Soil erosion rates on sloping cultivated land on the Chinese Loess Plateau

Soil erosion rates on sloping cultivated land on theLoess Plateau near Ansai, Shaanxi Province, China:An investigation using 137Cs and rill measurements

X. Zhang,1 T. A. Quine2 and D. E. Walling21Institute of Mountain Disasters and Environment, Chinese Academy of Sciences, Chengdu, Sichuan Province, China

2Department of Geography, University of Exeter, Amory Building, Rennes Drive, Exeter, Devon EX4 4RJ, UK

Abstract:Sediment yields from the rolling hills area of the Loess Plateau in northern China (10 00025 000 t km2 yr1)are amongst the highest in the world. The sediment is believed to derive from both the deep gullies that dissectthe rolling plateau and the steep cultivated fields on the slopes of the mounds between the gullies. However,there are few reliable data for erosion rates on the cultivated fields and it is suspected that current estimates

(10 00016 000 t km2 yr1) based on empirical relationships (derived from erosion plot studies) exceed thetrue values. This study sought to address the need for more information concerning erosion of the cultivatedfields through derivation of erosion rates frommeasurements of rill volume and caesium-137 (137Cs) inventoriesfor typical fields near the village of Ansai, Shaanxi Province. The derived erosion rates are discussed and

compared with estimates based on empirical relationships derived from erosion plot data.Where erosion rate estimates based on both rill volume data and 137Cs inventories are available, they show

good agreement in the pattern of downslope variation. Both show a sharp decline in erosion rates at a slope

length of c. 50 m. This is tentatively attributed to a change from transport-limited to detachment-limitedconditions, where rill incision reaches the undisturbed loess at the base of the plough layer. No such decline isvisible in the predictions based on empirical relationships derived from erosion plot data. Further evidence is

presented that supports the suggestion that these empirical relationships overestimate erosion rates at slopelengths in excess of c. 50 m. It is tentatively suggested that the rates of soil erosion from sloping cultivated fieldsin the rolling hills area are more likely to lie in the range 800010 000 t km2 yr1 than in the higher rangesuggested by the empirical relationships. # 1998 John Wiley Sons, Ltd.

Hydrol. Process., Vol. 12, 171189 (1998)

KEY WORDS soil erosion; sloping cultivated land; caesium-137 inventory; rill measurement; Loess Plateau,

China

INTRODUCTION

Sediment yield data for the Yellow River indicate that the Loess Plateau of China suers some of the highestsoil erosion rates in the world. Within the Loess Plateau, the most severe contemporary erosion is observed inthe rolling hills area, where sediment yields are in the range 10 00025 000 t km2 yr1 (cf. Gong and Xiong,1979). The sediment is commonly believed to derive from both the deep gullies that dissect the rolling plateauand the steep cultivated fields on the slopes of the mounds between the gullies. Erosion in this area, therefore,gives rise to serious on-site consequences as a result of soil loss from cultivated fields and severe o-siteproblems associated with the eroded sediment (cf. Tang, 1985; Douglas, 1989; Wen, 1993).

CCC 08856087/98/01017119$1750 Received 28 August 1996# 1998 John Wiley & Sons, Ltd. Accepted 6 February 1997

HYDROLOGICAL PROCESSES, VOL. 12, 171189 (1998)

Correspondence to: T. A. Quine.

Sediment yield data are particularly valuable measures of erosion in this environment because there isvery little evidence for sediment storage on slopes or valley floors and, therefore, in the absence of artificialsediment trapping (check dams, etc.), sediment delivery ratios have been found to approach 1 (Mou andMeng, 1980). While sediment yield data provide a useful measure of landscape-scale erosion, it is alsoimportant to establish reliable erosion rate estimates for the cultivated land of the mound slopes. Given thevery high sediment delivery ratios in the area, such erosion rate data would facilitate assessment of the relativecontributions of the mound and the gully areas to total sediment production. The data are also needed toallow evaluation of the eects of soil conservation measures, implemented on the cultivated land of themound region, in reducing sediment production. The need for such data has been well recognized and, sincethe 1940s, runo plots have been established at several locations in the rolling plateau to monitor erosionrates on cultivated sloping land. The results from this long-termmonitoring have been used to develop severalsimilar empirical relationships between erosion rates and slope angle and length (cf. Jiang et al., 1991). Theserelationships have been used to derive estimates of the erosion rates from cultivated land in the rolling plateauregion which range from 10 00016 000 t km2 yr1 and are, therefore, similar to the local sediment yields.Because the sediment delivery ratios are close to 1, the similarity between the erosion rate estimates and thelocal sediment yields could only occur if the erosion rates in the gully areas were approximately the same asthose on the cultivated land. Since the 1980s, there has been growing interest in the relative contributions ofsediment from the gullies and fields and this has led to suggestions that the erosion rates estimated for thecultivated land from the empirical relationships may overestimate the true values. There is, therefore, a clearneed for additional information concerning erosion rates on the cultivated mound slopes, to allow moreaccurate assessment of both the potential on-site eects of erosion and the relative contributions of themound and gully areas to total sediment production.The study reported here aims to address the need for such data by assembling erosion rate estimates for

sloping cultivated land using the caesium-137 (137Cs) technique and measurements of rill dimensions. Theresulting erosion rate data are compared with predictions derived using the empirical relationships, andexplanations for the contrasts between the estimates are examined. Tentative conclusions are drawn concern-ing the relative contributions of the mounds and gully slopes to sediment production in the rolling hills area.

THE STUDY AREA

The study area lies near the town of Ansai in an area where the landforms are typical of the rolling loessplateau (Figure 1). Geomorphologically, the rolling plateau in the area can be divided into two units withapproximately equal areas; namely, the mound region between the gullies and the gullies themselves. Themound crests (Mao) are at an altitude of 13401380 m a.s.l, whilst the valley floors are at 10001050 m a.s.l.The mound slopes are relatively gentle (0308), while the gully slopes are very steep (35708). The loess in thearea is about 200 m thick; Malan Loess (Q3) usually underlies the gentle mound slopes, while WuchengLoess (Q1) and Lishi Loess (Q2) underlie some of the steep gully slopes. Tertiary red clay and Mesozoicsandstone outcrop at the foot of the gully and creek slopes. The loess is medium loess with a typicalcomposition of: 12.4% sand (0.250.05 mm); 71.7% silt (0.050.005 mm); and 15.9% clay (50005 mm).The climate in Ansai is characterized by cold dry winters and warm moist summers. The mean annual

temperature is 98C, and the mean monthly temperature is 228C in July and 88C in January. The meanannual precipitation is 549.1 mm, with maximum and minimum recorded values of 957.8 mm (1964)and 351.3 mm (1986). Seventy-five percent of the annual precipitation falls during the flood seasons ofJuneSeptember and most of this occurs in a few heavy storms. The maximum daily precipitation of136.5 mm, with a maximum intensity of 45 mm in 30 minutes, was observed on 16 July 1989. The averageerosion rate in the area, based on river sediment load data, is 14 000 t km2 yr1.The mound region has been cultivated for several centuries, with only small areas used as cemeteries

excluded. The main crops are beans and millet. The fields investigated in this study lie on a mound, 3 kmNWof the town of Ansai, which is typical of the area, because despite its distance from the nearest village and the

HYDROLOGICAL PROCESSES, VOL. 12, 171189 (1998) # 1998 John Wiley & Sons, Ltd.

172 X. ZHANG, T. A. QUINE AND D. E. WALLING

low productivity, the whole mound surface is cultivated. The mound is elongated with a length of 1.2 km in aNWSE direction and a width of 0.4 km (Figure 2). The elevation of the mound crest is 1358 m a.s.l. Above1300 m a.s.l themound has a short flat crest and relatively gentle slopes (12148). On the lowermound slopes,below 1300 m a.s.l, the slopes are steeper (25308). The slopes are moderately convex below the crest andbelow field margins, almost linear over the central sections and characterized by slight concavities at lowerfield margins.

METHODOLOGY

Two locations were selected on the mound for this study (Figure 2). Field A, located on a relatively gentleslope of the upper part of themound, has a slope length of 90 m and an average slope angle of 10.58 (Figure 3).The second location consisted of fields B and C (Figure 2). Field B, on the crest of the ridge, was characterizedby low slope angles (5.515.58) and short slope lengths (1522 m). Field C, located on the steep slopes immed-iately downslope of Field B, varied in slope length from 32 to 54 m, and in angle from 238 to 338 (Figure 3).Samples of soil for caesium-137 analysis were collected from all three fields. Because Field Awas incised by

a shallow gully and, therefore, characterized by high variation in planform curvature over a short distance(cf. Figure 3a), samples were collected at grid intersections (3.75 m intervals across the slope and 6 mintervals downslope) from an area of 30 m 90 m, to provide an indication of both across slope anddownslope variation in 137Cs inventories. Fields B and C did not exhibit shallow gullies and samples werecollected along three downslope transects (cf. Figures 2 and 3) to examine downslope variation in 137Csinventories. Two sampling methods were employed. Where caesium-137 inventories alone were required,bulk samples were collected using a 6.9 cm diameter core tube, which was driven into the ground manually toa depth of 5060 cm. Sampling to this depth ensured that all 137Cs-contaminated soil in the profile wasrecovered. Where caesium-137 depth distributions were required, depth incremental samples were collectedusing a 9.5 cm diameter core tube comprising two segments, which could be separated to facilitate sectioningof the core. All samples were air-dried, disaggregated, passed through a 2 mm sieve and weighed. The 137Cscontent of the 52 mm fraction of each sample was measured by gamma spectrometry using a hyperpurecoaxial germanium detector and multichannel analyser system. Caesium-137 was detected at 662 keV and

Figure 1. Photograph of the rolling Loess Plateau near Ansai, Shaanxi Province, China

# 1998 John Wiley & Sons, Ltd. HYDROLOGICAL PROCESSES, VOL. 12, 171189 (1998)

SOIL EROSION RATES 173

Figure 2. Location map of the study area near Ansai, Shaanxi Province, China. Within inset B the location of Field A is labelled 1,the location of Fields B and C is labelled 2



Figure 3. The topography of the sampled fields: (a) Field A; (b) Transects 13 over Fields B and C (a single mean transect over Field Ais also shown for comparison)



counting times, which were typically about 25 000 or 55 000 s, provided results with an analytical precision ofapproximately +6% (2 SD).Rill measurements were limited to Field A. Measurements were undertaken from 30 m downslope

(upslope of this point there was little visible sign of rilling) to the base of the field. At 2 m intervals in thedownslope direction, a tape was extended for 38 m across the slope (topographically defined zone betweenplanform convexities) and the location, depth and width of each rill (deeper than 1 cm) was recorded. Localresidents indicated that much of the rilling had occurred during a heavy storm in August 1992 (c. one monthbefore sample collection and rill measurement) and that such storms occurred once every 510 years.Detailed topographic data were also collected from each field. In Field A, topographic measurements were

undertaken at 2 m intervals (across and downslope) over the area sampled for 137Cs and surveyed for rilldimensions. In Fields B and C topographic data were recorded at 2 m intervals along each of the transectssampled for 137Cs.

The caesium-137 data

The caesium-137 technique. The basis for using 137Cs measurements to estimate soil erosion rates has beenwell documented elsewhere (cf. Walling and Quine, 1991) and only a brief summary is provided here. The137Cs now present in the environment (in those areas unaected by fall-out deposition from the Chernobylaccident) was derived from atmospheric testing of atomic weapons during the period from the mid-1950s tothe mid-1970s. After deposition on mineral soils, the 137Cs fall-out is strongly and rapidly adsorbed andsubsequent redistribution occurs only in association with sediment particles. Measurement of the spatialdistribution of 137Cs inventories, therefore, provides a qualitative indication of net soil redistribution over thelast four decades. The total 137Cs fall-out input per unit area (reference inventory) for the site is derived bysampling adjacent undisturbed and uneroded areas. This is then compared with 137Cs inventories fromsampled locations at the study site. Where the reference inventory exceeds the 137Cs inventory for thesampling point, soil erosion has occurred (loss of 137Cs in association with eroded soil). Where the 137Csinventory from the sampling point exceeds the reference inventory, net soil aggradation has occurred(deposition of 137Cs in association with deposited soil). By establishing and applying numerical relationshipsbetween soil loss and 137Cs loss and between soil gain and 137Cs gain, it is possible to convert the qualitativeevidence of soil redistribution provided by the 137Cs measurements to quantitative estimates of soil erosionand aggradation rates. This process, often termed calibration, is also discussed in detail elsewhere (Wallingand Quine, 1990; Quine, 1995). When applied in this way, the 137Cs technique provides information on soilredistribution resulting from all processes over the last four decades.

The local reference inventory. The identification of suitable undisturbed level sites to act as reference sitesin the rolling Loess Plateau is problematic because of the intensive cultivation of the mound slopes andvalley floors. However, a small area of undisturbed grassland was found between and surrounding a groupof tombs (over 50 years old). This was deemed to be a suitable reference site because it lay within 1 km ofthe sampled fields and had a similar altitude. Three sectioned core samples were collected from this grass-land. The caesium-137 inventories from the three cores were 251.5, 236.5 and 274.1 mBq cm2, respectively.The mean value of 254.0 mBq cm2 was considered to be representative of the local reference level. Com-parison with reference inventories at other locations in the Loess Plateau shows a strong similarity (Table I).

Table I. Caesium-137 reference inventories at locations within the Loess Plateau

Site Date sampled Mean annual precipitation Caesium-137 inventory(mm) (mBq cm2)

Luchuan 1988 622 253Xifeng 1991 565 260Ansai 1992 549 254



Depth distributions of caesium-137. The depth distribution of 137Cs at the tomb grassland site is illustrated inFigure 4a. This distribution is typical of an undisturbed site, with retention of 68% of the caesium-137 in theupper 7.5 cm and a sharp decline in activity below that depth. This provides further confirmation of thevalidity of using data from this site to establish the reference inventory of the study area.Figure 4b shows the depth distribution of 137Cs from a mid-slope position in Field A. There is minimal

variation in the concentration of 137Cs within the plough layer (015 cm) and the inventory of 113 mBqcm2 represents 55% loss of 137Cs. These characteristics are typical of an eroded location.The depth distribution shown in Figure 4c, from the base of Field C, shows 137Cs present to depths

in excess of 40 cm and the total inventory of 300 mBq cm2 represents a 20% excess of 137Cs. Thesecharacteristics are consistent with a cultivated profile subject to significant aggradation.These data, and that provided by the other sampling points where depth incremental sampling was

undertaken, confirm that 137Cs behaviour accords with expectations and the assumptions of the technique atthis site.

Figure 4. Depth distributions of 137Cs from (a) the reference site; (b) a mid-slope (eroding) location on Field A; (c) a slope foot(depositional) location on Field B (Transect 3)



Downslope variation in caesium-137 inventories. Downslope variation of 137Cs inventories for each of thefields is shown in Figure 5. For Field A (Figure 5a) the data represent the mean value for each downslopedistance, while for Fields B and C (Figure 5b, c and d), individual point values are used. In Field A the 137Csinventories range from 26 to 201 mBq cm2, with an area-weighted mean of 107 mBq cm2 (n 112). Themean value equates to a 57% loss of the 137Cs input to the field, indicating significant erosion and export ofsoil. Transects 13, from Fields B and C, are characterized by 137Cs inventories with a range from 10 to332 mBq cm2 and area-weighted means of 7886 mBq cm2 (total n 58). The loss of 6669% of the137Cs input is evidence of even more serious soil loss from Fields B and C than from Field A.In each of the fields there is a reduction in 137Cs loss or a net 137Cs gain at the lower boundary (Figure 5).

On the basis of other studies in the Loess Plateau (Quine et al., 1993; Zhang et al., 1994), and conversationwith the farmers, this is believed to be the result of the accumulation of soil at the boundary as a result ofgradual downslope displacement of soil by tillage. Soil deposition at the lower field boundaries anddownslope transfer of soil at the upper field boundaries accounts for the formation of the noticeable step of0.51.5 m between Field B and Field C (cf. Figure 3) and a drop of c. 1.5 m between Field A and theadjacent downslope field.Despite this role of tillage in influencing the pattern of 137Cs redistribution in the boundary zones, the

overall pattern of 137Cs redistribution appears to be dominated by water erosion (cf. Quine et al., 1997). Thisis evidenced by the net loss of 137Cs from each slope, by the large areas of each slope subject to 137Cs loss inexcess of 50% and by the gradual downslope decline in 137Cs inventories over the upper section of each slope.

Figure 5. The downslope variation in 137Cs inventories at the study fields: (a) Field A; (b) Transect 1; (c) Transect 2; (d) Transect 3.In (b), (c) and (d) the vertical dotted line represents the location of the boundary between Fields B (upslope) and C (downslope)



Estimation of erosion rates from 137Cs data. In order to use the 137Cs data to investigate soil erosion on thesloping cultivated land, it is necessary to convert the measurements of 137Cs loss and gain to estimates of soilerosion and aggradation, respectively. A number of approaches have been proposed to undertake this con-version (cf. Walling and Quine, 1990; Quine, 1995), but the authors favour the use of a mass balance model tosimulate 137Cs loss and gain with specified erosion rates and thus to establish calibration relationships. Zhanget al. (1990) have developed a mass balance model that has provided reliable erosion rate estimates in otherstudies in the area and which demands minimal parameterization, viz:

X Y 1 hH

N19631

Re hv 2

where X is the measured caesium-137 inventory at the sampling point (Bq m2), Y is the local caesium-137reference inventory (Bqm2, h is the depth of annual soil loss (m),H is the depth of the plough layer (m),N isthe year of sampling, Re is the total soil erosion rate (kg m

2 yr1), and v is the specific density of the ploughlayer (kg m3). These relationships were reconfigured to derive Equation (3), which was used to deriveerosion rate estimates from the measured 137Cs inventories.

Re Hv 1 X

Y

1=N1963 !3

Implicit in the use of this relationship is the assumption that all 137Cs present in the soil profile is mixed evenlythrough the plough layer. Where water erosion has occurred, the use of this relationship may lead to someoverestimation of soil loss because, during the period of fall-out, 137Cs would have accumulated at the soilsurface between cultivation episodes and soil lost from the surface during this period would have beenenriched in 137Cs compared with the plough layer as a whole (cf. Quine, 1995). Nevertheless, if this potentiallimitation is recognized, the approach can provide reliable estimates of erosion with limited parameterization(H and v).Recent studies have demonstrated that soil tillage may make a significant contribution to total soil

redistribution (cf. Quine et al., 1993, 1994, 1996; Govers et al., 1993, 1996). Therefore, because this study isfocused on the problem of water erosion, it is important to separate the contributions of both water erosionand tillage to total soil and 137Cs redistribution. This has been achieved by estimating rates of soil redistri-bution by tillage for each of the points that were sampled for 137Cs.Experimental studies (Lindstrom et al., 1990, 1992; Govers et al., 1994; Lobb et al., 1995) have indicated

that the relationship between soil redistribution and local topography may be described by the followingrelationships:

Qst kS m 4

Rt @Qst@x

5

where Qst is the downslope flux of soil that occurs as a result of a single tillage operation (kg m1), S is the

tangent of the downslope angle, k and m are constants (kg m1) and Rt is the rate of soil redistribution bytillage (kg m2). These relationships are characterized by high coecients of determination (typically0.640.81) and they, therefore, provide the basis for estimating rates of soil redistribution by tillage usingtopographic data. However, the experimental data available for determining the values of k andm have beenderived using mouldboard ploughs pulled by powerful tractors (Lindstrom et al., 1990, 1992; Govers et al.,1994). These data are inappropriate in the study area because the soil is cultivated by hand or using a simple



plough and animal power. The values of k and m used in this study (15 and 20 kg m1, respectively) were,therefore, derived using a semi-deterministic model of soil redistribution by tillage which is describedelsewhere (Quine et al., 1993).In order to separate the contributions of water erosion and tillage to total soil redistribution, the relation-

ships described above [Equations (4) and (5)] were used, with the topographic data collected in the field, toestimate the medium-term average rates of soil redistribution by tillage at each point sampled for 137Cs. Thistillage rate (Rt) was then subtracted from the total soil redistribution rate (Re) derived from Equation (3) toprovide a corrected water erosion estimate (Rw) for each sampled location. Table II summarizes both theuncorrected total erosion and corrected water erosion estimates.

Table II. 137Cs percentage residuals and erosion rate estimates derived from 137Cs data (uncorrected total erosion andcorrected water erosion rates) and from rill dimensions

Field 137Cs 137Cs-derived total 137Cs-derived water Rill-derivedresidual erosion rate erosion rate rates(%) (kg m2 yr1) (kg m2 yr1) (kg m2 yr1)

A upper 40 3.65 3.56B Transect 1 47 4.74 4.52B Transect 2 63 7.32 7.31B Transect 3 72 10.66 9.91A lower 62 7.18 7.33 12.51C Transect 1 74 10.44 10.99C Transect 2 71 8.45 8.74C Transect 3 67 9.70 9.58A total 57 6.41 6.50 9.76Transect 1 66 8.41 8.71Transect 2 69 8.07 8.28Transect 3 69 9.74 9.49

Rill erosion data

Rill erosion rates (taken to represent the annual rate for the preceding year) were calculated for eachcross-slope transect using the following relationship:

Er BD

L

Xini1widi 6

where Er is the rill erosion rate (kg m2 yr1), assuming a cross-slope transect of downslope length of 1 m;

wi is the width of rill i m; di is the depth of rill i (m); n is the number of rills in the cross-slope transect; BD isthe bulk density of the eroded material (1350 kg m3); and L is the (cross-slope) length of the cross-slopetransect (38 m).The downslope variation in the estimates of rill erosion rates derived using this procedure is shown in

Figure 6a and downslope variations in rill depth and width are shown in Figure 6b and 6c. A number offeatures of the pattern of rilling are worthy of note.

. From 30 to 50 m downslope many small rills develop within the plough layer (15 cm) and the rillerosion rate increases rapidly to its peak value of (24 kg m2 yr1).

. c. 50 m downslope many of the small rills coalesce to form three large rills which incise to the hardloess underlying the plough layer; the rill erosion rate gradually decreases.

. c. 63 m downslope lateral expansion of the large rills within the plough layer leads to a slight increasein rill erosion rate.



Figure 6. Downslope variation in rilling on Field A: (a) rate and frequency (over the 38-m cross-slope transect); (b) depth; (c) width



. c. 74 m downslope two of the remaining three rills combine to form a single large rill which incisesdeeply (35 cm at 76 m) into the hard subplough layer; this coincides with a sharp increase in rill erosionrate.

. 76 m to base of field the two rills follow deep and permanent profile concavities to the base of thefield; incision of the subplough layer ceases and there is a rapid decline in rill erosion rate.

The total volume of the rills over the 2040 m2 was 18.9 m3, representing a rate of soil loss of 12.51 kgm2 yr1 (12 510 t km2 yr1) over the surveyed area and 9.76 kg m2 yr1 (9760 t km2 yr1) over thewhole slope from crest to field base (assuming minimal rill erosion over the unsurveyed upper 30 m).

DISCUSSION OF THE EROSION RATES

Comparison of the erosion rates derived from rill and 137Cs measurements

The pattern of downslope variation in 137Cs-derived water erosion rates for Field A shows some agreementwith the pattern of rilling discussed above (Figure 7). The 137Cs-derived rates demonstrate the same rapidincrease to a maximum at c. 50 m downslope (54 m in the case of the 137Cs data) followed by a decline to60 m, an increase to 66 m and then a further decline towards the lower edge of the field. However, rill-derivedrates show a much more rapid decline towards the base of the field (7090 m) than the 137Cs-derived rates.This may reflect a gradual reduction in erosion rates at the base of the field, over the c. 40 years representedby the 137Cs rates, as the form of the field base has evolved in response to the erosion.In contrast to the agreement in terms of pattern, there is a clear dierence in the magnitude of the rates

(Figure 7; Table II), with the rates of rill erosion typically 1.7 times larger than the 137Cs-derived rates. This isnot unexpected because the 137Cs-derived rates represent medium-term (c. 40 year) average rates, whereas therill-derived rates represent annual rates for an erosion season with a c. five-year return period.Three conclusions can be drawn from this comparison of the rill-derived and 137Cs-derived erosion rate

estimates. First, the comparison indicates that the 137Cs-derived pattern of water erosion estimates is likely to

Figure 7. Comparison of water erosion rates for Field A derived from 137Cs measurements, the empirical relationship [Equation (9)]and measured rill dimensions



provide a reliable representation of the pattern of water erosion in this environment. Secondly, thecomparison provides a clear indication that rill erosion is the dominant soil redistribution process on thestudy field, accounting for the majority of the measured redistribution of 137Cs (cf. Table II; Quine et al.,1997). Thirdly, the comparison indicates that the rates of water erosion derived from the 137Cs measurementsare likely to be reliable. These conclusions are particularly important for the following analysis in which thepattern and magnitude of the 137Cs-derived rates are compared with erosion rate predictions derived fromempirical relationships based on erosion plot data.

Comparison of the erosion rates derived from 137Cs measurements with predictions basedon empirical relationships

Since the 1940s, erosion plots have been used to study water erosion rates at several locations on slopingcultivated land in the Loess Plateau, including Tianshui, Xifeng, Suide, Zizhou and Lishi. These investi-gations have demonstrated that good relationships can be found between annual erosion rates from the plotsand the slope angles and lengths of the plots. The study of most relevance to the present discussion wascarried out by the Northwest Institute of Soil and Water Conservation of the Chinese Academy of Sciencesbetween 1985 and 1989, on sloping cultivated land at Chafang Village, near Ansai, 15 km away from thestudy site. The study employed six standard runo plots (width 5 m and horizontal length 20 m) withslope angles of 5, 10, 15, 20, 25 and 288 and four runo plots of dierent slope lengths (10, 20, 30 and 40 m;width 5 m) with a slope angle of 308. On the basis of the five-year dataset, Jiang et al. (1991) were able todevelop the following relationships between annual erosion rates and slope angles and lengths:

M 202553S1308 r2 099 7M 376499L0397 r2 099 8M 10338S1114L0350 r2 091 9

whereM is the mean erosion rate over the five-year period (t km2 yr1), S is the slope angle (8) and L is theslope length (m). These relationships are similar to those derived by other researchers based on plot data fromTianshui, Zizhou, Xifeng, Suide and Lishi. Similar relationships have also been found in other environments.For example, Govers (1991) found that a relationship of the same form as Equation (9) could be used todescribe rill erosion in a field study in the loess belt of Belgium, although he found slope angle (gradient) andlength coecients of 1.45 and 0.75, respectively. Govers et al. (1996), in reviewing past work, suggest that theslope angle (gradient) coecient is typically greater than 1, and often c. 1.4, and the slope length coecientusually lies between 0 and 1, with values close to 0.5 being typical. Despite the dierent representation ofslope angle, Equation (9) is in broad agreement with thewider literature and it was, therefore, used to estimatethe water erosion rates that would be expected for each of the study fields based on the erosion plot data.Table III summarizes the results. Two contrasts are immediately apparent. First, on the low slope angle,crest Field B, the rates predicted by Equation (9) are only 5386% of the 137Cs-derived rates. Secondly, onthe steeply sloping Field C, the rates predicted by Equation (9) greatly exceed the 137Cs-derived rates(151179%). These contrasts demand attention.The first deviation that requires explanation is the high 137Cs-derived erosion rates on the upper part of the

slopes, in areas where relatively little erosion is predicted by Equation (9). Two possible explanations can beconsidered; first, that the 137Cs-derived values are overestimates, and, secondly, that the values obtainedfrom Equation (9) are underestimates. There are two possible sources of overestimation in the derivation of137Cs-derived erosion rates: (1) the role of tillage in leading to soil loss from the upper slopes may have beenunderestimated (although this could explain deviation in the erosion rate estimates at the upper edge of thefields, it does not readily explain either the deviation over the whole of the crest fields or the significant netexport of 137Cs from these fields): (2) the calibration procedure discussed above, which assumes uniformmixing of the 137Cs throughout the plough layer.



Nevertheless, even if allowance is made for possible surface enrichment of 137Cs during the period ofatmospheric fall-out, and for preferential loss of 137Cs in association with fine sediment, through the use ofmore complex calibration procedures (cf. Quine, 1995), there remains a significant deviation between the137Cs-derived erosion rate estimates and those calculated using Equation (9). It is, therefore, necessary toconsider the possibility that Equation (9) underestimates the true erosion rate. In considering this possibilityit is important to note that the experimental data, from which Equation (9) was derived, were limited to slopelengths of 20 m for low slope angles. It is possible that the constrained slope length leads to the operation ofa more limited array of erosion processes on the plots than is seen in the landscape. One possible mechanismto explain higher landscape rates of water erosion on gentle slopes is as follows. During heavy storms, whenrill networks are established on the long sloping fields and the plough soil becomes saturated, it is possiblethat headward extension of the rill systems occurs owing to rill wall and head-cut collapse. This could lead tobackward extension of the rill systems on to the gently sloping ground of the slope crest areas. This processwould not occur on the short erosion plots because the limited slope length would prevent the establishmentof an initial rill network. In the absence of independent corroborative evidence, this explanation must beconsidered to be tentative. Nevertheless, there is also no clear evidence to suggest that the 137Cs-derived ratesare overestimates.In analysis of the second important contrast between the 137Cs-derived rates and those predicted by

Equation (9), namely the higher values predicted by Equation (9) for the steeper lower parts of the fields, it ispossible to draw on independent evidence. Figure 7 shows the rill erosion rates, the 137Cs-derived erosion ratesand the water erosion rates predicted using Equation (9), for Field A. As has been indicated, the 137Cs-derivedrates and the rill erosion rates conform to similar patterns. In contrast, the pattern predicted usingEquation (9) deviates quite markedly, especially from the rill-derived rates. While the rill- and 137Cs-derivederosion rates peak at 50 and 54 m, respectively, the values predicted by Equation (9) continue to rise to a peakat 75 m, and only then decline towards the base of the field. Two points merit further consideration. First,over slope lengths similar to the erosion plots employed in the development of Equations (7)(9), the erosionrate estimates derived from Equation (9) are seen to be similar to those derived from rill volumes and 137Csinventories. However, at slope lengths that exceed the length of the erosion plots, the erosion rate estimatesderived from Equation (9) deviate from the rill- and 137Cs-derived data. This could be expected on statisticalgrounds, given the hazards associated with extrapolating a regression relationship beyond the limits of theoriginal data. Secondly, possible process-based causes for the breakdown in the predictions of the empiricallyderived relationship [Equation (9)] may be identified, based on the rill erosion observations. As indicated

Table III. Topographic attributes and water erosion rate estimates, derived from 137Cs data and the empiricalrelationship [Equation (9)], for each field

Field Slope length Slope 137Cs-derived Rate derived from(m) angle erosion rate Equation (9)

(8) (kg m2 yr1) (kg m2 yr1)

A upper 30.0 5.2 3.56 1.77B Transect 1 15.8 5.5 4.52 3.88B Transect 2 21.7 8.3 7.31 3.91B Transect 3 14.5 15.0 9.91 6.76A lower 60.0 13.0 7.33 7.84C Transect 1 32.0 31.4 10.99 16.60C Transect 2 53.9 23.4 8.74 14.21C Transect 3 46.1 33.0 9.58 17.18A total 90.0 10.5 6.50 6.26Transect 1 48.3 24.0 8.71 12.18Transect 2 76.6 19.2 8.28 11.35Transect 3 61.1 29.0 9.49 14.71



above, over the slope section from 30 to 50 m from the slope crest, the rill erosion rate increased as the rillsincised the plough layer. Given the erodible nature of the loess plough soil, it may be assumed that erosionover this part of the slope was largely transport limited and, therefore, dominantly controlled by dischargeand velocity. Under these circumstances, the erosion rate would be expected to show a good relationship withslope length and angle. However, beyond 50 m downslope the decline in rill erosion rates appears to coincidewith the maximum rill depth reaching the base of the plough layer. At this point further rill incision appearsto have been reduced by the more resistant nature of the underlying undisturbed loess. Over this slope section,therefore, the rill erosion may have been partially detachment limited. Under these circumstances, thebreakdown of the relationship with discharge and velocity (slope length and angle) is not unexpected.If this explanation of the deviation between the erosion rate estimates provided by Equation (9) and the

rill- and 137Cs-derived data is correct, it suggests that at a critical point, probably at a slope length in excess ofthe lengths used in the plot studies, the relationship between erosion and slope angle and length breaks downowing to a change from transport-limited to detachment-limited conditions. It seems likely that this mayoccur when rill incision reaches the base of the plough layer. Some support for the existence of a threshold isprovided by examination of the cumulative erosion rate estimates for Field C (Figure 8). Figure 8 shows thecomparison between cumulative erosion rates (sediment transport per unit slope width) derived from 137Csmeasurements and from Equation (9). Cumulative rates are used to reduce the eect of small-scale variabilityevident in the 137Cs data (Figure 5). The erosion rates from Field B (the upper part of each transect) havebeen excluded from the calculation because of the deviation discussed above. For Transect 1 (total length48 m) there is a close agreement in pattern between the 137Cs-derived and predicted cumulative erosion rates,although the latter must be reduced (multiplied by 0.65) to obtain the fit shown. For Transects 2 and 3, thepredicted values must again be reduced (multiplied by 0.75) to obtain a fit with the 137Cs-derived data.However, in this case agreement is only found until a total slope length of c. 50 m is reached. After this point,there is significant divergence, with the 137Cs-derived values being lower than the predicted values. Althoughsome uncertainty is evidently associated with this analysis, the general pattern is consistent with both the137Cs-derived data and the observations of the rill network from Field A.In conclusion, the 137Cs-derived data, with support from the rill measurements, suggest that the empirical

relationships derived from plot studies overestimate water erosion rates on steeply sloping cultivated fields.For such steep fields with a total slope length of less than 50 m, it may be tentatively suggested that the ratesmay be overestimates by a factor of 1.331.5. On steep slopes in excess of 50 m in length, the degree ofoverestimation is likely to increase with increasing slope length. However, there is some evidence that theempirical relationships may underestimate erosion rates on slope crest fields of low slope angle. Where thecrest represents a large proportion of the whole slope and slope angles are relatively low, the two opposingtendencies may cancel each other out (cf. Field A total, Table III).

Implications for sediment sources on the rolling Loess Plateau

The field-scale erosion rates derived in this study from 137Cs measurements, and the equivalent estimatesderived from Equation (9), are shown plotted against slope angle in Figure 9. It should be noted that theserates are spatially integrated point data, not values derived from whole field characteristics. These spatiallyintegrated field data were regressed against slope angle and the relationships found are summarized inTable IV. The slope coecients (a) associated with the regression of the 137Cs-derived rates are considerablylower than those derived by Jiang et al. (1991) mentioned above Equation (7) and by Liu et al. (1994),using erosion plot data from Ansai, Tianshui and Suide. These results strongly suggest that relationshipsderived using data from short (550 m), steep erosion plots may not be appropriate for the long, steep slopesthat characterize the area. Figure 9 and the regression relationships (Table IV) highlight the degree ofoverestimation by the empirical relationship indicated by the 137Cs-derived rates.Any extrapolation of such results in terms of sediment sources in the region must clearly be tempered with

caution, since they are based on a very small sample of fields. However, if the apparent tendency of theempirical relationships to overestimate erosion rates from cultivated slopes is a more general phenomenon, a



Figure 8. Comparison of cumulative erosion rates from Field C derived from 137Cs measurements and empirical relationships:(a) Transect 1; (b) Transect 2; (c) Transect 3



Figure 9. Plots of field erosion rates versus field slope angle: based on 137Cs measurements and the empirical relationship [Equation (9)]for: (a) individual field data; (b) whole transect data

Table IV. Values of the exponents and constants for the relationship E cSa obtained by regressing erosion ratesagainst slope angles, where E is the erosion rate (t km2 yr1) and S is the slope angle (8)

Equation (9) predictions 137Cs-derived data

Individual fields Whole transects Individual fields Whole transects

r2 0.930 0.989 0.880 0.998c 384 939 1974 2840a 1.10 0.81 0.49 0.35



re-evaluation of the estimates of the relative contributions of sediment from the slopes and the gullies derivedusing such relationships is necessary. The data presented here certainly support the suggestion that theestimates of sediment contribution from the cultivated slopes of 10 00016 000 t km2 yr1, derived fromthe empirical relationships, are likely to be overestimates, and that rates of soil loss from the cultivated areaof 800010 000 t km2 yr1, suggested by the 137Cs data, may be closer to the true value. This, in turn,would indicate that a higher percentage of sediment transported into the rivers is derived from the gullyslopes. This is consistent with a range of other evidence currently coming to light (Zhang et al., 1997).

CONCLUSION

Application of the caesium-137 technique to the investigation of soil erosion on cultivated land in the LoessPlateau, near Ansai, has provided important insights into the rates and processes of erosion acting on therolling cultivated land. Downslope variation in rill erosion rates was also studied by measurement of rilldimensions along a series of cross-slope transects. The results of this analysis were in close agreement withthe 137Cs-derived erosion rate data, confirming the potential of the 137Cs technique in this environment.In total, four transects were studied using the 137Cs technique and rates of erosion were found to vary from

65009500 t km2 yr1, with highest rates (870011 000 t km2 yr1) on the steep lower slope sections.These rates of erosion are closely related to slope angle, but they dier significantly from the rates predictedby empirical relationships that have been established using data from erosion plot studies. The results of thisstudy suggest that the latter may seriously overestimate erosion rates on slopes for which the slope lengthexceeds the length of the erosion plots. This overestimation of the water erosion rates by the empiricalrelationships appears to be a result of the limitation of water erosion by non-topographic factors (possiblyhigh shear strength within the subplough layer) as the depth of incision increases. On the studied transectsoverestimation by the empirical relationship was most significant at slope lengths in excess of c. 50 m.If the results of this investigation are representative of the wider landscape in the area, then current

regional estimates of sediment yield from the cultivated mound slopes, based on the erosion plot empiricalrelationships, overestimate the true values by c. 30%. There is a clear need for further investigation of soilerosion on long slopes in the area under normal field conditions rather than under the artificial constraintsimposed by erosion plots.

ACKNOWLEDGEMENTS

This research was undertaken as part of a project entitled: Use of radioisotopes in the assessment of soilerosion and sedimentation problems in China which was funded by The Royal Society and the University ofExeter Research Fund. This support is gratefully acknowledged. The authors are also grateful to Mr MengQingmai and the Middle Yellow River Bureau for oering logistical support for fieldwork; to Mr WangYukuan for assistance with sample collection and processing; to Mr Jim Grapes for overseeing the gammaspectrometry and to Mr Rodney Fry for graphical work.

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Soil erosion rates on sloping cultivated land on the Chinese Loess Plateau