PUBLICATIONS. Water Resources Research

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1 PUBLICATIONS Water Resources Research RESEARCH ARTICLE 1.12/214WR15867 Key Points: Existing approaches to use 7 Be for quantifying soil loss possess limitations A new approach is proposed to document short-term soil redistribution The approach is validated using data collected from an experimental plot Correspondence to: P. Porto, paolo.porto@unirc.it Citation: Porto, P., and D. E. Walling (214), Use of 7 Be measurements to estimate rates of soil loss from cultivated land: Testing a new approach applicable to individual storm events occurring during an extended period, Water Resour. Res., 5, , doi:1.12/214wr Received 26 MAY 214 Accepted 1 OCT 214 Accepted article online 7 OCT 214 Published online 29 OCT 214 Use of 7 Be measurements to estimate rates of soil loss from cultivated land: Testing a new approach applicable to individual storm events occurring during an extended period Paolo Porto 1,2 and Des E. Walling 2 1 Dipartimento di Agraria, Universita degli Studi Mediterranea di Reggio Calabria, Calabria, Italy, 2 Department of Geography, College of Life and Environmental Sciences, University of Exeter, Exeter, UK Abstract The techniques available for documenting rates and patterns of soil redistribution in the landscape have many limitations and the value of those employing fallout radionuclides (FRNs), including caesium-137 ( 137 Cs) and excess lead-21 ( 21 Pb ex ) is being increasingly recognized. However, the use of 137 Cs and 21 Pb ex measurements is best suited to investigations of longer-term soil redistribution rates (i.e., 5 6 years for 137 Cs and 1 years for 21 Pb ex ). For many purposes, a much shorter timeframe is required. Beryllium-7 ( 7 Be), another FRN (half-life 53 days), offers the potential to document soil redistribution associated with individual events or short periods of heavy rainfall. However, existing approaches for using 7 Be possess important limitations related to both the timing of the study period and its length. This contribution reports the development of a new approach that permits estimation of the soil loss associated with all individual events or short periods of rainfall occurring during a study period extending over a year or more. The approach was validated using data collected from an erosion plot located in southern Italy. The close agreement of the measured and estimated values demonstrates the validity of the new approach which has the potential to greatly increase the scope for using 7 Be measurements to document short-term soil redistribution associated with individual storm events. 1. Introduction Increasing concern for both the on-site and off-site impacts of soil erosion [e.g., Clark et al., 1985; Wood and Armitage, 1997; Boardman and Poesen, 26; Montgomery, 27] has emphasized the need for improved methods of quantifying rates and patterns of soil redistribution within the landscape. The techniques available for documenting soil erosion rates possess many limitations [see Loughran, 1989], but the use of fallout radionuclides (FRNs), including caesium-137 ( 137 Cs) and excess lead-21 ( 21 Pb ex ) is attracting increased attention. The approach has now been successfully used in many areas of the world [Zapata, 22; Zapata and Nguyen, 21; Walling, 21; Matisoff and Whiting, 211]. The many advantages associated with the use of FRNs for documenting soil erosion rates have been noted by Walling [22] and one key advantage is the ability to obtain spatially distributed information on soil redistribution rates within the landscape, without the need to install erosion plots or utilize other techniques, such as erosion pins, which can interfere with natural processes [see Shi et al., 211]. Other advantages include the capacity to generate retrospective information on the basis of a single site visit. The use of FRNs to document soil redistribution rates does, however, need to take account of several limitations and constraints. Probably the most significant are those related to the timeframes or time windows involved. These reflect both the half-life of the FRN used and the temporal record of the fallout. In the case of 137 Cs (half-life 3.17 years), the approach, as commonly used, generates estimates of soil loss that are averaged over the period since either the commencement of bomb fallout in the mid 195s or the period of peak fallout in the early 196s (i.e., circa 1963). This timeframe therefore currently extends to 5 6 years. For 21 Pb ex (half-life 22.3 years) the timeframe is less clearly defined, but such measurements are likely to reflect erosion occurring over the past 1 years. However, they will be more sensitive to recent erosion, due to the shorter half-life of this radionuclide and the essentially continuous nature of 21 Pb fallout [see Porto et al., 29, 213]. In some respects, the ability to provide a time-integrated assessment of the medium-term or longer-term mean annual rate of soil loss can be seen as an important advantage. However, there are many PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 83

2 1.12/214WR15867 circumstances where a much shorter timeframe (e.g., <1 year) is required, for example, when assessing the impact of land use change or investigating contrast in the rates of soil loss associated with different crops or land management practices. Beryllium-7 ( 7 Be) is another FRN, but one with a very much shorter half-life (53 days) [see Kaste et al., 22]. It offers the potential to document rates of soil loss associated with individual events or short periods (e.g., several weeks) of heavy rainfall [see Blake et al., 1999; Walling et al., 1999; Wilson et al., 23; Schuller et al., 26; Sepulveda et al., 28; Benmansour et al., 211]. However, despite this potential to provide a valuable complement to 137 Cs and 21 Pb ex in documenting rates and patterns of soil loss [see Mabit et al., 28], there have been relatively few attempts to exploit and develop the use of 7 Be. Walling [213] has speculated on the reasons underlying the limited attention directed to using 7 Be to provide a tracer for documenting short-term (days to weeks) soil redistribution associated with individual events or short periods of heavy rainfall. Possible reasons include the initial preoccupation with the use of 137 Cs and the increased complications and more demanding requirements associated with applying 7 Be measurements, which primarily reflect its shorter half-life. Initial attempts to apply 7 Be measurements were largely based on the same basic approach as used in most 137 Cs studies to estimate rates of soil loss from uncultivated soils [e.g., Blake et al., 1999; Walling et al., 1999; Schulleretal., 26; Sepulveda et al., 28; Navas et al., 28; Benmansour et al., 211; Shi et al., 211]. This involved sampling the study site after a storm event or short period of heavy rainfall and comparing the measured inventories with a reference inventory measured at a nearby reference site that had experienced neither erosion nor deposition. Where the measured inventory for a sampling point within the study site was lower than the reference inventory, erosion was assumed to have occurred. Measured inventories greater than the reference value were assumed to be indicative of deposition. The degree of reduction or increase of the inventory at the sampling point relative to the reference inventory was used in conjunction with the characteristics of the 7 Be depth distribution to estimate the amount of erosion or deposition at the sampling point. The short half-life of 7 Be greatly limits the time available for significant downward migration and the occurrence of the radionuclide is limited to a very shallow surface layer (e.g., 2 cm). Interception and storage of a significant proportion of the 7 Be fallout by a vegetation cover could greatly influence both the magnitude and the spatial variability of the soil inventory and compromise the assumptions of the approach. As a result studies employing 7 Be have generally been limited to bare soils. Because the occurrence of 7 Be in the soil is limited to a very shallow surface layer, its application for quantifying soil loss is restricted to sheet erosion that results in limited surface lowering. In this respect, it differs significantly from 137 Cs and 21 Pb ex which can be used to quantify the combined effect of rill and sheet or interrill erosion, due the presence of these radionuclides to a much greater depth. Key problems associated with using essentially the same approach for 7 Be as used with 137 Cs are largely a reflection of the short half-life of 7 Be and the resulting need to focus on individual events or short periods of rainfall, as distinct from longer-term rates of soil loss. The 137 Cs approach is based on the existence of relatively stable radionuclide inventories at both the reference site and the other sampling points, which reflect the accumulation of bomb fallout over a period extending from the 195s to the 197s, and where the primary control on changes in the inventory is removal or addition of soil containing the radionuclide as a result of erosion or deposition, respectively. In contrast, with 7 Be, the relatively rapid decay of the fallout input means that this exerts the primary control on the magnitude of both the reference inventory and the inventories measured at the sampling points over time. It is only possible to estimate the magnitude of soil loss at a sampling site, by comparing the 7 Be inventory measured at that site after an event or short period of rainfall with the inventory measured at the reference site, if it can be assumed that the two were the same prior to the event and that there was no spatial variability of the inventory across the study site prior to the event. A preceding event that caused significant erosion and deposition would necessarily cause spatial variability in the inventory across the study site and change the magnitude of the inventories at the sampling points relative to the reference inventory and therefore negate these assumptions. The approach developed from that used with 137 Cs can therefore only be applied to an event that follows an extended period with no erosion (i.e., a period with little or no rainfall, during which any spatial variability in the inventory across the site inherited from previous storm events causing erosion, would be removed by radioactive decay). Alternatively, cultivation of the site would mix the 7 Be into the plough layer and reduce activities below the level of detection and thereby reset the inventory to zero and provide an alternative starting point. These constraints represent a major limitation of the approach. It would, for example, PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 831

3 1.12/214WR15867 only be possible to document the erosion associated with the first event of a wet season rather than all events in the wet season. Furthermore, if the major erosive events occurred after the beginning of the wet season and were preceded by more minor events that, nevertheless, still caused erosion, it would not be possible to study the major events. In addition, the period covered by such measurements needs to be very short (i.e., a single event or a short period of heavy rainfall), to generate reliable estimates of soil loss. If the length of the period is extended, the relationship between the reduction in the inventory at the sampling point, relative to the reference inventory, and the magnitude of the soil loss would change during the period considered, with the result that the amount of soil loss would be underestimated. Walling et al. [29] used a hypothetical example to demonstrate that if the period extended to 4 weeks, and a series of rainfall events occurred during that period, the total erosion could be underestimated by of the order of 4%. An alternative approach to using 7 Be to quantify soil loss, such as that documented by Wilson et al. [23] does provide potential to overcome these problems. However, the need for the sampling points to be sampled both before and after the investigated storm event and to measure the fallout input associated with the event means that it is far more demanding. Furthermore, as reported, the procedure was applied to a short 3 day period, which experienced a number of thunderstorms. Its possible adaptation to cover a much longer period with several separate events was not discussed. Walling et al. [29] working in south-central Chile, attempted to overcome the important constraints related to both the need to focus on the first event occurring after an extended dry period and to limit the period studied to a few days, outlined above. Their study focused on the impact of forest harvesting on soil loss and the potential for using trash barriers to reduce erosion and needed to document soil loss associated with storm events occurring throughout the main wet season. The approach developed used a mass balance model to calculate the change in 7 Be inventory occurring at a sampling point after each day, in response to fallout input, radioactive decay and soil loss (reduction) or deposition (increase). Estimates of the 7 Be activity in rainfall were obtained by regular sampling (approximately monthly) of the reference site and relating the change in inventory over the period to both rainfall inputs and the effects of decay. By assuming that all fallout inputs occurred as wet fallout, it was possible to estimate the mean 7 Be activity of rainfall during the sampling interval. This permitted the record of daily 7 Be fallout to be synthesized, based on the record of daily rainfall. The soil loss occurring at the sampling point on individual days during the study period was estimated using an optimization procedure to calculate the amount of erosion occurring on each day with significant rainfall required to produce a match between the predicted and measured 7 Be inventory at the sampling point at the end of the study period. Soil loss was assumed to occur only on days with significant rainfall and was further assumed to be directly proportional to the rainfall erosivity expressed by the E 3 I 3 parameter in the RUSLE model [see Renard et al., 1997]. Using the approach outlined above, it was possible to commence the study period ahead of the main wet season and to extend this period to cover almost 3 months. The reference site was sampled at the beginning and end of the period and on two intermediate occasions, in order to estimate the 7 Be activity in rainfall and to provide information on changes in the 7 Be depth distribution. The study site was sampled at the end of the study period and it was assumed that the initial inventory at the sampling points was the same as the inventory sampled at the reference site at the beginning of the study period, since the study period followed an extended dry period. Comparison of the soil loss estimated for the study period with that which would have been estimated by applying the conventional approach to the extended period (based on a simple comparison of the inventories of the cores collected from the sampling points with that of the reference site) indicated that the latter was only 44% of the former value. In addition, the conventional approach provided no information on the distribution of soil loss during the study period. The approach developed by Walling et al. [29], which is summarized above, affords a means of using 7 Be measurements to document soil loss over an extended period [Schuller et al., 21]. It introduces flexibility into the starting point of the study period and provides estimates of soil loss for individual events or days during the study period. However, its reliance on the assumption that the amount of erosion that occurs during individual storms is directly proportional to the rainfall erosivity must be seen as a limitation. It is likely that soil loss will also be influenced by antecedent conditions and that soil loss will vary through the wet season in response to exhaustion of the supply of readily mobilized soil. The study reported in this contribution explored the possibility of developing an alternative, although similar, approach, that permits direct estimation of the soil loss associated with individual events or short periods of rainfall during a lengthy study period (e.g., >6 months), by resampling the inventories at the sampling points within the study area after each event. The resulting inventory values can then be used to calculate a point-specific PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 832

4 1.12/214WR15867 reference inventory for each event and to estimate the soil loss for each event individually. In order to provide an objective assessment of the validity of the results generated using this approach and thereby address concerns regarding a number of other problems potentially facing the successful use of 7 Be measurements to estimate soil loss [Taylor et al., 213] as well as the use of fallout radionuclides in soil erosion investigations more generally [Parsons and Foster, 211], the study was undertaken using an erosion plot. This permitted the estimates of soil loss derived from the 7 Be measurements for individual events or short periods to be directly compared with the measured values of soil loss for the same events or periods. 2. Using 7 Be to Document Soil Erosion Rates and the New Approach In essence, the basis for using 7 Be measurement to document erosion rates is that this short-lived fallout radionuclide is rapidly and strongly fixed to the surface soil in most environments and commonly exhibits a well-defined exponential depth distribution [Wallbrink and Murray, 1996; Walling et al., 1999; Wilson et al., 23]. Most of the 7 Be is held within the upper 1 cm of the soil. If erosion occurs, the removal of a thin surface layer of soil will reduce the inventory or areal activity density at a sampling point. If the inventory remaining at this sampling point can be measured and compared with that found at a nearby reference site, experiencing neither erosion nor deposition, the reduction in inventory can be related to the exponential depth distribution found at the reference site, in order to estimate the depth or amount of soil removed. More specifically, the vertical distribution of 7 Be in the soil profile at a reference site can be represented by the following exponential function [see Walling et al., 1999] where x mass depth from soil surface (kg m 22 ); C(x) concentration (Bq kg 21 )of 7 Be at depth x; C() the mass activity density (Bq kg 21 ) of the surface soil (at x 5 ); CðxÞ5CðÞe 2x=h (1) h relaxation depth (kg m 22 ) describing the profile shape and representing the mass depth at which C(x) reduces to 1/e C(). Integration of equation (1) over the shallow depth to which 7 Be is found gives the reference areal activity density (Bq m 22 ) for an uneroded soil viz. ð1 ð1 A ref 5 CðxÞdx5 ce 2x=h dx5h CðÞ (2) Considering the exponential form of the depth distribution, the areal activity density below mass depth x, A(x), (Bq m 22 ), is therefore ð1 AðxÞ5 CðxÞdx5A ref e 2x=h (3) x For an eroded site, assuming that erosion has removed a thin layer of mass depth R (kg m 22 ) at a sampling point, the 7 Be areal activity density remaining at this eroded point A (Bq m 22 ) will be lower than A ref. The mass of soil eroded per unit area is equal to R (kg m 22 ) the mass depth removed. By setting x 5 R in equation (3), the remaining areal activity density at the sampling point can be represented as A5AðRÞ5A ref e 2R=h (4) The mass of soil per unit area eroded from the sampling point, R, can therefore be calculated as R5h Ln A ref A (5) In some situations, the erosion process may result in enrichment of the mobilized soil in fines and, since 7 Be will be preferentially associated with the finer fractions of the soil, the mobilized soil will also be enriched in 7 Be. Failure to take this into account will result in overestimation of the mass of soil eroded. Following PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 833

5 1.12/214WR15867 existing conversion models developed for 137 Cs by Walling and He [1999] and adapted to 7 Be by Walling et al. [211], a correction factor P can be incorporated into equation (5), where P represents the enrichment ratio or the ratio of the 7 Be activity in mobilized sediment to that in the original soil R5 h P Ln A ref (6) A The approach used for estimating soil loss described above can be further extended to permit estimation of deposition for sampling points where the measured inventory exceeds the reference inventory [see Walling et al., 1999]. As discussed by Walling et al. [29] and emphasized above, use of equations (5) and (6), although attractive in their simplicity, involves a number of assumptions or requirements that restrict their application. They mean that only one event or only a short period containing several events can be investigated and that the timing of the event or short period is heavily constrained by the need to ensure that the effects of past erosion on 7 Be inventories across the study site have been removed either by the occurrence of a substantial period of time with no erosion or by cultivation of the site. The approach developed in the current study builds on that reported by Walling et al. [29] and aims to overcome these limitations by resampling the sampling points after each major event or short period of heavy rainfall, in order to extend the study period. In this situation, it can no longer be assumed that the inventory measured at the reference site represents the inventory that would have existed at the sampling point after the event or short period of rainfall, in the absence of erosion caused by that rainfall. The inventory measured at a sampling point will be influenced both by the erosion occurring at the sampling point during the event under investigation and also that occurring in previous periods. The reference inventory required to represent A ref in equation (6) must therefore be determined for each sampling points independently, by taking the inventory measured at the sampling point after the preceding event and using a mass balance procedure with a daily time step to calculate the inventory existing at the sampling point after the subsequent event in the absence of erosion. This value can be directly compared with the measured inventory, in order to estimate the amount of soil removed by erosion using equation (6). This mass balance model takes the form AðtÞ5Aðt21Þexp ð2kþ1fðtþ (7) where A(t 2 1), (Bq m 22 ), represents the 7 Be areal activity density existing at the end of the previous day, k, (days) represents the radioactive decay occurring during the intervening day, and F(t), (Bq m 22 ) represents the fallout input (flux) during the day under consideration. Application of equation (7) ideally requires measurements of the 7 Be activity of rainfall in order to calculate the fallout flux for each day. However, no direct measurements of fallout were available to the erosion plot study undertaken by the authors because of the remote location of the site (4 km from the home University in Reggio Calabria), which made it difficult to establish a rainfall sampling program, the lack of laboratory facilities to process rainfall samples to extract and measure their 7 Be activity [see Wallbrink and Murray, 1994; Wilson et al., 23] and limited gamma detector capacity. The values of FðtÞ for each day were therefore estimated using the same approach as proposed by Walling et al. [29]. This assumes that 7 Be fallout is dominated by wet deposition, as demonstrated by researchers such as Wallbrink and Murray [1996], and reconstructs the fallout record using the record of daily rainfall and estimates of the 7 Be concentration in rainfall derived from measurements of the changing inventory at the reference site. If the reference inventory A ref is measured at the end of each significant rainfall event or short period of heavy rainfall and the equivalent value is available for the preceding event, it is possible to estimate the mean 7 Be activity of the rainfall C m, (Bq l 21 ) for the intervening period using equation (8). Equation (8) establishes the value of C m required to produce the observed change in A ref between the two measurements of the reference inventory, while, taking account of radioactive decay, i.e., C m 5 A ref ðt5tþ2a ref ðt5þexp ð2ktþ ð T IðtÞexp ½2kðT2tÞŠdt (8) where I(t), (l m 22 ), is the daily rainfall, and T is the number of days in the period considered. In the study reported by Walling et al. [29], the reference site was sampled less frequently (at approximately monthly PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 834

6 1.12/214WR15867 intervals) and equation (8) was applied to these intervals to calculate a mean value of C m for each period. The depth distribution of Gulf of Taranto 7 Be was established on each occasion that the reference site was CALABRIA sampled and this enabled the values of h required by equation (6) Cosenza Tyrrhenian Sea Crotone to vary through the study period. Catanzaro The lack of direct measurements of 7 Be fallout for the study period Vibo must be seen as a limitation of the Valentia Ionian Sea study. However, a similar situation Study Area is likely to be faced by many studies where 7 Be could potentially be Reggio Calabria 2km used to quantify soil redistribution 5km rates, particularly in developing countries. The need to establish a Figure 1. The study area. rainfall sampling program and undertake measurements of the 7 Be activity of the rainfall associated with individual events measurements could represent a major obstacle. In the approach used by the authors only measurements of the 7 Be activity of soil samples are required. Furthermore, it could be argued that by deriving estimates of fallout inputs from measurements of the soil inventory at the reference site, the potential for introducing errors might be reduced. Attention focuses solely on soil inventories and their changes through time and there is no requirement to combine these with measurements of fallout inputs. 3. The Plot Experiment I T A L Y 3.1. The Experimental Plot The study site is located in a rural area 4 km north of Reggio Calabria in southern Italy (Figure 1). The area experiences a Mediterranean climate, with an average annual rainfall of 11 mm, most of which falls during the period extending from September to May. The soil is a Typic Hapludand [Soil Survey Staff, 26] with a silty loam texture (clay 5 4%, silt 5 76%, and sand 5 2%). In 25, the Department of Agriculture of the University Mediterranea of Reggio Calabria established five 5 m 3 25 m experimental plots (Figure 2) to monitor runoff and erosion rates under different crop covers. The plots were aligned with their long axes parallel with the line of steepest slope (1.%), and their construction involved minimal disturbance to the site. Each plot is isolated from the others by a sheet metal cutoff wall extending 3 cm into the soil and protruding 2 cm above the ground surface. Since their establishment, four plots have supported different cropping and tillage systems, while plot no. 1, used as a control, has been maintained in a bare condition by frequent tillage operations [see Porto and Walling, 212a, 212b, for further details]. The experimental investigation reported relates to the bare plot and extends over a 18 month period starting in June 211 and continuing until the end of 212. Twenty significant storm events that generated both runoff and soil loss were recorded during the study period. No rills were observed on the study plot during this period and sheet erosion can therefore be assumed to be the dominant cause of soil loss. Rainfall data are provided by a recording rain gauge located adjacent to the study. Runoff and soil loss from the plot are intercepted by a gutter located along the lower end of the plot, and then diverted into a collection system consisting of a storage tank of known dimensions, installed below the base of the plot (see Figure 2). The collecting tank was emptied shortly (i.e., 2 3 days) after the end of each rainfall event, when the sediment has settled. The volume of clear water was recorded to document the amount of runoff from the plot, and this water was subsequently removed, leaving the sediment deposited on the bottom of the tank. This sediment was collected, dewatered, oven dried, and weighed to determine the mass collected. PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 835

7 Water Resources Research 1.12/214WR15867 Figure 2. The experimental framework Soil Sampling and the 7Be Measurements The soil sampling strategy was designed to keep the number of samples collected and requiring analysis for 7Be activity to a minimum, because of the need to transport samples to a laboratory in the UK for analysis and the limited number of samples that could be analyzed during the projected study period. The short half-life of 7Be means that samples cannot be stockpiled for analysis when detector capacity exists. Analysis must be undertaken before the activity decays below the detection limit. Collection of soil samples from the study plot for 7Be analysis involved two separate sampling programs for each rainfall event that occurred during the study period. The first was designed to establish the magnitude of soil redistribution rates within the plot associated with the event and was undertaken shortly (i.e., 2 3 days) after the event. In this case, two parallel transects oriented parallel to the long axis of the plot were established and a total of 1 bulk cores (five for each transect) were collected using a 1.2 cm diameter core tube inserted into the soil to a depth of 2 cm. Care was taken not to disturb the surface of the plot during the sampling exercise and the positions of the two transects were varied from event to event, in order to avoid resampling an area already disturbed by previous sampling. For the reasons outlined above, the 1 bulk cores collected after each event were bulked and mixed and only one composite sample was analyzed for 7Be content. The second coring program, again undertaken shortly after each event, aimed to establish both the magnitude and the depth distribution of the 7Be inventory at an undisturbed reference site with minimum slope. This reference site was established 1 m outside the boundary of the study plot at the beginning of the experiment in June 211 (see Figure 2). At that time the surface of the reference site was tilled, in order to reduce the 7Be activity in the surface soil to below the level of detection. The plot was subsequently maintained in a bare condition to replicate the experimental plot. In this case, two 15.6 cm diameter cores were collected to a depth of 2 cm using a custom-built coring device. The position of the sampling points within the reference site was changed for each occasion the site was sampled, in order to ensure that the cores were collected from undisturbed points within the site. The design of the core tube permitted it to be inverted and fixed to a custom-built screw-driven extrusion device which enabled the core to be extruded in very small increments, starting from the surface. A similar device is described by Mabit et al. [214]. In the early stages of the study, a 2 mm depth increment was used, but subsequently this was reduced to 1 mm. The matching PORTO AND WALLING C 214. American Geophysical Union. All Rights Reserved. V 836

8 1.12/214WR15867 individual depth increments extruded from the two core tubes were bulked to provide a single composite sample for each 1 or 2 mm depth increment down to 2 cm. Due to technical problems caused by the short-time interval between the events and the need to limit the number of samples sent for analysis, no soil samples were collected from the study plot or the reference site for the events that occurred on 5 and 11 December 212 and the two events were combined with that occurring on 19 December 212, with sampling occurring after that event, which marked the end of the experiment. The composite samples derived from the bulk soil cores, the depth incremental samples, and the samples of sediment collected from the tank were sent to the laboratory of the Geography Department at the University of Exeter, UK, for processing and analysis. All samples were initially oven dried at 45 C, mechanically disaggregated, and passed through a 2 mm sieve. A representative aliquot of the <2 mm fraction, consisting of 1 g of each bulk sample and 4 g for the composite core sections, was then loaded into a plastic pot or a Petri dish for determination of its 7 Be activity. Beryllium-7 activities in the soil and sediment samples were measured by gamma-ray spectrometry at kev, using a high-resolution low energy coaxial HPGe detector coupled to an amplifier and PC-based data collection system. The detector efficiency was calibrated using a multiradionuclide standard with a similar bulk density and grain size to the soil samples, produced using a certified liquid standard. Count times were typically 8, s, providing results with an analytical precision of 1% at the 95% level of confidence. For the composite sample collected from the plot, the measurement of mass activity density was used to calculate the areal activity density (inventory) for the plot. In the case of the depth incremental samples collected from the reference site, the values of mass activity density obtained for each depth increment were used to establish the total 7 Be inventory and the associated depth distribution for the reference site. In addition, the absolute grain size composition of the <2 mm fraction of each sample was determined using a Micromeritics Digisizer laser granulometer, following treatment with hydrogen peroxide to remove the organic component and chemical dispersion with sodium hexametaphosphate. 4. Results 4.1. Measurements of Soil Loss From the Experimental Plot Measurements of soil loss were obtained from the study plot for the 2 events generating runoff and soil loss that occurred during the study period extending from June 211 to December 212. The individual values of soil loss E (kg m 22 ) are presented in Table 1. The values of soil loss for the individual events ranged between.16 and 1.5 kg m 22. The data presented in Table 1 demonstrate that during the study period the values of soil loss from the experimental plot were relatively low by local standards. Furthermore, in a previous investigation, that involved the same plot and which covered the period 26 29, the mean annual soil loss was 85.4 t ha 21 yr 21 [see Porto and Walling, 212a]. If only the 15 events that occurred in 212 are considered, the annual soil loss is only 18.4 t ha 21 yr 21, which is much lower than the mean value for the period Be Inventories and Depth Distributions at the Reference Site and Estimation of Fallout Inputs At the start of the experiment at the beginning of June 211, both the reference site and the study plot had been recently tilled and their 7 Be inventories were measured and confirmed to be zero. The 7 Be inventories associated with the sectioned cores collected subsequently from the reference site, shortly after the individual events, are reported in Table 1. The rainfall totals listed for each event in Table 1 represent the total rainfall recorded during the period extending from the collection of samples at the end of the previous event to the collection of samples for the designated event. However, most of the total was associated with the designated event. The 7 Be depth distributions associated with these cores are depicted in Figure 3, with depth expressed as mass depth. All the profiles conform to the general form expected for this radionuclide, with a maximum activity at the soil surface and an exponential decline with depth. Equation (1) was fitted to each profile to derive the values of h listed in Table 1. The fitted depth distributions are also depicted in Figure 3. When assessing the goodness of fit of the exponential depth distributions, it is important to recognize that it is the fit to the upper part of the measured depth distribution, rather than the overall fit, that is of critical importance when PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 837

9 1.12/214WR15867 Table 1. The Data Assembled for the Individual Events, Including the Inventory Measured at the Reference Site Shortly After the Rainfall Events (A ref ), the Rainfall Amount, the 7 Be Concentration in the Rainfall During the Same Period Estimated From the Change in Inventory and the Rainfall Amount (C m ), the Shape Parameter (h ) Associated With the Depth Distribution Measured at the Reference Site After the Event, the Inventory (A(t)) Associated With the Composite Sample collected From the Plot Shortly After the Rainfall Event and the Measured Soil Loss From the Plot (E) Code Event A ref (Bq m 22 ) Rainfall Amount (mm) C m (Bq l 21 ) h (kg m 22 ) A(t) (Bq m 22 ) E (kg m 22 ) EV-1 14 Jul EV-2 23 Sep EV-3 12 Oct EV-4 14 Nov EV-5 2 Dec EV-6 3 Jan EV-7 18 Jan EV-8 3 Feb EV-9 9 Feb EV-1 17 Feb EV Feb EV-12 8 Mar EV Apr EV May EV Sep EV Oct EV Nov EV Dec estimating soil loss. The maximum rate of soil loss measured from the plot for the events studied was 1 kg m 22. This is equivalent to a surface lowering of 1 mm. The goodness of fit of the exponential depth distribution can therefore be most effectively assessed by comparing the measured 7 Be activity of the surface ( 2 or 1 mm) slice with that predicted by the fitted depth distribution for a depth of 1. or.5 mm, respectively. For the depth distributions shown in Figure 3, there is close agreement between the measured and predicted values. The Normalized RMSE value for a comparison of the two sets of values for the set of 18 events is 9.7%. This is seen to confirm the validity of using equations (4 6) to estimate the amount of erosion associated with the individual events. The values of h presented in Table 1 provide some evidence of a general trend, with low values associated with low inventories at the beginning of the study period and values increasing as more rainfall occurs and the inventory increases. When the inventory subsequently declines the h values also decline. This is similar to the pattern described by Walling et al. [29] for a study site in south-central Chile. The measured values of A ref, together with the rainfall records for the intervening periods were used to calculate the value of C m for each selected period, using the procedure represented in equation (8). The values of C m estimated for the individual periods extending from the end of the previous event to the end of the given event are listed in Table 1 and were used to reconstruct the record of daily 7 Be fallout required to implement the mass balance accounting procedure represented by equation (7). The record of daily rainfall totals for the study period, the reconstructed record of daily 7 Be fallout, and the reconstruction of the changing reference inventory are shown in Figure 4 for the entire 19 month study period Be Inventories Within the Experimental Plot The values of 7 Be inventory A(t) (Bq m 22 ) measured for the experimental plot after each main event are listed in Table 1. As explained above, these values represent the 7 Be inventory of the composite sample derived from the samples collected from the 1 sampling points Converting 7 Be Measurements into Soil Loss In the study reported here, the estimates of soil loss for the individual events or periods of heavy rainfall were estimated by applying equation (6) to the inventory value associated with the composite sample collected from the plot shortly after the event. In this application, A represents the inventory for the plot measured immediately after the event (i) being considered and A ref represents a plot-specific reference inventory (i.e., the inventory that would have occurred on the plot at the end of the event, had no erosion or soil redistribution occurred). A ref is estimated by taking the inventory A measured on the plot immediately after the previous event (i 2 1) and using equation (7) to reconstruct the inventory that would have existed on the plot after the event being considered. As explained above, restrictions on the number of samples that PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 838

10 1.12/214WR Be (Bq kg -1 ) Mass depth (kg m -1 ) Measured 4 Simulated Mass depth (kg m -1 ) Measured 4 Simulated Mass depth (kg m -1 ) Measured 4 Simulated Figure 3. Depth distributions of 7 Be in the surface soil of the reference plot shortly after the 18 rainfall events. The curves shown by the bold lines represent the fitted exponential depth distributions. could be analyzed made it impossible to determine a plot specific value of h for each event to use in equation (6). The value obtained at the reference site for the soil profile sampled immediately after the event was therefore used. In the case of the first event that occurred during the study period on 14 June 211, the reference inventory was calculated assuming that the 7 Be inventory across the plot was zero at the beginning of the study period in early June due to cultivation of both the experimental plot and the reference site. One potential limitation of this general approach is that it assumes that all the rainfall and soil loss occurs shortly before the plot was sampled after each significant event. For most of the events this was the case, but in some instances part of the rainfall had occurred prior to the main event, although this accounted for only a relatively small proportion of the total rainfall. In the case of the sampling undertaken shortly after the event occurring on 19 December 212, this reflected the erosion associated with the events occurring on 5, 12, and 19 December 212 and the total soil loss might therefore have been underestimated due to the increased duration of the period considered. PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 839

11 1.12/214WR Be fallout (Bq m -2 ) Rainfall (mm) 5 2 Jun 211 Jul Aug Sep Oct Nov Dec Jan 212 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 Figure 4. The daily rainfall record and the reconstructed records of daily fallout 7 Be input and daily changes in the local 7 Be reference inventory for the study period. A comparison of the mean grain size distribution of the sediment mobilized from the plot and collected in the tank and the grain size distributions of the surface soil collected from the 1 sampling points on the plot after each event is provided in Figure 5. Figure 5 indicates that the range of the grain size distributions of the mobilized sediment falls almost fully within the range of the grain size distributions associated with the surface soil of the plot. Other studies have produced similar findings where sheet or rill erosion were dominant [see, respectively, Porto et al., 23; Whiting et al., 21]. Consequently, there is no clear evidence of enrichment of the mobilized sediment in fines for the studied events and it was deemed unnecessary to incorporate a particle size correction into equation (6). A particle size factor P of 1 was therefore assumed for equation (6). The values of soil loss for the 18 storm events (with the final event including three separate events) estimated using the 7 Be measurements are presented in Figure 6, which compares these values with the measured soil loss for the same events. 5. Discussion The results presented in Figure 6 indicate that the estimates of soil loss from the experimental plot for the 18 events generated using the 7 Be measurements are in reasonable agreement with the measured soil loss from the plot. This conclusion Percentage finer Soil Sediment Diameter (µm) Figure 5. A comparison between the range of the measured grain size distributions for sediment mobilized from the erosion plot with the range of the grain size distributions of surface soil collected from the experimental plot. is further confirmed by the efficiency index of.955 obtained for the relationship between predicted and observed soil loss [see Nash and Sutcliffe, 197] and the Normalized RMSE value of 6.2% for the relationship. Overall, Figure 6 suggests that there is no clear tendency for over or underestimation, although the results indicate that low values of soil loss (i.e., <.1 kg m 22 ) are frequently overestimated by the values derived from the 7 Be measurements, whereas intermediate values of soil loss (i.e.,.4.8 kg m 22 ) show some evidence of being underestimated by the 7 Be measurements. Integrating the results PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 831

12 1.12/214WR15867 over the study period and considering the cumulative soil loss for the period, Figure 7 indicates good agreement between the two sets of values. In general, the values of cumulative soil loss estimated using the 7 Be measurements are within 61% of the measured value. Interestingly, Figure 7 indicates that the measured soil loss for the final event (.66 kg m 22 ), which comprises three separate events is, as suggested above, underestimated by the 7 Be measurements (.5 kg m 22 ), although the degree of underestimation is limited (i.e., 224%). For the study period as a whole, the measured soil loss was 4.15 kg m 22, whereas the value estimated using the 7 Be measurements was 4.25 kg m 22. The close agreement between the estimated and measured values of soil loss suggests that the potential limitations associated with the use of fallout radionuclides more generally [Parsons and Foster, 211] and 7 Be more specifically [Taylor et al., 213] to quantify rates or amounts of soil loss are of limited importance. In addition, a number of assumptions and uncertainties associated with the approach employed appear to be of limited importance in terms of introducing significant errors. These include: 1. The values of fallout input used with the mass balance procedure to estimate the reference inventory for individual events have been reconstructed using estimates of the 7 Be activity in rainfall derived from measurements of the change in inventory at the reference site, rather than being based on direct measurements of fallout input. The approach could be extended and refined to include direct monitoring of fallout inputs. 2. The resampling is likely to result in some disturbance of the plot surface by the collection of new cores. This could be reflected by the measured soil loss. However, this problem is likely to be of very limited importance, since the area covered by the 1 cores collected from the plot after each event was less than.1% of the total area of the plot. 3. The use in equation (6) of a value for the shape parameter h obtained from the reference site rather than the sampling point necessarily introduces some uncertainty. However, the close agreement between the measured soil los from the plot and that estimated using the 7 Be measurements suggests that this is not an important issue. 4. The measurements of soil loss from the plot involve some uncertainty. It is assumed that all sediment mobilized from the plot is collected in the tank, whereas some could be deposited at the base of the plot prior to being intercepted by the gutter and delivered to the tank. Equally, measurement of the Cumulative erosion (kg m -2 ) Estimated soil loss (kg m -2 ) Measured soil loss (kg m -2 ) Figure 6. A comparison of the soil loss for the 18 storm events estimated from the 7 Be measurements with the measured values of soil loss. Measured Estimated Event Figure 7. Cumulative soil loss from the study plot associated with the 2 events during the study period. mass of sediment collected by the tank could involve some errors. It is important to note that despite these uncertainties, the estimates of both the soil loss associated with individual events and the total soil loss for the study period are highly consistent with the measured values and the estimates of soil loss for the individual events show no systematic bias across the range of event magnitude. PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 8311

13 1.12/214WR15867 Acknowledgments The study reported in this paper was supported by a grant from MIUR PRIN , and by IAEA (technical contract 15478). It was developed as a contribution to the Panta Rhei Research Initiative of the International Association of Hydrological Sciences (IAHS). The authors are also indebted to the Department of the Agriculture of the University Mediterranea of Reggio Calabria for providing data for the measurements of soil loss from the experimental plots. The paper has benefited from the reviews provided by two anonymous reviewers. Their comments and suggestions are gratefully acknowledged. All the data used for producing figures and graphs in this manuscript are available by request to the corresponding author via (paolo.porto@unirc.it). 6. Conclusions The new approach to using 7 Be measurements to estimate soil loss for a series of individual events over an extended period (i.e., 19 months) described above overcomes the important limitations associated with the traditional approach, which restrict its application to the first event or short period of rainfall after an extended period with limited rainfall or after cultivation of the site. It offers significant advantages over the procedure for extending the time scale over which 7 Be measurements could be applied described by Walling et al. [29], in that it is able to provide estimates of soil loss for individual events rather than the total soil loss for the study period. In addition, there is in principle no limit to the length of the study period, although the need to resample the sampling points after each event could impose practical limitations in terms of disturbing the study area. In the study reported the interarrival time of the storm events was of the order of a week or more and in some cases much greater. There would seem no reason why a sequence of individual events with much shorter interarrival times could not be investigated, although this would clearly greatly increase the number of soil samples to be collected and requiring analysis. As indicated above, the study used to validate the proposed approach involved a number of simplifications aimed at reducing the number of samples requiring analysis for 7 Be activity. Application of the approach in other studies could aim to avoid these limitations by analyzing a greater number of samples. The estimates of soil loss obtained using the procedure described were validated by undertaking the 7 Be measurements on an erosion plot and comparing the soil loss for individual events estimated using the 7 Be measurements with the measured soil loss from the plot. The close agreement of the measured and estimated values of soil loss demonstrates the validity of the approach, and the limited importance of the various problem issues raised by Parsons and Foster [211] and Taylor et al. [213]. However, it must be recognized that an experimental plot represents a simplified representation of the natural landscape, which is likely to be characterized by greater complexity in terms of topography. If the approach was to be applied to more complex natural topography, there is likely to be a need to document both erosion and deposition. The same approach could be adopted to implement the procedure for estimating deposition used in the traditional approach [see Walling et al., 1999]. In the study described, the requirements for 7 Be assay were reduced by bulking the 1 cores collected from the plot after each erosion event and making a single measurement of 7 Be activity for the composite sample. This is acceptable for the erosion plot where soil loss is likely to be relatively uniform within the plot. However, in a natural landscape, there is likely to be a need to make point-specific measurements to represent the individual sampling points, in order to take account of the local topography and the occurrence of erosion and deposition at different points. In such situations, it is often important to document the spatial pattern of soil redistribution. This will increase the number of samples that require analysis and it is important that any study should be carefully designed to ensure that it is possible to deal with the number of samples expected, particularly if significant erosion events occur in close succession. The short half-life of 7 Be means that samples need to be analyzed fairly soon after collection and they cannot be stockpiled for extended periods. The approach described should be readily applicable to studies aimed at comparing soil loss on different soil types or slope conditions. Furthermore, it should be applicable to comparing soil loss under different crops and crop management. However, it should be recognized that to date 7 Be measurements have been primarily applied to bare soils, since the presence of a vegetation canopy can intercept and store 7 Be fallout, making the relationship between changes in the 7 Be inventory and soil loss more complex, and also result in spatial variability of fallout input to the soil surface. Further work is required to explore and overcome the additional complications introduced by a vegetation cover [e.g., Shi et al., 213]. The study reported focused on demonstrating the general validity of the approach. This was confirmed by the close agreement between the measured soil loss from the erosion plot for individual events and those estimated from the 7 Be measurements. Further work is clearly required to assess the various sources of uncertainty associated with the procedure described and to propagate these through the various calculations to provide a measure of the uncertainty associated with the final estimates of soil loss. References Benmansour, M., A. Nouira, A. Benkdad, M. Ibn Majah, H. Bouksirat, M. El Oumri, R. Mossadek, and M. Duchemin (211), Estimates of long and short term soil erosion rates on farmland in semi-arid West Morocco using caesium-137, excess lead-21 and beryllium-7 measurements, in Impact of Soil Conservation Measures on Erosion Control and Soil Quality, IAEA-TECDOC-1665, pp , Int. At. Energy Agency, Vienna. PORTO AND WALLING VC 214. American Geophysical Union. All Rights Reserved. 8312