using fallout lead-210 measurements to estimate soil erosion on cultivated land

Using Fallout Lead-210 Measurements to Estimate Soil Erosion on Cultivated LandD. E. Walling* and Q. He

ABSTRACTNaturally occurring fallout 21"Pb is strongly adsorbed by soils and

sediments and has been widely used as a tracer to establish the chronol-ogy of deposited sediments in various sedimentary environments. Thispaper reports an attempt to explore the potential for using fallout210Pb to estimate rates of water-induced soil erosion on cultivatedland. Soil cores were collected from both cultivated and undisturbedareas in a small catchment in Devon, UK, and land use practices wereshown to be the primary factor controlling the depth distribution offallout 210Pb. Based on existing knowledge of the behavior of 210Pb incultivated soils, a mass balance model has been developed that enableslonger-term (=100 yr) rates of erosion and deposition to be estimatedfrom values of unsupported 210Pb inventory for individual samplingpoints. In order to estimate longer-term soil redistribution rates, themass balance model was applied to an 8.54-ha cultivated field withinthe study catchment from which 167 bulk cores had been collectedat the intersections of a 20 by 20 m grid. Soil redistribution rateswithin the field ranged from -5.9 kg m~2 yr"1 (erosion) to 6.4 kg m~2

vr ' (deposition), and the mean erosion rate for the eroding area was1.95 kg m~2 yr"1. The pattern of soil redistribution within the studyfield reflected the influence of topography on sediment mobilizationand transport. The results obtained confirm the potential for usingfallout :l"Ph measurements to estimate rates and patterns of water-induced soil erosion on cultivated land.

WATER-INDUCED SOIL EROSION and associated off-site environmental impacts have attracted grow-

ing concern over recent decades, and there is an increas-ing need to obtain reliable information on rates of soilloss. Yet, such information is frequently difficult to ob-tain using traditional monitoring techniques, due to bothproblems of representativeness and the costs involved(Loughran, 1989). Throughout the past decade, the po-tential for using nuclear weapon-produced 137Cs (Cs-137, half-life 30.2 yr) fallout to quantify rates and pat-terns of soil redistribution by sheet and rill erosion formedium-term timescales (=40 yr) has been successfullydemonstrated in a wide range of environments in differ-ent regions of the world (Ritchie and McHenry, 1990;Walling and Quine, 1991, 1992; Pennock et al., 1995;Walling, 1998).

There are, however, two important limitations to thegeneral application of the 137Cs technique. These relateto the global pattern of 137Cs fallout inputs and the addi-

D.E. Walling and Q. He. Dep. of Geography, Univ. of Exeter, Exeter,EX4 4RJ, UK. Received 2 September 1998. *Corresponding author([email protected]).

Published in Soil Sci. Soc. Am. J. 63:1404-1412 (1999).

tional fallout of 137Cs that occurred in many parts ofEurope in 1986 as a result of the Chernobyl accident.It has been shown that nuclear weapon-derived 137Csinputs were significantly lower in the Southern Hemi-sphere than in the Northern Hemisphere and that inputsto equatorial areas were considerably less than those tothe mid-latitude areas of Europe and North America(Larsen, 1985). For example, whereas contemporary137Cs inventories in North America and Europe are com-monly in the range 2000 to 4000 Bq m~2, values as lowas 420 Bq m*2, 270 Bq m~2, and 252 Bq m~2 have beenreported in Australia, New Zealand, and Zimbabwerespectively (Hewitt, 1996; Owens and Walling, 1996;He and Walling, 1997; Wallbrink, 1997). The low 137Csinventories associated with these areas of reduced re-ceipt of fallout introduce measurement problems interms of both detection limits and the long count timesrequired to obtain results with an acceptable degreeof precision. Since nuclear weapon-derived fallout wasprimarily received during the late 1950s and 1960s, in-ventories will be further reduced in the future becauseof radioactive decay. In areas where Chernobyl-derived137Cs fallout was received, the relationship between con-temporary 137Cs inventories and medium-term rates oferosion and deposition has been complicated by thedifficulty of distinguishing the Chernobyl-derived com-ponent of the total 137Cs input. Furthermore, there isincreasing evidence that Chernobyl-derived inputs of137Cs were more spatially variable than the nuclearweapon-derived inputs, and this variability introducesfurther complexity into the use of 137Cs to estimate ero-sion rates. Because of these limitations on the use of137Cs in certain areas of the world, there is a need toexplore the use of alternative tracers.

Naturally derived 210Pb (Pb-210, half-life 22.2 yr), an-other relatively long-lived fallout radionuclide, is ad-sorbed by soil particulate material and subsequentlyredistributed within the landscape in a manner similarto 137Cs, but its potential as a tracer for studying soilredistribution has to date received only limited atten-tion. Lead-210 is a natural product of the 238U decayseries that is derived from the decay of gaseous 222Rn(half-life 3.8 d), the daughter of 226Ra (half-life 1622 yr).Radium-226 exists naturally in soils and rocks. The 210Pbin soils generated in situ by the decay of 226Ra is termedsupported 210Pb and is in equilibrium with 226Ra. On theother hand, upward diffusion of a small portion of the222Rn produced in the soil and rock introduces 2l°Pb into

WALLING & HE: FALLOUT LEAD-210 MEASUREMENTS TO ESTIMATE SOIL EROSION 1405

the atmosphere, and its subsequent fallout provides aninput of this radionuclide to surface soils and sedimentsthat will not be in equilibrium with its parent 226Ra(Robbins, 1978). Fallout 210Pb is commonly termed un-supported or excess 210Pb when incorporated into soilsor sediments in order to distinguish it from the 210Pbproduced in situ by the decay of 226Ra. The amount ofunsupported or atmospherically derived 210Pb in a soilor sediment sample can be calculated by measuring boththe 210Pb and 226Ra activities and subtracting the 226Ra-supported 210Pb component from the total 210Pb in thesample. The required measurements of 210Pb and 226Raactivity can be made by direct gamma spectrometryusing low-energy, low-background HPGe detectors(Joshi, 1987).

The annual deposition of B7Cs has been characterizedby great temporal variation related to the timing ofthe large-scale atmospheric testing of nuclear weapons.Most 137Cs fallout occurred during the period extendingfrom the late 1950s to the early 1970s. Peak falloutrates in the Northern Hemisphere occurred in 1963 andfallout rates declined to very low values by 1972. Incontrast, deposition of fallout 210Pb from the atmospherehas been relatively constant through time because of itsnatural origin (Turekian et al., 1977; Nozaki et al., 1978;Nevissi, 1985; Graustein and Turekian, 1986; Crickmoreet al., 1990). Deposition fluxes of fallout 210Pb have beendocumented for many parts of the world, either throughanalysis of 210Pb in rainfall or analysis of unsupported210Pb in stable, undisturbed soils. Values obtained ex-hibit significant global variation, with deposition ratesreported by Turekian et al. (1977), Robbins (1978), andAppleby and Oldfield (1992) varying"from 23 Bq m~2

yr~' to 367 Bq m~2 yr~'. The limited information ondeposition fluxes precludes detailed examination of theglobal patterns involved, but Robbins (1978) indicatesthat values are greater in mid-latitude regions, andAppleby and Oldfield (1992) indicate that values arereduced over the oceans and generally increase fromwest to east over the continents, due to the predominantwest-east movement of air masses.

Like 137Cs, 210Pb has been shown to have a strongaffinity for sediment particles (Van Hoof and Andren,1989; He and Walling, 1996a). As a result, unsupported210Pb has been widely used to establish the chronologyof lake, estuarine, and marine sediments deposited dur-ing the past 100 to 150 yr by assuming either a constantflux of unsupported 2l°Pb to the depositing sediment ora constant concentration in the deposited sediment andby relating the downcore reduction in unsupported 210Pbconcentrations to its decay constant and the sedimentdeposition rate (e.g., Appleby and Oldfield, 1978; Krish-naswami and Lal, 1978; Robbins, 1978; Wise, 1980; Ben-ninger and Krishnaswami, 1981; McCall et al., 1984;Wan et al., 1987; Crickmore et al., 1990). A similarapproach has been used for dating river floodplain, salt-marsh sediments, and peat bogs (e.g., Walling and He,1994; He and Walling, 1996b; Buscail et al., 1997; Jensen,1997; Kirn et al., 1997).

Despite the widespread use of fallout 210Pb in sedi-ment chronology studies, its potential as a tracer for

studying water-induced soil and sediment redistributionwithin the landscape has been less widely recognizedand exploited. Upon reaching the land surface as falloutfrom the atmosphere, unsupported 210Pb will be rapidlyadsorbed by the clay minerals and organic matter in thesurface soil, and, as in the case of 137Cs, its subsequentredistribution in the soil and across the land surface willbe controlled by its interaction with land use practices,erosion, and sediment transport processes. Recent stud-ies have investigated the behavior of fallout 210Pb incatchment soils under different land use conditions(Dorr and Miinnich, 1989, 1991; Walling et al., 1993,1995; Wallbrink and Murray, 1996; He and Walling,1997; Smith et al., 1997). Activities in surface soils werefound to vary significantly according to land use, whichaffects both soil properties and the post-depositionalredistribution of 210Pb within the soil profile. This featureof the occurrence of unsupported 210Pb has been usedas a basis for fingerprinting fluvial suspended sedimentsources by several researchers (e.g., Walling et al., 1993;He and Owens, 1995; Collins et al., 1997; Wallbrink etal., 1998), since, for example, concentrations in surfacematerial from uncultivated pasture or rangeland will bemuch greater than those from cultivated soils becauseof the mechanical mixing of the latter by tillage. Withits strong affinity for soil particles and its relatively easydirect measurement, which uses low-background, low-energy gamma spectrometry, 210Pb also offers consider-able potential for use as a tracer for estimating soilerosion rates. Several researchers have recently at-tempted to exploit this potential (Walling et al., 1995;Wallbrink and Murray, 1996; He and Walling, 1997;Wallbrink, 1997); however, in several of these investiga-tions, fallout 210Pb was used in conjunction with 137Csand further studies are needed to explore the potentialfor using this radionuclide as an independent means ofquantifying soil redistribution rates, and thus, its poten-tial for use in areas where the application of 137Cs is re-stricted.

The study reported in this paper attempts to explorefurther the use of fallout 210Pb for quantifying rates ofsoil redistribution by water erosion on cultivated soils.In order to compare the behavior of fallout 210Pb insoils under different land use practices, soil cores werecollected from both cultivated and undisturbed landwithin the Moorlake catchment near Crediton in Devon,UK. These cores were sectioned in order to documentthe down-core variation of unsupported 210Pb concentra-tions in the soils. A mass balance model describing theredistribution of fallout 210Pb in the soil profile andacross the surface of cultivated land was developed. Adetailed program of soil coring was undertaken withina cultivated field in the study catchment, and the fallout210Pb inventories of the resulting cores were determined.The mass balance model was employed to derive erosionor deposition rates from the total fallout 210Pb invento-ries associated with the individual soil cores that werecollected from the field. The rates and patterns of soilredistribution established for the study field were closelyrelated to its topography and were consistent with exist-ing understanding of soil redistribution processes.

1406 SOIL SCI. SOC. AM. J., VOL. 63, SEPTEMBER-OCTOBER 1999

MATERIALS AND METHODSField Sampling and Laboratory Analysis

An 8.54-ha cultivated field at Aller Barton Farm, locatedin the Moorlake catchment near Crediton in Devon, UK, wasselected as the focus of this investigation. The field is underlainby Permian breccias and conglomerates on which brown earthsoils of the Crediton series (Dystric Eutrochrept) have devel-oped. The mean annual precipitation for the local area is =800mm. Field observations had already provided clear evidenceof significant soil erosion within this field. To document thespatial distribution of fallout 210Pb inventories within the field,bulk soil cores were collected at the intersections of a 20 by20 m grid, using a motorized percussion corer equipped with a6.9-cm-diam. core tube. In addition to the grid-based sampling,supplementary soil cores were collected from areas character-ized by marked topographic change in order to increase therepresentativeness of the sampling. In total, 167 bulk soil coreswere collected from the study site. Checks, involving 210Pbmeasurements on samples taken from the bottom of selectedcores, were used to ensure that all cores had penetrated tothe full depth of the unsupported 210Pb profile. Additionalinformation on the typical vertical distribution of fallout 210Pbactivity in the soil profile and the plow depth was obtainedfrom sectioned soil cores collected from representative siteswithin the field. A detailed topographic survey of both thecoring points and the entire field was made with an electronictheodolite and was undertaken in parallel with the coringprogram. To document the depth distribution of unsupported210Pb in undisturbed soils and to establish the local fallout 210Pbinventory representing the direct atmospheric 210Pb input tothe local area, both sectioned soil cores and bulk cores werecollected from stable, undisturbed sites in adjacent areas ofthe catchment for subsequent 210Pb analysis. Samples of surfacematerial were collected from the cultivated field to provideinformation on the grain-size composition of the originalsource soil. Suspended-sediment samples for particle-sizeanalysis were also collected from the stream that drains thecatchment during major storm events in order to provide infor-mation on the grain-size composition of mobilized sediment.

Measurements of the activities of unsupported 210Pb andother relevant radionuclides in the soil and sediment sampleswere undertaken simultaneously by gamma-ray spectrometry,using a high resolution, low background, low energy, hyper-pure n-type germanium coaxial -y-ray LOAX HPGe detector(EG&G Ortec, Oak Ridge, TN) coupled to an Ortec amplifierand multichannel analyzer. The samples were placed in plasticMarinelli beakers and sealed with PVC tape for 20 d prior toassay in order to achieve equilibrium between 226Ra and itsdaughter 222Rn. The efficiency of the detection system wascalibrated using soil samples prepared from standard solutionsthat contain 210Pb and 226Ra. In order to determine the detectorefficiency for samples of varying geometry and to accountfor variable self-adsorption effects, these calibration samplescontained different amounts of soil. The samples were placedon the detector and counted for >85 000 s, providing a preci-sion of approximately ±10% at the 90% level of confidencefor the gamma spectrometry measurements. The total 210Pbconcentrations of the samples were measured using the 46.5keV gamma ray for 210Pb, and the 226Ra concentrations weremeasured using the 351.9 keV gamma ray for 214Pb, a short-lived daughter of 226Ra. In order to account for 222Rn loss fromthe soil, the in situ 226Ra-supported 210Pb concentration that isassociated with individual soil cores has been derived fromthe measured 226Ra concentration using the relationship be-tween the average 226Ra concentration and the total 210Pb con-centration, which was established using samples from the

lower parts of the soil profile where atmospheric 210Pb wasassumed to be absent (Graustein and Turekian, 1986; Wall-brink and Murray, 1996). Unsupported 21t)Pb concentrationsfor the samples were calculated by subtracting the 226Ra-sup-ported 210Pb concentrations from the total 210Pb concentrations(Joshi, 1987). To establish the grain-size composition of bothoriginal soil and mobilized sediment, samples of surface soiland suspended sediment from the adjacent stream were ana-lyzed for their particle-size distributions. The grain-size distri-butions of the chemically dispersed mineral fractions of the<63-(xm sediment were measured using MasterSizer laser-diffraction equipment (Malvern Instruments, Malvern, UK).The >63-u,m sediment was analyzed by sieving. The organicmatter content of selected samples was determined by weightloss after ignition in a muffle furnace for 2 h at 600°C. Table1 lists typical values for the properties of the soils and sedi-ments studied.

The Depth Distribution of Fallout Lead-210 in SoilsFigure 1 shows the depth distribution of unsupported 210Pb

in two soil cores, one collected from an area of stable, undis-turbed permanent pasture and the other from the cultivatedfield where detailed sampling was undertaken. In commonwith other sites in Devon, UK, documented by He and Walling(1997), the unsupported 210Pb in these profiles extends signifi-cantly deeper than the initial distribution of the fallout 210Pb,which reflects post-fallout redistribution of this radionuclidein both undisturbed and cultivated soils. Significant differencesexist between the two cores in terms of both profile shapeand the associated concentrations of unsupported 2WPb. Theconcentration of fallout 210Pb in the undisturbed soil core isgreatest at the surface (with a value of 104 Bq kg^1) anddecreases exponentially with depth (Fig. 1A). Unsupported210Pb is found to a depth of 18 cm (or 151 kg m"2) in this core,and its total unsupported 210Pb inventory is =4930 Bq m~2.The mean bulk density of the soil within this core is -120 kgm~3, influenced by the relatively high organic matter content.He and Walling (1997) have attempted to model the depthdistribution of fallout 2KIPb in undisturbed soils using effectivediffusion and migration functions to represent its post-deposi-tional redistribution in the soil profile that is induced by physi-cal, physicochemical, and biotic processes, and these research-ers have successfully reproduced the observed exponentialdecline of concentration with depth.

In contrast to the distribution of unsupported 210Pb in undis-turbed soils, concentrations in cultivated soils will be relativelyuniform throughout the plow layer as a result of mixing causedby tillage. This feature is clearly shown by the depth distribu-tion of fallout 210Pb in the soil core collected from the cultivatedfield depicted in Fig. IB. The majority of the unsupported21(1Pb is contained within the top 20 cm (=220 kg m~2) of thiscore and the total unsupported 210Pb inventory is 3150 Bq m~2.The average plow depth in the study field is =20 cm, and theaverage unsupported 210Pb concentration of the soil within theplow layer is =14 Bq kg"1. The soil is relatively compact andthe mean bulk density of this core is «1070 kg m~3, which isconsiderably greater than that of the undisturbed soil core.The total unsupported 210Pb inventory of this core is signifi-

Table 1. Typical properties of the soils and sediments studied.

Undisturbed soilCultivated soilSuspended sediment

Organicmatter

21.57.2

12.1

Clay

171429

Silt(2-63 (Jim)

494366

Sand(>63 (im)

34435


cantly lower than that associated with the stable, undisturbedsoil core, indicating that loss of unsupported 210Pb has occurredfrom this location as a result of soil erosion and that this siteis, therefore, an eroding site.

A Mass Balance Model for Estimating Soil Erosionand Deposition Rates on Cultivated Soils

Existing studies that have used 137Cs measurements to inves-tigate water-induced soil erosion on cultivated soils have em-ployed a variety of approaches to establish calibration rela-tionships for converting the total inventories of soil cores intoestimates of soil redistribution rates that are associated withthe sampling points. These include empirical relationships(e.g., regression equations) and theoretical models (e.g., theproportional model, the gravimetric model, and mass balancemodels) (cf. Walling and Quine, 1990; Walling and He, 1999).The basic assumptions of these approaches are closely linkedto the known temporal distribution of nuclear weapon-derived 137Cs fallout inputs (see above). However, when usingunsupported 210Pb measurements to estimate soil redistribu-tion rates on cultivated soils, a mass balance approach mustbe employed, because the fallout input to the soil surface isessentially continuous. The application of this approach isdescribed below.

For cultivated soils, both erosional and depositional areasmay exist within an individual field. In a cultivated soil profile,the soil may be conveniently divided into two layers. Soilproperties (including the radionuclide content) will normallybe relatively uniform in the plow layer and will differ fromthose in the layer below the plow depth (Fig. Ib). In the caseof a soil profile experiencing erosion, cultivation and erosionwill represent the dominant processes controlling the redistri-bution of fallout 210Pb in the soil profile, and the accumulatedunsupported 210Pb will be restricted to the plow layer. Changesin the activity of the accumulated unsupported 210Pb withinthe plow layer will be associated with further deposition ofthe radionuclide from the atmosphere as well as loss thatresults from both soil erosion and radioactive decay, and thetotal unsupported 210Pb inventory will be less than the localreference inventory, AKt (Bq m~2). In contrast, for a soil profilefrom a site experiencing deposition, unsupported 210Pb will befound in the soil below the plow depth because of the progres-sive accumulation of sediment containing fallout 210Pb erodedfrom upslope, and the total fallout 210Pb inventory will begreater than the local reference inventory. The behavior and

A BUnsupported 21° Pb concentration Unsupported 2'° Pb concentration

(Bqkg'1) (Bqkg-1)0 30 60 90 120 0 7 14 21

3150 Bqm"'300-1

Fig. 1. Representative unsupported :"'Ph profiles associated withcores collected from undisturbed soils (A) and cultivated soils (B)in the study catchment.

fate of unsupported 210Pb in soils from eroding sites and sitesexperiencing deposition is considered in greater detail below.

Eroding SitesFor an eroding location, change in the activity of unsup-

ported 210Pb, A(t) (Bq m~2) per unit area with time / (yr), canbe expressed as

[i]where

X = decay constant of 210Pb (yr~!);7(f) = annual fallout 210Pb deposition flux (Bq irr2 yr"1);

F = proportion of the freshly deposited 210Pb fallout re-moved by erosion before being mixed into the plowlayer;

P = particle-size correction factor, defined as the ratio ofthe 21()Pb concentration of the mobilized sediment tothat of the original soil;

R = erosion rate (kg m~2 yr"1);D = the cumulative mass depth representing the average

plow depth (kg m~2).The first term on the right-hand side of Eq. [1] representsdeposition of the atmospheric 210Pb fallout, and the secondterm represents the loss associated with radioactive decay andwater-induced soil erosion. The incorporation of the particle-size correction factor P into Eq. [1] is necessary because ofthe strong association of fallout 210Pb with fine soil particlesand the grain-size selectivity of the erosion processes. Thevalue of P will reflect the grain-size composition of both mobi-lized sediment and the original soil. Because the grain-sizecomposition of mobilized sediment is commonly enriched infines relative to the original soil, P is generally greater than1.0 (He and Walling, 1996a). To estimate the value of P,information on the grain-size composition of both mobilizedsediment and the original soil is required. He and Walling(1996) have derived a relationship between P and the specificsurface area of mobilized sediment, 5ms (m2 g~l), and that ofthe original soil, Sos (m2 g"1), of the form

[2]

where v is a constant. The constant v reflects the interactionbetween the unsupported 210Pb and the soil particles, which isin turn influenced by both the physical and chemical properties(such as clay mineralogy and organic matter content) of thesoil. Results obtained by He and Walling (1996a) for cultivatedsoils with properties similar to those of the soils studied hereproduced a value of 0.76 for v, and this has been assumed tobe the value for the cultivated soil investigated in this study.

The introduction of F into Eq. [1] is necessary to accountfor the removal of freshly deposited 210Pb fallout by surfaceerosion before its incorporation into the plow layer by cultiva-tion. Because the deposition of fallout 210Pb occurs primarilyin association with precipitation, it will initially be distributedwithin a shallow layer near the soil surface (Nevissi, 1985;He and Walling, 1997). Results obtained from experimentsdemonstrate that unsupported 210Pb concentrations containedin topsoil prior to cultivation decline rapidly with increasingcumulative mass depth. If erosion occurs, the sediment mobi-lized from the soil surface will contain higher concentrationsof fallout 210Pb than sediment originating from lower in thesoil profile. He and Walling (1997) have shown that the initialdistribution of fallout 210Pb inputs associated with precipitation


can be approximated as

,-i/H [3]

where Q(x,t) (Bq kg"1) is the radionuclide concentration atcumulative mass depth x (kg m"2) from the soil surface, Af =1 (yr); and H (kg m~2) is the relaxation mass depth of theinitial distribution of fallout 210Pb in the soil profile, which canbe determined experimentally for local conditions (He andWalling, 1997). The constant H represents the depth of pene-tration of fallout 210Pb into the soil. High values of H willreflect a deeper penetration of the radionuclide into the soil.For an eroding site, if the erosion rate is known, then Eq. [3]can be used (when information on the local rainfall regime,erosion processes, and timing of cultivation is also known) toestimate the proportion of the freshly deposited fallout 210Pb(F) that was removed from the site by erosion. If sheet erosionis assumed, F can be expressed as

T = Py(\ - e"4"™) [4]where y is the proportion of the annual 210Pb fallout that issusceptible to removal by erosion prior to incorporation intothe soil profile by tillage. Equation [4] indicates that the relax-ation mass depth H is an important factor influencing theremoval of the recently deposited fallout from the site. For aconstant erosion rate, the smaller the value of H, the greaterthe proportion of the recently deposited fallout that will beremoved by erosion. The parameter 7 will be dependent onthe timing of cultivation and the local rainfall regime. Forexample, in situations when there is only one period with highintensity rainfall events that can generate surface runoff and,thus, erosion, and this occurs shortly before the single annualperiod of cultivation, all the unsupported 210Pb already accu-mulated at the soil surface as well as the fallout 210Pb inputdirectly associated with this rainfall will be susceptible to re-moval by erosion, and the value of -y can be assumed to be1.0. In cases where the period of high intensity rainfall occursimmediately after cultivation has been completed, the 210Pbaccumulated at the soil surface before this period of precipita-tion will have been incorporated into the plow layer, and onlythe fallout 2l°Pb directly associated with this rainfall will besusceptible to removal by erosion while it remains near thesurface. Under these circumstances, the value of -y may beapproximated by the ratio of the depth of this rainfall to thetotal annual rainfall. If there is more than one cultivationoperation and more than one period of high intensity rainfallthat can produce surface runoff each year, then the estimationof 7 will need to include consideration of the timing of precipi-tation inputs in relation to the cultivation operations.

Solution of Eq. [1] under continuous fallout input yields

A(t) = A(t0)e~

1(1- Py(l -

•><'-'•> At' [5]where ta (yr) is the year when cultivation started, and A(t0) =AK, is the fallout 210Pb inventory at t0. When deriving Eq.[5], it has been assumed that there was no erosion before to-Assuming that both the erosion rate R and the deposition flux7 are constant through time, then AKf = 7/\. The fallout 210Pbinventory for the soil profile A(t) (Bq m"2) can be representedas

/xe

- n

[6]The fallout 210Pb deposition flux 7 can be estimated from theunsupported 210Pb inventories of stable, undisturbed soils, AK!and the decay constant \. The average annual erosion rate,R, can be estimated from Eq. [6] when deposition flux 7, plowdepth D, and relaxation mass depth Hare known. In situationswhere cultivation has existed for >100 yr (i.e., t — ta > 100),a steady state can be assumed and Eq. [6] reduces to

[7]PR/D + XIf it is further assumed that 7?Ar <s 77, then F =and the erosion rate 7? can be estimated from the followingequation:

R = I - \A DHAH + yID PAf [8]

The concentration C'(x,t) (Bq kg"1) of the accumulated un-supported 210Pb at depth x in the plowed soil can be expressedas

C'(xjt) =

( i -n/D PR/D + \

0x < Dx > D [9]

Figure 2 depicts the relationships between soil erosion rateand percentage reduction in fallout 210Pb inventory relative tothe local reference inventory for a hypothetical eroding soilprofile that is associated with periods of cultivation of differentlength (with t - t0 taking the values of 20, 40, 60, and 100 yrrespectively). The following values were employed for therelevant parameters: 77 = 4.0 kg m~2, D = 200 kg m"2, AKt =5000 Bq m~2 or 7 = 156 Bq irT2 yr"1, P = 1.0, and y = 0.3.

Depositional SitesIn situations when^4(f) is greater than local reference inven-

tory AKt at a sampling point, deposition may be assumed. Theexcess unsupported 2WPb inventory, A^ (Bq m~2) (defined asthe measured total inventory A(t) less the local referenceinventory AKt), can be attributed to the accumulation of fallout210Pb associated with the deposition of sediment eroded fromthe upslope area, which can be expressed as

[10]

where R' (kg m~2 yr"1) is the deposition rate, and Cd(f') (Bqkg"1) is the unsupported 210Pb concentration of deposited sedi-ment at t' (yr). Cd(t') reflects the mixing of sediment and itsassociated unsupported 210Pb that is mobilized from all theeroding areas that converge on the aggrading point. Generally,Ca(t') can be assumed to be represented by the weightedmean of the unsupported 210Pb concentrations of the sedimentmobilized from the upslope contributing area, S (m2). Cd(f')can, therefore, be calculated using the following equation:

[11]

PR/D [1-

where Ce(f') (Bq kg"1) is the unsupported 210Pb concentrationof mobilized sediment, and P' is a further particle-size correc-tion factor that reflects differences in grain-size compositionbetween mobilized sediment and deposited sediment and isdefined as the ratio of the unsupported 210Pb concentration ofdeposited sediment to that of the mobilized sediment. As inthe case of P, a relationship between P' and the specific surface


120-,

1 GO-

60-

»4<H

20-

100

- 20 years- 40 years- 60 years100 years

0 10 20 30 40 50 60Percentage reduction in unsupported 2'°Pb inventory (%)

Fig. 2. Relationships between soil erosion rate and percentage reduc-tion in the unsupported 2l°Pb inventory derived using the massbalance model for an hypothetical eroding soil profile subject todifferent periods of continuous cultivation to the present.

Cultivated surface soilCultivated surface soilSuspended sedimentSuspended sediment /'/

63Particle size (um)

Fig. 3. A comparison of the grain-size distributions of the <63-u,mfractions of suspended sediment and cultivated surface soil fromthe study catchment.

area of deposited sediment, 5ds (m2 g"1), and of mobilizedsediment, Sms (m2 g~'), may be assumed to take the form of

P = Jds

sm[12]

Because the grain-size composition of the sediment depositedwithin a cultivated field will commonly be depleted in the finefractions relative to the mobilized sediment, P' is generally<1.0.

The unsupported 210Pb in the plow layer at a site experienc-ing erosion will comprise two components, one associated withfreshly deposited 210Pb fallout, O,(x,t), which has an exponentialdistribution near the soil surface, and the other associatedwith the accumulated fallout 210Pb in the soil profile, C'(x,t),which is uniformly distributed within the plow layer. The un-supported 210Pb concentration of mobilized sediment will beclosely related to that of the surface soil and can be expressedas

[13]

The first term on the right-hand side of Eq. [13] representsthe erosion of a proportion of the annually deposited 210Pbfallout from the eroding soil profile prior to its incorporationby tillage, and the second term represents removal of theaccumulated fallout 210Pb that is stored in the plow layer. UsingEq. [10], [11], and [13], mean annual soil deposition rate R'(kg m""2 yr~') can be calculated as

R' =

A^RdSA(t')/D)RdS

[14]

APPLICATION OF THE MASSBALANCE MODEL

The Fallout Lead-210 Reference Inventoryfor the Study Area

Analysis of unsupported 210Pb activities in the soilcores collected from stable, undisturbed sites within the

study catchment indicated an average fallout 210Pb in-ventory of =5170 Bq m"2, and this value has been takento represent the reference inventory for the study catch-ment. Assuming constant deposition fluxes, the annualatmospheric 210Pb deposition rates in this area are esti-mated to be =161 Bq m~2 yr^1. This value lies withinthe range of annual deposition fluxes of fallout 210Pb inBritain of 88 to 270 Bq m~2 yr~', as reported by Crick-more et al. (1990).

The Grain-Size Composition of Surface Soiland Suspended Sediment

Because of the practical difficulties associated within situ collection of sediment mobilized by soil erosion,its particle-size composition has been assumed to besimilar to that of the suspended sediment that was trans-ported by the stream draining the study catchment. This,however, only represents an approximation, since thegrain-size composition of mobilized sediment maychange during transport to and by the stream as a resultof within-field and upstream channel deposition, andsince some of the sediment mobilized by soil erosionmay be transported as bed load. On the other hand,field observations suggest that bed load transport ac-counted for only a very small proportion of the totalsediment transport by the stream draining the studycatchment. Figure 3 compares the grain-size composi-tion of the <63-|xm fractions of representative samplesof suspended sediment with surface soil from the studyfield, and data indicate that, even for the <63-u,m frac-tions, the suspended sediment is enriched in fines rela-tive to the original soil. More than 95% of the suspendedsediment is composed of particles of <63 pjn, while=43% of the surface soil from the cultivated field iscomposed of particles that are >63 jxm. It has beenassumed for simplicity that there is no significant spatialvariation in the grain-size composition of the surfacesoil of both erosional and depositional areas within thefield. The grain-size composition of the surface soil has,therefore, been assumed to be the average of that ofthe surface soil samples for which particle-size distribu-tions are depicted in Fig. 3. Using the mean grain-size


distribution measured for suspended sediment, valuesof 1.52 and 0.66 have been estimated for the particle-size correction factors P and P', respectively.

The Spatial Distributions of Fallout Lead-210Inventories and Soil Redistribution Rates

within the Study FieldFigure 4 presents a digital elevation model of the

cultivated field at Aller Barton Farm interpolated fromthe surveyed elevation data through the use of Gsharpcomputer software (Advanced Visual Systems, Wal-tham, MA). The height data were expressed relative toan arbitrary datum. This area is composed of a valleyhead and two valley sides and a relatively long valleybottom that runs along the middle of the field, linkingthe valley head and the field outlet. Figure 5A showsthe interpolated distribution of unsupported 210Pb inven-tories within the field, based on the measurements un-dertaken on the bulk soil cores. Significant spatial vari-ability of these inventories is evident within the field.Areas with reduced, unsupported 210Pb inventories arefound along the top and upper parts of the valley sides,while areas located in depressions along the valley bot-tom and near the field outlet are characterized by in-creased inventories. The average unsupported 210Pb in-ventory for the entire field is =4525 Bq m"2, and thissuggests that = 13 % of the direct atmospheric 210Pb inputhas been lost from the field as a result of soil loss associ-ated with erosion.

The mass balance model described previously hasbeen employed to estimate the soil redistribution ratesfrom the 210Pb inventories obtained for the samplingpoints in the study field. Values of the relevant parame-ters were estimated based on local conditions: H = 3.6kg m-2; D = 220 kg m"2; AK( = 5170 Bq m"2 or 7 =161 Bq m~2 yr"J; P = 1.52; P' = 0.66; v = 0.76; y =0.3; and t - t0 = 100 yr. The resulting spatial distributionof soil redistribution rates within the study field is illus-trated in Fig. 5B. The mean erosion rate for the erodingareas within the field was estimated to be 1.95 kg m"2

yr"1 (or 19.5 t ha"1 yr"1), and the mean deposition rate

for depositional areas 2.21 kg m 2 yr ' (or 22.1 t ha 'yr"1). The net erosion rate for the entire field was esti-mated to be 0.44 kg m"2 yr"1 (4.4 t ha"1 yr"1). Thesediment delivery ratio for this field is estimated to be41%. This relatively low value reflects the topographyof the field. The long valley bottom connecting the val-ley head and the field outlet significantly reduces thesediment transport capacity of surface runoff within thefield during large storm events. A substantial proportionof the sediment mobilized from the areas near the fieldboundaries and from the upper parts of the valley sidesis deposited within the valley bottom and near the fieldoutlet (Fig. 5B). The pattern of unsupported 210Pb inven-tories presented in Fig. 5 shows some evidence of thepossible influence of tillage on soil redistribution. Slopeconvexities are, for example, characterized by reducedinventories. Recent work in the use of 137Cs to estimaterates of soil erosion by water (Quine et al., 1997; Wallingand He, 1998) has attempted to include such tillageeffects in the procedures used to obtain erosion rateestimates, and the mass balance model described abovecould be further developed to incorporate these effects.The rates of soil redistribution derived from the fallout210Pb measurements represent long-term average values,since t - t0 has been assumed to be 100 yr.

Fig. 4. The topography of the study field at Aller Barton Farm (heightdata are relative to an arbitrary datum).

Fig. 5. The spatial distributions of unsupported 210Pb inventories (A)and soil redistribution rates estimated using the fallout 2'"l*h mea-surements (B) within the study field at Aller Barton Farm.


CONCLUSIONSThe strong affinity of fallout 210Pb for clay and organic

matter within the soil makes it an effective sedimenttracer for studying water-induced soil redistribution. Inundisturbed soils, concentrations of unsupported 210Pbdecrease approximately exponentially with increasingdepth from the soil surface, penetrating to depths of=18 cm. This reflects the continuous input of fallout210Pb to the soil surface from the atmosphere, post-depo-sitional downward movement associated with physical,physicochemical and biotic processes, as well as radioac-tive decay within the soil profile. In contrast, the distri-bution of fallout 210Pb in cultivated soils is relativelyuniform within the plow layer for an eroding or stablesite because of the mixing caused by tillage. At an erod-ing point within a cultivated field, the total unsupported210Pb inventory will be less than the local reference in-ventory measured for stable, undisturbed soils due tothe loss of fallout 2l°Pb associated with soil loss, whileat a depositional point it will be higher, because ofthe deposition of sediment containing unsupported 210Pbderived from the upslope contributing areas. The massbalance model proposed here for estimating rates ofsoil redistribution on cultivated soils from fallout 210Pbmeasurements takes account of the grain-size selectivityassociated with sediment generation, transport, and de-position. This model also includes consideration of thekey processes involved in the removal of unsupported210Pb from an eroding point and its subsequent deposi-tion at deposition sites. The spatial distributions of boththe unsupported 2l°Pb inventories and the estimated soilredistribution rates within the study field at Aller BartonFarm presented in Fig. 5 are closely related to the topog-raphy of the field, which exerts an important influenceon the processes involved in sediment mobilization,transport, and deposition.

The results obtained from this case study confirm thepotential for using fallout 210Pb in soil erosion investiga-tions. There is an increasing need for spatially distrib-uted information on rates of water-induced erosion andsediment deposition within the landscape, and 137Csmeasurements have provided one means of meeting thisrequirement. Fallout 210Pb measurements may offer analternative to 137Cs measurements in areas where theirapplication is limited by low inventories or compro-mised by the occurrence of significant Chernobyl-derived B7Cs fallout. Furthermore, in situations whereboth 137Cs and unsupported 210Pb measurements can beemployed, there is potential to use both fallout radionu-clides in combination, since the measurements of bothradionuclides can be undertaken simultaneously. Be-cause the two radionuclides estimate erosion rates fordifferent time periods, they may also provide a basisfor deriving additional information on the erosional his-tory of a study site by comparing the inventories offallout 137Cs and 210Pb.

ACKNOWLEDGMENTSThe study reported in this paper was funded by the UK

Natural Environment Research Council (Grant GR3/10293),

and it also represents a contribution to the InternationalAtomic Energy Agency Coordinated Research ProgrammeDl.50.05, "Assessment of soil erosion through the use of Cs-137 and related techniques as a basis for soil conservation,sustainable agricultural production, and environmental pro-tection," through Technical Contract 9562/R1. The assistanceof P. Whelan with sample collection and of J. Grapes withgamma-ray spectrometry and the cooperation of landownersin permitting access to their land for collection of soil coresand suspended sediment samples are gratefully acknowledged.


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using fallout lead-210 measurements to estimate soil erosion on cultivated land

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