediment yield, river incision and thermochronological data, are estimated for completing or updating the erosion database. In addition, most of the studies focused on tectonically active mountain ranges (Montgomery et al., 2001; Montgomery and Brandon, 2002; Dadson et al., 2003; Reiners et al., 2003), especially Himalaya (Burbank et al., 2003; Wobus et al., 2003; Thiede et al., 2004; Clift et al., 2008; Gabet et al., 2008). The Qilian Shan Mountains are considered as a tectonical response to the uplift of the Qinghai– Tibetan Plateau; however, only river incision rates (Hetzel et al., 2002; Pan et al., 2003; Pan et al., 2007) have been reported. So we should pay more attention to complete the erosion database and to explore the potential relationships between tectonics, climate, topography and erosion in these areas. This paper is designed to produce a better understanding how the topography and climate influence erosion rates through combining detailed data about three inland rivers as well as their tributaries originating from the Qilian Shan Mountains. Records of discharge, suspended sediment concentration and hydrochemical data, on a decadal-scale, are used to estimate average erosion rates for each drainage basin. Meanwhile, many topographic and climatic controlling variables are also measured, which provide us a basis for studying the relationship between the erosion rates and potential variables controlling erosion.

2. Geologic and geographic setting The study area spans almost the entire Qilian Shan Mountains, which are located along the northeast margin of the Qinghai–Tibetan Plateau. Due to the collision between the Indian subcontinent and Eurasia, Qinghai–Tibetan Plateau and its adjacent areas have been experiencing intense tectonic movement since early Cenozoic (Molnar and Tapponnier, 1975; Tapponnier et al., 2001; Royden et al., 2008). The Qilian Shan Mountains are constrained within a compressive belt by two left-lateral strike-slip faults (i.e. Altyn Tagh Fault and Haiyuan Fault) (Meyer et al., 1998), thereby, the deformation and fault folds occur widely. The terrane in the study areas primarily consisted of sedimentary rocks, such as siltstone and mudstone, partly metamorphic rocks (i.e. migmatite, gneiss etc.) and igneous rocks (i.e. granite and quartz diorite). Many inland rivers, originated from the high altitude areas of Qilian Shan Mountains, incise the tectonically active margin and then flow into the arid Hexi Corridor basin. These rivers, downcutting through the active deformation, together with the strikingly steep topography, contribute a major part in controlling the sediment flux and shaping landform. Therefore, the study of rivers in Qilian Shan Mountains is good at understanding the potential feedback mechanism between tectonics, climate and erosion in landscape evolution. Heihe River, Shule River, Shiyang River and their main tributaries are all involved in our study area, and 11 drainage basins are selected in this paper (Fig. 1). Moreover, these basins have abrupt topography and striking precipitation gradient; meanwhile, all the drainage basins are rarely inhabited with only small parts cultivated, so human influence can be considered negligible.

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3. Materials and methods 3.1. Erosion rates The erosion rates are derived from reliable estimation of total sediment load including suspended load, bed load and solute load (Table 1). The three sediment loads are calculated by daily discharge, daily suspended sediment concentration and main dissolved solids. The data of discharge and suspended sediment concentration are monitored at 11 hydrological stations (Fig. 1) with the record history between 1956 and 2000. These stations have been established in the upper reaches as well as the outlets of selected drainage basins. Note that the data of main dissolved solids with the record history between 1971 and 1980 are monitored at five of the hydrological stations (Changmabao, Yingluoxia, Binggou, Qilian, and Jiutiaoling), together with other six hydrochemical stations (Fig. 1). The data mentioned above are all collected by the Hydrology Bureau of Gansu Province, P.R. China. In each hydrological station, the real-time stages were monitored; and frequent cross-section surveys, including depths, velocities and suspended sediment concentrations of all survey points, were also implemented whenever the character of cross-section changed. Therefore, the measurements of daily discharge were based on realtime stage monitoring in conjunction with stage-discharge rating curves established by the results of every cross-section surveys. Similarly, a point-total rating relationship between total suspended sediment concentration and concentration for a special survey point was established in each cross-section survey. The daily suspended sediment concentrations were estimated by the point-total relationships and daily monitoring of suspended sediment concentrations for the special points. Suspended load could be calculated directly from averaged suspended concentration multiplying by discharge. Bed load measurement is an intractable problem, and it is not monitored in the 11 hydrological stations. But in general, the ratio of bed load contributing to total solid load could be a reliable agent to predict bed load from suspended load (Milliman and Meade, 1983; Summerfield and Hulton, 1994). In previous studies, Wang et al. (1998) suggested 14% as a ratio of bed load to suspended load in Changma River, which has a coarse sand–gravel bed like most other rivers in Qilian Shan Mountains. Since the rivers in Qilian Shan Mountains are similar to Changma River, we deduce that the other rivers in our study areas should have similar ratio of bed load to suspended load and assumed 14% for all rivers. Solute load could not be calculated directly from total dissolved solids, because there are no available data. But the main dissolved solids were monitored at midday with a measurement interval of ten days for five hydrological stations together with other six hydrochemical stations. The water samples of main dissolved solids were selected at the center of the river and then sent to the laboratory for analyses of ionized solid concentrations using spectrophotometer. Finally, the main dissolved solids could be calculated from the main dissolved solid concentrations multiplying by discharges which were simultaneous measuring data. However, the main dissolved solids − (i.e., K+, Ca2+, Na+, Mg2+, Cl−, SO2− 4 , and HCO3 ), representing most of the ionized solids in the water, could roughly equal to the total dissolved solids. Despite the fact that five hydrological stations mentioned above also monitor main dissolved solids, they do not provide synchronous data in parallel with daily discharge and suspended concentration. Harrison (1994) believes that dissolution only depends on the amount of water, and also suggests that solute load plotted as a function of discharge. Similarly, we also find a strong linear correlation (y = 0.85x + 5.29, x is discharge in m3/s, y is solute load in 104t/a, with a significant level of 5%) between discharge (simultaneous measuring data) and solute load (Fig. 2), which is accounted by main dissolved solids. Therefore, the linear equation

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Fig. 1. Shaded-relief map of study area in Qilian Shan Mountains. Rivers are shown in black lines with locations of hydrological stations (digits 1–11 with white pentacle) and hydrochemical stations (digits 12–17 with black cycle). White dashed lines delineate two major faults (Altyn Tagh Fault and Haiyuan Fault) modified by Meyer et al. (1998).

about discharge with solute load provides an opportunity to offset the deficiency of solute load data. Employing discharges of the 11 stations allow us to obtain a relatively accurate and synchronous solute load data set for each basin. The calculation of the three kinds of sediment loads in each hydrological station produces an average erosion rate of its upstream contributing area. Except Zhamashike and Yingluoxia both of which are located at the trunk of Heihe River, the rest of the nine hydrological stations are established at nine different rivers. There-

fore, Yingluoxia station also embodies the river information kept in Zhamashike station and Qilian station which locates at Babao River, a tributary of Heihe River (Fig. 1). In addition, there are three main sources of potential errors in our erosion rate calculations. First, the length of recording history for the three stations (i.e. Danghewan, Liyuanbao, and Shajintai) is shorter than others and some stations lack a few years data within their record history. If extremely episodic sediment delivery influx happened in these years, it could lead to underestimation of erosion rates. Second, error also happens to the

Table 1 The tabulation of the station, river, area, loads, discharge, record history and calculated erosion rate for each drainage basin in Qilian Shan Mountains. Site no.a — Coordinates River hydrologic station Latitude Longitude

Area/ km2

Suspended load/ (103 t/yr)

Bed load/ (103 t/yr)

Solute load/ (103 t/yr)

Total load/ (103 t/yr)

Erosion rateb/ (mm/yr)

Record historyc

1 — Danghewan 2 — Changmabao

39°39′N 94°53′E 39°39′N 96°51′E

13,762 10,910

687 2963

96 415

85 127

868 3505

0.02 0.12

1972–2000 1956–2000

— Binggou — Xindi — Liyuanbao — Zhamashike

39°36′N98°00′E 39°39′N98°49′E 38°58′N100°00′E 38°13′N99°59′E

6896 1582 2231 4585

692 670 408 1139

97 94 57 159

106 73 76 114

895 837 541 1412

0.05 0.20 0.09 0.12

1956–2000 1956–2000 1956–1989 1958–2000

2413 401 10,003d 2366 1082 153 842 146 455 72

56 331 21 21 10

91 189 80 73 63

548 2886 253 240 145

0.09 0.11 0.09 0.11 0.12

1956–2000 1956–2000 1957–2000 1956–2000 1959–1975

3 4 5 6

7 — Qilian 8 — Yingluoxia 9 — Jiutiaoling 10 — Zamusi 11 — Shajintai a b c d

38°12′N100°13′E 38°14′N100°11′E 37°52′N102°03′E 37°42′N102°34′E 37°28′N102°36′E

Danghe River Changma River Taolai River Danshui River Liyuan River Upper Heihe River Babao River Heihe River Xiying River Zamu River Huangyang River

Keyed to Site nos. in Fig. 1. Erosion rates are calculated assuming a mean rock density of 2650 kg/m3. Record history lists the monitoring years for each station, where some stations lost few years' data in their record history. This value of Heihe River's basin area reckoned in the upper Heihe River's basin area and Babao River's basin area.

B. Pan et al. / Earth and Planetary Science Letters 292 (2010) 148–157

Fig. 2. Scatter plots of the annual discharge versus annual solute load recorded by the 11 stations. The error-weighted regression (solid line) indicated a positive relationship and the equation is highly significant at 5% level. When the least-squares approach is used to fit linear regression, we find that the residual errors of some points are large. Therefore, each point is given a weight according to its residual error in order to fit an optimal linear regression.

assumption of the ratio of bed load to suspended load, which is likely to bring uncertainty into total solid loads in 10 of the drainage basins. Third, the extrapolation of solute loads is uncertain, though solute loads contribute less than total solid loads. Unfortunately, it is hard to provide the uncertainty analysis for the three main sources of potential errors. However, the suspended load, accounting for the major part of the total load, is calculated based on actual measuring data (i.e. daily discharge and daily suspended sediment concentrations) and we think that the suspended load is accurately estimated. So, we consider that the results are acceptable for the study. 3.2. Potential variables controlling erosion The purpose of variable selection is to involve adequate factors in controlling erosion. The definitions or calculations of the 13 potential variables controlling erosion are listed in Table 2.

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The composite digital elevation model (DEM, with a resolution of 3 ″, SRTM) of Qilian Shan Mountains and grid-based analysis tools are used to characterize the topography of our study areas. The eight topographic variables (Table 2) provided a wide data set to display various elements of the topography. Note that mean slope is measured over 3 × 3 cell neighborhood around the center cell (270 m × 270 m); however, the mean local relief is measured over a 10-km-diameter moving window. The two variables are both invoked to describe the different spatial scales of the steepness of terrain, by inference, the different effects on erosion rates. Moreover, the mean local relief has been defined as a mean of maximum–minimum elevation within each round cell (Ahnert, 1970), and the 10-km-diameter is chosen as a length scale spanning the width of the largest valleys in the range (Montgomery and Brandon, 2002). For comparing the data, all the topographic variables were measured by using standard GIS techniques and the results are listed in Table 3. Discharge and runoff, as defined in Table 2 and presented in Table 3, can be calculated from the records of the hydrological stations. Furthermore, the estimations of rainfall and temperature are based on data sets of 35 meteorological stations located in Qilian Shan Mountains and their adjacent ranges (Fig. 3). For the purpose of obtaining the basin-average values, the meteorological data, temperature and rainfall, were averagely and spatially interpolated into the digital elevation model. However, 13 of the meteorological stations just provided rainfall data in their monitoring; the estimation of temperature in our study is based on 22 stations (Fig. 3B). Most of the meteorological stations provided a relatively long monitoring result but the climate regimes in mountains are complicated owing to the influence of vertical zonation. Given this, three stations (i.e. Ning Ch., Shang Ch., and Xi Y.) established at different elevations along Xiying River were added in order to improve estimation precision, but they only had three year records from 2006 to 2008. Multiple linear regression model has been attested to be the best method to compare with the other four conventional interpolation methods (i.e. inverse distance weighted, spline, ordinary kriging, and trend) in Qilian Shan Mountains (Zhao et al., 2006). Therefore, the multiple linear regression model, involving influence of both the location and topographic factors (i.e. latitude, longitude, and elevation), is utilized in this work to calculate the optimum estimation

Table 2 Definitions or calculations of the potential controlling variables. Variable Topographic variables Basin area Maximal elevation Mean elevation Basin relief Mean slope Mean local relief Elongation ratio Basin roughness

Definition or calculation

Defined as a topographic boundary within which all runoff drain to a single outlet; and calculated from the topographic boundary delineated from drainage lines and interfluve's contour forms (km3) Defined as the maximum basin elevation and can be directly generated from digital elevation model (m) Defined Defined Defined Defined

as as as as

the arithmetical mean of all the points' elevation and can be calculated through spatial statistical analysis (m) a mean of slope all over each 3 × 3 cell neighborhood around the center cell (270 m × 270 m) in each basin (m) a mean of slope all over the grid cell in each basin (degree) a mean value of maximum–minimum elevation over all the 10-km-diameter round cell in each basin (m)

Defined as the ratio of the diameter of a circle with the same area (as that of the basin) to the length of the basin (no units) Calculated as the ratio of surface area to projective area in each basin (no units)

Climatic variables Discharge Calculated by averaging daily mean discharge (volume/time) over the record history (m3/s) Runoff Defined as mean annual discharge (volume) divided by basin area (mm/a) Rainfall Calculated from the interpolation of annual rainfall recorded by 35 meteorological stations, of which 32 stations were established by Meteorological Bureau of Gansu Province, P.R. China, while the rest three were established by us in 2006 (mm/a) Temperature Calculated from the interpolation of annual temperature recorded by 22 meteorological stations, of which 19 stations were established by the Meteorological Bureau of Gansu Province, P.R. China, while the rest three were established by us in 2006 (°C) Trunk Total trunk stream power per unit channel length (W/m) is defined by: Ω = γQs, where γ is the specific weight of water (9810 N/m3), Q is the water discharge stream power (m3/s), and s is the energy slope (m/m) which may be approximated byvalue the slope of the channel bedrainfall (Knighton, 1999). of annual average and temperature. Specifically, a linear

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Table 3 Topographic and climatic variables of study basins in Qilian Shan Mountains. Drainage basin

Danghe Basin Changma Basin Taolai Basin Danshui Basin Liyuan Basin Upper Heihe Basin Babao Basin Heihe Basin Xiying Basin Zamu Basin Huangyang Basin

Maximal elevation

Mean elevation

Basin relief

Mean slope

Mean local relief

Elongation ratio

Basin roughness

Discharge

Runoff

Mean rainfall

Mean temperature

Trunk stream power

m

m

m

deg

m

–

–

/(m3/s)

/(mm/yr)

mm/yr

°C

W/m

5646 5766 5308 5544 5072 4879 4917 5012 4903 4861 4353

3872 3970 3885 3916 3121 3925 3612 3679 3526 3484 3283

3472 3695 3290 3750 3296 2052 2210 3333 2650 2847 2022

9.5 16.0 16.9 23.8 17.9 13.0 15.7 17.3 23.7 22.1 20.5

773 1105 1217 1729 1180 918 1029 1123 1340 1283 1342

0.41 0.48 1.79 0.27 0.54 0.53 0.62 0.50 0.69 1.15 0.33

1.98 2.86 3.99 3.62 2.59 2.94 3.51 4.34 3.24 2.97 1.99

3.52 8.71 6.24 2.51 2.14 7.14 4.41 15.97 3.15 2.37 1.22

8.07 25.16 28.54 49.98 30.23 49.13 57.62 50.35 91.92 88.81 84.90

189 155 141 138 186 260 363 287 414 404 486

1.9 1.8 1.8 1.5 4.1 1.7 3.8 2.8 5.5 5.3 5.8

852 790 1258 813 299 584 432 4245 560 470 331

Note. — means that elongation ratio and basin roughness are dimensionless.

Fig. 3. The spatial distribution of mean rainfall (A) and mean temperature (B) in Qilian Shan Mountains. (A) The interpolation of rainfall was estimated by MLR model combining with IDW using records of 35 meteorological stations. The linear regression relationship for rainfall was established by 26 modeling stations, however, the rest 9 validation stations (i.e. Jin T., Min L., Wu W., Yu M., Wu Sh., Shang Ch., Bing G., Zhu L., and Bian D.) were employed to calculate residual errors, by which IDW was used for further interpolation. (B) The estimation of temperature followed the same procedure as rainfall using 22 meteorological stations. The linear regression relationship for temperature was established by 16 modeling stations and the rest validation stations were Jin T., Yong Ch., Zhang Y., Ning Ch., Qi L. and An X.

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regression relationship between the mean rainfall (Pmean) and location/topographic factors is established as the following: Pmean = 296:7942 + 19:5832X−334:6037Y + 210:5436H

ð1Þ

where H is the elevation in meter, X is the longitude in degree, and Y is the latitude in degree. The same practice is used to establish a linear relationship between the mean temperature (Tmean) and location/topographic factors as expressed in the following: ð2Þ

Tmean = 12:8869−0:8115X−3:9478Y−13:2261H

where H, X, and Y are defined as before. Additionally, the data of rainfall and temperature are standardized before being used to estimate the two linear regression equations. Moreover, four conventional interpolation methods are also employed to compare with the multiple linear regression (MLR) model in this paper. To compare the five models, the original data set is divided into a modeling data set and a validation set of measuring stations. Predictions on the locations of the validation points and the measured values at these locations are compared by root mean square deviations. Root mean square deviations are given for the five interpolation methods (Table 4); and the results indicate that the MLR model also appears to be the most accurate method for interpolating climatic variables. Furthermore, in order to improve the precision of estimation, the residual errors of MLR model, which are calculated from the discrepancy between observed values and estimated values, are interpolated using the method of IDW (more reliable than the other three conventional methods). These interpolation results of residual errors are then added to the values estimated from MLR model. Eventually, the revised data of the rainfall and temperature distribution in Qilian Shan Mountains are illustrated in Fig. 3 and the values for each basin are presented in Table 3. 4. Results and discussion 4.1. Potential controls on erosion rates The results indicate that the average decadal-scale erosion rate of Qilian Shan Mountains is about 0.08 mm/yr. However, the spatial distribution of erosion rates is not uniform with an order of magnitude variation (Fig. 4). For example, the maximum erosion rate, measured at Xindi station at the outlet of Danshui basin, is 0.20 mm/yr, while the minimum value, recorded in Danghewan station at the outlet of Danghe basin, is only 0.02 mm/yr. Moreover, these data display a significant variation of the annual erosion rates for each basin within their respective record history (Fig. 4). The data for the erosion rates are distributed across a wide range of the values; at the same time, potential variables controlling erosion such as basin area, runoff, mean slope, mean local relief, elongation ratio, rainfall and trunk stream power, also show at least an order of

Table 4 Root mean square deviations of rainfall and temperature for five interpolation methods. Method

Inverse distance weighted (IDW) Spline Ordinary kriging (OK) Trend Multiple linear regression (MLR) model

Root mean square deviation Rainfall (Pmean)

Temperature (Tmean)

118.1 136.4 124.4 128.6 98.8

1.659 3.643 2.033 3.221 0.634

Note that the prediction of the five methods was using the same modeling data set and the same validation set of measuring stations.

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magnitude variation. Where these data sets spanning a wide range of values for the erosion rates as well as potential variables controlling erosion are available, they can be used to do an exploratory analysis. In previous studies, correlation and regression analysis has been widely used as a good method to study the relationship between the erosion rates and the potential variables (Milliman and Syvitski, 1992; Summerfield and Hulton, 1994; Harrison, 2000). In an attempt to determine which variables are of importance on erosion rates and to explore the relationships among these potential variables, we also use this method here with the Pearsonian correlation matrix for 13 potential variables controlling erosion and erosion rate in Table 5. The correlation analysis presented in Table 5 shows higher correlation of erosion rates with some topographic variables than any climatic variables. For example, erosion rates are highly correlated with mean local relief (0.72) and mean slope (0.61). Moreover, there is a significant positive correlation (0.91) between these two variables, both of which refer to terrain steepness. Actually, the mean local relief and mean slope could convert with each other via a linear function, as long as they are calculated over analysis window of the same diameter (Montgomery and Brandon, 2002). While the mean slope is stronger influenced by the resolution of DEM than mean local relief (Polidori et al., 1991), the latter appears to be a better predictor of erosion rates. The mean local relief has been coupled with the erosion rate as a linear relationship in mid-latitude drainage basins (Ahnert, 1970), subsequently this result is endorsed in some landscape-scale studies of interaction between tectonics and erosion (Summerfield and Hulton, 1994; Pazzaglia and Brandon, 1996). Alternatively, the linear relationship has the limited influence on the steep topography of tectonically active mountain ranges, where small changes in relief can lead to large changes in erosion rates related to landslide (Schmidt and Montgomery, 1995; Burbank et al., 1996; Montgomery and Brandon, 2002). In contrast to the previous studies, a linear relationship between the mean local relief and decadal-scale erosion is observed in Qilian Shan Mountains (Fig. 5), which are tectonically active mountain ranges with steep topography. In this study, the mean local relief is most highly correlated with erosion rates than any other potential variables controlling erosion, and the regression is significant at 5% confident level. At the same time, maximum value of mean local relief is parallel with the maximum erosion rate, and vice versa (Danshui basin and Danghe basin, respectively). Accordingly, the mean local relief can be seen as a direct determinant of decadal-scale erosion in Qilian Shan Mountains. The results indicate a negative relationship between the erosion rate and basin area (− 0.48), though the correlation is not strong. Previously, Schumm and Hadley (1961) noted that erosion rates in small basins should be higher than in larger basins, mostly because the smaller the drainage basin, the greater the ratio of upland areas to valley-floor areas, and thus the greater the proportion of areas for sediment production than that for sediment storage in the small basin. In this study, however, all of our drainage basins have large proportions of upland areas where high relief/slope is prevailing. Therefore, the apparent higher coefficient (−0.48) for basin area than some variables may result from the strong correlation between basin area and mean slope (−0.74) or mean local relief (−0.63). Similarly, we also find a negative relationship between the erosion rate and elongation ratio (− 0.42) which relates to the square root of the areas and characters of the shape of a basin, where the correlation is still not strong. Basin area and elongation ratio both have limited influence on erosion rates compared with topographic variables referred to as terrain steepness (i.e. mean slope and mean local relief), which indicates neither the area nor the shape of a basin plays the most important role on the spatial distribution of erosion rate in Qilian Shan Mountains. Specially, both the maximal elevation and mean elevation failing to associate with erosion rate indicate that the increasing elevation does not enhance erosion rate directly. On the other hand, the

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Fig. 4. The erosion rates for the 11 drainage basins. Note that the erosion rate with the asterisk* (Heihe Basin) is averaged over the entire drainage basin, including Upper Heihe Basin and Babao Basin; and the erosion rates in parentheses are the variation ranges of the annual mean erosion rates. The spatial distribution of average erosion rates was not uniform, showing an order of magnitude variation between the largest in Danshui Basin (0.2 mm/yr) and the lowest in Danghe Basin (0.02 mm/yr).

unobvious correlation between the basin relief and erosion rate also does not support the notion that basin relief is an important controlling variable on erosion rates (Schumm, 1963; Summerfield and Hulton, 1994). However, the mean local relief and mean slope, presenting two different spatial scales of terrain steepness in this study, both show a strong correlation with the erosion rate. These results agree with the viewpoint that the erosion occurring at a point is dominated by the terrain steepness of that point (slope) or its specific extension range (local relief), rather than the terrain steepness of the whole basin (Summerfield, 1991). In our study areas, the major erosion process is hillslope process dominated by water erosion, such as sheet erosion, rill erosion and gully erosion. Moreover, all the basins are characterized by the bedrock channel type, which indicates that the capacity of sediment transport exceeds supply rate for all size ranges supplied from upstream and from local slope erosion. The excess transporting capacity of the basins also could be evidenced from no correlation (0.00) between erosion rate and trunk stream power which expresses the river energy of a basin. Therefore, we speculate that the amount of

eroded material is probably determined by the amount and the velocity of overland flowing water accruing at local hillslope, which consequently could affect hillslope erosion. However, the overland flow will decrease with decreasing slope due to the increasing infiltration rate, and vice versa (Fox et al., 1997). Despite no direct evidence for infiltration rate in our study areas, we find a positive relationship between runoff and mean slope (0.73) or mean local relief (0.48) in these arid areas. For example, two adjacent basins, Changma Basin and Danghe Basin, have similar basin areas and rainfall, however, the more than 2-fold difference of runoff between the two basins probably results from quite different mean slope and mean local relief. Further, the velocity of flowing water should increase with increasing local relief or slope. The importance of local relief or slope on both the amount of overland flowing water and the velocity of flowing water could explain why there is a relatively high correlation of erosion rates with mean local relief or mean slope. Although a decoupling relationship between local relief and longterm erosion rates in high-relief landscapes has been proposed (Burbank et al., 1996; Montgomery and Brandon, 2002), we consider

Table 5 Pearsonian correlation matrix for all the potential controlling variables and erosion rate. Maximal Mean Basin elevation elevation relief Area 0.67⁎ Maximal elevation Mean elevation Basin relief Mean slope Mean local relief Elongation ratio Basin roughness Discharge Runoff Rainfall Temperature Trunk stream power

0.59 0.67⁎

Mean slope

Mean local Elongation Basin Discharge Runoff relief ratio roughness

0.53 − 0.74⁎⁎ − 0.63⁎ 0.85⁎⁎ − 0.32 − 0.10 0.35 − 0.38 − 0.17 − 0.01 0.18 0.91⁎⁎

⁎ Correlation is significant at the 0.05 level (2-tailed). ⁎⁎ Correlation is significant at the 0.01 level (2-tailed).

− 0.04 − 0.01 0.09 0.03 0.06 − 0.01

0.01 0.11 0.32 0.23 0.26 0.28 0.39

0.59 0.19 0.41 0.23 − 0.31 − 0.31 0.02 0.61⁎

− 0.77⁎⁎ − 0.76⁎⁎ − 0.47 − 0.60⁎ 0.73⁎ 0.48 0.01 0.05 − 0.27

Rainfall

Temperature Trunk stream Erosion power rate

− 0.55 − 0.86⁎⁎ − 0.57 − 0.77⁎⁎ 0.37 0.08 − 0.09 − 0.21 − 0.23 0.87⁎⁎

− 0.65⁎ − 0.77⁎⁎ − 0.84⁎⁎ − 0.54 0.54 0.23 0.00 − 0.29 − 0.43 0.80⁎⁎ 0.87⁎⁎

0.48 0.09 0.21 0.32 − 0.10 − 0.08 0.01 0.63⁎ 0.88⁎⁎ − 0.14 − 0.13 − 0.27

− 0.48 − 0.08 0.05 0.03 0.61 0.72⁎ − 0.42 0.23 − 0.01 0.37 0.03 − 0.03 0.00

B. Pan et al. / Earth and Planetary Science Letters 292 (2010) 148–157

Fig. 5. Scatter plots of mean local relief versus average erosion rate. Error bars (1σ) in erosion rates calculated by standard deviation show the variation ranges for each basin. The regression (solid line) indicates a linear relationship between mean local relief and average erosion rate, with the significant level of 5%.

that the topographic control, like aspects of the local terrain steepness (i.e. mean local relief and mean slope), plays the most important role in spatial distribution of erosion rates throughout Qilian Shan Mountains, on account of the discrepancy between the short-term erosion rates and the long-term average erosion rate in tectonically active mountain ranges (Kirchner et al., 2001). However, in Qilian Shan Mountains the mean local relief and mean slope are below the threshold, and the climatic regime is characterized by less rainfall; so the pore pressure is hard to be at risk of triggering landslides. In addition, the linear relationship between erosion rates and mean local relief also indicates that the tectonic forcing has less influence on the erosion in our study areas. Even if tectonic forcing landslides do occur occasionally, the mass accumulating on the foot slope during the form of landslides cannot be transported out of river systems immediately in this arid climatic condition. Therefore, we consider that the topographic control on spatial distribution of erosion rates is applicable in short timescale.

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Furthermore, rainfall, discharge and runoff, all of which are the proxies of flowing water, often play important roles in either the longterm erosion rates (Reiners et al., 2003; Clift et al., 2008) or the shortterm erosion rates (Galy and France-Lanord, 2001; Gabet et al., 2008), but the notion is not widely accepted (Milliman and Syvitski, 1992; Summerfield and Hulton, 1994; Riebe et al., 2001; Montgomery and Brandon, 2002; Aalto et al., 2006). In this study, none of the three climatic variables (i.e. discharge, runoff and rainfall) shows a close correlation with the decadal-scale erosion rates. Runoff, normalized by a basin area, has a higher correlation coefficient (0.37) than discharge and rainfall, probably due to the influence of basin area (correlation coefficient, −0.48). Temperature, highly correlated with runoff (0.79) and rainfall (0.87), also has insignificant effect on the erosion rate. The unclear correlations for the erosion rates versus all the climatic variables indicate that the climate has less effect on the spatial distribution of erosion rates in Qilian Shan Mountains. Nevertheless, the variation of the annual erosion rate, in individual basin, showed a strong association with the discharge, as well as the runoff. As illustrated in Fig. 6, the annual erosion rates increase with the discharge in individual basin and the positive correlations are significant at 1% confident level, except the two drainage basins (Danghe Basin and Liyuan Basin). This makes us reconsider the importance of the flowing water in individual basin, where the significant correlation between discharge and annual erosion rates could be elicited easily, owing to constant topographic variables. Therefore, the significant variations of annual erosion rates, for each basin, could be attributed to the climatic control. Even though the discharge and runoff could affect the variation of the annual erosion rate in individual basin, the influence of climatic control on the spatial distribution of erosion rates, for all basins, is still weak. This seemingly paradoxical phenomenon is due to the less rainfall and more infiltration in this arid climatic regime. Runoff is not perfectly correlated with rainfall (0.87) probably due to the effect of glacier melting; however, the main source of water supply for the basins is still the rainfall. As mentioned above, hillslope erosion is more affected by the local relief or slope; thereby, the intrabasin pattern of local relief or slope should have more influence on the spatial distribution of erosion rate compared with runoff and rainfall. So, we suggest that the topographic control plays the most important role in the spatial distribution of erosion rate and the climatic control determines the variations of annual erosion rates for individual basin.

Fig. 6. Scatter plots of the annual erosion rate versus discharge from individual station. Note that there is no regular pattern relationship between annual erosion rates and discharge, but the annual erosion rates increased with the discharge in individual basin. For all these basins, except Liyuan Basin and Danghe Basin, the linear correlations (note the logarithmic axes) are significant at 1% confident level. The calculation of annual erosion rate is based on the same method as that of average erosion rate, except that the data here is from a single year.

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4.2. Decadal erosion rates versus long-term erosion rates Most of the stations are located near the junction of active mountains to the passive plains; therefore, these results could give a general condition of the erosion rate in these tectonically active mountain ranges. But the erosion rates for study basins are lower than the long-term (103–106) river incision rates (0.09–0.25 mm/yr) in the eastern Qilian Shan Mountains (Pan et al., 2003; Pan et al., 2007) and (0.3–0.4 mm/yr) in the western Qilian Shan Mountains (Hetzel et al., 2002). Additionally, in geological timescales, apatite fission-track data imply the exhumation rates in northern Qilian Shan Mountains of 0.11–0.43 mm/yr over the early to middle Miocene (106–107), assuming a geothermal gradient of 30 °C/km (George et al., 2001). Despite the fact that the erosion rates estimated over different timescales may not be valid for direct comparison (Gardner et al., 1987), the inconsistent erosion rates over different timescales raise the question of whether we are underestimating the short-term erosion rates using modern river data. We consider that the methods by which erosion rates are measured could significantly influence the apparent rates of erosion. The river incision is concentrated erosion on the channel and it should be larger than the average erosion for basin as a whole, therefore, it is reasonable that the decadal erosion rates calculated by total sediment load in our study are low compared with the incision rates (103–106) estimated by river terraces. Moreover, the inconsistency could be attributed to the variation of erosional regimes in the past caused by climate change or tectonic uplift. A 29-million-year record of the oxygen isotope has implied a shift to more arid conditions at the NE margin of the Tibetan plateau due to the active uplift event at 12 Ma B.P. (Dettman et al., 2003); and a process of stepwise aridification has enhanced this arid conditions during the Quaternary glaciation (Wu et al., 2007). In the Holocene interglaciation global warming has not resulted in continuous high precipitation in study areas; on the contrary, rapid climatic change combined with 10 dry events also characterizes an arid condition especially during the late Holocene (Chen et al., 2001). Thus, the sustained aridification from the middle Miocene to the late Holocene could have contributed to more arid climatic regimes, and induces a lower erosion rate in Qilian Shan Mountains at present. That could explain why the exhumation rates measured by apatite fission-track data are larger than the modern erosion rates. Our interpretation of attributing the inconsistency of erosion rates over different timescales to climatic change can be further corroborated by the significant positive relationship between annual erosion rates versus discharge for individual basin on decadal timescale. Also, evidence of sedimentary formation indicates that the northern Tibetan Plateau has experienced multiple phases of tectonic uplift since middle Miocene (Song et al., 2001; Sun et al., 2005), which maintains the growth of Qilian Shan Mountains (Hetzel et al., 2004). So it is complicated to directly compare the difference between modern erosion rates and the long-term exhumation rates caused by tectonic uplift, as the erosional regimes at present are quite different since the middle Miocene owing to rapid climatic change. But still it is reasonable to compare the Quaternary river incision rates with the modern erosion rates. Likewise, rapid climatic change to more arid conditions is associated with tectonic uplift during the Quaternary (Li and Fang, 1998; Wu et al., 2007). In previous study, river incision has been considered to roughly balance with tectonic uplift (Maddy, 1997). In view of this, the tectonic uplift could increase river incision, further convincing us that the long-term river incision rates are larger than decadal erosion rates. On the other hand, the tectonic-driving surface uplift could also enhance terrain steepness because of the increased river incision. The conclusion that erosion rates are strongly associated with mean local relief or mean slope on decadal timescale lets us consider the potential increasing of erosion due to the enhanced terrain steepness. Therefore, we suggest that the potential increasing of erosion due to surface-uplift-rising terrain steepness

could be smaller than the decreasing of erosion due to climatic change to more arid condition. 5. Conclusion Decadal-scale erosion rates, estimated by total sediment load, present the average erosion rate in Qilian Shan Mountains of about 0.08 mm/yr, and display significant variations of annual erosion rates for each basin. Correlation analyses indicate that some topographic variables, like aspect of terrain steepness, mean local relief and mean slope, contribute more to the spatial erosion distribution. But, for individual drainage basin, we find that the annual erosion rates increase with increasing discharge, as well as runoff. Therefore, we suggest that topographic control plays the most important role in spatial erosion distribution in Qilian Shan Mountains; meanwhile, climatic control should contribute to the variations of annual erosion rates for each basin. In addition, under topographic control, the increased basin elevation or relief does not directly enhance the erosion rate; and this supports the viewpoints that erosion rates are dominated by the local terrain steepness of intrabasin rather than the terrain steepness of whole basins. We also emphasize a linear relationship between the mean local relief and decadal-scale erosion rate, in these tectonically active mountain ranges with steep topography. Additionally, the inconsistent erosion rates over different timescales in Qilian Shan Mountains probably could be attributed to rapid climatic change and tectonic uplift since the middle Miocene. Acknowledgements This research was financially supported by the National Science Fund for Distinguished Young Scholars (No. 40925001), the National Basic Research Program of China (No. 2005CB422001) and NSFC Innovation Team Project (No. 40421101). We acknowledge the Hydrology Bureau of Gansu Province, P.R. China and the Meteorological Bureau of Gansu Province, P.R. China for providing primary data. We really appreciate Bo Huang's assistance in data analyses, Amelie Joyce's revision of this paper, and two reviewers' constructing comments. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.epsl.2010.01.030. References Aalto, R., Dunne, T., Guyot, J.L., 2006. Geomorphic controls on Andean denudation rates. J. Geol. 114, 85–99. Ahnert, F., 1970. Functional relationships between denudation, relief, and uplift in large, mid-latitude drainage basins. Am. J. Sci. 268, 243–263. Beaumont, C., Jamieson, R.A., Nguyen, M.H., Lee, B., 2001. Himalayan tectonics explained by extrusion of a low-viscosity crustal channel coupled to focused surface denudation. Nature 414, 738–742. Brozovic, N., Burbank, D.W., Meigs, A.J., 1997. Climatic limits on landscape development in the northwestern Himalaya. Science 276, 571–574. Burbank, D.W., Leland, J., Fielding, E., Anderson, R.S., Brozovic, N., Reid, M.R., Duncan, C., 1996. Bedrock incision, rock uplift and threshold hillslopes in the northwestern Himalayas. Nature 379, 505–510. Burbank, D.W., Blythe, A.E., Putkonen, J., Pratt-Sitaula, B., Gabet, E., Oskin, M., Barros, A., Ojha, T.P., 2003. Decoupling of erosion and precipitation in the Himalayas. Nature 426, 652–655. Chen, F.H., Zhu, Y., Li, J.J., Shi, Q., Jin, L.Y., Wünemann, B., 2001. Abrupt Holocene changes of the Asian monsoon at millennial- and centennial-scales: evidence from lake sediment document in Minqin Basin, NW China. Chin. Sci. Bull. 46, 1942–1947. Clift, P.D., Hodges, K.V., Heslop, D., Hannigan, R., Van Long, H., Calves, G., 2008. Correlation of Himalayan exhumation rates and Asian monsoon intensity. Nature Geosci. 1, 875–880. Dadson, S.J., Hovius, N., Chen, H., Dade, W.B., Hsieh, M.L., Willett, S.D., Hu, J.C., Horng, M.J., Chen, M.C., Stark, C.P., Lague, D., Lin, J.C., 2003. Links between erosion, runoff variability and seismicity in the Taiwan orogen. Nature 426, 648–651.

B. Pan et al. / Earth and Planetary Science Letters 292 (2010) 148–157 Dettman, D.L., Fang, X.M., Garzione, C.N., Li, J.J., 2003. Uplift-driven climate change at 12 Ma: a long δ18O record from the NE margin of the Tibetan plateau. Earth Planet. Sci. Lett. 214, 267–277. Fox, D.M., Bryan, R.B., Price, A.G., 1997. The influence of slope angle on final infiltration rate for interrill conditions. Geoderma 80, 181–194. Gabet, E.J., Burbank, D.W., Pratt-Sitaula, B., Putkonen, J., Bookhagen, B., 2008. Modern erosion rates in the High Himalayas of Nepal. Earth Planet. Sci. Lett. 267, 482–494. Galy, A., France-Lanord, C., 2001. Higher erosion rates in the Himalaya: geochemical constraints on riverine fluxes. Geology 29, 23–26. Gardner, T.W., Jorgensen, D.W., Shuman, C., Lemieux, C.R., 1987. Geomorphic and tectonic process rates: effects of measured time interval. Geology 15, 259. George, A.D., Marshallsea, S.J., Wyrwoll, K.H., Chen, J., Lu, Y.C., 2001. Miocene cooling in the northern Qilian Shan, northeastern margin of the Tibetan Plateau, revealed by apatite fission-track and vitrinite-reflectance analysis. Geology 29, 939–942. Harrison, C.G.A., 1994. Rates of continental erosion and mountain building. Geol. Rundsch. 83, 431–447. Harrison, C.G.A., 2000. What factors control mechanical erosion rates? Int. J. Earth Sci. 88, 752–763. Hetzel, R., Niedermann, S., Tao, M.X., Kubik, P.W., Ivy-Ochs, S., Gao, B., Kubik, M.R., 2002. Low slip rates and long-term preservation of geomorphic features in Central Asian. Nature 417, 428–432. Hetzel, R., Tao, M.X., Stokes, S., Niedermann, S., Ivy-Ochs, S., Gao, B., Strecker, M.R., Kubik, P.W., 2004. Late Pleistocene/Holocene slip rate of the Zhangye thrust (Qilian Shan, China) and implications for the active growth of the northeastern Tibetan Plateau. Tectonics 23, 1–17. Kirchner, J.W., Finkel, R.C., Riebe, C.S., Granger, D.E., Clayton, J.L., King, J.G., Megahan, W.F., 2001. Mountain erosion over 10 yr, 10 k.y., and 10 m.y. time scales. Geology 29, 591–594. Knighton, A.D., 1999. Downstream variation in stream power. Geomorphology 29, 293–306. Li, J.J., Fang, X.M., 1998. Uplift of Tibetan Plateau and environmental changes. Chin. Sci. Bull. 44, 2117–2124. Maddy, D., 1997. Uplift-driven valley incision and river terrace formation in Southern England. J. Quat. Sci. 12, 539–545. Meyer, B., Tapponnier, P., Bourjot, L., Metivier, F., Gaudemer, Y., Peltzer, G., Shunmin, G., Zhitai, C., 1998. Crustal thickening in Gansu–Qinghai, lithospheric mantle subduction, and oblique, strike-slip controlled growth of the Tibet Plateau. Geophys. J. Int. 135, 1–47. Milliman, J.D., Meade, R.H., 1983. World-wide delivery of sediment to the oceans. J. Geol. 91, 1–21. Milliman, J.D., Syvitski, J.P.M., 1992. Geomorphic/tectonic control of sediment discharge to the ocean: the importance of small mountainous rivers. J. Geol. 100, 525–544. Molnar, P., 2003. Nature, nurture and landscape. Nature 426, 612–614. Molnar, P., England, P., 1990. Late Cenozoic uplift of mountain ranges and global climate change: chicken or egg? Nature 346, 29–34. Molnar, P., Tapponnier, P., 1975. Cenozoic tectonics of Asia: effects of a continental collision. Science 189, 419–426. Montgomery, D.R., Brandon, M.T., 2002. Topographic controls on erosion rates in tectonically active mountain ranges. Earth Planet. Sci. Lett. 201, 481–489. Montgomery, D.R., Balco, G., Willett, S.D., 2001. Climate, tectonics, and the morphology of the Andes. Geology 29, 579–582. Pan, B.T., Burbank, D., Wang, Y.X., Wu, G.J., Li, J.J., Guan, Q.Y., 2003. A 900 k.y. record of strath terrace formation during glacial–interglacial transitions in northwest China. Geology 31, 957–960. Pan, B.T., Gao, H.S., Wu, G.J., Li, J.J., Li, B.Y., Ye, Y.G., 2007. Dating of erosion surface and terraces in the eastern Qilian Shan, northwest China. Earth Surf. Proc. Land. 32, 143–154.

157

Pazzaglia, F.J., Brandon, M.T., 1996. Macrogeomorphic evolution of the post-Triassic Appalachian mountains determined by deconvolution of the offshore basin sedimentary record. Basin Res. 8, 255–278. Pinet, P., Souriau, M., 1988. Continental erosion and large-scale relief. Tectonics 7, 563–582. Polidori, L., Chorowicz, J., Guillande, R., 1991. Description of terrain as a fractal surface, and application to digital elevation model quality assessment. Photogramm. Eng. Rem. S. 57, 1329–1332. Reiners, P.W., Ehlers, T.A., Mitchell, S.G., Montgomery, D.R., 2003. Coupled spatial variations in precipitation and long-term erosion rates across the Washington Cascades. Nature 426, 645–647. Riebe, C.S., Kirchner, J.W., Granger, D.E., Finkel, R.C., 2001. Minimal climatic control on erosion rates in the Sierra Nevada, California. Geology 29, 447–450. Roering, J.J., Kirchner, J.W., Dietrich, W.E., 1999. Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology. Water Resour. Res. 35, 853–870. Royden, L.H., Burchfiel, B.C., Van Der Hilst, R.D., 2008. The geological evolution of the Tibetan plateau. Science 321, 1054–1058. Ruxton, B.P., McDougall, I., 1967. Denudation rates in northeast Papua from potassium– argon dating of lavas. Am. J. Sci. 265, 545–561. Schmidt, K.M., Montgomery, D.R., 1995. Limits to relief. Science 270, 617–620. Schumm, S.A., 1963. The disparity between present-day denudation and orogeny. U.S. Geol. Surv. Prof. Pap. 454-H, 1–13. Schumm, S.A., Hadley, R.F., 1961. Progress in the application of landform analysis in studies of semiarid erosion. U.S. Geol. Surv. Circ. 437, 14. Song, C.H., Fang, X.M., Li, J.J., Gao, J.P., Zhao, Z.J., Fan, M.J., 2001. Tectonic uplift and sedimentary evolution of the Jiuxi Basin in the northern margin of the Tibetan Plateau since 13 Ma BP. Sci. China Ser. D 44, 192–202. Summerfield, M.A., 1991. Sub-aerial denudation of passive margins: regional elevation versus local relief models. Earth Planet. Sci. Lett. 102, 460–469. Summerfield, M.A., Hulton, N.J., 1994. Natural controls of fluvial denudation rates in major world drainage basins. J. Geophys. Res. 99, 13871–13883. Sun, J.M., Zhu, R.X., An, Z.S., 2005. Tectonic uplift in the northern Tibetan Plateau since 13.7 Ma ago inferred from molasse deposits along the Altyn Tagh Fault. Earth Planet. Sci. Lett. 235, 641–653. Tapponnier, P., Xu, Z.Q., Roger, F., Meyer, B., Arnaud, N., Wittlinger, G., Yang, J.S., 2001. Oblique stepwise rise and growth of the Tibet Plateau. Science 294, 1671–1677. Thiede, R.C., Bookhagen, B., Arrowsmith, J.R., Sobel, E.R., Strecker, M.R., 2004. Climatic control on rapid exhumation along the Southern Himalayan Front. Earth Planet. Sci. Lett. 222, 791–806. Wang, X.H., Chen, Y.L., Tian, F.W., 1998. Numerical method for estimating the quantity of bedload transport in river. J. Hydraul. Eng. (in Chinese) S1, 98–101. Willett, S.D., 1999. Orogeny and orography: the effects of erosion on the structure of mountain belts. J. Geophys. Res. 104, 28957–28981. Wobus, C.W., Hodges, K.V., Whipple, K.X., 2003. Has focused denudation sustained active thrusting at the Himalayan topographic front? Geology 31, 861–864. Wu, F.L., Fang, X.M., Ma, Y.Z., Mark, H., Volker, M., An, Z.S., Miao, Y.F., 2007. PlioQuaternary stepwise drying of Asia: evidence from a 3-Ma pollen record from the Chinese Loess Plateau. Earth Planet. Sci. Lett. 257, 160–169. Zhang, P.Z., Molnar, P., Downs, W.R., 2001. Increased sedimentation rates and grain sizes 2–4 Myr ago due to the influence of climate change on erosion rates. Nature 410, 891–897. Zhao, C.Y., Nan, Z.R., Cheng, G.D., Zhang, J.H., Feng, Z.D., 2006. GIS-assisted modelling of the spatial distribution of Qinghai spruce (Picea crassifolia) in the Qilian Mountains, northwestern China based on biophysical parameters. Ecol. Model. 191, 487–500.