# Lionel Mabit · William Blake Editors

# Assessing Recent Soil Erosion Rates through the Use of Beryllium-7 (Be-7)

Assessing Recent Soil Erosion Rates through the Use of Beryllium-7 (Be-7)

Lionel Mabit • William Blake Editors

# Assessing Recent Soil Erosion Rates through the Use of Beryllium-7 (Be-7)

Editors Lionel Mabit Soil and Water Management and Crop Nutrition Subprogramme Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture International Atomic Energy Agency Vienna, Austria

William Blake School of Geography, Earth and Environmental Sciences University of Plymouth Plymouth, UK

#### ISBN 978-3-030-10981-3 ISBN 978-3-030-10982-0 (eBook) https://doi.org/10.1007/978-3-030-10982-0

Library of Congress Control Number: 2018966852

© International Atomic Energy Agency (IAEA) 2019. This book is an open access publication.

Open Access provided with a grant from the International Atomic Energy Agency.

The opinions expressed in this publication are those of the authors/editors and do not necessarily reflect the views of the International Atomic Energy Agency, its Board of Directors, or the countries they represent.

Open Access This book is licensed under the terms of the Creative Commons Attribution 3.0 IGO license (https://creativecommons.org/licenses/by/3.0/igo/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the International Atomic Energy Agency, provide a link to the Creative Commons license and indicate if changes were made.

The use of the International Atomic Energy Agency's name for any purpose other than for attribution, and the use of the International Atomic Energy Agency's logo, shall be subject to a separate written license agreement between the International Atomic Energy Agency and the user and is not authorized as part of this CC-IGO license. Note that the link provided above includes additional terms and conditions of the license.

The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

# Preface

The Soil and Water Management & Crop Nutrition (SWMCN) Subprogramme of the Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture supports IAEA Member States and FAO Member Countries in the use of fallout radionuclides (FRNs) techniques for assessing soil redistribution patterns and magnitudes to reduce the impact of soil erosion on agro-ecosystems.

From all available FRNs (e.g. 137Cs, 210Pbex, 239+240Pu), Beryllium-7 (7 Be) is the only soil tracer that permits the gathering of short-term soil redistribution information. This natural cosmogenic isotope was used in this context for the first time at the end of the 1990s. Developments over the past decades now permit investigation of erosion processes not only during short extreme weather events but also over extended periods of up to several months.

The SWMCN Subprogramme has actively sought to refine the use of <sup>7</sup> Be in close collaboration with the School of Geography, Earth and Environmental Sciences at the University of Plymouth, UK, and with the help of scientists from developed and developing countries. This book reflects the latest developments obtained and the state of the art related to the use of this natural tracer of soil and sediment.

This handbook presents the foundation of the <sup>7</sup> Be method and provides guidelines for the practical applications of basic and advanced approaches of this technique. It assists scientists, technicians and students to assess the impact of soil erosion events and further support the development of land management and climate-smart agriculture policies for future sustainable food security.

Vienna, Austria Lionel Mabit

Plymouth, UK William Blake

# Contents


# **Chapter 1 The Use of Be-7 as a Soil and Sediment Tracer**

**A. Taylor, W. H. Blake, A. R. Iurian, G. E. Millward and L. Mabit**

# **1.1 Origin and Agro-Environmental Behaviour of 7Be**

# *1.1.1 Atmospheric Production of 7Be*

Beryllium-7 (7Be) (T1/2 - 53.3 days) is a cosmogenic fallout radionuclide (FRN) produced in the upper atmosphere by cosmic ray spallation of nitrogen and oxygen. As reported by Kaste et al. (2002), rates of production are dependent upon solar activity with greater production in the stratosphere than the troposphere and generally increased production occurring at higher latitudes owing to cosmic ray deflection towards the poles.

Following its formation, 7Be becomes associated with aerosols and its flux is then controlled by complex atmospheric transport processes, which display seasonal variations largely linked to atmospheric mixing and precipitation patterns. During

A. Taylor (B) · G. E. Millward

G. E. Millward e-mail: G.Millward@plymouth.ac.uk

W. H. Blake

A. R. Iurian

L. Mabit

Soil and Water Management and Crop Nutrition Subprogramme, Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture, International Atomic Energy Agency, Vienna, Austria e-mail: L.Mabit@iaea.org

© International Atomic Energy Agency (IAEA) 2019 L. Mabit and W. Blake (eds.), *Assessing Recent Soil Erosion Rates through the Use of Beryllium-7 (Be-7)*, https://doi.org/10.1007/978-3-030-10982-0\_1

Consolidated Radioisotope Facility (CoRiF), University of Plymouth, Plymouth, UK e-mail: alex.taylor@plymouth.ac.uk

School of Geography, Earth and Environmental Sciences, University of Plymouth, Plymouth, UK e-mail: william.blake@plymouth.ac.uk

Terrestrial Environment Laboratory, IAEA Laboratories Seibersdorf, Seibersdorf, Austria e-mail: A.Iurian@iaea.org

the spring months at mid latitudes, increased stratosphere-troposphere exchange can occur during folding of the tropopause leading to higher concentrations of 7Be in the troposphere (Kaste et al. 2002). Once in the troposphere, 7Be is subjected to vertical mixing through convective circulation, which is likely to increase during warmer months and serves to transport 7Be enriched air to the lower troposphere, increasing its availability for precipitation scavenging. Given that precipitation scavenging is the main mechanism for the removal of 7Be from the atmosphere, seasonal and latitudinal climatic conditions exert a strong influence upon atmospheric concentrations (Kusmierczyk-Michulec et al. 2015).

# *1.1.2 7Be Fallout*

Wet deposition governs 7Be delivery to the Earth's surface while dry deposition only accounts for approximately 10% of the overall fallout (Kaste et al. 2002). Activity concentration of 7Be in rainwater (Bq L−1) is conditional on its availability for scavenging and is influenced by a number of factors including rainfall rates and volumes (Ioannidou and Papastefanou 2006).

The term 'washout' refers to situations when rainfall scavenging exceeds the availability of 7Be in the atmosphere leading to a reduction in 7Be rainwater activity concentration across an event and following high magnitude or prolonged rainfall events. In contrast, greater activity concentrations during low magnitude events can be related to efficient scavenging of 7Be by fine droplets where there is an abundance of 7Be-bearing aerosols (Ioannidou and Papastefanou 2006). The processes of atmospheric circulation and depletion not only affect the activity concentrations of 7Be on a temporal scale, but are also likely to increase its spatial variability (Taylor et al. 2016). 7Be deposition (Bq m−2) is significantly correlated to the amount of rainfall received on an event basis and, therefore, seasonal depositional fluxes reflect monthly rainfall volumes (Doering and Akber 2008).

# *1.1.3 7Be Sorption Behaviour in Soils and Sediments*

Upon deposition and infiltration into the soil surface, 7Be is known to be rapidly adsorbed to fine soil particles (Fig. 1.1), which is supported by laboratory batch studies, high partition coefficients (Kd > 105) in aquatic systems and shallow depth distributions displayed in a range of soil types (Taylor et al. 2013). 7Be shows preferential adsorption to fine sediment fractions (Taylor et al. 2014), which are likely to be readily mobilised in hillslope systems. In solutions of pH 5–6 and in the absence of humic acid, 7Be is likely to be present as Be2+ and the hydrolysed species, BeOH+; both of these forms are highly reactive, resulting in rapid sorption rates (Kaste et al. 2002). The rapid adsorption together with a short half-life (the latter precludes the effects of diffusion and bioturbation over time) leads to distributions typically extend-

**Fig. 1.1** Schematic diagram of 7Be production and fallout. 7Be is produced by cosmic ray spallation in the upper atmosphere and becomes associated with aerosols. 7Be-bearing aerosols are scavenged by precipitation and, consequently, wet deposition is the dominant pathway to the Earth's surface. 7Be is rapidly adsorbed to soil particles and remains cohesive under oxic field conditions

ing to around 20 mm below the soil surface and an exponential decrease with depth (Fig. 1.2). Where soils remain aerated and free from waterlogged conditions, as is the case in most agricultural field sites, 7Be is likely to remain adsorbed to soil particles (Taylor et al. 2012). Both characteristics (i.e. rapid adsorption and cohesive behaviour) are key prerequisites for 7Be application as a soil redistribution tracer.

# **1.2 The Use of 7Be as a Soil Redistribution Tracer**

The application of FRN tracers (e.g. 7Be, 137Cs, 210Pbex, Pu) provides distinct and additional advantages over traditional soil monitoring techniques by enabling retrospective estimates of soil redistribution from relatively few site visits. Through carefully planned sampling programmes, high spatial resolution estimates of soil redistribution can be acquired, which are unlikely to be achieved using conventional methods (Walling et al. 1999). In this regard, the use of nuclear and iso-

topic techniques enables rigorous assessment of soil conservation measures and, if applied over extended time periods, can help to determine the sustainability of agricultural systems.

FRN tracing techniques have been commonly applied to assess soil redistribution at the hillslope scale using 137Cs (T1/2 -30.2 years) and 210Pb (T1/2 -22.3 years). The half-life of these radionuclides enables redistribution estimates relating to mediumterm (i.e. decadal) timescales, providing important information with regard to soil loss or gain in an historical context. However, the application of these decadal-scale radionuclides does not allow for determination of soil redistribution as a result of recent changes in land use or recent rainfall events. This is an important consideration given the need for assessment of soil conservation measures with increasing recognition of soil as a finite global resource. The short-lived 7Be is, therefore, complementary to the other FRN tracers in enabling estimates of soil redistribution across much shorter timescales such as rainfall events or wet seasons.

The premise for using 7Be as a soil redistribution tracer is that the tracer will be rapidly adsorbed to soil particles upon fallout, thus establishing an inventory (7Be activity per unit area) (Bq m−2) at a sampling site. A key assumption of the technique is that 7Be will remain adsorbed to soil particles across the timescale of the study and, therefore, any changes in inventory (i.e. depletion or gain) at a sampling point can only occur as a result of fallout, radioactive decay and/or soil redistribution processes. The 7Be inventory at a site, which experiences soil redistribution, can be compared directly to the 7Be inventory at a stable location, referred to as a reference site, where there is no loss or gain in inventory as a result of soil redistribution. The inventory at a reference site is established only through 7Be atmospheric fallout and, given that this is predominantly delivered by precipitation, reference sites are typically level areas which retain the fallout without loss except for radioactive decay. Alongside the important tracer assumptions of rapid adsorption upon fallout and cohesive behaviour during the period of study, it is also crucial that the reference site receives the same fallout deposition as the eroding area of interest, which requires both sites to be in close proximity. In addition to this, it is also assumed that the fallout received at the study site will be uniform so any differences in inventory across the study area can be attributed to soil redistribution. If these assumptions hold, then any reduction in inventory at a sampling location with respect to the reference inventory can be attributed to soil loss and a gain in inventory would suggest soil deposition, given that the redistribution of 7Be (as a cohesive tracer), will only occur in line with movement of the sediment to which it is adsorbed.

To quantify the mass of soil eroded or deposited (kg m−2), it is essential to determine the depth distribution of 7Be in the soil profile and, in particular, the relaxation mass depth (referred to as *h*0) a value, which describes the shape of the 7Be distribution. This is an essential component of the commonly applied soil redistribution model described below. On the basis of this, any change in 7Be inventory at a sampling location can be fitted to the mass of soil redistribution required to implement that change. An example is given in Fig. 1.3, which shows a loss of 100 Bq m−<sup>2</sup> at the eroded location (i.e. inventory of 300 Bq m−2) with respect to the stable reference inventory (i.e. 400 Bq m−2). By establishing the exponential shape of the 7Be profile, the conversion model is able to estimate the mass depth of soil required to reduce the inventory by 100 Bq m−2.

The specific conversion model used to derive soil redistribution magnitudes (Profile Distribution Model [PDM]) is detailed in Blake et al. (1999) and Walling et al. (2009) and the basis of this is outlined in Appendix 1.1. In addition, a worked example of this model is provided in Chap. 4.

# **1.3 Examples of the Application of 7Be as a Soil Redistribution Tracer**

Blake et al. (1999) and Walling et al. (1999) carried out the first comprehensive investigation into the use of 7Be to estimate short-term soil redistribution by studying the impact of a heavy rainfall event at an agricultural site in southwest England. The 7Be depth distributions from this study site are shown in Fig. 1.4. The key requirement of uniform 7Be fallout across the study location was satisfied owing to the soil 7Be inventory being reset (i.e. reduced to below detectable limits) by ploughing prior to

**Fig. 1.3** Conceptual diagram of the premise for using 7Be as a soil erosion tracer. The figure shows the 7Be inventory (400 Bq m−2) and depth distribution at a stable reference location, which has been established by 7Be atmospheric fallout. The eroded and depositional zones (representing a neighbouring hillslope area for example) have received the same fallout as the reference location, thus, an inventory has been established but the zones have experienced depletion or enhancement of the 7Be inventory as a result of soil erosion and soil deposition respectively. This simplified conceptual diagram can be compared to examples of measured 7Be inventories in Fig. 1.4

the commencement of the investigation. There was also a period of low intensity rainfall prior to the erosive event, which established a measurable 7Be inventory without causing significant soil redistribution. A reference baseline inventory was estimated from neighbouring undisturbed pasture locations against which the slope inventories could be compared. The depth profile was determined in a non-eroded part of the study field. The PDM was used to determine soil redistribution rates and results indicated high levels of soil export from the site as a consequence of the intense rainfall event and compacted soil conditions, highlighting the pressing need for soil conservation measures to maintain soil fertility and to prevent sediment from entering catchment watercourses.

As highlighted by Mabit et al. (2014), an important advantage in the use of 7Be as a soil erosion tracer is the ability to assess the effectiveness of recent soil conservation measures or the impacts of land use change. Schuller et al. (2006) applied the approach proposed by Blake et al. (1999) to document the effects of recent forest clearance upon slope soils in a timber harvesting region of Chile. Through the 7Be approach, the use of mitigation strategies could be evaluated and, in this case, the need for further improvements in soil conservation strategies was identified. Sepulveda et al. (2008) aimed to assess the effects of land management practice (in this case stubble burning) by using a combined FRN approach (7Be in conjunction with

**Fig. 1.4** 7Be depth distributions at a stable reference location (**a**), eroded hillslope locations (**b** and **c**) and a depositional hillslope location (**d**) [based on Walling et al. (1999)]. Note the depleted 7Be inventories at the eroding sites and the increased inventory at the depositional site with respect to the reference location

137Cs). Here, the combined use of FRNs was able to compare impacts associated with different land management scenarios across a range of timescales, providing key information with regard to the sustainability of the agricultural system. Blake et al. (2009) also applied a combined approach and used 7Be in conjunction with 137Cs and 210Pb to determine post wildfire sediment budgets at hillslope sites in southeast Australia. Data identified major sediment source areas and focussed attention on the implications of wildfire for water quality management.

Blake et al. (1999) and Sepulveda et al. (2008) identified the occurrence of extreme erosion events by comparing short term erosion rates with medium-term estimates derived from 137Cs. Walling et al. (1999) showed that medium-term erosion rates at the study site were approximately 5 times lower than the short-term rates, suggesting that the studied rainfall event may not have been representative of seasonal patterns in rainfall. Owing to this, adjustments to the model were suggested by Walling et al. (2009) to enable the PDM to be applied across a greater timescale, encompassing a number of erosive rainfall events and improving representativeness. Thus, a method was developed for extending the use of the PDM to periods covering a few months or wet seasons. Within this extended timescale approach, the fundamental aspects of the model remain similar to the conventional approach whereby 7Be inventories at a sample point are compared to a reference baseline and the depth distribution of 7Be is measured. However, for the approach to be applied across multiple erosive rainfall events it is crucial to consider changes in the 7Be inventory across the study period to avoid underestimation of erosion rates. Additional components of the model are, therefore, included whereby loss of inventory at a sampling point is accounted for by estimating the relative erosivity of each rainfall event and ongoing radioactive decay. Similarly, assessment of inventory gain accounts for additional 7Be fallout during the study period alongside soil redistribution. The application of this modified approach was piloted by Schuller et al. (2010), with soil conservation measures shown to be less effective across an extended time period, which encompassed a range of rainfall events, demonstrating the value of considering soil erosion in a long-term context.

Recent plot studies have validated the method on a site-specific basis by demonstrating comparability between the 7Be-derived soil redistribution budget and direct measurements (e.g. Porto and Walling 2014; Shi et al. 2011).

#### **1.4 The Requirement for a Standardised Approach**

FRN tracers are likely to be used in a wide range of environments to assess soil redistribution and, as such, numerous methodological approaches for establishing the key model parameters have been applied. Although it is necessary to tailor sampling approaches to local environmental conditions, it is also important that the approach is standardised, as far as is practicable, to ensure data quality and aid comparability (Mabit et al. 2008).

7Be has the potential to be a valuable decision support tool for catchment managers although to achieve robust estimates of soil redistribution using the PDM it is crucial to accurately estimate its key parameters namely:(1) the reference 7Be inventory, and (2) the 7Be depth distribution (the latter to ensure an accurate value of *h*0). It is also important to consider whether the selective transport of particle size fractions is occurring during rainfall events given preferential association of 7Be to fine soil fractions (<63 µm). Failure to account for preferential adsorption to fine particles can lead to overestimation of soil erosion rates since a large proportion of the 7Be inventory is associated with the fine sediment fractions, which are likely to be readily mobilised during rainfall events. Hence a relatively large deficit in 7Be inventory could actually equate to a low mass of soil loss.

The requirement for standardising procedures is of particular importance for determining 7Be depth distributions in light of recent studies, which demonstrate how the choice of sampling method can influence results (Baumgart et al. 2016; Ryken et al. 2016). Determining 7Be depth distributions in soils is a practical challenge and one that requires careful consideration of the sampling site, both in terms of stability and uniformity (Ryken et al. 2016) as well as a precise sampling method. The latter requires a technique that allows fine depth increments (2 mm depths) to be collected throughout the 7Be profile enabling enough detail to be able to accurately determine *h*0. Mabit et al. (2014) designed and tested a reproducible tool and a modus operandi, which permits collection of fine soil increments in a range of soil types and provides a basis for standardising the sampling method for *h*<sup>0</sup> determination.

In practice, developing a robust sampling strategy to establish model parameters and assess soil redistribution is likely to require a balance between the number of samples required to ensure data quality and the capacity for sample analysis. As with any field operations, preliminary knowledge of the agro-environmental conditions and background data (e.g. land use history; soil hydrological properties) at the sampling site is beneficial and will help to streamline a pragmatic sampling programme.

Against this background, Chap. 2 provides a guideline for undertaking a soil redistribution study using 7Be as a tracer by outlining a standard approach for establishing key conversion model parameters.

#### **Glossary**


$$\begin{array}{c} \text{(kg m}^{-2}) \text{ rather than metric units (mm). This provides a more accurate measure of depth in the context of the soil distribution models.}\\ \text{the context of the soil distribution models.}\\ \text{Profile Distribution Model (PDM)} \quad \text{Simple model to convert} \text{ } ^\dagger \text{Be inventory loss} \\ \text{into soil version amounts by linking inventory} \\ \text{change to the depth profile to derive the mass} \\ \text{depth of soil loss. This model is applied to sink.}\\ \text{gle events over a short period of time.} \end{array}$$

#### **Appendix 1.1: The Profile Distribution Model**

The exponential depth distribution of 7Be in a soil profile can be described as:

$$C(\mathbf{x}) = c e^{-\mathbf{x}/h\_0} \tag{1.1}$$

where *Cx* (Bq kg−1) is the 7Be activity at mass depth *x* (kg m−2), *c* is a constant value and *h*<sup>0</sup> is the relaxation mass depth, the depth at above which 63.2% of the 7Be inventory can be found.

Erosion rates (kg m−2) can be estimated by comparing the 7Be inventories at the sample site, *A* (Bq m−2), to the reference inventory, *Aref* (Bq m−2). Where a mass of soil has been lost (*h*) (kg m−2) changes in the sample site inventories can be represented as:

$$A = \int\_{-h}^{\infty} C(\alpha) d\alpha = A\_{ref} e^{h/h\_0} \tag{1.2}$$

Erosion rate, *h* (kg m−2, negative), can, therefore, be calculated as:

$$h = h\_0 \ln(A/A\_{ref})\tag{1.3}$$

Deposition of material is reflected in an excess of 7Be inventory at the sample site with respect to the reference site. The depth of deposition, *h* (kg m−2, positive), can be calculated as:

$$h' = \left(A - A\_{ref}\right) / C\_d \tag{1.4}$$

Where *Cd* (Bq kg−1) is the mean activity concentration of 7Be in the deposited sediment.

The 7Be activity concentration in the eroding sediment at each upslope point, *Ce* (Bq kg−1), can be calculated from the loss of inventory divided by the mass of soil loss:

1 The Use of Be-7 as a Soil and Sediment Tracer 11

$$C\_e = \left(A\_{ref} - A\right) / h \tag{1.5}$$

The mean activity concentration of soil mobilised from the study area, *S* (m2), can then be calculated as:

$$C\_{\rm d} = \int\_{S} hC\_{\rm e}dS / \int\_{S} hdS \tag{1.6}$$

#### **References**


The opinions expressed in this chapter are those of the author(s) and do not necessarily reflect the views of the International Atomic Energy Agency, its Board of Directors, or the countries they represent.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 3.0 IGO License (https://creativecommons.org/licenses/by/3.0/igo/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the International Atomic Energy Agency, provide a link to the Creative Commons licence and indicate if changes were made.

The use of the International Atomic Energy Agency's name, and the use of the International Atomic Energy Agency's logo, shall be subject to a separate written licence agreement between the International Atomic Energy Agency and the user and is not authorized as part of this CC-IGO licence. Note that the link provided above includes additional terms and conditions of the licence.

The images or other third party material in this chapter are included in the chapter's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Chapter 2 How to Design a Be-7 Based Soil Distribution Study at the Field Scale: A Step-by-Step Approach**

**W. H. Blake, A. Taylor, A. Toloza and L. Mabit**

#### **2.1 Key Sample Sets and Associated Data**

A 7Be-based soil redistribution budget is based on several key datasets (Table 2.1) which have strict rules on collection locations and timings, depending on the time period of application. Overall, the methodological approach follows the principles of other FRN techniques (e.g. the 137Cs approach) but with necessary differences linked to the short half-life of 7Be and its delivery dynamics. The difference in delivery dynamics also provides the added advantage of opportunity for assumptions underpinning the approach to be tested in field and by laboratory experimentation (Taylor et al. 2014). As summarized in Table 2.1, some datasets are mandatory to convert measurement of 7Be inventory into soil redistribution amounts. Other datasets are advised under some circumstances to assist with data interpretation and improve the quality of soil distribution estimates. Fundamental considerations for the collection of all these datasets are outlined in the following section.

W. H. Blake (B)

A. Taylor

A. Toloza · L. Mabit

e-mail: A.Toloza@iaea.org

L. Mabit e-mail: L.Mabit@iaea.org

School of Geography, Earth and Environmental Sciences, University of Plymouth, Plymouth, UK e-mail: william.blake@plymouth.ac.uk

Consolidated Radioisotope Facility (CoRiF), University of Plymouth, Plymouth, UK e-mail: alex.taylor@plymouth.ac.uk

Soil and Water Management and Crop Nutrition Subprogramme, Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture, International Atomic Energy Agency, Vienna, Austria

<sup>©</sup> International Atomic Energy Agency (IAEA) 2019

L. Mabit and W. Blake (eds.), *Assessing Recent Soil Erosion Rates through the Use of Beryllium-7 (Be-7)*, https://doi.org/10.1007/978-3-030-10982-0\_2


#### **2.2 Reference Site Selection and Sampling**

As outlined in Chap. 1, 7Be inventory data are used to construct an FRN budget for the hillslope, to evaluate relative differences to the reference inventory, and this budget is subsequently converted into a soil redistribution budget (described in detail in Chap. 4). Accurate and representative determination of the reference inventory, and associated uncertainty is therefore a fundamental requirement since estimates of soil redistribution pattern and amount relies on this key value.

Reference sites serve two purposes in 7Be studies: (1) to determine a mean reference inventory (i.e. the areal activity of 7Be (Bq m−2) in the soil surface unaffected by erosion), and (2) to determine the depth distribution of 7Be in the undisturbed soil prior to erosion, to derive *h*0. The first requirement is based on collection of bulk soil cores, and the second on the collection of at least one sectioned core. Both need to be determined at a flat, stable location near the study plot, as for 137Cs studies, but it is essential that the land-use history of the location for the depth profile is exactly the same as the study plot. This is important as the *h*<sup>0</sup> value determined must be representative of the eroding soil surface. In practice, the best location for both these measures is a flat area that has been cultivated at the same time and in the same manner as the study plot (Fig. 2.1).

Sample designs for bulk cores need to account for potential FRN spatial variability within the reference site (Sutherland 1996; Mabit et al. 2012; Kirchner 2013) and also deliver sufficient mass of soil for sample analysis (Chap. 3). However, sample numbers are often constrained in 7Be tracing investigations owing to the short half-life

**Fig. 2.1** Experimental design to establish a hillslope 7Be budget over largely bare soil

and availability of sufficient gamma detection facilities. Considering this limitation, Taylor et al. (2013) recommend that all studies should state a reference inventory with suitable upper and lower limits (i.e. ±2σ) (Owens and Walling 1996) and this should be incorporated into subsequent soil redistribution estimates (Chap. 4). Spatial variability in inventory within a plot is most likely due to local redistribution of soil by rain splash and micro-topography and accumulation of rain-splashed particles in hollows. To capture such variability at any given reference site, it is recommended that each sample integrates several cores and then this process is replicated to provide a minimum of 10–15 spatially-integrated reference samples for analysis (Fig. 2.1). Bulk soil cores need to be taken to a consistent depth that is below the known depth penetration of 7Be in the study soil. Depth penetration is typically 20–30 mm (Blake et al. 1999; Doering et al. 2006; Sepulveda et al. 2008; Wallbrink and Murray 1996). In this regard, we strongly advise undertaking a preliminary investigation for trial depth-profile dataset at the study area to ensure the complete profile is captured whilst avoiding dilution of the sample by overestimating the profile depth. This will allow the researcher (1) to establish the maximum depth penetration of 7Be in the soil of the investigated area and (2) to use this depth to determine the maximum depth collection of the remaining bulk cores to be collected (e.g. 0–30 mm in the reference site). Any vegetation on the ground surface must be included in the sample as this will carry part of the recent 7Be inventory (Iurian et al. 2015). When collecting spatiallyintegrated cores, it is important that the total sum of the core areas that comprise one sample is recorded and that the depth penetration of all cores is consistent at 1 mm precision.

When characterising the 7Be depth profile, it is essential that section cores are sampled from a soil surface that has experienced the same cultivation practice as the study slope but in a location that has remained undisturbed by erosion or deposition processes. Variability due to rain splash, as noted above, can present challenges in selection of the appropriate position of the core. It is highly recommended that more than one section core is collected but this is often limited by gamma detector resource availability. An alternative is to collect 3 replicate section cores and combine the respective layers from each core into integrated samples to capture, but not to quantify, spatial variability within the flat, uneroded reference area. The recommended tool for standardized section core sample collection is the Fine Increment Soil Collector (FISC) (Mabit et al. 2014; Fig. 2.2) which is proven to collect high precision depth profile data suitable for supporting 7Be inventory conversion (Ryken et al. 2016).

It is also common practice to establish a rainfall collection and monitoring station at the reference site to permit assessment of the dynamic of 7Be delivery in relation to inventory development and its radioactive decay in the study area under investigation (Fig. 2.3). Sampling of reference cores through a time period also serves to benchmark and/or validate rainfall-based inventory assessment (Wallbrink and Murray 1994; Walling et al. 2009). The importance of this when applying the event scale PDM is to validate the stability of the reference site. With high resolution rainfall data and rainwater samples, we can use the modelled inventory as a benchmark for confidence in our choice of reference site. For this purpose, rainfall data need to be collected using a tipping bucket rain gauge (Fig. 2.4) that provides 15 or 30 min interval

**Fig. 2.2** Fine Increment Soil Collector (Mabit et al. 2014)

rainfall intensity data. Alongside rainfall monitoring, bulk rainfall samples need to be collected at a minimum of monthly intervals but preferably at event-scale intervals (depending on rainfall regime) and analysed for 7Be concentration (Bq L−1). Samples should be collected in pre-acidified polypropylene containers with an attached funnel for rainfall capture (Fig. 2.3) and 7Be extracted following protocols described by (Taylor et al. 2016); (see Appendix 2.1 for standard operating procedure).

A time series of the relative inventory at a study site (e.g. Fig. 2.3) can then be calculated as follows, where for each *daily time step*:

$$A(t) = A(t-1) \cdot \exp(-\lambda) + F(t) \tag{2.1}$$

where *A(t* − *1)* is the 7Be inventory of the previous day (Bq m−2), λ is the radioactive decay constant (daily time step) and *F(t)* is the fallout contribution of the current day. It is common practice to determine the start point either through collection of a suite of reference inventory cores (Walling et al. 2009) or to assume zero due to tillage of the soil surface and dilution of the 7Be signal within the soil profile. Table 2.2 shows a spreadsheet coding example to create a cumulative inventory dataset.

**Fig. 2.3** Example of reference inventory development and decay record based on rainfall sampling and analysis for 7Be alongside rainfall monitoring (Blake et al. 1999)

**Fig. 2.4** Examples of tipping bucket rain gauge (left) and rainfall sampler (right)

#### **2.3 Sample Design Options for Soil Redistribution**

The 7Be approach is most suited to erosion studies performed on bare soil surfaces (no vegetation) or with little vegetation cover. The method is limited to quantification of erosion by rain splash, sheet wash and shallow rill development since once rill incision goes beyond the depth of the 7Be depth profile, eroded soil is exported in the absence of the tracer signal. The selection of study site is very much dependent on the


**Table 2.2** Coding for Microsoft Excel spreadsheet to calculate cumulative inventory from rainfall data and rainwater 7Be activity concentration data

research question but, in any case, a basic pilot study will serve useful in determining the presence of a sufficient 7Be inventory in the region to make the approach viable and, as described above, to evaluate the typical depth penetration of 7Be to inform bulk core sample depth.

The 7Be approach may be applied at different spatial scales depending upon the questions being asked by land managers and the constraints imposed by the key assumptions discussed in Chap. 1. In this context, there are three main ways to design a soil core sampling strategy within the study hillslope: (1) sampling along transects from upper to lower slope (Schuller et al. 2006); (2) high resolution grid sampling (Walling et al. 1999; Blake et al. 1999); (3) spatially-integrated sampling within defined geomorphic landscape units (Wallbrink et al. 2002; Blake et al. 2009).

At the field scale, the single transect (Fig. 2.1) or a multi-transect sampling is the most straightforward and cost-effective approach in terms of field sample collection and laboratory processing work effort. Transects can, however, be limited in terms of spatial representativeness depending on local topography and research questions to be addressed. A high-resolution regular grid approach is effective for evaluation of spatial variability and will provide more representative information on soil export and sediment delivery ratio from a larger study area than transects. However, this approach is highly limited by the analytical demand of a large number of samples, which is hampered further by the short half-life of 7Be. The geomorphic landscape unit approach offers a compromise between the limited spatial representativeness of the transect approach and the analytical demands of the grid approach. However, it should be pointed out that multiple reference sites may be required in some geomorphic landscapes.

#### **2.4 Sampling for Particle Size Selectivity Correction**

Particle size selectivity during soil erosion processes is well-known (Bernard et al. 1992) and users of soil loss assessment or measurement approaches need to make a decision on the relevance of this specific process to their own study site. Taylor et al. (2014) describe how particle size selectively of soil erosion processes can be accounted for in the 7Be conversion model. Application of this method requires specific samples to be collected during or after the erosion event being studied.

Particle size correction requires representative samples of (1) uneroded soil, (2) mobilised soil and (3) deposited soil to be collected (Fig. 2.5). The first can simply be represented by the bulk cores collected for depth profile determination (i.e. in a non-eroding but cultivated site). The third requirement above can be represented by the samples collected to determine inventory in areas of sediment accumulation. The second, the characterisation of mobilised soil, requires more careful planning since after an erosion event, such material has either left the study site or been, in part, deposited at the foot slope. Taylor et al. (2014) propose that such material can be collected with Gerlach troughs installed in the study site or simple equivalent sediment trap systems. Alternatively, to avoid the need to install equipment prior to the event, a rainfall simulator could be used to mobilise material from a representative area, and the material captured for analysis. This needs to be done under rainfall conditions similar to the erosive event.

All samples collected need to be analysed for particle size distribution (Chap. 4).

# **2.5 Summary: Designing a Basic Small Scale 7Be Pilot Study Sampling Programme at the Plot Scale**

The procedures described in this chapter can be practised and developed within the context of a simple pilot study framework designed to test the viability of using 7Be as a tracer in any given landscape. A step-by-step approach is detailed below:

**Step 1**: Having located your study site and secured permission from the landowners for its investigation, collect 3 topsoil samples (20 mm depth) after significant rainfall (e.g. >sufficient rainfall to develop a measurable inventory for the study area over an extended time period) and analyse them for 7Be content to confirm if significant and measurable inventory of this radioisotope is present in the study area;

**Step 2**: Collect a trial section core to evaluate the depth penetration of 7Be in the study soil;

**Step 3**: Select the reference site in the study area and, if possible, the study plot location (prior to soil erosion taking place). Set up a rain gauge and, if required, rain sampling equipment. Note the timing of the last cultivation and, if this was some time prior to current time within which rainfall had occurred, collect a set of reference cores to establish the baseline (t - 0) inventory. Note this will be zero by default if plot study begins immediately after cultivation and mixing of existing 7Be inventory into the soil profile;

**Step 4**: After erosion has taken place within a target study plot (a) collect 10–15 spatially-integrated bulk reference cores from the non-eroding reference site to the depth of maximum 7Be penetration (e.g. 20–30 mm) following the information provided by the test core (in step 2), (b) collect up to 3 section cores from a flat, non-eroding area that has experienced the same cultivation practice as the study plot using the FISC and either analyse cores separately or combine layers to create a spatially integrated depth profile depending on analytical resource, (c) collect spatially-integrated cores along three transects within the study plot (Fig. 2.1) with 5–15 samples per transect depending on your analytical resource;

**Step 5**: Undertake necessary sampling for particle size correction if desired;

**Step 6**: Bring all recovered soil samples to laboratory (i) for preparation prior to gamma spectrometry (Chap. 3) measurements and, when necessary, (ii) for performing particle size distribution analysis by laser granulometry.

**Fig. 2.5** Schematic diagram of sampling protocol for including particle size selectivity in 7Be soil erosion study (uneroded soil **s**; mobilised soil **m**; deposited soil **d**)

#### **Glossary**


# **Appendix 2.1: Protocol for Extraction of 7Be from Rainwater**

According to Taylor et al. (2016), prior to deployment of rainfall collectors, 10 mL HCl (2.5 M) is added to each bottle to prevent adsorption of 7Be to vessel walls during the sampling period. Due care must be taken when handling acid in accordance with your institutions Health and Safety code. Collectors may be exposed for periods of between 3 and 35 days depending on the frequency and magnitude of rainfall. Generally, samples comprise fallout from a number of events across the sample period and are therefore, referred to as integrated samples. At the point of sampling, funnels should be rinsed with a known volume of HCl (1 M) and the bottles replaced with acid-cleaned bottles.

Each sample should be checked to ensure pH is < 2 and then filtered to remove any coarse debris (e.g. using Whatman grade number 41 filter papers). 7Be can then be pre-concentrated from solution by co-precipitation with MnO2 following the method detailed by Short et al. (2007).

1 mL of 0.2 M KMnO4 is added per litre of rainwater sample and the pH adjusted to 8–10 using concentrated NH4OH.

Once at the desired pH, 1 mL of 0.3 M MnCl2 is added to the sample whilst stirring. MnO2 precipitate is then allowed to settle for 24 h prior to removal by vacuum filtration using 0.45 μm cellulose nitrate filter paper.

Filter paper is then air dried, fixed with cellophane and sealed in a suitable container prior to analysis by gamma spectrometry. For each rainwater sample, duplicate 1 L subsamples should ideally be treated and the precipitate combined for filtration. Where rainfall samples are of low volume, a single 1 L sample may be treated. Samples should be considered to provide a representative sub-sample of rainfall for the period.

Repeatability can be tested by analysing triplicate subsamples separately and Relative Standard Deviation (RSD) between triplicates determined. This should typically be <10% (Taylor et al. 2016).

7Be recovery from solution using the coprecipitation method was tested by Taylor et al. (2016) by reprecipitating the filtrate from 3 samples. In each case, the 7Be activity in the filtrate was below Minimum Detectable Activity (MDA). MDA values for these samples were <10% of the total activity, suggesting that 7Be recovery using the above method is >90%, in agreement with Short et al. (2007).

#### **References**


The opinions expressed in this chapter are those of the author(s) and do not necessarily reflect the views of the International Atomic Energy Agency, its Board of Directors, or the countries they represent.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 3.0 IGO License (https://creativecommons.org/licenses/by/3.0/igo/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the International Atomic Energy Agency, provide a link to the Creative Commons licence and indicate if changes were made.

The use of the International Atomic Energy Agency's name, and the use of the International Atomic Energy Agency's logo, shall be subject to a separate written licence agreement between the International Atomic Energy Agency and the user and is not authorized as part of this CC-IGO licence. Note that the link provided above includes additional terms and conditions of the licence.

The images or other third party material in this chapter are included in the chapter's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Chapter 3 Measurement of Be-7 in Environmental Materials**

**A. R. Iurian and G. E. Millward**

#### **3.1 Overview of Digital Gamma Spectrometry Systems**

Gamma-ray spectrometry is the only 'routine' method for measuring the natural cosmogenic radionuclide 7Be. Activity concentrations (Bq kg−1) of 7Be are determined by analysing the 477.6 keV gamma energy emitted by the first excited state of 7Li (branching ratio 10.44%) (DDEP 2017) as it achieves the ground state. A typical gamma-spectrometric system consists of a semiconductor crystal detector, liquid nitrogen or mechanical cooling system, preamplifier, detector bias supply, linear amplifier, analogue-to-digital converter (ADC), multi-channel analyser (MCA) of the spectrum, and output data devices (ANSI 1999). An example of a typical gamma detector is given in Fig. 3.1.

High purity germanium (HPGe) detectors currently represent the most widely used gamma-detector systems. The semiconductor crystal is manufactured from ultrapure germanium (impurity level 109 atoms cm−3) in various shapes and in a range of sizes for a wide range of applications (Debertin and Helmer 1988). The specification of a HPGe detector is defined by *(i) the energy resolution, (ii) the detection efficiency* and *(iii) the peak*-*to*-*Compton ratio* (see Glossary). When purchasing a HPGe semiconductor detector, these key parameters need to be considered together with the detector material and configuration, detector volume, window material and its thickness. Excepting the ultra-low energy configurations, all detector types commercially available are suitable for the measurement of 7Be activity concentrations.

A. R. Iurian (B)

G. E. Millward

Terrestrial Environment Laboratory, IAEA Laboratories Seibersdorf, Seibersdorf, Austria e-mail: A.Iurian@iaea.org

Consolidated Radioisotope Facility (CoRiF), University of Plymouth, Plymouth, UK e-mail: G.Millward@plymouth.ac.uk

<sup>©</sup> International Atomic Energy Agency (IAEA) 2019

L. Mabit and W. Blake (eds.), *Assessing Recent Soil Erosion Rates through the Use of Beryllium-7 (Be-7)*, https://doi.org/10.1007/978-3-030-10982-0\_3

**Fig. 3.1 a** Example of a HPGe gamma detector showing the detector head, the cartridge containing electronic management system and the dip-stick which is immersed in liquid nitrogen to cool down the detector to 77 K; **b** the detector encased in a lead shield with the dip stick immersed in a liquid nitrogen tank. *NB: The liquid nitrogen tank should be filled on a regular basis (every 7*–*10 days) to maintain a fully operational detector*

#### **3.2 Preparation of Samples**

#### *3.2.1 Sample Management*

A fundamental consideration for the analyst when managing a set of soil, sediment or rainwater samples is the relatively short half-life of 7Be and its low activity in the majority of environmental materials. It is important, therefore, that the laboratory is well organised and ready to process the samples for 7Be analysis as soon as possible after collection so that a relatively high emission of gamma rays can be taken advantage of. Additionally, maintenance of a high standard of cleanliness in order to prevent contamination of the detector end cap or potential inter-contamination between samples should be prioritized.

#### *3.2.2 Soil Samples*

Samples of soil will normally consist of a range of particle sizes. Gamma spectrometric analysis of fallout radionuclides (FRN) in bulk soils should typically be performed on dried, homogenised material that has been sieved to less than 2 mm (Pennock and Appleby 2002) noting that some applications may require sieving to a smaller particle size. Typically, soil samples are oven-dried at 105 °C until a constant weight is reached (commonly for 24 h). A practical alternative is sample freeze-drying, which disaggregates the solids and makes subsequent sample processing more effective. Furthermore, oven-dried samples are disaggregated using a mortar and pestle and size fractionation of the dried solid can then be carried out on the ground sample using a metal or plastic sieve with a defined mesh size. Appendix 3.1 summarises the sample preparation and the associated packing protocol.

#### *3.2.3 Samples of Rainwater*

Samples of rainwater from the study site are required to assess the atmospheric deposition flux of 7Be during a period, encompassing the sampling campaign (see Chap. 2). The protocol for extraction of 7Be from rainwater is presented in Appendix 2.1. 7Be can be pre-concentrated from solution by co-precipitation with MnO2 following the method detailed by Short et al. (2007). The precipitate is recovered on glass fibre filters which are placed in a Petri dish of suitable diameter and allowed to dry before counting on an HPGe gamma detector.

#### *3.2.4 Sample Geometry*

Subsequent to physical processing samples, for analysis, can have masses in the range from a few grams to several kilograms, according to the aims of the project and its sample collection requirements. There are a range of measurement geometries, from Marinelli beakers (0.25–1 L) to small vials (~5 cm3) capable of holding a wide range of solid weights (from about 3 g of material to 4 kg) (Fig. 3.2). The choice of the container geometry for 7Be analysis depends on the matrix and on the available amount of material. It is essential that the weights of both empty and filled sample holders are registered on a calibrated laboratory balance to at least 2 decimal places (or at least 4 decimal places for volume calibration standards).

**Fig. 3.2** Several examples of containers used to perform gamma spectrometric analysis of solid phases. From left to right: 1 L Marinelli beaker; 300 mL Marinelli beaker; 90 mm diameter plastic Petri dish; 50 mm diameter Petri dish; 4 mL plastic vial (commonly used for conducting analysis using well detectors). To comply with laboratory safety, the radioactive standards are bound in red tape

Prior to purchasing any sample/standard container (especially for Marinelli beaker geometries), the analyst should determine the diameter of the detector end cap so that the container with an appropriate internal diameter will fit as close as possible on the detector end cap. For cylindrical and vial containers, it is recommended to place the samples on a holder (e.g. of light polycarbonate matrix) to assure the reproducibility of the sample-detector arrangement for all samples, including the measurement of the standard. The use of such holders will prevent contamination of the detector end cap, which can be further protected with a thin sheet of cling film or, in the case of well detectors, the sample vial covered in film. Care should be also taken to ensure that the sample/standard container external surface is free of particulate matter.

It is recommended that the geometries of the standard and the soil samples are identical; any differences between them, such as in the sample filling height (e.g. because of insufficient sample amount) or in soil chemical composition, will imply the need for geometry corrections (see Glossary). It is important to note that if the containers are being re-used, the analyst needs to carry out acid cleaning and drying procedures before refilling them. The packing date, nominal weight and an identification code should be indicated on each sample container after packing. As regards filter-mounted samples, these should be measured after placing them in cylindrical Petri dishes of appropriate diameter. Similar contamination precautions are to be taken for the filter geometry as for the other container types discussed above.

#### **3.3 Calibration Approaches**

An accurate and precise calibration of a gamma detector is essential for high quality results in the determination of 7Be activity concentrations. The calibration of a gamma spectrometric system involves two major steps:


Energy calibration is commonly performed using point sources (e.g. 152Eu, 137Cs) or multinuclide standards covering the energy range of interest (Fig. 3.3). The construction of the full energy peak efficiency curve is performed following (1) a *semi*-*empirical approach* (based on measurement of standard point sources or multinuclide standard sources of soil or liquid matrix), or (2) *Monte Carlo methods* (using a detailed description of the detector and the source). In both cases, the efficiency calibration procedure involves (1) true photopeak efficiency determination for the gamma energies of the radionuclides included in the certified standard source, and (2) the construction of the efficiency curve (within a range of energies given by the radionuclides present in the source) by polynomial fitting. Discrepancies between simulated (Monte Carlo) and experimental efficiency values should be determined and included as an uncertainty component in the uncertainty budget of the 7Be activity value. Note that different detectors and different system-sample configurations will result in different values of the true photopeak efficiencies, which should finally produce the same result of the radionuclide activity value for the actual sample. Coincidence summing corrections should be performed for relevant nuclides present in the calibration source and decaying through a cascade of successive photon emissions (e.g. 60Co, 88Y, 139Ce). These can be determined through general or dedicated codes (Vidmar et al. 2010). Coincidence summing correction factors depend on the nuclide decay scheme, sample geometry and composition, and on detector parameters. The factor is equal to unity in cases where the radionuclide has no cascade of gamma-rays.

#### *3.3.1 Semi-empirical Calibration Method*

For routine environmental sample analyses, efficiency calibration of gamma detectors can be performed using (a) multiple standard point sources or standard volume sources of mixed radionuclides (for soils measurements), or (b) filters spiked with standard solution (for 7Be precipitate analysis). Considering the short half-life of 7Be, standard sources containing 7Be are not commercially available. When purchasing a standard for efficiency calibration, it is essential that these should carry a certificate of calibration from a metrological labora-

**Fig. 3.3** Print screen capture of the gamma detector energy calibration performed using a multiradionuclide standard and the GammaVision commercial software. Note the interpolated 477.6 keV gamma energy of 7Be between 391.7 keV (113Sn) and 661.7 (137Cs). The upper box is the energy table; the middle box is a plot of the gamma-ray energy against the channel number; the lower box shows the 7Be peak

tory accredited for the preparation of standards. An appropriate calibration standard should have low overall uncertainties of each radionuclide in the source (up to 2–3%), as this uncertainty is further propagated into the uncertainty of 7Be activity. The analyst should be aware that specific international regulations apply for the import of radioactive sources. After purchasing, the calibration standard solution (commonly delivered in sealed glass vial) must be gravimetrically diluted for subsequent use. Furthermore, the analyst shall choose how to use the diluted standard solution for the detector efficiency calibration. Bear in mind that special safety procedures and authorisations apply to the laboratories handling radioactive sources as regards to the risk of radioactive contamination. Appendix 3.2 details a recommended step-by-step approach for the preparation of a multi-nuclide calibration standard of soil matrix.

An example of a multi-nuclide standard solution suitable for 7Be measurements will comprise artificial radionuclides such as 241Am, 109Cd, 57Co, 139Ce, 203Hg, 113Sn, 85Sr, 137Cs, 60Co and 88Y, with energy lines from 59 to 1836 keV. Such multi-nuclide standard can be used to calibrate gamma detectors for efficiency in the vicinity of the gamma emission from 7Be (477.6 keV) which lies between that of 113Sn at 391.7 keV, 85Sr at 514.0 keV (difficult to determine accurately due to the overlapping with the 511 keV annihilation peak) and 137Cs at 661.7 keV (DDEP 2017), as presented in Fig. 3.4. A disadvantage in the short half-lives of some nuclides (e.g. 203Hg, 113Sn)

**Fig. 3.4** The efficiency calibration curve of a HPGe detector using a multi-nuclide standard solution containing 10 artificial radionuclides (plotted in Microsoft Excel spreadsheet). Note the 7Be gamma emission is interpolated between the gamma energies of 113Sn and 85Sr. After the decay of shortlived radionuclides i.e. 85Sr, 113Sn and 203Hg, the closest lower energy for interpolation will be 139Ce. An interpolation of 7Be energy between 139Ce and 137Cs will led to an increased efficiency value for 7Be

present in the standard must be recognized, thus making the source useful over the whole spectra region only for a short period of time (i.e. a few months).

#### (i) *Preparation of a secondary soil calibration standard*

A soil sample should be collected, preferably from an area where fallout radionuclides are minimal (e.g. subsoil) and prepared as in Sect. 3.2.2. The detection and quantification of the background gamma radiation in the soil sample is required. Then the prepared soil fraction below 2 mm particle size is spiked with an aliquot of the liquid standard. It is highly important to ensure that the soil-liquid standard mixing is complete, ensuring the spiked material is homogeneous (see step-by-step instruction in Appendix 3.2). The spiked soil is dried and an appropriate sample holder (selected from those in Fig. 3.2), with a similar geometry to the samples, is then selected and filled with the dried spiked soil. The secondary soil standard can then be used to calibrate the detector for efficiency (Fig. 3.5). If there are differences in geometry (different containers and/or filling height) and/or matrix (e.g. different chemical composition) between the soil samples and the calibration source, an efficiency transfer factor should be determined to correct this difference, as ratio between the efficiency of the sample and the efficiency of the standard.

#### (ii) *Preparation of a secondary liquid calibration standard*

**Fig. 3.5** Print screen capture of the gamma detector efficiency calibration performed using a multinuclide standard and the GammaVision commercial software. The upper box is the energy table; the middle box is a plot of the efficiencies against the gamma-ray energies; the lower box shows the 7Be peak

In this case, the liquid standard commonly purchased in a glass vial is diluted following the steps in Appendix 3.2, and further poured in different geometries and used as a secondary liquid standard. In this case, the efficiency transfer factor needs to be considered for 7Be activity calculation in soil samples, to account for the difference in matrix between the calibration source and the sample (regardless the sample filling height).

#### (iii) *Preparation of a secondary filter standard*

A secondary filter standard can be obtained by spiking a filter paper in similar size with the sample (e.g. Whatman filter) with a known content standard solution. This is achieved using a calibrated automatic pipette that is used to add the standard solution dropwise onto the filter. Here the analyst must take care to ensure a homogenous distribution of the standard solution on the filter so that the calibration is coherent with the distribution of precipitate on the sample filter. The spiked filter should then be air-dried prior to sealing in a plastic Petri dish of appropriate diameter.

#### *3.3.2 Monte Carlo Approach*

The advanced user may prefer to use Monte-Carlo coding to construct the efficiency curve for a certain sample holder without the need of a certified standard solution. Monte Carlo approaches for automatic efficiency calibration (e.g. LabSOCS—Laboratory SOurceless Calibration Software) (Bronson and Wang 1996) are commonly integrated into some commercial software of gamma detectors. These codes include several options for detector type and configuration, sample shape and volume (e.g. point, disc, and cylinder), sample/source matrix, source-to-detector distance and for the type of fit used to describe the efficiency-energy dependency (linear, quadratic, polynomial) (Jovanovic et al. 1997; Bronson and Wang 1996). For each particular sample, the analyst needs to create a specific sample geometry based on the holder dimensions (diameter and wall thickness), sample filling height, chemical composition of the sample matrix and density. It is also important for the analyst to know the precise details of the technical characteristics of the gamma detector or to obtain a 'characterisation file' of the detector from its manufacturer in order to run the codes. However, no programming knowledge is necessary to use the available commercial codes. The efficiencies generated for a specific sample can be saved and stored by the analysis software and used to automatically derive the radionuclide activity without performing an experimental calibration. However, the experimentally obtained efficiencies can be as well included in the analysis software, in case these data are available.

The automatic calibration by the Monte Carlo approach eliminates the cost of purchasing, tracking, and disposing of radioactive standards. However, the analytical results still need to be validated using certified reference materials in similar matrices. The main constraints in the application of Monte Carlo approaches are related to uncertainties of the detector configuration (e.g. shape and size of the effective crystal volume, photons and electron interaction probability and angular distributions) and measurement traceability to primary standards.

# **3.4 Data Handling and 7Be Analysis**

Analyses of 7Be can be challenging because of low activity concentrations and, therefore, high counting uncertainties. Sample measurements are completed after performing the energy and efficiency calibrations. Data evaluation is commonly realised using specialised gamma software, provided by the detector manufacturer or made 'in-house'. Prior to spectrum analysis, 7Be nuclear data (gamma energy, half-life and emission probability) should be included in the software library. The stability of the spectrometer should be checked during the measurement and during routine quality assurance procedures. Despite the apparent simplicity of gammaray measurements, bear in mind that there are a number of correction factors to the spectrum counting data that must be considered for the determination of 7Be activity concentration e.g. decay correction to the sampling date, efficiency transfer factor, background correction, instrument dead time correction (IAEA 2004), while a correction for soil moisture content is applied to the dried soil sample mass.

A flow chart of 7Be measurement by gamma-ray spectrometry is presented in Fig. 3.6. Sample counting times need to be long enough (typically between 86,000

**Fig. 3.6** Schematic protocol for 7Be analysis by gamma-ray spectrometry (MDA - Minimum Detectable Activity)

and 259,000 s) to meet laboratory standard statistical uncertainty of the measurement result (commonly between 10 and 30% for 7Be in environmental samples).

Based on the information provided in the library, the instrument-specific gamma evaluation software will identify the 7Be peak and analyse the number of counts within its peak area (Fig. 3.7). Furthermore, following default automated sequences; the software is able to report the activity concentration (Bq kg−1), combined standard uncertainty and minimum detectable activity of the radionuclide found by the peaksearch routine (Debertin and Helmer 1988). However, to achieve reliable results using the library approach, any shift effect in the spectrum should be corrected and energy calibration should be precise enough to achieve no more than one or two channels deviation between 7Be reference energy and the one calculated from the calibration curve (IAEA 2002).

**Fig. 3.7** Print screen capture of a gamma spectrum registered with the GammaVision commercial software and showing the 7Be peak at 477.56 keV and its net area and gross/net count rate (peak data box), measurement starting time and live time (upper right part of the screen)

Measurement results are commonly reported with associated combined uncertainty at the 95% confidence level (JCGM 2008). For detailed information on the determination of each uncertainty component, readers can refer to Lépy et al. (2015). The detection limit (LD) provides the detection capabilities of a measurement system.

#### *3.4.1 Quality Assurance*

In routine laboratory practice, it is necessary to validate the measurement results for certain working conditions. Both internal and external validation methods are an important part of 'good laboratory practice' and also a requirement of ISO/IEC 17025 for 'in-house' methods (ISO/IEC 17043 2010; ISO/IEC 17025 2017). The internal validation procedure can be employed using distinctive approaches:


Note that because of its short half-life, there are no reference materials available which contain 7Be. However, it is a common practice to check the accuracy of the laboratory procedure for radionuclides emitting gamma rays in the vicinity of 7Be energy (e.g. 137Cs) in samples of similar matrix and geometry.

In addition, external validation can be achieved through: (i) inter-laboratory comparison exercises and/or (ii) participation in international proficiency tests for radionuclide determination in soil and water samples such as the ones organized regularly by IAEA and its Member States.

#### **Glossary**


<sup>1</sup>Debertin and Helmer (1988).

<sup>2</sup>Knoll (2000).


#### **Appendix 3.1: Soil Sample Preparation Prior to Gamma Analysis**


<sup>3</sup>ANSI (1999).

<sup>4</sup>ISO 11929 (2010).


#### **Appendix 3.2: Preparation of a Secondary Soil Calibration Standard**

#### (A) *Opening and Diluting the Mixed Traceable Standard Solution*


#### (B) *Dosing a Soil Sample with the Mixed Standard Solution*


achieve <1% uncertainty of the counting statistics of the peaks of interest within a reasonable counting time when measuring the calibration standard.


For safety, any particle transfer process should be completed in a fume hood and the operator should be protected with a mask.


#### **References**


ISO/IEC 17043. (2010). *Conformity assessment - General requirements for proficiency testing*.


Knoll, G. F. (2000). *Radiation detection and measurement* (3rd ed., 802 p). Wiley.


The opinions expressed in this chapter are those of the author(s) and do not necessarily reflect the views of the International Atomic Energy Agency, its Board of Directors, or the countries they represent.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 3.0 IGO License (https://creativecommons.org/licenses/by/3.0/igo/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the International Atomic Energy Agency, provide a link to the Creative Commons licence and indicate if changes were made.

The use of the International Atomic Energy Agency's name, and the use of the International Atomic Energy Agency's logo, shall be subject to a separate written licence agreement between the International Atomic Energy Agency and the user and is not authorized as part of this CC-IGO licence. Note that the link provided above includes additional terms and conditions of the licence.

The images or other third party material in this chapter are included in the chapter's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Chapter 4 Conversion of Be-7 Activity Concentrations into Soil and Sediment Redistribution Amounts**

**W. H. Blake, A. Taylor, A. R. Iurian, G. E. Millward and L. Mabit**

### **4.1 Implementing the Event-Scale Profile Distribution Model**

The Profile DistributionModel (PDM) is described in detail byWalling and He (1999) and Blake et al. (1999). Here, alongside an overview of the basic components, we provide step-by-step guidance to its implementation and simple encoding within Microsoft Excel.

This simple conversion model relies on exponential decline in 7Be activity concentration with depth wherein the shape of the profile is described by *h*<sup>0</sup> (See Chap. 1, Sect. 1.2). A first necessary step is to establish a specific *h*<sup>0</sup> value for the site under investigation. This can be achieved by plotting the depth profile from your reference area as an x–y plot and fitting an exponential function (see Table 4.1 and Fig. 4.1).

W. H. Blake (B)

G. E. Millward e-mail: G.Millward@plymouth.ac.uk

A. R. Iurian

L. Mabit

Soil and Water Management and Crop Nutrition Subprogramme, Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture, International Atomic Energy Agency, Vienna, Austria e-mail: L.Mabit@iaea.org

© International Atomic Energy Agency (IAEA) 2019

School of Geography, Earth and Environmental Sciences, University of Plymouth, Plymouth, UK e-mail: william.blake@plymouth.ac.uk

A. Taylor · G. E. Millward Consolidated Radioisotope Facility (CoRiF), University of Plymouth, Plymouth, UK e-mail: alex.taylor@plymouth.ac.uk

Terrestrial Environment Laboratory, IAEA Laboratories Seibersdorf, Seibersdorf, Austria e-mail: A.Iurian@iaea.org

L. Mabit and W. Blake (eds.), *Assessing Recent Soil Erosion Rates through the Use of Beryllium-7 (Be-7)*, https://doi.org/10.1007/978-3-030-10982-0\_4


**Table 4.1** Example of the depth profile data used in Fig. 4.1 where the 7Be concentrations have been determined with a 2-sigma error

aAnalytical uncertainty

**Fig. 4.1** 7Be activity concentration against mass depth with a fitted exponential line to derive the value of h0

It is important that measures of depth are represented as mass depth i.e. mass of soil for the core slice divided by the area of the core with units of kg m−2. This accounts for changes in bulk density and is a more precise measure of depth than true depth. *h*<sup>0</sup> is derived by taking the reciprocal of the exponent of the line. In the case of the depth profile shown in Fig. 4.1, *h*<sup>0</sup> is derived from:

$$\frac{1}{0.133} = 7.5 \text{(kg m}^{-2}\text{)}$$

**Table 4.2** An example grid cell layout with example inventory data (±is analytical uncertainty) where coding presented in Table 4.3 is required to determine *h*, *Cd* and *h* (see Chap. 1, Appendix 1.1), without particle size correction. Calculated values following Table 4.3 are shown in italics


To run the PDM in Excel, the key components of the model can be coded into a cell grid as illustrated in Table 4.2. In this example, the reference inventory value is set at 524 ± 46 Bq m−<sup>2</sup> (n - 15 where uncertainty represents 2 standard deviations). The sample points 1–10 are erosional (i.e. an inventory deficit as compared to the activity recorded in the reference area) and sample points 11 and 12 are depositional (i.e. an inventory excess as compared to the activity recorded in the reference area).

Coding required for columns D, E, F and G to calculate *h*, *Cd* and *h* respectively (see Chap. 1, Appendix 1.1 for relevant model equations) is provided in Table 4.3.

The PDM may also be applied using a specific Microsoft Excel Addin—developed byWalling and He (1999) and refined byWalling et al. (2002)—which is available at the IAEA website (see http://www-naweb.iaea.org/nafa/swmn/modelstool-kits.html).

#### **4.2 Accounting for Size Selectivity of Erosion and Deposition Processes in the Profile Distribution Model**

As pointed out in the Sect. 2.4 of the Chap. 2, some advanced users will need to account for particle size selectivity associated with soil erosion processes to convert inventory loss into soil erosion amounts. Different approaches are described in the literature (see Taylor et al. 2014 or Yang et al. 2013). Here, we describe the method


**Table 4.3** Coding for columns D, E, F and G in Table 4.2 to derive the key elements of the PDM as described in Sect. 1.2

proposed by Taylor et al. (2014) and compare to other methods so users can make an informed decision about which approach to take.

The PDM assumes that the soil profile is top-sliced by erosion and that loss of inventory is directly related to the mass depth of soil lost (see Fig. 1.3). However, enrichment of 7Be in fine soil fractions (Fig. 4.2) means that these can be preferentially removed by erosion processes resulting in an augmented inventory deficit relative to erosion amount (Blake et al. 2009; Taylor et al. 2014). It should be noted that in some cases where soil has an overall fine texture and rainfall is of high magnitude, particle size correction may be less important (e.g. Porto and Walling 2014)

The approach suggested by Taylor et al. (2014) accounting for particle size selectivity follows the principles of the method proposed by He and Walling (1996) wherein particle size correction factors P and P for eroding and depositional sites respectively are calculated based on measurements of 'geometric' Specific Surface Area (SSA unit in m<sup>2</sup> g−1). P is derived from:

where *Sm* is the mean SSA of the mobilised fraction and *Ss* is the mean SSA of the bulk soil material and *v* is a constant describing the relationship (i.e. the power function exponent) between 7Be concentration and SSA (Fig. 4.2).

*Ss*

*P* is derived from:

$$P' = \left(\frac{S\_d}{S\_m}\right)^v \tag{4.2}$$

where *Sd* is the mean SSA of the deposited material.

The SSA of soil and sediment samples is most commonly performed using laser granulometry. It is also possible to derive SSA from particle size data derived by gravitational sedimentation methods, most commonly the pipette method (Day 1965).

It is important at this stage to consider that amounts of erosion estimated using a conversion model consider *inventory deficit* i.e. the amount of 7Be inventory lost from a specific area due to soil erosion. This inventory deficit is converted to mass depth soil loss using the exponential shape of the 7Be distribution in the soil profile (Eq. 1.1). In this context, Taylor et al. (2014) propose that when correcting erosion rates (mass depth lost, kg m−2) for particle size enrichment it is, therefore, necessary to apply the correction factor to the *inventory deficit* only (i.e. *A* minus *Aref* ) which has the effect of suppressing the loss in inventory according to the particle size of the fraction mobilised. If fine sediment is preferentially mobilised by erosion processes, failure to account for this will lead to overestimation of erosion.

In the case of the above, following the principles of He et al. (2002), a particle-size corrected erosion rate, *hc*, can be calculated using the following equation (compare to Eq. 1.2):

$$h\_c = h\_0 \ln \frac{A\_{ref}}{A\_{ref} - \left(A\_{ref} - A\right)/P} \tag{4.3}$$

For estimates of deposition, the 7Be concentration of deposited material needs to be adjusted according to the particle size of the deposited fraction relative to the eroded fraction. The equation to provide corrected deposition rates, *h <sup>c</sup>*, is (compare to Eq. 1.4):

$$h\_c' = \left(A - A\_{ref}\right) / C\_{d,c} \tag{4.4}$$

where *Cd,c* is the weighted mean concentration of sediment mobilised from the upslope contributing area (Blake et al. 1999; Walling et al. 1999) which has been corrected for particle size enrichment during erosion, and then corrected for depletion during deposition (He et al. 2002). The particle size corrected concentration of deposited material from an individual eroding point (*cd* ) can be estimated using the following function:

$$cd' = P'P'A\_{ref} \left(1 - e^{-h/h\_0}\right) / h \tag{4.5}$$

These data processing requirements need to be considered in the context of the sampling challenges detailed in Chap. 2.

The above equations can be used to modify the Excel-based PDM model coding provided in Table 4.3.

There are several challenges with particle size correction that all users must be aware of. Determining the relationship between the activity concentration and SSA to gain the value of the exponent, *v,* in Eqs. (4.1) and (4.2), requires particle size separation experiments (Taylor et al. 2014) and use of a laser granulometer or quantitative sieving (and application of SSA theory which makes assumptions about particle sphericity). Sampling for Ss and Sd is relatively straightforward (sampled in field from stable and deposition sites) but sampling for Sm is less straightforward. Options for this include rainfall simulation experiments on the hillslope after the erosion event to collect representative eroded material, installation of Gerlach troughs in study field prior to anticipated erosion events or estimating SSA of eroded material from remaining soil-and comparison with uneroded material (see Yang et al. 2013)

All particle size corrections require a necessary simplification of reality since soil characteristics are highly variable within and between sites. Example data illustrating the influence of particle size correction approaches on soil erosion estimate results are given in Sect. 4.4.

#### **4.3 Extended Time Series Conversion Model: The Theory**

If an advanced user wishes to apply the 7Be approach over a longer time period, for example over a wet season that contains notable erosional events in series, an alternative approach is required (Walling et al. 2009). Modifications to the PDM approach are required to account for inventory flux (Bq m−2), decay and the erosivity of events.

Failure to account for these factors has been shown to lead to underestimation of redistribution rates (Walling et al. 2009). In this approach, the cumulative change in inventory at the sample site is considered rather than a direct comparison to the stable reference value for each day. A reference inventory for the field site is required, however, to provide an indication of erosion or deposition at each individual sample location.

The basic principle of the extended time-series model is that the amount of erosion estimated by 7Be inventory deficit and deposition estimated by 7Be inventory excess needs to be apportioned across the time period of study while allowing for the effects of radioactive decay. The problem of the PDM over extended time periods is considered by Walling et al. (2009) for a hypothetical scenario where: (1) the reference inventory begins at zero due to extended dry period, (2) a single rainfall event of same intensity takes place each week with same erosivity, (3) *h0* remains the same. The results (Fig. 4.3) demonstrate that the 7Be approach increasingly underestimates the erosion rate with substantial error as time progresses into the study period (e.g. 30% after 2–3 weeks; 50% after 3 months). In addition to this issue of decay of the earlier erosion event signals, there are other potential complications linked to temporal distribution of 7Be during the study period, temporal distribution of erosion (rainfall erosivity), potential variability of other key parameters through time, especially on freshly ploughed surface, e.g. *h*0.

In this context, every user needs to consider the sensitivity of their study data to these issues and either take action or acknowledge these limitations and the uncertainty introduced into their results.

In this section we present a step-by-step approach to implementing the extended time series model in Microsoft Excel based on Walling et al. (2009). There are three main components: (1) calculating relative erosivity of rainfall, (2) estimating soil loss and (3) estimating deposition.

The aim of the extended time series model is to allow 7Be measurements to be extended over a longer timeframe that is more representative for some environments for example where erosion takes place over a prolonged wet season.

In addition to the evidence collected for the PDM, the extended time series model requires a reconstructed record of daily fallout deposition (Bq m−<sup>2</sup> d−1) for the whole study period and a time series of daily (where appropriate) relative erosivity (see below). Together, these account for the effects of time variant erosion and the time variant fallout as well as for the radioactive decay.

The first step in applying the model is the same as for the PDM (Sect. 4.1) namely to determine whether the site is erosional or depositional i.e. compare inventory at erosional point (*A*) or depositional point (*A* ) to reference inventory *Aref* .

The second step is to build a mass balance model framework used to define the 7Be inventory at the end of each day *A(t)* (Bq m−2). This is determined from: (i) the 7Be inventory of the previous day *[A(t* − *1)]*, (ii) effects of radioactive decay [λ], (iii) any fallout input (that day [*F(t)*], (iv) any loss in 7Be inventory due to erosion [*Aloss*]. Of course, the mass balance must ultimately be solved for the latter element. These components are linked together as follows:

$$A(t) = A(t-1)\exp(-\lambda) + F(t) - A\_{loss}(t)\tag{4.6}$$

A*loss* (t) in Eq. (4.6) will reflect (i) amount of soil eroded [*R(t)*] as a mass depth i.e. kg m−2, (ii) existing inventory at the point [*A(t)*], and (iii) depth distribution of inventory i.e. *h0* (for that day) i.e.:

$$A\_{loss}(t) = \left[A(t-1)\exp(-\lambda) + F(t)\right] \ast \left[1 - \exp\left(-\frac{R(t)}{h\_0(t)}\right)\right] \qquad (4.7)$$

In the prior equations, the amount of soil eroded *R(t)* is assumed to be proportional to the rainfall erosivity for that daily time-step and can be expressed as following:

$$R(t) = E\_r(t) \* C\tag{4.8}$$

In Eq. (4.8), *C* is a constant that links relative erosivity (i.e. Er) to erosion amount. The value of *C* differs between sample points but at any one sample point it remains constant through the study period.

To derive *C* and hence *R(t)*, the user must establish a continuous mass balance for the study period for each sampling point experiencing erosion. Guidance on setting this up in Microsoft Excel is given in the next section. The value of *A(t)* at the end of the study can then be related to the measured inventory (*A*) at the time of sampling. Note the value at the start is equal to the measured reference inventory at the beginning of the study (often zero due to cultivation of extended dry period). Given all the data that have been derived up to this point, the mass balance can be solved for *C* using the optimising Solver routine in Microsoft Excel. This so called 'what-if analysis' tool basically finds the optimum value of C to explain the measured inventory within the constraints of the mass balance detailed in the worksheet.

Application of *C* to the *Er(t)* values in the time series then gives the estimated erosion amount for the sample point. An example of spreadsheet coding is given in Sect. 4.4.

As noted above, in the extended time-series model, a key part of the process is using rainfall erosivity to apportion erosion potential across the study period. For the study period in question, a measure of relative erosivity is required for each event occurring during the study period.

Arguably, we need knowledge of site specific thresholds for erosion initiation based on rainfall patterns and dynamics and site-specific conditions need consideration e.g. runoff initiation processes. Walling et al. (2009) used high resolution rainfall data (minimum 30 min interval data) to evaluate temporal distribution of erosivity (*Er*). This approach is linked to RUSLE daily values of erosivity based on the product of the total kinetic energy of rainfall (*E*) and maximum 30 min rainfall intensity (*I*30) i.e. *EI*30. This means a continuous rainfall record at study site is required (30 min totals). It should be noted that a measure of relative erosivity in this context is more important than an absolute value. Local empirical data, if available, may be more appropriate at some sites. Taylor (2012) followed procedures outlined by Yin et al. (2007) and Morgan (2001) to derive *EI*<sup>30</sup> following Schuller et al. (2010).

#### **4.4 Implementing the Extended Time Series Model**

The extended time series model can be implemented in a variety of ways. We propose here one version for coding inMicrosoft Excel as an example to develop from. Such an approach permits the user to see the model working step-by-step and to troubleshoot any coding errors or data anomalies that emerge.

The model structure comprises a series of columns that represent the time series of daily fallout, erosion etc. (Table 4.4) and a set of 'model interface' cells where primary data is inputted and results are calculated.

To permit cell O7 to show the most likely erosion rate, the Solver Routine must be run. This requires the actual measured inventory at the sample point to be entered into the Solver dialogue box (Fig. 4.4) and the routine run so the value of O5 is adjusted to equal the measured inventory. The routine does this by adjusting the unknown constant C until the value of O7 is equal to the inventory measured.

The extended time series model is an appropriate approach to address the challenge of using 7Be across multiple rainfall events. In addition to the requirements of the PDM, it requires rainfall data and site-specific determination of relative erosivity. Implementation of this advanced model requires careful coding and usage of data. Users need to be aware of specific sample point attributes and relationships to other points and to ensure that each working step is traceable in case of a need to revisit data.


**Table 4.4** Microsoft Excel coding for time series and mass balance columns. It is assumed user has a basic knowledge of Microsoft Excel and that the column headings are entered in the first row

4 Conversion of Be-7 Activity Concentrations into Soil … 55


**Fig. 4.4** Dialogue box for Miscrosoft Excel Solver command set up to work with the user interface cells in Table 4.5. Note where the value of the measured inventory needs to be entered

#### **4.5 Hillslope Sediment Budget Examples and Inclusion of Uncertainty**

The data presented in Table 4.2 can be used to check model coding by comparing model outputs derived with this dataset to the results presented in Table 4.6. It is important to note that Table 4.6 is provided for checking of the central result only and does not include an uncertainty. It is critical that users report their soil erosion estimates with an appropriate uncertainty and that the means by which the uncertainty has been determined is transparent to the reader of reports and subsequent publications.

Uncertainty can be derived from a range of different factors within the sampling and analysis process (Fig. 4.5). The most obvious source of uncertainty is the analytical error originating from the gamma spectrometry measurement (see Chap. 3) which can easily be propagated through to the resulting soil erosion estimate. This is, however, arguably less environmentally relevant than other factors. An alternative

**Table 4.5** Microsoft Excel coding for user interface cells (linked to cells described in Table 4.4). Note that until the Microsoft Excel Solver is run using the coding provided below, the numbers in the results cell are arbitrary. Using the 'Solver' command the modelled inventory can be fitted to the measured inventory to allow cell O5 to equal the sample point inventory by changing the constant. Values of *h*<sup>0</sup> and particle size correction can be changed manually in cells O3-4 for scenario testing


**Table 4.6** Model output data using the demonstration dataset in Table 4.2 (where *P* - 1.61 and *P'* -0.82)


**Fig. 4.5** Potential sources of uncertainty in 7Be-based estimates of soil erosion (Taylor et al. 2013)

and more relevant approach is to work with the uncertainty derived from repeated reference inventory measurements. Herein, the coefficient of variation between cores represents a real-world measure of local variability which should be accounted for in erosion estimates. In practice, the model can be run with the upper and lower limits of the reference inventory and the range of outputs used accordingly for each sample point. It should be noted that results from points that differ marginally from the inventory might switch between eroding and depositing depending in reference uncertainty. Similarly, where a spatial integration approach (see Chap. 2) has been adopted in plot sampling, variability in inventory within zones can be considered. Whichever approach is selected, the user must report what was performed with full transparency.

Any approach taken to determine and report uncertainty will have inevitable sitespecific and study-specific caveats. Users are encouraged to explore potential sources of uncertainty and undertake suitable sensitivity analysis when running conversion models to convince the scientific and stakeholder communities of data quality and the environmental relevance of results.

#### **Glossary**


estimates using 7Be over a longer period (e.g. wet season) to be accounted for.

Sensitivity analysis Process to link uncertainty in the output of a model to different sources of uncertainty in its inputs with the aim of an increased understanding of the relationships between input and output variables.

#### **References**


The opinions expressed in this chapter are those of the author(s) and do not necessarily reflect the views of the International Atomic Energy Agency, its Board of Directors, or the countries they represent.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 3.0 IGO License (https://creativecommons.org/licenses/by/3.0/igo/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the International Atomic Energy Agency, provide a link to the Creative Commons licence and indicate if changes were made.

The use of the International Atomic Energy Agency's name, and the use of the International Atomic Energy Agency's logo, shall be subject to a separate written licence agreement between the International Atomic Energy Agency and the user and is not authorized as part of this CC-IGO licence. Note that the link provided above includes additional terms and conditions of the licence.

The images or other third party material in this chapter are included in the chapter's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# **Chapter 5 Research into Practice—Linking Be-7 Evidence to Land Management Policy Change for Improved Food Security**

**M. Benmansour, W. H. Blake and L. Mabit**

#### **5.1 The Importance of the Short-Term Perspective for Land Management Policy Makers**

The short-term perspective on soil redistribution in the landscape offered by 7Be is essential to policy makers with responsibility for developing efficient land management strategies to support food and water security. Soil conservation is vital for enhancement of food production on hillslopes of agroecosystems. Mobilisation of eroded soil and transfer downstream leads to siltation of river channels, lakes and reservoirs, which presents a credible threat to river basin ecosystem service provision and water security. In addition, energy security is threatened by siltation behind hydropower dams. The short-term perspective of this cosmogenic radioisotopic tool means it can provide relatively rapid assessment of very recent changes in practice. Because of its agro-environmental behaviour, this short-lived radioisotope a reliable natural isotopic tracer to assess the effectiveness of recent soil conservation strategies (Mabit et al. 2008; Taylor et al. 2013).

The key challenge that many policy organisations face is obtaining convincing and scientifically sound evidence upon which realistic and wise informed decisions can be based. While many conventional methods are capable of determining on site

M. Benmansour

Centre National de l'Energie, des Sciences et des Techniques Nucléaires (CNESTEN), Rabat, Morocco e-mail: benmansour64@yahoo.fr

W. H. Blake

L. Mabit (B)

e-mail: L.Mabit@iaea.org

School of Geography, Earth and Environmental Sciences, University of Plymouth, Plymouth, UK e-mail: william.blake@plymouth.ac.uk

Soil and Water Management and Crop Nutrition Subprogramme, Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture, International Atomic Energy Agency, Vienna, Austria

<sup>©</sup> International Atomic Energy Agency (IAEA) 2019

L. Mabit and W. Blake (eds.), *Assessing Recent Soil Erosion Rates through the Use of Beryllium-7 (Be-7)*, https://doi.org/10.1007/978-3-030-10982-0\_5

erosion rates at a point (e.g. rainfall simulation, erosion pin measurements, survey techniques), the scaling of these measurements to the wider hillslope or landscape unit is challenging. This is especially the case given that equipment associated with many conventional approaches interferes with either farming activities themselves or natural soil erosion processes.

An advantage of 7Be is that this isotopic tracer is integrated into the natural hydrological cycle. Delivered naturally via rainfall to the soil surface and redistributed via erosion processes, it operates without any interference by deployment of measurement equipment. In addition, the method can be applied retrospectively and sampling strategies driven by field observations after an erosion event. The method is not without complications and challenges but if undertaken with care and due attention to assumptions and limitations (as described in Chaps. 1–4), the above advantages offer opportunity to gain critical information on soil and sediment redistribution to support policy decisions on soil conservation and environmental management.

#### **5.2 Linking Nuclear Techniques in Soil Erosion and Conservation to Policy Change**

Early studies conducted in the 1990s outlined the principles and opportunity for use of 7Be as a soil erosion and soil redistribution tracer (Wallbrink and Murray 1996; Blake et al. 1999; Walling et al. 1999; Blake et al. 2002). This foundation-laying research has since had a wider impact on soil conservation and environmental management policy through applied studies of the method around the world. This has been facilitated by research development and refinement performed within IAEA's Coordinated Research Projects (CRPs) such as the CRP D1.50.08 "*Assess the effectiveness of soil conservation techniques for sustainable watershed management using fallout radionuclides*" (2002–2008), the CRP D1.20.11 "*Integrated Isotopic Approaches for an Area*-*wide Precision Conservation to Control the Impacts of Agricultural Practices on Land Degradation and Soil Erosion*" (2009–2013) and more recently through the on-going CRP D1.50.17 "*Nuclear Techniques for a Better Understanding of the Impact of Climate Change on Soil Erosion in Upland Agro*-*ecosystems*" (2016–2021). Following the CRPs activities, several guidelines were produced by the SWMCN Subprogramme of the Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture (e.g. IAEA 2014; Mabit et al. 2018).

Impact on policy has been further extended worldwide to several IAEA Member States and FAO Member Countries by methodology transfer and capacity-building activities within IAEA national and/or regional technical cooperation projects (e.g. RAF5075 "*Enhancing Regional Capacities for Assessing Soil Erosion and the Efficiency of Agricultural Soil Conservation Strategies through Fallout Radionuclides in Africa*") which includes targeted training courses on the use of 7Be as a tracer to support soil conservation policy by leading researchers. As a result of these outreach and science-policy impact activities, application of this specific methodology has been extended to a range of soil conservation challenges, in collaboration with national and international organisations responsible for environmental management policy to support food and water security or management of forest resources.

For example, Blake et al. (2009) undertook a landscape sediment budget approach with 7Be alongside 137Cs and 210Pb to evaluate the post-fire loss of topsoil and nutrients from forest affected by wildfire to a major water supply reservoir in Australia, in collaboration with the government agency responsible for developing policy on fire management for water quality and quantity. Under future climates, wildfire will exacerbate threats to water security. The applied fallout radionuclide (FRN) research demonstrated that burning of surface vegetation can invigorate hillslope hydrological response with marked increases in sediment and nutrient delivery to river networks and reservoirs. Negative water quality effects include for example high turbidity, toxic algal blooms and fish kills with implications for water supply at critical times in the water year. Through quantifying post-fire runoff and nutrient yield processes, the research informed catchment management decisions, policies and water resource risk assessment in Australia. Similarly, researchers in Chile, applied 7Be using a transect approach (Schuller et al. 2006) for evaluation of the impact of forest harvesting on soil erosion fine sediment yields and for contribution to improve the effectiveness of mitigation measures before, and after clear-cut operations and during the establishment of the new plantations. This work demonstrated the benefit of using 7Be to document the effects of recent forest clearance upon slope soils in a timber harvesting operation. The short-term perspective of 7Be meant the use of mitigation strategies could be assessed and, in this case, a high sediment delivery ratio indicated to policymakers the need for further soil conservation strategies.

#### **5.3 Example Impact Case Study: Support Provided by The 7Be Technique to Shape Soil Conservation Policy in Morocco**

#### *5.3.1 Soil Erosion and Conservation Policy Challenges in Morocco*

Soil erosion is the main land degradation process in Morocco, which is affecting up to 40% of its land area. About two million hectares of Moroccan agricultural lands are affected by soil erosion by water (Dahan et al. 2012). On average, soil erosion ranges from 5 to 20 t ha−<sup>1</sup> yr−1, but exceeds these magnitudes in northern and north-western basins. For example, in the pre-Rif hills region, soil erosion exceeds 50 t ha−<sup>1</sup> yr−1(HCEFLCD 2017). Out of a total area of 20 million ha of watershed in Morocco, 50% is estimated to be subjected to very high erosion risks with a yearly soil loss of around 100 million tons. This annual soil loss leads to a reduction of 75 million m<sup>3</sup> of downstream dam water storage capacity. Each year about 0.5% of the country's reservoir storage capacity is lost. These soil erosion and conservation challenges require both spatially representative data on soil erosion amounts and sediment delivery ratios. The highly dynamic nature of land use change and implementation of new conservation policies, however, means that longor medium-term FRN approaches are not recommended to deliver the data required by policymakers on the extent of the problem and the level of success in conservation approaches applied (Mabit et al. 2008). Consequently, researchers in Morocco have been using the 7Be methodologies outlined in this book to tackle these challenges and the obtained data have been used to assist development of new soil conservation policy in a wide range of settings.

#### *5.3.2 From the Laboratory to the Field: The Approach*

FRN methodologies have been successfully used by the "Centre National de l'Energie, des Sciences et des Techniques Nucléaires" (CNESTEN) in many cultivated areas of Morocco for supporting soil conservation strategies tested or implemented by the government. The research has shaped soil conservation policy with the collaboration of "Institut National de Recherche Agronomique (INRA) from the Ministry of Agriculture andMaritime Fisheries and "Centre de Recherche Forestière" (CRF) from the "Haut Commissariat des Eaux et la Lutte contre la Désertification" (HCEFLCD). Fallout 7Be was applied in combination with 137Cs and 210Pb to estimate soil erosion in agricultural or forest fields under different land uses in the regions of Rabat, Tétouan, Casablanca and Fes (Fig. 5.1) both before and after implementation of recommended soil conservation approaches. The transect sampling strategy was generally adopted (see Chap. 2) and FRNs were determined at CNESTEN Laboratory using gamma detectors (see Chap. 3). Key studies where the 7Be approach has been integrated into policy-development research:


**Fig. 5.1** Locations of the study areas - (1) Marchouch site (region of Rabat), (2) Herchane site (region of Tétouan), (3) Oued Mellah watershed (region of Casablanca) and (4) Allal Fassi (region of Fes)

# *5.3.3 Key Findings and Policy Impacts from 7Be Application in Morocco*

Previous investigations using other FRNs (137Cs or 210Pbex) allowed establishment of the long-term soil erosion rates of the three investigated regions, which ranged from 8 to 58 t ha−<sup>1</sup> yr−<sup>1</sup> (Benmansour et al. 2013; Benmansour et al. 2016; Yassin et al. 2017). The net soil erosion rates appeared to be closely related to the rainfall, slope and the past land use. The sediment delivery ratio in all areas is generally high reaching 80 to 100% which led to implementation of soil conservation strategies to keep fertile soil material on the hillslopes. The short-term perspective of 7Be enabled the effectiveness of these soil conservation strategies to be assessed and underpinned their wider adoption in the landscape. Figure 5.2 reports the mean values of shortterm erosion amounts estimated at different study sites and corresponding to fields under conventional tillage or without management and those corresponding to fields under soil conservation practices.

Soil redistribution data from 7Be measurements indicated that soil loss had been reduced significantly under no-till as compared to conventional tillage in Rabat and Tétouan regions. Indeed, soil erosion rates were lowered by 50% for the Marchouch site (Fig. 5.2a) and by 40% for the Harchane site (Fig. 5.2b). At the Oued Mellah watershed, the results highlighted that high density Atriplex plantations reduced soil loss by approximately 57 to 80% compared to Atriplex plantations with low density while for the site under fruit plantations and cereals, soil erosion has been decreased by 58% compared to bare soils (Fig. 5.2c). For Allal Fassi Watershed, erosion was lowered by 54% for soil under young Allepo pine, dry stones and gabions compared to soil under only Allepo pine and dry stones and by 51% for agricultural fields under cereals and fruit plantation as compared to bare soils (Fig. 5.2d). These findings have emphasised the need for wider adoption of these proven soil conservation approaches in the Moroccan landscape. Indeed, the no-till practice tested by Moroccan INRA researchers in their experimental sites is being applied and transferred by the Ministry of Agriculture to agricultural farms that have similar agro-environmental conditions as the experimental stations of INRA. The demonstrated high performance of soil conservation practices tested by HCEFLCD in the investigated watersheds means they will be adopted at a wide scale.

The relevant results derived from the application of these FRNs for short and longer-term erosion rates in Morocco were presented jointly by CNESTEN and HCEFLCD at the 12th Session of *United Nation Convention for Combating Desertification, COP12*, Turkey, October 2015. The impact of this research on policy was emphasised by a lead policy maker, the Head of the Forestry Research Centre of Morocco's High Commission of Forest and Water and Combating Desertification (HCEFLCD). He spoke about the role of isotopic techniques in tackling the effects of climate change, particularly drought leading to a reduction of up to 75% in grain yields: "*Using isotopic techniques, we were able to accurately assess soil erosion and the effectiveness of soil conservation practices and make concrete recommendations to policy makers… These all delivered real change for people who rely on the land for their livelihoods.*" (IAEA 2016).

# **5.4 Future Trends and Opportunities in Using 7Be**

The above science-to-policy examples in Morocco illustrate the fundamental role that the short-term perspective on soil redistribution rates provided by 7Be can play in the development and implementation of soil erosion policy. The need for such information has never been so crucial. Against threats from soil erosion, it is predicted that global food production must increase by 70% to feed the projected growth of the world's population (from 7 to 9 billion by 2050) (FAO 2017). Extreme weather (wet and/or dry) events may become more frequent with changing global climate with impacts on soil quality and erodibility. Developing community resilience to such recurrent climatic events demands 'win–win' systems of soil conservation that permit enhancement of land productivity while protecting ecosystem services in the

**(c)**

**(d)**

**Fig. 5.2** Short soil erosion rates under different land uses associated with the study sites:Marchouch (**a**), Herchane (**b**), OuedMellah (**c**) and AllalFassi (**d**). *LD* Low density; *HD* High density; *E* East exposure; *W* West exposure

wider river basin. Key information and guidance provided by nuclear and isotopic tools such as the 7Be technique provides valuable support to convince policy makers and farmers to adopt and promote widely existing effective climate smart soil conservation strategies.

#### **References**


The opinions expressed in this chapter are those of the author(s) and do not necessarily reflect the views of the International Atomic Energy Agency, its Board of Directors, or the countries they represent.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 3.0 IGO License (https://creativecommons.org/licenses/by/3.0/igo/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the International Atomic Energy Agency, provide a link to the Creative Commons licence and indicate if changes were made.

The use of the International Atomic Energy Agency's name, and the use of the International Atomic Energy Agency's logo, shall be subject to a separate written licence agreement between the International Atomic Energy Agency and the user and is not authorized as part of this CC-IGO licence. Note that the link provided above includes additional terms and conditions of the licence.

The images or other third party material in this chapter are included in the chapter's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.