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DIVISION S-6-SOIL & WATER MANAGEMENT & CONSERVATION

Using Fallout Lead-210 Measurements to Estimate Soil Erosion on Cultivated Land

^a Dep. of Geography, Univ. of Exeter, Exeter, EX4 4RJ, UK

d.e.walling{at}exeter.ac.uk

	ABSTRACT

TOP ABSTRACT INTRODUCTION Materials and methods Application of the mass... Conclusions REFERENCES

 
Naturally occurring fallout ²¹⁰Pb is strongly adsorbed by soils and sediments and has been widely used as a tracer to establish the chronology of deposited sediments in various sedimentary environments. This paper reports an attempt to explore the potential for using fallout ²¹⁰Pb to estimate rates of water-induced soil erosion on cultivated land. Soil cores were collected from both cultivated and undisturbed areas in a small catchment in Devon, UK, and land use practices were shown to be the primary factor controlling the depth distribution of fallout ²¹⁰Pb. Based on existing knowledge of the behavior of ²¹⁰Pb in cultivated soils, a mass balance model has been developed that enables longer-term (100 yr) rates of erosion and deposition to be estimated from values of unsupported ²¹⁰Pb inventory for individual sampling points. In order to estimate longer-term soil redistribution rates, the mass balance model was applied to an 8.54-ha cultivated field within the study catchment from which 167 bulk cores had been collected at the intersections of a 20 by 20 m grid. Soil redistribution rates within the field ranged from -5.9 kg m^-2 yr^-1 (erosion) to 6.4 kg m^-2 yr^-1 (deposition), and the mean erosion rate for the eroding area was 1.95 kg m^-2 yr^-1. The pattern of soil redistribution within the study field reflected the influence of topography on sediment mobilization and transport. The results obtained confirm the potential for using fallout ²¹⁰Pb measurements to estimate rates and patterns of water-induced soil erosion on cultivated land.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Materials and methods Application of the mass... Conclusions REFERENCES

 
WATER-INDUCED SOIL EROSION and associated off-site environmental impacts have attracted growing concern over recent decades, and there is an increasing need to obtain reliable information on rates of soil loss. Yet, such information is frequently difficult to obtain using traditional monitoring techniques, due to both problems of representativeness and the costs involved (Loughran, 1989). Throughout the past decade, the potential for using nuclear weapon–produced ¹³⁷Cs (Cs-137, half-life 30.2 yr) fallout to quantify rates and patterns of soil redistribution by sheet and rill erosion for medium-term timescales (40 yr) has been successfully demonstrated in a wide range of environments in different 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 the general application of the ¹³⁷Cs technique. These relate to the global pattern of ¹³⁷Cs fallout inputs and the additional fallout of ¹³⁷Cs that occurred in many parts of Europe in 1986 as a result of the Chernobyl accident. It has been shown that nuclear weapon–derived ¹³⁷Cs inputs were significantly lower in the Southern Hemisphere than in the Northern Hemisphere and that inputs to equatorial areas were considerably less than those to the mid-latitude areas of Europe and North America (Larsen, 1985). For example, whereas contemporary ¹³⁷Cs inventories in North America and Europe are commonly in the range 2000 to 4000 Bq m^-2, values as low as 420 Bq m^-2, 270 Bq m^-2, and 252 Bq m^-2 have been reported in Australia, New Zealand, and Zimbabwe respectively (Hewitt, 1996; Owens and Walling, 1996; He and Walling, 1997; Wallbrink, 1997). The low ¹³⁷Cs inventories associated with these areas of reduced receipt of fallout introduce measurement problems in terms of both detection limits and the long count times required to obtain results with an acceptable degree of precision. Since nuclear weapon–derived fallout was primarily received during the late 1950s and 1960s, inventories will be further reduced in the future because of radioactive decay. In areas where Chernobyl-derived ¹³⁷Cs fallout was received, the relationship between contemporary ¹³⁷Cs inventories and medium-term rates of erosion and deposition has been complicated by the difficulty of distinguishing the Chernobyl-derived component of the total ¹³⁷Cs input. Furthermore, there is increasing evidence that Chernobyl-derived inputs of ¹³⁷Cs were more spatially variable than the nuclear weapon–derived inputs, and this variability introduces further complexity into the use of ¹³⁷Cs to estimate erosion rates. Because of these limitations on the use of ¹³⁷Cs in certain areas of the world, there is a need to explore the use of alternative tracers.

Naturally derived ²¹⁰Pb (Pb-210, half-life 22.2 yr), another relatively long-lived fallout radionuclide, is adsorbed by soil particulate material and subsequently redistributed within the landscape in a manner similar to ¹³⁷Cs, but its potential as a tracer for studying soil redistribution has to date received only limited attention. Lead-210 is a natural product of the ²³⁸U decay series 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 ²¹⁰Pb in soils generated in situ by the decay of ²²⁶Ra is termed supported ²¹⁰Pb and is in equilibrium with ²²⁶Ra. On the other hand, upward diffusion of a small portion of the ²²²Rn produced in the soil and rock introduces ²¹⁰Pb into the atmosphere, and its subsequent fallout provides an input of this radionuclide to surface soils and sediments that will not be in equilibrium with its parent ²²⁶Ra (Robbins, 1978). Fallout ²¹⁰Pb is commonly termed unsupported or excess ²¹⁰Pb when incorporated into soils or sediments in order to distinguish it from the ²¹⁰Pb produced in situ by the decay of ²²⁶Ra. The amount of unsupported or atmospherically derived ²¹⁰Pb in a soil or sediment sample can be calculated by measuring both the ²¹⁰Pb and ²²⁶Ra activities and subtracting the ²²⁶Ra-supported ²¹⁰Pb component from the total ²¹⁰Pb in the sample. The required measurements of ²¹⁰Pb and ²²⁶Ra activity can be made by direct gamma spectrometry using low-energy, low-background HPGe detectors (Joshi, 1987).

The annual deposition of ¹³⁷Cs has been characterized by great temporal variation related to the timing of the large-scale atmospheric testing of nuclear weapons. Most ¹³⁷Cs fallout occurred during the period extending from the late 1950s to the early 1970s. Peak fallout rates in the Northern Hemisphere occurred in 1963 and fallout rates declined to very low values by 1972. In contrast, deposition of fallout ²¹⁰Pb from the atmosphere has been relatively constant through time because of its natural origin (Turekian et al., 1977; Nozaki et al., 1978; Nevissi, 1985; Graustein and Turekian, 1986; Crickmore et al., 1990). Deposition fluxes of fallout ²¹⁰Pb have been documented for many parts of the world, either through analysis of ²¹⁰Pb in rainfall or analysis of unsupported ²¹⁰Pb in stable, undisturbed soils. Values obtained exhibit significant global variation, with deposition rates reported by Turekian et al. (1977), Robbins (1978), and Appleby and Oldfield (1992) varying from 23 Bq m^-2 yr^-1 to 367 Bq m^-2 yr^-1. The limited information on deposition fluxes precludes detailed examination of the global patterns involved, but Robbins (1978) indicates that values are greater in mid-latitude regions, and Appleby and Oldfield (1992) indicate that values are reduced over the oceans and generally increase from west to east over the continents, due to the predominant west–east movement of air masses.

Like ¹³⁷Cs, ²¹⁰Pb has been shown to have a strong affinity for sediment particles (Van Hoof and Andren, 1989; He and Walling, 1996a). As a result, unsupported ²¹⁰Pb has been widely used to establish the chronology of lake, estuarine, and marine sediments deposited during the past 100 to 150 yr by assuming either a constant flux of unsupported ²¹⁰Pb to the depositing sediment or a constant concentration in the deposited sediment and by relating the downcore reduction in unsupported ²¹⁰Pb concentrations to its decay constant and the sediment deposition rate (e.g., Appleby and Oldfield, 1978; Krishnaswami and Lal, 1978; Robbins, 1978; Wise, 1980; Benninger and Krishnaswami, 1981; McCall et al., 1984; Wan et al., 1987; Crickmore et al., 1990). A similar approach has been used for dating river floodplain, saltmarsh sediments, and peat bogs (e.g., Walling and He, 1994; He and Walling, 1996b; Buscail et al., 1997; Jensen, 1997; Kim et al., 1997).

Despite the widespread use of fallout ²¹⁰Pb in sediment chronology studies, its potential as a tracer for studying water-induced soil and sediment redistribution within the landscape has been less widely recognized and exploited. Upon reaching the land surface as fallout from the atmosphere, unsupported ²¹⁰Pb will be rapidly adsorbed by the clay minerals and organic matter in the surface soil, and, as in the case of ¹³⁷Cs, its subsequent redistribution in the soil and across the land surface will be controlled by its interaction with land use practices, erosion, and sediment transport processes. Recent studies have investigated the behavior of fallout ²¹⁰Pb in catchment soils under different land use conditions (Dörr and Münnich, 1989, 1991; Walling et al., 1993, 1995; Wallbrink and Murray, 1996; He and Walling, 1997; Smith et al., 1997). Activities in surface soils were found to vary significantly according to land use, which affects both soil properties and the post-depositional redistribution of ²¹⁰Pb within the soil profile. This feature of the occurrence of unsupported ²¹⁰Pb has been used as a basis for fingerprinting fluvial suspended sediment sources by several researchers (e.g., Walling et al., 1993; He and Owens, 1995; Collins et al., 1997; Wallbrink et al., 1998), since, for example, concentrations in surface material from uncultivated pasture or rangeland will be much greater than those from cultivated soils because of the mechanical mixing of the latter by tillage. With its strong affinity for soil particles and its relatively easy direct measurement, which uses low-background, low-energy gamma spectrometry, ²¹⁰Pb also offers considerable potential for use as a tracer for estimating soil erosion rates. Several researchers have recently attempted to exploit this potential (Walling et al., 1995; Wallbrink and Murray, 1996; He and Walling, 1997; Wallbrink, 1997); however, in several of these investigations, fallout ²¹⁰Pb was used in conjunction with ¹³⁷Cs and further studies are needed to explore the potential for using this radionuclide as an independent means of quantifying soil redistribution rates, and thus, its potential for use in areas where the application of ¹³⁷Cs is restricted.

The study reported in this paper attempts to explore further the use of fallout ²¹⁰Pb for quantifying rates of soil redistribution by water erosion on cultivated soils. In order to compare the behavior of fallout ²¹⁰Pb in soils under different land use practices, soil cores were collected from both cultivated and undisturbed land within the Moorlake catchment near Crediton in Devon, UK. These cores were sectioned in order to document the down-core variation of unsupported ²¹⁰Pb concentrations in the soils. A mass balance model describing the redistribution of fallout ²¹⁰Pb in the soil profile and across the surface of cultivated land was developed. A detailed program of soil coring was undertaken within a cultivated field in the study catchment, and the fallout ²¹⁰Pb inventories of the resulting cores were determined. The mass balance model was employed to derive erosion or deposition rates from the total fallout ²¹⁰Pb inventories associated with the individual soil cores that were collected from the field. The rates and patterns of soil redistribution established for the study field were closely related to its topography and were consistent with existing understanding of soil redistribution processes.

	Materials and methods

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Field Sampling and Laboratory Analysis
An 8.54-ha cultivated field at Aller Barton Farm, located in the Moorlake catchment near Crediton in Devon, UK, was selected as the focus of this investigation. The field is underlain by Permian breccias and conglomerates on which brown earth soils of the Crediton series (Dystric Eutrochrept) have developed. The mean annual precipitation for the local area is 800 mm. Field observations had already provided clear evidence of significant soil erosion within this field. To document the spatial distribution of fallout ²¹⁰Pb inventories within the field, bulk soil cores were collected at the intersections of a 20 by 20 m grid, using a motorized percussion corer equipped with a 6.9-cm-diam. core tube. In addition to the grid-based sampling, supplementary soil cores were collected from areas characterized by marked topographic change in order to increase the representativeness of the sampling. In total, 167 bulk soil cores were collected from the study site. Checks, involving ²¹⁰Pb measurements on samples taken from the bottom of selected cores, were used to ensure that all cores had penetrated to the full depth of the unsupported ²¹⁰Pb profile. Additional information on the typical vertical distribution of fallout ²¹⁰Pb activity in the soil profile and the plow depth was obtained from sectioned soil cores collected from representative sites within the field. A detailed topographic survey of both the coring points and the entire field was made with an electronic theodolite and was undertaken in parallel with the coring program. To document the depth distribution of unsupported ²¹⁰Pb in undisturbed soils and to establish the local fallout ²¹⁰Pb inventory representing the direct atmospheric ²¹⁰Pb input to the local area, both sectioned soil cores and bulk cores were collected from stable, undisturbed sites in adjacent areas of the catchment for subsequent ²¹⁰Pb analysis. Samples of surface material were collected from the cultivated field to provide information on the grain-size composition of the original source soil. Suspended-sediment samples for particle-size analysis were also collected from the stream that drains the catchment during major storm events in order to provide information on the grain-size composition of mobilized sediment.

Measurements of the activities of unsupported ²¹⁰Pb and other relevant radionuclides in the soil and sediment samples were undertaken simultaneously by gamma-ray spectrometry, using a high resolution, low background, low energy, hyperpure n-type germanium coaxial -ray LOAX HPGe detector (EG&G Ortec, Oak Ridge, TN) coupled to an Ortec amplifier and multichannel analyzer. The samples were placed in plastic Marinelli beakers and sealed with PVC tape for 20 d prior to assay in order to achieve equilibrium between ²²⁶Ra and its daughter ²²²Rn. The efficiency of the detection system was calibrated using soil samples prepared from standard solutions that contain ²¹⁰Pb and ²²⁶Ra. In order to determine the detector efficiency for samples of varying geometry and to account for variable self-adsorption effects, these calibration samples contained different amounts of soil. The samples were placed on the detector and counted for >85000 s, providing a precision of approximately ±10% at the 90% level of confidence for the gamma spectrometry measurements. The total ²¹⁰Pb concentrations of the samples were measured using the 46.5 keV gamma ray for ²¹⁰Pb, and the ²²⁶Ra concentrations were measured using the 351.9 keV gamma ray for ²¹⁴Pb, a short-lived daughter of ²²⁶Ra. In order to account for ²²²Rn loss from the soil, the in situ ²²⁶Ra-supported ²¹⁰Pb concentration that is associated with individual soil cores has been derived from the measured ²²⁶Ra concentration using the relationship between the average ²²⁶Ra concentration and the total ²¹⁰Pb concentration, which was established using samples from the lower parts of the soil profile where atmospheric ²¹⁰Pb was assumed to be absent (Graustein and Turekian, 1986; Wallbrink and Murray, 1996). Unsupported ²¹⁰Pb concentrations for the samples were calculated by subtracting the ²²⁶Ra-supported ²¹⁰Pb concentrations from the total ²¹⁰Pb concentrations (Joshi, 1987). To establish the grain-size composition of both original soil and mobilized sediment, samples of surface soil and suspended sediment from the adjacent stream were analyzed for their particle-size distributions. The grain-size distributions of the chemically dispersed mineral fractions of the <63-µm sediment were measured using MasterSizer laser-diffraction equipment (Malvern Instruments, Malvern, UK). The >63-µm sediment was analyzed by sieving. The organic matter content of selected samples was determined by weight loss after ignition in a muffle furnace for 2 h at 600°C. Table 1 lists typical values for the properties of the soils and sediments studied.

View larger version (19K): [in this window] [in a new window]   Fig. 1 Representative unsupported 210Pb profiles associated with cores collected from undisturbed soils (A) and cultivated soils (B) in the study catchment

A Mass Balance Model for Estimating Soil Erosion and Deposition Rates on Cultivated Soils
Existing studies that have used ¹³⁷Cs measurements to investigate water-induced soil erosion on cultivated soils have employed a variety of approaches to establish calibration relationships for converting the total inventories of soil cores into estimates of soil redistribution rates that are associated with the sampling points. These include empirical relationships (e.g., regression equations) and theoretical models (e.g., the proportional model, the gravimetric model, and mass balance models) (cf. Walling and Quine, 1990; Walling and He, 1999). The basic assumptions of these approaches are closely linked to the known temporal distribution of nuclear weapon–derived ¹³⁷Cs fallout inputs (see above). However, when using unsupported ²¹⁰Pb measurements to estimate soil redistribution rates on cultivated soils, a mass balance approach must be employed, because the fallout input to the soil surface is essentially continuous. The application of this approach is described below.

For cultivated soils, both erosional and depositional areas may exist within an individual field. In a cultivated soil profile, the soil may be conveniently divided into two layers. Soil properties (including the radionuclide content) will normally be relatively uniform in the plow layer and will differ from those in the layer below the plow depth (Fig. 1b). In the case of a soil profile experiencing erosion, cultivation and erosion will represent the dominant processes controlling the redistribution of fallout ²¹⁰Pb in the soil profile, and the accumulated unsupported ²¹⁰Pb will be restricted to the plow layer. Changes in the activity of the accumulated unsupported ²¹⁰Pb within the plow layer will be associated with further deposition of the radionuclide from the atmosphere as well as loss that results from both soil erosion and radioactive decay, and the total unsupported ²¹⁰Pb inventory will be less than the local reference inventory, A_ref (Bq m^-2). In contrast, for a soil profile from a site experiencing deposition, unsupported ²¹⁰Pb will be found in the soil below the plow depth because of the progressive accumulation of sediment containing fallout ²¹⁰Pb eroded from upslope, and the total fallout ²¹⁰Pb inventory will be greater than the local reference inventory. The behavior and fate of unsupported ²¹⁰Pb in soils from eroding sites and sites experiencing deposition is considered in greater detail below.

Eroding Sites
For an eroding location, change in the activity of unsupported ²¹⁰Pb, A(t) (Bq m^-2) per unit area with time t (yr), can be expressed as

(1)

where

decay constant of ²¹⁰Pb (yr^-1);

I(t)

annual fallout ²¹⁰Pb deposition flux (Bq m^-2 yr^-1);

proportion of the freshly deposited ²¹⁰Pb fallout removed by erosion before being mixed into the plow layer;

P

particle-size correction factor, defined as the ratio of the ²¹⁰Pb concentration of the mobilized sediment to that 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] represents deposition of the atmospheric ²¹⁰Pb fallout, and the second term represents the loss associated with radioactive decay and water-induced soil erosion. The incorporation of the particle-size correction factor P into Eq. [1] is necessary because of the strong association of fallout ²¹⁰Pb with fine soil particles and the grain-size selectivity of the erosion processes. The value of P will reflect the grain-size composition of both mobilized sediment and the original soil. Because the grain-size composition of mobilized sediment is commonly enriched in fines relative to the original soil, P is generally greater than 1.0 (He and Walling, 1996a). To estimate the value of P, information on the grain-size composition of both mobilized sediment and the original soil is required. He and Walling (1996) have derived a relationship between P and the specific surface area of mobilized sediment, S_ms (m² g^-1), and that of the original soil, S_os (m² g^-1), of the form

(2)

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

The introduction of into Eq. [1] is necessary to account for the removal of freshly deposited ²¹⁰Pb fallout by surface erosion before its incorporation into the plow layer by cultivation. Because the deposition of fallout ²¹⁰Pb occurs primarily in association with precipitation, it will initially be distributed within a shallow layer near the soil surface (Nevissi, 1985; He and Walling, 1997). Results obtained from experiments demonstrate that unsupported ²¹⁰Pb concentrations contained in topsoil prior to cultivation decline rapidly with increasing cumulative mass depth. If erosion occurs, the sediment mobilized from the soil surface will contain higher concentrations of fallout ²¹⁰Pb than sediment originating from lower in the soil profile. He and Walling (1997) have shown that the initial distribution of fallout ²¹⁰Pb inputs associated with precipitation can be approximated as

(3)

where C_i(x,t) (Bq kg^-1) is the radionuclide concentration at cumulative mass depth x (kg m^-2) from the soil surface, t = 1 (yr); and H (kg m^-2) is the relaxation mass depth of the initial distribution of fallout ²¹⁰Pb in the soil profile, which can be determined experimentally for local conditions (He and Walling, 1997). The constant H represents the depth of penetration of fallout ²¹⁰Pb into the soil. High values of H will reflect 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) to estimate the proportion of the freshly deposited fallout ²¹⁰Pb ( ) that was removed from the site by erosion. If sheet erosion is assumed, can be expressed as

(4)

where is the proportion of the annual ²¹⁰Pb fallout that is susceptible to removal by erosion prior to incorporation into the soil profile by tillage. Equation [4] indicates that the relaxation mass depth H is an important factor influencing the removal of the recently deposited fallout from the site. For a constant erosion rate, the smaller the value of H, the greater the proportion of the recently deposited fallout that will be removed by erosion. The parameter will be dependent on the timing of cultivation and the local rainfall regime. For example, in situations when there is only one period with high intensity rainfall events that can generate surface runoff and, thus, erosion, and this occurs shortly before the single annual period of cultivation, all the unsupported ²¹⁰Pb already accumulated at the soil surface as well as the fallout ²¹⁰Pb input directly associated with this rainfall will be susceptible to removal by erosion, and the value of can be assumed to be 1.0. In cases where the period of high intensity rainfall occurs immediately after cultivation has been completed, the ²¹⁰Pb accumulated at the soil surface before this period of precipitation will have been incorporated into the plow layer, and only the fallout ²¹⁰Pb directly associated with this rainfall will be susceptible to removal by erosion while it remains near the surface. Under these circumstances, the value of may be approximated by the ratio of the depth of this rainfall to the total annual rainfall. If there is more than one cultivation operation and more than one period of high intensity rainfall that can produce surface runoff each year, then the estimation of will need to include consideration of the timing of precipitation inputs in relation to the cultivation operations.

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

(5)

where t₀ (yr) is the year when cultivation started, and is the fallout ²¹⁰Pb inventory at t₀. When deriving Eq. [5], it has been assumed that there was no erosion before t₀. Assuming that both the erosion rate R and the deposition flux I are constant through time, then . The fallout ²¹⁰Pb inventory for the soil profile A(t) (Bq m^-2) can be represented as

(6)

The fallout ²¹⁰Pb deposition flux I can be estimated from the unsupported ²¹⁰Pb inventories of stable, undisturbed soils, A_ref and the decay constant . The average annual erosion rate, R, can be estimated from Eq. [6] when deposition flux I, plow depth D, and relaxation mass depth H are known. In situations where cultivation has existed for >100 yr (i.e., t - t₀ > 100), a steady state can be assumed and Eq. [6] reduces to

(7)

If it is further assumed that Rt << H, then PRt/H, and the erosion rate R can be estimated from the following equation:

(8)

The concentration C'(x,t) (Bq kg^-1) of the accumulated unsupported ²¹⁰Pb at depth x in the plowed soil can be expressed as

(9)

Figure 2 depicts the relationships between soil erosion rate and percentage reduction in fallout ²¹⁰Pb inventory relative to the local reference inventory for a hypothetical eroding soil profile that is associated with periods of cultivation of different length (with t - t₀ taking the values of 20, 40, 60, and 100 yr respectively). The following values were employed for the relevant parameters: .

View larger version (20K): [in this window] [in a new window]   Fig. 2 Relationships between soil erosion rate and percentage reduction in the unsupported 210Pb inventory derived using the mass balance model for an hypothetical eroding soil profile subject to different periods of continuous cultivation to the present

(10)

where R' (kg m^-2 yr^-1) is the deposition rate, and C_d(t') (Bq kg^-1) is the unsupported ²¹⁰Pb concentration of deposited sediment at t' (yr). C_d(t') reflects the mixing of sediment and its associated unsupported ²¹⁰Pb that is mobilized from all the eroding areas that converge on the aggrading point. Generally, C_d(t') can be assumed to be represented by the weighted mean of the unsupported ²¹⁰Pb concentrations of the sediment mobilized from the upslope contributing area, S (m²). C_d(t') can, therefore, be calculated using the following equation:

(11)

where C_e(t') (Bq kg^-1) is the unsupported ²¹⁰Pb concentration of mobilized sediment, and P' is a further particle-size correction factor that reflects differences in grain-size composition between mobilized sediment and deposited sediment and is defined as the ratio of the unsupported ²¹⁰Pb concentration of deposited sediment to that of the mobilized sediment. As in the case of P, a relationship between P' and the specific surface area of deposited sediment, S_ds (m² g^-1), and of mobilized sediment, S_ms (m² g^-1), may be assumed to take the form of

(12)

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

The unsupported ²¹⁰Pb in the plow layer at a site experiencing erosion will comprise two components, one associated with freshly deposited ²¹⁰Pb fallout,C_i(x,t), which has an exponential distribution near the soil surface, and the other associated with the accumulated fallout ²¹⁰Pb in the soil profile, C'(x,t), which is uniformly distributed within the plow layer. The unsupported ²¹⁰Pb concentration of mobilized sediment will be closely related to that of the surface soil and can be expressed as

(13)

The first term on the right-hand side of Eq. [13] represents the erosion of a proportion of the annually deposited ²¹⁰Pb fallout from the eroding soil profile prior to its incorporation by tillage, and the second term represents removal of the accumulated fallout ²¹⁰Pb that is stored in the plow layer. Using Eq. [10], [11], and [13], mean annual soil deposition rate R' (kg m^-2 yr^-1) can be calculated as

(14)

	Application of the mass balance model

TOP ABSTRACT INTRODUCTION Materials and methods Application of the mass... Conclusions REFERENCES

 
The Fallout Lead-210 Reference Inventory for the Study Area
Analysis of unsupported ²¹⁰Pb activities in the soil cores collected from stable, undisturbed sites within the study catchment indicated an average fallout ²¹⁰Pb inventory of 5170 Bq m^-2, and this value has been taken to represent the reference inventory for the study catchment. Assuming constant deposition fluxes, the annual atmospheric ²¹⁰Pb deposition rates in this area are estimated to be 161 Bq m^-2 yr^-1. This value lies within the range of annual deposition fluxes of fallout ²¹⁰Pb in Britain of 88 to 270 Bq m^-2 yr^-1, as reported by Crickmore et al. (1990).

The Grain-Size Composition of Surface Soil and Suspended Sediment
Because of the practical difficulties associated with in situ collection of sediment mobilized by soil erosion, its particle-size composition has been assumed to be similar to that of the suspended sediment that was transported by the stream draining the study catchment. This, however, only represents an approximation, since the grain-size composition of mobilized sediment may change during transport to and by the stream as a result of within-field and upstream channel deposition, and since some of the sediment mobilized by soil erosion may be transported as bed load. On the other hand, field observations suggest that bed load transport accounted for only a very small proportion of the total sediment transport by the stream draining the study catchment. Figure 3 compares the grain-size composition of the <63-µm fractions of representative samples of suspended sediment with surface soil from the study field, and data indicate that, even for the <63-µm fractions, the suspended sediment is enriched in fines relative to the original soil. More than 95% of the suspended sediment is composed of particles of <63 µm, while 43% of the surface soil from the cultivated field is composed of particles that are >63 µm. It has been assumed for simplicity that there is no significant spatial variation in the grain-size composition of the surface soil of both erosional and depositional areas within the field. The grain-size composition of the surface soil has, therefore, been assumed to be the average of that of the surface soil samples for which particle-size distributions are depicted in Fig. 3. Using the mean grain-size distribution measured for suspended sediment, values of 1.52 and 0.66 have been estimated for the particle-size correction factors P and P', respectively.

View larger version (20K): [in this window] [in a new window]   Fig. 3 A comparison of the grain-size distributions of the <63-µm fractions of suspended sediment and cultivated surface soil from the study catchment

View larger version (68K): [in this window] [in a new window]   Fig. 4 The topography of the study field at Aller Barton Farm (height data are relative to an arbitrary datum)

View larger version (63K): [in this window] [in a new window]   Fig. 5 The spatial distributions of unsupported 210Pb inventories (A) and soil redistribution rates estimated using the fallout 210Pb measurements (B) within the study field at Aller Barton Farm

	Conclusions

TOP ABSTRACT INTRODUCTION Materials and methods Application of the mass... Conclusions REFERENCES

 
The strong affinity of fallout ²¹⁰Pb for clay and organic matter within the soil makes it an effective sediment tracer for studying water-induced soil redistribution. In undisturbed soils, concentrations of unsupported ²¹⁰Pb decrease approximately exponentially with increasing depth from the soil surface, penetrating to depths of 18 cm. This reflects the continuous input of fallout ²¹⁰Pb to the soil surface from the atmosphere, post-depositional downward movement associated with physical, physicochemical and biotic processes, as well as radioactive decay within the soil profile. In contrast, the distribution of fallout ²¹⁰Pb in cultivated soils is relatively uniform within the plow layer for an eroding or stable site because of the mixing caused by tillage. At an eroding point within a cultivated field, the total unsupported ²¹⁰Pb inventory will be less than the local reference inventory measured for stable, undisturbed soils due to the loss of fallout ²¹⁰Pb associated with soil loss, while at a depositional point it will be higher, because of the deposition of sediment containing unsupported ²¹⁰Pb derived from the upslope contributing areas. The mass balance model proposed here for estimating rates of soil redistribution on cultivated soils from fallout ²¹⁰Pb measurements takes account of the grain-size selectivity associated with sediment generation, transport, and deposition. This model also includes consideration of the key processes involved in the removal of unsupported ²¹⁰Pb from an eroding point and its subsequent deposition at deposition sites. The spatial distributions of both the unsupported ²¹⁰Pb inventories and the estimated soil redistribution rates within the study field at Aller Barton Farm presented in Fig. 5 are closely related to the topography of the field, which exerts an important influence on the processes involved in sediment mobilization, transport, and deposition.

The results obtained from this case study confirm the potential for using fallout ²¹⁰Pb in soil erosion investigations. There is an increasing need for spatially distributed information on rates of water-induced erosion and sediment deposition within the landscape, and ¹³⁷Cs measurements have provided one means of meeting this requirement. Fallout ²¹⁰Pb measurements may offer an alternative to ¹³⁷Cs measurements in areas where their application is limited by low inventories or compromised by the occurrence of significant Chernobyl-derived ¹³⁷Cs fallout. Furthermore, in situations where both ¹³⁷Cs and unsupported ²¹⁰Pb measurements can be employed, there is potential to use both fallout radionuclides in combination, since the measurements of both radionuclides can be undertaken simultaneously. Because the two radionuclides estimate erosion rates for different time periods, they may also provide a basis for deriving additional information on the erosional history of a study site by comparing the inventories of fallout ¹³⁷Cs and ²¹⁰Pb.

	ACKNOWLEDGMENTS

 
The 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 International Atomic Energy Agency Coordinated Research Programme D1.50.05, "Assessment of soil erosion through the use of Cs-137 and related techniques as a basis for soil conservation, sustainable agricultural production, and environmental protection," through Technical Contract 9562/R1. The assistance of P. Whelan with sample collection and of J. Grapes with gamma-ray spectrometry and the cooperation of landowners in permitting access to their land for collection of soil cores and suspended sediment samples are gratefully acknowledged.

Received for publication September 2, 1998.

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