ACTA ECOLOGICA SINICA Volume 28, Issue 4, April 2008 Online English edition of the Chinese language journal Cite this article as: Acta Ecologica Sinica, 2008, 28(4), 1446í1455.
RESEARCH PAPER
Characteristics and spatial heterogeneity of Tamarix ramosissima Nebkhas in desert-oasis ecotones Liu Bing, Zhao Wenzhi*, Yang Rong Linze Inland River Basin Research Station, Laboratory of Basin Hydrology and Ecology, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China
Abstract: We investigated the morphological characteristics of Tamarix ramosissima Nebkhas in the desert-oasis ecotones that were located in Jinta County and Ejin, China. Also, we quantitatively analyzed the relationships among the morphological parameters, spatial pattern and spatial heterogeneity. The results indicate that (1) Most of Tamarix ramosissima Nebkhas is of independent type. The average values of Nebkhas height, volume and plant canopy diameter in the Gobi are smaller than those in the desert, whereas the average values of plant height and coverage are on the contrary. All parameter values in Ejin are larger than those in Jinta. (2) There are linear relationships between the long and the short axes, and the volume and the plant canopy diameter of the Tamarix ramosissima Nebkhas. The regression curve of Nebkhas height and area is parabolic, and that of the plant height and canopy diameter is parabolic in the Gobi while linear in the desert. (3) The spatial pattern shows a mosaic pattern in the Gobi, while it forms Nebkhas chain distribution along the wind orientation in the desert. (4) The spatial heterogeneity is mostly caused by the non-stochastic reason, and it is higher in Ejin than in Jinta. In addition, the conclusions indicate that the stimulative action of deep sand bury, caused by high strength aeolian accumulation, to the growth of Tamarix ramosissima and the feedback effect between Tamarix ramosissima and Nebkha are the adaptability mechanisms of Tamarix ramosissima Nebkhas. Key Words: desert-oasis ecotone; Nebkhas; morphological characteristic; spatial heterogeneity; Tamarix ramosissima
Nebkhas is one physiognomic type formed by the accumulation of sand within or around shrub when sand-driving wind meets with the block from the shrub[1]. In China, Nebkhas is mainly distributed over agro-pastoral transitional zones, desert steppe, typical steppe and desert-oasis ecotones[2–5], and its vegetation types comprise Caragana microphylla, Tamarix ramosissima, Nitraria L., Artemisia frigid and so on[6]. Nebkha is not only the symbol of soil erosion and degradation[1,2,7], but also a manifestation of desertification[2]. It plays an important role in obstructing quicksand from inbreaking oasis and conserving biodiversity in arid region. Since 1990’s, international scholars have conducted systematic research about Nebkhas. In the aspects of formation evolvement and morphological parameters, the research of Thomas & Dougill indicated that the orientation of Nebkha consists of the prevailing wind direction during dry seasons[8], and its formation is due to the transportation and redistribution of sand material[1–5,9–11]. Tengberg & Faso analyzed the rela-
tionships and transformation trend of the morphological parameters of Nebkhas in Tunisia, and proposed the tendency of morphological development[12]. Zhao et al. presented the upgrowth pattern and evolutionary phase of Caragana microphylla Nebkhas[13]. Xia et al. determined the ages of Tamarix ramosissima dunes in the Taklimakan Desert and the Lop Nur region of Xinjiang, China[14]. As for the ecological significance, Sterk et al.[15] and Whitford et al.[16] studied the feedback mechanism of fertile island effect of Nebkhas. Research on the restoration of arid degraded rangelands in northern Sinai conducted by Magdy et al.[17] indicated that Nebkhas was of significance to the biodiversity conservation. Tamarix ramosissima Nebkha is an important community type and the defence frontier of preventing and postponing desert from invading oases in desert-oasis ecotones[18]. In recent years, a shortage of water resource in the downstream of Heihe River caused the decay of Tamarix ramosissima Nebkhas and affected the survival of oases. However, there has been no
Received date: January 25, 2007; Accepted date: August 23, 2007 *Corresponding author. E-mail:
[email protected] Copyright © 2008, Ecological Society of China. Published by Elsevier BV. All rights reserved.
LIU Bing et al. / Acta Ecologica Sinica, 2008, 28(4):1446–1455
study internationally so far yet on Tamarix ramosissima Nebkhas. Therefore, aiming at Tamarix ramosissima Nebkhas in the Gobi and desert habitats in desert-oasis ecotones in Jinta County and Ejin Banner of the lower reaches of Heihe River, this paper studied the morphological characteristics, relationships between morphological parameters, and spatial pattern and heterogeneity of Tamarix ramosissima Nebkhas under ecological gradient, which provides not only scientific foundation for the construction and management of desert-oasis ecotones but also basic data for further research on Nebkhas.
1
Materials and methods
1.1 Study site The study site is located in the desert-oasis ecotone in Ejin Banner, Inner Mongolia (42°02ƍ–42°25ƍN; 101°26ƍ– 101°11ƍ E) and Jinta County of Gansu Province (40°25ƍN, 98°57ƍ– 99°087ƍE), lower reaches of Heihe River and arid inland river basins of Northwest China. The climate of Ejin Banner is of typical arid continent in the Eurasia Centre. The temperature ranges from –37.6°C (January) to 43.1°C (July), with an average value of 8.7°C. The total precipitation in the peripheral desert around oases of Ejin Banner varied from 25 mm to 50 mm, and the average annual evaporation was about 4200 mm. In Ejin Banner, the prevalent wind direction was northwest, the average annual wind speed changed from 2.9 m s–1 to 5 m s–1, and the annual average number of the days with gale (> 17 m s–1) was 70 d. The groundwater table varied from 2.18 m to 3.11 m below the earth's surface. On the other hand, the climate in the oasis of Jinta County is of typical temperate continent. The average temperature for many years was 8°C with the maximum 38.6°C in July and the minimum –29°C in January. The average annual precipitation and annual evaporation were 59.9 mm and 2538.6 mm, respectively. The annual average wind speed was 3.0 m s–1, and northwest wind was dominant. The annual average number of the days with gale in a whole year was 32 d. The groundwater table was less than 2–3 m below the surface in upper reaches of the main water channel of Zhengyixia Gorge. The zonal soil types included gray desert soil, sandy clay loam and sand soil. The typical xerophytic vegetation species consisted of Populus euphratica Oly, Haloxylon ammodendron, Tamarix ramosissima, Elaeagnus angustifolia etc. 1.2 Investigation method Based on an on-the-spot survey in field, in sample belts, 200 m away from the edges of the Gobi or the desert, a 100 m × 100 m plot was selected to represent the population characteristics of Tamarix ramosissima. In the middle ten days of August and September, 2006, the coordinate, height, long and short axes and orientation of Tamarix ramosissima Nebkha, and the plant canopy diameter, height and coverage of various types of vegetation on Nebkha dunes were determined. 1.3 Data analysis
Descriptive statistics and regression analysis on the raw data were conducted by using Spss13.0 and OriginPro7.0 software. Then the raw data that accorded with normal distribution were described as the regionalized variables. Through the geostatistic analysis with GS+ software, the theoretical semivariance model of the variation function was established to study the characteristics of the spatial heterogeneity. The formula to calculate the semivariogram function is as follows[19]: n 1 R ( h) [ z ( xi ) z ( xi h )]2 , i 1,2,3,", N (h) (1) ¦ 2 N ( h) i 1
where z(xi) and z(xi+h) denote 2 different values of the regional stochastic variable z at different sites xi and xi+h, respectively; N(h) is the number of spot pairs when the sampling intervals are all h; R(h) is the value of variation function, or semivariance. The fractal dimension was computed by using the semivariogram method where the fractal dimension D is estimated by D
4m 2
(2)
where m is the slope derived from the log(c(h)) versus log(h) plot, and D is the fractal dimension.
2
Results and analysis
2.1 Morphological characteristics The Tamarix ramosissima Nebkha dune is a convex and round or elliptic sanddune, with perfectly round peak and slow gradient. Most of Tamarix ramosissima Nebkhas is independent and usually forms Nebkha chains along the wind direction in the desert (Ejin 83°15', Jinta 53°13'). The vegetation coverage on the sanddunes was relatively high and varied from 0.30 to 0.47. The average values of Nebkha height, volume and plant canopy diameter in the Gobi were smaller than those in the desert, and the maximums, 4.47 m, 1133.5 m3, 534.5 m, respectively, occurred in Ejin desert, whereas the average values of plant height and coverage in the Gobi were higher than those in the desert, and the maximum values that appeared in Ejin Gobi were 2.27 m and 0.47 m, respectively. In addition, the average values of Nebkha height, volume and plant canopy diameter, height and coverage reached to maximums of 1.21 m, 3.38 m3, 42.3 m, 1.43 m and 0.30 in Jinta Gobi (Table 1). 2.2 Relationships between morphological parameters The relationship between long and short axes of Nebkha dunes was remarkably linear (R2 > 0.814), i.e., the increase and change of the length were in harmony with those of the width (Fig. 1). With the increase of Nebkha area, the height increased and reached to maximum and then decreased gradually. Thus, the regression curve was parabolic. Moreover, the peak values of the regression curves in diverse locations and habitats differed
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Table 1 Descriptive statistics of the morphological characteristics of Tamarix ramosissima Nebkha Gobi (n = 167) Nebkha Site
Ejin
Height (m)
Volume (m3)
Canopy diameter (m)
Height (m)
Nebkha Coverage
Height (m)
Volume (m3)
Plant Canopy Diameter (m)
Height (m)
Coverage
Mean
1.68
36.12
53.34
2.27
0.47
4.47
1133.52
534.51
1.89
0.31
Std deviation
1.42
98.73
83.65
1.36
0.17
3.16
4577.62
1933.51
0.83
0.13
1.17
5493.92
6990.76
1.85
0.03
10.02
20954358.52
3738444.51
0.68
0.02
0.50
0.52
0.66
0.27
0.10
0.50
12.63
21.72
0.43
0.02
3.21
792.22
479.14
7.15
0.90
18.02
26505.02
11246.23
l.48
0.55
Mean
2.17 (0.26) 1.21
5.09 (0.26) 4.86
3.39 (0.26) 24.24
2.07 (0.26) 1.43
–0.15 (0.26) 0.30
1.20 (0.41) 2.55
5.41 (0.41) 413.72
5.43 (0.41) 378.74
0.45 (0.41) 1.68
0.08 (0.41) 0.32
Std deviation
1.21
3.38
42.33
0.39
0.14
1.06
386.63
320.44
1.18
0.19
1.04
3.91
1784.03
0.15
0.02
1.13
149458.62
102645.23
1.40
0.04
0.32
0.35
2.54
0.60
0.05
1.40
27.42
18.75
0.50
0.10
2.50
55.38
310.83
2.67
0.88
6.00
1499.32
1079.46
7.63
0.70
3.82 (0.28)
4.43 (0.28)
5.18 (0.28)
0.13 (0.28)
0.98 (0.28)
1.38 (0.28)
1.09 (0.42)
0.84 (0.42)
4.17 (0.42)
0.13 (0.42)
Sample variance Minimum value Maximum value Skewness JinTa
Desert (n = 78) Plant
Sample variance Minimum value Maximum value Skewness
n: amount of Tamarix ramosissima Nebkha
Fig. 1 Relationships between long and short axes of Nebkhas dunes
LIU Bing et al. / Acta Ecologica Sinica, 2008, 28(4):1446–1455
Fig. 2 Relationships between Nebkhas area and height
from each other in the Gobi of Ejin Banner. The peak values in the Gobi and desert of Ejin were 2.85 m and 8.5 m, while they were 1.27 m and 3.45 m in the Gobi and desert of Jinta (Fig. 2). When plant canopy diameter increased, Nebkha volume also inclined to increase. Thus, there was an obviously linear relationship between Nebkha volume and plant canopy diameter, and whose R2 was between 0.787 and 0.882 (Fig. 3). In the Gobi, with plant canopy diameter increasing, plant height increased and reached the maximum of 7.48 m for Ejin or 2.45 m for Jinta, and then gradually decreased, indicating that the regression curve was parabolic, whereas in desert, the relation of plant height and canopy diameter was linear, and the value of R2 was 0.725 and 0.685 in Ejin and Jinta, respectively. Moreover, the plant height in Ejin was clearly larger than that in Jinta (Fig. 4). 2.3 Spatial pattern In desert-oasis ecotones, Tamarix ramosissima Nebkha was divided by others and formed patches in the Gobi on the edge of oases, while they took the form of Nebkha chains in the desert. Tamarix ramosissima Nebkha was distributed in big collective patches and the distribution pattern was rather apparent. In addition, the Nebkha density in the Gobi (1.67 dune·100 m–2) was obviously bigger than that in desert (0.78 dune·100 m–2), whereas the volumes had a reverse relation (Fig. 5).
2.4 Spatial heterogeneity on small scale Semivariogram function, one of the characteristics of geostatistics, is a measure for the variation degree of regional variables in sample space with separate distance. The results showed that the variational scope of nugget (C0) in Ejin was smaller than that in Jinta, and the scope of sill (C0+C) in Ejin was bigger than that in Jinta (Table 2), indicating that the spatial heterogeneity of Tamarix ramosissima Nebkha chiefly resulted from the variation caused by non-stochastic structural reason, and spatial heterogeneity in the desert of Ejin was higher than that in the desert of Jinta. In addition, the C0 and C0+C values of Nebkha height were equal in the desert of Jinta, the structural ratio was zero, and the figure of semivariance was pure gold nugget, indicating that Nebkha height followed stochastic distribution in such habitat. If the values of all structural ratios (C/(C0+C)) were bigger than 60% in different habitats, then the degree of stochastic variation was lower than the degree of structural variation, and the spatial autocorrelation was rather strong. However, the scope of the values for C/(C0+C) was between 0.00 and 0.963 in the desert of Jinta, i.e., the proportion of the variation caused by stochastic factors ranged from 3.7% to 100%. Namely, there was possibility that the spatial heterogeneity mainly resulted from the variation caused by stochastic reason.
LIU Bing et al. / Acta Ecologica Sinica, 2008, 28(4):1446–1455
Fig. 3 Relationships between Nebkhas volume and plant canopy diameter
Fig. 4 Relationships between plant canopy diameter and height
LIU Bing et al. / Acta Ecologica Sinica, 2008, 28(4):1446–1455
Fig. 5 Spatial pattern of the volume of Tamarix ramosissima Nebkha
Two indices that could best describe the morphological characteristics of Tamarix ramosissima Nebkha, namely, Nebkha volume and plant canopy diameter, were considered by the log-logit semivariance analysis. The results indicated that the diverse spatial heterogeneities would be reflected by the increase in log-logit semivariance values with distance between the sample plots increasing (Figs. 6 and 7). In Figs. 6a, 6c and 7a, with the increase in distance, the semivariogram curve wavily increased and then decreased, and the arisen inflexions implied that the spatial correlativity had a noticeable transformation. In Figs. 6b, 6d, 7b and 7c, the semivariogram would wavily increase, namely, the value of fractal dimension D increased and the spatial correlativity also gradually increased, whereas the semivariogram would wavily reduce and the spatial heterogeneity would fall off. The slope m of the semivariogram in desert was bigger than that in the Gobi (Figs. 6 and 7), and then the spatial heterogeneity in desert was
higher than that in the Gobi. The slope of the semivariogram was the most precipitous in desert of Jinta, that is to say, the spatial heterogeneity was the highest in desert of Jinta, while the slowest in the Gobi of Ejin, and the spatial heterogeneity was the lowest. Moreover, the m values of plant canopy diameter in various habitats except the desert and the Gobi of Jinta were all positive and the difference of the values was not so big.
3
Discussion
(1) Tamarix ramosissima Nebkha is a landscape type of desert sustained by groundwater. The observation data for Ejin and Jinta indicate that Nebkhas height, length and width varied from 1.05 m to 8.5 m (with an average of 1.76 m), from 0.7 m to 46.5 m (with an average of 5.74 m) and from 0.5 m to 20.5 m (with an average of 3.48 m), respectively. However,
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Table 2 Semivariogram models and parameters of morphological characteristics of Tamarix ramosissima Nebkha Gobi (n = 167) Nebkha Site
Ejin
Height
Volume
(m)
(m3)
Canopy diameter (m)
Height (m)
Nebkha Coverage
Plant
Height
Volume
(m)
(m3)
Canopy diameter (m)
Height (m)
Coverage
C0
0.001
0.051
0.035
0.006
0.002
0.050
0.752
0.506
0.004
0.001
C+C0
0.050
1.640
1.430
0.180
0.020
0.350
2.530
1.700
0.090
0.010 4.020
12.820
11.110
10.620
12.020
3.340
6.350
65.040
71.230
7.050
C/(C+C0)
0.990
0.969
0.976
0.965
0.851
0.860
0.703
0.703
0.959
0.878
R2
0.249
0.226
0.238
0.329
0.259
0.195
0.618
0.524
0.001
0.029
D
1.979
1.990
1.987
1.976
1.962
1.953
1.834
1.843
1.971
1.974
C0
0.009
0.001
0.398
0.011
0.005
0.194
0.223
0.106
0.094
0.001
C+C0
0.040
0.200
1.260
0.050
0.020
0.190
1.290
1.200
0.090
0.020
96.710
14.520
88.120
164.230
210.920
210.940
2.340
6.440
83.820
35.620
0.771
0.913
0.684
0.780
0.794
0.857
0.828
0.912
0.000
0.963
R
0.548
0.468
0.711
0.889
0.855
0.285
0.025
0.023
0.034
0.607
D
1.826
1.934
1.861
1.814
1.845
1.904
1.981
1.857
1.945
1.823
A0
Jinta
Desert (n = 78) Plant
A0 C/(C+C0) 2
n: amount of Tamarix ramosissima Nebkha
Fig. 6 Log-legit semivariograms of Nebkha volume
according to the investigation of Nickling & Wolfe in Mali, the scopes of Nebkhas height, length and width were between 0.35 m and 0.72 m (with an average of 0.57 m), 1.5 m and 19.7 m (with an average of 5.45 m), and 0.9 m and 12.5 m (with an average of 3.45 m), respectively[9]. So, the values of morphological parameters of Nebkhas in Mali were smaller than those in desert-oasis ecotones. In the central south area of
New Mexico, USA, Nebkhas height ranged from 0.2 m to 4.3 m, and the maximum values of the length and width could both reach 40 m[10]. In addition, the maximum Nebkhas height could be up to 3 m (with an average of 1.3 m), and the maximum length and width were both 30 m (with an average of 10 m)[6] in the bend of a river of Inner Mongolia Autonomous Region. In the latter two study regions, Nebkha height was
LIU Bing et al. / Acta Ecologica Sinica, 2008, 28(4):1446–1455
Fig. 7 Log-logit semivariograms of plant canopy diameter
smaller than that in desert-oasis ecotones, but Nebkha area was bigger than that in desert-oasis ecotones. Therefore, compared with previous studies, Nebkhas was special at large height in desert-oasis ecotones in extreme desert of China. (2) Tengberg & Faso pointed out that when Nebkhas was exposed to strong corrosion, the height would gradually reduce with increase in area, and then Nebkhas tended to finally die out[12]. In desert-oasis ecotones in extremely arid region of China, the regression curve of Nebkha area and height was parabolic (Fig. 2), indicating that Tamarix ramosissima Nebkhas is in retrogressive period. The present situation of the study area showed that Tamarix ramosissima shrubs were dying off and the sand dunes were suffering from the erosion of wind in Ejin. Nebkha volume was significantly linearly correlated with plant canopy diameter (Fig. 3), which accords with the conclusion proposed by Musick et al.[20] and Trujillo et al.[21] that the shrub is the crucially influencing factor of the morphological shape of Nebkhas. In addition, all values of the parameter indices in Ejin were larger than those in Jinta whether in the Gobi or in desert habitats, which shows that Tamarix ramosissima Nebkhas is more adapted to surviving in inclement nature conditions of Ejin. Nebkha is a kind of aeolian physiognomy formed by the pneumatic effect. In Ejin, the wind speed and the aeolian accumulation intensity were both high, and then rather rich sand source would emerge to deeply bury the Chinese tamarisk brush. Therefore, the adaptability
mechanism of Tamarix ramosissima Nebkhas should be attributed to the stimulative action of deep sand bury, caused by high strength aeolian accumulation, to the growth of Tamarix ramosissima and the feedback effect between Tamarix ramosissima and Nebkha. (3) The variation function of geo-statistics can characterize the landscape pattern very well. The results indicate that the range A0 of plant height, coverage and Nebkha height in desert of Jinta was larger than 100 m, and the spatial self-correlation in studied scale scope (100 m) vanished (Table 2). This means that the plot area was too small to factually reflect the spatial heterogeneity of Tamarix ramosissima Nebkhas because the data difference between plots was so big that the difference brought by the dissimilitude of space positions was sufficiently concealed[22]. Therefore, the future study about the spatial heterogeneity of Tamarix ramosissima Nebkhas should expand plot area to more scale scope. In addition, the study of Cambardella et al.[23] showed that the value of C/(C0+C) is bigger than 75%, between 75% and 25% or smaller than 25% mean that the spatial self-correlation of variables is strong, moderate or weak, respectively. So, the spatial autocorrelation of Tamarix ramosissima Nebkhas was relatively strong in the Gobi of Ejin and moderate in desert of Ejin and the Gobi of Jinta (Table 2). Furthermore, in small scale scope, a series of inflexions appeared in the log-logit semivariogram, reflecting that the
LIU Bing et al. / Acta Ecologica Sinica, 2008, 28(4):1446–1455
spatial autocorrelation had remarkable change around the inflexions. The greater the difference between fractal dimension D and 2, the bigger the value of m, and then the more evident the spatial autocorrelation[24]. In study, the slope of desert in Jinta was the steepest (Fig. 6) and the spatial heterogeneity was the strongest here, implying that variation of the spatial heterogeneity was mainly led by the graze disturbance. In addition, the slope of the log-logit semivariogram got negative value (Figs. 6 and 7) and the spatial heterogeneity had important variation, indicating that the spatial heterogeneity of Tamarix ramosissima Nebkhas was affected by environmental factors to a great degree in Jinta.
4
Conclusions
2003, 23(3): 230–235. [ 4 ] Wang X M, Dong Z B, Zhang J W, et al. Geomorphology of sand dunes in the northeast Taklimakan Desert. Geomorphology, 2002, 42(3): 183–195. [ 5 ] Wang X M, Dong Z B, Zhang J W, et al. Formation of the complex linear dunes in the central Taklimakan Sand Sea, China. Earth Surface Processes and Landforms, 2004, 26: 677– 686. [ 6 ] Yue X L, Ha S, Zhuang Y M, et al. Studies on sandy grassland Nebkhas—A review. Journal of Desert Research, 2005, 25(5): 738–743. [ 7 ] Dougill A J, Thomas A D. Nebkhas dunes in the Molopo Basin, South Africa and Botswana: Formation controls and their validity as indicators of soil degradation. Journal of Arid Environments, 2002, 50(3): 413–428.
(1) The average values of Nebkhas height, volume and plant canopy diameter in the Gobi are smaller than those in the desert, whereas the average values of plant height and coverage are on the contrary. In addition, all parameter values in Ejin are larger than those in Jinta. (2) The spatial pattern shows a mosaic pattern in the Gobi, while it forms Nebkhas chain distribution in the desert. (3) The spatial heterogeneity is mostly derived from the variation that is caused by the non-stochastic structural reason, and the extent of spatial heterogeneity in Ejin is higher than the one in Jinta. (4) The adaptability mechanism of Tamarix ramosissima Nebkhas was just the stimulative action of deep sand bury, caused by high strength aeolian accumulation, to the growth of Tamarix ramosissima and the feedback effect between Tamarix ramosissima and Nebkha.
[10] Langford R P. Nebkha (coppice dune) fields of south-central
Acknowledgements
[13] Zhao X, Zhao W Z, Bao Y. Eco-environmental fragility and
[ 8 ] Thomas A D, Dougill A J. Processes of Nebkhas dune formation and wind-blown nutrient deposition in the Molopo Basin, southern Africa. Soil Erosion Research for the 21st Century, 2001, 5: 490–493. [ 9 ] Nickling W G, Wolfe A S. The morphology and origin of Nabkhas, Region of Mopti, Mali, West Africa. Journal of Arid Environment, 1994, 28: 13–30. New Mexico, USA. Journal of Arid Environment, 2000, 46: 25–41. [11] Gunatilaka A, Mwango S B. Flow separation and the internal structure of shadow dune. Sedimentary Geology, 1989, 61: 125–134. [12] Tengberg A, Faso B. A comparative analysis of Nebkhas in central Tunisia and northern Burkina Faso. Geomorphology, 1998, 22(2): 181–192. rehabilitation in Bashang of Hebei Province. Beijing: China
The project was supported by the National Natural Science Foundation of China (No. 30771767). We would like to thank all participants in the surveys conducted in Linze Inland River Basin Research Station, Chinese Academy of Sciences, and Dr. Zijuan Wen from Department of Mathematics of Lanzhou University for the help and support in writing this paper. We gratefully acknowledge the anonymous reviewers for their valuable comments on the manuscript.
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