Measuring Soil Erosion Rates Using Natural (⁷Be, ²¹⁰Pb) and Anthropogenic (¹³⁷Cs, ^239,240Pu) Radionuclides

Abstract

This chapter examines the application of natural (⁷Be and ²¹⁰Pb) and anthropogenic fallout radionuclides (¹³⁴Cs, ¹³⁷Cs, ^239,240Pu) to determine soil erosion rates. Particular attention is given to ¹³⁷Cs because it has been most widely used in geomorphic studies of wind and water erosion. The chapter is organized to cover the formation and sources of these radionuclides; how they are distributed in precipitation and around the globe: their fate and transport in undisturbed and tilled soils; and their time scales of utility. Also discussed are methods for soil collection, sample preparation for ¹³⁷Cs analysis by gamma spectroscopy, and the selection of standards and instrument calibration. Details are presented on methods for calculating soil erosion, including empirical methods that are related to the Universal Soil Loss Equation (USLE), box models that compare ¹³⁷Cs activities in a study site to a reference site, and time dependent methods that account for the temporal inputs of ¹³⁷Cs and precipitation induced erosion. Several examples of recent applications, including the combination of radionuclides with other techniques or measurements, are presented. The chapter concludes with suggestions for future work: the value of new methods and instrumentation to allow for greater spatial resolution of rates and/or greater accuracy; the need to incorporate migration of radionuclides in the time-dependent models; the opportunities to concurrently use the global and Chernobyl signals to better understand temporal variation soil erosion processes and rates; and the importance of the use of these tracers to characterize C storage and cycling.

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1 Introduction

1.1 Soil Erosion; Nature of the Problem

Soil is among our most fundamental resources and soil processes help regulate atmospheric composition and climate. Soil anchors and sustains the vegetation that provides sustenance for animals and humans and provides fibers and material used in everything from cotton for clothing to lumber for homes to biomass for energy. The soil itself can be mined for key materials, minerals and metals, and energy. The foundations of most human structures – homes, buildings, and roads – are built on soil. Soil and soil processes filter water, reduce toxicity of airborne pollutants delivered to the land surface, and store carbon and nutrients. The value of soil in terms of ecosystem function and service has been estimated in the hundreds of billions of dollars per year (Pimental et al. 1995).

A comprehensive understanding of material fluxes on the earth surface and its effects on geochemical cycles (hydrologic, C, and N), atmospheric composition and climate, and ocean chemistry depends upon an understanding of soil and soil movement on the landscape including erosion, transport, and deposition. Soils sequester C and N from the atmosphere and retain certain metals during the weathering of rocks, but soil erosion either moves those materials to places of long-term storage or exposes soils to greater reactivity. Soils hold 2,300 Gt of carbon, about four times as much carbon as is in the atmosphere (Lal 2003). It has been suggested that if carbon on the landscape lost by erosion is replaced by new vegetative growth, then intermediate storage in fluvial systems of the eroded carbon represents a net removal of carbon from the atmosphere and may be the “missing” anthropogenic carbon (Harden et al. 1992; Stallard 1998). Others note that oxidation of a portion of the carbon in transport may produce 0.8–1.2 GtC per year. Thus anthropogenically enhanced soil erosion may reinforce global warming.

Soil is moved by a variety of processes including water (splash, sheetwash, rills), wind, ice (freeze-thaw, glaciers, periglacial), gravity (dry ravel, creep, toppling, debris flows, earthflows), tillage, and bioturbation. Erosion is often accelerated by disturbance (clearing, fire, plowing, overgrazing, compaction, or desiccation) that disrupts soil structure and removes vegetative covering. Oldeman (1994) estimated that 1,094 Mha (1 ha = 10⁴ m²) are affected by water erosion and 549 Mha by wind erosion. These numbers represent 12 and 6% of agricultural land areas, respectively. Total erosion of these areas is approximately 75 billion tons/year (Pimental et al. 1995).

The net loss of soil has both on-site and off-site consequences as summarized by Pimental et al. (1995). In croplands, the diminished fertility due to topsoil erosion requires fertilization or results in diminished yields, creates pressure to deforest new areas as fertility of existing cropland decreases, and results in the loss in water holding capacity of soils. Fertilization, in turn, often has its own consequences. Most fertilizers rely on fossil fuels to create, ship, and apply the material and the applied fertilizer has the potential for creating downstream water quality concerns. The additional water use required because of diminished soil retention taxes another critical resource. In forestlands, soil loss can change species composition, diminish water-holding capacity, and speed desertification. In suburban and urban areas, soil loss can reduce the ability of soils to sustain vegetative cover and trees helpful in addressing air, water, heat, and sound pollution.

Fine sediments derived from erosion of soil are disproportionately responsible for degradation of surface waters (Nelson and Logan 1983; Dong et al. 1984). Eroded soil impairs water quality (Sekely et al. 2002; Sharpley et al. 1994; Pote et al. 1996) to the point that drinking water supplies, aquatic environments, and opportunities for recreation are threatened. Eroded soil often harms aquatic environments by inhibiting light penetration (Yamada and Nakamura 2002), by siltation of rivers (Reiser 1998) and reservoirs (Williams and Wolman 1984), by eutrophication of waterways, lakes, and seas (Rabalais et al. 1999), and by contamination (Tarras-Wahlberg and Lane 2003). In 2000, the US Environmental Protection Agency reported that siltation debilitated 12% of the stream reaches assessed by states and tribes and was responsible for 33% of impairments to beneficial use (USEPA 2000). In areas where wind is an important process of erosion, the transported fine material can be a health problem, foul equipment, and cause abrasion requiring the repainting of structures (Lyles 1985).

History shows that civilization can collapse as the soil resource is depleted (Montgomery 2007; Diamond 2005; Hyams 1952). Plato ascribed the poor soils of his native Attica to erosion after land clearing and his view of the causative factors of poor soil was shared by Aristotle (Montgomery 2007). Loss of production associated with soil loss and degradation ultimately affected the stability of the Greek civilization as it did the Romans later. Lowdermilk (1953) describes a trail of societies from Judea to Syria to China where poor stewardship of the land and resulting erosion led indirectly to conquest or societal discord. More recent examples of societal dislocations (famine and migration) associated with soil erosion and land degradation include the Dustbowl of the 1930s, the Sahel of the 1970s, and Haiti.

1.2 Tools for Measuring Soil Erosion

Critical to the understanding and quantification of soil erosion are tools for its measurement. Erosion pins, sediment accumulated in reservoirs, measured sediment concentration in streamflow, photographic techniques, and soil tracers each have their usefulness and limitations. Sediment budgets (Dietrich and Dunne 1978) are often a basis for quantifying the various processes and paths that move soil on the landscape and result in local loss (erosion) and local gain (deposition) of soil.

A particularly useful tool for measuring soil erosion is a conservative tracer of the soil particles, especially when the tracer is relatively easy to measure. Important considerations in the use of a tracer are that the concentration of the tracer is relatively uniform; adsorption of the tracer to soil is strong and quick; variation in adsorption to various sizes or mineralogic/organic constituents is minor or can be accounted for; and methods exist to measure the tracer.

The best known of the tracers for estimating soil erosion are natural and anthropogenic radionuclides. The anthropogenic radionuclides found on the landscape were produced largely by atmospheric nuclear bomb testing and the fallout was distributed globally. The list of fission products is extensive, although many of these radionuclides are too short-lived to be useful tracers of soil erosion. Of the longer-lived fission products, the best known is ¹³⁷Cs, but the list of other useful tracers includes ¹³⁴Cs, ^238,239,240Pu, and ²⁴¹Am as minute solid particles or sorbed to soil particles; and ³H and ⁹⁰Sr as soluble tracers. The naturally-occurring radionuclides are produced by various nuclear reactions, or uranium or thorium decay chains (Porcelli and Baskaran 2011) and include ⁷Be, ²¹⁰Pb and a few others. ¹³⁷Cs, ⁷Be, and ²¹⁰Pb are each suitable as particle tracers because they have a global distribution, adsorb efficiently to soil particles and thus move with soil, and are relatively easily measured.

¹³⁷Cs is the most widely used radionuclide tracer for soil erosion (Ritchie and McHenry 1990). For years, Ritchie and Ritchie (2008) maintained a bibliography of publications that utilized ¹³⁷Cs in the study of soils and sedimentation. Figure 25.1, redrafted from Ritchie and Ritchie (2008) and updated here to include papers published after December 15, 2008, illustrates how widespread the use of ¹³⁷Cs as a tracer has been. There are a total of about 4,500 Cs references with the vast majority of the papers following the Chernobyl accident in 1986. In comparison, there are about 2,700 references to the use of ²¹⁰Pb in studies of soils and sedimentation. The use of ²¹⁰Pb in such studies now exceeds the use of ¹³⁷Cs. The use of ⁷Be as a tracer in the context of soils and sediment is relatively new and has resulted in about 90 papers to date. It should be noted that substantially less than half of the total number of papers have used the respective tracer to quantify soil erosion.

Fig. 25.1

The annual number of papers utilizing ¹³⁷Cs, ²¹⁰Pb, and ⁷Be in chronologic, geomorphic and sedimentologic studies. The total number of ¹³⁷Cs papers is now about 4,500. Modified and updated from Ritchie and Ritchie (2008)

1.3 Summary of Contents of Book Chapter and the Approach Used

This chapter focuses primarily upon the use of anthropogenic and naturally-occurring radionuclides to study soil erosion processes and to quantify rates of soil erosion. Many other processes affect soil and sediment transport and deposition and other radionuclides used in those studies are detailed in other chapters of this collection. Here we devote much of our attention to the anthropogenic radionuclide ¹³⁷Cs but we also look at other radionuclide tracers in part to show which radionuclides may be the most suitable for given applications. Specifically, we describe the source of the radionuclides; their characteristics, deposition, sorption, and transport; the methods of measurement; the assumptions associated with their use as tracers; the models used to estimate erosion with the tracers; the relative merits of different models and tracers for investigating soil erosion; recent applications of radionuclides in erosion studies; and foreseeable changes in the use of tracers and the tracers used.

2 Background

2.1 Radionuclides in the Environment

2.1.1 Sources of ¹³⁷Cs, ⁷Be, ²¹⁰Pb, and ^239,240 Pu

Radionuclides that have been used in studies of soil erosion on decadal time scales or less include ¹³⁴Cs, ⁷Be, ²¹⁰Pb, and ^239,240Pu but the most widely known of these is ¹³⁷Cs (t_1/2 = 30.1 years). ¹³⁴Cs (t_1/2 = 2.06 years), ¹³⁷Cs, ²³⁹Pu (t_1/2 = 4,110 years) and ²⁴⁰Pu (t_1/2 = 6,537 years) are present on the global landscape largely as a result of anthropogenic fallout from thermonuclear weapons testing primarily during the period 1954–1968 (Fig. 25.2). In parts of Europe, ¹³⁷Cs fallout from the nuclear reactor accident at Chernobyl in 1986 is superimposed on the global signal of fallout and the Pu isotopic signatures from stratospheric fallout and from Chernobyl are different from each other (Ketterer et al. 2011; Hong et al. 2011). Other accidental releases of Cs isotopes have created local zones of contamination. ²¹⁰Pb (t_1/2 = 22.3 years) is delivered to the landscape as a result of the decay of gaseous ²²²Rn in the ²³⁸U decay chain. In that chain, ²²⁶Ra in soils and rock decays to ²²²Rn (t_1/2 = 3.8 days) which is released to the atmosphere and undergoes a series of short-lived decays to ²¹⁰Pb which, as a particulate, is delivered to the landscape by wet and dry fallout. This ²¹⁰Pb is termed excess ²¹⁰Pb (²¹⁰Pb_xs) (Fig. 25.2). However, some ²²²Rn that occurs in the soil is trapped in mineral matter or unable to escape to the atmosphere during its 3.8 day half-life, and its decay builds the supported pool of ²¹⁰Pb in the soil (supported ²¹⁰Pb). ⁷Be (t_1/2 = 53.3 days) is produced by cosmic ray spallation of nitrogen (90%) and oxygen (10%) in the troposphere and stratosphere (Kaste et al. 2002; Kaste and Baskaran 2011) and then it is removed from the atmosphere and is delivered to the landscape often during large thunderstorms (Dibb 1989).

Fig. 25.2

Schematic illustration of fallout radionuclide sources used in erosion studies of decadal or shorter time scales. Left figure is a photograph of an atmospheric bomb test, the main source of global radioactive Cs and Pu fallout. Photo from: http://www.nv.doe.gov/news&pubs/photos&films/atm.htm. The middle figure illustrates excess ²¹⁰Pb fallout. The figure on the right illustrates the production of ⁷Be by cosmic ray spallation of oxygen and nitrogen in the stratosphere

¹³⁷Cs atmospheric fallout is at present very small and the negligible amount, if any, is due to eolian resuspension of near-surface soil particles with adsorbed ¹³⁷Cs. ²¹⁰Pb concentration is highest in air originating over continental regions (Turekian et al. 1983; Paatero and Hatakka 2000) and the activity of ²¹⁰Pb in the atmosphere decreases with altitude (Kownacka 2002) consistent with the sources of the radionuclide in soil and rock at the earth surface. ⁷Be is produced through spallation interactions of atmospheric O and N nuclei and the nucleonic component of the atmospheric cascade induced by galactic cosmic rays (Dorman 2004) (Fig. 25.2). Sugihara et al. (2000) suggest that 70% is produced in the stratosphere. ⁷Be is also added to the troposphere from the stratosphere by mixing along the polar front and the subtropical jet and by mixing in large synoptic storms (mid-latitude cyclones and hurricanes). ⁷Be concentration increases with altitude given the substantial reservoir in the stratosphere where concentrations may be an order of magnitude higher than in the upper troposphere (Lal and Peters 1967; Dutkiewicz and Husain 1985; Lal and Baskaran 2011). There appears to be some seasonality of the concentrations of ²¹⁰Pb and ⁷Be in the atmosphere with the highest values in late spring and summer (Turekian et al. 1983; Baskaran et al. 1993; Caillet et al. 2001). Valles et al. (2009) show a 2–3-fold variation in monthly concentrations of ⁷Be and ²¹⁰Pb. Greater emissions of ²²²Rn from snow-free areas and dry soils are thought to increase atmospheric concentrations of ²¹⁰Pb during summer (Olsen et al. 1985; Caillet et al. 2001). The seasonal peak in ⁷Be concentration in late spring and summer (e.g. El-Hussein et al. 2001) is thought to be caused by enhanced mixing of stratospheric air into the troposphere. Longer term fluctuation in ⁷Be fallout has been tied to variations in the flux of cosmic galactic primary radiation caused by the 11-year sunspot cycle (Azahra et al. 2003; Kikuchi et al. 2009).

¹³⁷Cs (+), ⁷Be (2+), and ²¹⁰Pb (2+, 4+) are strongly chemically active, so they rapidly become associated with aerosols and particles (0.7–2 μm; Ioannidou and Papastefanou 2006) and are delivered from the atmosphere to the earth surface predominantly in precipitation (Olsen et al. 1985). Snow is more efficient than rain at removing radionuclides from air (McNeary and Baskaran 2003; Ioannidou and Papastefanou 2006) and wet precipitation is more efficient than dry precipitation. Residence times in the troposphere are estimated to be 22–48 days (Durana et al. 1996) for ⁷Be and just a few days for the aerosols carrying the ²¹⁰Pb (Tokieda et al. 1996). ¹³⁷Cs also has a short residence time partly because the source of the radionuclide is now resuspension of soil particles that are coarser (Papastenfanou et al. 1995; Ioannidou and Papastefanou 2006). During the weapons testing era, ¹³⁷Cs residence time in the atmosphere was longer (~1–10 years) than it is today because of its injection into the stratosphere (Joshi 1987).

Although the first nuclear detonation was in 1945, ¹³⁷Cs was first detected in fallout in 1951 and over most of the globe it was below detection prior to about 1954, peaked in about 1963, and was effectively below detection by 1983 (Cambray et al. 1985) (Fig. 25.3). The data in Fig. 25.3, for the most part, are not based on actual ¹³⁷Cs fallout data because ¹³⁷Cs was not routinely monitored during the 1950–1983 time frame. Instead, ⁹⁰Sr fallout was usually monitored and ¹³⁷Cs fallout is inferred by assuming a ¹³⁷Cs/⁹⁰Sr ratio in the bomb fallout (Health and Safety Laboratory 1977; Robbins 1985). This ratio has been estimated to range from 1.4 to 1.65 and is characteristic of production rates of the isotopes and is independent of location. The ^239+240Pu depositional fluxes are less well known because certain data (i.e., the ratios of plutonium to ¹³⁷Cs, ⁹⁰Sr) are still classified by the U.S. Government. More recently, for example during the monitoring of Chernobyl fallout, deposition of ¹³¹I was monitored and the deposition of all other radionuclides was calculated from the ¹³¹I deposition density values using the relationships calculated by Hicks (1982). The overall geographic patterns of ⁹⁰Sr and ^239+240Pu differ slightly from those for ¹³⁷Cs and ¹³¹I primarily due to the differences in the nuclear fuel used in different tests, the size of the particles associated with the radionuclides, and the directions of travel of the clouds of radioactive particles from each test. The overall deposition of ⁹⁰Sr was very similar to that of ¹³⁷Cs. For most of the regions in the United States, the activity of ¹³⁷Cs was 10–20 times the activity of ^239+240Pu deposited (Beck 1999; CDC 2006).

Fig. 25.3

¹³⁷Cs fallout (Bq m⁻² month⁻¹) calculated as 1.45 times the average ⁹⁰Sr monthly fallout at the US DOE monitoring sites (Birmingham, AL; Los Angeles, CA; San Francisco, CA; Denver, CO; Coral Gables/Miami, FL; Argonne, IL; International Falls, MN; Columbia, MO; Helena, MT; New York, NY; Williston, ND; Wooster, OH; Tulsa, OK; Medford, OR; Columbia, SC; Vermillion, SD; and Green Bay, WI). Data from the Health and Safety Laboratory (1977). Also shown is the calculated ¹³⁷Cs inventory (Bq m⁻²) assuming that all the fallout to the soil surface remains in the soil and is subject only to radioactive decay. Chernobyl fallout is not included in this calculation

Because of the temporal variability with a peak ¹³⁷Cs fallout activity in 1963, that peak is often used as a time horizon in sediments to indicate the time of deposition of that layer of sediment. Linear sedimentation rates (cm year⁻¹) are then simply calculated as the depth of the layer (cm) divided by the time in years since 1963. The mass flux deposition rates (g cm⁻² year⁻¹) are calculated as the cumulative dry mass of sediment above the 1963 time horizon divided by the cross sectional area of the sediment core divided by the time in years since 1963 until the date of coring (Walling and He 1997a, b; Goodbred and Kuehl 1998).

Inspection of Fig. 25.3 shows that the ¹³⁷Cs depositional flux was highly variable, reflecting the times of atmospheric testing. There are peaks in fallout observed each year between 1954 and 1959, and much larger peaks in 1962, 1963 and 1964. The maximum global fallout of radioactive nuclides occurred in Spring 1964, but because most field data cannot resolve the 1962 to 1964 fallout peaks, the position of the maximum in ¹³⁷Cs is often assigned a date of 1963 (1964 in the southern hemisphere). In the late 1960s to mid-1970s, fallout decreased considerably, but the seasonal cycle reflecting precipitation can be seen through the 1970s.

As a result of the nuclear accident at Chernobyl in 1986, additional ¹³⁷Cs fallout occurred in some areas of Europe. It is estimated that the Chernobyl accident released from 10 to 16% as much ¹³⁷Cs to the environment as was emitted from all nuclear weapons tests (Flavin 1987). Little Chernobyl fallout occurred over North America (Roy et al. 1988). Note the much higher levels of ¹³⁷Cs deposition from Chernobyl than from stratospheric fallout (compare Figs. 25.3–25.5). For example, the lowest contours on the Europe map following Chernobyl are ~2 kBq m⁻² (light yellow in Fig. 25.4) De Cort et al. (1998) whereas in Fig. 25.3 the largest fallout values in the US following bomb testing are ~3,000 Bq m⁻² (3 kBq m⁻²). Monthly deposition values are 20–30 times less than the lowest fluxes deposited from Chernobyl. The highest Chernobyl fluxes are ~1,480 kBq m⁻², a value 10,000× larger than the peak monthly fallout from atmospheric weapons testing (~140 Bq m⁻² month⁻¹) and a value at least 100× larger than the inventory in US soils (8–13 kBq m⁻², Fig. 25.5). Delivery of ¹³⁷Cs from the atmosphere is again currently near zero (Quine 1995). The much higher deposition of Chernobyl-derived ¹³⁷Cs over northern Europe is significant, because in these locations it has swamped the prior global fallout signature and has had the effect of “resetting” the ¹³⁷Cs soil erosion clock to 1986 because downcore soil inventories and soil activities near the soil surface are now dominated by Chernobyl-derived ¹³⁷Cs. This is not the case over most of the rest of the world, as the ¹³⁷Cs fallout from Chernobyl was minimal (Department of National Health and Welfare 1986). Consequently, the current distribution of ¹³⁷Cs in soils in northern Europe is dominated by Chernobyl fallout and in the US by stratospheric fallout. This resulted because Chernobyl was characterized by the relatively intermittent release of a full range of radionuclides at relatively low temperatures with very heavy local fallout from tropospheric transport. Weapons testing fallout was at a high temperature with more uniform stratospheric transport, longer residence times, and with much less pronounced local fallout (Joshi 1987). Pu atom ratios can be used to distinguish between Chernobyl and stratospheric fallout. The ²⁴⁰Pu/²³⁹Pu atom ratio was about 0.38 in Chernobyl fallout and 0.18 in stratospheric fallout (Ketterer et al. 2011). Further, the distribution of Pu from Chernobyl was much more localized than was ¹³⁷Cs. Pu isotopes were specifically associated with non-volatile fuel particles (Mietelski and Was 1995) whereas ¹³⁷Cs volatilized in the reactor accident and was more widely dispersed over much of northern Europe and Russia. ⁷Be and ²¹⁰Pb deposition on the other hand continues as natural processes continue to produce these radionuclides.

Fig. 25.4

¹³⁷Cs fallout deposition over Europe following the Chernobyl accident. Modified from EC/IGCE, Roshydromet (Russia)/Minchernobyl (Ukraine)/Belhydromet (Belarus) (1998)

Fig. 25.5

¹³⁷Cs depositional flux in the continental United States from global fallout (CDC 2006)

2.1.2 ¹³⁷Cs, ⁷Be and ²¹⁰Pb in Precipitation

Deposition of radionuclides occurs both by dry and wet fall. The vast majority of ⁷Be falls in association with rainfall. Workers have reported dry fall as making up 3–10% of total fallout (Wallbrink and Murray 1994; McNeary and Baskaran 2003; Salisbury and Cartwright 2005; Ioannidou and Papastefanou 2006; Sepulveda et al. 2008). Dry deposition of ²¹⁰Pb appears to be more variable than ⁷Be because of the importance of resuspended soil and dust in contributing to the flux (Todd et al. 1989). The monthly atmospheric depositional flux (wet plus dry) of both ⁷Be and ²¹⁰Pb varies by about a factor of 5 over the course of a year (Matisoff et al. 2005) but exhibits a maximum in the spring (Turekian et al. 1983; Olsen et al. 1985; Dibb 1989; Todd et al. 1989; Robbins and Eadie 1991; Koch et al. 1996; Baskaran et al. 1997) and represents the variability in the quantity of precipitation (Turekian et al. 1983; Koch et al. 1996; Baskaran et al. 1997) and, to a lesser extent, the seasonality in stratospheric ⁷Be production and troposphere-stratosphere exchange (Turekian et al. 1983; Todd et al. 1989; Koch et al. 1996). ⁷Be and ²¹⁰Pb deposition during precipitation events is well correlated to precipitation amount (Caillet et al. 2001; Ciffroy et al. 2003; Su et al. 2003) reflecting the fact that wet fall is a dominant delivery mechanism. Caillet et al. (2001) found that ⁷Be deposition was slightly better correlated with precipitation than ²¹⁰Pb deposition (r² = 0.66 for ⁷Be vs. 0.55 for ²¹⁰Pb). The better correlation with ⁷Be is due to the fact that more of the ²¹⁰Pb comes from dry deposition and ⁷Be is often derived from the stratosphere during large thunderstorms. Quine (1995) reported that ¹³⁷Cs delivery from global fallout was also highest in spring and early summer. Callender and Robbins (1993) observed an annual cycle of ¹³⁷Cs deposition in the high sedimentation environment of Oahe Reservoir (South Dakota, USA).

Given the correlation between fallout and precipitation amounts during events, it is not surprising that the annual fallout of ¹³⁷Cs, ⁷Be and ²¹⁰Pb is correlated to annual precipitation. In most places, the precipitation-normalized annual depositional fluxes have remained constant (Baskaran 1995). Ritchie and McHenry (1978) noted that the variation in ¹³⁷Cs inventory in the northcentral US was best explained by mean annual precipitation. Rowan (1995) found that variation in mean annual precipitation (900–2,000 mm) explained 75% of the variation in ¹³⁷Cs inventory in the Exe basin in the United Kingdom. Lance et al. (1986) found a linear relationship between the inventory of ¹³⁷Cs in soils and average annual precipitation in the southern USA. Baskaran et al. (1993) observed that ²¹⁰Pb fluxes increased with precipitation and Gallagher et al. (2001) found that ²¹⁰Pb inventory was significantly higher on the wetter west coast of Ireland than on the east coast. Our survey of annual delivery of ⁷Be reported by workers (Turekian et al. 1983; Dibb 1989; Papastefanou and Ionannidou 1991; Baskaran et al. 1993; Caillet et al. 2001; Ayub et al. 2009) as compared to annual precipitation shows a strong correlation: r ² = 0.72 (Fig. 25.6).

Fig. 25.6

Linear relationship between ⁷Be depositional flux and annual precipitation

The fallout of ¹³⁷Cs over the globe as indicated by soil inventories is higher in the mid-latitudes than equatorial areas, and higher in the Northern Hemisphere than in the Southern Hemisphere (Stokes and Walling 2003; Walling et al. 2003). Collins et al. (2001) found inventories that were almost an order of magnitude higher in mid-latitudes of the Northern Hemisphere. Figure 25.7 illustrates the general pattern of inventories by latitude across the globe and Fig. 25.8 illustrates the reconstructed global fallout of ¹³⁷Cs as of 1970 indicating both the localized fallout from the test sites and the global fallout. McHenry et al. (1973), summarizing several studies, noted that fallout in the USA increased to the north and to the east (Fig. 25.5). Sarmiento and Gwinn (1986) developed a semi-empirical model for the deposition of ⁹⁰Sr (and hence ¹³⁷Cs) that is based on latitude, time since 1954, and the monthly precipitation. The distribution of bomb-derived ¹³⁷Cs fallout over the globe is relatively smooth in contrast to the Chernobyl fallout (compare Figs. 25.4 and 25.5) because the global fallout signal is due to a series of nuclear explosions that reached into the stratosphere allowing ¹³⁷Cs to be well mixed in the atmosphere. In contrast, the plume of radioactive debris from Chernobyl did not extend higher than a few km into the atmosphere and thus prevailing winds, and then rainout, determined the pattern of fallout. ^239,240Pu was also vaporized during bomb testing and its global distribution is similar to that of ¹³⁷Cs. However, this did not occur during Chernobyl, so the Pu was delivered as fine particulates and therefore its distribution was not widespread (Mietelski et al. 1996; Ketterer et al. 2004; Brudecki et al. 2009). Global fallout flux of ²¹⁰Pb is summarized in Baskaran (2011). The inventories of ²¹⁰Pb are lower in the Southern Hemisphere than the Northern Hemisphere because of the smaller percentage of land area. The radon flux from the oceans is negligible compared to the continents (Turekian et al. 1977) thus with less continental area in the Southern Hemisphere there will be a lower atmospheric concentration and less deposition of ²¹⁰Pb. ⁷Be inventories should be similar in both hemispheres because of its stratospheric source.

Fig. 25.7

Variation in bomb-derived ⁹⁰Sr (a surrogate for ¹³⁷Cs) by latitude band (from Stokes and Walling 2003)

Fig. 25.8

Global distribution of bomb-derived ¹³⁷Cs fallout illustrating high fallout near testing sites and a strong latitudinal distribution (from Aoyama et al. 2006)

2.1.3 ¹³⁷Cs,⁷Be and ²¹⁰Pb in Soils

Once the radionuclides ¹³⁷Cs, ⁷Be and ²¹⁰Pb reach the earth surface, they rapidly sorb to the mineral grains and organic materials of soil particles (Tamura and Jacobs 1960). Cs fixation to soil material depends strongly on soil composition and mineralogy. There is a complicated pattern of preferred sorption of radionuclides to finer particle sizes and to organic materials (He and Walling 1996; Wallbrink and Murray 1996; Motha et al. 2002) and clays (Hawley et al. 1986; Wang and Cornett 1993; Balistrieri and Murray 1984). ¹³⁷Cs is a 1+ cation and its sorption exceeds that of all other alkali ions (Schultz et al. 1959). Lomenick and Tamura (1965) suggested that the adsorption is almost non-exchangable. Riise et al. (1990) estimated that less than 10% of Cs was leachable. ⁷Be reaches the earth surface as a Be²⁺ cation with high charge density which makes it prone to adsorption. ²¹⁰Pb likewise reaches the surface as a 2+ or 4+ cation and is rapidly adsorbed. Partition coefficients, K_d, for these radionuclides are ~10⁵ (Olsen et al. 1986; You et al. 1989; Hawley et al. 1986; Steinmann et al. 1999) indicating that these radionuclides are sufficiently particle-bound that they are suitable for tracing erosion, transport, and deposition of soil.

There are, however environments in which ¹³⁷Cs might fail as a conservative particle tracer. Some previous studies of radiocaesium in soils have failed because K_d values have been derived under conditions very different from those in situ. The partitioning of Cs in organic-rich soils is reversible and the partition coefficients can be low. Where the soils are peaty or podzolic, the mobility of cesium is considerably greater than in other soils (Sanchez et al. 1999). In acidic soils in coniferous forests in N. Europe Dorr and Munnich (1989) found that Cs migrated faster than ²¹⁰Pb and suggested that chemical exchange was occurring between the organic and hydrous phases. It is generally believed that radiocaesium retention in soils and sediments is due to the presence of a small number of highly selective sites. Cremers et al. (1988) found that strong Cs adsorption by the solid phase was regulated by the availability of frayed edge sites on illite and is inhibited by the presence of competing poorly hydrated alkali cations (K⁺ or NH ⁺₄ ). Where geochemical migration of Cs is significant, workers should turn to alternatives such as Pu isotopes.

In soil, cesium has a low mobility; the majority of cesium ions are retained in the upper 20 cm of the soil surface and usually they do not migrate below a depth of 40 cm (Korobova et al. 1998; Matisoff et al. 2002a). For example, vertical migration patterns of ¹³⁷Cs in four agricultural soils from southern Chile indicated that approximately 90% of the applied cesium was retained in the top 40 cm of soil and as much as 100% was found in the upper 10 cm (Schuller et al. 1997).

¹³⁷Cs uptake by plants also affects its downcore migration. Clay and zeolite minerals strongly bind cesium cations in interlayer positions of the clay particles and therefore reduce the bioavailability of ¹³⁷Cs and its uptake by plants (Paasikallio 1999). Plant uptake of ¹³⁴Cs in a peat soil was decreased by a factor of 8 when zeolites were added (Shenber and Johanson 1992).

The kinetics of sorption are less understood, but Baskaran and Santschi (1993) reported that approximately 80% of ⁷Be became associated with particulates within an hour of a rainfall event. In a study where ¹³⁴Cs was applied in solution to the surface of soils, it was adsorbed in the upper 2.5 cm of the soil (Owens et al. 1996). These results largely mimic the findings of Rogowski and Tamura (1970) who applied ¹³⁷Cs to the soil surface and also found penetration of only a few cm. This modest penetration during infiltration suggests a timeframe for adsorption of up to 10 min if typical rates of infiltration for these silty sand soils are used.

Some proportion of the radionuclide fallout is retained on vegetation. Doering et al. (2006) observed that 18% of ⁷Be was retained on vegetation whereas only about 1% of ²¹⁰Pb_xs was retained on vegetation. These differences almost surely reflect the much shorter halflife of ⁷Be than any differences in affinity for organic material. Very little ¹³⁷Cs is typically on vegetation today because of the negligible fallout. Plants may also take up radionuclides from soil. Coughtrey and Thorne (1983) supposed that plant uptake could result in a 0.2% loss in ¹³⁷Cs per year. Numerous studies have shown that radioactive contaminants move through the food chain and can exceed health standards (Davis 1986; Revelle and Revelle 1988). For example, mushrooms have been reported to uptake as much as 50% of the ¹³⁷Cs inventory in the soil and moose, caribou, sheep and milk consumption have all had radioactive residues that restrict their consumption (Korky and Kowalski 1989).

2.1.4 Radionuclide Profiles in Undisturbed Soils

The simplest profile of the set of radionuclides most commonly used in soil erosion studies may be that of ⁷Be (Fig. 25.9; see also Kaste and Baskaran 2011). From a peak concentration at the surface, it decreases exponentially down core to non-detectable values below 2–3 cm (Bonniwell et al. 1999; Wilson et al. 2003; Doering et al. 2006). In the case of ⁷Be, some fraction is associated with the vegetation growing on the surface (Doering et al. 2006 reported 18%) or associated with organic litter. The half-life of ⁷Be is just 53.3 days thus there is a relatively brief period to mix/move the radionuclide downward before the radionuclide decays (Walling et al. 2009). Only very rarely has ⁷Be been measured deeper than a couple of cm in the soil. Kaste et al. (1999a, b) noted a second down-profile peak in activity that they hypothesized might be caused by subsurface pipeflow quickly taking the ⁷Be cation to depth before sorption.

Fig. 25.9

The distribution of radionuclides ⁷Be, ¹³⁷Cs, and ²¹⁰Pb_xs in this upland soil from near Corwin Springs, Montana, USA is characteristic of undisturbed soils. ⁷Be activity is highest at the surface and little is found below 3 cm. ¹³⁷Cs displays a subsurface peak in activity, in this case between 2 and 3 cm of depth, and no radionuclide activity below 10 cm. ²¹⁰Pb_xs displays a surface peak in activity. ²¹⁰Pb_xs activity is negligible below 10 cm (from Whiting et al. 2005)

The next simplest profile may be that of ²¹⁰Pb (Figs. 25.9 and 25.10). As with ⁷Be, ²¹⁰Pb_xs is delivered by wet and dry fallout to the surface and mixed downward in the soil profile. In the case of ²¹⁰Pb however, there is both the atmospherically derived ²¹⁰Pb_xs and the steady background ²¹⁰Pb activity (called supported ²¹⁰Pb) maintained by continuous in situ decay of ²²⁶Ra in soil and rock (Goldberg and Koide 1962). The surface maximum in activity decreases exponentially downcore to the value of the supported ²¹⁰Pb. Most ²¹⁰Pb_xs is found in the upper 10 cm of soil (Bonniwell et al. 1999; Doering et al. 2006). The greater penetration of ²¹⁰Pb_xs than ⁷Be is due to its greater half-life of 22.3 years. With more time to operate, downward migration extends further.

Fig. 25.10

Comparison of ¹³⁷Cs and ²¹⁰Pb activities in profiles from undisturbed and tilled soils. Soils collected in Ohio, USA. After Matisoff et al. (2002a, b)

The ¹³⁷Cs profile is typically more complicated (Figs. 25.9 and 25.10). Over much of the globe, the undisturbed ¹³⁷Cs profile features a subsurface maximum and then an exponential decrease below that. Very little ¹³⁷Cs is found below 20 cm (Owens and Walling 1996) in most locales. Unlike the other two radionuclides, the delivery of ¹³⁷Cs was not steady (Fig. 25.3). It was first detected in fallout in 1951, peaked in about 1963, and was negligible by the early 1980s. In the absence of constant replenishment to the surface, the peak in concentration has migrated below the surface by several cm. In areas receiving significant Chernobyl fallout after the nuclear plant accident in 1986, the distribution of ¹³⁷Cs from stratospheric fallout is swamped by the Chernobyl fallout so that global fallout can no longer be identified. This interpretation is supported by Pu isotope data which show “hot” Chernobyl-derived Pu particles at depth while stratospheric Pu is found both above and below the Chernobyl Pu and the ¹³⁷Cs profile mimics the Pu profile (Matisoff et al. 2011). Additional support can be seen in Fig. 25.11, where the Pu profile is from global fallout (as determined from Pu isotopes, not shown here), but the ¹³⁷Cs is derived primarily (as determined by its relatively high activity) from Chernobyl fallout. (Note the much higher activity of ¹³⁷Cs in Fig. 25.11 compared to that in Figs. 25.9 or 25.10 indicating a Chernobyl source to the soil collected in Sweden in Fig. 25.11 and a global fallout source to the soils collected in the USA shown in Figs. 25.9 and 25.10.)

Fig. 25.11

¹³⁷Cs and ^239+240Pu data from a core collected in 2008 in Skogsvallen, Sweden and a non-local bioturbation model fit to the data. Note that the Pu is derived from global fallout (as determined from Pu isotopes, not shown here), but the ¹³⁷Cs is derived primarily from Chernobyl fallout (as determined by its relatively high activity)

2.1.5 Downcore Migration of Radionuclides in Soils

The radionuclides delivered to the soil surface are moved downward by soil processes including bioturbation, leaching, diffusion, and translocation. Movement can be enhanced by disturbance such as plowing. The depth of penetration of each radionuclide into the soil is determined by the rate of this downward movement and the half-life of each radionuclide. DeJong et al. (1986) argue for low leachability of ¹³⁷Cs but some workers have found substantial mobility, particularly in peaty soils. Kaste et al. (1999a, b) report that as pH increases, ⁷Be can be desorbed.

Since the Chernobyl accident there have been a number of studies on the migration of ¹³⁷Cs and other radionuclides into the soil. Several authors have reported that ¹³⁷Cs penetration decreases exponentially downcore (Miller et al. 1990; Walling and Woodward 1992; Wallbrink and Murray 1996; Doering et al. 2006). Several studies have described the downcore transport of ¹³⁷Cs in terms of a diffusion-advection equation for a sorbed radionuclide (Konshin 1992; Bossew and Kirchner 2004; Shimmack et al. 1997; Rosen et al. 1999). These studies have concluded that the model fails to describe the rapid downward migration of the radionuclides shortly after fallout so that a non-linearity or irreversible sorption process leads to a decrease in the migration rate over time. This may help explain why the ^239,240Pu and ¹³⁷Cs profiles match in Fig. 25.11 even though the ^239,240Pu was delivered from stratospheric fallout whereas the ¹³⁷Cs was delivered from Chernobyl fallout.

Recently it has been suggested that ¹³⁷Cs transport is facilitated by colloidal transport (Flury et al. 2004; Chen et al. 2005), but colloidal transport in a natural, unsaturated media is small (Honeyman and Ranville 2002; Lenhart and Saiers 2002). Février and Martin-Garin (2005) conducted laboratory experiments that demonstrated retention of anionic radionuclides by microbial activity. Bundt et al. (2000) noted enrichment of radionuclides of Pb, Pu, and Cs at depth in preferential flow paths.

The transport of radionuclides in soils also can be facilitated by burrowing organisms such as earthworms, ants, termites and pocket gophers. Some of these bioturbating organisms are present in soils in numbers that can approach tens of millions per square meter and they actively mix the soil to depths ranging from a few centimeters to a few meters (Johnson et al. 1990; Müller-Lemans and van Dorp 1996; Gabet 2000; Gabet et al. 2003). Darwin (1881) first reported the role of earthworms in facilitating the downward migration of objects by ingesting soil and/or plant matter at depth and depositing it onto the surface as casts. This mixing style incorporates both random (diffusive) and directed (advective) processes and has been termed “conveyor-belt” feeding (Rhoads and Stanley 1964; Rhoads 1974; Powell 1977) or “non-local” mixing (Boudreau 1986a, b; Robbins 1986). Earthworms have been suggested to be the most important factor controlling the vertical transport of radionuclides in central European soils, with the potential to turn over the top layer of soil within 5–20 years (Müller-Lemans and van Dorp 1996). It is possible to model mixing by bioturbation in soils as a diffusive process and burial as an advection velocity. Kaste et al. (2007) used this approach and reported bio-diffusion mixing coefficients of 1–2 cm² year⁻¹ in a grassland in California (USA) and from a forested landscape in Australia, and inferred that the more actively bioturbated soils exhibit higher erosion rates. This approach treats the downward migration as a burial velocity and while it may simulate well the downcore profiles, it does not account for the directed recycling of tracer from depth (non-local mixing) as demonstrated by Robbins et al. (1979) using aquatic oligochaetes. Alternatively it is possible to model mixing by bioturbation as a diffusive process and the downward migration as a burial caused by non-local feeding in which the organisms place soil from depth onto the soil surface (Jarvis et al. 2010). Figure 25.11 is an application of the non-local bioturbation model to Chernobyl fallout at a site in Sweden and yields a bioturbation coefficient of 0.1 cm² year⁻¹ and a feeding rate of 0.002–0.003 year⁻¹ over the top 20 cm. In other words, this bioturbation model can account for the burial of the radionuclides by recycling 0.2–0.3% of the top 20 cm of the soil column each year.

2.1.6 Effects of Tillage on Soil Profiles

The radionuclide profiles in tilled soils exhibit considerable differences from the profiles in undisturbed soils (Matisoff et al. 2002b). Undisturbed soils show either a surface maximum (⁷Be, ²¹⁰Pb) or a near surface peak (¹³⁷Cs) followed at depth by a decrease to a constant activity (²¹⁰Pb) or to near zero (⁷Be, ¹³⁷Cs) (Fig. 25.9). Plowing of agricultural soils will mix soils to depths of 10–30 cm creating a relatively uniform concentration over the plow depth (Wise 1980 in Martz and deJong 1985; Owens et al. 1996). The distribution of radionuclides in the tilled soils is largely homogeneous because plowing mixes surface soils, which are enriched in radionuclides, with deeper soils, which are depleted in both ²¹⁰Pb and ¹³⁷Cs (Fig. 25.10).

Figure 25.12 illustrates a generalized model of the distribution of ⁷Be, ¹³⁷Cs and ²¹⁰Pb in a soil profile. All three isotopes are deposited on the surface through wet and dry fallout. Each radionuclide is distributed differently in the soil because of differences in half-lives, delivery rates, delivery histories, and land use. An undisturbed soil will exhibit higher radionuclide activities near the soil surface, which reflects their surficial input and slow downward transport. The shorter half-life of ⁷Be compared to ²¹⁰Pb results in less downward migration of ⁷Be. Hence ⁷Be is found only at the soil surface but some ²¹⁰Pb will migrate down core. In addition, some ²¹⁰Pb is produced in the soil by in situ decay of ²²²Rn resulting in some ²¹⁰Pb activity at all depths in the soil. Because ¹³⁷Cs had its peak delivery in the early 1960s and almost no delivery before 1951 or since 1975 (or had its peak delivery in 1986 in areas affected by Chernobyl fallout) its activities have a distinct peak at some depth (~10 cm) in the soil. Plowing homogenizes ²¹⁰Pb and ¹³⁷Cs within the plowed layer, but because of its short half-life and constant input, ⁷Be activities are highest at the surface and are homogeneous only immediately after plowing. Because ¹³⁷Cs fallout occurred at a distinct instance of time, its distribution will remain homogeneous within the soil profile, even after the cessation of plowing. On the other hand, ²¹⁰Pb, like ⁷Be, is continuously deposited on the land surface. Its distribution will remain homogeneous if the soil is plowed annually, but it will accumulate at the surface and slowly rebuild a profile with decreasing activity with depth if tillage ceases.

Fig. 25.12

Schematic illustration of soil profiles of ⁷Be, ¹³⁷Cs, and ²¹⁰Pb in undisturbed soils (no-till) and in soils that have been mixed by plowing (traditional tillage)

Because ⁷Be, ¹³⁷Cs, and ²¹⁰Pb have different distributions in the soil profile, erosion of the soil to different depths will yield an assemblage of radionuclides in the eroded material that is characteristic of only one depth. Shallow erosion produces proportionally larger amounts of ⁷Be and ²¹⁰Pb because these radionuclides are concentrated near the surface. Deeper incision yields progressively less additional ⁷Be and no additional ⁷Be below about 1 cm. The proportional contribution of ¹³⁷Cs increases to the depth of its maximum. Erosion below that depth yields incrementally more ²¹⁰Pb and ¹³⁷Cs but at progressively decreasing rates. Below some depth in the soil (~15–30 cm), deeper erosion yields little if any additional ¹³⁷Cs. ²¹⁰Pb yield continues to grow in correspondence to the constant supported ²¹⁰Pb activity.

Sediment eroded from a soil will have a radionuclide signature corresponding to the tillage practice and the depth of erosion. Thus radionuclide signatures in suspended sediments can provide a means of tracing particles eroded from the landscape and can identify soil sources and be used to quantify the erosion (Whiting et al. 2001). The distinct distributions of radionuclides permit in principle the use of multiple mass balances to quantitatively estimate the areal extent of rill and sheet erosion and the characteristic depth of erosion associated with each mechanism (Wallbrink et al. 1999; Whiting et al. 1999, 2001). In essence, it is possible to infer the “recipe” for erosion – for example, 1 part sheet erosion to 10 parts rill erosion – on the basis of the total yield of radionuclides and sediment.

2.2 Concept of Inventory

The inventory, or standing stock, of a radionuclide represents the total amount of a radionuclide per unit area and is determined by atmospheric delivery, radioactive decay, gain, and loss. Gain typically reflects deposition and loss typically reflects erosion or leaching. In the case of ¹³⁷Cs, local inventories at stable locations (neither eroding or depositing) are steadily dropping because contemporary fallout to replenish the stock is essentially zero (Fig. 25.3). In 2010, ¹³⁷Cs inventories are less than half of what they were in 1974, except in areas affected by Chernobyl fallout. ²¹⁰Pb inventories at stable sites are more or less steady because annual contributions (fallout) to the stock and variation in the delivery from year-to-year are both small compared to the total inventory. For instance, fallout of ²¹⁰Pb in a typical year represents no more than 3% of the stock of ²¹⁰Pb_xs. ⁷Be inventories at stable sites tend to vary over the year due to the variation in delivery with the seasons and the short half-life of 53 days. Individual storms can deliver >50% of the ⁷Be inventory particularly when the precipitation event arrives after a period of drought lasting weeks to months.

To use these tracers to quantify erosion or deposition, the amount of the radionuclides in a vertical column of soil (the measured inventory) is compared to the expected amount in the soil profile based upon fallout (the expected inventory). The fundamental idea is that the inventory (stock) of radionuclides will be changed only by additions of radionuclides as wet- and dry-fallout or by sediment deposition or by losses by decay and soil erosion. If the measured inventory is less than the expected inventory, then erosion has occurred and the soil loss is proportional to the ratio of the inventories. If the inventory is greater than the expected inventory, deposition has occurred.

2.2.1 The Spatial Variability of Inventory

Erosion and deposition are the primary causes of variation in radionuclide inventory. But other factors also influence the inventory and these include: (1) random spatial variability, (2) systematic spatial variability, (3) sampling variability, and (4) precision in measurement (Owens and Walling 1996). Random spatial variability can be tied to local soil properties, microtopography (i.e. Lance et al. 1986), and localized vegetation distributions. Systematic variation is caused by gradients in precipitation, slope, aspect, windfields, and soil types. Sampling variability is tied to the area of collection with large areas of collection featuring lower variability (Loughran et al. 1988). Owens and Walling (1996) and Foster et al. (1994) estimate variation associated with sampling area is approximately 5%. Finally, measurement precision is an important source of variability and is typically about 10%. Owens and Walling (1996) concluded that local variation in ¹³⁷Cs inventory was relatively large thus single measurements were unlikely to be appropriate measures of activity. Their summary of their own work and the work of others showed a range in coefficient of variation in Cs inventories of 5–47% with an average value of 29%. For ⁷Be, Wilson et al. (2003) found a coefficient of variation of 33% in inventories. It might be expected that with the shorter halflife that local variation might add substantially to variability, but that does not appear to be the case.

The change in the inventory of a radionuclide tracer is the basis for estimating soil erosion. In using a radionuclide to quantify erosion, one assumes that the erosion that removes soil also removes the radionuclide tracer. Ideally there is equivalence between the mass loss relative to the potentially erodible material and the radionuclide loss relative to the potentially lost material (inventory). However, radionuclides can still be used to quantify erosion in the absence of equivalence if the tracer loss:soil loss relationship can be quantified. For instance, preferential erosion of certain sized particles enriched in radionuclides might appear to invalidate the assumption of equivalence, but the ability to describe this enrichment will permit determination of erosion.

2.3 Time Scales of Utility

Fundamental to the use of tracers to measure rates of soil erosion is the time span over which the loss is calculated. In other words, to determine the rate of erosion using radionuclides, the denominator – time in this case – must be established. Using ¹³⁷Cs as an example, delivery to the earth surface began around about 1954, peaked in about 1963, and was effectively below detection by 1983 (except in parts of Europe). If we ignore for the moment various other issues, we might reasonably calculate the amount of erosion by measuring the amount of Cs in the soil lost relative to the amount we would expect based upon fallout (accounting for decay). To determine a rate, we do not know anything about the timing of erosion in this interval since deposition so we will assume that the erosion occurred over the period since 1954 when deposition began. In such a scenario, the erosion rate is determined for a period of 56 years (assuming 2010 as the measurement date).

What sets the shortest and longest scales for the use of a radionuclide to estimate erosion? If erosion rate is being determined retrospectively, these are the considerations for the timescale of utility. In the case of a retrospective analysis, the scientist is typically measuring one time the inventory of the radionuclide at a site where erosion occurred and comparing this inventory to the inventory at a reference site without erosion or to the inventory expected given the estimated fallout. The changes in inventory are converted to soil loss and the rate is determined by the time since deposition.

If repeated measurements of inventory are made and made sufficiently far apart in time, the erosion of soil over shorter time periods can be examined. What is “sufficiently far apart in time?” To estimate erosion a difference in inventory must be measurable. It is typical that analytical errors in activity are at least 10%. In the case of ¹³⁷Cs, a 10% uncertainty in measured activity when compared to the decay rate, corresponds to a resolution in time no finer than 5 years (~10% of the mean life of the ¹³⁷Cs). Longer time scales, at least a decade (Walling and Quine 1990), are typically needed to produce measurable changes in ¹³⁷Cs inventories. In the case of Pb, this finest resolution is about 3 years (~10% of the mean life of ²¹⁰Pb). For ⁷Be, the variable flux means that under certain circumstances, the finest resolution is a matter of days or at the scale of individual precipitation events. One factor influencing the timeframe over which changes in inventory can be recognized is the distribution of the tracer in the soil. If the bulk of the tracer is at the surface, significant amounts of the tracer can be removed with a given amount of erosion. Less of the tracer will be removed by the same amount of erosion if the same inventory is distributed more deeply in the soil. In summary, the amount of erosion; the half-life; the history of deposition, erosion, and mixing of the surface fallout into the soil profile; and the precision in measurement are the keys to the timescale of utility for the various radionuclides. Section 25.4, which summarizes the major classes of models for estimating erosion rates using ¹³⁷Cs and their assumptions, will treat this subject further.

3 Collection and Measurement of Samples

3.1 Soil Collection

In order to determine soil radioactivity inventories it is necessary to collect intact soil cores and measure vertical profiles of the radioactivity. Since the radioactivity of ¹³⁷Cs has often migrated downcore to depths of 20 cm or more, push cores, for example the types used by golf courses to examine turf quality, are too short. Accordingly, hammer-driven cores and soil pits are used to obtain deeper cores. If high resolution profiling of the cores is desired, for example to obtain a ⁷Be profile, then the diameter of the tube needs to be large enough to collect sufficient sample to measure the radionuclide activities in a reasonable counting time. Typical push or hammer cores obtain a 1-in. diameter tube, and by using extension rods the tubes can be collected to a depth of 60-cm or more. However, this type of coring method causes significant (often ~20–30%) compaction of the soil, so that the true depths are poorly known even if they are compaction corrected. Compaction can be minimized by using a larger diameter tube, but it is more difficult to obtain deeper cores with a larger diameter tube. High-resolution soil profiles are easier to obtain from soil pits (Wilson et al. 2003) but the digging and sampling of soil pits is tedious and slower. Alternatively, thin layers of soil may be scraped from the surface of a large area to obtain high resolution vertical profiles (Walling et al. 1999a, b) – a method that is also quite tedious to construct. Regardless of the sampling technique used, it is necessary to know the surface area sampled since radionuclide inventories are expressed as activity per unit area.

After collection, the soil samples need to be dried, ground with a mortar and pestle to a fine texture, placed in standardized geometries, and analyzed by gamma spectroscopy for their radionuclide activities.

3.2 ¹³⁷Cs Measurement

The measurement of ¹³⁷Cs is accomplished by gamma spectroscopy. ¹³⁷Cs undergoes β⁻ (negatron) decay and emits gamma energies at 31.82 keV (relative intensity = 1.96%), 32.19 keV (relative intensity = 3.61%), 36.40 keV (relative intensity = 1.31%), and 661.66 keV (relative intensity = 85.21%). The two lowest energy photopeaks usually cannot be baseline resolved, so they are not used. The photopeak at 36.40 keV has been used, but it is not an ideal choice for measurement because the weak gamma in that energy range undergoes significant sample self absorption for which a large correction is necessary (Cutshall et al. 1983), its relative intensity is fairly small, and, depending on what other isotopes are being analyzed in the same spectrum, that portion of the spectrum may not have good photopeak separation. The photopeak at 661.66 keV is usually used because the relative intensity is much larger, the spectrum background and the efficiency are relatively constant in that part of the spectrum, and there are no other peaks that overlap or interfere. However, the detector efficiency for solid-state detectors is low at that energy requiring large sample sizes or long counting times to acquire a suitable peak for quantitation.

There are several different types of detectors capable of measuring ¹³⁷Cs. While Si detectors are commonly used for X-ray analyses, their efficiencies are too low at the higher energies needed for ¹³⁷Cs detection. The most common detectors that can measure the 661.66 keV photopeak of ¹³⁷Cs include NaI and Germanium (HPGe) semiconductors, although it is possible to use other detectors, such as Cd-Te, Cd-Zn-Te, and Hg-I. These other detectors have an advantage of reasonably good photopeak resolution and peak to Compton ratio while not require liquid nitrogen cooling. Their disadvantage is that for most applications they are too small and have a very low efficiency at 661.66 keV and therefore require counting times that are too long for practical applications. However, larger crystals are being developed and they may eventually replace NaI and HPGe detectors. NaI detectors have the advantages of being relatively inexpensive, have the highest efficiency of all the detectors discussed here, and requiring no liquid nitrogen for cooling. However, the photopeak energy resolution for NaI detectors is very poor and in most samples the ¹³⁷Cs photopeak is not visually detectable. Quantitation of a non-visual photopeak requires complex peak separation software, and since the peaks are not visually obvious, the use of NaI detectors to measure ¹³⁷Cs in soils and sediments seems a “bit like magic” or at the very least results in a lack of confidence in the results. High purity germanium detectors (HPGe) provide the easiest, and most accurate quantitation of the 661.66 keV photopeak of ¹³⁷Cs. These detectors provide excellent energy resolution and peak to Compton ratios over most of the applicable gamma-ray spectrum, so that ²¹⁰Pb, ⁷Be, ¹³⁴Cs, ¹³⁷Cs and ⁴⁰K and other gamma-emitting isotopes may all be determined at the same time from a single spectrum. However, they are more expensive than the other types of semiconductors discussed here and they require liquid nitrogen cooling. Other analytical techniques, such as alpha and beta spectroscopy for the determination of ²¹⁰Pb and ICP-MS for the determination ^239,240Pu are discussed in more detail in other chapters (Ketterer et al. 2011).

3.3 Calibration and Standards

Calibration of a detector for ¹³⁷Cs analyses consists of both an energy calibration and an efficiency calibration. The purpose of the energy calibration is to assign the correct photopeak to its appropriate energy. This is accomplished by counting a series of known radionuclides (energies) to determine their channel positions on the energy spectrum. The efficiency calibration is required to relate measured counts to the absolute values of the sample activities and it depends on kind and size of the detector, instrument settings, sample geometry (i.e., the size and shape of the container), sample volume, and shielding (background activities). Consequently, it is necessary to calibrate the energy and efficiency of each machine for every amplifier setting and sample geometry that will be used. Typical efficiencies for the low energy ²¹⁰Pb photopeak (46.52 keV) are ~0.5% and the efficiencies are about a factor of 3–5 less at the higher energies of ⁷Be (477.59 keV) and ¹³⁷Cs (661.66 keV). Because of these low efficiencies and the low activities in most samples (some Chernobyl samples are an exception) counting times of about 1 day are needed to obtain enough counts to reduce the counting error to <10%. Typical self-absorption correction factors (Cutshall et al. 1983) at the low energy of ²¹⁰Pb can range from 10 to 80% depending on the size and shape of the sample while the self-absorption correction factor at the higher energy of ¹³⁷Cs is negligible.

Determining the efficiency requires the use of a standard for which the activity is known. Unfortunately there are no commercially available standards of soils or sediments that are suitable for the efficiency determination of the entire suite of radionuclides commonly measured (²¹⁰Pb, ⁷Be, ¹³⁷Cs, ⁴⁰K) although there are a couple of samples that can be used as Quality Assurance samples or as a laboratory standard for efficiency calibration for ¹³⁷Cs, such as NIST 4350B Columbia River Sediment and International Atomic Energy Agency Reference Material IAEA-375. A list of primary standards available for the calibration of instruments and chemical procedures is given in Baskaran et al. (2009). In particular, RGU-1 (IAEA – 400 μg g⁻¹ with ²³⁸U concentration with all its daughter products in secular equilibrium) is a suitable standard for the calibration of ²¹⁰Pb. Alternatively, it is possible to prepare a standard by spiking a “clean” soil or sediment with the appropriate radionuclides of known activities (for example, Amersham plc QCY44 or NG4 Mixed Radionuclide Solutions) and then placing those prepared soils in the appropriate container for the efficiency calibration of that geometry.

4 Methods for Calculating Soil Erosion

Soil erosion can be calculated by the change in the inventory of radionuclides. While the same basic approaches can be used with any of the radionuclides, we detail the use of ¹³⁷Cs in erosion studies because it was for ¹³⁷Cs that the methods were originally developed.

Estimation of the erosion rate using ¹³⁷Cs inventories is typically addressed as an inverse problem with known ¹³⁷Cs inventories, cultivation and precipitation histories. The simplest method to estimate erosion rates is by a comparison of the ¹³⁷Cs inventory in soil cores with a reference value from a nearby non-eroded site. The non-eroded site represents the expected baseline fallout to the local geographic area, so that an eroded site would be expected to have less inventory compared to the non-eroded site. Various models have been applied to ¹³⁷Cs inventories where the erosion rate is assumed to be correlated to the percent of the ¹³⁷Cs inventory lost from a site (Ritchie et al. 1974; Spomer et al. 1985; Brown et al. 1981; Kachanoski and deJong 1984; DeJong et al. 1986; Lowrance et al. 1988; Soileau et al. 1990; Montgomery et al. 1997; Walling et al. 1999a, b; Fornes et al. 2005). These methods have been recently reviewed (Walling et al. 2002; Poreba 2006) in more detail than we present below and an analysis of these methods led Zapata et al. (2002) to conclude that there are uncertainties associated with the model selection used to estimate erosion rates, that most of the models do not address short-term changes in erosion rates such as those related to changes in land use and management practices, and that the methodology needs further standardization of the protocols for its general application worldwide.

4.1 Empirical, Non-Linear Model

Studies conducted in the 1960s and early 1970s in which ¹³⁷Cs inventory loss was compared with soil loss estimated using the Universal Soil Loss Equation (Wischmeier and Smith 1978) showed a strong, non-linear empirical relationship at several sites following the equation

$$ {\hbox{E}} = 0.00{87}{{\hbox{P}}^{{{1}.{18}}}} $$

(25.1)

where E is erosion rate (g cm⁻² year⁻¹) and P is the percent ¹³⁷Cs inventory lost from the study site (Ritchie et al. 1974). Percent radionuclide inventory lost is defined as

$$ {\hbox{P}} = ({{\hbox{I}}_{\rm{ref}}}-{{\hbox{I}}_{\rm{site}}})/{{\hbox{I}}_{\rm{ref}}}^*{1}00 $$

(25.2)

where I_ref is the ¹³⁷Cs inventory from an undisturbed reference site (Bq m⁻²) and I_site is the ¹³⁷Cs inventory for the study site. This led to the development of a number of models to calculate erosion rate on the basis of percent inventory lost. In essence, the model assumes a uniform distribution of ¹³⁷Cs throughout the soil profile so that erosion removes a proportional fraction of the inventory. This approach can result in significant error in the estimation of erosion rate in areas where land use, conservation practices, precipitation or other environmental conditions are not constant throughout the sampling period. For example, if atmospheric ¹³⁷Cs fallout were confined to the upper layer of soil prior to being eroded or distributed within the cultivation layer, a singular erosion event occurring just after the atmospheric fallout peak in 1964 (following the peak in stratospheric fallout) or in 1986 (following Chernobyl fallout in Europe) would remove a disproportionate amount of ¹³⁷Cs inventory and result in an overestimate of the soil erosion rate throughout the sampling period. Conversely, a major erosion event today will remove only a small fraction of the inventory because of the downward migration of ¹³⁷Cs in the intervening time period and may result in an underestimate of the erosion rate. The use of a reference site does not solve this problem.

4.2 Linear Box Model Methods

There are two major classes of models that linearly correlate the percent ¹³⁷Cs inventory lost with erosion rate. One approach assumes that the total ¹³⁷Cs inventory is eligible for erosion (Linear 1-Box model; Brown et al. 1981; Spomer et al. 1985) and those in which only the ¹³⁷Cs inventory within a surface or tillage layer is eligible for erosion (Linear-2Box model; DeJong et al. 1986; Lowrance et al. 1988; Soileau et al. 1990; Montgomery et al. 1997). The key difference between the Linear-1Box and Linear-2Box models lies in the vertical distribution of ¹³⁷Cs. The Linear-1Box model assumes (sometimes incorrectly) that the entire ¹³⁷Cs inventory is confined to the tillage layer, whereas the Linear-2Box model allows for some portion of the inventory to reside beneath the tillage layer where it is unavailable for erosion. Spomer et al. (1985) used the Linear-1Box model to describe soil erosion during the period 1954–1974, so that

$$ {\hbox{E}} = {\hbox{D}}{{\hbox{P}}_{\rm{L}}}{\hbox{K}}/{\hbox{T}} $$

(25.3)

where D is the average tillage mixing depth (cm), K is the dry bulk density of the soil (g cm⁻³), and T is the time since the onset of ¹³⁷Cs deposition (y). P_L is defined as

$$ {{\hbox{P}}_{\rm{L}}} = ({{\hbox{I}}_{\rm{ref}}} - {{\hbox{I}}_{\rm{site}}})/{{\hbox{I}}_{\rm{ref}}} $$

(25.4)

The Linear-2Box model (i.e., tillage depth < ¹³⁷Cs penetration depth) described soil erosion with the relationship

$$ {\hbox{E = D}}{{\hbox{P}}_{\rm{till}}}{\hbox{K}}/{\hbox{T}} $$

(25.5)

P_till is analogous to P_L, but the inventory is confined to the tillage layer or to the same depth as the tillage layer at reference sites. Comparisons of results obtained with both the Linear 1-Box and Linear 2-box models indicate little differences in derived erosion rates at Spomer et al.’s (1985) field site (Fornes et al. 2005).

4.3 Time-Dependent Model Methods

Some approaches (detailed in Ritchie et al. 1974) are limited in their use because the relationship between erosion rate and ¹³⁷Cs inventory is incorrectly assumed to be independent of time or cultivation, even failing to account for the radioactive decay of ¹³⁷Cs (Kachanoski and deJong 1984). These various approaches produced a wide range of erosion rates at a single site (Fornes et al. 2000) confirming that model assumptions significantly influence ¹³⁷Cs-derived soil erosion rates. Thus, these models are limited because they are single time-step models that do not consider the time-dependent nature of ¹³⁷Cs fallout (Kachanoski and deJong 1984; Spomer et al. 1985; Walling et al. 1999a, b) or the downcore migration of ¹³⁷Cs (Figs. 25.9–25.11).

It is possible to obtain improved estimates of soil erosion rates based upon changes in ¹³⁷Cs inventories by addressing issues associated with model assumptions and changes in soil conservation practices by modeling the time-dependent ¹³⁷Cs fallout, precipitation and soil cultivation (Kachanoski and deJong 1984; Walling and He 1997a, b; Zhang et al. 1999; Fornes et al. 2005). Using this approach, the equation describing the rate of change of total ¹³⁷Cs inventory is

$$ \partial {\hbox{I}}/\partial {\hbox{t}} = {\hbox{F}}({\hbox{t}}) - {\hbox{EC}}({\hbox{t}}) - {\hbox{\ rmlambda I}} $$

(25.6)

where I is ¹³⁷Cs inventory (Bq cm⁻²), E is erosion rate (g cm⁻² year⁻¹), C(t) is the concentration of ¹³⁷Cs (Bq g⁻¹), F(t) is the time-dependent atmospheric fallout of ¹³⁷Cs (Bq cm⁻²), and λ is the radioactive decay constant (year⁻¹). Temporal variation of ¹³⁷Cs fallout, F(t), can be derived from the measured fallout data (Fig. 25.3) with the magnitude adjusted to the local ¹³⁷Cs reference inventory (Health and Safety Laboratory 1977; Cambray et al. 1989). This model can be kept compatible with the Linear-1Box and Linear-2Box models, by assuming steady-state erosion and cultivation. Soil erosion rates can also be calculated under more detailed constraints such as precipitation-dependent erosion and ephemeral homogenization of the cultivated layer (Walling and He 1997a, b; Zhang et al. 1999; Fornes et al. 2005) for more accurate and realistic erosion rates.

Figure 25.13 illustrates the differences in calculated erosion rates that model assumptions governing the choice of time step exert on the calculated erosion rates. In these simulations of Fornes et al. (2005), the erosion rate decreased by a factor of three as the model time step was increased from 1 month to 20 years. With a single 20-year time step, erosion rates are virtually the same as those estimated by Spomer et al. (1985) because Spomer et al. (1985) used a Linear-1Box model to describe soil erosion during a single time interval of 1954–1974. The modest differences between the 20-year time step and those reported by Spomer et al. (1985) can be explained by noting that the cultivation depth used in the Fornes et al. (2005) simulations was 10 cm, but Spomer et al. (1985) used a 15 cm cultivation depth. Deposition, cultivation, and erosion in the Spomer et al. (1985) model occur in a single step beginning c. 1954 and ending when the core was collected in 1974. The Fornes et al. (2005) model incorporates a monthly time step (Fig. 25.13) so the 20-year interval is approximated by 240 monthly time steps of deposition and erosion. These results indicate that ¹³⁷Cs-derived erosion rates are highly sensitive to the length of the time step used in the model because of the combination of the timing of the fallout, cultivation, and erosion. These results suggest that models that fail to account for temporal variations in atmospheric deposition and/or cultivation practices can grossly miscalculate erosion rates.

Fig. 25.13

Calculated ¹³⁷Cs inventories in a soil subject to atmospheric deposition of ¹³⁷Cs, periodic (annual) cultivation, and erosion over the time period 1954–1974. Note that inclusion of monthly data results in an erosion rate about 3 times larger than that calculated from the soil inventory only at the end of the 20-year time period. After Fornes et al. (2005)

4.4 Tillage Erosion

While the radionuclide inventory in a core and/or the downcore profile of a radionuclide in that core may indicate erosion, the models described above do not necessarily inform the cause of that erosion. The pattern of radionuclide inventories in a field may be strongly influenced by tillage translocation rather than water erosion. For example, poor agreement has been reported between spatially-distributed ¹³⁷Cs -derived soil redistribution rates with those derived from water erosion (Quine 1999). Reduced inventories on hillslope convexities and deposition in hollows have been attributed to soil loss caused by tillage redistribution rather than by water erosion (DeJong et al. 1983; Lobb et al. 1995). Consequently, several workers have developed models which attempt to distinguish the two drivers of radionuclide redistribution and thereby obtain an estimate of the erosion caused solely by water erosion (Govers et al. 1994, 1996; Lobb and Kachanoski 1999). Van Oost et al. (2006) provide a review of the literature on tillage erosion and conclude that based on a global data set tillage erosion rates are comparable to or higher than water erosion rates. They note that because of the widespread use of tillage practices, the high translocation rates resulting from tillage, and the effects of tillage on soil properties, that tillage erosion should be considered in soil landscape studies.

The most widespread used tillage model treats tillage erosion as a diffusion-type process (Govers et al. 1994). The model of Govers et al. (1994) relates the rate of soil translocation to the soil bulk density, the average soil translocation distance in the direction of tillage, and the depth of tillage. They treat translocation distances resulting from a single tillage pass to be linearly and inversely related to slope and that multiple passes in opposing directions results in a net downslope transport. Additional assumptions are that the tillage depth and soil bulk density do not vary in space, tillage soil translocation can be expressed as a linear function of the slope gradient, and tillage is conducted in opposing directions. Using the continuity equation they determine that the tillage erosion may be written as

$$ E = - \frac{{\partial {Q_s}}}{{\partial x}} = - D{\rho_b}b\frac{{\partial h}}{{\partial x}} = {k_{{til}}}\frac{{{\delta^2}h}}{{\delta {x^2}}} $$

(25.7)

where E is the tillage erosion rate (kg m⁻² a⁻¹); Q_s is the rate of soil translocation in the direction of tillage (kg m⁻¹ a⁻¹); D is the tillage depth (m); ρ_b is the soil bulk density (kg m⁻³); x is the distance (positive downslope) (m); d is the average soil translocation distance in the direction of tillage (m a⁻¹) (=a + bS where a and b are regression constants (m a⁻¹) and S is the slope tangent (positive upslope; negative downslope) (dimensionless)); h is the height at a given point of the hillslope (m); and k_til (=−Dρ_bb) is the tillage transport coefficient (kg m⁻² a⁻¹).

This model has been applied to a number of studies to compare different plowing directions (Van Muysen et al. 2002; St Gerontidis et al. 2001; De Alba 2001; Quine and Zhang 2004; Heckrath et al. 2006), and erodability of the landscape (Lobb et al. 1999) as affected by implement characteristics (tool shape, width, length) and operational parameters (tillage depth, speed, tillage direction). Reported implement erosivities as characterized by the tillage transport coefficient are fairly consistent and range from 400 to 800 kg m⁻² year⁻¹ for mechanized plowing and from 70 to 260 kg m⁻² year⁻¹ for non-mechanized agriculture (Van Oost et al. 2006). Van Oost et al. (2006) also report that decreasing tillage depth and plowing along contour lines substantially reduce tillage erosion rates and can be considered as effective soil conservation strategies.

4.5 Wind Erosion

Compared to water there has been relatively little work using ¹³⁷Cs to study aeolian processes of erosion and deposition. Recently, however, the application of ¹³⁷Cs to study wind erosion has received some attention (Sutherland and deJong 1990; Sutherland et al. 1991; Chappell 1996, 1998; Yan and Zhang 1998; Yan et al. 2001; Yan and Shi 2004; Hu et al. 2005). The determination of the wind erosion rate is important in assessing the extent and intensity of desertification and the effectiveness of counter-measures.

Calculation of wind erosion rates has been based on the same proportional inventory models that are sometimes used to estimate erosion by water (Sutherland and deJong 1990; Walling and Quine 1993), although it is recognized that these models sometimes suffer from the same issues affecting their use to quantify water erosion – failure to account for surface enrichment of ¹³⁷Cs and ¹³⁷Cs dilution by tillage. Mass balance models (Kachanoski and deJong 1984; Zhang et al. 1990) are more suitable for assessing soil erosion in soils where ¹³⁷Cs is distributed uniformly, such as croplands. In settings where the ¹³⁷Cs profile is not homogeneous, such as grasslands, the profile distribution model is more appropriate. The calculation of wind erosion loss in these models (Yan et al. 2001; Hu et al. 2005) is estimated by

$$ {\hbox{E}} = {\hbox{CPR}}*{\hbox{Bd}}*{\hbox{DI}}*{10^4}{\hbox{/T}} $$

(25.8)

where E is the net wind erosion rate of the sample site (Mg ha⁻¹ a⁻¹); Bd is the bulk density of the soil (Mg m⁻³); DI is the sampling depth increment (assumed = plow depth in farmlands, Sutherland and deJong 1990; Walling and Quine 1993) and in undisturbed soils it is approximately the depth over which ¹³⁷Cs is found (~0.1–0.3 m); T is the time period between the year of initial ¹³⁷Cs fallout (assumed to be the year of maximum fallout, 1963) and the sampling year of the study; CPR is the percentage residual at a sampling point in the field relative to the native control area (%):

$$ {\hbox{CPR}} = ({\hbox{CPI}} - {\hbox{k}}*{\hbox{CRI}})*{1}00/\left( {{\hbox{k}}*{\hbox{CRI}}} \right) $$

(25.9)

where CPI is the ¹³⁷Cs inventory at the sampling site (Bq m⁻²); k is a coefficient of ¹³⁷Cs redistribution caused by snow-blown and vegetation removal (sometimes set =1; =0.95 in Yan et al. 2001); and CRI is the ¹³⁷Cs inventory at the reference site (Bq m⁻²).

Studies using this model to quantify wind erosion yield rates that range from 300 to 8,400 Mg m⁻² a⁻¹ depending on the vegetative cover (Yan et al. 2001; Yan and Shi 2004; Hu et al. 2005) where grasslands exhibit the least erosional loss and croplands and dunelands the highest. In one study (Li et al. 2005), an attempt was made to estimate the relative magnitudes of both wind and water erosion in the same study area, and the authors report that wind erosion can account for at least 18% of the total soil loss.

5 Recent Applications

In this section, we describe new applications of ¹³⁷Cs and other radionuclides in studies of surface erosion and deposition.

5.1 Single Event Erosion Measurement

One limitation of the longer-lived radionuclides ¹³⁷Cs and ²¹⁰Pb is their inability to quantify erosion over short time periods; for instance, the erosion occurring during a single storm. ¹³⁷Cs and ²¹⁰Pb are unsuitable for such studies because the change in inventory due to erosion during a single event is small compared to the total inventory. Walling and Quine (1990) estimated that at least a decade of erosion is necessary to produce a large enough change in ¹³⁷Cs inventory (t_1/2 = 30.1 years) that the difference is measurable. Following this reasoning, at least 5–8 years of erosion would be required to recognize erosion using changes in ²¹⁰Pb_xs inventory (t_1/2 = 22.3 years). ⁷Be has a sufficiently short halflife (t_1/2 = 53 days) that Blake et al. (1999), Walling et al. (1999a, b) and Wilson et al. (2003) used the radionuclide to estimate erosion occurring during single rainfall events. The workers determined the pre-storm and post-storm inventory of ⁷Be as well as the delivery with precipitation. The erosion during the single event studied by Wilson et al. (2003) corresponded to 23% of the average annual erosion rate determined by ¹³⁷Cs and the mass-balance approach yielded an erosion amount that matched the erosion determined from sediment flux off the field.

Vitko (2007) used ⁷Be to recognize redistribution of plowed soil from ridges into adjacent furrows finding that fields plowed along contour had greater retention of ⁷Be than fields plowed up-down the slope presumably due to less soil erosion and/or greater deposition.

5.2 Sediment Sources

The radionuclides ⁷Be, ¹³⁷Cs, and ²¹⁰Pb have been used individually and in tandem to quantify the relative contributions of different processes of erosion to sediment. Nagle et al. (2007) used the activity of ¹³⁷Cs in suspended sediments to determine the provenance of sediment. Collins and Walling (2007) utilized ¹³⁷Cs and several other constituents in a multivariate sediment mixing model to identify principle sources of fine sediment. He and Owens (1995) used ¹³⁷Cs, ²¹⁰Pb_xs, and ²²⁶Ra in tandem to provide radionuclide fingerprints of cultivated land, uncultivated land, and stream banks and their contributions to the sediment pool. Walling and Woodward (1992) used ⁷Be, ¹³⁷Cs, ²¹⁰Pb_xs to distinguish sediment from surficial and channel sources and the trend in ⁷Be during the studied event allowed them to recognize changing sources. Brigham et al. (2001) used ²¹⁰Pb_xs, ⁷Be, and ¹³⁷Cs as separate tracers to determine the relative importance of surficial and streambank erosion. There was substantial variation in the estimated percentage of sediment from surface soil erosion – ¹³⁷Cs = 34%, ²¹⁰Pb_xs = 71%, ⁷Be = 91%. Gellis and Landwehr (2006) used ¹³⁷Cs and unsupported ²¹⁰Pb, stable isotopes (del ¹³C and del ¹⁵N), total carbon, nitrogen, and phosphorus to successfully partition sources of fine-grained suspended sediment in the Pocomoke River watershed from cropland, forest, channel and ditch banks, and ditch beds. Devereux et al. (2010) used concentrations of 63 elements and two radionuclides to fingerprint fine sediment sources by both physiographic province (Piedmont and Coastal Plain) and source locale (streambanks, upland and street residue).

Here we consider several specific examples of the use of tracers in source identification. Whiting et al. (2005) established the contribution of streambanks to the suspended sediment flux with a two-component mixing model that used the distinctive radionuclide signatures of the streambanks and of the landscape soils to define the end members of the mixing model (Fig. 25.14). Sediment delivered to the channel by erosion of the soil surface has relatively high activities of ⁷Be and ²¹⁰Pb because of the atmospheric delivery of the radionuclides to the soil surface (Fig. 25.12). Sediment delivered to the channel by bank erosion (largely toppling) has much lower radionuclide activities because the low-activity material from deeper in the bank dilutes the high activity material from atop the bank. The height of the collapsed bank is so much larger than the depth of penetration of ⁷Be into the soil that the activity of ⁷Be in the eroded bank material is effectively zero. The depth to which the bank material is removed corresponds to that part of the soil profile where only the low-activity supported ²¹⁰Pb is found. Consequently, the ²¹⁰Pb activity of the bank material is much lower than the surface activity and is similar to the constant value that reflects in situ decay of soil minerals.

Fig. 25.14

The suspended sediment samples (o) along Soda Butte Creek in Yellowstone National Park, Wyoming, USA, are intermediate between two endmember sources for fine sediment: bank material (diamond) and surficial soils (square)

In another study, Whiting et al. (2001) used the distinct distribution of ⁷Be, ¹³⁷Cs, and ²¹⁰Pb with depth in soils on an agricultural plot (Fig. 25.12) and the measured radionuclide flux in runoff in multiple mass balances to quantitatively estimate the areal extent of rill and sheet erosion and the characteristic depth of erosion associated with each mechanism. They examined 15.5 million possible combinations of the depth and areal extent of rill and sheet erosion and found that the best solution to the mass balances corresponded to rills eroding 0.38% of the basin to a depth of 35 mm and sheetwash eroding 37% of the basin to a depth of 0.012 mm. Rill erosion produced 29 times more sediment than sheet erosion.

The identification of sources and depositional locations identified by the radionuclide ratios as discussed herein can be the basis for quantifying a sediment budget. Blake et al. (2002) used ⁷Be and ¹³⁷Cs to quantify various elements of a sediment budget – soil erosion and remobilization from hillslopes, erosion and deposition in river channels, and floodplain deposition. ¹³⁷Cs has been a common tool for characterizing soil redistribution on landscapes (Walling and Quine 1992; Owens et al. 1997; Walling et al. 2003; Kaste et al. 2006).

5.3 Pu as a Tracer

^239,240Pu may be a promising substitute for ¹³⁷Cs measurements. Stratospheric ^239,240Pu is also bomb-derived, behaves similarly once delivered to the earth surface, and gives equivalent information. In fact, Figs. 25.11 and 25.15 show how similar the profiles for the two radionuclides can be and Fig. 25.16 illustrates the strong correlation between ¹³⁷Cs and ^239,240Pu inventories. There are several reasons why ^239,240Pu may become used more often than ¹³⁷Cs. With the development of a method for using inductively coupled plasma mass spectrometry (ICPMS) and high sample through-put, the use of ^239,240Pu may be more cost effective (Ketterer and Szechenyi 2008). Moreover, ¹³⁷Cs half-life (t_1/2 = 30.1 years) is such that peak inventories were observed in the mid- to late-1960s, and by 2010 inventories are only ~40% of original values and dropping. The halflife of both Pu isotopes is several thousand years. Finally, the ²⁴⁰Pu/²³⁹Pu values in fallout in the 1950s and after 1965 differ which may allow partial differentiation of the time frame of erosion.

Fig. 25.15

Comparison of ¹³⁷Cs and ^239+240Pu profiles in undisturbed prairie soils from Konza Prairie, KS. Plutonium data courtesy of Michael Ketterer

Fig. 25.16

¹³⁷Cs inventory vs. ^239,240Pu inventory for soil auger samples from 54 sites in the Murder Creek, Georgia USA watershed (from Stubblefield et al. ms)

5.4 Use with Other Techniques and in Other Settings

Recently we have seen the use of the fallout radionuclides in conjunction with other erosion measurement techniques. Fondran (2007) combined the use of multiple mass-balances of radionuclides and a laser line scanner with sub-millimeter vertical resolution. With the laser line scanner, Lorimor was able to measure changes in topography (erosion and deposition) and compare these results to the estimates of the depth and areal extent of rills and sheetwash as determined from the multiple mass balances. In the same study, rare earth element tagged soils were deployed to provide information on the proportion of sediment delivered from the top of the slope compared to the middle and bottom of the slope (Stubblefield et al. 2006). O’Farrell et al. (2007) used pond sediment volumes, ¹³⁷Cs and ²¹⁰Pb activities, and ¹⁰Be and ²⁶Al activities to examine different approaches and timeframes for estimating landscape denudation. Walling et al. (1999a, b) used ⁷Be and ¹³⁷Cs respectively to evaluate event and decadal erosion rates. The conjunctive use of fallout radionuclides (Mabit et al. 2008) especially with other radionuclides, promises to provide key information on variation in denudation rates over time driven by changes in climate and landuse.

Yet other applications include using radionuclide based sedimentation estimates to test predictions of floodplain sedimentation (Siggars et al. 1999) and to compare aerial photography-derived and radionuclide-derived meander migration rates (Black et al. 2010) or accretion rates (Provansal et al. 2010). Various workers have used ⁷Be and/or ²¹⁰Pb to investigate resuspension in rivers and estuaries (Fitzgerald et al. 2001; Wilson et al. 2003, 2005, 2007; Jweda et al. 2008), erosion after forest harvesting (Schuller et al. 2006), and wildfire (Blake et al. 2009).

While the use of radionuclides in surficial studies has focused on tracing fine materials, Salant et al. (2006) used ⁷Be to recognize and track medium and coarse sand released from an impoundment. Fisher et al. (2010) likewise used ⁷Be to constrain the timescales of sediment storage associated with large woody debris.

6 Future Directions

Although there are about 5,000 papers in the literature devoted to the radionuclides discussed in this chapter there is still room for improvement in the methodologies and applications. From a technological perspective, improvements in instrumentation and detection and lowering of costs should enable greater numbers of samples to be collected and analyzed. For example, the development of larger, low cost gamma detectors that do not require liquid nitrogen cooling will enable a more routine use of the equipment, field deployment and more detailed spatial resolution. This could lead to watershed scale or even landscape scale studies. Another technological improvement could be the development of ICP-MS methods for the measurement of ¹³⁷Cs and ²¹⁰Pb. Measurement of gamma decays is inefficient because it measures only those atoms that undergo decay during the counting period. But the vast majority of the atoms of interest do not undergo decay during the counting period, especially for the longer lived isotopes. Instead, mass measurements have the advantage of measuring all the atoms that are present in the sample. While ICP-MS methods have been developed for Pu isotopes (Ketterer et al. 2002) it appears that natural levels of ¹³⁷Cs and ²¹⁰Pb cannot be detected by current instrumentation. However, with improvements in ICP-MS technology this may change and permit cost-effective analyses of much larger numbers of samples. As with the development of larger low cost gamma detectors, the development of these techniques could enable much higher spatial resolution studies. For example studies comparing ^239,240Pu-derived erosion rates as a surrogate for ¹³⁷Cs-derived erosion rates can be done now, since there are already ICP-MS methods for ^239,240Pu and larger numbers of samples can be run for ^239,240Pu than for ¹³⁷Cs.

Earlier in this chapter we demonstrated that the derived erosion rate is model dependent, and in particular, also depends on the time interval used to evaluate erosion. But these models do not account for the steady, downward migration of the radionuclides. Further progress will require the incorporation of the downward migration into the time dependent erosion models. Furthermore, these models will need to be more comprehensive in their treatment of the downward migration process. Particle mixing by bioturbation as well as solute transport with adsorption will both need to be included in models to enable a better description of the vertical profiles as a function of time. Furthermore, there is evidence that the downward migration process is not steady, and may be affected by non-linear adsorption and/or flow through macropores or channels. A more rigorous evaluation and treatment of these processes needs investigation and incorporation into the models.

It may be possible to use the much better ¹³⁷Cs soil data sets collected following Chernobyl than the older soil profiles collected a couple of decades after stratospheric fallout to constrain erosion models, quantify soil properties, and improve estimates of soil transport and sources. Even more intriguing is the possibility of combining from the same soil column ¹³⁷Cs profiles that are dominated by Chernobyl fallout with ^239,240Pu profiles derived from global fallout because this will enable comparison of two different tracers over two different time periods within the same soil profile. Furthermore, it may be possible to find locations where the ¹³⁷Cs signal from stratospheric fallout is comparable in magnitude to the ¹³⁷Cs fallout from Chernobyl. In such a situation it may be possible to identify and separate the two overlapping signals which will help constrain soil processes and model coefficients.

Finally, soil fertility and C sequestration in soils remain global issues. Thus, accurately determining soil erosion rates, which clearly impacts soil fertility and affects estimates of C sequestration and C removal, remains an important component in research on these topics. Similar studies could also be done to relate past and current erosion rates to land usage to provide both estimates of the historical impacts of land usage on erosion and also future impacts of land usage on C storage and cycling.